Gas-Phase Enthalpies of Formation and Enthalpies of Sublimation of

Article pubs.acs.org/JPCA

Gas-Phase Enthalpies of Formation and Enthalpies of Sublimation of Amino Acids Based on Isodesmic Reaction Calculations Olga V. Dorofeeva* and Oxana N. Ryzhova Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia S Supporting Information *

ABSTRACT: Accurate gas-phase enthalpies of formation (ΔfH°298) of 20 common α-amino acids, seven uncommon amino acids, and three small peptides were calculated by combining G4 theory calculations with an isodesmic reaction approach. The internal consistency over a set of ΔfH298 ° (g) values was achieved by sequential adjustment of their values through the isodesmic reactions. Four amino acids, alanine, β-alanine, sarcosine, and glycine, with reliable internally self-consistent experimental data, were chosen as the key reference compounds. These amino acids together with about 100 compounds with reliable experimental data (their accuracy was supported by G4 calculations) were used to estimate the enthalpies of formation of remaining amino acids. All of the amino acids with the previously established enthalpies of formation were later used as the reference species in the isodesmic reactions for the other amino acids. A systematic comparison was made of 14 experimentally determined enthalpies of formation with the results of calculations. The experimental enthalpies of formation for 10 amino acids were reproduced with good accuracy, but the experimental and calculated values for 4 compounds differed by 11−21 kJ/mol. For these species, the theoretical ΔfH298 ° (g) values were suggested as more reliable than the experimental values. On the basis of theoretical results, the recommended values for the gas-phase enthalpies of formation were also provided for amino acids for which the experimental ΔfH°298(g) were not available. The enthalpies of sublimation were evaluated for all compounds by taking into account the literature data on the solidphase enthalpies of formation and the ΔfH298 ° (g) values recommended in our work. A special attention was paid to the accurate prediction of enthalpies of formation of amino acids from the atomization reactions. The problems associated with conformational flexibility of these compounds and harmonic treatment of low frequency torsional modes were discussed. The surprisingly good agreement between the ΔfH°298(g) values calculated from the atomization and isodesmic reactions is largely the result of a fortuitous mutual compensation of various corrections used in the atomization reaction procedure.

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° (g) value of methionine has amino acids. Recently, the ΔfH298 been calculated by G3 and G4 methods using the atomization and bond separation reactions.7 The calculated values are in good agreement with the refined experimental data. G3(MP2)//B3LYP and G3 methods have been used to estimate ° (g) value the enthalpy of formation of cysteine.11 The ΔfH298 was calculated using the standard procedure through atomization reactions and the correction for a mixture of conformers; the calculated value is about 5 kJ/mol less than the experimental. The enthalpies of formation of methionine and cysteine have been also calculated at the CCSD(T)/6-311+ +G(3df,2p)//B3LYP/6-31G(2df,p) level using the recently developed connectivity-based hierarchy (CBH).12 This approach was designed to improve the isodesmic bond separation scheme, and it showed a reasonable agreement with the experimental value for methionine. On the other hand, the calculated value for cysteine was substantially less than experimental one. The G4 calculation, based on the computed

INTRODUCTION The 20 naturally occurring α-amino acids are the building blocks of all peptides, and the understanding of their influence on the biological activity depends on the knowledge of thermochemical data. For this reason, they were extensively studied both experimentally and theoretically. Although the ° ) were measured for solid-phase enthalpies of formation (ΔfH298 all 20 common α-amino acids,1 their experimental investigations are still in progress2−9 because there are some significant discrepancies in the reported data. The sublimation enthalpy (ΔsubH°298) measurements are less common compared to combustion calorimetry experiments and were performed only for the half of amino acids,10 and thus the experimental gas-phase enthalpies of formation are only known for 10 common α-amino acids. Determination of an enthalpy of sublimation is a challenging experimental problem and this often results in a poor accuracy. To satisfy the need of chemists for reliable thermochemical data, the gas-phase enthalpies of formation of amino acids can be predicted by theoretical calculations. Different composite quantum chemical methods are now most often used to accurately predict the thermochemistry of © 2014 American Chemical Society

Received: February 7, 2014 Revised: April 17, 2014 Published: April 25, 2014 3490

dx.doi.org/10.1021/jp501357y | J. Phys. Chem. A 2014, 118, 3490−3502

The Journal of Physical Chemistry A

Article

Table 1. Enthalpies of Formation of Amino Acids Calculated by the G4 Method (in kJ/mol) atomization reaction

a

isodesmic reactions

compound

ΔfH°298a

ΔfH°298

number of reactions

number of reference amino acids

(max−min)b

Ala β-Ala Sar Gly γ-Abu Val Leu Ile Met Cys Ser Pro N-PhGly α-PhGly Phe N-Bn-α-Ala N-Bn-β-Ala Lys Asn Gln Asp Glu Thr Tyr Arg His Trp Gly-Gly Gly-Gly-Gly Ala-Ala

−425.9 −420.7 −388.5 −393.8 −441.6 −476.5 −497.8 −496.9 −431.7 −397.2 −584.6 −389.6 −277.0 −287.2 −321.8 −320.6 −313.7 −463.8 −613.2 −629.5 −795.6 −817.8 −624.4 −497.6 −411.5 −292.4 −252.6 −575.2 −774.2 −645.8

−427.8 −420.3 −387.9 −394.1 −442.0 −475.8 −497.6 −496.7 −429.8 −395.5 −584.7 −389.5 −275.6 −285.4 −319.6 −318.2 −311.4 −465.0 −615.2 −631.6 −796.8 −819.4 −624.6 −497.0 −410.8 −289.4 −247.6 −576.0 −772.6 −646.3

4 6 14 25 32 27 36 37 24 35 40 6 44 43 39 48 53 42 54 48 70 62 65 82 37 65 24 51 15 56

0 1 2 3 4 5 6 7 8 9 10 6 12 13 14 15 16 17 18 19 20 21 22 23 24 25 24 23 9 24

1.9 3.2 7.3 6.2 8.2 7.5 5.6 5.9 2.6 5.2 4.6 4.3 5.6 6.5 7.6 7.7 7.7 4.9 6.1 5.6 6.5 5.3 5.3 10.4 7.4 7.8 6.9 9.7 16.8 11.2

Value for the lowest energy conformer. bDifference between maximum and minimum values obtained from isodesmic reactions.

