1346
J . Phys. Chem. 1993,97, 1346-1350
Conformational Analysis of 1,2-Dimetboxyethane by ab Initio Molecular Orbital and Molecular Mechanics Calculations: Stabilization of the TGG‘ Rotamer by the 1,5 CHJ/O Nonbonding Attractive Interaction Seiji Tsuzuki,’ Tadafumi Uchimaru, and Kazutoshi Tanabe National Chemical Laboratory for Industry, I - 1 Higashi, Tsukuba-shi, Ibaraki 305, Japan
Tsuneo Hirano Department of Chemistry, Faculty of Science, Ochanomizu University, 2- I - I Otsuka, Bunkyo-ku, Tokyo 1 12, Japan Received: July 10, 1992; In Final Form: November 30, 1992
Abinitiomolecularorbitalcalculationsat theMP3/6-31 1+G*//HF/6-311+GS levelshow that relativeenergies of TTT, TGT, TTG, GTG, GTG’, TGG, TGG’, GGG, and GGG’ rotamers of 1,2-dimethoxyethane are 0.0, 0.51,1.65,3.47,3.34,2.24,0.53, 1.97, and 2.30 kcal/mol, respectively. Populations of rotamers predicted from calculated AG’s at 273.15 K agree satisfactorily with the gas-phase electron diffraction results reported by Astrup. The high stability of the TGG’ rotamer can be ascribed to the 1,5 CH3/O nonbonded attractive interaction from ab initio molecular orbital and molecular mechanics points of view. The GGG and GGG’ rotamers are also stabilized by the same interaction. The distances between the 2-oxygen atom and the nearest hydrogen atom of the 6-methyl group in the HF/6-311+G* geometries of these three rotamers are 2.569,2.963, and 2.591 A, respectively. With a comparison between the ab initio and molecular mechanics conformational energies, a stabilization of 1.2-1.4 kcal/mol is found to be characteristic for a pair of the CHs/O nonbonding interactions. The presence of this attractive interaction is also confirmed from the molecular orbital calculation of dimethyl ether dimer. and concluded that the TGT rotamer is 0.61 kcal/mol less stable than the TTT rotamer.I9 However, the cause of the large population of the TGG or TGG’ rotamer, which is suggested by Astrup for the gas phase, is not certain. In addition, the importance of the use of a large basis set in conformationalenergy Calculation by ab initio MO methods has recently been especially for molecules containing electronegativeatoms like 1,2-dihal0ethane.~~-~~ We calculate relative energies of all possible rotamers of 1,Zdimethoxyethane using a larger basis set with electron correlation and vibrational energycorrection. Thecauseof thestabilityof the TGG’rotamer is discussed on the basis of a conformational analysis by molecular orbital and molecular mechanics calculations.
I. Introduction
The study of the conformational preference of 1,Zdimethoxyethane has been the focus of considerable attention for more than three because the torsional interaction of this molecule is a key to understanding the structure of cyclic and acyclicp o l y e t h e r ~ . ~ lHowever, -~~ the conformationalpreference of 1,2-dimethoxyethanehas been a controversial issue. While analyses of infrared and Raman spectra showed that the CH2CH2 bond is gauche in the ~ r y s t a l a, ~mixture of the trans (T) and gauche (G) rotamers was found in liquid and gas phases.1J,6*11 Iwamoto reported that the trans form was more stable in the liquid phase.6 On the other hand, Ogawa et al. reported that the gauche form was preferable.ll Viti et al. reported from the measurement of IH NMR in the liquid phase that the gauche 11. Computational Technique form was 0.1 1-0.83 kcal/mol more stable than the trans form.I0 The GAUSSIAN 86 program37was used for the molecular Astrup reported from electron diffraction