An automated efficient conformation search of l -serine by the scaled hypersphere search method

Chemical Physics Letters 652 (2016) 209–215

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Research paper

An automated efficient conformation search of L-serine by the scaled hypersphere search method Naoki Kishimoto a,⇑, Manami Harayama a, Koichi Ohno a,b a b

Department of Chemistry, Faculty of Science and Graduate School of Science, Tohoku University, Aramaki, Sendai 980-8578, Japan Institute for Quantum Chemical Exploration, Minato-ku, Tokyo 108-0022, Japan

a r t i c l e

i n f o

Article history: Received 20 February 2016 In final form 12 April 2016 Available online 13 April 2016

a b s t r a c t Stable conformers of L-serine were automatically explored by applications of the scaled hypersphere search (SHS) method to equilibrium structures maintaining the chemical bond skeletons of serine. Energy barriers for conformational changes of L-serine were estimated from the heights of obtained transition structures. Zero-point-corrected electronic energies and Gibbs free energies of the 24 lowest energy conformers and 21 transition structures were calculated at 100, 298, and 400 K by a composite quantum chemistry method (Gaussian-4). Relative populations of 24 conformers including nine new conformers were calculated from the Gibbs energies assuming thermal equilibrium. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction The conformations of several amino acids have been investigated both experimentally and theoretically. Different from amino acids in aqueous solution, an isolated amino acid in vacuum prefers a non-ionized structure rather than a zwitterionic form. In the case of L-serine (HOCH2CH(NH2)COOH), individual calculations have been carried out at different levels of computational theory [1–4]. Serine is an interesting molecule for the conformation search, because different types of hydrogen bonding among ACH2OH, ANH2, and ACOOH groups in the molecule can result in a large number of stable conformers. Gronert and O’Hair calculated 51 conformers of L-serine using second-order Møller–Plesset calculations and a split-valence basis with polarization and diffuse functions (MP2/6-31+G⁄) after a trial conformational search using the semi-empirical method (AM1) and the following Hartree–Fock geometry optimizations (HF/6-31G⁄) [4]. Based on the results of this conformational search, stable conformers were examined by microwave (MW) spectroscopy of jet-cooled L-serine molecules in gas phase [5] as well as infrared (IR) spectroscopy of matrixisolated L-serine molecules [6]. In another study, a conformational search of serine was performed at the HF/3-21G⁄ level of study, and 61 conformers were found after re-optimization calculation using density functional theory (DFT) with a hybrid functional, large basis set, and polarization and diffuse functions (B3LYP/6-311+ +G⁄⁄) [7]. In a recent IR study [8], Gibbs free energies of the 14 lowest energy conformers were calculated at temperatures of 0 and ⇑ Corresponding author. E-mail address: [email protected] (N. Kishimoto). http://dx.doi.org/10.1016/j.cplett.2016.04.039 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.

441 K. The nine most stable conformers obtained in Ref. [7] as well as twelve conformers in Ref. [6] are included in the 14 conformers listed in Ref. [8]. For flexible molecules which have internal rotations, that can form intramolecular hydrogen bonds, a large amount of time is required to determine stable conformers or minimum energy pathways for conformational changes at a high level of computational theory. A scaled hypersphere search (SHS) method [9–11] for uphill walking on a potential energy surface, a core technique in the global reaction route mapping (GRRM) program [12], can automatically explore possible isomerization pathways including transition states (TSs) and dissociation pathways [13], and the SHS theory has been applied to investigate decomposition and reverse synthetic pathway of glycine [14]. In this study, we have used the SHS theory to obtain stable conformers of L-serine and pathways between conformers. A full exploration of conformational space to find possible structural isomers yields isomeric equilibrium structures, stable conformers, and dissociation pathways, however, this requires significant computational time even with the SHS method. Concerning flexible molecules, exploration along lowenergy reaction pathways can prevent a continuous search of structural isomers after rearrangements of chemical bonds. Therefore, in this study of the SHS conformational exploration of L-serine, we have combined a lower-energy pathway search with a bond length judgment. Quantitative ratios of the seven observed L-serine conformers in the supersonic jet were obtained in the microwave spectroscopic study [5]. Experimental studies for isolated serine molecules require heating of a solid sample, followed by rapid cooling of molecules in a supersonic beam, and this treatment can maintain

