17696 Phys. Chem. Chem. Phys., 2011, 13, 17696–17703 This journal is c the Owner Societies 2011

Cite this: Phys. Chem. Chem. Phys., 2011, 13, 17696–17703

Quantum-chemical predictions of redox potentials of carbamates in

methanolw

Luisa Haya,aFrancisco J. Sayago,

bAna M. Mainar,

aCarlos Cativiela

band

Jose S. Urieta*a

Received 16th May 2011, Accepted 16th August 2011

DOI: 10.1039/c1cp21576k

Redox potentials for two stepwise anodic oxidations of a series of carbamates in methanolic

solution have been calculated using ab initio and DFT quantum mechanical methods.

Hartree–Fock method and Density Functional Theory at the B3LYP level, together with

6-31G(d), 6-31G(d,p) and 6-311++G(2df,2p) basis sets have been used for the calculation. The

Polarizable Continuum Model (PCM) is used to describe the solute–solvent interactions of

carbamates, and those of their radical-cations and cations. Linear relationships were observed

between the theoretically predicted redox potential values and the corresponding anodic peak

potentials obtained by cyclic voltammetry or the corresponding calculated energies of the Highest

Occupied Molecular Orbital (HOMO) of these carbamates.

Introduction

Electroorganic synthesis represents an attractive, low cost synthetic

method for producing small-scale, high purity compounds of high

added value. Electrode reactions allow the generation under mild

conditions of radical cations and radical anions of neutral species

that can be the starting point of a wide variety of synthetic

transformations. In many cases, it is also possible to achieve good

yields in processes that are impossible or very difficult to carry out

by means of conventional reactions.1

The electrochemical oxidation of carbamates in methanol has

been investigated as a synthetic route for the generation and

trapping of N-acyliminium cations, this being an alternative

way to reduce N-alkoxycarbonyllactams.2 In fact, the anodic

oxidation of carbamates in methanol usually yields several types

of products,3 the main one being the a-methoxylated derivative.

The a-methoxylated carbamates are versatile intermediates for

functionalization in a-positions to nitrogen. Subsequent

treatments allow the introduction of a broad variety of

nucleophiles in a-positions. Some of these can be converted

into their corresponding amino acids,4,5 being useful building

blocks in peptide synthesis.6

The mechanism of the electrochemical oxidation of carbamates

has been previously proposed by Shono et al.3 As an example,

Fig. 1 shows the steps corresponding to the electrochemical

a-methoxylation of tert-butyl pyrrolidine-1-carboxylate. The first

step is an electron transfer that yields a carbocation radical. This

carbocation radical loses a second electron and a proton to give the

N-acyliminium cation, which immediately reacts with methanol.

Although this mechanism is well established, to the best of

our knowledge, the redox potentials and the kinetic para-

meters involved in these a-methoxylation processes have never

been reported.

Fig. 1 a-Methoxylation of tert-butyl pyrrolidine-1-carboxylate.

a Group of Applied Thermodynamics and Surfaces (GATHERS),Aragon Institute for Engineering Research (I3A), Facultad deCiencias, Universidad de Zaragoza, Zaragoza 50009, Spain.E-mail: urieta@unizar.es; Fax: +34 976 761 202;Tel: +34 976 761 298

bAmino Acids & Peptides Group, Department of Organic Chemistry,Instituto de Ciencia de Materiales de Aragon, Universidad deZaragoza-CSIC, 50009 Zaragoza, Spain.E-mail: cativiela@unizar.es; Fax: +34 976 761 210;Tel: +34 976 761210

w Electronic supplementary information (ESI) available. See DOI:10.1039/c1cp21576k

PCCP Dynamic Article Links

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This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 17696–17703 17697

In electrode processes, the tendency of an electroactive

substance to undergo electron transference is given by its

redox potential. The knowledge of this potential is a key to

understanding the process and is very useful for optimizing the

efficiency and selectivity of the reaction.

