Experimental and Computational Thermochemical ... - ACS Publications

10530

J. Phys. Chem. B 2010, 114, 10530–10540

Experimental and Computational Thermochemical Study of Sulfur-Containing Amino Acids: L-Cysteine, L-Cystine, and L-Cysteine-Derived Radicals. S-S, S-H, and C-S Bond Dissociation Enthalpies Maria Victoria Roux,* Concepcioń Foces-Foces, and Rafael Notario Instituto de Quı´mica Fı´sica “Rocasolano”, CSIC, Serrano 119, 28006 Madrid, Spain

Manuel A. V. Ribeiro da Silva,* Maria das Dores M. C. Ribeiro da Silva, and Ana Filipa L. O. M. Santos Centro de InVestigaçaõ em Quı´mica, Department of Chemistry, Faculty of Science, UniVersity of Porto, Rua do Campo Alegre, 687, P-4169-007 Porto, Portugal

Eusebio Juaristi Departamento de Quı´mica, Centro de InVestigacioń y de Estudios AVanzados del IPN, Apartado Postal 14-740, 07000 Me´xico D.F., Me´xico ReceiVed: March 22, 2010; ReVised Manuscript ReceiVed: June 16, 2010

This paper reports an experimental and theoretical study of the standard (p° ) 0.1 MPa) molar enthalpies of formation at T ) 298.15 K of the sulfur-containing amino acids L-cysteine [CAS 52-90-4] and L-cystine [CAS 56-89-3]. The standard (p° ) 0.1 MPa) molar enthalpies of formation of crystalline L-cysteine and L-cystine were calculated from the standard molar energies of combustion, in oxygen, to yield CO2(g) and H2SO4 · 115H2O, measured by rotating-bomb combustion calorimetry at T ) 298.15 K. The vapor pressures of L-cysteine were measured as function of temperature by the Knudsen effusion mass-loss technique. The standard molar enthalpy of sublimation, at T ) 298.15 K, was derived from the Clausius-Clapeyron equation. The experimental values were used to calculate the standard (p° ) 0.1 MPa) enthalpy of formation of L-cysteine in the gaseous phase, ∆fH°m(g) ) -382.6 ( 1.8 kJ · mol-1. Due to the low vapor pressures of L-cystine and since this compound decomposes at the temperature range required for a possible sublimation, it was not possible to determine its enthalpy of sublimation. Standard ab initio molecular orbital calculations at the G3(MP2)//B3LYP and/or G3 levels were performed. Enthalpies of formation, using atomization and isodesmic reactions, were calculated and compared with experimental data. A value of -755 ( 10 kJ · mol-1 was estimated for the enthalpy of formation of cystine. Detailed inspections of the molecular and electronic structures of the compounds studied were carried out. Finally, bond dissociation enthalpies (BDE) of S-H, S-S, and C-S bonds, and enthalpies of formation of L-cysteine-derived radicals, were also computed. 1. Introduction Structure and energetics are two of the most fundamental and, therefore, important concepts in modern chemistry,1 and they have been studied by a variety of experimental and theoretical methods. The energy of a compound, along with its molecular structure, represents the most important properties by which it may be characterized. Knowledge of energies is essential for studies of chemical equilibrium, kinetics, and stability of molecules. The enthalpy of formation of a molecule is the thermochemical property that permits the evaluation of the feasibility of putative reaction paths in a synthetic process, i.e., to determine its thermodynamic viability. Thus, thermochemical information such as enthalpies of formation is useful for the designs of synthetic strategies that will allow the preparation of a desired product in good yields and under suitable conditions. In principle, analysis of the energetics associated with a particular synthetic route also permits the elimination of * To whom correspondence should be addressed. E-mail: victoriaroux@ iqfr.csic.es (M.V.R.); [email protected] (M.A.V.R.d.S.).

competing reaction paths with the concomitant reduction in the cost of the process and minimal formation of undesirable side products. Quantitative data on the molecular enthalpies of formation have been traditionally obtained from experiments2-4 or, because of the impossibility of experimentally measuring all known compounds, by means of additivity methods,2 or more recently via computational methodologies.5-9 Nevertheless, it should be pointed out that the accuracy of theoretical calculations can be only judged by a comparison to accurate experimental results. The aim of this work is to determine the gas-phase enthalpy of formation of the sulfur-containing amino acid L-cysteine and its corresponding dimer L-cystine, which is composed of two cysteine units joined by a disulfide bond (shown in Figure 1). Both molecules are components in proteins and polypeptides. Cysteine is the only amino acid with a reactive sulfur moiety, the side chain being a thiol group. The strong nucleophilicity of cysteine makes it a key component of the active site in many enzymes.10,11 The thiol is susceptible to oxidization to give the disulfide derivative cystine, which serves an important structural

10.1021/jp1025637  2010 American Chemical Society Published on Web 07/23/2010

Thermochemical Study of S-Containing Amino Acids

J. Phys. Chem. B, Vol. 114, No. 32, 2010 10531

Figure 1. Schematic formulas of cysteine (1) and cystine (2).

role in many proteins. Indeed, the prototype of a protein disulfide bond is cystine. The thiol-disulfide interchange reaction is important to a number of subjects in biochemistry,12,13 including the renaturing of proteins and stabilization of proteins in solution. Thus, thermodynamic data regarding the relative energetics of the thiol and disulfide functional groups is essential for understanding the driving force and mechanism of biochemical processes. Disulfide bonds are important cross-linking groups that result during the vulcanization of rubber. Cysteine is essential for the production of glutathione, γ-glutamylcysteinylglycine, a ubiquitous tripeptide which plays a number of vital roles in maintaining the redox balance in the cell, and thus affects growth, differentiation, and proliferation of cells.14 It is also critical for the metabolism of a number of essential biochemicals, including coenzyme A, heparin, biotin, and lipoic acid.15 Cysteine is the most effective amino acid at scavenging radicals in solution, attributable to the ease with which it forms a radical at the sulfur atom.16 Cystine has been shown to protect the body against damage induced by alcohol and cigarette smoking as a detoxification agent.17 Of special interest is the determination, from thermochemical data, of the bond dissociation enthalpy of the S-S bond in cystine. The disulfide linkage plays an important role in determining the biological activity of numerous proteins, enzymes, and antibiotics. Covalent disulfide bonds are important determinants of the shapes of proteins because S-S bonds between cysteine residues stabilize folded conformations.18,19 Covalent linkages of amino acids in proteins are largely limited to the peptide bond. The most common exception to this rule is the disulfide bond, a sulfur-sulfur chemical bond that results from an oxidative process that generally links nonadjacent cysteine residues to a protein. Proteins that contain disulfide bonds can be divided in two classes: those in which the cysteine-cysteine linkage is a stable part of their final folded structure and those in which pairs of cysteine residues interchange between the reduced and oxidized states. In the first class the disulfide bonds may contribute to the folding pathway of the protein and to the stability of the tertiary or quaternary structure of its native state.20 For the second, the oxidativereductive cycling of the disulfide bond may be central to a protein’s activity as an enzyme or may be involved in protein’s activation and deactivation.21-23 Disulfide bonds are critical for the maturation and stability of secretory and cell-surface proteins. In eukaryotic cells, disulfide bonds are introduced in the endoplasmic reticulum, when the redox conditions are optimal to support their formation.24 These bonds are often crucial for the stability of a final protein structure, and the mispairing of cysteine residues can prevent proteins from attaining their native conformation and lead to misfolding.25 Despite the importance of these amino acids, there are not reliable experimental data for their enthalpies of formation; the NIST Chemistry Webbook4 reports four experimental enthalpies of combustion of L-cysteine determined by Sabbah and Mi-

