author's personal copy - hashemite university · 2016. 4. 20. · author's personal copy structure...

This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution

and sharing with colleagues.

Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party

websites are prohibited.

In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information

regarding Elsevier’s archiving and manuscript policies areencouraged to visit:

http://www.elsevier.com/authorsrights

http://www.elsevier.com/authorsrights

Author's personal copy

Structure and potential energy surface of Na+/0�(O2)n (n = 1–3) complexesJamal N. Dawoud ⇑, Ismail I. Fasfous, Tareq K. HarahshehDepartment of Chemistry, Faculty of Science, Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan

a r t i c l e i n f o

Article history:Received 1 September 2013Received in revised form 28 October 2013Accepted 28 October 2013Available online 5 November 2013

Keywords:Density functional theorySodium ion complexesSodium peroxideElectrostatic interactionOxygen

a b s t r a c t

The bonding and structures of sodium oxides complexes, Na+/0�(O2)n, were studied at various levels ofdensity functional theory (DFT). The neutral sodium complexes have stronger binding energies thanthose of cationic sodium complexes. The mono-ligated complex exhibited the shortest Na–O distanceand the strongest bond dissociation energy in these two sets of complexes. In addition, the neutral andcationic sodium complexes have identical sequential bond dissociation energy trends that are highlydependent on the strength of the electrostatic interaction within the complex.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

For a long time, the study of alkali metal–ligand complexes hasbeen in the domain of gas-phase spectroscopist and theoreticianwith little concerning on testing the level of method applied on cal-culations. In addition alkali metal exchanged EMT zeolites havebeen studied by different techniques since they are of great inter-est for base catalysis [1,2]. In particular, the basicity of sodium EMTzeolites has been determined by adsorption of pyrrole [1] and car-bon monoxide [3–5]. Recently, atmospheric chemists with aninterest in the upper reaches of the atmosphere have become inter-ested in the link between the chemistry of metal ions in the iono-sphere [6] and macroscopic phenomena such as sporadic metallayers [7]. Sodium is an important atmospheric metallic speciessince the existence of sporadic sodium layers have been observed[8,9]. Sodium cations are formed directly in the lower thermo-sphere via hyperthermal collisions during meteoroid ablation[10] as well as indirectly from sodium via photoionization andcharge transfer with ambient NO+ and Oþ2 ions [6].

Cationic sites in mesoporous structures, in particular Li+/Na+/K+

sites in zeolites, have long attracted attention and stimulated vigor-ous research due to high-catalytic activity, selectivity and revers-ible gas adsorption on zeolites. This represents the basis ofseveral technological processes such as atmosphere pollution con-trol, gas storage and gas separation such as nitrogen or oxygen sep-aration from air [11–14]. The interaction of the weakly non-polar O2molecules to neutral Na and Na+ ions has been theoretically studied

extensively with limited numbers of work using experimentalmeans [15–20]. Despite these efforts, there are still a number ofunsettled questions including fundamental query about the natureof bonding between them. In addition, none of these theoretical andexperimental studies consider the binding of more than one O2ligand to Na metal in neutral or ion form.

The bonding and formation of Na0/+---O2 complexes have beenstudied experimentally [15,21–23] and theoretically [15,17,26,27]by a number of workers. The thermodynamics and bond dissocia-tion energies of the superoxide Na�O2 and [Na�O2]+ adducts havebeen the subject of considerable controversy over the last three dec-ades [26–29]. The thermal stability of the gaseous Na�O2 was exten-sively investigated in terms of its heat of formation and bondstrength (i.e. binding energy of Na---O2). Seven measured valuesof binding energy of Na�O2 complex were made using differentexperimental means. These results were not able to resolve the con-troversy. The bond dissociation of Na� � �O2 has been calculatedbased on the measurements of sodium concentration in oxygen-richflame using laser-induced fluorescence techniques. This experi-mental technique was used by different groups of researches. Thevalues of the dissociation energy were not consistent and estab-lished to be 55.9 ± 3.1 kcal mol�1 [30], 40.6 ± 6.0 kcal mol�1 [31],39.0 ± 5.0 kcal mol�1 [22] and 58.1 ± 1.9 kcal mol�1 [25]. Further-more, Steinberg and Schofield were reanalyzed the vaporizationdata of Na2O and inferred that the Na�O2 species was the major com-position of the vapor above Na2O [24]. Therefore, in mass spectro-metric studies of the vapor above Na2O did not detect theexistence of the Na � Oþ2 complex after the electron impact ioniza-tion due to its instability [24,25]. The lowest bond dissociationenergy of Na� � �O2 was found to be 33.5 kcal mol�1 that estimated

2210-271X/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.comptc.2013.10.025

⇑ Corresponding author.E-mail address: [email protected] (J.N. Dawoud).

Computational and Theoretical Chemistry 1027 (2014) 62–72

Contents lists available at ScienceDirect

Computational and Theoretical Chemistry

journal homepage: www.elsevier .com/locate /comptc


from the ionization potential of Na�O2 and the bond dissociation ofNa � Oþ2 complex [25]. Afterwards, many theoreticians were focusedon studying the interaction modes between the sodium metal andmolecular oxygen using different levels of ab initio method. Brieflythe theoretical calculations showed that the geometry of Na�O2 andNa � Oþ2 adducts were not the same with different bond dissociationenergies [17,26,27,32]. The structure parameters and binding ener-gies of Na � Oþ2 complex were calculated using different theoreticalmethods. The Na � Oþ2 molecular geometry was optimized at theSCF level using the modified coupled-pair functional (MCPF) meth-od [33]. A linear geometry was obtained for the complex with abinding energy of 6.0 kcal mol�1 that is far below the measured va-lue of 13.0 ± 5.0 kcal mol�1 reported in a photoelectron study [34].However, this obtained value was found 20% lower than the bestestimated value of 7.2 kcal mol�1 for the binding energy of Na � Oþ2complex [32]. Finally, Lee, Soldán and Wright reported the geometryand bond dissociation energies of Na+/0�O2 complexes that were cal-culated at the RCCSD and RCCSD(T) levels of theory [17]. They foundthat the Na+�O2 complex exhibits a linear configuration with a bonddissociation energy of 4.6 ± 0.3 kcal mol�1 whereas the Na�O2 com-plex has a T-shaped structure with larger bond dissociation energyof 36 ± 3.0 kcal mol�1. Note here that the calculated bond dissocia-tion energies at high levels of ab initio methods yielded lower valuesthan observed experimentally by 36% for Na+�O2 complex. For thesuperoxide Na�O2 complex, the obtained bond dissociation valueswere strongly consistent with those measured in the range of 33–46 kcal mol�1.

In this work, we have undertaken a DFT study of the potentialenergy surface (PES) of the ground state of the Na+/0�(O2)ncomplexes, n = 1–4, where molecular geometries, binding ener-gies and their thermodynamic quantities are determined for theglobal, local and transition states. The sequential bond dissocia-tion of Na+/0�(O2)n (n = 1–4) complexes were computed and dis-cussed in terms of the strength of electrostatic interactionswithin these complexes. Our results are then compared withthe available experimental and theoretical data that reported inthe literature.

