Effect of Orbital Interactions between Vicinal Bonds and between

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX-XXX

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Effect of Orbital Interactions between Vicinal Bonds and between Hydroxy Groups on the Conformational Stabilities of 1,2-Ethanediol and 2,3-Butanediols Nobuyuki Hayashi,*,† Tomomi Ujihara,† and Hirotaka Ikeda‡ †

Food Research Institute, National Agriculture and Food Research Organization (NARO), 2-1-12 Kannondai, Tsukuba, Ibaraki 305-8642, Japan ‡ Materials Science Department, MOLSIS Inc., 1-28-38 Shinkawa, Chuo-ku, Tokyo 104-0033, Japan S Supporting Information *

ABSTRACT: The geometries of the two hydroxy groups in 1,2-ethanediol or 2,3-butanediols are more stable in a gauche orientation than those in an anti orientation. This has been generally explained in terms of the gauche effect, which is stabilization due to antiperiplanar electron delocalization between an antibonding orbital of the C−O bond (σCO*) and a bonding orbital of the C−H or C−C bond (σCH or σCC). However, a C−C single bond rotation simultaneously determines the geometries of the six vicinal bonds. Therefore, it is important to understand the effects on conformational stability of other interactions of the bond orbitals adjacent to the rotating C1−C2 bond. Bond model analysis revealed that antiperiplanar bond orbital interactions as a whole contribute to the higher stabilities of hydroxy/hydroxy gauche conformers, where the C−O/C−H or C−O/C−C combination including the σCO*/σCH or σCO*/σCC delocalization is not the dominant interaction stabilizing hydroxy/hydroxy gauche conformers. Rather, our results show that a large destabilization due to the antiperiplanar C−O/C−O combination in hydroxy/hydroxy anti conformers relatively increases the stabilities of hydroxy/hydroxy gauche conformers. This destabilization results mainly from the repulsion between the antiperiplanar bonding orbitals (σCO/σCO), which have a larger overlap compared to the synclinal σCO/σCO combination. The sum of the interbond energies between the vicinal bond orbitals of these 1,2-alkanediols is more advantageous for stability in gauche conformers. In addition, interactions between the gauche-oriented hydroxy groups provide large stabilization energies and the corresponding interactions in anti conformers are negligible. The relative conformational stabilities of 1,2-ethanediol and erythro-2,3-butanediol can be explained by the interactions between the antiperiplanar bond orbitals, between the vicinal bond orbitals, or between the hydroxy groups in addition to the combination of interactions between the vicinal bond orbitals and between the hydroxy groups. In contrast, in threo-2,3-butanediol, differences in the relative stabilities of the three conformers can be understood by the combination of the interactions between the vicinal bond orbitals and between the hydroxy groups.

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more frequently than an anti orientation.11 This preference has often been explained by the stabilization resulting from electron delocalization between an antibonding orbital of the C−X bond (σCX*) and a bonding orbital of the C−H bond (σCH) (Figure 1a). 11 However, rotation about a C−C single bond simultaneously determines the geometries of the six vicinal bonds. Therefore, when these molecular conformations are discussed in terms of interactions between vicinal bond orbitals, it is important to focus on not only interactions such as σCX*/ σCH electron delocalization but also other interactions between bond orbitals. In antiperiplanar bond orbital interactions,

INTRODUCTION

1,2-Diols are important structural units found in many organic molecules, ranging from familiar compounds such as carbohydrates to bioactive compounds.1,2 The rotation of the C1−C2 single bond in 1,2-alkanediols generates conformers. The two hydroxy groups can adopt either a gauche or anti form in stable staggered conformations. Previous studies on the conformations of 1,2-ethanediol 1 and 2,3-butanediols (erythroisomer 2 and threo-isomer 3) revealed that the gauche conformers are more stable than the anti conformers.3−10 This advantage of the gauche conformer externally appears to result from the gauche effect. 1,2-Difluoroethane is a wellknown typical example of the gauche effect. The two electronegative substituents (X) such as fluoro groups at the 1,2-position of the carbon backbone adopt a gauche orientation © XXXX American Chemical Society

Received: August 13, 2017 Revised: October 13, 2017 Published: October 13, 2017 A

DOI: 10.1021/acs.jpca.7b08085 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

(4.9%), g−Tt′ (2.8%), g−Tg′+ (1.8%), g+Tt′ (1.5%), g+Tg′− (1.1%), g−Tg′− (0.7%), and g−G−t′ (0.03%)], and 17 conformers for 3 [g+G−t′ (36.2%), g−G−g′+ (18.3%), g−G+t′ (15.5%), g+G−g′+ (11.2%), g−G+g′− (8.0%), g−G+g′+ (7.4%), tTt′ (0.8%), g+Tt′ (0.5%), g+G+g′+ (0.4%), g−G−g′− (0.3%), g−Tt′ (0.3%), g+Tg′+ (0.3%), g−Tg′+ (0.2%), tG+t′ (0.1%), tG−t′ (0.1%), g−Tg′− (0.1%), and g+G+t′ (0.03%)]; in water, 10 conformers for 1 [g−G+t′ (35.3%), g−G+g′+ (25.2%), g−G+g′− (22.4%), g+G+t′ (6.0%), tG+t′ (3.3%), g+G+g′+ (1.9%), g−Tg′+ (1.8%), tTt′ (1.7%), g−Tt′ (1.6%), and g−Tg′− (0.7%)], 14 conformers for 2 [g+G−t′ (32.9%), g+G+g′− (19.4%), g−G+t′ (15.1%), g−G+g′+ (10.9%), tTt′ (3.5%), g−Tt′ (3.1%), g+Tg′− (2.9%), g+Tt′ (2.8%), g−Tg′+ (2.4%), g−Tg′− (2.2%), g−G−t′ (1.5%), g+G+t′ (1.3%), g−G−g′− (1.3%), and tG+t′ (0.8%)], and 18 conformers for 3 [g+G−t′ (41.0%), g−G−g′+ (18.6%), g−G+t′ (12.2%), g−G+g′+ (8.5%), g+G−g′+ (6.1%), g−G+g′− (3.8%), tTt′ (1.4%), g−G−g′− (1.2%), g+G+t′ (0.9%), g+G+g′+ (0.9%), g+Tt′ (0.9%), g+Tg′+ (0.8%), g−G−t′ (0.8%), tG−t′ (0.7%), tG+t′ (0.6%), g−Tt′ (0.6%), g−Tg′+ (0.6%), and g−Tg′− (0.4%)] except for the number of the enantiomers. These conformers are labeled according to the rule defined in a previous report (see Figure S1).9 Bond Model Analysis. The bond model analysis was proposed and developed by Inagaki et al. and applied to investigate the bond interactions in molecules and transition states.13 It has successfully disclosed the importance of germinal bond interactions in small ring molecules,13 germinal bond participation of pericyclic reactions,19 and the origin of the thermodynamic stabilities of biradicals20 and branched alkanes.21 The method describes an electronic structure of a molecule or transition state, obtained at the Hartree−Fock level, by linear combination of bond orbitals that consist of atomic or hybrid orbitals of two bonded atoms. The bond orbitals are obtained by minimization of electron populations of antibonding and vacant orbitals. Using the bond orbitals, the total electronic energy can be divided into the energies of the bond orbitals and those between the bond orbitals, which are defined as bond energies and interbond energies, respectively. We used the interbond energies to evaluate the bond interactions of the diols in this work. The electronic structures of the diol conformers geometrically optimized at the M06-2X/6-311+ +G(d,p) level were calculated at the HF/6-31G(d) level. The interbond energies were obtained using the bond model analysis program, which is available on the web from http:// orbitalphase.web.fc2.com/. Prediction of 1H NMR Chemical Shifts. Isotropic values (σ) of the diol conformers optimized at the M06-2X/6-311+ +G(d,p) level were calculated at the B3LYP(GIAO)/6311+G(2d,p) level using the Gaussian 09 program.15 The solvent effect (water) was taken into account by IEFPCM.16−18 Chemical shifts (δ) were obtained from the isotropic values (σ) using the following equation: δ = (31.9181 − σ)/1.0507.22 Weighted time-averaged chemical shifts were obtained from 10 conformers for 1, 14 conformers for 2, and 18 conformers for 3 optimized in water. Computation of OH/OH Scalar Coupling Constants. Scalar coupling constants (h2J) between hydroxy groups were calculated at the B3LYP/6-311++G(d,p) level for the g−G+t′ conformer of 1, g+G−t′ conformer of 2, and both g+G−t′ and g−G+t′ conformers of 3.