nadakis (-2248.8 ( 0.6 kJ · mol-1)26 and Sunner (-2267.7 ( 2.1 kJ · mol-1),27 both by rotating bomb combustion calorimetry, and by Huffman and Ellis (-2248.9 ( 2.1 kJ · mol-1)28 and Becker and Roth (-2229 ( 3 kJ · mol-1),29 both by static bomb combustion calorimetry. These values cover a range of ca. 39 kJ · mol-1. The situation of the available thermochemical data for L-cystine is even worse. The NIST Chemistry WebBook4 reports four old values for the standard enthalpy of combustion, -4248.0 ( 3.8, -4230.0 ( 3.8, -4201.2, and -4158.2 kJ · mol-1, given, respectively, by Sunner27 from rotating bomb combustion calorimetry and by Huffman and Ellis,28 Becker and Roth,29 and Emery and Benedict,30 these last three by static bomb combustion calorimetry. The values given by these authors cover a range of ca. 90 kJ · mol. In 1999, a surprisingly low value for the standard enthalpy of combustion of L-cystine (-3618.9 kJ · mol-1) was reported by Yang et al.31 In this paper, we report the standard (p° ) 0.1 MPa) molar energies of combustion in oxygen at T ) 298.15 K, determined by rotating bomb combustion calorimetry, for the two title amino acids. The Knudsen effusion mass-loss technique was used to measure vapor pressures as a function of temperature of L-cysteine. From the temperature dependence of the vapor pressure, the molar enthalpy and entropy of sublimation at the mean temperature of the experimental temperature range were derived, through the Clausius-Clapeyron equation. Standard molar enthalpy, entropy, and Gibbs energy of sublimation, at the temperature of T ) 298.15 K, were calculated using estimated values for the heat capacity differences between the gas and the crystal phases for L-cystine. From these values the standard molar enthalpy of formation in the gas state of L-cysteine was determined. For L-cystine it was not possible to determine the enthalpy of sublimation using the available techniques of Knudsen effusion or Calvet microcalorimetry due to the extremely low vapor pressure of this compound. G3(MP2)//B3LYP and/or G3 calculations were performed aiming to obtain additional thermochemical information about S-S bond dissociation enthalpy (BDE)32 in L-cystine and S-H and S-C bond dissociation enthalpies in L-cysteine. Finally, standard molar gas-phase enthalpies of formation, at T ) 298.15 K, for the two amino acids and for cysteine-derived radicals were also computed. 2. Experimental Section Compounds and Purity Control. L-Cysteine, [CAS 52-904] and L-cystine [CAS 56-89-3] were commercially available from Fluka (both BioUltra g99.5). The samples were carefully dried under vacuum and no further purification was performed. Differential Scanning Calorimetry. The behavior of the samples as a function of temperature was studied by differential scanning calorimetry. A DSC Pyris 1 instrument from PerkinElmer equipped with an intracooler unit was used to study the fusion process and the possible existence of phase transitions in the temperature intervals where the thermochemical measure-

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J. Phys. Chem. B, Vol. 114, No. 32, 2010

ments were made. The DSC calorimeter was previously calibrated in temperature and energy with reference materials. Temperature and power scales were calibrated33-37 at heating rates of 0.04 and 0.17 K s-1. The temperature scale was calibrated by the melting temperature of the high-purity reference materials: hexafluorobenzene, tin, and indium.36 The power scales were calibrated with high-purity indium.36 Thermograms of samples hermetically sealed in aluminum pans were recorded in a nitrogen atmosphere. All the pans with the samples were weighed on a Mettler AT21 microbalance with a detection limit of 1 × 10-6 g before and after the experiments to confirm that no product had volatilized. After calibration, several runs with high-purity benzoic acid and indium as reference materials36 were performed under the same conditions as the experimental determinations. The accuracies associated with temperature and enthalpy of fusion measurements were calculated as the percentage deviation of the experimental data with regard to the values given in the literature;36 in all the cases, these were lower than 0.2 and 2.0% for temperature and enthalpy determinations, respectively.37 Different scans at heating rates of 0.04 and 0.17 K · s-1 were performed to determine the possible existence of phase transitions in the samples over the temperature range from T ) 260 to 440 K and 500 K for L-cysteine and L-cystine, respectively. A fresh sample was used for each run. Combustion Calorimetry. The combustion experiments were performed with an isoperibolic rotating bomb calorimeter, as described previously in the literature38,39 The energy equivalent of the calorimeter was determined by combustion of benzoic acid, NIST Thermochemical Standard 39i, with a certified mass energy of combustion, under bomb conditions, of -26 434 ( 3 J · g-1,40 according to the procedure described by Coops et al.41 The calibration results were corrected to give the energy equivalent of the calorimeter, ε(calor), corresponding to the average mass of 3969.2 g of water added to the calorimeter. Ten calibration experiments yielded a value of ε(calor) ) 20 369.0 ( 2.3 J · K-1; the quoted uncertainty is the standard deviation of the mean. In all combustion experiments, the crystalline compounds were burnt in pellet form, in oxygen atmosphere, at a pressure of p ) 3.04 MPa and in the presence of 15.00 cm3 of deionized water, following the procedure described by Waddington et al.42 Temperature measurements were collected in time intervals of 10 s, with a precision of (1 × 10-4 K, using a quartz crystal thermometer (Hewlett Packard HP 2804 A), interfaced to a PC, programmed to acquire data, to control the calorimeter temperatures, and to compute the adiabatic temperature change through the LABTERMO program.43 In all combustion experiments, the ignition temperature was chosen so that the final temperature was as close as possible to T ) 298.15 K and the rotation of the bomb was started when the temperature rise in the main period reached about 63% of its final value and continued throughout the experiment, according to the procedure suggested by Good et al.44 The electrical energy for ignition was determined from the change in potential difference across a capacitor when ca. 40 V were discharged through the platinum ignition wire. The massic energy of combustion of the cotton thread fuse, for which the empirical formula is CH1.686O0.843, was taken as ∆cu° ) -16 240 J · g-1,44 a value that was previously confirmed in our laboratory. n-Hexadecane (Aldrich, mass fraction >0.999), stored under nitrogen, was used as a combustion auxiliary for the two compounds, for the purpose