The formal redox potential can be obtained directly from

potentiometric measurements when the systems are reversible

in the electrochemical sense. However, for irreversible systems

this direct measurement is not possible and, in this case,

theoretical calculations can be used to obtain adequate

estimations of the redox potentials.

Some research groups have demonstrated an excellent

concordance between experimental and calculated standard

redox potentials for several series of reversible systems.7–11

However, to the best of our knowledge, these studies have never

been applied to chemical and electrochemically irreversible

processes, as in the case of the electrochemical oxidation of

carbamates.

In this work, the theoretical redox potentials have been

obtained by means of calculations using the appropriate thermo-

dynamic cycles together with Hartree–Fock (HF) method and

Density Functional Theory (DFT) at the B3LYP level, and

6-31G(d), 6-31G(d,p) and 6-311++G(2df,2p) basis sets.

Self-consistent reaction field (SCRF) has been used to describe

the solute–solvent interactions.

Additionally, cyclic voltammetry experiments have been

carried out to obtain information about the irreversible

character of the process. The voltammograms have also been used

to test the theoretical values of the oxidation potentials of

carbamates. Moreover, correlations have been established between

the experimental peak potentials in the voltammograms and the

theoretical oxidation potential values or the HOMO energies

of the electroactive species. These correlations are valuable

tools that can be used for a quick estimation of the redox

potentials of similar carbamates.

Experimental and theoretical calculation

Materials

Carbamates were selected (Fig. 2) on the bases of different

structures. In this context, acyclic, cyclic, bicyclic or aromatic

compounds were taken into account. All substrates were prepared

following standard procedures involving the corresponding

commercially available amine with di(tert-butyl) dicarbonate

and (dimethylamino)pyridine (DMAP) in THF, using classical

protecting methodologies common in organic chemistry.

All compounds were identified by spectroscopical data and

their purity (499%) was confirmed on the basis of analytical

measurements.

For the voltammetric experiments, the supporting electrolyte,

tetrabutylammonium perchlorate (TBAP) (purity Z 99%),

methanol (purity Z 99.8%), silver nitrate (purity Z 99.5%)

and a silver wire (purity Z 99,99%) were supplied by Fluka,

Panreac, Prolabo and Goodfellow, respectively.

Instrumentation

The cyclic voltammograms were obtained using a potentiostat

V2.1, custom-built by the Scientific Instrument Service of the

University of Zaragoza. Validation of this potentiostat was

carried out using the potassic ferrocyanide/ferricyanide redox

couple (Eo0 = 0.253 V vs. Ag/AgCl (sat.)).12

An undivided standard three electrode Pyrex cell (90 ml,

Metrohm) was used, the working electrode and the counter

electrode being a glassy carbon (GC) disk (3 mm diameter)

and a Pt disk (3 mm diameter), respectively.

The electrolyte voltammetric cell solutions consisted of

6 mM carbamate solutions with a supporting electrolyte

(0.1 M) in methanol. The cyclic voltammograms were carried

out in a potential range from �1 V to 2 V and a scan rate

between 5 mV s�1 and 400 mV s�1. All the electrolytic

solutions were deaerated with Ar for at least 10 min.

Electrodes preparation

In order to prevent potential drift in the liquid–liquid junction,

conventional aqueous reference electrodes were avoided and a

suitable organic electrode was built. This consisted of a pure silver

wire (1 mm diameter) immersed in a solution of silver nitrate

(0.01 M) and supporting electrolyte (tetrabutylammonium

perchlorate, 0.1 M) using methanol as a solvent. This reference

electrode was extended to the vicinity of the working electrode

surface by means of a Luggin capillary containing a solution

of the supporting electrolyte in methanol (0.1 M).

The GC and Pt electrodes were polished at the beginning of

each experiment with alumina suspension (particle size = 0.1 mmMetrohm) and were rinsed thoroughly with water to obtain a

clean renewed electrode surface.

Computational studies

The absolute values of redox potentials of carbamates were

calculated using the thermodynamic cycles shown in Fig. 3,

where DGog and DGo

sol are the standard variation of the Gibbs

energy related to the process taking place in gas and liquid

Fig. 2 Reduced form of the carbamates studied.

