research article understanding the polar character trend in a...

Research ArticleUnderstanding the Polar Character Trend in a Series ofDiels-Alder Reactions Using Molecular Quantum Similarity andChemical Reactivity Descriptors

Alejandro Morales-Bayuelo12 and Ricardo Vivas-Reyes2

1 Departamento de Ciencias Quımicas Universidad Nacional Andres Bello Republica 275 8370146 Santiago Chile2 Grupo de Quımica Cuantica y Teorica Programa de Quımica Facultad de Ciencias Exactas y NaturalesUniversidad de Cartagena Colombia

Correspondence should be addressed to Alejandro Morales-Bayuelo alejandrmoralesuandresbelloedu

Received 1 March 2014 Revised 4 April 2014 Accepted 4 April 2014 Published 7 July 2014

Academic Editor Daniel Glossman-Mitnik

Copyright copy 2014 A Morales-Bayuelo and R Vivas-Reyes This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In molecular similarity there is a premise ldquosimilar molecules tend to behave similarlyrdquo however in the actual quantum similarityfield there is no clear methodology to describe the similarity in chemical reactivity and with this end an analysis of charge-transfer(CT) processes in a series of Diels-Alder (DA) reactions between cyclopentadiene (Cp) and cyano substitutions on ethylene hasbeen studied The CT analysis is performed in the reagent assuming a grand canonical ensemble and the considerations for anelectrophilic system using B3LYP6-31119866(119889) andM06-2X6-311 +119866(119889 119901)methods An analysis for CT was performed in agreementwith the experimental resultswith a good statistical correlation (119877

2= 09118) relating the polar character to the bond force constants

in DA reactions The quantum distortion analysis on the transition states (TS) was performed using molecular quantum similarityindexes of overlap and coulomb showing good correlation (119877

2= 08330) between the rate constants and quantum similarity indexes

In this sense an electronic reorganization based onmolecular polarization in terms ofCT is proposed therefore new interpretationson the electronic systematization of the DA reactions are presented taking into account that today such electronic systematizationis an open problem in organic physical chemistry Additionally one way to quantify the similarity in chemical reactivity was showntaking into account the dependence of the molecular alignment on properties when their position changes in this sense a possibleway to quantify the similarity of the CT in systematic form on these DA cycloadditions was shown

1 Introduction

Since its discovery the Diels-Alder (DA) reactions havebecome one of the most relevant reactions in syntheticorganic chemistry due to their ability to create cyclic unsat-urated compounds with a predictable stereochemistry andregioselectivity [1ndash8] For its amazing performance and utilityespecially in organic chemistry its discovery was recognizedby the Nobel Prize in Chemistry DA reactions have beenmechanistically classified as pericyclic reactions [9 10] Theviability of these chemical processes has been related to thewell-known Woodward-Hoffmann rules [11 12] But somemechanistic aspects of DA reactions still remain which havenot been explicated in appropriate way and therefore its

electronic systematization is an open problem in organicchemistry until today and can be considered as a bottleneckin DA reactions

Analysis based on the orbital symmetry regioselectivityand stereoselectivity in DA reactions confirms that manycharacteristics of DA reactions are modulated essentiallyby charge transfer (CT) processes between the diene anddienophile for this reason it is studied in this work In thissense CT appears as a key factor that allows us rationalize thenature of the mechanism in terms of the transition state (TS)and the activation energy associated with the process in DAreactions [1ndash12] From the CT point of view the DA reactionsare classified into the following types (a) the nonpolar DAreactions with low CT in the TS (b) the polar DA reactions

Hindawi Publishing CorporationJournal of Quantum ChemistryVolume 2014 Article ID 239845 19 pageshttpdxdoiorg1011552014239845

2 Journal of Quantum Chemistry

with high CT in the TS) with a zwitterionic character andfinally (c) the ionic DA reactions where the charge separationis preserved along the reaction path [1ndash12]

Since the implementation of DA reactions in currentorganic chemistry an enormous amount of experimentaland theoretical work has been devoted to the study of themechanism and selectivity of these DA cycloadditions Thereactivity and selectivity of these processes have been treatedprincipally within the frontier molecular orbital (FMO)approximations [21ndash26] transition state theory (TST) [2728] andmore recently using the reactivity descriptors definedin density functional theory (DFT) [1ndash8 29ndash50]

One of the fields in quantum chemistry for feasibil-ity study through the TSs in the DA reactions is themolecular quantum similarity (MQS) presenting possibleways of electronic systematization [51ndash78] In this sense wepresent a combined approach ofMQS and chemical reactivitydescriptors supported in DFT [79ndash84] to study the electronicreorganization in terms of the formation of the zwitterioniccharacter and their CT analysis along the series of reactionsshown in Figure 1 and Table 1 In the supplementary informa-tion (SI) is shows the structural geometries

The electronic reorganization for these DA reactions hasbeen studied widely by Domingo et al and coworkers [15ndash17] and they have postulated an electronic reorganizationcharacterized by nucleophilic attack centers towards elec-trophilic centers to study the synchronicity in the bond for-mation and also have studied the pseudodiradical characterto these organic systems [85 86] However other reactivityparameters such as the polar character have been littlestudied for this reason this study seeks to propose anelectronic reorganization that can be able to explain the polarcharacter in terms of CT and the subsequent formation of thezwitterionic character along the reaction paths in systematicform

The reaction rate constants analyzed in this contributionare shown in Table 1 These DA reactions have served asthe most dramatic examples of pure electronic effects onrates that are not complicated by significant steric effectsLarge fluctuations have been observed in terms of reactionrates as an example the reaction involving Cp + 2CN itsrate is estimated in the order of 104 while the 2cCN dropsdramatically to 91 Another example of this drastic changecan be seen in the Cp + 4CN reaction which has a reactionrate estimated in the order of 107 while the reference reaction(Cp + Et) is estimated in the order of 10minus5 taking into accountthat these experimental values have a factor of 105119896 (Mminus1Sminus1)In order to determine a possible electronic rationalization ofthese large fluctuations in this study direct considerations onthe electronic density in terms of reactivity descriptors andMQS are used

Recently the chemical reactivity and quantum similarityrelationship in order to understand the electronic reorgani-zation and molecular polarization using quantum similaritydescriptors [87ndash91] has been studied As the similarities inchemical reactivity depend on molecular properties and dueto the crucial role of the electronic density in MQS it is quitenatural that a close relation exists between chemical reactivity

and quantum similarity (QS) [92ndash103] Consequently thisstudy analyzes the chemical reactivity and MQS relationshipto postulate a possible way of electronic systematization onthe DA reactions of Table 1 in DFT framework Additionallyusing similarity relations Woodward-Hoffmann postulatedthe well-known rules through the FMO [11 12] therefore inthis studywe used theMQSfield to postulate a possible expla-nation of the polar character consistent with the experimentalresults and describe the similarity on the chemical reactivityof these cycloadditions in the DFT context

The structure of this paper will be as follows The theoryand computational details are described in Sections 2 and 3respectively and the results and discussions are developedin Section 4 and finally in Section 5 the most importantconclusions are discussed

2 Theory

21 Global and Local Reactivity Descriptors The global reac-tivity descriptors have a very well-known history in quantumchemistry that has been justified from theoretical point ofview in the DFT framework [79ndash84] such as chemical poten-tial (120583) [79ndash84] hardness (120578) [104] and softness (119878) [105 106]and these global descriptors are calculated using Koopmanstheorem ldquoie the energies of the higher occupied molecularorbital (HOMO) and the lowest unoccupied molecular orbital(LUMO) are equal to the negative of first ionization potentialand of the electronic affinity resprdquo and three-point differentialstatistical as

120583 asympIP + EA

2=

120576119867

+ 120576119871

2 (1)

120578 asymp 120576119871minus 120576119867 (2)

119878 =1

120578 (3)

The chemical potential (see (1)) can be interpreted as ameasure of the tendency of an electron to escape fromthe electronic cloud and the hardness (120578) is a measure ofthe resistance imposed by the system to the changes inthe electronic distribution In these equations (120576

119871) and (120576

119867)

represent the energies of theHOMO and LUMO respectivelyUsing (1) and (2) the electrophilicity (120596) index [107] is

defined as

120596 asymp1205832

2120578 (4)

where (120596) is other global property and represents thestabilization energy of the system when it is saturated byelectrons from the external environment in this sense theelectrophilicity is dependent on the saturation condition[79ndash82 108] determined by the chemical potential (120583) andhardness (120578) and obtained as

Δ119873max asymp minus120583

120578 (5)

Journal of Quantum Chemistry 3

Table 1 Reaction rate constant (119870) with the factor 105 k [Mminus1Sminus1] and activation energy (kcalmoL) for the DA reactions of cyclopentadiene(Cp) as nucleophile with dienophiles at 20∘C see [13] reported by Sauer et al [14] and also see [15ndash20]

Reactions (R-V) X1 X2 X3 X4 Dienophile TS-Y 119870 (105 k [Mminus1Sminus1])a

R-1 H H H H Etb TS-Et sim10minus5

R-2 H CN H H 1CN TS-1CN 104R-3 CN H H CN 2tCN TS-2tCN 81R-4 H CN H CN 2cCN TS-2cCN 91R-5 CN CN H H 2CN TS-2CN 48 times 10

4

R-6 CN CN H CN 3CN TS-3CN 48 times 105

R-7 CN CN CN CN 4CN TS-4CN 43 times 107

aRate constant (119870)bReference reaction

The energy reduction by CT effects is obtained by mathemat-ical development using Taylor series for the total energy andtruncated to second order as

Δ119864 asymp minus (120596) = minus1205832

2120578 (6)

The stabilization energy equation (6) can be associated withthe electronic population in the microstates associated with agrand canonical ensemble and could determine the relativeelectrons concentration in the total electron density Thedescriptors displayed in (1)ndash(4) depend on (119873) and (](119903))and they provide information on the reactivity and stabilityof a chemical system [79ndash82] Local properties are obtainedtaking into account the energy variation with respect to theexternal potential and this variation depends on the position(119903) and can be defined as selectivity indexes within thesewe have the Fukui functions [18ndash20 79ndash82 109ndash111] whichexplain the selectivity of a region in a molecule and aredefined mathematically as

⟨119891 ( 119903)⟩ asymp (120575120583

120575] ( 119903))

119873

= (120597120588 ( 119903)

120597119873)

]( 119903)= (

1205972119864

120597119873120597120592 ( 119903)) (7)

The Fukui function is interpreted as the chemical potentialchange by external perturbation or the variation in the elec-tronic density when the electrons number changesThe Fukuifunction ⟨119891

+(119903)⟩ using the Yang and Mortier condensed

approach is calculated the Mulliken charge in the atom (119896)is labeled as 119902

119896for the systems with (119873) (119873 + 1) and (119873 ndash 1)

electrons respectively and calculated at the same geometry[109ndash112]

⟨119891+

119896( 119903)⟩ asymp int

119896

[120588119873+1

( 119903) minus 120588 ( 119903)] 119889119903 = [119902119896(119873 + 1) minus 119902

119896(119873)]

⟨119891minus

119896( 119903)⟩asympint

119896

[120588119873( 119903) minus 120588

119873minus1( 119903)] 119889119903 = [119902

119896(119873) minus 119902

119896(119873 minus 1)]

(8)

With 119902119896(119873) denoting the electronic population of the atom

(119896) in the system under study these Fukui functions in the

atomic orbital condensate (AOC) approximation considersonly the contribution of the frontier orbitals of an atom [112]

⟨119891+

119896( 119903)⟩ asymp int

119896

120588119871( 119903) 119889 119903 = 119871

119896119902

⟨119891minus

119896( 119903)⟩ asymp int

119896

120588119867( 119903) 119889 119903 = 119867

119896119902

(9)

with (119867119896119902) and (119871

119896119902) representing the electronic populations

on the atom (119896) of the LUMO and HOMO frontier orbitalsrespectively

Using chemical reactivity descriptors based on themolec-ular recognition we consider each reaction of Table 1 ascycloaddition reactions by interaction of the nucleophilecommon (Cp) labeled as (A) with electrophiles labeled as (B)and the corresponding cycloadducts (C)