available experimental data, the ΔfH°298(g) values of −424.8 ± 2.0 kJ/mol and −389.0 ± 4.0 kJ/mol were suggested for alanine and sarcosine, respectively. Later, our predictions were confirmed by the new experimental measurements for alanine (−426.3 ± 2.9 kJ/mol, DL-form)3 and sarcosine (−388.0 ± 1.0 kJ/mol).8 In the present work, we use the G4 theory19 combined with isodesmic reaction scheme20 to calculate the enthalpies of formation of different amino acids with a high accuracy. It is known that the amino acids are multiconformer systems with numerous local minima associated with different conformational arrangements of the side chain. The enthalpies of formation of these molecules have to be calculated by taking into account the multiple low-energy conformations. In order to accurately predict the contribution of conformers to the enthalpy of formation, not only the relative energies of conformers but also the energy barriers that separate different conformers are needed. However, such detailed conformational analysis represents a great challenge. To avoid these difficulties, we used an isodesmic reaction approach where only the lowest energy conformer was considered for all compounds. For the most effective error compensation, the amino acids were used as the product in all isodesmic reactions. Relying on the four amino acids with reliable internally self-consistent experimental data, the accurate gas-phase enthalpies of formation have been determined for 27 amino acids and three small peptides. A high accuracy was achieved due to the use of a large number of

atomization energies and taking into consideration the equilibrium mixture of conformers, led to the ΔfH°298(g) value of histidine13 which is substantially different from that estimated from group contribution values14 (unfortunately, there is no experimental value for comparison). Six α-amino acids, glycine, alanine, valine, leucine, isoleucine, and proline, have been examined theoretically by quantum chemical computations at the G3(MP2)//B3LYP level.15 A comparison ° and available experimental between the computed ΔfH298 values showed the large discrepancies between two sets of values for alanine, valine, leucine, and proline. However, as shown later, this difference becomes insignificant if the revised experimental data for alanine and proline are considered. Stover et al.16 have computed the enthalpies of formation of all the naturally occurring amino acids from the G3(MP2) atomization energies and by an isodesmic reaction approach using glycine as a product and CH4 as the reactant where possible. The discrepancies between the results of two approaches vary in the range of 0−9 kJ/mol. In our previous works, the enthalpies of formation of glycine, alanine and two uncommon amino acids, β-alanine and sarcosine, have been calculated by G3X and G4 methods applied to both the atomization and isodesmic reactions.17,18 The calculated values were in close agreement with the experimental for glycine and β-alanine, whereas a large difference has been observed for alanine and sarcosine. On the basis of the computational results and analysis of the 3491



Article

Table 2. Enthalpies of Formation (ΔfH298 ° ) in Both Condensed and Gaseous Phases and Enthalpies of Sublimation (ΔsubH298 ° ) of Amino Acids (in kJ/mol) experiment

calculation ΔfH°298(g)

compound Ala

ΔfH298 ° (cr)

ΔsubH298 °

ΔfH298 ° (g)

−604.2 ± 2.0 −562.7 138.1 ± 0.8 (455 K) −561.1 ± 0.7 −559.5 ± 0.6

β-Ala

Sar

Gly

−560.0 −604.2 −560.0 −564.3 −558.0 −310.0 −547.1 −559.1 −507.1 −513.2 −513.2 −517.2 −528.2 −535.2

± ± ± ± ± ± ± ± ± ± ± ± ±

1.7 2.0 1.0 1.1 0.3 1.5 1.1 0.9 0.3 0.3 0.7 0.4 0.8

144.8 ± 4.2 132.8 ± 1.0 (414 K)

−414.7 ± 4.2

138.3 135.2 ± 2.0 138.0 ± 2.7 134.0 ± 2.0

−465.9 −424.8 −426.3 −424.0

137.9 ± 1.7

−421.2 ± 1.9

146.0 ± 1.0 123.8 ± 1.0k 129.2 ± 0.7

± ± ± ±

2.2 2.0 2.9 2.0

−367.2 ± 1.0 −389.4 ± 1.0 −388.0 ± 1.0

130.5 ± 2.0 (414 K) −528.5 −528.6 ± 0.3

γ-Abu

Val

−527.5 −528.5 −528.1 −524.0 −528.1 −581.1 −560.7

± ± ± ± ± ± ±

0.5 0.4 0.5n 0.8 0.5 0.3 4.7o

−581.1 ± 0.3 −618.6 ± 0.5 −618.0

136.4 138.1 136.5 140.0

± ± ± ±

0.4 (455 K) 4.6 2.0 (419 K) 5.0m

−390.5 ± 4.6

136.4

−392.1 ± 0.6

134.4 ± 1.5 140.0 ± 2.0

−393.7 ± 1.5 −441.0 ± 2.0

139.0 ± 4.0 (465 K) 139.1 ± 3.0

−442.0 ± 3.0

162.8 ± 0.8 (455 K)

Leu

−628.9 −617.9 −614.7 −614.7 −642.2 −648.6 −637.4

± ± ± ±

1.9 0.6 1.3 1.3

−455.1 ± 1.0

138.9 ± 3.0

−475.8 ± 3.0

± 0.3

−637.4 ± 0.9

Ile

162.8

−637.4 −639.7 ± 0.8 −638.1

150.6 ± 0.8 (455 K) 150.6 148.7 ± 6.5 (459 K) 139.8

−486.8 ± 1.2 −497.6 ± 3.0

120.0 ± 0.8 (455 K) −637.8 ± 0.9 −638.1 Met −577.5 ± 0.7 −588.4 ± 3.0

141.4 125.1 ± 0.8 (455 K) 164.0 ± 4.0

−496.7 ± 3.0 −413.5 ± 4.1

3492

referencea

this workb

other works

reference

38 39 40 41 42 43 44 1 17, recommended 3 (DL-Ala) 45, 46 44 47 3, recommended 48 49, 50 49, 50, this work 8, recommended 51 38 52 39 40 42 43 53 54 1 55 56 17, recommended 45, 46 57 58 recommended 59 39 40 54 1 60 recommended 51 59 39 40 1 61 recommended 38 39 40 1 recommended 40 62 56

−427.8

−415.9c −424.7d −423.1e −421.3f −419.2g −434.3h

14 15 15 16 16

−420.3

−420.5c −419.1i −430.6h

14 3

−387.9

−387.9c −387.3j

14 8

−394.1

−390.0c −392.7d −391.6e −384.5f −387.4l −401.4h

14 15 15 16 16

−442.0

−441.2c

14

−475.8

−466.1c −475.5d −473.4e −472.4f −470.7g

14 15 15 16 16

−497.6

−486.8c −496.6d −494.8e −494.1f −492.5g

14 15 15 16 16

−496.7

−486.8c −494.5d −492.1e −493.3f −492.0g −412.1c −428.2j −428.9f

14 15 15 16 16 14 7 16

−429.8



Article

Table 2. continued experiment

calculation ΔfH298 ° (g)

compound

Cys

Ser

ΔfH298 ° (cr) −577.5 ± 0.7 −534.1 ± 0.6 −529.2 ± 1.1

−529.2 −732.7 −734.7 −730.2 −731.5

± ± ± ± ±

1.1 0.3 1.6 0.6 1.5

Pro

N-PhGly

α-PhGly Phe

−515.2 −515.2 −507.6 −524.4 −515.2 −396.7 −396.7 −396.7 −445.5 −445.5 −459.0 −466.0