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17698 Phys. Chem. Chem. Phys., 2011, 13, 17696–17703 This journal is c the Owner Societies 2011

phase, respectively, and DGosolv,i are the solvation energies, that

is, the variation of the Gibbs energy that corresponds to the

process of transferring the molecule i from gas to liquid phase,

keeping temperature and pressure constant.

The total change in standard Gibbs energy for each

half-electrode reaction is given by eqn (1) and (2) respectively:

DGo(sol,I) = DGo

(g,I) + DGo(solv,Ox1) � DGo

(solv,Red1) (1)

DGoðsol;IIÞ ¼ DGo

ðg;IIÞ þ DGoðsolv;Ox2Þ þ DGo

ðsolv;HþÞ � DGoðsol;Ox1Þ

ð2Þ

These changes in Gibbs energy for each oxidation half-

reaction are related to the standard redox potentials, Eo,

according to eqn (3):

Eo = �DGosol/nF (3)

where n is the number of electrons transferred to the electro-

active species (n = �1, in our case) for each reaction, and F is

the Faraday constant.

Considering the size of the molecules studied, the optimizations

of their structures in the gas phase were performed at the HF/

6-31G(d) level. The calculations of the Gibbs energies for the two

gas-phase oxidation processes, DGog, were obtained at two

different levels of theory, HF and B3LYP using three basis

sets, 6-31G(d), 6-31G(d,p) and 6-311++G(2df,2p). The

Polarizable Continuum Model (PCM)13,14 of solvation was

used to calculate the solvation energies, DGosolv,i. The zero-point

energies and thermal corrections together with entropies were

used to convert the internal energies of radical carbocations,

cations and neutral species to the Gibbs energies at 298.15 K.15

All quantum theoretical calculations were performed by

using the Gaussian 09.16

Results and discussion

Cyclic voltammetry

The voltammogram in Fig. 4(a) shows the background current

levels in the absence of carbamates, while voltammograms in

Fig. 4(b–h) belong to the selected carbamates (1–7), at scan

rate 100 mV s�1. For carbamates 2–7 (Fig. 4(c–h)), a single

wave is observed at all scan rates. Anodic peaks appear at

1.20 V, 1.43 V, 1.47 V, 1.50 V, 1.55 V and 1.60 V, respectively.

According to the mechanism proposed, and the nature of the

chemical species involved in the oxidation processes, these

peaks can be assigned to the first one-electron transfer step.

A different behaviour can be observed in the voltammogram

shown in Fig. 4(b) corresponding to tert-butyl indoline-1-

carboxylate (1), in which two oxidation peaks appear. The

first peak potential (Epa = 0.90 V) can be assigned to the first

oxidation step generating a radical carbocation of 1, whereas

the second oxidation peak (Epa = 1.23 V) could be associated

with the oxidation peak of carbamate 2 (Fig. 4(c)) easily

obtained from 1 under the experimental conditions.

The effect of the scan rate was considered. When the scan

rate increases, the anodic peak potentials shift 0.15 V in the

positive direction for each tenfold increase in the scan

rate. According to Bard and Faulkner,18 this fact indicates

the non-reversible electrochemical character of the considered

process.

Redox potentials

Tables 1 and 2 show the gas phase Gibbs energy, Gog, the

calculated solvation energies of the species involved in the

thermodynamic cycles, DGosolv,i, and the total change in Gibbs

energy of the half-reactions, DGosol, together with the resulting

calculated absolute electrode potentials, Eabs.

According to the PCM model, the solvation energy involves

electrostatic and non-electrostatic interactions between solute and

solvent. The non-electrostatic term includes cavity formation

energy, dispersion and repulsion energies. A detailed revision

of the model has been carried out by Tomasi et al.19 The

required value of the e parameter for methanol (32.613) is

gathered in Gaussian 09.