A + B 997888rarr C (10)

Obtaining the expressions for (5) and (6)

Δ119873max = minus120583B minus 120583A120578B + 120578A

(11)

Δ119864AB = minus(120583B minus 120583A)

2

2 (120578B + 120578A) (12)

One of the important features to study in the DA reactionsis the regioselectivity The regional or local electrophilicity atthe active sites of the reagents in polar DA processes maybe described on mathematic models using an extension ofthe global electrophilicity index introduced by Maynard etal [82] Considering 119878 = 1120578 and taking in account thesummatory rule for 119878 119878 = sum

119896119878+

119896

119878+

119896see [82] we have for (6)

120596 =1205832

2120578=

1205832

2119878 =

1205832

2sum

119896

119878+

119896= sum

119896

120596119896 (13)

Using (13) we can define a semilocal electrophilicity con-densed to the atom (119896) as

120596119896=

1205832

2119878+

119896(14)


and using the local softness and Fukui function (119891+119896( 119903))

relationship [82]

119878+

119896= 119878119891+

119896( 119903) (15)

therefore we have for (14)

120596119896=

1205832

2119878+

119896=

1205832119878

2119891+

119896( 119903) = 120596119891

+

119896( 119903) (16)

Using (16) with 120596 = minusΔ119864 we have

120596119896= 120596119891+

119896( 119903) = (

(120583B minus 120583A)2

2 (120578B + 120578A))119891+

119896( 119903) (17)

In this sense also we can write Δ119873max in (11) in terms of theFukui function 119891

+

119896(119903) as

Δ119873max (119896) = (minus120583B minus 120583A120578B + 120578A

)119891+

119896( 119903) (18)

In this study (17) and (18) as descriptors for the polar ornonpolar character in terms of local CT are used On theother hand as the reactions have the sense of promotingthe maximum superposition of HOMO and LUMO frontierorbitals according to Fukui et al [109ndash111] the molecularalignment is crucial and critical on the chemical reactivitytherefore in this study the quantum effects on the electronicdensity produced by the cyano substitutions along the DAreactions using amethodology based onmolecular alignmentas the MQS field are examined

22 Similarity Indexes The similarity indexes were intro-duced by Carbo-Dorca and coworkers almost thirty yearsago [63 70ndash78] they defined the quantum similaritymeasureZAB between molecules A and B with the electronic densities120588A(1199031) and 120588B(1199032) based on the idea of minimizing theexpression for the Euclidean distance as

1198632

AB (120588A (1199031) 120588B (119903

2))

= int1003816100381610038161003816120588A(1199031) minus 120588B(1199032)

1003816100381610038161003816

2

11988911990311198891199032

= int (120588A (1199031))2

1198891199031+ int (120588B (119903

2))2

1198891199032

minus 2∬120588A (1199031) 120588B (119903

2) 11988911990311198891199032

= 119885AA + 119885BB minus 2119885AB

(19)

Overlap integral is involving the 119885AB between the electronicdensity of the molecules A and B and 119885AA and 119885BB are self-similarity of the molecules A and B respectively [65] usingthis framework the quantum similarity indexes are defined

In the QS framework the axiomatic properties of theEuclidean distance can be mentioned and defined accordingto M Deza and E Deza [66] as follows let H be a set A

function 119866 H times H rarr R+ is called a distance (or similarity)onH If and only if forall120588

119860(1199031) 120588119861(1199032) isin H there holds

(i) 119863 (120588A (1199031) 120588B (119903

2)) ge 0 (non-negativity) (20)

(ii) 119863 (120588A (1199031) 120588B (119903

2)) = 119863 (120588B (119903

2) 120588A (119903

1))

(symmetry) (21)

(iii) 119863 (120588A (1199031) 120588B (119903

2)) = 0 (reflexivity) (22)

Using these mathematical and axiomatic properties in thisstudy the definition of similarity in quantum object setssupported in an pre-Hilbert vector space is explained wherethe scalar product and an attached norm are defined [67]In this sense one of the most important properties in theMQS field used in this study is the definition of a centroidorigin which shifts to choose a reference system within theMQS measures using the fact of their linear independenceaccording to Carbo-Dorca et al [68 69]

The most common way to describe the quantum similar-ity index is by the cosine function introduced by Besalu [113]and this index can be expressed mathematically as

Carbo-index (119868AB) =∬120588A (119903

1) 120588B (119903

2) 11988911990311198891199032

radicint (120588A (1199031))2

1198891199031int (120588B (119903

2))2

1198891199032

(23)

or also in function of the elements of (Z) and an operator (Ω)as

119868AB

=∬120588A (119903

1)Ω (1199031 1199032) 120588B (119903

2) 11988911990311198891199032

radicint120588A (1199031)Ω (1199031) 120588A (119903

1) 1198891199031int 120588B (119903

2)Ω (1199032) 120588B (119903

2) 1198891199032

=119885AB (Ω)

119885AA (Ω) 119885BB (Ω)

(24)

Equations (23) and (24) are mathematically defined in theinterval (0 1] where 0 means complete (dis)similarity and 1the self-similarity and calculates only the measures of ldquoshapesimilarityrdquo Other alternative of quantum similarity indexis the Hodgkin-Richards index (HK) [114] and this indexappears naturally when the arithmetic mean is used and canbe defined mathematically as

(HR) 119868AB =2119885AB (Ω)

119885AA (Ω) + 119885BB (Ω) (25)

However this HR index can be interpreted as a scaled Euclid-ian distance according to Carbo-Dorca [115] In this sensethe chemical reactivity analysis of the molecular densityfunctions is made in terms of molecular alignment in theMQS framework

23 Molecular Alignment in the DA Reactions From chem-ical reactivity to molecular similarity the arrangement or


+

X1

X3

TS-YR-V

2X

4X

Figure 1 The transition structures (TSs) to the reactions (R)between cyclopentadiene (Cp) and ethylene derivatives (Et-nCN)with 119899 = 0 1 2 2-cis 2-trans 3 4 and their cycloadducts (C)respectively

alignment of the molecules plays a central role and theMQS values are strongly dependent on the alignmentmethodconsidered Taking into account this dependence manyalignment methods have been proposed ranging from thoseused in CoMFA and CoMSIA methods which are in threedimensions (3D) and allow obtaining steric electrostaticand hydrophobic maps among others [116] These methodshave been proposed in order to find alignment pattern thatyields the best results by molecular alignment therefore thetopogeometrical superposition algorithm alignment methodto handle flexible molecules (TGSA-Flex) [117] is used Thismethod is based on the comparison of the types of atomsand distances between them and the recognition of the largestcommon substructure in the aligned molecules These typesof search algorithms constitute an important field of scientificinterest [118] In this study we decided to superimpose theTSs of Figure 1 using the TS-Et for the reaction R-1 asreferences of these TSs and are indicated in Figure 2

On the other hand the TGSA-Rigid alignment method[119] also was used in order to study the electronic andstructural flexibility in each DA reactions (see Figure 1) withrespect to the TGSA-Flex [117]

3 Computational Details

Due to that the DFT provides a powerful unified frameworkfor the rationalization of the chemical system responsesfront to perturbations (ie chemical reactivity) All themolecular structures were optimized and carried out usingthe Berny analytical gradient optimization method [120 121]with the help of GAUSSIAN 09 suite of programs [122] usingDFT methods The B3LYP exchange-correlation functional[123ndash125] together with standard 6-31G(d) base set [126]the orbital energies using (U)B3LYP6-31G(d) level werecomputed

B3LYP6-31G(d) Kohn-Sham wave functions have pro-vided good predictions of potential surface energy (PES)that have been consistent with many experimental results[127ndash131] Presently it is known that the B3LYP calculationscan illustrate the structure of the TSs in polar DA reactionsinvolving cyclopentadiene and this is confirmed by the com-pilation of deuterium secondary kinetic isotope effects andresults of quantum chemical calculations for cycloadditionbetween cyclopentadiene and E-2-phenylnitroethene [131132] Additionally in this study these results were also testedusing theM06-2X6-311 + G(dp) method [133]

In this sense the B3LYP in many cases has replaced thetraditional ab initiomethods and for this reason was used inthis study additionally this calculation level can be adequatefor the purpose of this study in order to characterize thedispersion energy for the (HOMO) and (LUMO) frontierorbitals which are important on the chemical reactivity inthe reactions studied [109ndash111] The stationary points werecharacterized by frequency calculations to verify that all TSshave only one imaginary frequency The solvent effects ofdioxane were taken into account through full optimizationsusing the polarizable continuum model (PCM) developedby Tomasirsquos group [110] in the self-consistent reaction field(SCRF) [111]

In this study the CT processes are analyzed in thereactants initially and along each reaction path in this sensethe intrinsic reaction coordinates (IRC) paths to verify theenergy profiles connecting each TS with the two minima ofthe proposed mechanisms using the second-order Gonzalez-Schlegel integration method were calculated [134 135] Ingeneral when the molecular alignment in the both TGSA-Flex and TGSA-rigid programs is executed the coordinatesof the first molecule considered to be fixed in space areread and the number of heavy atoms is determinedThen allinteratomic distances are calculated and stored in a matrixthat will be later used to retrieve these distance values thusavoiding recomputing them at later stages Additionally bothTGSA programs were evaluated by means of parameters ascomputational time number of superposed atoms and theindex of fit between the compared structures by Girones andCarbo-Dorca [117 119] respectively which for this reasonwere used in this study

On the other hand to calculate the reactivity descriptorsthe MolReactivity program version 10 (2014) made by ourresearch group [136ndash140] was used taking into account (1)ndash(18) in order to characterize the interaction energy fromclosed-shell (steric) repulsion CT from occupied-vacantorbital interactions and polarization effects among otherreaction parameters Finally theMPWB1K hybrid metafunc-tional was used due to that it is a general functional thatincludes covalent partial (TS) hydrogen and weak bonds Inthis sense it is used in order to validate the thermochemicalvalues and the accuracy of DA reactions that can haveinteractions obviously beyond the capability of B3LYP (eghydrogen bonding catalysis or 120587-stacking) [141]

4 Results and Discussion

The reactivity descriptors are defined in DFT [92 93 97] andallow us establish the nonpolar or polar nature on the DAreactions [15ndash17 31] In this study a possible explanation ofthe electronic reorganization in terms of CT takes the charac-teristics of a grand canonical ensemble and the considerationsfor an electrophilic system defined by chemical potential (120583)hardness (120578) in a sea of mobile electrons with zero chemicalpotential [79] in DFT framework Taking into account thatin the DA reactions studied (see Figure 1) the nucleophile(Cp) is common and the polar nature can be explained bythe electrophilicity increased in the dienophiles and their CT


H8

H9

H15

H10

H11

H13H12

H14

H17H16C1

C2

C3

C4

C5

C6

C7

Hydrogen

Carbon atom

(a)

1085

1085

1085

1085

1084

1084

1410

1410

14101521

1521

2230

2230

10911105

1087

1087

1400

(b)

Figure 2 Concerted TS of (119862119904) point group to the reference reaction (Cp + Et) is used for the molecular superposition in the molecular

alignment

respectively On the other hand the dioxane solvation effectson these reactions are carried out However such effects havenot incidence on the geometric and electronic parameters ofthe structures according to Domingo et al [15ndash17] In thissense the global and local reactivity indexes are shown inTable 2

In Table 2 we can see the higher chemical potentialassociated to the reaction between (Cp + 4CN) with a valuesof Δ120583 = 4021 eV These results are in agreement with thehigh experimental reaction rate for this reaction estimatedin the order of 107 while the lowest potential difference isobtained in the reaction (Cp + Et) with a value of Δ120583 =03555 eV and is in agreement with the low experimentalreaction rate for this reaction estimated in the order of 10minus5These values are consistent with the respective hardness andthe electrophilicity values found for the reaction (Cp +4CN) Δ120578 = 0724 eV Δ120596 = 5272 eV and for the reaction(Cp + Et) are Δ120578 = 1005 eV and Δ120596 = 00697 eV respec-tively These high differences between the values of the Δ120578

and Δ120596 are consistent with the experimental reaction rate(see Table 1)