2. Computational details

All the calculations were carried out using the Gaussian 03 pro-gram [35]. Geometry optimizations were calculated using a varietyof DFT methods including UB3LYP, UB3P86 and UB3PW91. The ba-sis sets applied here are 6-31+G(d), 6-311+G(df) and 6-311++G(df)where these basis sets have polarization and diffuse functions thatare suitable and flexible to study the PES of Na+/0�(O2)n (n = 1–4)complexes.

Together the intrinsic reaction coordinate (IRC) [36,37] and thevibration frequency tests were performed to verify which mini-mum does the saddle point join and calculate the zero point energy(ZPE) for each stationary point and its thermodynamic propertiesat T = 298 K. All the optimized structures were confirmed to realminima or transition state on the potential energy surface by thefrequency calculations. For density functional theory (DFT), thebinding energy was calculated by simply subtracting the total en-ergy of the complex from the un-complexed moieties, and thencorrected for basis set superposition error (BSSE) using the fullcounterpoise method [38,39]. In particular, the thermodynamicquantities, DH� and DG�, for the complex denoted as Na+/0�(O2)nmay be calculated as,

Naþ=0 þ nO2 ! Naþ=0 � ðO2Þnðn : 1—3Þ

The binding enthalpy of the Na+/0�(O2)n complex was calculatedusing the following formula [40]

DH� ¼X

products

ðEo þ HÞcorr �X

reactants

ðEo þ HÞcorr ð1Þ

where ðEo þ HÞcorr is the corrected electronic energy included thezero point energy plus the thermal correction to enthalpy. This termis calculated directly from the frequency test of each stationarypoint. The same procedure has been applied for calculating DG�

for the Na+/0�(O2)n complexes.Note here, the sequential bond dissociation energies of the

Na+/0�(O2)n complex are calculated at different orientations forthe global and local states according to the following equation

Naþ=0 � ðO2Þn ! Naþ=0 � ðO2Þn�1 þ O2ðn : 1—3Þ

To explain the differences in the bond dissociation energyvalues that obtained, the atomic charge distributions of theNa+/0�(O2)n complex at different configurations were calculated,according to the natural bond orbital (NBO) analysis [41]. For sim-plicity the charge distribution spread over an orbital centered at aparticular atom is treated as a point charge at the location of theatom as applied elsewhere [42]. Using these point charges the elec-trostatic contribution ‘‘Eelec.’’ to the binding energy of the Na+/0�(O2)n complex is calculated as a pair-wise sum of point chargeslocated on each atomic site of O2 and Na+/0 atom were calculatedusing the form,

Eelec: ¼ �1n

X4

n¼1

X2

i¼1

qNa � ðqOi Þn4peo � rNa—Oi

ð2Þ

where n represents the number of O2 molecules in the complex, qNa,qOi are the point charges located on Na and O atoms separated byrNa—Oi and eo is the permittivity of the vacuum.

3. Results and discussion

3.1. The Na+�O2 complex

The potential energy surface of the complex, in its triplet state3R�, showed the existence of one global minimum (linear struc-ture) and one saddle point transition state (tee configuration) usingthe IRC diagram (result not shown). Our findings agreed well withother theoretical calculations using high ab initio methods of theNa+�O2 complex [17,32].

As shown in Table 1, the optimized geometries of the Na+�O2complex in different orientations have been performed at variouslevels of DFT methods. These structures were presented in Fig. 1Our best values of the optimized geometrical parameters of theNa+�O2 linear structure was found to have a distance, rNa–O= 2.376 Å and rO–O = 1.205 Å that calculated on the basis of theUB3P86/6-31+G(d) method. These values were in excellent agree-ment with the results of the RCCSD(T) and UB3LYP calculationsthat done by Lee et al. [17]. For the harmonic vibration frequencies,The Na+�O2 complex was found to exhibit two types of stretchingfrequencies of w1 = 151 cm�1 (Na–O stretch), and w2 = 1698 cm�1

(O–O stretch) as presented in Table 2. These values agreed wellwith the values of the vibration frequencies that obtained previ-ously using UB3LYP and UMP2 levels of theory [17], which yieldedfrequencies of �155 cm�1 and �1614 cm�1 for w1 and w2,respectively.

For the T-shaped transition state structure, our calculations ofthe optimized geometry showed that the Na+ ion is directed to-ward the mid of the O2 bond at a distance of 2.707 Å, calculatedon the basis of the UB3LYP/6-311+G(df) method, which agreedwell with a 2.707 Å that calculated by Lee et al. [17] and 2.689 Åthat obtained by Partridge et al. [32]. The vibration frequency testshows that the T-shaped structure exhibits one imaginary

J.N. Dawoud et al. / Computational and Theoretical Chemistry 1027 (2014) 62–72 63


frequency of 138i cm�1 plus two others frequencies of 98 cm�1 and1610 cm�1 (O–O stretch). Our best values of the calculated fre-quencies, on the basis of UB3LYP/6-311+G(df) method, were closedwell to those calculated using UB3LYP/aug-cc-pVQZ method by Leeet al. [17] (see Table 2).

The binding energy values were calculated, including zero-pointenergy (ZPE) and BSSE correction, for the minimum and transitionstate structures of the complex at various levels of DFT using6-311+G(df) basis set function. These results were presented inTable 3. Interestingly, the UB3LYP, UB3P86 and UB3PW91 calcula-tions of the binding energy were closed to each other, indicatingthat the results were consistent for Na+�O2 complex. Our best value

for the binding energy of the linear structure was calculated andfound to be 4.82 kcal mol�1, which agreed well with4.60 ± 0.3 kcal mol�1, that calculated using the RCCSD(T) level oftheory [17] and slightly lower than 5.49 kcal mol�1 calculatedusing the BP86/SVP+ method [43]. Our results also were slightlylower than 5.7 and 6.0 kcal mol�1 that estimated by Spears [15]and Chong et al. [34], respectively. For thermodynamics quantities,DG� of the linear structure was calculated at 298.15 K and found tobe 0.29 kcal mol�1 which falls within the experimental range(�0.2–0.8 kcal mol�1) [15]. The DH� value was calculated according

Table 1Geometrical parameters of the Na+�O2 complexa at various configurations.

Geometry Method Basis set r(O–O) r(Na–O) h(�)b

Linear Na+�O2 UB3LYP 6-31G(d) 1.211 2.338 180.06-31+G(d) 1.212 2.354 180.06-311+G(d) 1.203 2.357 180.06-311+G(df) 1.202 2.347 180.0

Free O2 6-311+G(df) 1.205 – –UB3PW91 6-31G(d) 1.205 2.396 180.0

6-31+G(d) 1.205 2.400 180.06-311+G(d) 1.196 2.415 180.06-311+G(df) 1.195 2.396 180.0

Free O2 6-311+G(df) 1.198 – –UB3P86 6-31G(d) 1.204 2.371 180.0

6-31+G(d) 1.205 2.376 180.06-311+G(d) 1.195 2.380 180.06-311+G(df) 1.195 2.369 180.0

Free O2 6-311+G(df) 1.198 – –

Linear Na+�O2c UB3LYP aug-cc-pVTZ 1.202 2.360 180.0

Linear Na+�O2c RCCSD(T) aug-cc-pVQZ 1.205 2.371 180.0

T-shaped TS UB3LYP 6-31G(d) 1.219 2.688 76.96-31+G(d) 1.219 2.781 77.26-311+G(d) 1.209 2.796 77.46-311+G(df) 1.209 2.775 77.3

UB3PW91 6-31G(d) 1.212 2.792 77.46-31+G(d) 1.211 2.933 78.06-311+G(d) 1.202 2.963 78.36-311+G(df) 1.202 2.932 78.2

UB3P86 6-31G(d) 1.212 2.755 77.26-31+G(d) 1.211 2.868 77.76-311+G(d) 1.201 2.897 77.96-311+G(df) 1.202 2.862 77.8

T-shaped TSc RCCSD(T) aug-cc-pVQZ 1.214 2.707 77.1

T-shaped TSc UB3LYP aug-cc-pVQZ 1.210 2.704 77.1

T-shaped TSd MCPF – 1.211 2.689 77.0

a All the bond lengths are in (Å), and the bond angles are in degrees.b \Na—O1—O2 bond angle.c Taken from Ref. [17].d Taken from Ref. [32].