Tables 1 and 2 show the second absolute redox potential,

E(II), as a criterion of consistency between the experimental

measurements and theoretical calculations. At any level of

theory used in this work, the calculated formal potential Eabs(II)

is lower than Eabs(I), and the reaction rate is determined by the

first step.20 These results are consistent with the electrode

kinetics since only one single irreversible wave appears in the

voltammograms (Fig. 4(c–h)).

In order to compare the theoretical absolute values of the redox

potentials (Tables 1 and 2) to the experimental anodic peak

potentials measured versus an Ag/Ag+ (0.01 M, methanol), it

is necessary to convert all absolute values of electrode

potentials to the relative scale of the Ag/Ag+ electrode used

as reference. To carry out this conversion, initially a value of

5.24 V for the absolute standard potential of the Ag/Ag+ (aq)

electrode has been adopted.21 Then, the absolute potential of

the reference electrode in methanol can be obtained from this

value by means of the following equation:

EoðAgþ=AgÞaqAbs�EoðAgþ=AgÞmetAbs ¼ ða

o;aq

Agþ�ao;met

AgþÞ=nF ð4Þ

where, Eo(Ag+/Ag)Abs is the absolute standard electrode

potential of the system Ag/Ag+ and ao is the real solvation Gibbs

energy of Ag+. Superscripts aq and met denote the solvents used,

water and methanol, respectively. The corresponding values

employed for ao;aqAgþ

and ao;met

Agþare �114.4 kcal mol�1 and

�120.8 kcal mol�1.22 Finally, the redox potential of the

Ag/Ag+ (0.01 M, methanol) electrode is obtained from

Eo(Ag+/Ag)Abs using the Nernst equation. The necessary

Fig. 3 Thermodynamic cycles of two half-reaction for oxidation of

carbamates.

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activity coefficient value of the Ag+ ion 0.01 M in methanolic

solution containing 0.1 M tetrabutylammonium perchlorate is

estimated by using an adequate version of the Bates–Guggenheim23

approximation to the Debye–Huckel equation. The permittivity

of methanol is considered and additional linear term on the

ionic strength with a coefficient 0.124 is included. Anyways, the

deviation when using concentration in the Nernst equation

instead of activity is inside the uncertainty of the constant to

convert absolute to relative potentials.

The calculated formal redox potential of the studied

carbamates, referred to the conventional standard electrode

Ag/Ag+ (0.01 M, methanol) can be seen in Table 3. According

to the data reported in this table, HF and B3LYP levels provide

significantly different values. Considering the voltammograms

in Fig. 4(b–h), the values obtained with the HF level seem to be

too negative, according to the values of the potential where the

intensities begin to be significant.

Additionally, the B3LYP level takes into account the elec-

tronic effects due to the presence of p-systems and/or hetero-

atom-containing compounds. Then, it can be concluded that

the B3LYP level is more suitable than the HF level.

On the other hand, the basis set 6-311++G(2df,2p)

provides values that are too large for the redox potential,

exceeding for several systems the corresponding experimental

peak potentials. This is in spite of the large amounts of

computational resources used by this basis set. The values

obtained by using the B3LYP level and 6-31G(d) and

6-31G(d,p) basis sets are both very similar and seem to be

the most adequate. Moreover, our calculations with the

B3LYP level and 6-31G(d) basis set give the best results when

compared with the experimental results for the standard

reversible system quinone/hydroquinone. The theoretical

potential value vs. NHE is 0.655 V and the experimental value

0.700 V.25

For the carbamates included in this work, the theoretical

interval of formal redox potentials vs. the electrode Ag/Ag+

(0.01 M, methanol) is from 0.60 V to 1.52 V with B3LYP/

6-31G(d) and from 0.61 V to 1.51 V with B3LYP/6-31G(d,p).

It is noteworthy that the knowing of the redox potentials is

important, and the computational procedure appears to be a

valuable tool for the estimation of the most favourable

position for the introduction of the nucleophiles.