Figure 1. Bond orbital interactions in a 1,2-disubstituted ethane. (a) Electron delocalization between antiperiplanar bonding and antibonding orbitals in a gauche conformer and (b) interaction between synclinal bonding orbitals.

stabilizing effects due to electron delocalization can also be expected for combinations other than σCX*/σCH. For example, Pophristic and Goodman demonstrated that σCH*/σCH electron delocalizations are one factor contributing to the stable conformation of ethane.12 On the other hand, because synclinal (gauche-oriented) bond orbital interactions result in conformational destabilization due to repulsion between occupied orbitals (Figure 1b), the smaller this destabilization becomes, the more the relative stability of a conformer increases. However, the comprehensive effects of these antiperiplanar and synclinal bond interactions on conformational stability have not been fully elucidated. Furthermore, in 1,2-diol structures, the interactions between the gauche-oriented hydroxy groups need to be investigated. The aim of the present study is to gain insight into the effects of orbital interactions in the vicinity of the C1−C2 bond of 1,2alkanediols on conformational stability. To this end, interactions between the vicinal bond orbitals and between orbitals in the hydroxy groups of three diols (1, 2, and 3) were analyzed using the bond model analysis.13

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COMPUTATIONAL DETAILS Geometry Optimizations and Vibrational Analyses of Diols (1, 2, and 3). For 1,2-ethanediol 1, each C1−C2, C1− O1, or C2−O2 bond was rotated at 120° intervals to generate 27 geometries used as initial structures. Similarly, for 2,3butanediols 2 and 3, 27 geometries generated by rotating each C2−C3, C2−O1, or C3−O2 bond at 120° intervals were used as initial structures. All calculations were conducted at the M062X/6-311++G(d,p) level14 using the Gaussian 09 program.15 The solvent effect (water) was taken into account using the integral equation formalism polarized continuum model (IEFPCM) with a dielectric constant of ε = 78.3553.16−18 The number of optimized structures obtained was as follows: in vacuum, 10 conformers for 1 [g−G+t′ (44.6%), g−G+g′+ (26.0%), g−G+g′− (17.0%), g+G+t′ (8.3%), tG+t′ (1.3%), g+G+g′+ (1.1%), g−Tg′+ (0.7%), tTt′ (0.5%), g−Tt′ (0.2%), and g−Tg′− (0.2%)], 11 conformers for 2 [g+G−t′ (46.3%), g−G+t′ (18.1%), g+G+g′− (15.2%), g−G−g′+ (7.7%), tTt′ B


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EXPERIMENTAL SECTION General Information. All chemicals were obtained from commercial suppliers and used without further purification. 1,2Ethanediol 1 (purity > 99.5%) was purchased from Wako Pure Chem. Ind. Ltd. (Osaka, Japan). Erythro-2,3-butanediol 2 (purity > 97.0%) and threo-2,3-butanediol 3 (purity = 99%) were purchased from Tokyo Chem. Ind. (Tokyo, Japan) and Sigma-Aldrich Co. (St Louis, MO, USA), respectively. NMR Experiments. 1H NMR spectra of diols 1, 2, and 3 were obtained using 5.0 mM diol D2O or H2O/D2O (9:1) solutions at 298 K on an Avance 400 spectrometer (400 MHz, Bruker Biospin, Rheinstetten, Germany) with a broad-band observe (BBO) cryogenic probe (BBO 400 BB-H & F-D) under the following conditions: acquisition time, 4.0 s; relaxation delay, 1.0 s; number of scans, 32. 1H NMR chemical shifts were reported as ppm using TMS (δ = 0.0000 ppm) in CCl4 as an external standard inserted in an NMR tube (ϕ = 5 mm) equipped with a coaxial cell. The same chemical shift values were obtained in D2O and H2O/D2O (9:1) solutions.