Na O OO O

Na

+0.007 +0.004

+0.989

+0.151-0.144+0.993

Linear structure T-shaped structure

Fig. 1. The NBO analysis of the atomic charge distributions of the Na+�O2 complex atdifferent configurations obtained on the basis of the UB3LYP/6-311+G(df) method.

Table 2Harmonic vibration frequencies of the Na+�O2 complex that calculated at differentmethods of DFT using the 6-311+G(df) basis set.

Method Vibration frequencies (cm�1)

Linear Na+�O2 minimumUB3LYP 175.6 (r), 84.4(p), 1658.6(r)UB3P86 159.9 (r), 81.2(p), 1702.0(r)UB3PW91 150.8(r), 78.9(p), 1698.2(r)UB3LYP/aug-cc-pVQZa 168.6 (r), 14.6 (p), 1656.7(r)UMP2/6-311G(2d)a 137.2 (r), 34.0 (p), 1569.7(r)

TS-T shaped transition stateUB3LYP 98.2(a1), 138.4i(b2), 1610.0(a1)UB3P86 70.5(a1), 137.7i(b2), 1657.7(a1)UB3PW91 65.9 (a1), 132.5i(b2), 1656.3(a1)UB3LYP/aug-cc-pVQZa 110.1 (a1), 122.6i(b2), 1613.0(a1)

a Taken from Ref. [17].

64 J.N. Dawoud et al. / Computational and Theoretical Chemistry 1027 (2014) 62–72


to Eq. (1) and has a value of �4.22 kcal mol�1, calculated on the ba-sis of UB3P86/6-311+G(df) method. This value agreed well withthe RCCSD(T) calculated value of �4.59 kcal mol�1 [17].

It is worthwhile to mention here that O2 molecule has a nega-tive quadrupole moment [44] and thus, the interaction betweenNa+ ion and O2 moiety in linear structure is highly attractive,whereas the interaction between them in T-shaped structure isof repulsive nature. This will push the Na+ ion farther away fromO2 molecule (2.71 Å) compared with the separation between themin linear structure (2.35 Å). The natural bond orbital (NBO) analysisof the atomic charge distribution of the Na+�O2 complex shown thatNa+ ion still retains most of its positive charge in linear andT-shaped structures (see Fig. 1). In linear configuration, we foundthat the p electrons of O2 moiety is partially polarized since thenearest oxygen atom to Na+ exhibits a charge of �0.144, whereasthe other one exhibits a charge of +0.151. For T-shaped structure,the p electrons of O2 moiety was slightly affected by Na+ ion sinceboth oxygen sites exhibited almost zero atomic charge distribu-tion. Thus, the binding energy in linear structure was stronger thanthat in T-shaped structure as concluded from the difference in theelectrostatic interaction of the complex in these configurations.

3.1.1. The Na+�(O2)2 and Na+�(O2)3 complexesTogether IRC and vibration frequency tests, result not shown, of

the potential energy surface of the Na+�(O2)2, in its quintet state(5A1), and Na+�(O2)3, in its septet state (7A2), complexes, show theexistence of one global minimum and one transition state struc-tures for the two complexes as shown in Figs. 2 and 3, respectively.For the Na+�(O2)2 complex, the global minimum exhibits a linearconfiguration with a D1h symmetry, whereas the transition stateexhibits a T-shaped structure with a C2v symmetry as concluded

from the optimized geometries of the complex as presented inFig. 2. A trigonal planer with a D3h symmetry and a Y-shaped struc-ture with a C2v symmetry were obtained for the global minimumand transition states of the Na+�(O)3 complex, respectively asshown in Fig. 3.

As shown in Figs. 2 and 3, the Na+–O distances in Na+�(O2)2(2.357 Å, linear) and Na+�(O2)3 (2.376 Å, trigonal planar) are longerthan in Na+�O2 (2.347 Å, linear) while the variation in the O2 bondlength in these complexes was insignificant (less than 0.007 Å).This was occurred as a result of an electrostatic interaction oc-curred without any kind of electronic transfer between the metalion and O2 moiety. The NBO analysis of atomic charge distributionsand spin density populations of these complexes, in their minima,indicates that the mono-ligated complex, Na+�O2, has the highest pelectron polarization where the charge of the oxygen atom nearestto Na+ ion decreases in the order Na+�O2 (do = �0.144) > Na+�(O2)2(do = �0.136) > Na+�(O2)3 (do = �0.126) as presented in Fig. 4. Con-sequently, the strength of Na+ and O2 bonding decreases as goingfrom mono to triply ligated complexes due to increasing in theion-ligand distance and decreasing in the electrostatic energy aspresented in the next section.

For the transition states structures, the distances between theNa+ ion and O2 moiety is larger than those of distances in theirminima. For T-shaped structure, the (O2)�Na+---O2 distance wasfound to be 2.789 Å whereas for Y-shaped structure, the(O2)2�Na+---O2 distance was found to be 2.818 Å (calculated onthe basis of the UB3LYP/6-311+G(df) method, see Figs. 2 and 3).Consequently, these structures have a weak ion-ligand interactionand hence exhibit less stability than their minima structures.

The binding energy of the Na+�(O2)n (n: 2,3) complexes was cal-culated at various levels of DFT. In all cases, the UB3P86 and

Table 3Binding energy (BE), thermodynamic quantities, DH�; DG� and BSSE, for the Na+�O2 complexes, at various levels of DFT. The units are in kcal mol�1.

Structure Method Basis set BE DH� DG� BSSE

Linear Na+�O2 UB3LYP 6-311+G(df) 4.82 �4.96 0.29 0.79UB3PW91 6-311+G(df) 4.00 �4.07 1.00 0.76UB3P86 6-311+G(df) 4.10 �4.22 0.93 0.79Expta – – – �0.2–0.8 –RCCSDb aug-cc-pV5Z 4.60 ± 0.3 �4.59 – –BP86c SVP+ 5.49 – – –

T-shaped TS1 UB3LYP 6-311+G(df) 1.15 – – 0.36UB3PW91 6-311+G(df) 0.60 – – 0.33UB3P86 6-311+G(df) 0.64 – – 0.34

a Taken from Ref. [15].b Taken from Ref. [17].c Taken from Ref. [43].