The higher value of Δ119873max was obtained for the reaction(Cp + 4CN) with Δ119873max = 08403e (see Table 2) and is inagreementwith the high experimental reaction rate estimatedin the order of 107 and showing a strong polar character thelowest value is obtained for the reaction of (Cp + Et) witha value Δ119873max = 00546e showing a nonpolar characteraccording to the electronic classification of the DA reactions[1ndash8 11 12] In this sense the polar character may be relatedwith the zwitterion character associated to the TSs In orderto study CT processes the local reactivity rates are displayedin Table 3

The higher values of 119891+(119903) = 05000 are to Et showinghigher susceptibility to attack by nucleophile centers associ-ated with Cp (Table 3) however the electronic reorganiza-tions have a nonpolar path according to Δ119873max = 00546e(see Table 2) whereas the lowest value of 119891+(119903) = 02789 isfor 4CN and has a polar electronic reorganization accordingto Δ119873max = 08403e these trends from the nonpolarity topolarity are consistent with the local electrophilicity valuesfrom 120596

1= 04275 for the 4CN to 120596

1= 00005 for the Et

However when the local electrophilicity is analyzed in theisomers the following values were found 2cCN with 120596

1=

02043 and of 2tCNwith 1205961= 02124 evidencing higher local

electrophilicity character in the transisomer however thelocal CT in the cis-isomer is slightly higher with Δ119873max 1 =

01577e whereas for the transisomer it is Δ119873max 1 = 01576eThese outcomes are consistent with the experimental

trend shown in Table 3 Therefore in this study we canrelate the local trend of the CT in terms of Δ119873max 1(119896)with the experimental reaction rate trend presenting theorigins of the polar character in these DA reactions from1CN with Δ119873max 1 = 01321e to Δ119873max 1 = 02343e for4CN

Figure 3(a) shows a high correlation (1198772 = 09118)between the equations model used in this study and theexperimental reaction rates On the other hand Figure 3(b)also shows good correlation (1198772 = 09667) between the localelectrophilicity (17) with respect to the experimental reactionrates however these values cannot accurately describe theexperimental trend of the 2tCN and 2cCN isomers For thisreason with the intention of analyzing the polar character inthe CT the distortion (quantum similarity) on the TSs withrespect to theTS-Et (see Figure 1) from theMQSpoint of viewis analyzed


0123456789

0 005 01 015 02 025

Series 1Linear (series 1)

y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka

apk = logKbStandard deviation with respect to TS reference

Standard deviationb

(a) log119870 versus local CT (Δ119873max 1(119896))

0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc

cStandard deviation with respect to TS reference

1205961(17)b

bLocal electrophilic (1205961)

(b) log119870 versus local electrophilicity (1205961)

Figure 3 Correlation analysis (a) log 119870 versus local CT (Δ119873max 1(119896)) and (b) log 119870 versus local electrophilicity (1205961) with the standard

deviation respectively

In order to study the electronic and structural flexibilityeffects due to the systematic variations of the cyan groups(-CN) actually the distortion models in pericyclic reactionsare important tools in the structural and electronic analysison TSs and energy profiles according to Ess et al [142ndash144]The quantum distortion in this study is described with thesimilarity indexes therefore a high quantum distortion ofoverlap and coulomb means (dis)similarity and the largestEuclidean distances taking into account that the similarityindexes are mathematically defined in the interval (0 1]

where 0 means complete (dis)similarity and 1 the self-similarity

In order to characterize the steric and electronic effectsusing TGSA-Flex alignment method the structural distortioncan be associated with the MQS overlap and the electronicdistortion can be associated with the MQS-coulomb ThisTGSA-Flex method is compared with the TGSA-rigid Aspointed out by Carbo-Dorca [77 78] the molecular densi-ties functions should be referred to a common origin andtherefore first density differences are used which leads toconsider the distances between electronic densities takinginto account that the MQS varies with the origin selected

and the Euclidean distances not In Table 4 the overlapindexes values and the Euclidean distance of overlap areshown In Tables 5 and 6 the coulomb indexes valuesare shown respectively Finally the Euclidean distance ofcoulomb using TGSA-rigid is depicted in Table 7 in orderto relate the MQS of the TSs with the TS-Et referencestate

The molecular quantum similarity values using theoverlap operator are shown in Table 4 The higher valueof quantum similarity of 07045 is obtained when the TS-4CN with TS-Et are compared with a Euclidean distance ofoverlap of 23096 (see Table 5) quantifying the effects fromthe structural point of view due to the presence of the 4 cyan(-4CN) groups in the TS-4CN with respect to ethylene

The lowest values of quantum similarity 09284 areobtained when the TS-3CN is compared with TS-4CN and aEuclidean distance of 12073 (Table 5) Additionally the quan-tum similarity of TS-4CN with respect to other membersof the series analyzed shows the same experimental trendThis similarity trend also can be observed in the Euclideandistance values of overlap (Table 5)With the aim of study the


Table 2 Global reactivity descriptors in electronvolt (eV) and the softness in (eVminus1)

Cab120583 (eV)c 120578 (eV)d 119878 (eVminus1)e 120596 (eV)f Δ119873max (e)

g

Cp minus30171 27546 03630 08261 mdash4CN minus70381 20306 04925 60984 084033CN minus64193 26331 03798 39124 063152CN minus56441 29749 03361 26770 045852cCN minus56200 28861 03465 27359 046362tCN minus57124 28745 03479 28380 047881CN minus46949 32609 03067 16899 02789Et minus33726 37593 02660 07564 00546aC compoundbExp trendcChemical potential (120583)dHardness (120578)eSoftness (119878)fGlobal electrophilicity (120596)gSaturation condition (Δ119873max) (11)

Table 3 Local reactivity descriptors

Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2

4CN 02789 04275 02343 02789 04275 023433CN 03642 03912 02299 02686 02885 016962CN 04968 02992 02278 02404 01448 011022cCN 03402 02043 01577 03402 02043 015772tCN 03292 02124 01576 03292 02124 015761CN 04735 01108 01321 03001 00702 00837Et 05000 00005 00273 05000 00005 00273aC compoundbExp trendcFukui functiondLocal electrophilicity (120596119896) (17)eLocal saturation condition (Δ119873max(119896)) (18)

distortion effects in Table 6 is shown the coulomb similarityvalues together with the Euclidean distance of coulomb

In Table 6 the quantum similarity values using thecoulomb operator are shown and the higher similarity valueof 09277 is found between the TS-Et and TS-4CN witha Euclidean distance of 154726 (Table 7) The lowest valueof similarity of 09867 is found between TS-3CN and TS-4CN with a Euclidean distance of 57883 (Table 7) Thevalues associated with the quantum similarity distortion ofEt (reference state) with other members of the series are inagreement with the experimental trend (see Table 1) Thesevalues allow us associate the higher distortion of 4CN withthe higher fluctuation of the reaction rates estimated in 107for 4CN from the structural and electronic distortion pointof view (see Tables 4ndash7)

The main difference between the TGSA-rigid and TGSA-Flex is that the TGSA-rigid was originally designed tosuperpose rigid molecules simply based on atomic numbersmolecular coordinates and connectivityWhile the algorithmTGSA-flex is further developed to enable handling rotationsaround single bonds in this way common structural featureswhich were not properly aligned due to conformationalcauses can be brought together thus improving the molec-ular similarity picture of the final alignment these effects

can be important on the quantum similarity in the cis- andtransisomers In this sense the values associated with thestructural flexibility on the quantum similarity of overlapusing the Carbo-Dorca index (24) are shown in Table 8

In Table 8 the higher structural flexibility value of 05088is found between the TS-4CN and TS-2tCN the lowestsimilarity value of 08348 we can see between the TS-2tCNand TS-1CN The similarity to the TS-2cCN with TS-1CNis estimated in 06644 presenting large differences in thestructural flexibility on the TS-2tCN and TS-2cCN respec-tively Another example of this fact is found when the TS-Etreference with the TS-2cCN obtaining 07193 is comparedwhereas for TS-Et with TS-2tCN it is 06899 presentinghigher structural distortion These results show that thegeometric isomers are distorted by the structural flexibilityeffects with the aim of comparing the structural distortion onthe isomers using the Hodgkin-Richards indexes of overlapusing (25) in Table 9 and this index can be related to theinformation on the angle subtended between two electronicdensities along these DA cycloadditions

In Table 9 the higher value of 05008 was found betweenthe TS-2tCN and TS-4CN and the lowest value of 08288was found between the TS-2tCN with TS-1CN and is inagreement with the values found using the Carbo-Dorca


Table 4 Molecular quantum similarity matrix of overlap using the TGSA-rigid alignment method

Sab TS-4CN TS-3CN TS-2CN TS-2cCN TS-2tCN TS-1CN TS-EtTS-4CN 10000TS-3CN 09284 10000TS-2CN 08598 08318 10000TS-2cCN 08580 09171 08183 10000TS-2tCN 08499 09154 08222 08277 10000TS-1CN 07829 08373 09021 09020 09086 10000TS-Et 07045 07483 08075 08072 08075 08836 10000aS state (Table 1)bExp trend

Table 5 Molecular quantum similarity matrix using the overlap Euclidean distances using the TGSA-rigid alignment method


Table 6 Molecular quantum similarity matrix of coulomb using the TGSA-rigid alignment method

Sab TS-Et TS-1CN TS-2tCN TS-2cCN TS-2CN TS-3CN TS-4CNTS-Et 10000TS-1CN 09733 10000TS-2tCN 09561 09789 10000TS-2cCN 09529 09788 09659 10000TS-2CN 09528 09795 09648 09612 10000TS-3CN 09394 09629 09842 09835 09746 10000TS-4CN 09277 09518 09733 09693 09703 09867 10000aS state (Table 1)bExp trend

Table 7 Molecular quantum similarity matrix using the coulomb Euclidean distances using the TGSA-rigid alignment method



Table 8 Molecular quantum similarity Carbo-Dorca matrix of overlap using the TGSA-Flex alignment method


Table 9 Molecular quantum similarity Hodgkin-Richards of overlap using the TGSA-Flex alignment method


index (see Table 8) For the other isomer TS-2cCN showslow similarity of 06918 when it is compared with the TS-Etreference state however the TS-2tCN shows more similaritywith 06635 These values have significant differences byflexibility effects between the two geometric isomers anotherexample of this fact is found comparing the TS-4CN withrespect to TS-2cCN (05511) and for the TS-2tCN (05008)Therefore we can associate this diminution in the reactionrate with quantum similarity effects

In Figure 4 a high correlation (1198772 = 09499) betweenthe Carbo-Dorca and Hodgkin-Richards index was foundShowing a structural consistency on the TSs is studied Toanalyze the electronic flexibility in the TSs in Tables 10 and11 the coulomb Carbo-Dorca (24) and Hodgkin-Richardsindexes (25) are studied respectively

In Table 10 the higher electronic distortion value of08855 using the coulomb operator is between the TS-4CNand TS-Et states and is in agreement with the electronicdistortion of overlap using the TGSA-Flex alignmentmethod(see Table 8) so we can associate this distortion increasedof the TS-4CN with the high experimental rate constantestimated in 107 On the other hand the reference stateTS-Et has the lowest distortion when it is compared withthe TS-1CN state These distortion results to the TS-Etstate are in agreement with the experimental trend (4CNgt 3CN gt 2CN gt 2cCN gt 2tCN gt 1CN) Therefore thiselectronic flexibility study quantifies the degree of distortionon the TSs in systematic form from the TS-Et to TS-4CN(see Figure 1) In order to compare the Carbo-Dorca values

with respect to the Hodgkin-Richards values in Table 11the MQS-coulomb using the Hodgkin-Richards index isshown

Comparing the Hodgkin-Richards index using thecoulomb operator with those obtained in Table 10 usingthe Carbo-Dorca index this latter shows lowest quantumsimilarity values (values close to 000) and therefore moredistortion effects can be characterized in this way Figure 5shows the correlation between the two electronic distortionindexes

In Figure 5 this high correlation (09483) shows theHodgkin-Richards index as a scaled distance according toCarbo-Dorca [115] is consistent with the Euclidean distancetrends from the TS-4CN to TS-Et (see Tables 5 and 7)