± 0.5 ± 0.5 ± 2.6 ± ± ± ± ± ±

0.5 0.6 0.6 0.6 0.6 0.6

ΔsubH298 °

ΔfH298 ° (g)

146.8 ± 2.9 147.7 ± 3.0

−430.0 ± 10.0 −429.8 ± 3.0

146.6 ± 1.4

−382.6 ± 1.8

133.7 ± 3.0

−395.5 ± 3.0

146.8 ± 3.0 96.7 ± 0.8 (455 K) 127.4 ± 1.0 (406 K) 149.0 ± 4.0 122.9q

−366.2 ± 4.0 −392.3

125.7 ± 128.0 ± 115.9r 121.1 ± 165.0 ± 160.1 ±

−389.5 −268.7 −280.8 −275.6 −280.5 −285.4

4.0 2.0 3.0 6.0 3.0

−584.7 ± 3.0

± 4.0 ± 2.1 ± 3.0 ± 6.0 ± 3.0

± 0.8

−466.9 ± 0.9 −466.0

154.0 ± 0.8 (455 K) 154.0 149.0 ± 6.0 146.4

−312.9 ± 1.2 −319.6 ± 4.0

referencea 7 recommended 62 11

recommended 63 56 5 recommended 40 43 50, 64 50, 64, this work 65 6 recommended 66 66, this work recommended 66 recommended 48 38 40 1 67 recommended

N-Bn-α-Ala N-Bn-β-Ala Lys

Asn

Gln

Asp

Glu

Thr

−470.4 ± 3.1 −470.4 ± 3.1 −678.7 ± 1.5 −1082.2 ± 2.2 −678.7 −793.2 −789.4 ± 0.7 −789.4 ± 4.7 −789.4 ± 0.7 −823.6 −826.4 ± 0.7 −834.3 ± 4.6 −826.4 ± 0.7 −976.9 ± 0.8 −973.3 ± 0.8 −987.4 ± 11.3 −975.9 ± 1.9 −973.3 ± 0.8 −1009.6 −1003.3 ± 1.2 −1009.7 ± 0.7 −1025.5 ± 2.0 −1009.7 −805.7 ± 0.8 −807.2 ± 0.8 −790.0 ± 3.1 −790.0 ± 3.1

171.6 ± 3.7 159.0 ± 4.0

213.7

174.2 ± 4.0

194.8 ± 4.0

176.5 ± 4.0

−318.2 ± 4.0 −298.8 ± 4.8 −311.4 ± 4.0

−465.0 ± 3.0

−615.2 ± 4.0

−631.6 ± 4.0

−796.8 ± 4.0

190.3

−819.4 ± 4.0

165.4 ± 4.0

−624.6 ± 4.0 3493

recommended 28 recommended 54 56 recommended 68 1, 68 2 recommended 59 1, 59 2 recommended 68 1, 68 69 56 recommended 68 70 1, 68 56 recommended 38 1, 38 9 recommended

this workb

other works

reference

−425.1g −435.1p −378.1c −387.4i −395.0f −391.6g −398.7p −567.8c −578.2f −578.2g

16 12 14 11 16 16 12 14 16 16

−389.5

−373.3c −388.5d −385.9e −381.2f −387.0g

14 15 15 16 16

−275.6

−280.8c

14

−319.6

−302.2c −322.6f −313.8g

14 16 16

−318.2

−324.7d −310.7e −318.8d −303.7e −443.4c −451.5f

28 28 28 28 14 16

−615.2

−590.5c −604.2f −610.0g

14 16 16

−631.6

−611.2c −621.7f

14 16

−796.8

−786.7c −790.4f −793.3g

14 16 16

−819.4

−807.4c −813.8f −815.9g

14 16 16

−624.6

−603.7c 618.8f −618.8g

14 16 16

−395.5

−584.7

−285.4

−311.4 −465.0



Article

Table 2. continued experiment

calculation ΔfH298 ° (g)

compound Tyr

Arg

His

Trp

Gly-Gly Gly-Gly-Gly Ala-Ala

ΔfH298 ° (cr) −692.6 −685.1 −693.9 −682.5 −682.5 −637.7 −634.8 −621.2 −621.2 −466.7 −441.8 −435.4 −466.7 −412.4 −415.3 −415.3 −747.7 −747.7

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1.5 2.9 1.4 1.4 3.2 2.3 1.7 1.7 2.8 2.6 1.5 2.8 0.8 0.9 0.9 1.3 1.3

ΔsubH298 °

185.5 ± 4.0

210.4 ± 5.0

177.3 ± 4.0

167.7 ± 5.0 171.7 ± 5.0

ΔfH298 ° (g)

−497.0 ± 4.0

−410.8 ± 5.0

−289.4 ± 4.0

−247.6 ± 5.0 −576.0 ± 5.0 −772.6 ± 7.0

−807.3 ± 1.9 −807.3 ± 1.9

118.0 ± 8.0 161.0 ± 5.0

−646.3 ± 5.0

referencea 51 1, 51 56 5 recommended 56 71 5 recommended 72 65 56 recommended 38 1, 38 recommended 55 recommended recommended 55 73 recommended