Roux et al. of minimizing the carbon soot residue formation. Its mass-related energy of combustion was found to be ∆cu° ) -47 132.7 ( 2.6 J · g-1. The amount of nitric acid produced was determined through Devarda’s alloy method,45 and corrections for nitric acid formation were based on -59.7 kJ · mol-1 for the molar energy of formation of 0.1 mol · dm-3 HNO3(aq) from N2(g), O2(g), and H2O(l).46 At T ) 298.15 K, an estimated value of pressure coefficient of mass energy, (∂u/∂p)T ) -0.2 J · g-1MPa-1, typical for most organic solids,47 was used for the compounds studied. Corrections to the standard state were made by following the procedures given by Hubbard et al.48 The relative atomic masses used for the elements were those recommended by the IUPAC Commission in 2005.49 The specific densities used to calculate the true mass from apparent mass in air were F ) 1.677 g · cm-3,50 for L-cystine, and F ) 1.367 g · cm-3 for L-cysteine, determined from the ratio mass/ volume of a pellet of the compound (made in vacuum, with an applied pressure of 105 kg · cm-2). Knudsen Effusion Technique. The vapor pressures of the two amino acids were measured as function of temperature, using the mass-loss Knudsen effusion method. The Knudsen apparatus and the measuring procedure have been previously described.51 In this apparatus, the aluminum effusion cells are placed in cylindrical holes inside three aluminum blocks, each one maintained at a constant temperature different from the other two blocks. The exact areas and the transmission probability factors (Clausing factors) of the orifices of the effusion cells, made in platinum foil of 0.0125 mm thickness, are presented in the Supporting Information, Table S1. The measurements were extended through a chosen temperature interval corresponding to measured vapor pressures in the range 0.1-1.0 Pa. In each effusion experiment, the loss of mass, ∆m, of the samples, during a convenient effusion time period t, is determined by weighing the effusion cells with a precision of (0.01 mg, before and after the effusion period in a system evacuated to a pressure near 1 × 10-4 Pa. At the temperature T of the experiment, the vapor pressure p is calculated by the Knudsen equation

p ) (∆m/Aowot)(2πRT/M)1/2

(1)

where Ao represents the area of the effusion orifice, wo is the respective Clausing factor, R is the gas constant, and M is the molar mass of the effusing vapor. Computational Details. Standard ab initio molecular orbital calculations52 were performed with the Gaussian03 series of programs.53 Energies were obtained using the Gaussian-3 theory, at the G3(MP2)//B3LYP54 and/or G355 levels. G3(MP2)//B3LYP is a variation of G3(MP2)56 theory that uses the B3LYP density functional method57 for geometries and zero-point energies. The B3LYP density functional used is a linear combination of Hartree-Fock exchange, Becke58 exchange, and Lee, Yang, and Parr (LYP)59 correlation. Two modifications have been made to derive G3(MP2)//B3LYP. First, the geometries are obtained at the B3LYP/6-31G(d) level instead of MP2(FU)/6-31G(d). Second, the zero-point energies are obtained at the B3LYP/6-31G(d) level and scaled by 0.96 instead of HF/6-31G(d) scaled by 0.8929. All of the other steps remain the same with the exception of the values of the higherlevel correction parameters.54

Thermochemical Study of S-Containing Amino Acids G3 corresponds effectively to calculations at the QCISD(T)/ G3large level, G3large being a modification of the 6-311+ G(3df,2p) basis set, including more polarization functions for the second row (3d2f), less on the first row (2df), and other changes to improve uniformity. In addition, some core polarization functions are added.55 Single-point energy calculations are carried out on MP2(full)/6-31G(d) optimized geometries, incorporating scaled HF/6-31G(d) zero-point vibrational energies, a so-called higher-level correction to accommodate remaining deficiencies, and spin-orbit correction for atomic species only.55 Due to the lack of symmetry and the internal rotational degrees of freedom by free rotation of the SH, NH2, COOH, and OH groups with respect to the carbon skeleton, cysteine and cystine exhibit a large number of low-energy conformers. In this study, we have optimized the molecular structures of 10 and 9 of the lowest-energy conformers of cysteine and cystine, respectively. G3(MP2)//B3LYP and/or G3-calculated energies at 0 K, and enthalpies at 298 K, for all the conformers studied here are given in Tables 10, 11, and 12. All of these structures are minima on the potential energy surface.


b c 3e O (g) + - + 4 2 2 2 b d 116e - H2O(l) f aCO2(g) + N2(g) + 2 2 e(H2SO4 · 115H2O)(l) (3)

(

)

CaHbOcNdSe(cr) + a +

(

)

Table 3 presents the derived standard molar values for the energy, ∆cU°m(cr), and enthalpy, ∆cH°m(cr), of combustion reaction 3, as well as the standard molar enthalpies of formation, in the crystalline phase, ∆fH°m(cr), at T ) 298.15 K. TABLE 1: Typical Combustion Results, at T ) 298.15 K, for the Compounds Studieda m(cpd)/g m′(fuse)/g m′′(n-hex)/g Ti/K Tf/K ∆Tad/K εi/J · K-1 εf/J · K-1 εcorr / J · K-1 ∆m(H2O)/g -∆U(IBP)b/J ∆U(fuse)/J ∆U(n-hex)/J ∆U(HNO3)/J ∆U(ign)/J ∆U(carb)/J ∆U∑/J -∆cu°/J · g-1

We have also reoptimized the geometries of the lowest-energy conformers of cysteine and cystine at the MP2(full)/631G(3df,2p) level to obtain more reliable molecular structures. The charge distribution was analyzed using a population partition technique, the natural bond orbital (NBO) analysis of Reed and Weinhold.60-62 The NBO analysis was performed using the NBO program63 implemented in the Gaussian 03 package.53