In order to relate the CT with the electronic distortionusing quantum similarity in the DA reactions studied (seeFigure 1) Figure 6 shows the relation between the electronicquantum similarity of coulomb and CT in the DA reactionsAccording to Bultinck et al [72] naturally there is a correla-tion between distortion (quantum similarity) of coulomb andchemical reactivity in this sense new insights on the role ofCT in the electronic distortion are shown

Figure 6 shows acorrelation (1198772 =07127) betweenCarbo-Dorca distortion and CT and their standard deviation withrespect to the TS-Et reference state Such effects have directresponses in the electronic density In this sense we canrelate the trend found in the zwitterion character with ahigh distortion on the electronic density associated with theCarbo-Dorca similarity index Therefore we can associate


010002000300040005000600070008000

0 1000 2000 3000 4000 5000 6000 7000 8000Hodgkin-Richards index

y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc

cStandard deviation with respect to TS referencebHodgkin-Richards index

aCarbo-Dorca index

CIaH-KIa

Figure 4 Carbo-Dorca index versus Hodgkin-Richards index using the overlap operator for the TSs (see Figure 1) Note in this graphicalthe Carbo-Dorca and Hodgkin-Richards indexes are normalized from 0 to 100 with the standard deviation respectively

880089009000910092009300940095009600

8200 8400 8600 8800 9000 9200 9400 9600Hodgkin-Richards index

Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa

Figure 5 Carbo-Dorca index versus Hodgkin-Richards index using the coulomb operator for the TSs (see Figure 3) Note in this graphicalthe Carbo-Dorca and Hodgkin-Richards indexes are normalized from 0 to 100 with the standard deviation respectively

088089

09091092093094095096

0 005 01 015 02 025Charge transference (CT)

Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc

cStandard deviation with respect to TS referencebCharger transfer (CT)

aCarbo index

aCarbo I aCTb

Figure 6 Correlation analysis between Carbo-Dorca index and charge transfer CT in the reactions of Table 1 Note in this graphical theCarbo-Dorca indexes are normalized from 0 to 100 with the standard deviation respectively


Table 10 Molecular quantum similarity Carbo-Dorca matrix of coulomb using the TGSA-Flex alignment method


Table 11 Molecular quantum similarity matrix of coulomb using the TGSA-Flex alignment method


Charge transfer Zwitterion characterCN

CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+

Figure 7 Zwitterion status in polar reaction is reported in this studyThis electronic reorganization is due to polarization effects on the(CT)

CT with the electronic reorganization and the zwitterioncharacter in these DA reactions (see Table 1) (Figure 7)

In Figure 7 we can associate the zwitterion character withthe value of Δ119873max = 08403e (see Table 2) formed by theincreases of CT (polar character) reported in this study andthat can be related to the electronic distortion (quantumsimilarity) This zwitterion character is the first step to theformation of the aromatic nature in the TSs of the polar reac-tions (R-2 to R-7) see Table 1 The aromatic nature of theseTSs has been confirmed theoretically using geometry-basedindices such as the harmonic oscillator model of aromaticity(HOMA) the para-delocalization indices (PDI) [145 146]the nucleus-independent chemical shift (NICS) and themagnetic susceptibility exaltations [147] Additionally thisstudy presents new consideration on the analysis of CT in theinteraction energy taking into account that the CT is partof the interaction energy with the molecular polarizationthe closed-shell repulsion and the dispersion according toEss et al [142ndash144] relating the electronic and structural

quantum distortion from the MQS in terms of the cyanosubstitutions

Taking into account the correlation (1198772 = 07127) betweenCarbo-Dorca distortion and CT (Figure 6) in this studythe CT (Δ119873max) with the electronic quantum similarity ofcoulomb to describe the character polar trend using (26) isrelated Taking the TS-4CN as a reference

Δ119873max (TS4CN) MQS (Coulomb)

= Character polar trend(26)

with

Δ119873max (TS4CN) = 08403 (27)

(see Table 2) Consider

MQS (Coulomb) = 0 lt MQS (Coulomb) lt 1 (28)

ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441

MQS (Coulomb) TS-4CN versus

Relative characterpolar trend08403

- TS-2C (09440) = 07932

(29)


0123456789

088 089 09 091 092 093 094 095 096minus1Carbo index (coulomb)

y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb

bCI Carbo-Dorca index

Figure 8 Carbo-Dorca index of Coulomb versus experimental rate constants (see Table 1) Note in this graphical the Carbo-Dorca indexesare normalized from 0 to 100 with the standard deviation respectively

In (29) the MQS values of coulomb are in Table 10 and wecan see the character polar trend along the reactions withrespect to TS-4CN and the relative character polar along theDA reactions is a possible form of study

With the aim of study the electronic distortion and theexperimental rate constant trend (see Table 1) is shown inFigure 8 with a high correlation 119877

2 = 08330 between theCarbo-Dorca index of coulomb and the natural log (log 119870 =119875119870)According to the finding of Geerlings et al [97 148]

Figure 8 depicted an alternative relation between the Carbo-Dorca indexes and chemical reactivity descriptors One ofthe remaining problems in this approach is the orientationtranslational and conformational dependence of 119885 (see (24)and (25)) on the measurement of the MQS however thisproblem was resolved using the autocorrelation functionconcept of the property considered that for this study is theCT along the DA reactions and such autocorrelation wastestedwith the standard deviation respectivelyTherefore thisresult shows a possible way of unification of the chemicalreactivity and QS in DFT framework [148 149] In this sensewe can think that this hybrid methodology (joining theMQS with chemical reactivity) provides new insights for theelectronic systematization of the DA reactions in the DFTframework which is an open problem in organic physicalchemistry

A molecular orbital analysis in the DA reactions stud-ied can take into account that the concerted inter- andintramolecular multicenter 120587 interactions can be related tothe nodal properties (symmetry) of the HOMO (120587) andLUMO (120587lowast) frontier orbitals In this sense the regiospeci-ficity of such DA interactions can be defined by the molec-ular polarization parallel to the nodal plane of the orbitalsproduced by the (120587) and (120587lowast) DA interactions thereforethe stereospecificity of such interactions can be associatedwith the electronic distortion perpendicular to the nodalplane of the orbitals produced by the HOMO-1 (120590) HOMO(120587) LUMO (120587lowast) and LUMO + 1 (120590lowast) interactions mixedaccording to ldquoprinciple of Orbital Distortionrdquo [150] and these

electronic interactions exceed to the steric effects yieldingthe bonds in the cycloadducts respective These results areconsistent with the stereoselectivity analysis reported byHouk et al [151]

On the other hand the zwitterionic character and themolecular polarization reported in this study in terms ofa grand canonical ensemble can be understood as a rela-tive increase in the number of available microstates in themolecular space producing chemical potential differencesand promoting the electron transfer from regions of higherpotential to regions of lower chemical potential Additionallythe CT related with theMQS allows understanding the originof the polar character using the quantum similarity Finallyin the TSs when the CT in the electronic reorganizationincreases the ionic character of the bonds formed decreasestherefore the force constants increase and we can relate thepolar character with the bond force constants in these DAreactions

On the other hand in this study the four features onsimilarities sugared by Rouvray et al [152ndash155] analogiescomplementarities and equivalence and scaling relationshipsfor the role of molecular similarity in the chemical and physi-cal scienceswere exploited exploring a possiblemethodologyto understand the similarity on the chemical reactivity andconsistency with the experimental results which today is abottleneck in the MQS field

5 Conclusions and Perspective

In this study the CT processes in a series of reactions betweencyclopentadiene (Cp) with cyano substitution on ethylenewere analyzed proposing a possible electronic systemati-zation to the DA reactions The analysis of the CT takesplace initially in the reagents assuming a grand canonicalensemble and using the considerations of an electrophilicsystem using B3LYP6-31G(d) and M06-2X6-311 + G(dp)methods The DA reactions studied have the nucleophile(Cp) common therefore the increases of the polar charactercan be explained by the nature of the electrophilic carbons


in the dienophiles and its CT respectively in this sense ananalysis of CT using the Δ119873max 1(119896) is performed and theseΔ119873max 1(119896) values have a good statistical correlation (1198772 =09118) with the experimental rate constants using reactivitymodels based on molecular recognition descriptors

To study the quantum distortion using similarity descrip-tors the Et-TS of the (Cp + Et) in the reference reaction inorder to study the electronic and structural effects on theTSs using the MQS field was used as molecular alignmentpattern taking into account that the similarity indexes aremathematically defined in the interval (0 1] where 0 meanscomplete (dis)similarity and 1 the self-similarity The higherstructural and electronic effects are presented in the TS-4CNwith respect to TS-Et and are agreeing with the CT values andthe experimental rate constants (1198772 = 07127) In this sensethis study shows a good complementarity between quantumsimilarity and chemical reactivity in the DFT frameworkgenerating similarity sequences and describing the polarcharacter through CT and molecular polarization effectsin this sense new insights on the electronic reorganizationassociated with the DA reactions are shown consistent withthe experimental results

Additionally one of the most important fields in thequantum similarity is the measurement of similarity on reac-tivity properties that vary with the position change takinginto account the dependence of the molecular alignment inthe (MQS) values In this sense the property to quantifythe degree of similarity chosen in this study is the (CT)that allowed us to describe the chemical reactivity of thesereactions in a systematic way and determining the similarityon the (CT) along the reactions and in terms of the polarcharacter trend

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Alejandro Morales-Bayuelo expresses his thanks to the Uni-versidad Nacional Andres Bello (UNAB) by a fellowshipCONICYT (63100003) Ricardo Vivas-Reyes is indebted tothe Universidad de Cartagena (Cartagena de Indias Colom-bia) for the continuous support to this research group

References

[1] F Fringuelli and A Tatacchi Diels-Alder Reactions SelectedPractical Methods Wiley New York NY USA 2001

[2] P B Karadakov D L Cooper and J Gerratt ldquoModern valence-bonddescription of chemical reactionmechanismsDiels-Alderreactionrdquo Journal of the American Chemical Society vol 120 no16 pp 3975ndash3981 1998

[3] H Lischka E Ventura andM Dallows ldquoThe Diels-Alder reac-tion of ethene and 13-butadiene an extended multireferenceab initio investigationrdquo ChemPhysChem vol 5 no 9 pp 1365ndash1371 2004

[4] E Kraka AWu andD Cremer ldquoMechanism of the diels-Alderreaction studied with the united raction valley approach mech-anistic differences between symmetry-allowed and symmetry-forbidden reactionsrdquo Journal of Physical Chemistry A vol 107no 42 pp 9008ndash9021 2003

[5] H Isobe Y Takano Y Kitagawa et al ldquoSystematic comparisonsbetween broken symmetry and symmetry-adapted approachesto transition states by chemical indices a case study of theDiels-Alder reactionsrdquo Journal of Physical Chemistry A vol 107 no 5pp 682ndash694 2003

[6] O Diels and K Alder ldquoSynthesen in der hydroaromatischenReiherdquo Justus Liebigs Annalen Der Chemie vol 460 no 1 pp98ndash122 1928

[7] K N Houk R J Loncharich J F Blake and W L JorgensenldquoSubstituent effects and transition structures for Diels-Alderreactions of butadiene and cyclopentadiene with cyanoalkenesrdquoJournal of the American Chemical Society vol 111 no 26 pp9172ndash9176 1989

[8] K C Nicolaou S A Snyder T Montagnon and G Vassi-likogiannakis ldquoThe Diels-Alder reaction in total synthesisrdquoAngewandte Chemie International Edition vol 41 no 10 pp1668ndash1698 2002

[9] I Fleming Frontier Orbitals and Organic Chemical ReactionsJohn Wiley and Sons New York NY USA 1976

[10] I FlemingPericyclic Reaction OxfordUniversity Press OxfordUK 1999

[11] R BWoodward and R Hoffmann ldquoThe conservation of orbitalsymmetryrdquo Angewandte Chemie International Edition vol 8no 11 pp 781ndash853 1969

[12] R B Woodward and R HoffmannThe Conservation of OrbitalSymmetry Academic Press New York NY USA 1970