this workb

other works

reference

−497.0

−481.9c −497.5f −490.4g

14 16 16

−410.8

−395.8f

16

−289.4

−221.8c −275.3f −292.3j −289.5s −215.0c −249.4f

14 16 13 13 14 16

−576.0

−571.9c

14

−772.6 −646.3

−623.7c

14

−247.6

Except for Ala, β-Ala, Sar, and Gly, the recommended ΔfH298 ° (g) values are those calculated in this work. The selected experimental values of ΔfH°298(cr) are given without uncertainties if there is a doubt about their reliability; see text for details. The recommended enthalpy of sublimation is ° (g) and ΔfH298 ° (cr). bValues calculated from isodesmic reactions are given. estimated as a difference between the recommended values of ΔfH298 c Calculated using the additive scheme. dG3(MP2)//B3LYP value for the most stable conformer. eG3(MP2)//B3LYP value averaged over the population of conformers. fG3(MP2) value calculated from atomization energies. gG3(MP2) value calculated by an isodesmic reaction approach. h W1U value, this work. iG3 value for a mixture of conformers. jG4 value for a mixture of conformers. kRevisited data of ref 50. The ΔsubH°298 value ° (cr) = 118.2 J·K−1·mol−1 (ref 4) and Cp,298 ° (g) = 105.2 J·K−1·mol−1 calculated in this work. lCCSD(T)/CBS. was recalculated using the Cp,298 m Weighted mean of values in refs 40, 42, 43, 52, corrected to 298 K. n“Best value” selection is based on the available 11 experimental measurements. o Most likely this value is a misprint. The value of −580 kJ/mol corresponds to the reported enthalpy of combustion. pCCSD(T)/6-311+ +G(3df,2p)//B3LYP/6-31G(2df,p) value taking into account multiple conformations, at the connectivity-based hierarchy (CBH-2) rung. qRevisited ° value was recalculated using the Cp,298 ° (cr) = 151.2 J·K−1·mol−1 (ref 74) and Cp,298 ° (g) = 120.6 J·K−1·mol−1 calculated in data of ref 50. The ΔsubH298 this work. rRevisited data of ref 66. The ΔsubH°298 value was recalculated using the C°p,298(cr) = 176.6 J·K−1·mol−1 (ref 66) and C°p,298(g) = 163.3 J·K−1· mol−1 calculated in this work. sG4 value for the most stable conformer. a

arginine (Arg), L-histidine (His), and L-tryptophan (Trp). In addition to these common amino acids, the seven uncommon amino acids, β-alanine (β-Ala), sarcosine (Sar), γ-aminobutyric acid (γ-Abu), N-phenylglycine (N-PhGly), α-phenylglycine (αPhGly), N-benzyl-α-alanine (N-Bn-α-Ala), and N-benzyl-βalanine (N-Bn-β-Ala), for which the experimental ΔfH298 ° (g) data are available, have also been studied in this work. And last, the enthalpies of formation of three small peptides, Nglycylglycine (Gly-Gly), N-(N-glycylglycyl)glycine (Gly-GlyGly), N-DL-alanyl-DL-alanine (Ala-Ala) have been calculated; for two of them the experimental ΔfH298 ° (cr) are known.

isodesmic reactions with different reliable reference species involved in these reactions. Earlier, the same procedure has been applied to the nitro compounds and organic azides.21,22 The isodesmic reaction calculations have revealed some inconsistency in the available experimental data for nitromethane and nitrobenzene,21 and the new experimental measurements23 confirmed our theoretical predictions. ° (g) values and the On the basis of the calculated ΔfH298 experimental ΔfH298 ° (cr) values, the enthalpies of sublimation have also been proposed for the amino acids studied in this work. The experimental values of the enthalpy of solution and those determined for the enthalpy of sublimation allow the determination of the enthalpy corresponding to the transfer of the solute amino acids from the gas state to solution (solvation enthalpy), and, therefore, the study of solvation thermodynamics of amino acids. In this paper, we have computed the enthalpies of formation of the 20 naturally occurring amino acids, L-alanine (Ala), glycine (Gly), L-valine (Val), L-leucine (Leu), L-isoleucine (Ile), L-methionine (Met), L-cysteine (Cys), L-serine (Ser), Lproline (Pro), L-phenylalanine (Phe), L-lysine (Lys), Lasparagine (Asn), L-glutamine (Gln), L-aspartic acid (Asp), Lglutamic acid (Glu), L-threonine (Thr), L-tyrosine (Tyr), L-

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COMPUTATIONAL DETAILS All ab initio and density functional theory (DFT) calculations were performed using the Gaussian 03 package of programs.24 Geometry optimizations, vibrational frequency and potential energy calculations were performed for all of the molecules using the DFT/B3LYP/6-31G(d,p) method. Conformational analysis was carried out for most of the amino acids with the exception of several molecules, for which the atom coordinates of the most stable conformers were known from the literature: Ile,25 Cys,26 Ser,27 N-Bn-α-Ala and N-Bn-β-Ala,28 Lys,29 Glu,30 Thr,31 Arg,32 His,33 and Gly-Gly-Gly.34 Our structures 3494



Article

Table 3. Enthalpy of Formation of γ-Aminobutyric Acid Calculated from Isodesmic Reactions Using G4 Energies (in kJ/mol) ΔfH298 °

reactiona H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) CH3CH2CH2CH3 average of reactions with Ala H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) average of reactions with β-Ala H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) average of reactions with Sar H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) H2NCH2CH2CH2C(O)OH (γ-Abu) average of reactions with Gly average of all reactions a

+ + + + +

CH(CH3)3 → H2NCH(CH3)C(O)OH (Ala) + CH3CH2CH2CH2CH3 (CH3)2CHNH2 → H2NCH(CH3)C(O)OH (Ala) + CH3CH2CH2CH2NH2 CH3OCH(CH3)2 → H2NCH(CH3)C(O)OH (Ala) + CH3CH2CH2OCH2CH3 C6H5CH(CH3)2 + CH3CH3 → H2NCH(CH3)C(O)OH (Ala) + C6H5CH2CH3 + CH3CH2CH2CH3 NH2C(O)NCH(CH3)2 + CH3CH3 → H2NCH(CH3)C(O)OH (Ala) + NH2C(O)NHCH2CH3 +

+ + + + +

CH3CH3 → H2NCH2CH2C(O)OH (β-Ala) + CH3CH2CH3 CH3CH2NH2 → H2NCH2CH2C(O)OH (β -Ala) + CH3CH2CH2NH2 CH3CH2OH → H2NCH2CH2C(O)OH (β -Ala) + CH3CH2CH2OH CH3C(O)OH → H2NCH2CH2C(O)OH (β -Ala) + CH3CH2C(O)OH C6H5CH3 → H2NCH2CH2C(O)OH (β -Ala) + C6H5CH2CH3

+ CH3NHCH3 → CH3NHCH2C(O)OH (Sar) + CH3CH2CH2NH2 + N(CH3)3 → CH3NHCH2C(O)OH (Sar) + CH3CH2CH(CH3)NH2 + + + + +

CH3CH3 → H2NCH2C(O)OH (Gly) + CH3CH2CH2CH3 CH3NH2 → H2NCH2C(O)OH (Gly) + CH3CH2CH2NH2 CH3OCH3 → H2NCH2C(O)OH (Gly) + CH3CH2OCH2CH3 C6H6 → H2NCH2C(O)OH (Gly) + C6H5CH2CH3 HC(O)H → H2NCH2C(O)OH (Gly) + CH3CH2C(O)H

−440.7 −443.7 −439.4 −442.6 −442.9 -441.9 −442.6 −443.9 −442.0 −443.6 −440.2 -442.5 −440.1 −445.0 -442. 6 −441.9 −439.6 −441.9 −438.9 −442.5 -441.0 -441.9

The full list of isodesmic reactions is given in Table S3 of Supporting Information; the average of 32 reactions is −442.0 kJ/mol.