O O Na+ O O1.202 A

o2.357 A

o

Structure A,

O O

Na+

O

O

1.202 Ao

2.789 Ao

2.352 Ao

1.209 Ao

T-shaped TS, C2v

Fig. 2. Optimized geometries for the minimum and transition states of theNa+�(O2)2 complex that obtained on the basis of the UB3LYP/6-311+G(df) method.

O O

Na+

OO

OO

1.209 Ao

2.818 Ao

1.202 Ao

2.367 Ao

120.0o

O

O

Na+

OO

OO1.202 A

o

2.376 Ao

120.0o

Y-shaped TS, C2v Structure B, D3h

Fig. 3. Optimized geometries for the minimum and transition states of theNa+�(O2)3 complex that obtained on the basis of the UB3LYP/6-311+G(df) method.



UB3W91 computed values of the binding energy and their thermo-dynamic properties were consistent for the di- and tri-ligated com-plexes whereas the UB3LYP calculated values were larger than theothers by 1.5–2.3 kcal mol�1 as presented in Table 4. These calcu-lations showed that the total binding energy was increased withthe number of O2 molecules as a result of increasing the bondswith Na+ ion. In addition, the negative sign of DH� indicates thatthe formation of these complexes is of an exothermic process.

3.1.2. Sequential bond energies of Na+�(O2)n (n: 1–4)The bond dissociation energies (BDE) have only been calculated

for the global minima for these ion complexes. Note here the tetra-ligated complex, Na+�(O2)4, was also taken into account. The geo-metrical optimization test of this complex show that the four O2molecules were preferred to arrange in a tetrahedral (Td) shapearound the sodium ion, where the r(Na–O) distances = 2.404 Å and\ðO—Na—OÞ ¼ 110:1�, calculated on the basis of the UB3LYP/6-311+G(df) method, as shown in Fig. 5. As expected the Na–O dis-tance in Na+�(O2)4 complex was the longest among these four ioncomplexes. The BDE of Na+�(O2)n (n: 1–4) complexes were calcu-lated using various DFT methods and the results were listed inTable 5. In all cases, the UB3P86 and UB3PW91 computed valuesof the BDE were consistent for these sodium ion complexes,whereas the BDE values calculated on the basis of the UB3LYPmethod were the largest among these three methods by�0.7 kcal mol�1. Our calculations show that the BDEs follow theordering, Na+�(O2) > Na+�(O2)2 > Na+�(O2)3 > Na+�(O2)4. This wasconsistent with the Na–O distances trend where the mono-ligated

complex exhibits the shortest Na–O distance and hence it has thestrongest Na+---O2 interaction.

To explain the calculated BDEs trend for these four ion com-plexes, the NBO atomic charge distribution were calculated andused to estimate the electrostatic energy of a single Na---O2 ineach complex using Eq. (2). These results were listed in Table 5.The electrostatic energies values were found to follow the sametrend as obtained for the BDEs, in which the electrostatic energywas decreased with the number of O2 molecules. This occurs as aresult of decreasing the charges on the Na+ and the nearest oxygen

O

O

Na

OO

OO

Na O O

Na O OO O

+0.993 -0.144 +0.151

+0.007 +0.880 +1.113

+0.981-0.136+0.146

+0.015+0.882+1.110

+0.022

+0.883

+1.110

Linear Na+ (O2)2, S = 2 Trigonal planar Na+ (O2)3, S = 3

Linear Na+ O2, S = 1

O O+1.000

0.000 0.000

+1.000

Free O2, S = 1

+0.968

-0.126

+0.138

Fig. 4. The NBO analysis of atomic charge distributions, spin states (S) and atomic spin densities, in black solid line, of the minima of the Na+�(O2)1–3 complexes obtained onthe basis of the UB3LYP/6-311+G(df) method.

Table 4Binding energy (BE), thermodynamic quantities, DH� , DG� and BSSE for the Na+�(O2)2–3 complexes, at various levels of DFT. The units are in kcal mol�1.


Na+---(O2)2 (A) UB3LYP 6-311+G(df) 9.29 �8.99 2.36 1.66UB3PW91 6-311+G(df) 7.74 �7.60 6.33 1.61UB3P86 6-311+G(df) 7.90 �7.84 4.73 1.72

T-shaped TS UB3LYP 6-311+G(df) 5.84 – – 1.22UB3PW91 6-311+G(df) 4.43 – – 1.22UB3P86 6-311+G(df) 4.58 – – 1.26

Na+---(O2)3 (B) UB3LYP 6-311+G(df) 13.38 �12.77 2.44 2.38UB3PW91 6-311+G(df) 10.95 �10.26 4.77 2.37UB3P86 6-311+G(df) 11.31 �10.65 4.34 2.47

T-shaped TS UB3LYP 6-311+G(df) 10.27 – – 1.06UB3PW91 6-311+G(df) 7.91 – – 2.03UB3P86 6-311+G(df) 8.14 – – 2.12

Na+

O

O

O

O

O

O

O O

110.1o

2.404 Ao

1.202 Ao

Fig. 5. Optimized geometry of the minimum state of the Na+�(O2)4 complex thatobtained on the basis of the UB3LYP/6-311+G(df) method.



atomic site of O2 molecule and hence increases the separation be-tween the Na+ ion and O2 molecule in these complexes (see Figs. 1–3 and 5). The interaction forces within these complexes werehighly dependent on the strength of electrostatic energy sincethere was no any kind of electronic transfer such as r- or p-backdonations in these ion complexes [45].

3.2. The Na�O2 complex

The IRC diagram, result not shown, of the superoxide Na�O2complex, in its doublet state (2A2), showed the existence of oneminimum and one transition state structures. The minimum stateof the Na�O2 complex has a T-shaped structure in which, the Naatom was oriented toward the mid of the O–O bond in a right angleand hence has a C2v symmetry with a r(Na–O) = 2.150 Å andr(O–O) = 1.349 Å and \ðNa—O—OÞ ¼ 71:7� [calculated on the basisof the UB3LYP/6-311++G(df) method] (see Table 6). The O–O bondlength in Na�O2 (1.349 Å) agreed well with the experimental value

of 1.34 ± 1 Å for O–O bond length in gaseous superoxo anion O�2[46], 1.36 Å that calculated on the basis of PB86/SVP method [43]and also in good agreement with other theoretical calculations re-sults of the Na�O2 complex (1.35 Å [26] and 1.34 Å [29]). This con-firmed that the Na�O2 is a superoxide compound where an electrontransferred from 3s orbital of Na atom to p�2p orbital of O2 molecule.Furthermore, the vibration frequency test of the Na�O2 complex at

Table 5Sequential bond dissociation energies (BDE) and electrostatic interaction energy‘‘Eelec.’’ for minima structures of the Na+�(O2)n (n: 1–4) complexes, at various levels ofDFT. The units are in kcal mol�1.

Structure Method Basis set BDE Eelec.a

The Na+�O2 complexLinear Na+�O2 UB3LYP 6-311+G(df) 4.82 26.48

UB3PW91 6-311+G(df) 4.06 25.17UB3P86 6-311+G(df) 4.16 25.93

The Na+�(O2)2 complexLinear (O2)�Na+---O2 UB3LYP 6-311+G(df) 4.41 24.12

UB3PW91 6-311+G(df) 3.73 22.70UB3P86 6-311+G(df) 3.79 23.78

The Na+�(O2)3 complexTrigonal planar (O2)2�Na+---O2 UB3LYP 6-311+G(df) 3.92 21.63

UB3PW91 6-311+G(df) 3.07 20.98UB3P86 6-311+G(df) 3.23 21.43

The Na+�(O2)4 complexTetrahedral (O2)3�Na+---O2 UB3LYP 6-311+G(df) 3.72 18.97

UB3PW91 6-311+G(df) 2.96 18.43UB3P86 6-311+G(df) 3.08 18.82

a Electrostatic energy calculations were performed in gas phase.