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the ratio of conformers in the vapor to some degree. Therefore, to compare the experimental ratios of stable conformers with theoretical ones, we must calculate Gibbs (free) energy at evaporation and lower temperatures. It should be noted that Raman spectra of L-serine and L-threonine in aqueous environment were observed, and they were simulated with Boltzmann-weighted stable conformers obtained by the cluster model calculation with a zwitterion embedded in seven water molecules [15]. 2. Computational methods An automated exploration of the stable conformers of serine was performed using the GRRM program [12] at the MP2/6-31G level of theory. We started from the optimized geometry of a well-known conformer (conformer Ia in Ref. [5] or 1 in Ref. [8]). To find other conformers efficiently, a limited search for lowenergy isomers is useful. We explored the largest five anharmonic downward-distorting directions along the reaction coordinates around the obtained equilibrium structures. Also, bond length judgment was applied to all covalent bonds in the serine molecule (shown in the structural formula below) to prevent a further reaction route search after ‘dissociation’ of the specified bonds.

obtained from the G4 calculation are also shown in Fig. 1. Conformers were ordered based on their relative G4 energies at 0 K (DE0, zero-point-corrected electronic energy = Gibbs energy at 0 K (DG0)) and numbered accordingly. Because the ratios of observed conformers in the previous study have been relative to conformer 2 (as numbered in this study, but in Ia in Ref. [5] and 1 in Ref. [8]) [5], we have subtracted the G4 energy of conformer 2 from the calculated G4 energies. In recent studies using MP4/6-311++G(d,p) [5], B3LYP/6-311++G(d,p) [7], and DFT (B3LYP/6-31++G⁄⁄ with harmonic zero-point vibrational energy correction or B2PLYP-D3/ maug-cc-pVTZ with anharmonic zero-point vibrational energy correction) calculations [8], it was concluded that the zero-pointcorrected electronic energy of conformer 2 is lower than that of conformer 1 by 1.0 kJ/mol. This was also suggested by MP2/6-31 +G⁄ calculations in 1995 [4]. However, in this study, we confirmed that the zero-point-corrected electronic energy of conformer 1 is lower than that of conformer 2 within 0.5 kJ/mol using the G4 composite calculations at 0 K. In Table 1, transition states are listed with Gibbs energy values (D4 GT) at T = 0, 100, 298, and 400 K. TS n/m indicates a transition state between two conformers (n and m). The calculated energy of TS 7/11 is lower than that of conformer 11 at low temperature, while the energy of this state is higher than that of conformer 11 at both 298 and 400 K. Several transition states connected to stable conformers and with energies greater than 12.00 kJ/mol in D4 G0 were selected, as listed in Table 1. Cartesian coordinates of the transition states listed in Table 1 are also provided in Supporting Information 2. As introduced in a previous study by Hernández et al. [15], the conformations of L-serine can be classified by torsion angles:

ðbackboneÞ u1 : HAOACðCa Þ@O, u2 : OðHÞACðOÞACa ðHÞAN;

u3 : CðOOHÞACa ðHÞANðHÞAH;