Four amino acids, Ala, β-Ala, Sar, and Gly, were chosen as the key reference compounds. Until recently the experimental data on Ala were contradictory (Table 2). In our previous study,17 we have readjusted to 298.15 K the original published experimental values of enthalpy of sublimation40,42,43 using the calculated value of C°p,298(g), and have proposed the value of −424.8 ± 2.0 kJ/mol for the gas-phase enthalpy of formation of Ala. This value was in a good agreement with that calculated by G3X method. Later, the similar value (−426.3 ± 2.9 kJ/mol) has been determined from the new experimental investigation of DL-alanine.3 Because the properties of DL-alanine may be different from those of L-alanine, the value proposed in ref 17 was accepted for Ala in all further calculations in this work. First of all, the Ala was used to estimate the enthalpy of formation of β-Ala, whose consistent experimental values were obtained by several authors3,45,46 (Table 2). The result obtained from six isodesmic reactions with Ala as reference compound (Table S3 of Supporting Information) is in excellent agreement with that obtained recently by Ribeiro da Silva et al.3 The experimental value of −421.2 ± 1.9 kJ/mol3 is recommended for the gas-phase enthalpy of formation of βAla, and this value was used in isodesmic reaction calculations for all the other amino acids. Next, Ala and β-Ala were utilized to calculate the enthalpy of formation of Sar. The average of 14 isodesmic reactions (−387.9 kJ/mol, Table S3 of Supporting Information) entirely agrees with the experimental value of −388.0 ± 1.0 kJ/mol recently determined by Amaral et al.8 The last value is recommended for Sar. At the next step, Ala, β-Ala, and Sar were used to estimate the ΔfH298 ° value of Gly. A good agreement has been established between the isodesmic reaction calculations for Gly (−394.1 kJ/mol, Table S3 of Supporting Information) and the value of −393.7 ± 1.5 kJ/mol proposed in our previous study based on the analysis of available experimental data17 (Table 2). The last value is accepted in the present work. Thus, the selected experimental values of gas-

are in agreement with the lowest energy conformers of the 20 amino acids recently obtained by Stover et al.16 except for Ser, Pro, Lys, and Glu for which the conformers with lower energies were used in the present work. The optimized geometries of the lowest energy conformers were used as inputs for further G4 calculations.19 For the three small amino acids, Ala, β-Ala, and Gly, the ΔfH°298(g) values were also calculated by W1U method35 (this expensive method has been proposed as a more accurate alternative to G3 theory). The optimized Cartesian coordinates of the most stable conformers of all compounds are summarized in Table S1 of the Supporting Information. The G4 enthalpies of formation were calculated using both the atomization36 and isodesmic reaction20 procedures. The calculation through atomization reaction involves the use of experimental enthalpies of formation of gaseous atoms at T = 0 K and thermal corrections for elements in their standard states; the corresponding values were taken from the reference book by Gurvich et al.37 For isodesmic reaction, the resulting enthalpy of formation was calculated combining the G4 enthalpy of reaction with the enthalpies of formation of reference molecules. The experimental ΔfH298 ° values for reference species involved in isodesmic reactions are given in Table S2 of the Supporting Information. In Table 1, the G4 enthalpies of formation calculated from atomization reaction are compared with those obtained from isodesmic reactions. For each species, the number of isodesmic reactions designed is given; the ΔfH°298 value in the column “isodesmic reactions” corresponds to the average of all reactions. The full list of reactions is presented in Table S3 (Supporting Information). The number of reference amino acids used in the isodesmic reaction calculations is also given in Table 1. The selection of these reference species requires some explanations. 3495



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Table 4. Use of Amino Acids as Reference Species in Isodesmic Reaction Calculationsa

a

Species used as the reference in isodesmic reaction calculations are indicated by the color circles. The red circles correspond to the amino acids for ° values are in good agreement with calculated ones. The green circles indicate the amino acids whose experimental which the experimental ΔfH298 ΔfH°298 values are seemingly unreliable, and hence the calculated values were used in isodesmic reaction calculations. The blue circles stand for the species for which the experimental values are missing. For example, Ala, β-Ala, Sar, Gly, and γ-Abu were used to construct the isodesmic reactions for Val.

phase enthalpy of formation of Ala, β-Ala, Sar, and Gly (Table 2) were used in this work in isodesmic reaction calculations. The internal consistency of these values is clearly demonstrated in Table 3, where the above-mentioned four amino acids are used to estimate the enthalpy of formation of γ-Abu. As we can see, each of reference amino acids leads to almost the same ° (γ-Abu, g) that agrees well with the value of Δ fH 298 experimental one. The average of all isodesmic reactions is recommended for the gas-phase enthalpy of formation of γ-Abu in Table 2. After that, the new compound, Val, was considered; ° value was estimated from the isodesmic reaction its ΔfH298 calculations (Table S3, Supporting Information) using the earlier accepted enthalpies of formation of Ala, β-Ala, Sar, Gly, and γ-Abu. The ΔfH°298 values for remaining amino acids were obtained in the same way; the compounds with previously estimated enthalpies of formation were used in the isodesmic reaction calculations for new amino acids. In other words, in each step, a new reference amino acid was added while all values determined in previous steps were frozen. Table 4 shows the amino acids that were used in isodesmic reactions for each of compounds studied in this work. A large number of isodesmic reactions with different reference species were considered in

each case to decrease the error associated with the uncertainty of the experimental ΔfH°298 values of reference species. About 100 compounds (Table S2 of the Supporting Information) with reliable experimental enthalpies of formation were used in the isodesmic reactions. The accuracy of their ΔfH298 ° values was supported by the G4 calculations applied to atomization reaction; as seen from Table S2 of Supporting Information, the discrepancy between the most of experimental and calculated values is near the uncertainty of experimental enthalpies of formation. The proposed sequential approach was used to assess the internal consistency over the experimental ΔfH298 ° values of four key amino acids and estimated values of other amino acids; it is also served as a diagnostic tool to identify experimental data that may require re-examination.