Table 6Geometrical parameters of the Na.O2 complexa at different configurations.

Geometry Method Basis set r(O–O) r(Na–O) h(�)b

T-shaped Na�O2 UB3LYP 6-31++G(d) 1.356 2.141 71.06-311++G(d) 1.350 2.152 71.06-311++G(df) 1.349 2.150 71.7

UB3PW91 6-31++G(d) 1.344 2.143 71.06-311++G(d) 1.339 2.154 71.06-311++G(df) 1.338 2.152 71.0

UB3P86 6-31++G(d) 1.342 2.136 71.06-311++G(d) 1.338 2.148 71.06-311++G(df) 1.337 2.145 71.0

BP86 c SVP 1.360 – –BP86 c SVP+ 1.370 – –

Linear TS UB3LYP 6-31++G(d) 1.327 1.987 180.06-311++G(d) 1.321 1.987 180.06-311++G(df) 1.319 1.985 180.0

UB3PW91 6-31++G(d) 1.317 1.991 180.06-311++G(d) 1.3.11 1.989 180.06-311++G(df) 1.310 1.988 180.0

UB3P86 6-31++G(d) 1.316 1.984 180.06-311++G(d) 1.310 1.982 180.06-311++G(df) 1.309 1.980 180.0

a All the bond lengths are in (Å), and the bond angles are in degrees.b \Na—O1—O2 bond angle.c Taken from Ref. [43].

Table 7Binding energy (BE), thermodynamic quantities, DH� , DG� and BSSE, for the Na�O2complexes, at various levels of DFT. The units are in kcal mol�1.


T-shaped Na---(O2) UB3LYP 6-311++G(df) 31.55 �32.31 �25.83 0.82UB3PW91 6-311++G(df) 29.44 �30.19 �23.71 0.92UB3P86 6-311++G(df) 33.51 �34.12 �27.62 0.89Exp.a – 39 ± 5 – – –Exp.b – 33.5 – – –URCCSDc aug-cc-pV5Z 36 ± 3 – – –B3LYP d SVP+ 34.7 – – –

Linear TS UB3LYP 6-311++G(df) 18.64 – – 1.32UB3PW91 6-311++G(df) 16.48 – – 1.49UB3P86 6-311++G(df) 20.15 – – 1.47

a Taken from Ref. [32].b Taken from Ref. [25].c Taken from Ref. [17].d Taken from Ref. [43].

O O

O ONa+0.938

-0.469 -0.469

-0.027

+0.514 +0.514

Na O O+0.952 -0.653 -0.229 0.000 0.000

+1.000 +1.000+0.010 +0.357 +0.633

T-shaped structure Linear structure Free O2

Fig. 6. NBO atomic charge distribution and atomic spin densities, in black solid line,of free O2 and Na�O2 complex at different configurations calculated on the basis ofthe UB3LYP/6-311++G(df) method.



the level of UB3LYP/6-311++G(df) showed the highest vibration ex-ists at around 1153 cm�1, which agreed well with the experimentalvalue of 1095 cm�1 [47] and 1130 cm�1 calculated by BP86/SVP+ method [47] for O–O stretching. For the transition state, theUB3LYP, UB3P86 and UB3PW91 methods using different basis setsshowed that the Na�O2 complex has a linear structure, in which theNa atom interacted with either side of O2 molecule, where the dis-tances r(Na–O) = 1.987 Å and r(O–O) = 1.327 Å that calculated on thebasis of the UB3LYP/6-31++G(d) method (see Table 6). At the levelof UB3LYP/6-311++G(df), the vibration frequencies of the linearstructure were found to be of w1 = 87i cm�1, w2 = 97 cm�1 andw3 = 1266 cm�1 (O–O stretch).

The binding energy of the minimum and transition state struc-tures of the Na�O2 complex was calculated at various levels of DFTusing a 6-311++G(df) basis set function. These results were listedin Table 7. On average the T-shaped structure exhibits strongerbinding energy than that of linear structure by a �14 kcal mol�1.Our best value for the binding energy of the T-shaped structureis 33.5 kcal mol�1, which agreed well with the lower set of exper-imental results (33.5–44.0 kcal mol�1) and all other values thatdetermined at high levels of ab initio methods (see Table 7). For lin-ear structure, the variation in the values of the binding energieswere found to be in the range 1.0–2.5 kcal mol�1 as presented inTable 7. On the basis of the UB3LYP/6-311++G(df) method, thebinding energy between the Na atom and O2 molecule was foundto be 18.8 kcal mol�1. Thermodynamic quantities for T-shapedstructure have been calculated at various levels of DFT using 6-311++G(df) basis set and listed in Table 7. The negative sign ofDH� value indicates that the formation of the complex is of an exo-thermic process.

As shown in Fig. 6, the NBO atomic charge distributions andspin densities of T-shaped and linear structures were determinedon the basis of the UB3LYP/6-311++G(df) method. Compared tofree O2 molecule, each oxygen site in the two structures has a

Table 8NBO analysis of bond order (BO) of O2 moiety in Na�O2 complex at differentconfigurations and free O2 on the basis of the UB3LYP/6-311++G(df) method.

Structure BO of O2 Bond length w(O–O) (cm�1)

T-shaped Na�O2 1.299 1.349 1155.2Linear Na�O2 1.336 1.319 1266.8Free O2 1.855 1.205 1633.6

Fig. 7. Optimized structures for the minima and transition states of the Na�(O2)2complex that obtained on the basis of the UB3LYP/6-311++G(df) method.

NaO

O

O

O O

O

2.287 Ao

2.365 Ao

1.241 Ao

1.220 Ao

2.291 Ao

1.227 Ao

1.259 Ao

119.8o

Na

O O

O

O

O

O

2.288 Ao

1.265 Ao

2.282 Ao

2.282 Ao

1.245 Ao

1.245 Ao 121.9

o

NaO

O

O O2.361 A

o1.265 A

o119.5

o

O

O

2.291 Ao1.243 A

o

Na

O

OO O

2.337 Ao

2.288 Ao

1.275 Ao

2.353 Ao

134.0o

O O

1.235 Ao

103.3o

C2v, (C) Cs, (D)

C2v, (TS1) Cs, (TS2)

Fig. 8. Optimized structures for the minima and transition states of the Na�(O2)3 complex obtained on the basis of the UB3LYP/6-311++G(df) method.



negative charge distribution and positive lower spin densitypopulations as a result of an electron transfers from Na atom tothe anti-bonding p�2p orbital and hence reducing the bond orderof O2 moiety in the complex as presented in Table 8. Note here asmall negative density (�0.027) on Na site in T-shaped structureis due to polarization effects. This was also reflected in the bondlength of O2 moiety since linear and T-shaped structures havelonger O–O distances than in free O2 (see Table 8). On the basisof the longest O–O distances, the T-shaped structure has the lowestO–O vibration frequency than in either linear structure or free O2.