the methyl groups)/gauche (between the hydroxy groups), anti (between the methyl groups)/anti (between the hydroxy groups), anti (between the methyl groups)/gauche (between the hydroxy groups), and gauche (between the methyl groups)/anti (between the hydroxy groups), respectively. The designations (E) and (T) refer to the erythro and threo isomers, respectively. Second gauche conformers of 1 and 2 have an enantiomeric relationship with the gauche conformer and GG(E) shown in Figures 2a and 3a, respectively, and therefore are not shown in the figures. In erythro-isomer 2, GG(E) is more stable than AA(E). The stabilities of threo-isomer 3 conformers decrease in the order of GG(T), AG(T), and GA(T) (Figure 3a), and this trend in relative stability agrees well with those reported previously.3−10 Conformational structures and the energies of these structures in water were calculated using IEFPCM and shown to be similar to the results obtained in vacuum (Figures 2b and 3b). Although the most stable anti conformer of 1,2-ethanediol 1 is g−Tg′+ in water, unlike tTt′ in vacuum, the energy difference between g−Tg′+ and tTt′ is only 0.2 kJ/mol. Therefore, the stabilities of these conformers would be equivalent in water. To evaluate these computational results, theoretically calculated 1H NMR chemical shifts were compared with experimental values observed for the compounds dissolved in deuterium oxide. The chemical shifts of all conformers obtained from geometrical optimization were calculated at the B3LYP(GIAO)/6-311+G(2d,p) level and were scaled using the Pierens method.22 The predicted values were calculated as a weighted average based on the relative abundance of each conformer. The computational results agree well with the experimental data (Table 1). Interactions between the C1−C2 Vicinal Bond Orbitals of 1,2-Ethanediol. We investigated the bond interactions for both the gauche and anti conformers shown in Figure 2a by analyzing the electronic structures of these conformers using the bond model analysis. This analysis can evaluate the bond orbital interactions in molecules and transition states, and many successful applications have been reported to date.13 The sum of the interbond energies between the antiperiplanar bond orbitals of 1 is lower in the gauche conformer than that in the anti conformer by 0.133 au (Table 2). This result shows that the antiperiplanar interactions contribute to the higher stability of the gauche conformer. In contrast, the sum of the interbond energies between the synclinal bond orbitals is higher by 0.069 au in the gauche form than that in the anti form. However, the vicinal bond orbital interactions as a whole contribute to the higher stability of the gauche conformer because the thermodynamic advantage of the antiperiplanar interactions in the gauche conformer is larger than the disadvantage of the synclinal interactions by 0.064 au. In accordance with the accepted explanation of the gauche effect,11 antiperiplanar σCH/σCO* electron delocalizations in the gauche conformer have the lowest energies (−0.100 and −0.134 au) of any antiperiplanar electron delocalization, and this contributes to stabilizing the gauche conformer. In contrast, the σCO/σCO* interaction in the anti conformer results in a destabilization energy of 0.012 au. However, it is important to understand that electron delocalization of an antiperiplanar bond pair can occur in two directions: from a bonding orbital (σ1) of a bond to an antibonding orbital (σ2*) of another bond (σ1/σ2*) and in the opposite direction (σ1*/σ2). For a combination of antiperiplanar C−H and C−O bonds, although

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RESULTS AND DISCUSSION Geometry Optimization. Geometry optimization and vibrational analysis of diols (1, 2, and 3) in vacuum were conducted at the M06-2X/6-311++G(d,p) level. In the C1−C2 rotamers of 1,2-ethanediol 1, the gauche form is more stable than the anti form, as shown in Figure 2a. 2,3-Butanediols have two conformers [GG(E) and AA(E)] in the erythro-isomer 2 and three conformers [GG(T), AG(T), and GA(T)] in the threo-isomer 3 as stable C2−C3 rotamers (Figure 3a). Here, the designations GG, AA, AG, and GA refer to gauche (between

Figure 2. C1−C2 rotamers of 1,2-ethanediol 1 and the relative Gibbs energies optimized at the M06-2X/6-311++G(d,p) level. C


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Figure 3. C2−C3 rotamers of 2,3-butanediols (2 and 3) and their relative Gibbs energies optimized at the M06-2X/6-311++G(d,p) level.

Table 1. Proton Chemical Shifts (ppm) of 1,2-Ethanediol 1 and 2,3-Butanediols (2 and 3) Observed in 1H NMR Spectra and Calculated at the B3LYP(GIAO)/6-311+G(2d,p)//M06-2X/6-311++G(d,p) Level

compound 1 2 3

experimental (exp) H1 (H2) 3.47 Me1 (Me4) 0.94 0.95

H2 (H3) 3.52 3.43

calculated (calcd) H1 (H2) 3.59 Me1 (Me4) 0.98 1.02

H2 (H3) 3.67 3.37

Δ(calcd − exp) H1 (H2) 0.12 Me1 (Me4) 0.04 0.07

H2 (H3) 0.15 −0.06

σCO* electron delocalization. However, because the interbond energy of the reverse delocalization (σCH*/σCH) is at the same level as the σCH/σCH* interaction, the C−H/C−H combination generates a larger stabilization energy (−0.061 to −0.059 au) than the C−H/C−O combination. Although the anti conformer has two antiperiplanar C−H/C−H combinations, the gauche form is more stable in antiperiplanar bond orbital interactions than the anti form due to the high instability of the C−O/C−O combination (0.114 au) in the anti form. This instability mainly results from the repulsive interaction between

σCH/σCO* electron delocalization certainly affords the lowest energy, σCH*/σCO electron delocalization, which is in the opposite direction of σCH/σCO* delocalization, results in stabilization energies of only −0.041 and −0.001 au. Therefore, the net stabilization by the antiperiplanar C−H/C−O combination remains at −0.056 and −0.026 au, including the repulsion between the bonding orbitals. On the other hand, in the case of an antiperiplanar C−H/C−H combination, stabilization due to σCH/σCH* electron delocalization (−0.096 to −0.068 au) is somewhat smaller than that due to the σCH/ D


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Table 2. Interbond Energies (au) between the C1−C2 Vicinal Bond Orbitals of 1,2-Ethanediol 1 Conformers Optimized in Vacuuma conformer

bond/bond

1 gauche (g−G+t′)

C1−H1/C2−H3 C1−H1/C2−H4 C1−H1/C2−O2 C1−H2/C2−H3 C1−H2/C2−H4 C1−H2/C2−O2 C1−O1/C2−H3 C1−O1/C2−H4 C1−O1/C2−O2 total antiperiplanar total synclinal total vicinal C1−H1/C2−H3 C1−H1/C2−H4 C1−H1/C2−O2 C1−H2/C2−H3 C1−H2/C2−H4 C1−H2/C2−O2 C1−O1/C2−H3 C1−O1/C2−H4 C1−O1/C2−O2 total antiperiplanar total synclinal total vicinal

1 anti (tTt′)

a

subtotal (s) (s) (a) (a) (s) (s) (s) (a) (s)

(a) (s) (s) (s) (a) (s) (s) (s) (a)

0.151 0.113 −0.026 −0.059 0.183 0.021 0.034 −0.056 0.004 −0.141 0.505 0.365 −0.061 0.211 0.004 0.211 −0.061 0.004 0.004 0.004 0.114 −0.008 0.437 0.429

Occ−Occ (σ/σ)

Occ−Vac (σ/σ*)

Vac−Occ (σ*/σ)

0.147 0.116 0.109 0.101 0.181 0.021 0.043 0.080 0.008

0.001 −0.004 −0.134 −0.096 0.004 0.002 −0.003 −0.041 0.000

0.004 0.001 −0.001 −0.068 0.001 −0.006 −0.009 −0.100 −0.003

0.098 0.218 0.001 0.218 0.098 0.001 0.001 0.001 0.093

−0.082 −0.004 0.003 −0.004 −0.082 0.003 0.000 0.000 0.012

−0.082 −0.004 0.000 −0.004 −0.082 0.000 0.003 0.003 0.012

(Δ = 0.000) (Δ = 0.000) (Δ = 0.000)

(Δ = 0.133) (Δ = −0.069) (Δ = 0.064)

Occ, bonding orbital; Vac, antibonding orbital; (a), antiperiplanar; (s), synclinal; Δ, difference from the gauche conformer.