Fig. 4 (a) Background current levels in the absence of carbamates, and cyclic voltammograms of 6 mM carbamates: (b) tert-butyl indoline-1-carboxylate

(1), (c) tert-butyl 1H-indole-1-carboxylate (2), (d) tert-butyl (S,S)-octahydro-1H-indole-1-carboxylate (3), (e) tert-butyl piperidine-1-carboxylate (4),

(f) tert-butyl pyrrolidine-1-carboxylate (5), (g) tert-butyl diethylcarbamate (6), and (h) 1-tert-butyl 2-methyl (S)-pyrrolidine-1,2-dicarboxylate (7). Scan rate

100 mV s�1, with tetrabutylammonium perchlorate as supporting electrolyte, glassy carbon (GC) as working electrode, Pt as counter electrode and

Ag/Ag+ (0.01 M, methanol) in methanol as reference electrode.Publ

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17700 Phys. Chem. Chem. Phys., 2011, 13, 17696–17703 This journal is c the Owner Societies 2011

Table 1 Gas-phase Gibbs energies, Go(g), calculated at the levels of HF/6-31G(d), HF/6-31G(d,p) and HF/6-311++G(2df,2p), and PCM solvation

energies, DGo(solv), of the species involved in the oxidation processes, together with the total changes of Gibbs energy, DGo

(sol), and the absoluteoxidation potentials, Eabs, of the two-half reactions

No.b

Go(g)

a DGo(solv)/kJ mol�1 DGo

(sol)c/kJ mol�1 Eabs/V

Ox1 Red1d Red2 Ox1 Red1

d Red2 (I) (II) (I) (II)

6-31G(d) 6-31G(d) 6-31G(d) 6-31G(d)1 �706.14341 �705.92637 — �23.2 �169.5 — 423.5 — 4.390 —2 �704.99980 �704.77452 — �21.3 �180.5 — 432.3 — 4.480 —3 �709.56880 �709.31769 — �18.4 �175.4 — 502.2 — 5.205 —4 �593.69549 �593.43867 �592.90238 �18.6 �182.4 �191.3 510.4 270.4 5.290 2.8035 �554.68878 �554.43058 �553.89315 �20.6 �190.3 �195.9 508.1 276.7 5.266 2.8676 �555.82973 �555.57089 �555.02536 �17.7 �183.4 �193.1 513.9 293.9 5.327 3.0467 �781.29070 �781.03027 �780.49394 �33.9 �185.2 �195.1 532.4 269.5 5.518 2.793

6-31G(d,p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)1 �706.17268 �705.95597 — �23.3 �169.4 — 422.9 — 4.383 —2 �705.02650 �704.80133 — �21.2 �180.3 — 432.1 — 4.478 —3 �709.60658 �709.35608 — �18.4 �175.2 — 500.9 — 5.192 —4 �593.72693 �593.47074 �592.93310 �18.6 �182.2 �191.1 509.0 273.9 5.276 2.8395 �554.71697 �554.45947 �553.92063 �20.5 �189.9 �195.8 506.7 280.1 5.252 2.9036 �555.86158 �555.60338 �555.05650 �17.9 �183.6 �192.9 512.2 297.8 5.309 3.0877 �781.32240 �781.06259 �780.52494 �34.2 �185.1 �195.0 531.2 272.9 5.506 2.829

6-311++G(2df,2p) 6-311++G(2df,2p) 6-311++G(2df,2p) 6-311++G(2df,2p)1 �706.36993 �706.14841 — �23.8 �170.6 — 434.8 — 4.506 —2 �705.22654 �704.99654 — �21.3 �181.2 — 446.4 — 4.627 —3 �709.79708 �709.54563 — �19.3 �176.4 — 503.1 — 5.214 —4 �593.89188 �593.63392 �593.09772 �19.2 �184.0 �191.4 512.5 271.7 5.312 2.8165 �554.87339 �554.61392 �554.07632 �21.7 �191.7 �196.1 511.3 278.3 5.299 2.8846 �556.01888 �555.75961 �555.21410 �19.3 �187.0 �193.5 513.0 297.0 5.317 3.0787 �781.55458 �781.29267 �780.75612 �34.8 �185.9 �196.5 687.7 269.8 5.562 2.796

a Energies are in atomic units, Hartree (1 Hartree = 2623.61722 kJ mol�1). b For the list of studied carbamates, see Fig. 1. c Solvation Gibbs

energies for H+ in methanol is �1103.3 kJ mol�1.17 d The values of the electron spin operator hS2i for the radical cations were between 0.78 and

0.75 at UHF level.