L-cystine

L-cysteine

0.59924 0.00287 0.16864 297.2123 298.1562 0.90947 74.59 73.66 20378.62 2.3 18600.51 46.61 7948.4 52.77 1.10 4.13 15.86 17590.61

0.53131 0.00310 0.10524 297.3862 298.1494 0.73032 74.40 73.53 20376.53 1.8 14934.66 50.34 4960.26 44.42 1.09 14.82 18566.98

a

3. Results 3.1. Experimental Results. Phase Transitions. No solid-solid phase transition was found in L-cysteine and L-cystine in the temperature interval from T ) 263 to 440 K and 500 K, respectively. Experimental Enthalpies of Formation in the Condensed State. The results of one combustion experiment of each compound studied are given in Table 1, in which ∆m(H2O) is the deviation of the mass of water added to the calorimeter from 3969.2 g, the mass assigned to ε(calor), ∆UΣ is the correction to the standard state, and the other symbols have the same meaning as those previously defined by Hubbard et al.48 and Westrum.64 The internal energy associated to the isothermal bomb process, ∆U(IBP), was calculated through

∆U(IBP) ) -{ε(calor) + cp(H2O,l)∆m(H2O)}∆Tad + (Ti - 298.15)εi + (298.15 - Ti - ∆Tad)εf + ∆U(ign) (2)

m(cpd) is the mass of compound burnt in each experiment; m′ (fuse) is the mass of the fuse (cotton) used in each experiment; m′′ (n-hex) is the mass of n-hexadecane used as auxiliary of combustion; Ti is the initial temperature rise; Tf is the final temperature rise; ∆Tad is the corrected temperature rise; εi is the energy equivalent of the contents in the initial state; εf is the energy equivalent of the contents in the final state; εcorr is the energy equivalent of the calorimeter corrected for the deviation of mass of water added to the calorimeter; ∆m(H2O) is the deviation of mass of water added to the calorimeter from 3969.2 g; ∆U(IBP) is the energy change for the isothermal combustion reaction under actual bomb conditions; ∆U(fuse) is the energy of combustion of the fuse (cotton); ∆U(n-hex) is the energy of combustion of n-hexadecane used as auxiliary of combustion; ∆U(HNO3) is the energy correction for the nitric acid formation; ∆U(ign) is the electric energy for the ignition; ∆U(carb) is the correction energy for carbon soot formation; ∆UΣ is the standard state correction; ∆cu° is the standard mass energy of combustion. b ∆U(IBP) includes ∆U(ignition).

TABLE 2: Individual Values of Standard (p° ) 0.1 MPa) Mass Energies of Combustion, ∆cu°, of the Compounds, at T ) 298.15 K -∆cu°/(J · g-1)

where ∆Tad is the calorimeter temperature change corrected for the heat exchange, work of stirring, and frictional work of bomb rotation. Detailed results of each combustion experiment, for the compounds studied, are given in the Supporting Information, Tables S2 and S3. The individual values of ∆cu°, together with the mean value, 〈∆cu°〉, and its standard deviations are given in Table 2. The values of ∆cu° refer to the general idealized combustion reaction, represented by eq 3:

L-cystine

L-cysteine

17597.54 17601.65 17578.41 17590.61 17584.16 17594.76

18558.90 18566.98 18568.28 18560.87 18576.79 18563.16 -〈∆cu°〉/(J · g-1)

L-cystine

17591.2 ( 3.5 a

L-cysteine a

18565.8 ( 2.6a

Mean value and standard deviation of the mean.

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Roux et al.

TABLE 3: Derived Standard (p° ) 0.1 MPa) Molar Energies of Combustion, ∆cU°m, Standard Molar Enthalpies of Combustion, ∆cH°m, and Standard Molar Enthalpies of Formation, ∆fH°m, for the Crystalline Compounds, at T ) 298.15 K compound

(-∆cU°m(cr))/ (kJ · mol-1)

(-∆cH°m(cr))/ (kJ · mol-1)

(-∆fH°m(cr))/ (kJ · mol-1)

4227.2 ( 2.2 2249.4 ( 1.0

4234.6 ( 2.2 2253.7 ( 1.0

1045.4 ( 2.3 529.2 ( 1.1

L-cystine L-cysteine

∆gcrSm(〈T〉, p(〈T〉)) ) ∆gcrH°m(〈T〉)/〈T〉

The (p,T) values, calculated from the (p,T) equations for within the experimental range of pressures used, 0.1-1.0 Pa, are given in Table 6. The enthalpy of sublimation, g H°m(T ) 298.15 K), of L-cysteine was at T ) 298.15 K, ∆cr calculated through eq 5, from the enthalpy of sublimation, at the mean temperature 〈T〉 of the experiment: L-cysteine,

The uncertainties of the standard molar energies and enthalpies of combustion are twice the overall standard deviation of the mean and include the uncertainties in calibration and in the values of the auxiliary quantities used.65,66 To derive ∆fH°m(cr) from ∆cH°m, at T ) 298.15 K, the standard molar enthalpies of formation of H2O(l), -285.830 ( 0.042 kJ · mol-1,67 CO2(g), -393.51 ( 0.13 kJ · mol-1,67 and H2SO4 in 115H2O(l), -887.81 ( 0.42 kJ · mol-1,46 were used. Enthalpy of Sublimation. The integrated form of the Clausius-Clapeyron equation, ln(p/Pa) ) a - b (T/K)-1, where g H°m(〈T〉)/R, was used to derive a is a constant and b ) ∆cr the standard molar enthalpy of sublimation, at the mean temperature of the experimental temperature range, of L-cysteine. The experimental results obtained from each effusion cell, together with the residuals of the Clausius-Clapeyron equation {102∆ ln(p/Pa)}, derived from least-squares adjustments, are summarized in Table 4, for L-cysteine.