Table 3. Calculated Intramolecular OH/OH Scalar Coupling Constants (h2J) and OH/O Distances in Gauche Conformers of 1,2-Diols conformer −

+

1 (g G t′) 2 (g+G−t′) 3 (g+G−t′) 3 (g−G+t′) methanol dimer

Figure 4. Interactions between the vicinal C−O bonding orbitals (σCO) in 1,2-ethanediol 1.

h2

J (Hz) 0.12 0.20 0.26 0.10 1.15

OH/O distance (Å) 2.31 2.24 2.19 2.28 1.93

longer and smaller than those of the hydroxy groups of a methanol dimer, respectively. These results indicate that the intramolecular hydrogen bonds in these 1,2-diols are indeed weak compared to a typical hydrogen bond. As in the previous section, we investigated the orbital interactions between the hydroxy groups of 1,2-ethanediol 1 using the bond model analysis in terms of the O−H bond orbitals, lone pair orbitals on the oxygen atoms, and vacant orbitals on the hydrogen and oxygen atoms arising from splitvalence basis sets or polarization functions. Table 4 shows that the synclinal hydroxy groups have a relatively large stabilization energy (−0.147 au), whereas there is little stabilization energy between the antiperiplanar hydroxy groups (−0.004 au). This stabilization energy (−0.147 au) is larger than any of the stabilization energies of the vicinal bond orbitals of 1, and therefore, this interaction contributes significantly to the higher stability of the gauche conformer. This stabilization energy is largely attributable to the interactions of the two lone pair orbitals on O2 with the vacant orbital on H5 (−0.061 and −0.034 au) and with the O1−H5 antibonding orbital (σ*O1H5) (−0.025 and −0.012 au), which are considered general components of a hydrogen bond. In addition, there are

the bonding orbitals (the σCO/σCO interaction, 0.093 au) shown in Figure 4. The overlap between the bonding orbitals (σCO/ σCO) in the anti orientation is larger than that in the gauche orientation; the overlap integral values are 0.054 and 0.022, respectively. The interactions between the synclinal bond orbitals result from four C−H/C−O and two C−H/C−H combinations in the anti form and three C−H/C−H, two C−H/C−O, and one C−O/C−O combinations in the gauche form. The synclinal C−H/C−H combinations have large destabilization energies (0.113−0.211 au), whereas destabilization due to the synclinal C−H/C−O and C−O/C−O combinations is negligible (0.004−0.034 au). Therefore, the sum of the synclinal interbond energy of the gauche conformer is higher than that of the anti conformer. Interactions between Orbitals in the Hydroxy Groups of 1,2-Ethanediol. A weak intramolecular hydrogen bond between synclinal hydroxy groups in 1,2-diol systems has been discussed to date.5−10,23 As Table 3 shows, the OH/O distances and h2J values of the g−G+t′ conformer of 1, g+G−t′ conformer of 2, and both g+G−t′ and g−G+t′ conformers of 3 are much E


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Table 4. Interbond Energies (au) between the Orbitals in the Hydroxy Groups of 1,2-Ethanediol 1 Conformers Optimized in Vacuuma conformer

orbital/orbital

subtotal

Occ−Occ

Occ−Vac

Vac−Occ

1 gauche (g−G+t′)

O1−H5/O2−H6 O1−H5/LP1(O2) O1−H5/LP2(O2) O2−H6/LP1(O1) O2−H6/LP2(O1) O1−H5/H6(Vac) O2−H6/H5(Vac) O1−H5/O2(Vac) O2−H6/O1(Vac) LP1(O1)/H6(Vac) LP2(O1)/H6(Vac) LP1(O2)/H5(Vac) LP2(O2)/H5(Vac) total O1−H5/O2−H6 O1−H5/LP1(O2) O1−H5/LP2(O2) O2−H6/LP1(O1) O2−H6/LP2(O1) O1−H5/H6(Vac) O2−H6/H5(Vac) O1−H5/O2(Vac) O2−H6/O1(Vac) LP1(O1)/H6(Vac) LP2(O1)/H6(Vac) LP1(O2)/H5(Vac) LP2(O2)/H5(Vac) total

−0.004 −0.010 −0.001 0.001 −0.001 0.000 −0.011 −0.027 0.001 0.000 0.001 −0.034 −0.061 −0.147 (Δ = 0.000) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.002 −0.002 0.000 0.000 0.000 0.000 −0.004 (Δ = 0.143)

0.003 0.002 0.025 0.000 −0.002

−0.002

−0.005 −0.012 −0.025 0.000 0.000

1 anti (tTt′)

a

0.000 −0.011 −0.027 0.000 0.000 0.001 −0.034 −0.061 0.000 0.000 0.000 0.000 0.000

0.000

0.000 0.000 0.000 0.000 0.000

0.000 0.000 −0.002 −0.002 0.000 0.000 0.000 0.000

Occ, bonding orbital or lone pair; Vac, antibonding or vacant orbital; LP, lone pair; Δ, difference from the gauche conformer.

Table 5. Interbond Energies (au) between the C2−C3 Vicinal Bond Orbitals of erythro-2,3-Butanediol 2 Conformers Optimized in Vacuuma conformer

bond/bond

2 GG(E) (g+G−t′)

C2−H/C3−H C2−H/C3−Me C2−H/C3−OH C2−Me/C3−H C2−Me/C3−Me C2−Me/C3−OH C2−OH/C3−H C2−OH/C3−Me C2−OH/C3−OH total antiperiplanar total synclinal total vicinal C2−H/C3−H C2−H/C3−Me C2−H/C3−OH C2−Me/C3−H C2−Me/C3−Me C2−Me/C3−OH C2−OH/C3−H C2−OH/C3−Me C2−OH/C3−OH total antiperiplanar total synclinal total vicinal

2 AA(E) (tTt′)

a

subtotal (s) (a) (s) (s) (s) (a) (a) (s) (s)

(a) (s) (s) (s) (a) (s) (s) (s) (a)

0.308 −0.085 0.019 0.053 0.075 0.043 −0.064 0.012 0.000 −0.106 0.467 0.362 −0.115 0.203 0.001 0.203 −0.064 0.005 0.001 0.005 0.147 −0.032 0.419 0.387

Occ−Occ (σ/σ)

Occ−Vac (σ/σ*)

Vac−Occ (σ*/σ)

0.309 0.143 0.009 0.068 0.068 0.147 0.109 0.020 0.009

−0.001 −0.154 0.012 −0.002 0.008 −0.117 −0.049 −0.002 0.000

0.002 −0.077 −0.006 −0.011 0.000 0.012 −0.128 −0.009 −0.006

0.103 0.210 −0.001 0.210 0.157 −0.003 −0.001 −0.003 0.115

−0.112 −0.005 0.003 −0.004 −0.112 0.005 0.000 0.002 0.017

−0.112 −0.004 0.000 −0.005 −0.112 0.002 0.003 0.005 0.017

(Δ = 0.000) (Δ = 0.000) (Δ = 0.000)