ðside chainÞ

In this study, bond dissociation was judged by threshold bond lengths: these are 1.2 times longer than covalent bonds in the initially optimized conformer (the bond length is also shown in the structural formula above). Obtained conformers and transition structures were re-optimized at the MP2/aug-cc-pVDZ level of theory. Thermodynamic quantities such as enthalpy and entropy were also calculated at the MP2/aug-cc-pVDZ level of theory. A quantum chemistry composite method (Gaussian-4 theory (G4) [16]) in Gaussian 09 [17] was utilized to calculate zeropoint-corrected electronic energies (G4 energy at 0 K, this E0 equals to G4 free energy G0 at 0 K) and G4 free energies (GT) including thermal-corrected energies at temperature T = 100, 298, and 400 K for transition structures and low-energy conformers of Lserine. The G4 calculation [16] includes geometry optimization using DFT (B3LYP/6-31G(2df,p)), and the zero-point vibrational energy is obtained from the DFT calculation. In the G4 method [16], electron correlation effects are calculated by the coupledcluster theory (CCSD(T)) and fourth-order Møller–Plesset perturbation theory (MP4) to obtain accurate results, and some parameters are also introduced for energy corrections. 3. Results and discussion Seventy-seven equilibrium structures (conformers) of L-serine and 140 transition states have been calculated with MP2/aug-ccpVDZ by the GRRM program. Twenty-four low-energy conformers from the G4 calculation are shown in Fig. 1 (Cartesian coordinates are provided in the Supporting Information 1). Dipole moments

v1 : CðOOHÞACa ðHÞACb ðH2 ÞAOðHÞ; v2 : Ca ðHÞACb ðH2 ÞAOAH:

Obtained conformers were characterized by the five torsion angles with abbreviates for synperiplanar p(0° ± 30°), antiperiplanar P(180° ± 30°), synclinal c+(60° ± 30°), anticlinal C+(120° ± 30°) and the anti-clockwise direction for c(60° ± 30°) and C(120° ± 30°) like (u1u2u3v1v2) = (Ppc+cc+). The five torsion angles and the classification of conformers were listed in the Supporting Information 1. Transition states in Table 1 can be related to unchanged plural torsion angles, which is shown in the table with underlines. 3.1. Observed serine conformers and relative potential energy Not all calculated stable conformers have been identified experimentally. As shown in Table 2, conformer 7 and several other conformers have not been discussed in previous spectroscopic studies [5,10]. Regarding other conformers, seven conformers (conformers 1–6 and 12 in this study) have been detected by MW spectroscopy [5], and four conformers (9, 11, 14, and 17) were not observed. Observed relative ratios of seven conformers (Supporting Information in Ref. [5]) are listed in Table 2, and they can be ordered according to relative quantity is as follows:

2 > 1 > 3 > 5 > 4  6  12 (Ia > IIb > I’b > IIa > IIc  IIIbb  IIIbc, following the notation used in Ref. [5]). On the basis of potential energies, the conformer population order can be listed as follows:

1  2 > 3 > 4 > 5  6ð 7 > 8  9  10 > 11Þ > 12:

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Fig. 1. 24 most stable conformers of L-serine and their relative zero-point-corrected electronic energy at 0 K (DE0 (= DG0) by the composite G4 method) compared with conformer 2. Dipole moment (in Debye) is also shown. Cartesian coordinates are listed in Supporting Information 1.

Using matrix-isolation IR spectroscopy, six conformers (conformers 1–5 and 9 in this study) were identified, but conformers 6 and 12 were not determined experimentally [8]. It is interesting that conformer 9 (IIIaa [5]) was not observed in the microwave spectroscopy study [5], however, it was identified by the matrixisolation IR spectroscopy [8]. This phenomenon was attributed to conformational relaxation of conformer 9 induced by Ne atoms in the carrier gas of the supersonic molecular beam [5]. The calculated potential energy barrier of this conformational change from

conformer 9 (IIIaa [5]) to conformer 2 (Ia [5]) is D4 E0 0 (D4 G0 0) = 5.03 kJ/mol (= 11.76–6.73), as shown in Fig. 2. Here, the prime sign in D4 E0 0 indicates that the energy was not calculated from that of conformer 2. In the case of another observed conformer, for example, the calculated barrier height of conformational change from conformer 3 (I0 b [5]) to conformer 2 is D4 E0 0 (D4 G0 0) = 17.57 kJ/mol (= 19.17–1.60). This energy barrier is probably too high for conformational change induced by carrier gas atoms in the supersonic beam. The barrier height generally changes with