Table 2 Gas-phase Gibbs energies, Go(g), calculated at the levels of B3LYP/6-31G(d), B3LYP/6-31G(d,p) and B3LYP/6-311++G(2df,2p), and

PCM solvation energies, DGo(solv), of the species involved in the oxidation processes, together with the total changes of Gibbs energy, DGo

(sol), andthe absolute oxidation potentials, Eabs, of the two-half reactions

No.b

Go(g)

a DGo(solv)/kJ mol�1 DGo

(sol)c/kJ mol�1 Eabs/V

Ox1 Red1d Red2 Ox1 Red1

d Red2 (I) (II) (I) (II)

6-31G(d) 6-31G(d) 6-31G(d) 6-31G(d)1 �710.62090 �710.36464 — �19.2 �165.4 — 526.6 — 5.458 —2 �709.43534 �709.16837 — �16.7 �168.1 — 549.5 — 5.696 —3 �714.17290 �713.89083 — �15.1 �171.8 — 583.9 — 6.052 —4 �597.50219 �597.21622 �596.66410 �14.9 �176.7 �181.4 589.0 316.2 6.105 3.2775 �558.21274 �557.92343 �557.37152 �17.1 �183.9 �186.1 592.7 318.1 6.143 3.2976 �559.40222 �559.11199 �558.55478 �15.0 �177.8 �183.6 599.2 328.4 6.210 3.4047 �786.04838 �785.75976 �785.20671 �28.9 �172.3 �184.0 614.4 311.6 6.368 3.230

6-31G(d,p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)1 �710.64639 �710.39012 — �19.0 �165.3 — 526.5 — 5.457 —2 �709.45850 �709.19129 — �16.5 �168.0 — 550.1 — 5.701 —3 �714.20640 �713.92451 — �14.9 �171.5 — 583.5 — 6.048 —4 �597.52973 �597.24385 �596.69062 �14.9 �176.6 �181.5 588.8 318.8 6.103 3.3055 �558.23732 �557.94834 �557.39505 �17.1 �183.7 �186.0 592.1 321.6 6.137 3.3336 �559.42983 �559.13979 �558.58140 �14.9 �177.5 �183.4 598.9 331.4 6.207 3.4357 �786.07585 �785.78736 �785.23321 �29.0 �172.9 �183.6 613.5 315.5 6.359 3.270

6-311++G(2df,2p) 6-311++G(2df,2p) 6-311++G(2df,2p) 6-311++G(2df,2p)1 �710.85935 �710.59376 — �20.6 549.6 — 5.6962 �709.67342 �709.39661 — �18.0 573.9 — 5.9483 �714.41355 �714.12487 — �17.3 �171.3 — 604.0 — 6.2604 �597.70862 �597.41523 �596.86370 �17.4 �179.0 �182.5 608.7 315.8 5.308 3.2735 �558.40720 �558.11043 �557.55855 �19.3 �170.7 �175.9 627.8 315.0 6.507 3.2656 �559.60062 �559.30260 �558.74909 �16.9 �178.2 �182.9 621.2 319.7 6.439 3.3147 �786.32564 �786.02799 �785.47611 �31.8 �178.9 �189.6 634.4 309.9 6.575 3.212

a Energies are in atomic units, Hartree (1 Hartree = 2623.61722 kJ mol�1). b For the list of studied carbamates, see Fig. 1. c Solvation Gibbs

energies for H+ in methanol is �1103.3 kJ mol�1.17 d The values of the electron spin operator hS2i for the radical cations were between 0.76 and

0.75 at UB3LYP level.