∆gcrH°m(T ) 298.15K) ) ∆gcrH°m(〈T〉) + o (298.15 - 〈T〉) (5) ∆gcrCp,m

g Cp,m° was assumed as being For L-cysteine, the value of ∆cr -50 J · K-1 · mol-1, resembling estimations made by other authors,68 a value that our research group has already used for other organic compounds.69-76 In Table 7, the standard molar enthalpy, entropy, and Gibbs energy of sublimation of L-cysteine, at T ) 298.15 K, are presented. The sublimation study of L-cystine was unsuccessful, since this compound decomposed at the temperature range of necessary to volatilize the compound. For both amino acids, the standard molar enthalpies of formation in the crystalline state are given in Table 8 and, for L-cysteine, the standard molar enthalpies of formation in the gaseous state, as well as the standard molar enthalpy of sublimation, at T ) 298.15 K, are also presented. 3.2. Molecular and Electronic Structures. Amino acids are well-known to exist as zwitterions in the crystalline state as well as in aqueous solution, stabilized by electrostatic, polarization, and hydrogen-bonding interactions with the solvent. According to the Cambridge Structural Database77 (version 5.31, February 2010 update) L-cysteine exhibits two solid crystalline phases. The compound crystallizes in the monoclinic78-81 and in the orthorhombic81-85 systems and has been characterized by X-ray powder diffraction, single-crystal X-ray, and neutron diffraction analysis at room and at low temperature as well as at ambient and higher pressures. In the monoclinic form there are two independent molecules, both in its zwitterionic tautomer but with different conformation, +gauche versus trans, as measured by the N-C-C-S torsion angle (Figure 2). In the orthorhombic phase, the independent molecule adopt the +gauche or -gauche conformation depending on the pressure.81 In solution, the zwitterion form is also the most populated.86 L-Cystine was found to exhibit tetragonal87 and hexagonal phases.88-90 The structures were characterized by single-crystal analysis at room and at low temperatures as well as ambient

TABLE 4: Knudsen Effusion Results for L-Cysteine 102∆ ln(p/Pa)

p/Pa

(4)

T/K

t/s

orifices

small

medium

small

medium

410.23 412.23 414.17 416.22 418.21 420.18 422.21 424.16 426.18 428.21 430.14 432.18 434.21 436.12

21618 21618 21618 18296 18296 18296 13690 13690 13690 10119 10119 10119 10025 10025

A1-B4 A2-B5 A3-B6 A1-B4 A2-B5 A3-B6 A1-B4 A2-B5 A3-B6 A1-B4 A2-B5 A3-B6 A1-B4 A2-B5

0.0983 0.120 0.136 0.166 0.203 0.239 0.296 0.373 0.429 0.537 0.652 0.755 0.894 1.151

0.0929 0.109 0.130 0.166 0.194 0.227 0.301 0.341 0.410 0.513 0.590 0.709 0.890 1.031

6.7 6.5 -0.1 -0.1 0.8 -2.0 0.1 5.0 0.1 3.7 5.5 1.6 0.3 8.6

1.1 -2.8 -4.5 -0.2 -3.7 -7.2 1.9 -3.9 -4.5 -0.9 -4.6 -4.6 -0.2 -2.4

Table 5 presents the detailed parameters of the ClausiusClapeyron equation, together with the calculated standard deviations, the standard molar enthalpies of sublimation at the mean temperature of the experiments T ) 〈T〉, the equilibrium pressure at this temperature, p(〈T〉), and the entropy of sublimation, at equilibrium conditions, ∆crgSm(〈T〉,p(〈T〉)), for each orifice used and for the global treatment of all the (p,T) points obtained for L-cysteine, calculated as

TABLE 5: Experimental Results for L-Cysteine Where a and b are from Clausius-Clapeyron Equation, ln(p/Pa) ) a - b(K/T) g and b ) ∆cr H°m(〈T〉)/R (R ) 8.314 472 J · K-1 · mol-1) orifices

a

b

A1-A2-A3 B4-B5-B6 global results

38.94 ( 0.48 38.58 ( 0.38 38.76 ( 0.40

16944 ( 203 16816 ( 159 16880 ( 169

〈T〉 (K)

423.18

p(〈T〉) (Pa)

g ∆cr H°m(〈T〉) (kJ · mol-1)

g ∆cr Sm(〈T〉,p(〈T〉)) (J · K-1 · mol-1)

0.324

140.9 ( 1.7 139.8 ( 1.3 140.3 ( 1.4

331.5 ( 3.3

TABLE 6: Calculated (p,T) Values from the Vapor Pressure Equation for L-Cysteine p/Pa

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

T/K

411.1

418.1

422.4

425.4

427.8

429.8

431.5

433.0

434.3

435.5

Thermochemical Study of S-Containing Amino Acids TABLE 7: Values of the Standard (p° ) 0.1 MPa) Molar g g Enthalpy, ∆cr H°m, Entropy, ∆cr S°m, and Gibbs Energy g ∆crG°m, of Sublimation, at T ) 298.15 K, for L-Cysteine compound

g (∆cr H°m)/ (kJ · mol-1)

g (∆cr S°m)/ (J · K-1 · mol-1)

g (∆cr G°m)/ (kJ · mol-1)

L-cysteine

146.6 ( 1.4

243.9 ( 3.3

73.9 ( 1.7

TABLE 8: Standard (p° ) 0.1 MPa) Molar Enthalpies of Formation, in Crystalline and Gaseous Phases, and Standard Molar Enthalpy of Sublimation, at T ) 298.15 K compound L-cystine L-cysteine

(-∆fH°m(cr))/ (kJ · mol-1)

g H°m)/ (∆cr (kJ · mol-1)

(-∆fH°m(g))/ (kJ · mol-1)

1045.4 ( 2.3 529.2 ( 1.1

146.6 ( 1.4

382.6 ( 1.8

and increasing pressures. In both phases, the molecule appears as the zwitterionic tautomer as shown in Figure 2. In both compounds, the crystal cohesion can be mainly attributed to NsH · · · O intermolecular interactions that built up from three-dimensional networks reinforced in L-cysteine by SsH · · · O or SsH · · · S contacts depending on the temperature or pressure. In the gas phase, where the intermolecular interactions have no effect, amino acids are intrinsically flexible systems, occurring in their nonionized forms. Like other amino acids, the cysteine molecule has no symmetry and exhibits a significant internal rotational degree of freedom due to free rotation of the SH, NH2, COOH, and OH groups with respect to the carbon skeleton, exhibiting a large number of lowenergy conformers. Intramolecular hydrogen bonding becomes important in gaseous conformations. The energy barriers that separate different conformers are typically rather small for many conformations so that the thermal energy at room temperature enables the molecule to freely change from one conformation to another. Therefore, it is not generally feasible to isolate a specific conformer experimentally at room temperature.91 The presence of three H-bond donors and four H-bond acceptors in cysteine allows for the existence of 12 distinct types of hydrogen bonds.92 While H-bonds are certainly the main secondary interactions determining the occurrence and relative energies of the conformers of cysteine, other structural factors are also important. These include exchange, electrostatic, and hyperconjugative electronic effects, as well as steric and dispersive interactions.92 Several computational studies have been devoted to identify the conformers of cysteine. Among them we can cite a work by Gronert and Hair,93 which located 42 conformers at several levels of theory, including HF/6-31G(d) and MP2/6-31+G(d); recent work of Dobrowolski et al.94 located 51conformers using B3LYP and MP2 methods in conjunction with the aug-cc-pVDZ