(Δ = 0.074) (Δ = −0.048) (Δ = 0.025)

Occ, bonding orbital; Vac, antibonding orbital; (a), antiperiplanar; (s), synclinal; Δ, difference from the GG(E) conformer. F


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Table 6. Interbond Energies (au) between the Orbitals in the Hydroxy Groups of erythro-2,3-Butanediol 2 Conformers Optimized in Vacuuma conformer

orbital/orbital

subtotal

Occ−Occ

Occ−Vac

Vac−Occ

2 GG(E) (g+G−t′)

O2−H2/O1−H1 O1−H1/LP1(O2) O1−H1/LP2(O2) O2−H2/LP1(O1) O2−H2/LP2(O1) O1−H1/H2(Vac) O2−H2/H1(Vac) O1−H1/O2(Vac) O2−H2/O1(Vac) O1−H1/O2(Vac) LP2(O1)/H2(Vac) LP1(O2)/H1(Vac) LP2(O2)/H1(Vac) total [GG(E)] O2−H2/O1−H1 O1−H1/LP1(O2) O1−H1/LP2(O2) O2−H2/LP1(O1) O2−H2/LP2(O1) O1−H1/H2(Vac) O2−H2/H1(Vac) O1−H1/O2(Vac) O2−H2/O1(Vac) LP1(O1)/H2(Vac) LP2(O1)/H2(Vac) LP1(O2)/H1(Vac) LP2(O2)/H1(Vac) total [AA(E)]

−0.002 −0.005 0.006 0.001 −0.001 0.000 −0.015 −0.029 0.002 −0.029 0.002 −0.112 −0.017 −0.173 (Δ = 0.000) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.002 −0.002 0.000 0.000 0.000 0.000 −0.003 (Δ = 0.170)

0.009 0.040 0.015 0.000 −0.003

−0.008

−0.003 −0.045 −0.009 0.000 0.001

2 AA(E) (tTt′)

a

−0.001 −0.015 −0.029 0.000 −0.029 0.002 −0.112 −0.017 0.000 −0.001 0.000 −0.001 0.000

0.000

0.000 0.000 0.000 0.000 0.000

0.000 0.000 −0.002 −0.002 0.000 0.000 0.000 0.000

Occ, bonding orbital or lone pair; Vac, antibonding or vacant orbital; LP, lone pair; Δ, difference from the GG(E) conformer.

antiperiplanar interactions of GG(E) is larger by 0.025 au than the destabilization arising from the synclinal interactions. Antiperiplanar σCH/σCO* and σCC/σCO* electron delocalizations are present in GG(E). These interactions are usually associated with the gauche effect and have large stabilization energies (−0.128 and −0.117 au, respectively). However, bond orbital interactions in the antiperiplanar C−H/C−O and C− C/C−O combinations do not give rise to particularly large stabilizing effects because the reverse delocalizations (the σCH*/σCO and the σCC*/σCO) either do not or only modestly contribute to the stabilization of GG(E). The interbond energy attributed to the C−H/C−O combination remains at −0.064 au, and the C−C/C−O combination destabilizes the structure by 0.043 au due to the high energy of the σCC/σCO repulsion (0.147 au). The largest stabilization by electron delocalizations in GG(E) arises from the σCH/σCC* interaction of the antiperiplanar C− H/C−C combination (−0.154 au). In addition, because the reverse σCH*/σCC electron delocalization affords a stabilization energy of −0.077 au, the C−H/C−C combination provides a stabilization energy of −0.085 au including the σCH/σCC repulsion energy. The antiperiplanar C−H/C−H and C−C/C−C combinations in AA(E) also deliver large stabilization energies for both σ/σ* and σ*/σ electron delocalization (−0.112 au each). This C−H/C−H combination results in the largest stabilization energy (−0.115 au). In contrast, the C−C/C−C combination does not provide an outstanding stabilization energy (−0.064 au) because of the large destabilizations caused by the σ/σ

stabilization energies between the O1−H5 bonding orbital (σO1H5) and the vacant orbital on O2 and between the O2−H6 bonding orbital (σO2H6) and the vacant orbital on H5 (−0.027 and −0.011 au, respectively). Thus, interactions between the vicinal bond orbitals and between the orbitals in the hydroxy groups both contribute to the higher stability of the gauche conformer of 1,2-ethanediol 1. However, the contribution is much larger in the interaction between the hydroxy groups than that in the interaction between the vicinal bond orbitals. Although intramolecular hydrogen bonds in 1,2-diols may be weak, the interactions between their hydroxy groups of 1 have an effect enough to stabilize the conformation. Interactions between Vicinal Bond Orbitals on the C2−C3 of erythro-2,3-Butanediol. As with 1,2-ethanediol 1, the bond orbitals and interbond energies of erythro-2,3butandiol 2 were calculated for the two conformers [g+G−t′ of GG(E) and tTt′ of AA(E)] using the bond model analysis. The situation for C2−C3 vicinal bond orbital interactions in 2,3-butanediols is somewhat complicated in comparison with 1,2-ethanediol 1 due to the vicinal methyl groups. In the erythro-isomer 2, the sum of the interbond energies between the antiperiplanar orbitals is lower in GG(E) than that in AA(E) by 0.074 au (Table 5), indicating that these interactions contribute to the higher stability of the GG(E) conformer. On the other hand, the sum of the interbond energies between the synclinal bond orbitals is higher in GG(E) than that in AA(E) by 0.048 au. However, the vicinal bond orbital interactions as a whole contribute to the higher stability of GG(E) because the stabilization conferred by the G


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Table 7. Interbond Energies (au) between the C2−C3 Vicinal Bond Orbitals of threo-2,3-Butanediol 3 Conformers Optimized in Vacuuma conformer

bond/bond

3 GG(T) (g+G−t′)

C2−H/C3−H C2−H/C3−Me C2−H/C3−OH C2−Me/C3−H C2−Me/C3−Me C2−Me/C3−OH C2−OH/C3−H C2−OH/C3−Me C2−OH/C3−OH total antiperiplanar total synclinal total vicinal C2−H/C3−H C2−H/C3−Me C2−H/C3−OH C2−Me/C3−H C2−Me/C3−Me C2−Me/C3−OH C2−OH/C3−H C2−OH/C3−Me C2−OH/C3−OH total antiperiplanar total synclinal total vicinal C2−H/C3−H C2−H/C3−Me C2−H/C3−OH C2−Me/C3−H C2−Me/C3−Me C2−Me/C3−OH C2−OH/C3−H C2−OH/C3−Me C2−OH/C3−OH total antiperiplanar total synclinal total vicinal