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Table 1 Theoretical relative Gibbs free energies (D4 GT) at T = 0 (= D4 E0), 100, 298, and 400 K (in kJ/mol) calculated by the G4 composite method for transition states (TSs) of L-serine selected from the conformational search results, and torsion angle abbreviations (see text) for corresponding conformations. Torsion angle*

D4 GT

(u1u2u3v1v2)

0K

100 K

298 K

400 K

Confomer 2 TS 5/10

(Ia)** (IIa/10)

pPc+Pc+

0.00 6.98

0.00 7.13

0.00 8.31

0.00 9.34

TS 7/11a

(7/Ib)

pPc+cP/pPc+cc+

7.06

7.06

7.25

7.58

TS 3/7

(I0 b/7)

pPpcc/pPc+cP

7.19

7.16

7.31

7.62

TS 5/8

(IIa/8)

PpPPP/PpPPc

7.35

7.73

9.84

11.34

TS 6/15

(IIIbb/15)

pc+c+cc+/ppc+cP

9.83

9.74

9.82

10.12

PpPPP/Ppc+PP

TS 17/18

(Ic/18)

pPc+c+c/pPpc+c

11.50

11.86

13.99

15.44

TS 2/9

(Ia/IIIaa)

pPc+Pc+/ppc+Pc+

11.76

12.26

15.54

17.72

TS 15/23

ppc+cP/pC+c+c+c+

(>12.00)*** 12.18

12.06

12.17

12.49

TS 18/20

pPpc+c/pPc+PP

12.46

12.44

12.63

12.94

TS 17/21

(Ic/21)

pPc+c+c/ pC+c+c+P

14.56

14.88

16.14

16.99

TS 12/13

(IIIbc/13)

pc+c+c+c/pc+cc+c

14.76

14.82

16.24

17.41

TS 6/16

(IIIbb/16)

pc+c+cc+/pc+Pcc+

15.46

15.45

16.07

16.76

TS 2/3

(Ia/I0 b)

pPc+Pc+/pPpcc

19.17

19.40

21.40

22.97

TS 3/16

(I0 b/16)

pPpcc/pc+Pcc+

20.72

20.95

21.87

22.56

TS 4/8

(IIc/8)

PpC+c+c/PpPPc

24.62

24.91

27.50

29.35

pPc+cP/ppc+cP

25.11

25.58

27.61

28.95

TS 7/15 TS 2/17

(Ia/Ic)

pPc+c+c/pPc+Pc+

25.69

25.75

26.77

27.59

TS 9/22

(IIIaa/22)

ppc+Pc+/ppc+cc

26.24

25.90

26.21

26.85

TS 1/4

(IIb/IIc)

PpC+c+c/Ppc+cc+

26.68

27.03

30.20

32.54

TS 3/14

(I0 b/III0 ab)

pPpcc/ppccc

28.28

28.84

31.82

33.80

TS 4/5

(IIc/IIa)

PpC+c+c/PpPPP

36.58

36.73

38.70

40.20

(Cartesian coordinates are listed in Supporting Information 2). * Common abbreviations through the transition are underlined. ** Notation given in the MW study [5]. *** TSs (D4 G0 > 12.00 eV) connected to two conformers in Fig. 1 were selected. a Calculated DE0 (DG0) and DG at 100 K are lower than those for conformer 11.