measurement that orbital calculations. The basis sets implemented in the program several rotamers exist in the gas phase.I2 She reported that the were ~ s e d . ~ ~The - ~ Ogeometries were fully optimized using the energy difference between the TTT and TGT rotamers for the gradient optimization routine in the program. Default converthree consecutive bonds in the O-CH2-CH2-O bond sequence gence criteria were used for SCF and geometry optimization. was small and that the TGG or TGG’ rotamer, which is The electron correlation energy was corrected by the Mdlerunfavorable in the correspondingn-alkane, had a large population. Plesset perturbationmethod414swith the single-point computation Recently, Abe and Inomata reported from the measurement of on the geometries obtained by the Hartree-Fock methcd46 IH NMR in the gas phase that the gauche form was 0.3 kcalfmol Harmonic vibrational frequencies were evaluated at the HF/6more stable than the trans form.13 3 lG* level using the vibrational normal-mode analysis routine Several theoretical studies on the conformation of 1,2in the program. The calculated frequencies were scaled using a dimethoxyethane were reported.9J4,16-20 Pod0 et al. analyzed factor of 0.9 to correct the usual overestimation of vibrational the conformational preference using a semiempirical potential frequencies at the H F Zero-point and thermal vibraf u n ~ t i o n .Bressanini ~ et al. reported a Monte Carlo simulation tional energies and entropies were calculated by the standard of liquid 1,2-dimetho~yethane.~OAnderson and Karlstrom statistical thermodynamic procedure.49 The entropies of rotamers calculated the relative stability of six rotamers by the ab initio were calculated by the equation as the sum of the translational HartreeFock molecular orbital (MO) method using the double(StranS), rotational (S,,t), and vibrational (Svib) contributions by zeta plus polarizationquality basis set and reported that the TGT taking the multiplicity into account: rotamer is 1.0 kcal/mol less stable than the TTT rotamer.17 Barzaghi et al. calculated the relative energies of the TTT and (1) S = S,,,,,+ S,,,+ S,jb + R In M TGT rotamers with electron correlation energy correction by the second-order Maller-Plesset perturbation ab initio MO method Multiplicity (M), here, stands for the number of equivalent 0022-3654/93/2097- 1346$04.00/0
0 1993 American Chemical Society
Conformational Analysis of 1,2-Dimethoxyethane
The Journal of Physical Chemistry, Vol. 97, No. 7, 1993 1347
TABLE I: Energies of the TCT Rotamer of 1,2-Dimetboxyethaw Relative to Those of the TlT Rotamer, Calculated by the ab Initio Metbod’ method basis set
HF
MP2
MP3
MP4(SDO)
6-31G* 6-31+G* 6-311+G*d 6-31 1++G*
1.403 1.413 1.259 1.242
0.607 0.426 0.292 0.243
0.649 0.508 0.470
0.563 0.391
Energies in kcal/mol. HF/6-31G* geometries are used. The calculated energies of the TTT rotamer at the HF and MP2 levels are -306.980 20 and -307.849 37 hartrees, respectively. HF/6-3 1+G* geometries are used. The calculated energies of the TTT rotamer at HF, MP2, MP3, and MP4(SDQ) levels are -306.988 98, -307.870 44, -307.91 1 42, and -307.928 42 hartrees, respectively. HF/6-311+G* geometries are used. The calculated energies of the TTTrotamer at HF, MP2, and MP3 levels are -307.056 86, -307.996 97, and -308.035 88 hartrees, respectively. HF/6-31 I+G* geometries are used. The calculated energies of the TTT rotamer at HF, MP2, MP3, and MP4(SDQ) levels are -307.057 18, -307.997 91, -308.036 81, and -308.054 68 hartrees, respectively.