3 AG(T) (g−G+t′)

3 GA(T) (tTt′)

a

subtotal (a) (s) (s) (s) (s) (a) (s) (a) (s)

(s) (s) (a) (s) (a) (s) (a) (s) (s)

(s) (a) (s) (a) (s) (s) (s) (s) (a)

−0.127 0.166 0.014 0.133 0.021 0.037 0.032 −0.030 0.004 −0.119 0.371 0.251 0.155 0.166 −0.023 0.185 −0.040 0.016 −0.074 0.019 −0.001 −0.137 0.541 0.404 0.300 −0.095 0.008 −0.095 0.130 0.004 0.008 0.004 0.150 −0.040 0.454 0.414

Occ−Occ (σ/σ)

Occ−Vac (σ/σ*)

Vac−Occ (σ*/σ)

0.103 0.171 0.006 0.133 0.030 0.152 0.036 0.118 0.011

−0.138 −0.001 0.009 0.001 −0.003 −0.133 0.001 −0.048 0.000

−0.096 0.000 −0.005 0.001 −0.005 0.017 −0.006 −0.102 −0.006

0.158 0.159 0.133 0.183 0.169 0.005 0.090 0.025 0.009

−0.005 0.006 −0.147 0.001 −0.115 0.008 −0.062 −0.002 0.000

0.004 0.001 −0.011 0.002 −0.095 −0.002 −0.106 −0.006 −0.007

0.301 0.136 0.009 0.136 0.142 −0.003 0.009 −0.003 0.115

−0.001 −0.150 0.002 −0.086 −0.008 0.005 −0.003 0.003 0.018

−0.001 −0.086 −0.003 −0.150 −0.008 0.003 0.002 0.005 0.018

(Δ = 0.000) (Δ = 0.000) (Δ = 0.000)

(Δ = −0.017) (Δ = 0.170) (Δ = 0.153)

(Δ = 0.080) (Δ = 0.083) (Δ = 0.162)

Occ, bonding orbital; Vac, antibonding orbital; (a), antiperiplanar; (s), synclinal; Δ, difference from the GG(T) conformer.

Interactions between Orbitals in the Hydroxy Groups of erythro-2,3-Butanediol. GG(E) possesses the synclinal hydroxy groups that provide a large stabilization energy of −0.173 au (Table 6). This value is lower than any interbond energy between the vicinal bond orbitals of 2. On the other hand, there is little stabilization energy between the antiperiplanar hydroxy groups in AA(E). Therefore, the interactions between the synclinal hydroxy groups in GG(E) significantly increase conformational stability. Most of this stabilization energy comes from the interactions of the lone pair orbitals on O2 with the vacant orbital on H1 (−0.112 and −0.017 au) and with the antibonding orbital of O1−H1 (σ*O1H1) (−0.045 and −0.009 au). These interactions are both considered general components of a hydrogen bond. In addition, interactions between the bonding orbital of O1−H1 (σO1H1) and the vacant orbital on O2 and between the bonding orbital of O2−H2 (σO2H2) and the vacant orbital on H1 also contribute to the stabilization of GG(E) (−0.029 and −0.015 au, respectively). The energy difference in the hydroxy group interactions between GG(E) and AA(E) is 0.170 au, which is much larger than the energy difference for the entire suite of

repulsion (0.157 au). The sum of the interbond energy of the antiperiplanar bond orbitals without the C−O/C−O combination in AA(E) is 0.073 au lower than that of the antiperiplanar bond orbital interactions in GG(E). Therefore, the very large antiperiplanar destabilization energy of the C− O/C−O combination (0.147 au) results in the sum of the interbond energy between the antiperiplanar bond orbitals of GG(E), ultimately becoming lower than that of AA(E). This destabilization mostly results from the repulsive interaction between the bonding orbitals (the σCO/σCO interaction, 0.115 au) as with that of 1,2-ethanediol 1 (see Figure S2). The overlap between the bonding orbitals (σCO/σCO) in the anti orientation is larger than that in the gauche orientation; the overlap integral values are 0.053 and 0.022, respectively. Synclinal bond combinations with the C−O bond generate only small energies (0.000 to 0.019 au), whereas the C−H/C− H and C−H/C−C combinations provide large destabilization energies in many cases. The higher synclinal bond orbital interactions in GG(E) than those in AA(E) are attributed to the especially large destabilization energy between the C−H bonds (0.308 au). H


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Table 8. Interbond Energies (au) between the Orbitals in the Hydroxy Groups of threo-2,3-Butanediol 3 Conformers Optimized in Vacuuma conformer

orbital/orbital

subtotal

Occ−Occ

Occ−Vac

Vac−Occ

3 GG(T) (g+G−t′)

O1−H1/O2−H2 O1−H1/LP1(O2) O1−H1/LP2(O2) O2−H2/LP1(O1) O2−H2/LP2(O1) O1−H1/H2(Vac) O2−H2/H1(Vac) O1−H1/O2(Vac) O2−H2/O1(Vac) LP1(O1)/H2(Vac) LP2(O1)/H2(Vac) LP1(O2)/H1(Vac) LP2(O2)/H1(Vac) total O1−H1/O2−H2 O1−H1/LP1(O2) O1−H1/LP2(O2) O2−H2/LP1(O1) O2−H2/LP2(O1) O1−H1/H2(Vac) O2−H2/H1(Vac) O1−H1/O2(Vac) O2−H2/O1(Vac) LP1(O1)/H2(Vac) LP2(O1)/H2(Vac) LP1(O2)/H1(Vac) LP2(O2)/H1(Vac) total O1−H1/O2−H2 O1−H1/LP1(O2) O1−H1/LP2(O2) O2−H2/LP1(O1) O2−H2/LP2(O1) O1−H1/H2(Vac) O2−H2/H1(Vac) O1−H1/O2(Vac) O2−H2/O1(Vac) LP1(O1)/H2(Vac) LP2(O1)/H2(Vac) LP1(O2)/H1(Vac) LP2(O2)/H1(Vac) total

−0.001 −0.007 0.010 0.001 −0.001 −0.001 −0.015 −0.034 0.001 0.000 0.001 −0.045 −0.084 −0.175 (Δ = 0.000) −0.003 0.000 −0.007 −0.001 0.001 0.000 −0.014 −0.033 0.000 0.001 0.000 0.001 −0.123 −0.178 (Δ = −0.004) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 −0.002 −0.002 0.000 0.000 0.000 0.000 −0.003 (Δ = 0.171)

0.012 0.010 0.051 0.000 −0.002

−0.005

−0.009 −0.017 −0.041 0.000 0.001

3 AG(T) (g−G+t′)

3 GA(T) (tTt′)

a

−0.001 −0.016 −0.033 −0.001 0.000 0.001 −0.045 −0.084 0.006 0.000 0.044 −0.002 0.000