rapid decrease in temperature due to the adiabatic expansion of gas sample in vacuum, and we will discuss this point in the next section. Conformers 7 and 13 in Fig. 1 have not been found in the low energy conformer group even in recent theoretical calculations [5–8]. In addition, seven conformers (conformer 16, 18–23) were found in the same energy region as conformers 12–14 in the IR study [8] and conformers III0 ab–Ic in the MW study [5]. Regarding the torsion angle correlation in the backbone, the (u1u3) = (pc+) combination was found in 13 conformers among 24 stable conformers. This hydrogen bonding COOH  NH2 is related to another OH group in the side chain as (u1u3v2) = (pc+c+, 5 conformers), (pc+c, 4 conformers), and (pc+P, 4 conformers). Four pc+c+ (u1u3v2) conformers are in relatively low energy range (DE0 < 8 kJ/mol). 3.2. Gibbs energies of serine conformers The calculated relative G4 Gibbs energies (DGT) at T = 100, 298, and 400 K for 24 conformers (relative to conformer 2, i.e., conformer Ia in Ref. [5] and 1 in Ref. [8]) are listed in Table 2. The observed relative ratios of seven conformers (Supporting Information in Ref. [5]) were compared with those calculated theoretically estimated from the relative Gibbs energy assuming thermal equilibrium by the following equation: ½conf: X=½conf: 2 ¼ expðDG=RTÞ at temperature T, where [conf. X] and [conf. 2] are mole fractions of conformer X and conformer 2, respectively, and R is the gas constant. The theoretical relative ratio of conformer 1 (IIb [5]) is large (1.38) at low temperature (100 K), and it decreases with heating, as shown in Table 2. Thus, judging from the experimental relative ratio for conformer 1 (0.47(1)), the relative ratio

at high temperature, which is not significantly different from evaporation temperature, may be frozen in the supersonic beam. Neither conformer 9 (IIIaa [5]) nor 11 (Ib [5]) was detected in the MW study [5], although their free energies suggest that they are sufficiently stable to be observed at high temperature. Their theoretical relative ratios are more than 0.10 at 400 K, and conformer 9 has been observed in a recent IR study [8]. The barrier height for the conformational change from conformer 9 (IIIaa [5]) to conformer 2 (Ia [5]) decreases rapidly on cooling, as follows (shown in Fig. 2):

D4 G0 400 K = 13.16 kJ/mol (= 17.72–4.56), D4 G0 100 K = 6.02 kJ/mol (= 12.26–6.24), and D4 E0 0 (= DG0 0) = 5.03 kJ/mol (= 11.76–6.73). (Here, the prime sign in D4 G0 indicates that the Gibbs energy was not calculated from conformer 2.) The adiabatic expansion of gas in the supersonic jet leads to the rapid decrease of the barrier height. This conformational change (9 ? TS ? 2), due to the carrier gas in the supersonic beam, greatly effects the relative ratios of the conformers. The observed relative ratio (0.47(1)) for conformer 1 is 0.72 times smaller than the estimate (0.65) based on the thermal equilibrium at 400 K without modeling the relaxation effect. In addition, we have estimated the relative ratios of three conformers (1 (IIb [5]), 4 (IIc [5]), and 14 (III0 ab [5])), which have no low-energy relaxation pathways, nominally taking into account the relaxation effect. Results of these nominal estimates (Table 2) were obtained by utilizing the following relationship, ½conf: X=½conf: 2 ¼ x=ð1:00 þ 0:25Þ for conformer X (population x) with the relative population of conformer 2 (1.00) and conformer 9 (0.25) at T = 400 K. The relative ratios estimated by this assumption are

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Table 2 Theoretical relative Gibbs free energies (DGT in kJ/mol) at T = 100, 298, and 400 K calculated by the G4 composite method for 24 conformers (see Fig. 1) and relative ratios (in parentheses) estimated from DGT.