rotamers. For example, the multiplicity of the TGG’ rotamer is 4, because this has four equivalent rotamers (TGG’, TG’G, GGT, and G’GT). Conformational energies in terms of the total electronic energy including nuclear-nuclear repulsion, enthalpy, or Gibbs free energy, Le., E, H , or G, respectively, will be given relative to those of the TTT rotamer. Intermolecular interaction energies of dimethyl ether dimer and related complexes were calculated by using the MP2/6-3 1G* geometries of single monomeric molecules. Basis set superposition errorSo was corrected by thecounterpoisemethod.5’Themolecularmechanics program MM252*53 was used for molecular mechanics calculations with our recently refined parameters for ethersas4
TABLE II: Dihedral Angles of the Skeletal Bonds of Nine Rotamrs of 1,2-”ethoxyethrae Calculated at the HF/ 6-311+C* Level** rotamer
sym
TTT TGT TTG GTG GTG’ TGG TGG’ GGG
c2h c2
GGG‘
CI
C1-02-C3-C4
CI
c2 ci CI CI
c2
180.0 -174.7 -178.8 90.5 89.2 -178.4 -177.4 63.1 84.7
02423-CQ-05
C3-CW5-C6
180.0 73.4 179.3 177.9 180.0 66.0 71.2 48.0 73.4
180.0 -174.7 89.1 90.5 -89.2 79.9 -90.8 63.1 -80.7
Angles indegrees. Geometriesarefully optimidimposingsymmetry restrictions shown in the table. Numbering of atoms: (H3)CI-02The triad conformation of TGG’, for example, stands for the T, G , and G’ for the 043,C3-C4, and C4-05 bonds, respectively.
TABLE III: Energies of Rotamers of 1,2-Dimethoxyethane Relative to That of the TIT Rotamer rotamer
ab initio Mob
TTT TGT TTG GTG GTG’
0.508 1.645 3.466 3.344
0.0
molecular mechanicsC rotamer
0.0 0.500 1.838 3.611 3.598
TGG TGG’
GGG GGG’
ab initio Mob
molecular mechanicsc
2.242 0.529 1.971 2.298
2.641 1.767 4.705 3.709
a Energies in kcal/mol. MP3/6-31 1+G*//HF/6-311+GS. rameters shown in ref 54 are used. See text.
c
Pa-
are decreased by the use of a larger basis set up to the 6-311+G* basis set. The use of the further improved 6-31 l++G* basis set has little effect on the calculated energy difference. Due to these observations, we carried out relative energy calculations of all possible rotamers of 1,2dimethoxyethane at the MP3/&311+G*/ 111. Results and Discussion /HF/6-3 1 1+G* level. A. Ab Initio Molecular OrbitalCalculations of 1,2-Dimethoxy2. Geometries of Rotamers. The geometries of nine rotamers ethane. 1 Eflects of Basis Set and Electron Correlation on the of 1,Zdimethoxyethane were optimized at the HF/6-311+G* Calculated Relative Conformational Energies. The importance level. Calculated dihedral angles of the skeletal bonds of the of the use of a large basis set and the electron correlation correction nine rotamers are summarized in Table 11. Bond distances and for conformationalenergy calculation by ab initio MO methods valence angles are in Table VI (supplementary material). The has been claimed r e ~ e a t e d l y . ~ ~The - ~ Ienergy differencebetween geometry of the GG’G rotamer was also tried to be optimized. rotamers calculated at the H F level using a crude basis set often However, the geometry converged to the GTG conf0rmation.~6 does not agree with the experimental energy difference, since The calculated gauche dihedral angles of the TTG and TGT such a calculation has a large error and cannot reproduce the rotamers are 8 9 O and 73O, respectively. The calculated C-Csmall energy differencecorrectly. On the other hand, calculated 0-C gauche dihedral angles of the GTG, GTG’, and TGG’ conformational energies using a reasonably large basis set with rotamers are close to that of the TTG rotamer, and thecalculated electron correlationcorrectionhave high accuracy and agree with 044-0gauche dihedral angle of the TGG’rotamer is close the experimental ~ a l u e s . ~ ~ - ~ l to that of the TGT rotamer. On the other hand, the calculated 1,2-Dihaloethaneprefers the gauche conformation.55-66 This C-C-0-C gauche dihedral angles of the TGG, GGG, and GGG’ preference, which is called the “gauche effect”, has widely been rotamers are considerably smaller than that of the TTG rotamer, observed in molecules having two electronegativeatoms at 1,2and the 0-C-C-O gauche dihedral anglesof the TGG and GGG positions of a single bond.