[13] R Walsh and J M Wells ldquoThe kinetics of reversible Diels-Alder reactions in the gas phasemdashpart II Cyclopentadiene andethylenerdquo Journal of the Chemical Society Perkin Transactionsvol 2 pp 52ndash55 1976

[14] J Sauer H Wiest and A Mielert ldquoEine studie der Diels-Alder-reaktionmdashI Die reaktivit t von dienophilen gegenubercyclopentadien und 910-dimethyl-anthracen rdquo ChemischeBerichte vol 97 pp 3183ndash3207 1964

[15] L Domingo J M Aurell P Perez and R Contreras ldquoOriginof the synchronicity on the transition structures of polar Diels-Alder reactions Are these reactions [4 + 2] processesrdquo Journalof Organic Chemistry vol 68 pp 3884ndash3890 2003

[16] L Domingo and J Saez ldquoUnderstanding the mechanism ofpolar Diels-Alder reactionsrdquo Organic amp Biomolecular Chem-istry vol 7 pp 3576ndash3583 2009

[17] L Domingo J M Aurell P Perez and R Contreras ldquoQuan-titative characterization of the local electrophilicity of organicmolecules Understanding the regioselectivity on Diels-Alderreactionsrdquo Journal of Physical Chemistry A vol 106 pp 6871ndash6875 2002

[18] WYang RG Parr andR Pucci ldquoElectron density Kohn-Shamfrontier orbitals and Fukui functionsrdquoThe Journal of ChemicalPhysics vol 81 no 6 pp 2862ndash2863 1984

[19] P W Ayers W T Yang and L J Bartolotti ldquoFukui functionrdquoin Chemical Reactivity Theory A Density Functional View P KChattaraj Ed pp 255ndash267 CRC Press Boca Raton Fla USA2009


[20] P W Ayers and M Levy ldquoPerspective on density functionalapproach to the frontier-electron theory of chemical reactivityrdquoTheoretical Chemistry Accounts vol 103 no 3-4 pp 353ndash3602000

[21] A Szabo andN SOstlundModernQuantumChemistry DoverPublishing Mineola NY USA 1996

[22] C J Cramer Essentials of Computational Chemistry JohnWileyand Sons Chichester UK 2002

[23] T Sommerfeld ldquoLorentz trial function for the hydrogen atoma simple elegant exerciserdquo Journal of Chemical Education vol88 no 11 pp 1521ndash1524 2011

[24] K Fukui ldquoThe role of frontier orbitals in chemical reactions(Nobel lecture)rdquo Angewandte Chemie International vol 21 no11 pp 801ndash809 1982

[25] K Fukui T Yonezawa and H Shingu ldquoA molecular orbitaltheory of reactivity in aromatic hydrocarbonsrdquo The Journal ofChemical Physics vol 20 no 4 pp 722ndash725 1952

[26] M Bernard Organic Chemistry Reactions and MechanismsPearsons Upper Saddle River NJ USA 2004

[27] H Eyring ldquoThe activated complex and the absolute rate ofchemical reactionsrdquo Chemical Reviews vol 17 no 1 pp 65ndash771935

[28] K J Laidler and M C King ldquoThe development of transition-state theoryrdquo Journal of Physical Chemistry vol 87 no 15 pp2657ndash2664 1983

[29] P Geerlings P W Ayers A Toro-Labbe P K Chattaraj andF De Proft ldquoThe Woodward-Hoffmann rules reinterpreted byconceptual density functional theoryrdquo Accounts of ChemicalResearch vol 45 no 5 pp 683ndash695 2012

[30] P Hohenberg and W Kohn ldquoInhomogeneous electron gasrdquoPhysical Review vol 136 no 3B pp B864ndashB871 1964

[31] D H Ess G O Jones and K N Houk ldquoConceptual qual-itative and quantitative theories of 1 3-dipolar and Diels-Alder cycloadditions used in synthesisrdquoAdvanced Synthesis andCatalysis vol 348 pp 2337ndash2361 2006

[32] E Goldstein B Beno and K N Houk ldquoDensity functionaltheory prediction of the relative energies and isotope effectsfor the concerted and stepwise mechanisms of the Diels-Alderreaction of butadiene and ethylenerdquo Journal of the AmericanChemical Society vol 118 no 25 pp 6036ndash6043 1996

[33] F Bernardi A Bottini M A Robb M J Field I H Hillier andM F Guest ldquoTowards an accurate ab initio calculation of thetransition state structures of the Diels-Alder reactionrdquo Journalof the Chemical Society Chemical Communications vol 7 no 15pp 1051ndash1052 1985

[34] F Bernardi A Bottoni M J Field et al ldquoMC-SCF study of theDiels-Alder reaction between ethylene and butadienerdquo Journalof the American Chemical Society vol 110 no 10 pp 3050ndash30551988

[35] R E Townshend G Ramunni G Segal W J Hehre and LSalem ldquoOrganic transition states V the diels-alder reactionrdquoJournal of American Chemical Society vol 98 no 8 pp 2190ndash2198 1976

[36] W L Jorgensen D Lim and J F Blake ldquoAb initio study ofDiels-Alder reactions of cyclopentadiene with ethylene iso-prene cyclopentadiene acrylonitrile and methyl vinyl ketonerdquoJournal of the American Chemical Society vol 115 no 7 pp2936ndash2942 1993

[37] S Berski J Andres B Silvi and L R Domingo ldquoThe jointuse of catastrophe theory and electron localization functionto characterize molecular mechanisms a density functionalstudy of the Diels-Alder reaction between ethylene and 13-butadienerdquo Journal of Physical Chemistry A vol 107 no 31 pp6014ndash6024 2003

[38] L A Burke and G Leroy ldquoCorrigendumrdquo Theoretica ChimicaActa vol 44 no 2 pp 219ndash221 1977

[39] L A Burke G Leroy and M Sana ldquoTheoretical study of theDiels-Alder reactionrdquo Theoretica Chimica Acta vol 40 no 4pp 313ndash321 1975

[40] M Ortega A Oliva J M Lluch and J Bertran ldquoThe effectof the correlation energy on the mechanism of the Diels-Alderreactionrdquo Chemical Physics Letters vol 102 no 4 pp 317ndash3201983

[41] K N Houk Y T Lin and F K Brown ldquoEvidence for theconcerted mechanism of the Diels-Alder reaction of butadienewith ethylenerdquo Journal of the American Chemical Society vol108 no 3 pp 554ndash556 1986

[42] F K Brown and K N Houk ldquoThe STO-3G transition structureof the Diels-Alder reactionrdquo Tetrahedron Letters vol 25 no 41pp 4609ndash4612 1984

[43] M J S Dewar S Olivella and J J P Stewart ldquoMechanism of theDiels-Alder reaction reactions of butadiene with ethylene andcyanoethylenesrdquo Journal of the American Chemical Society vol108 no 19 pp 5771ndash5779 1986

[44] K N Houk and L L Munchausen ldquoIonization potentialselectron affinities and reactivities of cyanoalkenes and relatedelectron-deficient alkenes a frontier molecular orbital treat-ment of cyanoalkene reactivities in cycloaddition electrophilicnucleophilic and radical reactionsrdquo Journal of the AmericanChemical Society vol 98 no 4 pp 937ndash946 1976

[45] Y Cao S Osune Y Liang R C Haddon and K N HoukldquoDiels-alder reactions of graphene computational predictionsof products and sites of reactionrdquo Journal of the AmericanChemical Society vol 135 no 46 pp 17643ndash17649 2013

[46] T Karcher W Sicking J Sauer and R Sustmann ldquoSolventeffects on endo-exo selectivities in (4+2) cycloadditions ofcyanoethylenesrdquo Tetrahedron Letters vol 33 no 52 pp 8027ndash8030 1992


[48] B S Jursic ldquoComparison of AM1 and density functional theorygenerated transition state structures and activation energies forcyanoalkenes addition to cyclopentadienerdquo Journal ofMolecularStructure THEOCHEM vol 358 pp 139ndash143 1995

[49] V Branchadell ldquoDensity functional study of Diels-Alder reac-tions between cyclopentadiene and substituted derivatives ofethylenerdquo International Journal of Quantum Chemistry vol 61no 3 pp 381ndash388 1997

[50] G O Jones V A Guner and K N Houk ldquoDiels-Alderreactions of cyclopentadiene and 910-dimethylanthracene withcyanoalkenes the performance of density functional theoryand hartree-fock calculations for the prediction of substituenteffectsrdquo Journal of Physical Chemistry A vol 110 no 4 pp 1216ndash1224 2006


[51] R Ponec Topics in Current Chemistry Springer Berlin Ger-many 1995

[52] R Carbo-Dorca ldquoMathematical aspects of the LCAO MO firstorder density function (5) centroid shifting of MO shapefunctions basis set properties and applicationsrdquo Journal ofMathematical Chemistry vol 51 no 1 pp 289ndash296 2013

[53] F Fratev O E Polansky A Mehlhorn and V Monev ldquoAppli-cation of distance and similarity measures The comparison ofmolecular electronic structures in arbitrary electronic statesrdquoJournal of Molecular Structure vol 56 pp 245ndash253 1979

[54] O E Polansky and G Derflinger ldquoZur Clarrsquoschen TheorieLokaler Benzoider Gebiete in Kondensierten Aromatenrdquo Inter-national Journal of Quantum Chemistry vol 1 no 4 pp 3379ndash3401 1967

[55] P E Bowen-Jenkins D L Cooper and W G Richards ldquoAbinitio computation of molecular similarityrdquo Journal of PhysicalChemistry vol 89 no 11 pp 2195ndash2197 1985

[56] E E Hodgkin and W G Richards ldquoA semi-empirical methodfor calculating molecular similarityrdquo Journal of the ChemicalSociety Chemical Communications vol 17 pp 1342ndash1344 1986

[57] R Ponec and C Czech ldquoTopological aspects of chemicalreactivity On the similarity of molecular structuresrdquo ChemicalCommunications vol 52 pp 555ndash562 1987

[58] R Ponec and M Strnad ldquoPosition invariant index for assess-ment of molecular similarityrdquo Croatica Chemica Acta vol 66pp 1123ndash1127 1993

[59] D L Cooper and N L Allan ldquoA novel approach to molecularsimilarityrdquo Journal of Computer-Aided Molecular Design vol 3no 3 pp 253ndash259 1989

[60] D L Cooper and N L Allan ldquoMolecular dissimilarity amomentum-space criterionrdquo Journal of the American ChemicalSociety vol 114 no 12 pp 4773ndash4776 1992

[61] R Carbo-Dorca and B Calabuig ldquoMolecular quantum simi-larity measures and N-dimensional representation of quantumobjects I Theoretical foundationsrdquo International Journal ofQuantum Chemistry vol 42 no 6 pp 1681ndash1693 1992

[62] J Cioslowski and E D Fleischmann ldquoAssessing molecular sim-ilarity from results of ab initio electronic structure calculationsrdquoJournal of the American Chemical Society vol 113 no 1 pp 64ndash67 1991

[63] Carbo-Dorca and R Arnau M ldquoHow similar is a moleculeto another An electron density measure of similarity betweentwo molecular structuresrdquo International Journal of QuantumChemistry vol 17 no 6 pp 1185ndash1189 1980

[64] L Amat and R Carbo-Dorca ldquoUse of promolecular ASAdensity functions as a general algorithm to obtain startingMO in SCF calculationsrdquo International Journal of QuantumChemistry vol 87 no 2 pp 59ndash67 2002

[65] X Girones and R Carbo-Dorca ldquoModelling toxicity usingmolecular quantum similarity measuresrdquo QSAR and Combina-torial Science vol 25 pp 579ndash589 2006

[66] M M Deza and E Deza Encyclopedia of Distances SpringerBerlin Germany 2009

[67] S K Berberian Introduction To Hilbert Space Oxford Univer-sity Press New York NY USA 1961

[68] R Carbo-Dorca and E Besalu ldquoCentroid origin shift of quan-tum object sets and molecular point clouds description and

element comparisonsrdquo Journal of Mathematical Chemistry vol50 pp 1161ndash1178 2012

[69] L D Mercado and R Carbo-Dorca ldquoQuantum similarity anddiscrete representation of molecular setsrdquo Journal of Mathemat-ical Chemistry vol 49 no 8 pp 1558ndash1572 2011