DGT (theoretical relative ratio)

Conformer This work

IR [8]

MW [5]

T = 100 K

298 K

400 K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2* 1 4 3 6 7 –a 9 5 8 11 10 –a –a 13 –a 12 –a –a –a –a –a –a 14

IIb** Ia I0 b IIc IIa IIIbb –b –b IIIaa –b Ib IIIbc –b III0 ab –b –b Ic –b –b –b –b –b –b –b

0.27 (1.38) 0.00 (1.00) 1.75 (0.12) 3.95 (0.01) 5.71c 5.79c 5.83c 6.65c 6.24c 6.97c 7.52c 8.37c 8.97c 9.21c 9.73c 10.14c 10.36c 10.53c 10.84c 11.23c 11.20c 11.36c 11.71c 12.04c

0.74 (0.74) 0.00 (1.00) 2.44 (0.37) 5.77 (0.10) 6.27 (0.08) 6.57 (0.07) 5.28 (0.12) 7.52 (0.05) 5.13 (0.13) 7.09 (0.06) 7.11 (0.06) 7.41 (0.05) 9.37 (0.02) 9.25 (0.02) 8.88 (0.03) 10.82 (0.01) 9.73 (0.02) 10.69 (0.01) 9.95 (0.02) 10.66 (0.01) 9.94 (0.02) 9.90 (0.02) 10.96 (0.01) 11.96 (0.01)

1.45 (0.65) 0.00 (1.00) 2.87 (0.42) 6.98 (0.12) 6.60 (0.14) 7.12 (0.12) 4.81 (0.24) 8.06 (0.09) 4.56 (0.25) 7.10 (0.12) 6.86 (0.13) 6.80 (0.13) 9.57 (0.06) 9.32 (0.06) 8.27 (0.08) 11.23 (0.03) 9.25 (0.06) 10.66 (0.04) 9.29 (0.06) 10.19 (0.05) 9.07 (0.07) 9.07 (0.07) 10.34 (0.04) 11.81 (0.03)

Relax.d

Experimental relative ratio [5]

(0.52)e [9 ? 2] (1.00) [7 ? 3] (>0.34)e (0.10)e [8,10 ? 5] (>0.11)e [15,16 ? 6] (>0.10)e [11 ? 7,7 ? 3] [8 ? 5] (<0.07)e [9 ? 2] (0.00) [10 ? 5] (<0.10)e [11 ? 7] (<0.10)e [13 ? 12] (>0.10)e [13 ? 12] (<0.05)e (0.05)e [23 ? 15,15 ? 6] [16 ? 6] (<0.02)e [21,18 ? 17] (>0.05)e [20 ? 18,18 ? 17] (0.05)e [20 ? 18] (<0.04)e [21 ? 17] (<0.06)e (0.06)e [23 ? 15] (<0.03)e (0.02)e

0.47(1) 1.00 0.37(11) 0.12(5) 0.27(5) 0.14(2) – – –f – –f 0.15(4) – –f – – –f – – – – – – –

(Cartesian coordinates are listed in Supporting Information 1). * Notation given in the IR study [8]. ** Notation given in the MW study [5]. a Not listed in the IR study [8]. b Not listed in the MW study [5]. c Estimated relative population is under 0.01. d Possible relaxation pathways for conformation change via low barrier height (D4 G0 0 < 10.00 kJ/mol) determined by D4 G0 (Table 1) – DG0 (= DE0 in Fig. 1) of the corresponding conformer. e Nominally-estimated relative ratio after ideal conformation relaxation [9 ? 2] in a supersonic jet. For example, 0.52 = 0.65/(1.00 + 0.25). f Not observed in the MW study [5].

Fig. 2. Calculated energy (relative to conformer 9) for conformation change from conformer 9 to conformer 2 at T = 0 K (DE0 0 (= DG0 0), black line), 100 K (DG0 100 K, blue line), and 400 K (DG0 400 K, red line) by the composite G4 method. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