J. Phys. Chem. B, Vol. 114, No. 32, 2010 10535 basis set; and the most systematic theoretical study to date on the conformers of gaseous cysteine was very recently published by Wilke et al.,92 who have located 71 unique conformers of cysteine using the MP2/cc-pVTZ method. Two very recent studies have experimentally identified several conformers of cysteine in the gas phase. The presence of at least three, and possibly even six or more, conformers with and without intramolecular hydrogen bonding has been confirmed95 using an IR matrix isolation technique; and Sanz et al.96 have identified five conformers within 10 kJ · mol-1 using sophisticated laser ablation and Fourier-transform microwave (FTMW) spectroscopy. To our knowledge, there is only one theoretical paper devoted to the study of the conformers of cystine,97 locating 14 conformers. This is so because the ground-state potential energy surface (PES) of neutral cystine is rather complicated due to the large number of conformers (mostly rotamers) that might correspond to local minima. In this work, we have first identified a set of conformers of cysteine and cystine at low levels of theory, and then the most stable ones were reoptimized at higher levels. Finally, for the set of conformers within a 10 kJ · mol-1 range (10 and 9 conformers for cysteine and cystine, respectively) we have obtained their energies at G3(MP2)//B3LYP and/or G3 levels. The structures of the most stable conformers of cysteine and cystine obtained in this work, optimized at the B3LYP/6-31G(d) level, are shown in Figures 3 and 4, respectively. Their Cartesian coordinates are reported in the Supporting Information. The 10 conformers of cysteine are included among the 11 lowest-energy ones located by Wilke et al.92 using the MP2/ cc-pVTZ method. However, in the case of cystine, our conformers are much more stable than those located by Sawicka et al.,97 their most stable one being ca. 26 kJ · mol-1 less stable than ours. The lowest-energy conformer, for both cysteine and cystine, has been reoptimized at the MP2(full)/6-31G(3df,2p) level to obtain a more reliable molecular structure, and this is shown in Figures 5 and 6, respectively. Our study agrees with Wilke et al.,92 Sanz et al.,96 and Dobrowolski et al.94 in the structure of the most stable conformer of cysteine. The ordering of the other low-lying conformers is similar but not the same in the four studies, as it is shown in Table 9. The most stable conformer of cysteine (see Figure 5) contains three intramolecular hydrogen bonds, OsH · · · N with an H · · · N distance of 1.88 Å, SsH · · · OdC with an H · · · O distance of 2.60 Å, and S · · · HsN with an S · · · H distance of 2.65 Å. In the case of cystine (see Figure 6), at least five hydrogen bonds can be observed: OsH · · · N with an H · · · N distance of 1.87 Å, OsH · · · OdC with an H · · · O distance of 1.71 Å, two NsH · · · S with H · · · S distances of 2.74 and 2.82 Å, and NsH · · · OdC

Figure 2. Molecular structure of (a) L-cysteine in the monoclinic phase at 120 K showing the different conformations of the two independent molecules and (b) L-cystine in the tetragonal phase at room temperature.

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Roux et al.

Figure 5. MP2(full)/6-31G(3df,2p)-optimized structure of the lowestenergy conformer of cysteine.

Figure 3. B3LYP/6-31G(d)-optimized structures of the lowest-energy conformers of cysteine.

Figure 6. MP2(full)/6-31G(3df,2p)-optimized structure of the lowestenergy conformer of cystine.

TABLE 9: Comparison of Conformational Energies of Cysteine from the Current Work with Previously Computed Values (in kJ · mol-1)

Figure 4. B3LYP/6-31G(d)-optimized structures of the lowest-energy conformers of cystine.

with an H · · · O distance of 2.41 Å. The optimized geometrical parameters for cysteine and cystine have been collected in Tables S4 and S5 of the Supporting Information. A population analysis using the natural bond orbital (NBO) analysis, to obtain the natural atomic charges (the nuclear minus summed populations of the natural atomic orbitals on the atoms) that characterize the ground electronic state of the compounds studied has also been carried out. The calculated NBO charges located at all the atoms for cysteine and cystine are reported in Tables S4 and S5 of the Supporting Information. In cysteine, all the heavy atoms are negatively charged except the C atom of the carboxylic group, with a charge of 0.968. Partial negative charges are located at the N atom (-0.967), the two O atoms (-0.711 the O atom of the carbonyl group, and -0.788 the O atom of the OH group), and the C atoms of the CH (-0.166) and CH2 (-0.595) groups, and also the S atom has a slightly

conformer

G3(MP2)//B3LYPa

G3a

ref 92b

ref 96c

ref 94d

I II III IV V VI VII VIII IX X

0.0 4.8 5.6 6.1 6.4 6.6 8.3 8.8 9.2 9.4

0.0 5.0 5.7 7.1 7.2 6.7 8.3 9.3 9.5 9.6

0.0 4.9 6.0 5.8 6.6 6.6 7.6 9.5 8.5 9.7

0.0 3.9 5.1 5.4 7.0 6.3 9.2 9.4

0.0 5.3 5.8 6.7 6.2 8.7 10.2 -

a This work. b Focal point energy (CCSD(T)/CBS energy with anharmonic zero-point correction). c MP4/6-311++G(d,p)//MP2/ 6-311++G(d,p). d MP2/aug-cc-pVTZ plus zero-point corrections taken from ref 92.

negative charge (-0.034). In cystine, the behavior is very similar, with similar charges on the heavy atoms, but now the two sulfur atoms of the S-S bond are positively charged (0.136 and 0.091). 3.3. Theoretical Determination of the Enthalpies of Formation. G3(MP2)//B3LYP-calculated energies at T ) 0 K, enthalpies at T ) 298 K, and entropies, for the 10 lowest-energy conformers of cysteine and for the nine lowest-energy conformers of cystine, are given in Tables 10 and 11, respectively. G3calculated energetic parameters for cysteine conformers are given in Table 12. G3 calculations on cystine conformers were not carried out because of the size of the molecule.