[70] R Carbo-Dorca and X Girones ldquoFoundation of quantumsimilarity measures and their relationship to QSPR densityfunction structure approximations and application examplesrdquoInternational Journal of Quantum Chemistry vol 101 no 1 pp8ndash20 2005

[71] R Carbo-Dorca ldquoScaled Euclidian distances a general dissim-ilarity index with a suitably defined geometrical foundationrdquoJournal of Mathematical Chemistry vol 50 no 4 pp 734ndash7402012

[72] P Bultinck X Girones and R Carbo-Dorca ldquoMolecularquantum similarity theory and applicationsrdquo in Reviews inComputational Chemistry vol 21 chapter 2 p 127 2005

[73] R Carbo-Dorca and E Besalu ldquoCommunications on quantumsimilarity (2) a geometric discussion on holographic electrondensity theorem and confined quantum similarity measuresrdquoJournal of Computational Chemistry vol 31 no 13 pp 2452ndash2462 2010

[74] R Carbo-Dorca and L D Mercado ldquoCommentaries on quan-tum similarity (1) density gradient quantum similarityrdquo Journalof Computational Chemistry vol 31 no 11 pp 2195ndash2212 2010

[75] R Carbo-Dorca E Besalu and L D Mercado ldquoCommuni-cations on quantum similaritymdashpart 3 a geometric-quantumsimilarity molecular superposition algorithmrdquo Journal of Com-putational Chemistry vol 324 pp 582ndash599 2011

[76] M Randic ldquoOn characterization of molecular branchingrdquoJournal of the American Chemical Society vol 97 no 23 pp6609ndash6615 1975


[78] R Carbo-Dorca ldquoCollective Euclidian distances and quantumsimilarityrdquo Journal of Mathematical Chemistry vol 51 no 1 pp338ndash353 2013

[79] PW Ayers J S M Anderson and L J Bartolotti ldquoPerturbativeperspectives on the chemical reaction prediction problemrdquoInternational Journal of Quantum Chemistry vol 101 no 5 pp520ndash534 2005

[80] J L Gazquez ldquoPerspectives on the density functional theory ofchemical reactivityrdquo Journal of the Mexican Chemical Societyvol 52 pp 3ndash10 2008

[81] R G Parr L V Szentpaly and S Liu ldquoElectrophilicity indexrdquoJournal of the American Chemical Society vol 121 no 9 pp1922ndash1924 1999

[82] A T Maynard M Huang W G Rice and D G CovellldquoReactivity of the HIV-1 nucleocapsid protein p7 zinc fingerdomains from the perspective of density-functional theoryrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 95 no 20 pp 11578ndash11583 1998

[83] H Chermette ldquoChemical reactivity indexes in density func-tional theoryrdquo Journal of Computational Chemistry vol 20 no1 pp 129ndash154 1999


[84] S Liu ldquoConceptual density functional theory and some recentdevelopmentsrdquo Acta Physico-Chimica Sinica vol 25 pp 590ndash600 2009

[85] S Berski J Andres B Silvi and L R Domingo ldquoThe jointuse of catastrophe theory and electron localization functionto characterize molecular mechanisms A density functionalstudy of the Diels-Alder reaction between ethylene and 13-butadienerdquo Journal of Physical Chemistry A vol 107 no 31 pp6014ndash6024 2003

[86] A Morales-Bayuelo ldquoUnderstanding the electronic reorga-nization in the thermal isomerization reaction of trans-34-dimethylcyclobutene Origins of outward Pseudodiradical 2n +2120587 torquoselectivityrdquo International Journal of Quantum Chem-istry vol 113 no 10 pp 1534ndash1543 2013

[87] AMorales-Bayuelo and R Vivas-Reyes ldquoTheoretical model forthe polarization molecular and Huckel treatment of Phospho-Cyclopentadiene in an external electric field Hirschfeld studyrdquoJournal of Mathematical Chemistry vol 51 no 7 pp 1835ndash18522013

[88] A Morales-Bayuelo and R Vivas-Reyes ldquoTopological modelto quantify the global reactivity indexes as local in Diels-Alder reactions using density function theory (DFT) and localquantum similarity (LQS)rdquo Journal of Mathematical Chemistryvol 51 no 1 pp 125ndash143 2013

[89] A Morales-Bayuelo V Valdiris and R Vivas-Reyes ldquoMathe-matical analysis of a series of 4-acetylamino-2-(35-dimethyl-pyrazol1yl)-6-pyridylpyrimidines a simple way to relate quan-tum similarity to local chemical reactivity using the Gaussianorbitals localized theoryrdquo Journal of Theoretical Chemistry vol2014 Article ID 624891 13 pages 2014


[91] A Morales-Bayuelo R Baldiris J Torres J E Torres and RVivas-Reyes ldquoTheoretical study of the chemical reactivity andmolecular quantum similarity in a series of derivatives of 2-adamantyl-thiazolidine-4-one using density functional theoryand the topo-geometrical superposition approachrdquo Interna-tional Journal of Quantum Chemistry vol 112 no 14 pp 2681ndash2687 2012

[92] P Geerlings F De Proft and W Langenaeker ldquoConceptualdensity functional theoryrdquo Chemical Reviews vol 103 no 5 pp1793ndash1873 2003


[94] PW Ayers and R G Parr ldquoVariational principles for describingchemical reactions the Fukui function and chemical hardnessrevisitedrdquo Journal of the American Chemical Society vol 122 no9 pp 2010ndash2018 2000

[95] P Geerlings and F De Proft ldquoConceptual and computationaldft as a chemistrsquos toolrdquo in Recent Advances in ComputationalChemistry vol 1 pp 137ndash167 2002

[96] P W Ayers S B Liu and T L Li ldquoStability conditions fordensity functional reactivity theory an interpretation of thetotal local hardnessrdquo Physical Chemistry Chemical Physics vol13 pp 4427ndash4433 2011

[97] P Geerlings and F de Proft ldquoChemical reactivity as described byquantum chemical methodsrdquo International Journal ofMolecularSciences vol 3 pp 276ndash309 2002

[98] R F Nalewajski and R G Parr ldquoInformation theory atoms inmolecules andmolecular similarityrdquoProceedings of theNationalAcademy of Sciences vol 97 pp 8879ndash8882 2000

[99] P Bultinck and R Carbo-Dorca ldquoMolecular quantum simi-larity using conceptual DFT descriptorsrdquo Journal of ChemicalSciences vol 117 pp 425ndash435 2005

[100] R Vivas-Reyes A Arias J Vandenbussche C V Alsenoyand P Bultinck ldquoQuantum similarity of isosteres coordinateversus momentum space and influence of alignmentrdquo Journalof Molecular Structure THEOCHEM vol 943 no 1-3 pp 183ndash188 2010

[101] R Carbo-Dorca Molecular Similarity and Reactivity FromQuantum Chemical to Phenomenological Approaches KluwerAcademic Publishers 1995

[102] P Bultinck S V Damme and R Carbo-Dorca ChemicalReactivity Theory A Density Functional View CRC Press 2009

[103] J Mestres M Sola M Besalu M Duran and R Carbo-DorcaldquoElectron density approximations for the fast evaluation ofquantum molecular similarity measuresrdquo in A Molecular Sim-ilarity and Reactivity From Quantum Chemical to Phenomeno-logical Approaches pp 77ndash85 Kluwer Academic Publishers1995

[104] R G Pearson Chemical Hardness Wiley-VCH WeinheimGermany 1997

[105] W T Yang and R G Parr ldquoHardness softness and the fukuifunction in the electronic theory of metals and catalysisrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 82 no 20 pp 6723ndash6726 1985

[106] M T Chandra and A K Nguyen ldquoFukui function and localsoftness as reactivity descriptorsrdquo inChemical ReactivityTheoryA Density-Functional View P K Chattaraj Ed p 163 Taylorand Francis New York NY USA 2008


[108] R G Parr and W Yang ldquoDensity functional approach to thefrontier-electron theory of chemical reactivityrdquo Journal of theAmerican Chemical Society vol 106 no 14 pp 4049ndash40501984

[109] K Fukui ldquoRole of frontier orbitals in chemical reactionsrdquoScience vol 218 no 4574 pp 747ndash754 1982

[110] J Tomasi andM Persico ldquoMolecular interactions in solution anoverview of methods based on continuous distributions of thesolventrdquo Chemical Reviews vol 94 no 7 pp 2027ndash2094 1994

[111] E Cances BMennucci and J Tomasi ldquoA new integral equationformalism for the polarizable continuum model theoreticalbackground and applications to isotropic and anisotropicdielectricsrdquo Journal of Chemical Physics vol 107 article 30321997

[112] A D McLean and G S Chandler ldquoContracted Gaussian basissets for molecular calculations I Second row atoms Z=11-18rdquoThe Journal of Chemical Physics vol 72 no 10 pp 5639ndash56481980

[113] R Carbo-Dorca and E Besalu ldquoEMP as a similarity measurea geometric point of viewrdquo Journal of Mathematical Chemistryvol 51 no 1 pp 382ndash389 2013


[114] E E Hodgkin and W G Richards ldquoMolecular SimilarityrdquoChemische Berichte vol 24 p 1141 1988


[116] A Morales-Bayuelo H Ayazo and R Vivas-Reyes ldquoThree-dimensional quantitative structure-activity relationship CoM-SIACoMFA and LeapFrog studies on novel series of bicyclo[410] heptanes derivatives as melanin-concentrating hormonereceptor R1 antagonistsrdquo European Journal of Medicinal Chem-istry vol 45 no 10 pp 4509ndash4522 2010

[117] X Girones and R Carbo-Dorca ldquoTGSA-Flex extending thecapabilities of the Topo-Geometrical superposition algorithmto handle flexible moleculesrdquo Journal of Computational Chem-istry vol 25 no 2 pp 153ndash159 2004

[118] L Chen ldquoSubstructure and maximal common substructuresearchingrdquo in Computational Medicinal Chemistry For DrugDiscovery P Bultinck H De Winter W Langenaeker and J PTollenaere Eds p 483 Marcel Dekker New York NY USA2003

[119] X Girones D Robert and R Carbo-Dorca ldquoTGSA a molec-ular superposition program based on topo-geometrical consid-erationsrdquo Journal of Computational Chemistry vol 22 no 2 pp255ndash263 2001

[120] H B Schlegel ldquoOptimization of equilibrium geometries andtransition structuresrdquo Journal of Computational Chemistry vol3 pp 214ndash218 1982

[121] H B Schlegel ldquoGeometry optimization on potential energysurfacerdquo in Modern Electronic Structure Theory D R YarkonyEd World Scientific Publishing Singapore 1994

[122] M J Frisch G W Trucks H B Schlegel et al GAUSSIAN 09Revision C 01 Gaussian Wallingford Conn USA 2010

[123] A D Becke ldquoDensity-functional thermochemistry IIIThe roleof exact exchangerdquoThe Journal of Chemical Physics vol 98 no7 pp 5648ndash5652 1993

[124] C Lee W Yang and R G Parr ldquoDevelopment of the Colle-Salvetti correlation-energy formula into a functional of theelectron densityrdquo Physical Review B Condensed Matter vol 37pp 785ndash789 1998

[125] P J Stephens F J Delvin C F Chablowski and M J J FirschldquoAb initio calculation of vibrational absorption and circulardichroism spectra using density functional force fieldsrdquoPhysicalChemistry vol 98 no 45 pp 11623ndash11627 1994

[126] J A Pople P V SchleyerW J Hehre and L RadomAB INITIOmolecular orbital theory 1986

[127] S C Pellegrinet M A Silva and J M Goodman ldquoTheoreticalevaluation of the origin of the regio- and stereoselectivity inthe Diels-Alder reactions of dialkylvinylboranes studies onthe reactions of vinylborane dimethylvinylborane and vinyl-9-BBN with trans-piperylene and isoprenerdquo Journal of theAmerican Chemical Society vol 123 no 36 pp 8832ndash8837 2001