comparable with those derived from experiment [5] for conformer 1 (0.52 vs. 0.47(1) [5]), 4 (0.10 vs. 0.12(5) [5]), and 14 (0.05 vs. ‘‘not observed” [5]). Although this assumption is based on an ideal 100% conformational change (9 ? TS ? 2), the influence of the carrier gas on the relative ratios of conformers in the L-serine/Ne supersonic jet beam can be recognized, and other conformers may be affected by the carrier gas effect as well. However, the calculation of accurate relative ratios that take into account the influence of conformational relaxation is difficult, and we have estimated minimum or maximum relative ratios, as listed in Table 2. Previous Gibbs energy calculations [8] using DFT (B2LYP-D3/ maug-cc-pVTZ) with anharmonic zero-point vibrational energy

correction at T = 441 K resulted in 5.07 kJ/mol for conformer 9 (conformer 5 in Ref. [8]) relative to conformer 2 (conformer 1 in Ref. [8]). This energy of 5.07 kJ/mol can be converted to a theoretical relative ratio of 0.25 for conformer 9 at 441 K, which is similar to the result of this study (0.25) at 400 K. Notably, similar analysis for the relative ratios of a IIIaa-type conformer of L-threonine (CH3CH(OH)CH(NH2)COOH) resulted in a large values (0.43 by MP2/aug-cc-pvDZ (GRRM) and 0.61 by the G4 method (Gaussian09)) relative to a Ia-type conformer from Gibbs energy calculations [18], and this IIIaa-type conformer was observed in a previous MW study [19]. The calculated barrier height for conformational change (IIIaa ? Ia) is larger than those

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of L-serine by 3–4 kJ/mol in G4 energy due to the steric hindrance of the methyl group in L-threonine:

D4 G0 400 K = 16.61 kJ/mol (= 18.26–1.65), D4 G0 100 K = 9.97 kJ/mol (= 12.99–3.02), and D4 E0 0 (= D4 G0 0) = 9.20 kJ/mol (= 12.48–3.28). Judging from the value of D4 E0 0 (ca. 9 kJ/mol), the infrequent collisions with gas in the supersonic beam may not be sufficient to cause conformational changes due to the high barriers (for example, those larger than 10.00 kJ/mol) to these changes. Therefore, in this study, we determined the energy threshold for the relaxation pathways of L-serine conformers as D4 E0 0 (= D4 G0 0) < 10.00 kJ/mol.

First, TS 4/DC connects conformer 4 (IIc [5]) with H2CO + NH2CHC(OH)2. This TS requires D4 E0 0 (= D4 G0 0) = 182.21 kJ/mol from conformer 4, and this is the calculated minimum dissociation pathway. Thus, dissociation of L-serine can be induced by an input of ca. 180 kJ/mol energy. The second TS is involved in a three-body dissociation pathway. TS 17/DC connects conformer 17 (Ic in [5]) with H2CO + CH2 + NH2CHCO. The required energy is D4 E0 0 (= D4 G0 0) = 265.18 kJ/mol. The last TS is involved in a H2 dissociation pathway. TS 5/DC connects conformer 5 (IIa in [5]) with H2 + NH2CH (COH)COOH. The required electronic energy is D4 E0 0 (= D4 G0 0) = 361.8 kJ/mol from conformer 5. Cartesian coordinates of transition states (TS 4/DC, TS 17/DC, and TS 5/DC) are shown in Supporting Information 3. 4. Conclusions

3.3. Entropy in Gibbs energy As we have discussed, the relative Gibbs energy (DG) compared to conformer 2 (Ia [5]) of L-serine is dependent on both temperature and structure. The Gibbs energy consists of the enthalpy (DH), entropy (DS), and temperature (T) according to the relationship, DG = DH  TDS. The DG at a certain temperature depends on the structure, namely on the electronic energy (DE), which is included in the enthalpy (DH). Some conformers and transition states show a significant temperature dependence in DG (Tables 1 and 2). A steep positive temperature dependence was obtained for TS 2/9 (Ia/IIIaa). The increasing energy values of relative DH for TS 2/9 are DH100 K = 11.47 kJ/mol and DH400 K = 8.90 kJ/mol by MP2/aug-cc-pVDZ, and DH is not the decisive factor for the free energy increase. Here, the relative entropy (DS) is crucial, and the destabilization energy (TDS) by entropy for rotational and vibrational motion can be shown as follows (MP2/au-cc-pVDZ calculations, in kJ/mol): – TD4 S100 – TD4 S400

K K

= 0.003 (rotation) + 1.20 (vibration), and = 0.01 (rotation) + 9.61 (vibration).