3.2.1. The Na�(O2)2 and Na�(O2)3 complexesThe optimized geometries for the Na�(O2)2, in its quartet state

(4A1), and Na�(O2)3, in its sextet state (6A2), complexes were dis-played in Figs. 7 and 8. The IRC test, result not shown, for theNa�(O2)2 complex showed the existence of two minima and onetransition state structures. The global minimum exhibited a config-uration in which the substructure of Na with each O2 molecule hasa T-shaped orientation as illustrated in Fig. 7. This allowed for Naatom to interact with four oxygen sites of the two O2 molecules(structure A). For local minimum (structure B), the Na atom was di-rectly interacted with three oxygen atomic sites as presented inFig. 7. Note here the variation in the electronic energy of the twominima was attributed to the difference in the electrostatic energybetween them as presented in the next section. A linear structure

was obtained for the transition state in which the Na atom inter-acted with two oxygen atomic sites located on different O2 mole-cules. Apparently, the stability of these species was dependant onhow many O-sites interacted with Na atom in these three configu-rations. The vibration frequencies of the two minima structuresindicate that there are two frequencies for O–O stretching at�1240 cm�1 and 1400 cm�1 for the global (structure A) and�1200 cm�1 and 1500 cm�1 for the local minimum (structure B).Similar results were found for the transition state structure wherethe frequencies at �1270 cm�1 and 1470 cm�1 were assigned forO–O stretching.

The potential energy surface of the Na�(O2)3 complex was ex-plored using the IRC test (result not shown). Our findings showedthe existence of two minima and two transition states structures.The global minimum (structure D) has a Cs distorted trigonal

Table 9Binding energy (BE), thermodynamic quantities, DH� , DG� and BSSE, for the Na�(O2)2–3 complexes, at various levels of DFT. the units are in kcal mol�1.


Na---(O2)2 (A) UB3LYP 6-311++G(df) 43.06 �43.89 �29.21 1.34UB3PW91 6-311++G(df) 40.87 �41.66 �27.06 1.54UB3P86 6-311++G(df) 44.28 �45.09 �30.46 1.48

Na---(O2)2 (B) UB3LYP 6-311++G(df) 40.82 �41.11 �28.44 1.89UB3PW91 6-311++G(df) 38.74 �38.99 �26.37 2.07UB3P86 6-311++G(df) 42.02 �42.29 �29.68 2.05

Na---(O2)2 (TS) UB3LYP 6-311++G(df) 36.81 – – 2.34UB3PW91 6-311++G(df) 34.79 – – 2.51UB3P86 6-311++G(df) 38.01 – – 2.49

Na---(O2)3 (C) UB3LYP 6-311++G(df) 45.37 �45.06 �27.80 2.36UB3PW91 6-311++G(df) 42.22 �41.83 �24.72 2.57UB3P86 6-311++G(df) 45.90 �45.51 �29.79 2.56

Na---(O2)3 (D) UB3LYP 6-311++G(df) 45.35 �45.37 �25.42 2.49UB3PW91 6-311++G(df) 41.89 �41.77 �22.01 2.78UB3P86 6-311++G(df) 46.23 �46.25 �26.74 2.77

Na---(O2)3 (TS1) UB3LYP 6-311++G(df) 45.08 – – 2.35UB3PW91 6-311++G(df) 41.89 – – 2.54UB3P86 6-311++G(df) 45.81 – – 2.38

Na---(O2)3 (TS2) UB3LYP 6-311++G(df) 44.06 – – 2.46UB3PW91 6-311++G(df) 41.18 – – 2.67UB3P86 6-311++G(df) 44.79 – – 2.69

Na O O

O

O

O O

O

O

1.228 Ao

2.251 Ao

Na (O2)4, D4h

Fig. 9. Optimized structure for a minimum structure of the Na�(O2)4 complexobtained on the basis of the UB3LYP/6-311++G(df) method.

Table 10Sequential bond dissociation energies (BDE) and electrostatic interaction energy‘‘Eelec.’’ for minima structures of the Na�(O2)n, complex (n: 1–4), at various levels ofDFT. The units are in kcal mol�1.

Structure Method Basis set BDE Eelec. a

The Na�O2 complexT-shaped Na�O2 UB3LYP 6-311++G(df) 31.55 135.37

UB3PW91 6-311++G(df) 29.44 136.82UB3P86 6-311++G(df) 33.35 138.73

The Na�(O2)2 complexes(O2)�Na---O2 (A) UB3LYP 6-311++G(df) 11.15 60.78

UB3PW91 6-311++G(df) 10.08 61.24UB3P86 6-311++G(df) 10.55 61.70

(O2)�Na---O2 (B) UB3LYP 6-311++G(df) 9.48 63.36UB3PW91 6-311++G(df) 8.45 63.32UB3P86 6-311++G(df) 8.82 64.14

The Na�(O2)3 complexes(O2)2�Na---O2 (C) UB3LYP 6-311++G(df) 2.42 38.14

UB3PW91 6-311++G(df) 1.39 38.69UB3P86 6-311++G(df) 1.73 38.77

(O2)2�Na---O2 (D) UB3LYP 6-311++G(df) 2.45 38.93UB3PW91 6-311++G(df) 1.36 39.23UB3P86 6-311++G(df) 2.06 39.86

The Na�(O2)4 complexesSquare planar (O2)3�Na---O2 UB3LYP 6-311++G(df) 1.78 30.28

UB3PW91 6-311++G(df) 1.03 30.42UB3P86 6-311++G(df) 1.31 30.21

a Electrostatic energy was calculated for these complexes in gas phase.



planar geometry with a bent Na�O2 substructures as shown inFig. 8. For the other local minimum (structure C), the Na atom withthree O2 molecules were arranged in a distorted square pyramidal,in which the upper Na�O2 substructure has a linear shape and a T-shaped substructure for the Na atom bounded with each remainingO2 molecules as shown in Fig. 8. The frequency test, for the twominima, showed the existence of three frequencies at�1268 cm�1, 1345 cm�1 and 1550 cm�1 for O–O stretching sincethere were three O2 molecules in the complex with bond lengthsvaried in the range between those in a superoxide Na�O2 and Na+�O2 complexes (see Tables 1 and 6).

The DFT geometry optimization for the first order saddle pointsindicate the existence of two transition state structures, TS1 with a

C2v symmetry and TS2 with a Cs symmetry, as presented in Fig. 8.According to the IRC diagram (result not shown), TS1 structureexhibits larger electronic energy than that of TS2 structure sincethe Na atom in TS1 interacted with six oxygen atomic sites ratherthan with five oxygen atomic sites in TS2 structure. Furthermore,these structures have comparable three frequencies values for O–O stretching at �1300 cm�1, 1340 cm�1 and 1500 cm�1 that wererelatively closed to those of the two minima structures.