−0.002

−0.007 0.000 −0.052 0.001 0.000

0.000 −0.014 −0.033 −0.001 0.001 0.000 0.001 −0.123 0.000 −0.001 0.000 −0.001 0.000

0.000

0.000 0.000 0.000 0.000 0.000

0.000 0.000 −0.002 −0.002 0.000 0.000 0.000 0.000

Occ, bonding orbital or lone pair; Vac, antibonding or vacant orbital; LP, lone pair; Δ, difference from the GG(T) conformer.

vicinal bond interactions. Thus, although both the orbital interactions between the hydroxy groups and those between the vicinal bonds contribute to stabilizing the GG(E) conformer, the contribution of the former interactions is much larger. Interactions between Vicinal Bond Orbitals on the C2−C3 of threo-2,3-Butanediol. As mentioned above, the stabilities of the three conformers of threo-2,3-butandiol 3 as determined by DFT calculations increase in the order GG(T) > AG(T) > GA(T). However, the antiperiplanar bond orbital interactions contribute to increasing the conformational stabilities in the order AG(T) > GG(T) > GA(T), whereas the contribution from the synclinal bond orbital interactions increases in the order GG(T) > GA(T) > AG(T). Although neither the antiperiplanar nor synclinal bond orbital inter-

actions alone dictate the stabilities of the conformers, the sum of the interbond energies of the vicinal bond orbitals agrees with the conformational stability tendencies predicted by DFT calculations (Table 7). The properties of the interactions between the bond orbitals in the threo-isomer 3 are similar to those in the erythro-isomer 2. The antiperiplanar σCH/σCO* and σCC/σCO* electron delocalizations provide large stabilization energies (−0.147 to −0.102 au), whereas the bond orbital interactions in the antiperiplanar C−H/C−O or C−C/C−O combinations (−0.074 to −0.023 au) do not provide large stabilization energies because the reverse electron delocalizations (the σCH*/σCO and the σCC*/σCO) contribute modest or small stabilization energies (−0.062 to −0.011 au). One σCC*/σCO electron delocalizations in GG(T) destabilizes the rotamer by I


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stabilization due to the interactions between the hydroxy groups in these conformers is similar. Bond Model Analyses of the Conformers in Water. The interbond energies of the conformers in water shown in Figures 2b and 3b are similar to those of the conformers in vacuum. The data of the interbond energies are provided in the Supporting Information (Tables S1−S6). The relative conformational stabilities of 1,2-ethanediol 1 and erythro-2,3butanediol 2 can be explained by the interactions between the antiperiplanar bond orbitals, between the vicinal bond orbitals, or between the hydroxy groups in addition to the combination of interactions between the vicinal bond orbitals and between the hydroxy groups. In contrast, in threo-2,3-butanediol 3, when the sum of the interbond energies between the hydroxy groups is added to the sum of the vicinal interbond energies, the total energies agree with the tendency of the relative stabilities of the conformers. Thus, in the case of threo-2,3-butanediol 3 in particular, it appears to be important to evaluate the interbond energies both between the vicinal bonds and between the hydroxy groups.

0.017 au. This C−C/C−O combination is a destabilizing factor (0.037 au) due to σCC/σCO repulsion (0.152 au). On the other hand, the C−H/C−H combination in GG(T) affords the lowest interbond energy (−0.127 au) in the antiperiplanar combination, thereby helping stabilize GG(T). The lowest interbond energy is found in the antiperiplanar σCC*/σCH electron delocalization (−0.150 au) in GA(T). However, the C−O/C−O combination provides the large destabilization energy (0.150 au); consequently, the antiperiplanar bond orbital interactions are insufficient to stabilize GA(T) due to this destabilization, in contrast to GG(T) and AG(T). As with 1,2-ethanediol 1 and erythro-butanediol 2, this result is mostly caused by the repulsive interaction (0.115 au) between the antiperiplanar bonding orbitals in GA(T) (see Figure S2). The overlap between the bonding orbitals (σCO/σCO) in the anti orientation is larger than those in the gauche orientations. Synclinal bond combinations with the C−O bond generate only small or modest destabilization energies (0.004−0.032 au) or a slight stabilization energy (−0.001 au), whereas C−H/C− H and C−H/C−C combinations have large destabilization energies (0.133−0.300 au). The instability of the synclinal bond orbital interactions in GA(T) is attributed to the especially large destabilization energy between the C−H bonds (0.300 au). The sum of the synclinal interbond energies is exceptionally high in AG(T) due to the two C−H/C−C and one C−H/ C−H combination (0.166, 0.185, and 0.155 au, respectively). However, our finding that the sum of the interbond energies of the vicinal bond orbital interactions agrees with the conformational stability tendency shows that balance between vicinal bond orbital interactions is an important controlling factor for the conformational stability. Interactions between Orbitals in the Hydroxy Groups of threo-2,3-Butanediol. The GG(T) and AG(T) of threo2,3-butanediol 3 conformers have synclinal hydroxy pairs, and the bond model analysis revealed large stabilizations due to interactions between these hydroxy groups [−0.175 au for GG(T) and −0.178 au for AG(T)] (Table 8). The major contributors to these stabilization energies were the interactions of the lone pair orbitals on O2 with the vacant orbitals on H1 [−0.084 and −0.045 au for GG(T), −0.123 and −0.033 au for AG(T)] and with the antibonding orbital of O1−H1 (σ*O1H1) [−0.041 and −0.017 au for GG(T), −0.052 au for AG(T)]. These interactions are considered general components of a hydrogen bond. In addition, interactions between the bonding orbital of O1−H1 (σO1H1) and the vacant orbital on O2 [−0.033 au for GG(T) and AG(T)] and between the bonding orbital of O2−H2 (σO2H2) and the vacant orbital on H1 [−0.016 au for GG(T) and −0.014 au for AG(T)] also contribute to the stabilization of GG(T) and AG(T). GA(T) has little stabilization energy between the hydroxy groups, whereas interactions between the hydroxy groups contribute more significantly to the stabilization of GG(T) and AG(T) than do the interactions of the vicinal bond orbitals. Although AG(T) is much more stable than GA(T) according to the Gibbs energies of the conformers (Figure 3a), the sum of the interbond energies in the vicinal bond orbital interactions of these conformers is very similar. However, if the effects due to the hydroxy groups and vicinal bond orbitals are combined, AG(T) becomes significantly more stable (by 0.156 au) than GA(T). When the same concept is applied to GG(T), the relationship between the stabilities of GG(T) and AG(T) remains unchanged and is essentially controlled by the interactions between the vicinal bond orbitals, given that the