Similarly, the large DG change of conformer 4 (IIc in [5]) can also be ascribed to entropy change (DS) relative to conformer 2 by the following comparison (in kJ/mol): – TDS100 – TDS400

K K

= 0.05 (rotation) + 0.49 (vibration), and = 0.18 (rotation) + 4.12 (vibration),

Where DH100 K = 3.34 kJ/mol and DH400 K = 2.22 kJ/mol by MP2/ aug-cc-pVDZ calculations. The destabilization of the relative Gibbs energy suggests that conformer 2 is more favorable than other conformers (except for conformer 1 at low temperature) or other transition states. In addition, because the number of possible vibrational states increases with temperature, the Gibbs energy is stabilized at higher temperature through vibrational contributions to the entropy. The increasing rate of change in Gibbs energy depends on both the structure and vibrational modes, leading to a positive temperature dependence of DG for e.g. conformer 4 and TS 2/9 or negative dependence for conformers 7, 9, 11, 12, 15, 17, etc. A negative temperature dependence of DG was also calculated [8], by B2PLYP-D3/maug-cc-pVTZ with anharmonic zeropoint vibrational energy corrections, for conformers 2, 6, 9, 11, and 17. 3.4. Dissociation pathways We found transition states directly connected from stable conformers to a dissociation reaction (fragmentation) for the ground electronic state. Among these, three important transition states are described below.

Full conformational searching of amino acids, including a considerable number of complex intramolecular interactions, is important in biochemistry. In this study, we have explored more than 70 equilibrium structures of L-serine using an efficient automated algorithm with the scaled hypersphere surface (SHS) method, and nine new conformers have been found among 24 low energy conformers. To explore the conformations of a flexible molecule with quantum chemistry methods manually, trial optimization with a low-cost theoretical method should be first, followed by higher-level calculations on a smaller set of conformers. However, it can happen that new stable conformers can be found at dips in the potential energy surface during automated conformational search at a higher-level of calculations. Therefore, an efficient automated conformational exploration with high-level calculations can lead to new conformers under the limitation of computation time. Isomerization pathways without bond breaking were obtained as transition states for conformational changes, and observed conformational relaxation in a supersonic beam was examined by Gibbs energy calculation. The relative ratios of conformers studied in a previous microwave spectroscopy study [5] can be explained well by the Gibbs energies and the thermal equilibrium approximation with taking the relaxation effect into account. Most of the newly found conformers (e.g. conformer 7, 13, 16, . . .) have low relative ratios or a low-barrier isomerization pathway to a more stable conformer. Thus, reexamination experiments may fail to distinguish these conformers. For some transition states and conformers, the relative Gibbs energies showed significant positive temperature dependences, which was ascribed to the entropy of vibrational motion. A minimum-energy dissociation pathway shows energy barrier around ca. 180 kJ/mol from the fourth stable conformer. Acknowledgments N. K. acknowledges a research grant from the Institute for Quantum Chemical Exploration (IQCE). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2016.04. 039. References [1] C. Van Alsenoy, J.N. Scarsdale, H.L. Sellers, L. Schafer, Chem. Phys. Lett. 80 (1981) 124. [2] C. Van Alsenoy, S. Kulp, K. Siam, V. Klimkowski, J.D. Ewbank, L. Schafer, J. Mol. Struct. THEOCHEM 181 (1988) 169. [3] P. Tarakeshwar, S. Manogaran, J. Mol. Struct.: THEOCHEM 305 (1994) 205.

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