The binding energies of di- and tri-ligated sodium neutral com-plexes were calculated at different methods of DFT and listed inTable 9. For the di- and tri-ligated complexes, the binding energiesvalues calculated using the UB3LYP and UP3P86 methods wereconsistent and in good agreement whereas the UB3PW91

Fig. 10. The NBO analysis of the atomic charge distribution, spin state (S) and atomic spin density, in black solid line, of the minima structures of the Na.(O2)1–4 complexesobtained on the basis of the UB3LYP/6-311++G(df) method.



calculations yielded lowest binding energy values among thesemethods by �2.5 kcal mol�1. Similar to the sodium ion complexes,the binding energy for the minima structures (A and B) increaseswith the number of atomic oxygen sites interacted directly withNa atom. As shown in Table 9, structure A, surrounded by four oxy-gen atoms, has a larger binding energy than that of structure B,surrounded by three oxygen atoms, by a value of �2.5 kcal mol�1.This may be attributed to the difference in the electrostatic energyas presented in the next section. For the Na�(O2)3 complex, the twominima have relatively the same binding energy, the difference inthe binding energy values was less than 0.2 kcal mol�1. Note here,for structures C and D, the Na atom interacted directly with 5 and 6oxygen atomic sites, respectively. Furthermore the separation be-tween the Na atom and oxygen atomic sites in structure C wasslightly less than in structure D. These two factors worked oppo-sitely and hence yielded relatively the same binding energies forthe two minima. The thermodynamic data for these complexeswere calculated and also listed in Table 9. These results showedthat the formation of the di- and tri-ligated complexes at differentorientations were of an exothermic process.

3.2.2. Sequential bond energies of Na�(O2)n (n: 1–4)The bond dissociation energy (BDE) for removal one O2 mole-

cule was only calculated for minima configurations of these com-plexes. To have better understanding, the tetra-ligated complexwas also taken into account. Our DFT calculations shown that theNa�(O2)4 complex has a D4h square planar structure with a linearNa�O2 substructure (see Fig. 9). The BDEs of sodium neutral com-plexes were calculated at various levels of DFT and listed inTable 10. In all cases, the computed values of the BDEs wereconsistent for the mono-, di-, tri-, and tetra-ligated complexes.Our results showed that the BDE decreases in the order Na�O2 >Na�(O2)2 > Na�(O2)3 > Na�(O2)4. To explain this observed trend, theatomic charge distributions and spin densities of these complexeswere determined, on the basis of the UB3LYP/6-311++G(df) meth-od, using NBO analysis method. These results were presented inFig. 10. The atomic charge distributions and spin density popula-tions confirmed that the electron transferred from Na atom wasdelocalized on oxygen atomic sites directly interacted with Naatom in these complexes. In addition the negative small spin den-sity value of sodium atom was due to polarization effects withinthese complexes. These atomic charge values with the geometricalparameters for each complex were used to calculate the electro-static energy using Eq. (2) for a single Na�O2 moiety in the complex.As shown in Table 10, the electrostatic energy were found to followthe same observed BDE trend in which the electrostatic energy de-creases in the order Na�O2 > Na�(O2)2 > Na�(O2)3 > Na�(O2)4. Conse-quently, the variation in the BDE of these complexes wasattributed to the differences in the electrostatic interactions withinthese neutral complexes.

4. Conclusions

A computational study of cationic and neutral sodium oxidecomplexes, Na+/0�(O2)n (n: 1–3), at different levels of DFT was per-formed. The potential energy surfaces of these complexes werecompletely investigated, in which optimized structures for theminima and transition states were presented and found to agreewell with those reported from previous studies, where available.Large differences were obtained among the neutral and ion sodiumoxides complexes in terms of bonding, structures and their bindingenergies. The cationic sodium complexes exhibit weaker bindingenergies than these of neutral sodium complexes since the latterone have a Na–O ionic bond. The variation in O–O bond lengthwas insignificant, compared to free O2 bond length, in Na+�(O2)n

(n: 1–3) while the O–O bond length has been enlarged by �15%in neutral complexes. Furthermore, the increasing in the O–O bondlength in neutral sodium complexes was reduced with increasedO2 coordination.

The sequential bond dissociation energies (BDE) of the neutraland ionic sodium complexes show the same trend where themono-ligated complex has the strongest BDE. The two trends werehighly dependent on the electrostatic interaction in thesecomplexes.

Acknowledgement

JND would like to thank the Deanship of Research and GraduateStudies at the Hashemite University (Jordan) for the financialsupport of this work.

References

[1] D.M. Murphy, P. Massiani, R. Franck, D. Barthomeuf, Basic site heterogeneityand location in alkali cation exchanged EMT zeolites. An IR study usingadsorbed pyrrole, J. Phys. Chem. 100 (1996) 6731–6738.

[2] E.J.P. Feijen, J. Lievens, J.A. Martens, P.J. Grobet, P.J. Jacobs, Silicon andaluminum ordering in frameworks of FAU and EMT aluminosilicate zeolitescrystallized in presence of crown ethers, J. Phys. Chem. 100 (1996) 4970–4975.

[3] R. Larsson, R. Lykvist, B. Rebenstorf, On the IR frequency shift of carbonmonoxide adsorbed on positive surface ions, Z. Phys. Chem. Leipzig 263 (1982)1089–1104.

[4] H. Knözinger, S. Huber, IR spectroscopy of small and weakly interactingmolecular probes for acidic and basic zeolites, J. Chem. Soc., Faraday Trans. 94(1998) 2047–2059.

[5] K. Hadjiivanov, H. Knözinger, FTIR study of the low-temperature adsorptionand co-adsorption of CO and N2 on NaY zeolite: evidence of simultaneouscoordination of two molecules to one Na+ site, Chem. Phys. Lett. 303 (1999)513–520.

[6] J.M.C. Plane, The chemistry of meteoric metals in the Earth’s upperatmosphere, Int. Rev. Phys. Chem. 10 (1991) 55–106.

[7] R.M. Cox, J.M.C. Plane, An ion-molecule mechanism for the formation ofneutral sporadic Na layers, J. Geophys. Res. 103 (1998) 6349–6359.

[8] S.E. Dairc, J.M.C. Plane, S.D. Gamblin, P. Soldán, E.P.F. Lee, T.G. Wright, Atheoretical study of the ligand-exchange reactions of Na+�X complexes (X = O,O2, N2, CO2 and H2O): implications for the upper atmosphere, J. Atm. Solar-Terr. Phys. 64 (2002) 863–870.

[9] S.C. Collins, J.M.C. Plane, M.C. Kelley, T.G. Wright, P. Soldán, T.J. Kane, A.J.Gerrard, B.W. Grime, R.J. Rollason, J.S. Friedman, S.A. Gonzalez, Q. Zhou, M.Suizer, A study of the role of ion-molecule chemistry in the formation ofsporadic sodium layers, J. Atm. Solar-Terr. Phys. 64 (2002) 845–860.

[10] W.J. McNeil, E. Murad, S.T. L-Lai, Comprehensive model for the atmosphericsodium layer, J. Geophys. Res. 100 (1995) 16847–16855.

[11] A.R. Smith, J. Klosek, A review of air separation technologies and theirintegration with energy conversion processes, Fuel Process. Technol. 70 (2001)115–134.

[12] G. Reiss, Status and development of oxygen generation processes on molecularsieve zeolites, Gas Sep. Purif. 8 (1994) 95–99.

[13] R.V. Siriwardane, M.-S.h. Shen, E.P. Fisher, Adsorption of CO2, N2 and O2 onnatural zeolites, Energy Fuels 17 (2003) 571–576.