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Predictive methodologies

Cyclic voltammetry provides a great deal of information about

electrochemical systems and processes. In reversible redox

processes the corresponding oxido-reduction potential can be

obtained experimentally from anodic and cathodic peak

potentials, but this direct measure is not possible when the

electrochemical processes are irreversible.

Assuming that, the oxidation peak corresponds to a single

irreversible step oxidation, that is, a pure electrochemical step,

the following relation between the formal redox potential, Eo0,

and the anodic peak potential, Epa, can be established:18

Epa ¼ Eo 0 þ RT

ð1� aÞnaF0:780þ ln

D1=2Red

ko

!þ ln

ð1� aÞFuRT

� �1=2" #

ð5Þ

where a is the transfer coefficient, na is the number of electrons

involved in the rate determining step (being 1 in our case),

DRed is the diffusion coefficient of the species reduced, ko is the

standard rate constant, u is the linear potential scan rate, and

T, F and R have their usual meanings.

A similar equation can be reported for an opposite reduction

reaction with the same characteristics. However, for irreversible

processes, the equation is not practical for a direct determination

of Eo0 from the experimental Epa, because the kinetic

parameters should be previously known.

Due to the difficulties in predicting kinetic and thermo-

dynamic parameters for an irreversible electrochemical process, it

may be useful to establish a correlation between the computational

redox potential, Eo, and the anodic peak potential, Epa,

experimentally obtained. In fact, a linear correlation:

Epa = a + bEo (6)

has been presented previously for several reversible

processes.26

In this work we report a correlation which is referred to the

first electron step because only the peak corresponding to

this transfer appears. Fig. 5 shows the anodic peak potential

vs. calculated redox potentials related to Ag/Ag+ (0.01 M,

methanol) together with their lineal regression.

Table 3 Formal potentials for the two half-reactions of carbamatesoxidation (vs. Ag/Ag+ (0.01 M, methanol))

No.a Eo0(I)b Eo0(II)b Eo0(I)b Eo0(II)b

HF/6-31G(d) B3LYP/6-31G(d)1 �0.46 — 0.60 —2 �0.37 — 0.85 —3 0.36 — 1.20 —4 0.44 �2.05 1.26 �1.575 0.42 �1.98 1.29 �1.556 0.48 �1.80 1.36 �1.457 0.67 �2.06 1.52 �1.62

HF/6-31G(d,p) B3LYP/6-31G(d,p)1 �0.47 — 0.61 —2 �0.37 — 0.85 —3 0.34 — 1.20 —4 0.43 �2.01 1.25 �1.545 0.40 �1.95 1.29 �1.526 0.46 �1.76 1.36 �1.427 0.66 �2.02 1.51 �1.54

HF/6-311++(2df,2p) B3LYP/6-311++(2df,2p)1 �0.34 — 0.85 —2 �0.22 — 1.10 —3 0.36 — 1.41 —4 0.46 �2.03 1.46 �1.585 0.45 �1.97 1.66 �1.586 0.47 �1.47 1.59 �1.547 0.71 �2.05 1.72 �1.64a For the list of studied carbamates, see Fig. 1. b Redox potentials are

in volts.

Fig. 5 Anodic peak potentials of studied carbamates vs. formal redox potential (a) HF/6-31G(d), (b) HF/6-31G(d,p), (c) HF/6-311++G(2df,2p),

(d) B3LYP/6-31G(d), (e) B3LYP/6-31G(d,p), (f) B3LYP/6-311++G(2df,2p).

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17702 Phys. Chem. Chem. Phys., 2011, 13, 17696–17703 This journal is c the Owner Societies 2011

Good correlations were obtained for the several computation

procedures, especially for that considered as the best, B3LYP/

6-31G(d) and B3LYP/6-31G(d,p), being R2 = 0.97 in both

cases. These linear correlations can be used to predict the

formal redox potential for carbamates with a similar structure

to those considered in this work from the voltammetric peak

potentials.