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RESULTS AND DISCUSSION Gas-Phase Enthalpies of Formation. The ΔfH298 ° values calculated in this study from isodesmic reactions are compared with available experimental data and results of previous calculations in Table 2. As mentioned above, the experimental enthalpies of formation of Ala, β-Ala, Sar, and Gly accepted in this work agree well with those calculated from isodesmic 3496



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value of Val is in excellent agreement with the results of G3(MP2)//B3LYP and G3(MP2) calculations15,16 and differs from the experimental value by 21 kJ/mol. The results of two calorimetric measurements59,60 of enthalpy of formation of crystalline Val are in close agreement with each other, and, therefore, one can suggest that the experimental enthalpy of sublimation is substantially overestimated. For Leu, the calculated ΔfH298 ° (g) value differs from the experimental one by 11 kJ/mol. This discrepancy can be attributed to the uncertainties in the experimental ΔfH°298(cr) and ΔsubH°298 values. Although the results of two enthalpy of sublimation measurements are almost the same, their error, as shown in Table 2, may be sufficiently large. Moreover, the three reported experimental ΔfH°298(cr) values of Leu differ in the range of 5−11 kJ/mol.39,51,59 We can get a “formal” agreement between the experimental and calculated ΔfH298 ° (g) values by accepting the value of Tsuzuki and Hunt59 (−648.6 kJ/mol) for the enthalpy of formation of solid Leu. However, Hutchens et al.39 recalculated the data of Huffman et al.51 and found the ° (Leu, cr) = −637.4 kJ/mol. The more positive value of ΔfH298 last value is recommended in Table 2 because the same recalculation by Hutchens et al.39 for Gly has a better agreement with the values reported later42,54 than with the value of Tsuzuki and Hunt. 59 Nevertheless, the new calorimetric investigation of Leu would be extremely valuable as a check on the accuracy of the theoretical calculations. Calculated in this work ΔfH°298(g) values for Cys and N-Bnβ-Ala are 13 kJ/mol more negative than the experimental values. This disagreement remains unexplained because these two compounds have been recently investigated by the experienced thermochemists.11,28 The enthalpies of formation of Met and Cys were calculated by Ramabhadran et al.12 using the connectivity based hierarchy (CBH) developed to predict a reliable enthalpy of formation of all closed shell organic molecules. It should be noted, that their computed value for Met is in agreement with that recommended by Roux et al.,7 while the computed values for Cys are 7−19 kJ/mol more negative than the experimental value measured by Roux et al.11 (−382.6 kJ/mol). More negative values were also calculated by G311 and G3(MP2)16 methods (see Table 2). We agree with Ramabhadran et al.12 that it will be interesting to consider this further in future studies. A good agreement between the calculated and experimental ΔfH°298(g) values was obtained for 10 out of 14 compounds with the reported experimental data. Thus, an internal consistency exists between our calculated values and the experimental data for the most part of amino acids and large amount of the reference species involved in the isodesmic reactions. On the basis of this consistency, the computed gasphase enthalpies of formation are provided as recommended values for all compounds except for Ala, β-Ala, Sar, and Gly, for which the experimental values are accepted (Table 2). Earlier the enthalpies of formation of amino acids were calculated by different quantum chemical methods. G3(MP2) method was used to calculate the ΔfH298 ° (g) values of all 20 common α-amino acids,16 and the enthalpies of formation of 6 α-amino acids were calculated by G3(MP2)//B3LYP method.15 The values recommended in our work are in good agreement with G3(MP2)//B3LYP results, whereas the discrepancies in the range of 5−17 kJ/mol were found with the G3(MP2) values for Ala, Gly, Pro, Lys, Asn, Gln, Asp, Thr, Tyr, Arg, and His. The comparison with experimental data for Ala, Gly, and Pro suggests that the G3(MP2) method can

reactions. The values calculated earlier by G3(MP2)//B3LYP method15 are in a better agreement with the experiment than those calculated by G3(MP2) method.16 Large deviations of ∼9 kJ/mol were observed unexpectedly between the experimental values for Ala, β-Ala, and Gly and those calculated by W1U method. Although the W1U method showed the higher accuracy compared to G3 theory,35 this method was tested only on very small molecules, whereas its accuracy may be poor for larger molecules. Furthermore, it should be noted that we could not reproduce some of the ΔfH°298(g) values calculated by Parthiban and Martin,35 and thus one cannot exclude the possibility of an error in the W1U method implemented in Gaussian 03. As for the values estimated by group additivity method,14 the large deviation was observed for Ala because the group contribution values were obtained using the incorrect experimental results for this amino acid. Among the other amino acids with reported experimental ΔfH°298(g) values, a good agreement with the calculated values could be accepted for γ-Abu, Met, Pro, N-PhGly, α-PhGly, and Phe. The calculated values for γ-Abu, Met, and α-PhGly (Table 2) agree with the experimental ones within their error limits. The experimental gas-phase enthalpy of formation of Pro (−366.2 ± 4.0 kJ/mol)50 is 15−20 kJ/mol more positive than those calculated by different quantum chemical methods (Table 2). This value is based on the enthalpies of sublimation measured at the temperatures from 390 to 420 K by Sabbah and Laffitte50 and adjusted to T = 298 K by means of eq 1 ◦ ◦ ◦ ΔsubH298 = ΔsubHT◦ + [Cp,298 (cr) − Cp,298 (g)]

(T − 298.15)

(1)

The similar procedure for Sar that has been also studied by Sabbah and Laffitte,50 resulted in the overestimated ΔsubH298 ° value (146.0 kJ/mol), as has been recently shown by Amaral et al.8 However, a substantially lower value of enthalpy of sublimation of Sar may be obtained from the data of Sabbah and Laffitte50 (123.8 kJ/mol, see Table 2) if the calculated value of Cp,298 ° (g) is used in eq 1 together with the experimental value of C°p,298(cr). Table 2 shows that a similar recalculation for Pro decreases the enthalpy of sublimation and consequently results in a good agreement between the experimental and calculated ΔfH298 ° (g) values. Therefore, one might say that there is no contradiction between experiment and theory for Pro. The 7 kJ/mol discrepancy between experimental and calculated ΔfH298 ° (g) values for N-PhGly could be also due to possible error in the experimental ΔsubH298 ° value. As can be seen from Table 2, a certain improvement may be obtained by the readjustment of enthalpy of sublimation to T = 298.15 K. The only value of the gas-phase enthalpy of formation of Phe is provided in the reference book by Pedley.1 It is about 7 kJ/ mol larger than that calculated in our work. This value is based on the solid-phase enthalpy of formation38 and enthalpy of sublimation at 455 K reported by Svec and Clyde (154.0 kJ/ mol).40 Recently a somewhat lower value of ΔsubH298 ° was reported for Phe (149.0 kJ/mol).67 This value leads to the insignificant difference between experimental and calculated ΔfH298 ° (g) values (Table 2), and, therefore, one can suggest that the experimental and theoretical results are in a reasonable agreement. The available experimental data could not match well the calculated values only for four amino acids, Val, Leu, Cys, and N-Bn-β-Ala. Table 2 displays that the calculated ΔfH298 ° (g) 3497