[14] C.O. Areán, D. Nachtigallová, P. Nachtigall, E. Garrrone, M.R. Delgado,Thermodynamics of reversible gas adsorption on alkali-metal exchangedzeolites – the interplay of infrared spectroscopy and theoretical calculations,Phys. Chem. Chem. Phys. 9 (2007) 1421–1437.

[15] K.G. Spears, Ion-neutral bonding, J. Chem. Phys. 57 (1972) 1850–1858.[16] K. Hadjiivanov, P. Massiani, H. Kuözinger, Low-temperature CO and 15N2

adsorption and co-adsorption on alkali cation exchanged EMT zeolites: an FTIRstudy, Phys. Chem. Chem. Phys. 1 (1999) 3831–3838.

[17] E.P.F. Lee, P. Soldán, T.G. Wright, The heat of formation of NaOþ2 (X3R�) and

NaO2(X~ 2A2), Chem. Phys. Lett. 301 (1999) 317–324.[18] P. Soldán, V. Spirko, E.P.F. Lee, T.G. Wright, Structure and potential energy

surface for Na+�N2, J. Chem. Phys. 111 (1999) 3420–3425.[19] E.P.F. Lee, T.G. Wright, Preliminary calculations on the Na–N2 complex, Chem.

Phys. Lett. 392 (2004) 187–191.[20] A.E. Thompson, R.G.A.R. Maelagan, P.W. Harland, The ab-initio calculation of

the gas phase ion mobility of Na+ in N2, Chem. Phys. 248 (1999) 127–135.[21] P. Marshall, A.S. Narayan, A. Fontijn, Kinetic and thermochemical studies of the

recombination reaction Na + O2 + N2 from 590 to 1515 K by a modified high-temperature photochemistry technique, J. Phys. Chem. 94 (1990) 2998–3004.

[22] A.J. Hynes, M. Steinberg, K. Schofield, The chemical kinetics andthermodynamics of sodium species in oxygen-rich hydrogen flames, J. Chem.Phys. 80 (1984) 2585–2597.

[23] H. Figger, W. Schrepp, X.-h. Zhu, Chemiluminescent reaction between alkalidimers and oxygen molecules, J. Chem. Phys. 79 (1983) 1320–1325.

[24] M. Steinberg, K. Schofield, A re-evaluation of the vaporization behavior ofsodium oxide and the bond strengths of NaO and Na2O: implications for the



mass spectrometric analyses of alkali/oxygen systems, J. Chem. Phys. 94(1991) 3901–3907.

[25] D.L. Hidenbrand, K.H. Lau, Mass spectrum and sublimation pressure of sodiumoxide vapor: stability of the superoxide molecule NaO2, J. Chem. Phys. 98(1993) 4076–4081.

[26] H. Partridge, C.W. Bauschlicher Jr., M. Sodupe, S.R. Langhoff, Theoreticaldetermination of the alkali-metal superoxide bond energies, Chem. Phys. Lett.195 (1992) 200–206.

[27] P. Marshall, An ab initio study of the ionization of sodium superoxide, J. Chem.Phys. 95 (1991) 7773–7774.

[28] J.M.C. Plane, B. Rajasekhar, L. Bartolotti, Theoretical and experimentaldetermination of the lithium and sodium superoxide bond dissociationenergies, J. Phys. Chem. 93 (1989) 3141–3145.

[29] D.A. Horner, W.D. Allen, A.G. Csaszar, H.F. Schaefer III, The sodium superoxideradical: X2A2 and A2B2 potential energy surfaces, Chem. Phys. Lett. 186 (1991)346–355.

[30] M.J. McEwan, L.F. Phillips, Dissociation energy of NaO2, Trans. Faraday Soc. 62(1966) 1717–1720.

[31] D.E. Jensen, Alkali-metal compounds in oxygen-rich flames. A reinterpretationof experimental results, J. Chem. Soc. Faraday Trans. I (78) (1982) 2835–2842.

[32] H. Partridge, C.W. Bauschlicher Jr., M. Sodupe, S.R. Langhoff, Comment on:an ab initio study of the ionization of sodium superoxide, J. Chem. Phys. 96(1992) 7871.

[33] D.P. Chong, S.R. Langhoff, A modified coupled pair functional approach, J.Chem. Phys. 84 (1986) 5606–5610.

[34] T.G. Wright, A.M. Ellis, J.M. Dyke, A study of the products of the gas-phasereactions M + N2O and M + O3, where M = Na or K, with ultravioletphotoelectron spectroscopy, J. Chem. Phys. 98 (1993) 2891–2907.

[35] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman,J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar,J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A.Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa,M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox,H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann,O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K.Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S.

Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K.Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J.Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L.Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M.Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A.Pople, Gaussian 03, Revision B.05, Gaussian Inc., Pittsburgh PA, 2003.

[36] C. Gonzalez, H.B. Schlegel, An improved algorithm for reaction path following,J. Chem. Phys. 90 (1989) 2154–2161.

[37] C. Gonzalez, H.B. Schlegel, Reaction path following in mass-weighted internalcoordinates, J. Phys. Chem. 94 (1990) 5523–5527.

[38] S. Simon, M. Duran, J.J. Dannenberg, How does basis set superposition errorchange the potential surfaces for hydrogen-bonded dimers, J. Chem. Phys. 105(1996) 11024–11031.

[39] S.F. Boys, F. Bernardi, The calculation of small molecular interactions by thedifferences of separate total energies: some procedures with reduced errors,Mol. Phys. 19 (1970) 553–566.

[40] M.I. Alomari, J.N. Dawoud, Structure and potential energy surface of K+�CX2, J.Mol. Struct. (Theochem.) 939 (2010) 28–33.

[41] B. Bonelli, B. Civalleri, B. Fubini, P. Ugliengo, C. Otero Areán, E. Garrone,Experimental and quantum chemical studies on the adsorption of carbondioxide on alkali-metal-exchanged ZSM-5 zeolites, J. Phys. Chem. B 104 (2000)10978–10988.

[42] D. Liu, T. Wyttenbach, M.T. Bowers, Hydration of protonated primary amines:effects of intermolecular and intramolecular hydrogen bonds, Int. J. MassSpectrom. 236 (2004) 81–90.

[43] S.D. Elliott, R. Ahlrichs, An ab initio study of the monoxides and dioxides ofsodium, J. Chem. Phys. 109 (1998) 4267–4280.

[44] A.D. Buckingham, R.L. Disch, D.A. Dummer, Quadrupole moments of somesimple molecules, J. Am. Chem. Soc. 90 (1968) 3104–3107.

[45] J.N. Dawoud, I.I. Fasfous, A.F. Majdalawieh, A density functional theory study ofthe Cu+�O2 and Cu+�N2 adducts, Z. Naturforsch B 67 (2012) 118–126.

[46] R.J. Celotta, R.A. Bennett, J.L. Hall, M.W. Siegal, J. Levine, Molecular photo-detachment spectrometry. II. The electron affinity of O2 and the structure ofO�2 , Phys. Rev. A 6 (1972) 631–642.

[47] L. Andrews, Infrared spectra and bonding in the sodium superoxide andsodium peroxide molecules, J. Phys. Chem. 73 (1969) 3922–3928.


author's personal copy - hashemite university · 2016. 4. 20. · author's personal copy structure...

Documents