[128] T C Dinadayalane R Vijaya A Smitha and G N SastryldquoDiels-Alder reactivity of butadiene and cyclic five-membereddienes ((CH)4X X = CH2 SiH2 O NH PH and S) withethylene a benchmark studyrdquo Journal of Physical Chemistry Avol 106 no 8 pp 1627ndash1633 2002

[129] R Jasinski Koifman andA Baranski ldquoAB3LYP6-31G(d) studyof Diels-Alder reactions between cyclopentadiene and (E)-2-arylnitroethenesrdquo Central European Journal of Chemistry vol9 no 6 pp 1008ndash1018 2011

[130] B M El Ali ldquoAJSE Relaunched in cooperation with SpringerrdquoArabian Journal for Science and Engineering vol 36 no 1 p 12011

[131] M Kwiatkowska R Jasinski M Mikulska and A BaranskildquoSecondary alpha-deuterium kinetic isotope effects in [2+4]cycloaddition of (E)-2-phenylnitroethene to cyclopentadienerdquoMonatshefte Fur Chemie vol 141 no 5 pp 545ndash548 2010

[132] R Jasinski and A Baranski ldquoMolecular mechanism of Diels-Alder reaction between (E)-3 3 3-trichloro-1-nitropropeneand cyclopentadiene B3LYP6-31G(d) computational studyrdquoTurkish Journal of Chemistry vol 37 pp 848ndash852 2013

[133] Y Zhao andDG Truhlar ldquoTheM06 suite of density functionalsfor main group thermochemistry thermochemical kineticsnoncovalent interactions excited states and transition ele-ments two new functionals and systematic testing of fourM06-class functionals and 12 other functionalsrdquo TheoreticalChemistry Accounts vol 120 no 1ndash3 pp 215ndash241 2008

[134] C Gonzalez and H B Schlegel ldquoReaction path followingin mass-weighted internal coordinatesrdquo Journal of PhysicalChemistry vol 94 no 14 pp 5523ndash5527 1990

[135] C Gonzalez and H B Schlegel ldquoImproved algorithms for reac-tion path following higher-order implicit algorithmsrdquo Journalof Chemical Physics vol 95 pp 5853ndash5860 1991

[136] P Geerlings R Vivas-Reyes F De Proft M Biesemans and RWillem ldquoDFT based reactivity descriptors and their applicationto the study of organotin compoundsrdquo inMetal-Ligand Interac-tions vol 116 of NATO Science Series pp 461ndash495 2003

[137] P Geerlings R Vivas-Reyes F de Proft M Biesemans and RWillem ldquoDFT-based reactivity descriptors and their applicationto the study of organotin compoundsrdquo Cheminform vol 35 no49 2004


[139] P Bultinck C Van Alsenoy P W Ayers and R Carbo-DorcaldquoCritical analysis and extension of the Hirshfeld atoms inmoleculesrdquo Journal of Chemical Physics vol 126 no 14 ArticleID 144111 2007

[140] P K Chattaraj and D R Roy ldquoUpdate 1 of electrophilicityindexrdquo Chemical Reviews vol 107 no 9 pp PR46ndashPR74 2007


[142] D H Ess and K N Houk ldquoDistortioninteraction energycontrol of 13-dipolar cycloaddition reactivityrdquo Journal of theAmerican Chemical Society vol 129 no 35 pp 10646ndash106472007

[143] DH Ess andKNHouk ldquoTheory of 13-dipolar cycloadditionsdistortioninteraction and frontier molecular orbital modelsrdquoJournal of the American Chemical Society vol 130 no 31 pp10187ndash10198 2008

[144] A M Sarotti ldquoUnraveling polar Diels-Alder reactions withconceptual DFT analysis and the distortioninteraction modelrdquoOrganic and Biomolecular Chemistry vol 12 pp 187ndash199 2014


[145] H Jiao and P von Rague Schleyer ldquoAromaticity of pericyclicreaction transition structures magnetic evidencerdquo Journal ofPhysical Organic Chemistry vol 11 no 8-9 pp 655ndash662 1998

[146] F Feixas E Matito J Poater andM Sola ldquoOn the performanceof some aromaticity indices a critical assessment using a testsetrdquo Journal of Computational Chemistry vol 29 no 10 pp1543ndash1554 2008

[147] E Matito J Poater M Duran and M Sola ldquoAn analysis ofthe changes in aromaticity and planarity along the reactionpath of the simplest Diels-Alder reaction Exploring the validityof different indicators of aromaticityrdquo Journal of MolecularStructure THEOCHEM vol 727 no 1-3 pp 165ndash171 2005

[148] G Boon W Langenaeker F De Proft H De Winter J PTollenaere and P Geerlings ldquoSystematic study of the quality ofvarious quantum similarity descriptors Use of the autocorre-lation function and principal component analysisrdquo Journal ofPhysical Chemistry A vol 105 no 38 pp 8805ndash8814 2001

[149] P Seneta and F Aparicio ldquoDensity functional theory fragmentdescriptors to quantify the reactivity of a molecular familyapplication to amino acidsrdquo Journal of Chemical Physics vol 126Article ID 145105 2007

[150] E M Burgess and C L Liotta ldquoPrinciple of orbital distortionrdquoJournal of Organic Chemistry vol 46 no 8 pp 1703ndash1708 1981

[151] K N Houk M N Paddon-Row N G Rondan et al ldquoTheoryand modeling of stereoselective organic reactionsrdquo Science vol231 no 4742 pp 1108ndash1117 1986

[152] D H Rouvray ldquoDefinition and role of similarity concepts in thechemical and physical sciencesrdquo Journal of chemical informationand computer science vol 32 pp 580ndash586 1992

[153] D H Rouvray ldquoSimilarity studies 1The necessity for analogiesin the development of sciencerdquo Journal of Chemical Informationand Computer Sciences vol 34 no 2 pp 446ndash452 1994

[154] E C Kirby and D H Rouvray ldquoSixth international conferenceon mathematical chemistryrdquo Journal of Chemical Informationand Computer Sciences vol 36 no 3 pp 345ndash346 19961996

[155] S R Heller ldquoSimilarity in organic chemistry a summary of theBeilstein Institute Conferencerdquo Journal of Chemical Informationand Computer Sciences vol 32 pp 578ndash579 1992

Submit your manuscripts athttpwwwhindawicom

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Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


with high CT in the TS) with a zwitterionic character andfinally (c) the ionic DA reactions where the charge separationis preserved along the reaction path [1ndash12]

Since the implementation of DA reactions in currentorganic chemistry an enormous amount of experimentaland theoretical work has been devoted to the study of themechanism and selectivity of these DA cycloadditions Thereactivity and selectivity of these processes have been treatedprincipally within the frontier molecular orbital (FMO)approximations [21ndash26] transition state theory (TST) [2728] andmore recently using the reactivity descriptors definedin density functional theory (DFT) [1ndash8 29ndash50]

One of the fields in quantum chemistry for feasibil-ity study through the TSs in the DA reactions is themolecular quantum similarity (MQS) presenting possibleways of electronic systematization [51ndash78] In this sense wepresent a combined approach ofMQS and chemical reactivitydescriptors supported in DFT [79ndash84] to study the electronicreorganization in terms of the formation of the zwitterioniccharacter and their CT analysis along the series of reactionsshown in Figure 1 and Table 1 In the supplementary informa-tion (SI) is shows the structural geometries

The electronic reorganization for these DA reactions hasbeen studied widely by Domingo et al and coworkers [15ndash17] and they have postulated an electronic reorganizationcharacterized by nucleophilic attack centers towards elec-trophilic centers to study the synchronicity in the bond for-mation and also have studied the pseudodiradical characterto these organic systems [85 86] However other reactivityparameters such as the polar character have been littlestudied for this reason this study seeks to propose anelectronic reorganization that can be able to explain the polarcharacter in terms of CT and the subsequent formation of thezwitterionic character along the reaction paths in systematicform

The reaction rate constants analyzed in this contributionare shown in Table 1 These DA reactions have served asthe most dramatic examples of pure electronic effects onrates that are not complicated by significant steric effectsLarge fluctuations have been observed in terms of reactionrates as an example the reaction involving Cp + 2CN itsrate is estimated in the order of 104 while the 2cCN dropsdramatically to 91 Another example of this drastic changecan be seen in the Cp + 4CN reaction which has a reactionrate estimated in the order of 107 while the reference reaction(Cp + Et) is estimated in the order of 10minus5 taking into accountthat these experimental values have a factor of 105119896 (Mminus1Sminus1)In order to determine a possible electronic rationalization ofthese large fluctuations in this study direct considerations onthe electronic density in terms of reactivity descriptors andMQS are used

Recently the chemical reactivity and quantum similarityrelationship in order to understand the electronic reorgani-zation and molecular polarization using quantum similaritydescriptors [87ndash91] has been studied As the similarities inchemical reactivity depend on molecular properties and dueto the crucial role of the electronic density in MQS it is quitenatural that a close relation exists between chemical reactivity

and quantum similarity (QS) [92ndash103] Consequently thisstudy analyzes the chemical reactivity and MQS relationshipto postulate a possible way of electronic systematization onthe DA reactions of Table 1 in DFT framework Additionallyusing similarity relations Woodward-Hoffmann postulatedthe well-known rules through the FMO [11 12] therefore inthis studywe used theMQSfield to postulate a possible expla-nation of the polar character consistent with the experimentalresults and describe the similarity on the chemical reactivityof these cycloadditions in the DFT context

The structure of this paper will be as follows The theoryand computational details are described in Sections 2 and 3respectively and the results and discussions are developedin Section 4 and finally in Section 5 the most importantconclusions are discussed

2 Theory

21 Global and Local Reactivity Descriptors The global reac-tivity descriptors have a very well-known history in quantumchemistry that has been justified from theoretical point ofview in the DFT framework [79ndash84] such as chemical poten-tial (120583) [79ndash84] hardness (120578) [104] and softness (119878) [105 106]and these global descriptors are calculated using Koopmanstheorem ldquoie the energies of the higher occupied molecularorbital (HOMO) and the lowest unoccupied molecular orbital(LUMO) are equal to the negative of first ionization potentialand of the electronic affinity resprdquo and three-point differentialstatistical as

120583 asympIP + EA

2=

120576119867

+ 120576119871

2 (1)

120578 asymp 120576119871minus 120576119867 (2)

119878 =1

120578 (3)

The chemical potential (see (1)) can be interpreted as ameasure of the tendency of an electron to escape fromthe electronic cloud and the hardness (120578) is a measure ofthe resistance imposed by the system to the changes inthe electronic distribution In these equations (120576

119871) and (120576

119867)

represent the energies of theHOMO and LUMO respectivelyUsing (1) and (2) the electrophilicity (120596) index [107] is

defined as

120596 asymp1205832

2120578 (4)

where (120596) is other global property and represents thestabilization energy of the system when it is saturated byelectrons from the external environment in this sense theelectrophilicity is dependent on the saturation condition[79ndash82 108] determined by the chemical potential (120583) andhardness (120578) and obtained as

Δ119873max asymp minus120583

120578 (5)






4






2120578 (6)


⟨119891 ( 119903)⟩ asymp (120575120583

120575] ( 119903))

119873

= (120597120588 ( 119903)

120597119873)

]( 119903)= (

1205972119864

120597119873120597120592 ( 119903)) (7)






⟨119891+

119896( 119903)⟩ asymp int

119896

[120588119873+1

( 119903) minus 120588 ( 119903)] 119889119903 = [119902119896(119873 + 1) minus 119902

119896(119873)]

⟨119891minus

119896( 119903)⟩asympint

119896

[120588119873( 119903) minus 120588

119873minus1( 119903)] 119889119903 = [119902

119896(119873) minus 119902

119896(119873 minus 1)]

(8)




⟨119891+

119896( 119903)⟩ asymp int

119896

120588119871( 119903) 119889 119903 = 119871

119896119902

⟨119891minus

119896( 119903)⟩ asymp int

119896

120588119867( 119903) 119889 119903 = 119867

119896119902

(9)

with (119867119896119902) and (119871




A + B 997888rarr C (10)



(11)


2

2 (120578B + 120578A) (12)


119896119878+

119896

119878+


120596 =1205832

2120578=

1205832

2119878 =

1205832

2sum

119896

119878+

119896= sum

119896

120596119896 (13)