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CONCLUSIONS The present study revealed various effects of interactions between the vicinal bond orbitals on the conformational stabilities of the three 1,2-diols 1, 2, and 3. The antiperiplanar bond orbital interactions as a whole contribute to the higher stabilities of the hydroxy/hydroxy gauche conformers. This results from an increase in the relative stabilities of the gauche conformers due to the predominant destabilization energies of the C−O/C−O interactions in the hydroxy/hydroxy anti conformers, which are caused by the larger overlaps between the antiperiplanar bonding orbitals (the σCO/σCO interaction) compared to those between the synclinal bonding orbitals. Importantly, it does not result from the stabilization energies of the C−O/C−H or C−O/C−C combinations in the gauche conformers, including the antiperiplanar σCO*/σCH or σCO*/ σCC electron delocalization hitherto considered as the origin of the higher stabilities of the gauche conformers. Indeed, the σCO*/σCH or σCO*/σCC electron delocalization does not necessarily provide the largest stabilization energy in the interactions between antiperiplanar bond orbitals, although they are stabilizing factors. Furthermore, the sum of the interbond energies of a pair of antiperiplanar electron delocalizations (σ*/σ and σ/σ*) shows lower values (more stable) for the C−H/C−H, C−H/C−C, or C−C/C−C combinations than those for the C−O/C−H or C−O/C−C combinations, indicating that the latter combinations are not particularly advantageous. This tendency does not change in many cases even following addition of the repulsion energies between the bonding orbitals (σ/σ). The interactions between the synclinal bond orbitals in some hydroxy/hydroxy gauche conformers provide less stabilization energy as a whole than those in the hydroxy/hydroxy anti conformers. However, in many cases, the sum of the interbond energies between the vicinal bond orbitals is not decreased in the hydroxy/hydroxy anti conformers compared to those in the hydroxy/hydroxy gauche conformers. The only exception was threo-2,3butanediol 3 in water. In addition, interactions between the synclinal hydroxy groups generate stabilization energies that are larger than the sum of the interbond energies of the interaction between the antiperiplanar bond orbitals. In 1,2-ethanediol 1 and erythro-2,3-butanediol 2, the relative conformational stabilities can be explained by the interactions J


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(8) Das, P.; Das, P. K.; Arunan, E. Conformational Stability and Intramolecular Hydrogen Bonding in 1,2-Ethanediol and 1,4Butanediol. J. Phys. Chem. A 2015, 119, 3710−3720. (9) Wang, F.; Polavarapu, P. L. Predominant Conformations of (2R,3R)-(−)-2,3-Butanediol. J. Phys. Chem. A 2001, 105, 6991−6997. (10) Lopes Jesus, A. J.; Rosado, M. T. S.; Reva, I.; Fausto, R.; Eusébio, M. E.; Redinha, J. S. Conformational Study of Monomeric 2,3-Butanediols by Matrix-Isolation Infrared Spectroscopy and DFT Calculations. J. Phys. Chem. A 2006, 110, 4169−4179. (11) Goodman, L.; Gu, H.; Pophristic, V. Gauche Effect in 1,2Difluoroethane. Hyperconjugation, Bent Bonds, Steric Repulsion. J. Phys. Chem. A 2005, 109, 1223−1239. (12) Pophristic, V.; Goodman, L. Hyperconjugation not Steric Repulsion Leads to the Staggered Structure of Ethane. Nature 2001, 411, 565−568. (13) (a) Naruse, Y.; Ma, J.; Takeuchi, K.; Nohara, T.; Inagaki, S. pRelaxation of the Ring Strain: Design of Polycyclic Unsaturated Silicon Molecules. Tetrahedron 2006, 62, 4491−4497. and references therein. See also: (b) Orbital in Chemistry; Inagaki, S., Ed.; Springer: Heidelberg, Germany, 2009. (14) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (15) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2013. (16) Cancès, E.; Mennucci, B.; Tomasi, J. A New Integral Equation Formalism for the Polarizable Continuum Model: Theoretical Background and Applications to Isotropic and Anisotropic Dielectrics. J. Chem. Phys. 1997, 107, 3032−3041. (17) Mennucci, B.; Cancès, E.; Tomasi, J. Evaluation of Solvent Effects in Isotropic and Anisotropic Dielectrics and in Ionic Solutions with a Unified Integral Equation Method: Theoretical Bases, Computational Implementation, and Numerical Applications. J. Phys. Chem. B 1997, 101, 10506−10517. (18) Cancès, E.; Mennucci, B. New Applications of Integral Equations Methods for Solvation Continuum Models: Ionic Solutions and Liquid Crystals. J. Math. Chem. 1998, 23, 309−326. (19) Yasui, M.; Naruse, Y.; Inagaki, S. An orbital phase theory for the torquoselectivity of the ring-opening reactions of 3-substituted cyclobutenes: geminal bond participation. J. Org. Chem. 2004, 69, 7246−7249 and references therein. (20) Wang, Y.; Ma, J.; Inagaki, S. Stable silicon-centered localized singlet 1,3-diradicals XSi(GeY2)2SiX: theoretical predictions. J. Phys. Org. Chem. 2007, 20, 649−655 and references therein. (21) Ma, J.; Inagaki, S. Orbital Phase Control of the Preferential Branching of Chain Molecules. J. Am. Chem. Soc. 2001, 123, 1193− 1198. (22) Pierens, G. K. 1H and 13C NMR Scaling Factors for the Calculation of Chemical Shifts in Commonly Used Solvents Using Density Functional Theory. J. Comput. Chem. 2014, 35, 1388−1394. (23) Howard, D. L.; Jørgensen, P.; Kjaergaard, H. G. Weak Intramolecular Interactions in Ethylene Glycol Identified by Vapor Phase OH−Stretching Overtone Spectroscopy. J. Am. Chem. Soc. 2005, 127, 17096−17103.

between the antiperiplanar bond orbitals, between the vicinal bond orbitals, or between the hydroxy groups, in addition to the combination of interactions between the vicinal bond orbitals and between the hydroxy groups. In contrast, in threo2,3-butanediol 3, differences in the relative stabilities of the three conformers can be comprehended by understanding the combination of interactions between the vicinal bond orbitals and between the hydroxy groups. Thus, it is important to analyze from various directions the conformational stabilities of 1,2-diols based on the orbital interactions around the C1−C2 bond.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08085. Conformer’s labeling rule, interactions between the vicinal C−O bonding orbitals in 2,3-butanediols, interbond energies in water, and Cartesian coordinates and Gibbs energies of the diol conformers and methanol dimer (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: hayn@affrc.go.jp. Phone: +81-29-838-7297. Fax: +8129-838-7996. ORCID

Nobuyuki Hayashi: 0000-0002-0197-2405 Tomomi Ujihara: 0000-0001-5453-2107 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge Dr. Ikuko Maeda (Food Research Institute, NARO) for her assistance with the NMR experiments. We used the supercomputer at AFFRIT, MAFF, Japan for chemical calculations.

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REFERENCES

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Effect of Orbital Interactions between Vicinal Bonds and between

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