TABLE 10: G3(MP2)//B3LYP Results for Cysteine Conformers conformer

E0a

H298a

∆∆Hb

Sc

0 b ∆fH298K

0 (∆fH298K )correctedb

0 b ∆fG298K

χ


-721.066758 -721.065392 -721.065081 -721.064974 -721.064679 -721.064382 -721.063855 -721.063898 -721.063549 -721.063673

-721.057870 -721.056051 -721.055722 -721.055547 -721.055417 -721.055341 -721.054713 -721.054507 -721.054357 -721.054308

0.0 4.8 5.6 6.1 6.4 6.6 8.3 8.8 9.2 9.4

363.29 373.66 373.23 376.55 373.56 367.09 370.21 375.70 370.57 376.92

-398.89 -394.11 -393.26 -392.80 -392.45 -392.25 -390.60 -390.05 -389.66 -389.53

-391.58 -386.80 -385.95 -385.49 -385.14 -384.94 -383.29 -382.74 -382.35 -382.22

-259.14 -257.45 -256.47 -257.00 -255.76 -253.63 -252.91 -254.00 -252.08 -253.84

0.331 0.168 0.113 0.140 0.085 0.036 0.027 0.042 0.019 0.039

a

In hartrees. b In kJ · mol-1. c In kJ · mol-1 · K-1.

TABLE 11: G3(MP2)//B3LYP Results for Cystine Conformers conformer

E0a

H298a

∆∆Hb

Sc

0 b ∆fH298K

0 (∆fH298K )correctedb

0 b ∆fG298K

χ

I II III IV V VI VII VIII IX

-1440.959398 -1440.958897 -1440.958286 -1440.957830 -1440.957193 -1440.957500 -1440.957190 -1440.956456 -1440.955764

-1440.942327 -1440.941757 -1440.940835 -1440.940413 -1440.940067 -1440.940020 -1440.939996 -1440.938994 -1440.938635

0.0 1.5 3.9 5.0 5.9 6.1 6.1 8.8 9.7

531.93 525.52 534.50 540.20 537.83 540.41 533.77 552.44 531.13

-777.32 -775.83 -773.41 -772.30 -771.39 -771.27 -771.20 -768.57 -767.63

-764.10 -762.61 -760.19 -759.08 -758.17 -758.05 -757.98 -755.35 -754.41

-480.14 -476.74 -477.0 -477.59 -475.97 -476.62 -474.57 -477.50 -470.21

0.359 0.091 0.101 0.128 0.067 0.087 0.038 0.123 0.007

a

In hartrees. b In kJ · mol-1. c In kJ · mol-1 · K-1.

TABLE 12: G3 Results for Cysteine Conformers

a

conformer

E0a

H298a

∆∆Hb

Sc

∆fH0298Kb

∆fG0298Kb

χ


-721.579247 -721.577738 -721.577464 -721.577025 -721.576807 -721.576903 -721.576288 -721.576101 -721.575915 -721.575929

-721.570310 -721.568408 -721.568123 -721.567615 -721.567586 -721.567763 -721.567167 -721.566751 -721.566705 -721.566643

0.0 5.0 5.7 7.1 7.2 6.7 8.3 9.3 9.5 9.6

357.82 367.28 365.41 369.14 365.74 363.23 362.79 368.07 364.75 369.22

-397.07 -392.08 -391.33 -390.00 -389.92 -390.39 -388.82 -387.73 -387.61 -387.45

-263.00 -260.83 -259.52 -259.30 -258.21 -257.93 -256.23 -256.71 -255.60 -256.78

-0.410 0.171 0.101 0.092 0.059 0.053 0.027 0.033 0.021 0.033

In Hartress. b In kJ · mol-1. c In kJ · m

The standard procedure to obtain enthalpies of formation in Gaussian-n theories is through atomization reactions.98,99 The G3(MP2)//B3LYP calculated enthalpies of formation of the studied conformers of cysteine and cystine studied, using atomization reactions, are shown in Tables 10 and 11, respectively. Recently, Anantharaman and Melius100 have developed a bond additivity correction (BAC) procedure for the G3(MP2)// B3LYP method, applicable to compounds containing atoms from the first three rows of the periodic table including H, B, C, N, O, F, Al, Si, P, S, and Cl atoms. The BAC procedure applies atomic, molecular, and pairwise bond corrections to theoretical heats of formation of molecules. The procedure requires parameters for each atom type but not for each bond type. The authors have applied the method to an extended test suite involving 273 compounds, neutral and ions, and the average error was only 4.4 kJ · mol-1. We have carried out the BAC correction following the steps indicated in ref 100, and the values obtained are collected in Tables 10 and 11. To obtain the conformational composition of cysteine in the gas phase, at T ) 298 K, we need the ∆fG°m values. They can be calculated through eq 6:

where the sum of the entropy of the elements, in the case of the compounds studied, is calculated as eqs 7 and 8, for cysteine and cystine, respectively:

∑ S0(el) ) 3S0(C, s) + 7/2S0(H2, g) + 1/2S0(N2, g) + S0(O2, g) + S0(S, s)

(7)

∑ S0(el) ) 6S0(C, s) + 6S0(H2, g) + S0(N2, g) + 2S0(O2, g) + 2S0(S, s)

(8)

Using for the elements the entropy values at T ) 298 K taken from ref 101, ∆fG°m values have been obtained for all the conformers and collected in Tables 10, 11, and 12. Using eq 9:

xi )

∆fG°m(i)

e-[ n

RT

∑e

-[

]

∆fG°m(i) RT

(9) ]

i)1

∆fG°m(i) ) ∆fH°m(i) - T[S0(i) -

∑ S0(el)]

(6)

we have obtained the compositions in the gas phase at T ) 298 K for cysteine and cystine, as they are shown in Tables 10, 11, and

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Roux et al.