On the other hand, some authors, such as Winget et al.,27

have found that for reversible oxidation processes, a reasonable

linear correlation can be given between oxidation peak

potentials and the HOMO energies of the reduced species:

Epa = c + dEHOMO (7)

In this context, it must be pointed out that the calculation of the

HOMO energies is much less time consuming in computational

effort than in the case of redox potentials. For these, a large

amount of computational resources are necessary.

Correlation (7) also works well in the case of our

carbamates (R2 = 0.97 for the B3LYP/6-31G(d) method,

and R2 = 0.96 for the B3LYP/6-31G(d,p) method).

From eqn (6) and (7), a new correlation can be proposed:

EHOMO = e + f Eo (8)

This equation is consistent with the fact that the first

electrochemical reaction satisfies the requirements of Koopman’s

theorem,28 and thatDGosolv,i are low compared with theDGo

g values.

Fig. 6 shows the linear correlations between the formal

redox potential, Eo, and HOMO energies for our carbamates

calculated with the B3LYP/6-31G(d) and B3LYP/6-31G(d,p)

methods, being R2 0.99 and 0.97, respectively. The level and

basis sets used were previously considered as the most

adequate for the calculation of Eo, and they also provide the

best correlations EHOMO vs. Eo. The slope of the correlations is

experimentally consistent; the most easily oxidizable species

have higher HOMO energies.

According to the frontier molecular orbital theory, for

electrochemical oxidations, the electron is withdrawn from

the atoms where the HOMO orbital is localized. In our

compounds the HOMO orbitals are localized in the carbamate

group. In compounds tert-butyl (S,S)-octahydro-1H-indole-1-

carboxylate (3), tert-butyl piperidine-1-carboxylate (4), tert-butyl

pyrrolidine-1-carboxylate (5) and tert-butyl diethylcarbamate (6)

the influence of the neighbour groups (–CH2– and –CHz) on

the HOMO orbital should be similar. For molecules tert-butyl

indoline-1-carboxylate (1) and tert-butyl 1H-indole-1-carbo-

xylate (2) quantum chemical calculations show that the

HOMO orbital is localized in the carbamate group and on

the aromatic ring. The influence of a conjugated system

increases the electron density and raises the HOMO energy

and, as a consequence, the redox potential decreases. In contrast,

in the tert-butyl 2-methyl (S)-pyrrolidine-1,2-dicarboxylate (7)

the methoxycarbonyl group is an electron withdrawing group

and decreases the HOMO energy increasing the redox potential.

The previous correlations could be extended to other

families of compounds. The correlations are useful for a faster

calculation of the redox potential of similar carbamates.

Conclusions

The calculation of the redox potentials of some totally

irreversible systems in a non-aqueous solvent (methanol) has

been carried out using Hartree–Fock and density functional

theory at the B3LYP level and employing 6-31G(d), 6-31G(d,p)

and 6-311++G(2df,2p) as basis sets. The PCM solvation model

has been used to calculate the solvation energies.

At any level of theory used in this work, the calculated

formal potential Eabs(II) is lower than Eabs(I). These results are

in agreement with the experimental cyclic voltammograms in

which only a single irreversible wave merged.

A good linear relationship has been found between anodic peak

potentials and redox potentials for a series of carbamates. Also, in

order to achieve a faster calculation of the Eo of carbamates with

similar structures, we have proposed a correlation between formal

calculated redox potential and HOMO energy.

The best results for these systems were obtained using the

B3LYP level and 6-31G(d) and 6-31G(d,p) basis sets which,

moreover, require moderate computational resources.

Acknowledgements

Financial support from the Spanish Ministry of Science and

Innovation—FEDER (grants CTQ2010-17436 and CTQ2009-

14629-C02-02) and the Regional Government of Aragon

(research group E40 and E52) is gratefully acknowledged.

Fig. 6 Formal redox potential vs. HOMO energy (a) B3LYP/

6-31G(d), (b) B3LYP/6-31G(d,p).

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This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 17696–17703 17703

The authors acknowledge generous allocations of computer

time in Hermes Cluster from the Aragon Institute for

Engineering Research (I3A)—Universidad de Zaragoza.

Notes and references

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