120596119896=

1205832

2119878+

119896(14)



relationship [82]

119878+

119896= 119878119891+

119896( 119903) (15)


120596119896=

1205832

2119878+

119896=

1205832119878

2119891+

119896( 119903) = 120596119891

+

119896( 119903) (16)


120596119896= 120596119891+

119896( 119903) = (

(120583B minus 120583A)2

2 (120578B + 120578A))119891+

119896( 119903) (17)


+

119896(119903) as


)119891+

119896( 119903) (18)



1198632

AB (120588A (1199031) 120588B (119903

2))

= int1003816100381610038161003816120588A(1199031) minus 120588B(1199032)

1003816100381610038161003816

2

11988911990311198891199032

= int (120588A (1199031))2

1198891199031+ int (120588B (119903

2))2

1198891199032

minus 2∬120588A (1199031) 120588B (119903

2) 11988911990311198891199032

= 119885AA + 119885BB minus 2119885AB

(19)





(i) 119863 (120588A (1199031) 120588B (119903


(ii) 119863 (120588A (1199031) 120588B (119903

2)) = 119863 (120588B (119903

2) 120588A (119903

1))

(symmetry) (21)

(iii) 119863 (120588A (1199031) 120588B (119903




Carbo-index (119868AB) =∬120588A (119903

1) 120588B (119903

2) 11988911990311198891199032

radicint (120588A (1199031))2

1198891199031int (120588B (119903

2))2

1198891199032

(23)


119868AB

=∬120588A (119903

1)Ω (1199031 1199032) 120588B (119903

2) 11988911990311198891199032

radicint120588A (1199031)Ω (1199031) 120588A (119903

1) 1198891199031int 120588B (119903

2)Ω (1199032) 120588B (119903

2) 1198891199032

=119885AB (Ω)

119885AA (Ω) 119885BB (Ω)

(24)


(HR) 119868AB =2119885AB (Ω)

119885AA (Ω) + 119885BB (Ω) (25)




+

X1

X3

TS-YR-V

2X

4X













H8

H9

H15

H10

H11

H13H12

H14

H17H16C1

C2

C3

C4

C5

C6

C7

Hydrogen

Carbon atom

(a)

1085

1085

1085

1085

1084

1084

1410

1410

14101521

1521

2230

2230

10911105

1087

1087

1400

(b)


alignment






1= 04275 for the 4CN to 120596

1= 00005 for the Et


1=







0123456789

0 005 01 015 02 025


y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka


Standard deviationb


0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc


1205961(17)b














g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






4






2120578 (6)


⟨119891 ( 119903)⟩ asymp (120575120583

120575] ( 119903))

119873

= (120597120588 ( 119903)

120597119873)

]( 119903)= (

1205972119864

120597119873120597120592 ( 119903)) (7)






⟨119891+

119896( 119903)⟩ asymp int

119896

[120588119873+1

( 119903) minus 120588 ( 119903)] 119889119903 = [119902119896(119873 + 1) minus 119902

119896(119873)]

⟨119891minus

119896( 119903)⟩asympint

119896

[120588119873( 119903) minus 120588

119873minus1( 119903)] 119889119903 = [119902

119896(119873) minus 119902

119896(119873 minus 1)]

(8)




⟨119891+

119896( 119903)⟩ asymp int

119896

120588119871( 119903) 119889 119903 = 119871

119896119902

⟨119891minus

119896( 119903)⟩ asymp int

119896

120588119867( 119903) 119889 119903 = 119867

119896119902

(9)

with (119867119896119902) and (119871




A + B 997888rarr C (10)



(11)


2

2 (120578B + 120578A) (12)


119896119878+

119896

119878+


120596 =1205832

2120578=

1205832

2119878 =

1205832

2sum

119896

119878+

119896= sum

119896

120596119896 (13)


120596119896=

1205832

2119878+

119896(14)



relationship [82]

119878+

119896= 119878119891+

119896( 119903) (15)


120596119896=

1205832

2119878+

119896=

1205832119878

2119891+

119896( 119903) = 120596119891

+

119896( 119903) (16)


120596119896= 120596119891+

119896( 119903) = (

(120583B minus 120583A)2

2 (120578B + 120578A))119891+

119896( 119903) (17)


+

119896(119903) as


)119891+

119896( 119903) (18)



1198632

AB (120588A (1199031) 120588B (119903

2))

= int1003816100381610038161003816120588A(1199031) minus 120588B(1199032)

1003816100381610038161003816

2

11988911990311198891199032

= int (120588A (1199031))2

1198891199031+ int (120588B (119903

2))2

1198891199032

minus 2∬120588A (1199031) 120588B (119903

2) 11988911990311198891199032

= 119885AA + 119885BB minus 2119885AB

(19)





(i) 119863 (120588A (1199031) 120588B (119903


(ii) 119863 (120588A (1199031) 120588B (119903

2)) = 119863 (120588B (119903

2) 120588A (119903

1))

(symmetry) (21)

(iii) 119863 (120588A (1199031) 120588B (119903




Carbo-index (119868AB) =∬120588A (119903

1) 120588B (119903

2) 11988911990311198891199032

radicint (120588A (1199031))2

1198891199031int (120588B (119903

2))2

1198891199032

(23)


119868AB

=∬120588A (119903

1)Ω (1199031 1199032) 120588B (119903

2) 11988911990311198891199032

radicint120588A (1199031)Ω (1199031) 120588A (119903

1) 1198891199031int 120588B (119903

2)Ω (1199032) 120588B (119903

2) 1198891199032

=119885AB (Ω)

119885AA (Ω) 119885BB (Ω)

(24)


(HR) 119868AB =2119885AB (Ω)

119885AA (Ω) + 119885BB (Ω) (25)




+

X1

X3

TS-YR-V

2X

4X













H8

H9

H15

H10

H11

H13H12

H14

H17H16C1

C2

C3

C4

C5

C6

C7

Hydrogen

Carbon atom

(a)

1085

1085

1085

1085

1084

1084

1410

1410

14101521

1521

2230

2230

10911105

1087

1087

1400

(b)


alignment






1= 04275 for the 4CN to 120596

1= 00005 for the Et


1=







0123456789

0 005 01 015 02 025


y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka


Standard deviationb


0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc


1205961(17)b














g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



relationship [82]

119878+

119896= 119878119891+

119896( 119903) (15)


120596119896=

1205832

2119878+

119896=

1205832119878

2119891+

119896( 119903) = 120596119891

+

119896( 119903) (16)


120596119896= 120596119891+

119896( 119903) = (

(120583B minus 120583A)2

2 (120578B + 120578A))119891+

119896( 119903) (17)


+

119896(119903) as


)119891+

119896( 119903) (18)



1198632

AB (120588A (1199031) 120588B (119903

2))

= int1003816100381610038161003816120588A(1199031) minus 120588B(1199032)

1003816100381610038161003816

2

11988911990311198891199032

= int (120588A (1199031))2

1198891199031+ int (120588B (119903

2))2

1198891199032

minus 2∬120588A (1199031) 120588B (119903

2) 11988911990311198891199032

= 119885AA + 119885BB minus 2119885AB

(19)





(i) 119863 (120588A (1199031) 120588B (119903


(ii) 119863 (120588A (1199031) 120588B (119903

2)) = 119863 (120588B (119903

2) 120588A (119903

1))

(symmetry) (21)

(iii) 119863 (120588A (1199031) 120588B (119903




Carbo-index (119868AB) =∬120588A (119903

1) 120588B (119903

2) 11988911990311198891199032

radicint (120588A (1199031))2

1198891199031int (120588B (119903

2))2

1198891199032

(23)


119868AB

=∬120588A (119903

1)Ω (1199031 1199032) 120588B (119903

2) 11988911990311198891199032

radicint120588A (1199031)Ω (1199031) 120588A (119903

1) 1198891199031int 120588B (119903

2)Ω (1199032) 120588B (119903

2) 1198891199032

=119885AB (Ω)

119885AA (Ω) 119885BB (Ω)

(24)


(HR) 119868AB =2119885AB (Ω)

119885AA (Ω) + 119885BB (Ω) (25)




+

X1

X3

TS-YR-V

2X

4X













H8

H9

H15

H10

H11

H13H12

H14

H17H16C1

C2

C3

C4

C5

C6

C7

Hydrogen

Carbon atom

(a)

1085

1085

1085

1085

1084

1084

1410

1410

14101521

1521

2230

2230

10911105

1087

1087

1400

(b)


alignment






1= 04275 for the 4CN to 120596

1= 00005 for the Et


1=







0123456789

0 005 01 015 02 025


y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka


Standard deviationb


0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc


1205961(17)b














g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


+

X1

X3

TS-YR-V

2X

4X













H8

H9

H15

H10

H11

H13H12

H14

H17H16C1

C2

C3

C4

C5

C6

C7

Hydrogen

Carbon atom

(a)

1085

1085

1085

1085

1084

1084

1410

1410

14101521

1521

2230

2230

10911105

1087

1087

1400

(b)


alignment






1= 04275 for the 4CN to 120596

1= 00005 for the Et


1=







0123456789

0 005 01 015 02 025


y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka


Standard deviationb


0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc


1205961(17)b














g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


H8

H9

H15

H10

H11

H13H12

H14

H17H16C1

C2

C3

C4

C5

C6

C7

Hydrogen

Carbon atom

(a)

1085

1085

1085

1085

1084

1084

1410

1410

14101521

1521

2230

2230

10911105

1087

1087

1400

(b)


alignment






1= 04275 for the 4CN to 120596

1= 00005 for the Et


1=







0123456789

0 005 01 015 02 025


y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka


Standard deviationb


0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc


1205961(17)b














g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0123456789

0 005 01 015 02 025


y = 59249x minus 76046

R2 = 09118

ΔNmax(k)

log K

76335 0234360000 0229946812 0227819590 0157719084 0157600170 01321

13804 0003115015 0003323628 0036624667 0040028336 00457

ΔNmax(k)log Ka


Standard deviationb


0123456789

0 005 01 015 02 025 03 035 04 045

y = minus14892x + 8859

R2 = 09667

1205961 (eq 21)minus1

log K

042750391202992020430212401108

13804 0025715014 0066123627 0099924667 0101428340 01210

763356000046812195901908400170

log Ka

apk = logK

Standard deviationc


1205961(17)b














g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




g



Cab119891+

1( 119903)

c1205961

dΔ119873max 1

e119891+

2( 119903) 120596

2Δ119873max 2































010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of
























010002000300040005000600070008000


y = 0862x + 94912

R2 = 09499

Carb

o in

dex

10000 100006959 69366224 61255599 55115088 50085259 50315536 4997

21503 2166620019 2043719505 1992119344 1971818374 1893017181 18115

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


880089009000910092009300940095009600


Carb

o in

dex

y = 05501x + 43613

R2 = 09483

10000 100009531 94139263 88949242 88629238 88599020 83268855 8326

03316 0415103730 0553303528 0535103287 0502303434 0575203715 05937

Standard deviationc


aCarbo-Dorca index

CIaH-KIa


088089

09091092093094095096


Carb

o in

dexe

s

y = 04156x + 08402

R2 = 07127

09531 0234309263 0229909242 0227809238 015770902 01576

08855 01321

00190 0003100161 0003300142 0036600186 0040100231 00457

Standard deviationc


aCarbo index

aCarbo I aCTb








CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of







CN

CN CN

CN

NC NC

NCNC CNCN

CN

++

120575minus 120575+








with

Δ119873max (TS4CN) = 08403 (27)



ΔNmax(TS4CN)

- TS-3CN (09722) = 08169

- TS-2CN (09468) = 07956

- TS-2t (09439) = 07931

- TS-1CN (09164) = 07701

- TS-Et (08855) = 07441



- TS-2C (09440) = 07932

(29)


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0123456789


y = 11176x minus 99081

R2 = 0833

Log K

76334 0953160000 0926346812 0924219590 0923819084 0902000170 08855

00189 1380400161 1501500142 2362700182 2466700231 28337

log Ka

apk = logK

Standard deviationb


CIb



















Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of







Acknowledgments


References











































































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of
























































































































































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article understanding the polar character trend in a...

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