12. As can be observed, the most stable conformer of cysteine, conformer I, accounts for 33.1% (at the G3(MP2)//B3LYP level) or 41.0% (at the G3 level) of the composition in the gas phase. For cystine, conformer I accounts for 35.9% of the gas-phase composition, calculated at the G3(MP2)//B3LYP level. Using eq 10 n

∆fH°m(X) )

∑ xi∆fH°m(i)

(10)

i)1

the final value for the enthalpy of formation of cysteine is calculated as -387.4 kJ · mol-1, and a value of -761.4 kJ · mol-1 is obtained for cystine. The calculated enthalpy of formation of cysteine is in very good agreement with the experimental value measured in this work, -382.6 ( 1.8 kJ · mol-1; it is also in accord with the value estimated very recently by Sagadeev et al.102 using the additive method of group contribution, -378.1 kJ · mol-1. Carrying out the same type of calculations from our G3 data, an enthalpy of formation for cysteine of -393.2 kJ · mol-1 is obtained. Sagadeev et al.102 have reported a value of -386.1 kJ · mol-1, at the same G3 level of theory, but they do not give information about their optimized structure of cysteine. ∆fG°m values of -257.0 (from G3(MP2)//B3LYP) and -260.6 (from G3) kJ · mol-1 for cysteine, and -478.5 kJ · mol-1 for cystine have been obtained. We can also calculate the enthalpy of formation of cystine using its hydrogenation reaction to give cysteine

and from two isodesmic reactions using dimethyl disulfide and diethyl disulfide as reference, respectively:

The values obtained103,104 are -749.2, -747.4, and -746.4 kJ · mol-1, from reactions 11, 12, and 13, respectively. From these values and the one obtained from atomization, we can estimate an enthalpy of formation of -755 ( 10 kJ · mol-1 for cystine. The very similar values for the enthalpy of formation of one molecule of cystine versus two molecules of cysteine (-755 kJ · mol-1 versus 2 × -382.6 kJ · mol-1 ) -765.2 kJ · mol-1, respectively) is remarkable, given the substantial structural changes and differences in noncovalent interactions that take place in the cysteine-cystine interchange; in particular, as shown in Figures 5and 6, the type and nature of the hydrogen bonds present in cysteine and cystine are calculated to be rather different in the thiol and disulfide spices. This thermodynamic balance may be important in the thiol-disulfide equilibrium involved in so many biological systems. We have also calculated the bond dissociation enthalpy (BDE) of the S-S bond in cystine through the reaction

at the G3(MP2)//B3LYP level, yielding 279.4 kJ · mol-1. This value is in very good agreement with the mean value tabulated by Luo32 for dialkyl disulfides RS-SR, 277.0 kJ · mol-1. Also we can calculate the BDE of the S-H and C-S bonds in cysteine, through reactions 15 and 16, respectively:

the calculated BDE(S-H) values being 367.9 kJ · mol-1 (at G3(MP2)//B3LYP) and 367.3 kJ · mol-1 (at G3), in very good agreement with the mean value tabulated by Luo32 for alkanethiols H-SR, 365.7 kJ · mol-1. Using the average of both values, 367.6 kJ · mol-1, it is possible to calculate a value for the enthalpy of formation of cysteine-derived thiyl radical, -233.0 kJ · mol-1. The calculated BDE(C-S) values are 323.1 kJ · mol-1 (at G3(MP2)//B3LYP) and 323.7 kJ · mol-1 (at G3). This value is comparable to the experimental value, 312.5 ( 4.2 kJ · mol-1, measured105 for H3C-SH. And using the average BDE(C-S) value, 323.4 kJ · mol-1, and the experimental105 enthalpy of formation of mercapto radical, 143.0 ( 2.8 kJ · mol-1, a value of -202.2 kJ · mol-1 is obtained for the enthalpy of formation of cysteine-derived C-centered radical. We can also use isogyric reactions, defined as those reactions conserving the number of electron pairs, to calculate the enthalpies of formation of radicals, expecting a cancellation of errors in the correlation energy.106 The enthalpy of formation of cysteine-derived thiyl radical calculated from the isogyric reaction

is -235.2 kJ · mol-1, in very good agreement with the value calculated from reaction 15, -233.0 kJ · mol-1; and the value of the enthalpy of formation of cysteine-derived C-centered radical, calculated from the isogyric reaction

is -198.3 kJ · mol-1, also in very good agreement with the value calculated from reaction 16, -202.2 kJ · mol-1.


Figure 7. B3LYP/6-31G(d)-optimized structures of radicals derived from cysteine: (a) cysteine-derived thiyl radical, and (b) cysteine-derived C-centered radical.

The optimized structures of both radicals are shown in Figure 7. As can be observed, cysteine-derived thiyl radical is stabilized by two hydrogen bonds, OsH · · · N (1.88 Å) and NsH · · · S (2.65 Å), whereas cysteine-derived C-centered radical presents one OsH · · · N (1.88 Å) hydrogen bond. The structure of cysteine-derived thiyl radical optimized in this work is in accord with the minimum obtained by van Gastel et al.107 in a recent DFT study on its electronic structure. Acknowledgment. Thanks are due to Conselho de Reitores das Universidades Portuguesa (CRUP), Portugal, to Consejo Superior de Investigaciones Cientı´ficas (CSIC), Madrid, Spain, and to the Spanish Ministerio de Ciencia e Innovacioń for the joint research projects CRUP/CSIC.E39/08 and HP2007-0123. Thanks are also due to Fundaçaõ para a Cieˆncia e Tecnologia (FCT), Lisbon, Portugal, and to FEDER for financial support given to Centro de Investigaçaõ em Quı´mica da Universidade do Porto. A.F.L.O.M.S thanks FCT and The European Social Fund (ESF) under the Community Support Framework (CSF) for the award of the postdoctoral fellowship (SFRH/BPD/41601/ 2007). The support of the Spanish Ministerio de Ciencia e Innovacioń under Project CTQ2007-60895/BQU is also gratefully acknowledged. Supporting Information Available: Table S1 presents the exact areas and transmission probability factors for the platinum orifices of the Knudsen effusion apparatus, Tables S2 and S3 list the details of all the combustion calorimetry experiments, at T ) 298.15 K, for L-cystine and L-cysteine, Tables S4 and S5 collect the optimized geometrical parameters and the calculated NBO charges for the most stable confomers of cysteine and cystine, and Table S6 presents computational data for cysteine-derived radicals and molecules used as references in isodesmic reactions. Also included are the Cartesian coordinates for all the lowest-energy conformers of cysteine and cystine, and cysteine-derived radicals, optimized in this work. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Molecular Structure and Energetics. Vol 2: Physical Measurements; Liebman, J. F., Greenberg, A., Eds.; VCH: New York, 1987. (2) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: London, 1970. (3) Pedley, J. B. Thermochemical Data and Structures of Organic Compounds, Vol. 1, TRC Data Series; College Station, TX, 1994. (4) Afeefy, H. Y.; J. F. Liebman, J. F.; Stein, S. E. Neutral Thermochemical Data, in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Mallard, W. G., Linstrom, P. J., Eds.; National Institute of Standards and Technology: Gaithersburg, MD 20899, June 2005 Release(http://webbook.nist.gov).

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