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overestimate the ΔfH°298(g) values up to ∼20 kJ/mol. For some amino acids, the enthalpies of formation were also computed by G3, G4, and CCSD(T) methods;3,7,8,12 the calculated ΔfH298 ° (g) values agree well with those recommended in Table 2. The ΔfH°298(g) values of 25 amino acids were estimated by group additivity method.14 The difference between estimated and recommended in Table 2 values exceeds 5 kJ/mol (maximum deviation is 67.6 kJ/mol) for 20 species. Such large errors in the additive scheme estimations are, first of all, due to the use of the incorrect experimental data for some amino acids. It should be also noted that the amino acids are polyfunctional molecules, and a large number of group contributions is needed for calculating their enthalpy of formation. Unfortunately, the values for some groups are unknown or only known with relatively large uncertainties. Thus, it is not surprising that the quantum chemical methods (and even not the most accurate) give substantially more reliable estimations of ΔfH298 ° (g) values than the group additivity scheme. Enthalpies of Sublimation. On the basis of the recommended ΔfH°298(g) values and the available experimental enthalpies of formation of crystalline substances, the enthalpies of sublimation were estimated and summarized in Table 2. It is obviously that an accuracy of these values depends not only on the accuracy of the calculated ΔfH°298(g) values but also on the reliability of the reported experimental ΔfH°298(cr) values. The consistent and accurate experimental enthalpies of formation and sublimation are now known only for the five amino acids, namely Ala, β-Ala, Sar, Gly, and γ-Abu, for which these values were confirmed at least by the two independent investigations. As for remaining amino acids, the recommended enthalpies of sublimation differ in accuracy depending on the accuracy of ΔfH298 ° (cr) values. The enthalpies of formation of crystalline Val determined in two studies59,60 slightly differ from one another. The most recent value60 is provided in Table 2. The accuracy of the predicted enthalpy of sublimation is determined by the error in the calculated enthalpy of formation. Thus, as discussed above, the theoretical results strongly support a conclusion that the experimental enthalpy of sublimation (162.8 kJ/mol)40 is overestimated by approximately 20 kJ/mol. It was mentioned in the above discussion that some ambiguity exists in the reported ΔfH°298(cr) values for Leu. On the basis of this fact, it is possible that the recommended in Table 2 enthalpy of sublimation of this amino acid (139.8 kJ/ mol) is somewhat underestimated. The new experimental study of enthalpy of combustion of Leu is desirable. For this reason, our suggestion for ΔfH°298(cr) and ΔsubH°298 are presented without uncertainties. The enthalpy of formation of solid Ile was determined by Tsuzuki et al.38 Later, this value was slightly corrected39 by recalculating the standard internal energy change (see Table 2). There is also only a single value of enthalpy of sublimation for Ile.40 In order to have a reliable estimation of the enthalpy of sublimation, the additional studies of ΔfH298 ° (cr) and/or ΔsubH°298 are appropriate. ° (g) calculated in the On the basis of the value of ΔfH298 present work and the experimental value of ΔfH298 ° (cr),62 the enthalpy of sublimation of solid Met is predicted to be 147.7 kJ/mol. Table 2 shows that this value is in a good agreement with that obtained by Roux et al.7 from the reanalysis of the previously reported enthalpies of sublimation.62

The enthalpies of formation of crystalline Cys and N-Bn-βAla and their enthalpies of sublimation were recently determined by Roux et al.11,28 There are no previously reported ΔsubH298 ° values for these compounds. It was noted that our calculated ΔfH°298(g) values are 13 kJ/mol more negative than the experimental ones. Taking into account that our calculated values are internally consistent with the reliable experimental ° data for Ala, β-Ala, Sar, and Gly, we recommend the ΔsubH298 values for Cys and N-Bn-β-Ala by relying on theoretical results rather than on the experimental data. Three close values of the enthalpy of formation of crystalline Ser were determined by combustion calorimetry.5,56,63 The value selected in Table 2 is the mean of the two results.5,63 On the basis of the latter value and the ΔfH°298(g) value calculated in this work, the enthalpy of sublimation of Ser is suggested in Table 2. The enthalpy of sublimation of Ser was not determined experimentally. The ΔsubH°298 recommended for Pro, N-PhGly, α-PhGly, and Phe are based on the theoretical calculations, and their values (Table 2) are close to some of the reported experimental data. No experimental investigations of enthalpy of sublimation have ever been reported for Lys, Asn, Gln, Asp, Glu, Thr, Tyr, Arg, His, Trp, and Gly-Gly. The ΔsubH°298 values for these compounds (Table 2) are based on the available experimental ° (g) enthalpies of formation of crystalline substances and ΔfH298 values calculated in this work. Because of an ambiguity in the ΔfH°298(g)(cr) values for Lys and Glu, the recommended enthalpies of sublimation for these amino acids are given without uncertainties. The enthalpy of sublimation of Ala-Ala (118.0 kJ/mol) was determined by electron ionization mass spectrometry in combination with Knudsen effusion with a large error.73 A substantially larger value is recommended in Table 2 (161.0 kJ/ mol) on the basis of theoretical calculations. The enthalpies of sublimation of amino acids and peptides were estimated by Tyunina et al.67,73,75,76 using the proposed “structure - property” correlation models. However, the values suggested for the same compounds in the four publications67,73,75,76 are often very different; the discrepancy between the estimated values amounts to 10−90 kJ/mol. Therefore, these values could not be used as an additional proof for the ΔsubH298 ° (g) values recommended in Table 2. Comparison of Enthalpies of Formation Calculated from Atomization and Isodesmic Reactions. Amino acids are flexible molecules with several internal rotation degrees of freedom. The conformational flexibility of these molecules leads to a variety of local minima, and the conformational contribution to the computed ΔfH°298(g) value may amount to several kJ/mol and thus cannot be neglected in highprecision calculations of thermochemical data. The contribution of high-energy conformations can be estimated from the conformational energy differences based on Boltzmann averaging. This correction improves the agreement with an experiment.77 The vibrational frequencies for internal rotation are often very low, and hence another source of error in the ΔfH°298(g) calculation can arise due to the use of harmonic approximation for low-frequency modes. For approximate treatment of molecules with low-frequency internal rotations, Radom and co-workers78,79 recommended to calculate the ZPE (zero-point energy) and thermal contribution to enthalpy associated with the frequencies below 260 cm −1 using a free rotor approximation. Even in the isodesmic reaction scheme, this 3498



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about 3 kJ/mol (Figure 1c). On the other hand, the application of a free rotor approximation78,79 to the calculation of ZPE and thermal correction yields a negative contribution to the enthalpy of formation (Figure 1d). Thus, two different corrections may compensate each other if we combine them (Figure 1e). Since the ΔfH298 ° (g) values calculated from atomization reaction without any corrections agree well with the isodesmic reaction results (Table 1), we can assume that such a compensation occurs for amino acids. The results shown in Figure 1 indicate that the common practice to take into account the multiple conformers may result in a substantial error in the calculated enthalpy of formation for molecules with several low-frequency modes if the harmonic oscillator approximation is used to estimate the ZPE and thermal corrections. The ΔfH298 ° (g) values of cyclic hydrocarbons were calculated earlier by Notario et al.81 using the free rotor approximation in the evaluation of ZPE and thermal corrections. The largest correction of −1.3 kJ/mol was obtained for cyclopentane which has only one low frequency. However, this correction becomes more negative as the number of low frequencies increases to four in γ-Abu (Figure 1d).

procedure leads to the better agreement between the experimental and calculated enthalpies of formation when the reactants and products have different number of low-frequency modes, however, an error is usually minor when the reactants and products have similar internal rotations.80 In all isodesmic reactions (see Table 3 and Table S3 of Supporting Information), we use a set of products that are conformationally similar to the reagent structures to avoid the errors associated with the amino acids flexibility. This enables us efficiently cancel the errors. Indeed, Table 2 shows that the ΔfH298 ° (g) values calculated from isodesmic reactions agree well with the reliable experimental data for Ala, β-Ala, Sar, and Gly. This allows us to expect a high accuracy of the calculated values for the other amino acids. The calculation from atomization reaction requires consideration of multiple conformations of amino acids compared to isodesmic reaction approach. Some of the amino acids have a large number of stable conformers and this correction amounts to several kJ/mol. However, as can be seen from Table 1, the ΔfH298 ° (g) values for the most stable conformer calculated from atomization reaction are in close agreement with those obtained from isodesmic reactions, and hence with the experimental data. This seemingly unexpected result can be explained by compensation effects: the positive contribution to the enthalpy from multiple conformations is offset by the negative correction term due to the use of the free rotor approximation in the calculating ZPE and thermal contribution to enthalpy. For example, 36 higher energy conformers of γAbu (see Table 5 in ref 18) make the calculated G4 enthalpy of formation 9 kJ/mol more positive (Figure 1b) compared to the

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CONCLUSIONS The accurate values of the gas-phase enthalpies of formation are calculated in this study for all 20 common α-amino acids and some uncommon amino acids and small peptides by combining G4 theory calculation with an isodesmic reaction scheme. The reference ΔfH°298(g) values were determined by a sequential approach starting with literature-derived values of the enthalpy of formation of Ala, β-Ala, Sar, and Gly. The enthalpy of formation of the next amino acid, γ-Abu, was estimated using these four amino acids. In the following calculations, the γ-Abu was used together with the four above amino acids as the reference species, etc. Thus, the amino acids with previously determined enthalpy of formation were used to estimate the ΔfH°298(g) values of the remaining amino acids. Therefore, these predictions constitute an internally self-consistent set of enthalpies of formation of amino acids. A good agreement between the calculated and experimental values was obtained for 10 out of 14 amino acids (Ala, β-Ala, Sar, Gly, γ-Abu, Met, Pro, N-PhGly, α-PhGly, and Phe) for which the experimental data were reported. However, the calculated ΔfH298 ° (g) values differ from the experimental ones for Val, Leu, Cys, and N-Bnβ-Ala assuming the possible inaccuracy in the experimental measurements. A high accuracy of the recommended values is supported by the internal consistency of the calculated values with one another and with the experimental enthalpies of formation of about 100 reference compounds involved in the isodesmic reaction calculations. The ΔfH298 ° (g) values determined in this work allowed us either to predict or to improve the enthalpies of sublimation of the studied amino acids. The accuracy of these values is certainly determined by the precision of the available experimental values of ΔfH298 ° (cr). A special attention should be given to the agreement of the results obtained via atomization and isodesmic reaction schemes (Table 1). The experimental enthalpies of formation reflect a Boltzmann distribution of conformers that makes the enthalpies of formation more positive than if there were only one conformer present. A correction for the theoretical enthalpy of formation calculated via atomization energy can be estimated from the conformational energy differences based on Boltzmann averaging.77 An another source of an error in the

Figure 1. Deviations between experimental enthalpy of formation of γAbu and those calculated by G4 method from atomization reaction. Key: (a) G4 value for the most stable conformer; (b) G4 value corrected for the mixture of 36 conformers; (c) G4 value corrected for the mixture of 27 conformers; (d) G4 value for the most stable conformer, the free rotor approximation is used in the evaluation of ZPE and thermal correction; (e) G4 value includes correction “c” and “d”.

lowest energy conformer’s value (Figure 1a). However, the barrier heights between some conformers of γ-Abu may be low enough and then the conformer of higher energy may relax to the conformer of lower energy. Therefore, it will not be detected experimentally and should not be taken into account in a calculation of the enthalpy of formation. It is most likely that only a part of γ-Abu conformers has to be used to estimate the conformer correction. Assuming that only 3/4 of γ-Abu conformers may be considered as effective (thermally accessible) conformers, the conformer correction decreases by 3499



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calculations from atomization energy of nonrigid large molecules is the use of harmonic ZPEs and thermal corrections for enthalpies at 298 K. In this paper, we used the free rotor model,78,79 which approximately takes into account the effects of anharmonicity. This model predicts the lowering of enthalpies of formation of amino acids with respect to the values obtained with harmonic ZPEs and thermal corrections. Thus, it may be a fortuitous coincidence that the anharmonic correction to the ZPE almost exactly cancels the conformer distribution correction. Because of this cancelation, the ΔfH298 ° (g) values calculated for the most stable conformer in terms of atomization energies are in good agreement with an experiment and the results from error-canceling isodesmic reaction schemes. Therefore, while this may at first glance be surprising, the enthalpy of formation of the most stable conformer computed from atomization reaction may be in a better agreement with the experimental value than that corrected for conformational composition.

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ASSOCIATED CONTENT

* Supporting Information S

G4 energies and Cartesian coordinates for the lowest-energy conformers of all compounds optimized at the B3LYP/631G(2df,p) level (Table S1), experimental enthalpies of formation of reference compounds used in isodesmic reaction calculations and their comparison with values calculated by the G4 method from the atomization reaction (Table S2), and enthalpies of formation of gaseous amino acids calculated from isodesmic reactions using G4 energies (Table S3). This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(O.V.D.) E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of this manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Russian Foundation for Basic Research under Grant No. 14-03-00612. REFERENCES

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Gas-Phase Enthalpies of Formation and Enthalpies of Sublimation of

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