*3~6~-~3 Detailed MO calculations showed rotamersaresmaller than that oftheTGTrotamer. Thedecrease that the use of a large basis set including both polarization and of the gauche dihedral angles of these rotamers decreases the diffuse functions as well as the electron correlation energy distance between the 2-oxygen atom and the 6-methyl group. correction is necessary to reproduce this effect correctly.32-36.74.75 3. Relative Energies of Rotamers. Calculatedrelative energies In order to evaluatethe basis set and electron correlation effects of nine rotamers of 1,Zdimethoxyethaneare summarized in Table on the conformational energies of 1,Zdimethoxyethane,the energy 111. Zero-point and thermal vibrational energies and entropies difference between the TGT and TTT rotamers was calculated calculated from the scaled frequencies are shown in Table IV. at several levels as shown in Table I. The TGT rotamer is The multiplicity of the rotamer is considered in the calculation calculated tobe 1.2-1.4 kcal/mollessstable than theTTTrotamer of entropies. For example, the multiplicity of the TGG’ rotamer at the Hartree-Fock level. The MP2 level electron correlation is 4, because this rotamer has four equivalents: TGG’, TG’G, energy correction decreases the energy difference to 0 . 2 4 6 kcal/ GG’T, and G’GT. Enthalpies and Gibbs free energy differences mol. The energy differencescalculated at MP3 and MP4(SDQ) calculated from these values are listed in Table V, together with levels are 0.5-4.6 and 0.44.6kcal/mol, respectively. The relative the populations of rotamers at 273.15 K calculated from the energies obtained by the MP3 level correction are very close to corresponding Gibbs free energy differences. The TGG’ rotamer those by the MP4(SDQ) level. (The largest deviation is less than has the largest population, which agrees with the electron 0.1 kcal/mol.) The MP2 relative energies are always 0.2 kcal/ diffraction measurement by Astrup.I2 The calculated rotamer mol smaller than the corresponding MP3 relative energies. The ratios are close to those obtained from the gas electrondiffraction calculatedenergy differences with electron correlationcorrection measurement.’ 2 ~ ~ ~ I
Tsuzuki et al.
1348 The Journal of Physical Chemistry, Vol. 97, No. 7, 1993 TABLE Iv: Zero-Point Energy (ZPE), Tbermpl Energy (&-) for 273.15 K, a d Entropy (S) of Nine Rotamers of 1,2-”etboxyetW point ZPE Etherm0 S‘ rotamer
TTT TGT TTG GTG GTG‘ TGG TGG’ GGG GGG’
group C2h C2
CI C2
C, CI
CI C2
CI
Mb (kcal/mol)
I 2 4 2 2 4 4 2 4
86.409 86.404 86.423 86.423 86.419 86.426 86.473 86.722 86.503
(kcal/mol) 2.829 2.756 2.833 2.847 2.867 2.764 2.778 2.641 2.758
(cal/(mol K)) 83.687 84.801 87.041 86.310 86.508 87.066 86.860 83.673 86.789
Vibrationalenergiesandcntropiesat 273.15 K werecalculated based on the HF/6-31GS level harmonic frequencies scaled by a factor of 0.9. Multiplicity stands for the number of equivalent rotamers. For example, the TGG’ rotamer has the four equivalent rotamers TGG’, TG’G, G G T , and G’GT. Multiplicity is taken into account for the calculation of entropies (cf. eq I).
TABLE V
Relative Enthalpies AH, Relative Cibb Free
Energies AG, and Populations of Nine Rotamers of 1,2-Dimetboxyetbme‘ AIP rotamer
TTT TGT
TTG GTG GTG’ TGG TGG’ GGG GGG
(kcal/mol) 0.0 0.504 1.659 3.480 3.355 2.260 0.594 2.285 2.392
M
7
j
Is
(kcal/mol) 0.0 0.43 1 1.663 3.498 3.393 2.194 0.543 2.097 2.321
AG273l J * (kcal/mol) 0.0 0.127 0.747 2.782 2.623 1.271 -0.324 2.101 1.474
populationC
(W) 24.7 (13) 19.5 (23) 6.2 (3)
;:;
(59 2.4 44.8 (53c) 0.5 1.6 (‘)
a AH (AG) values are differences between the AH (AG) value of each rotamer and that of the TTT rotamer. Superscripts for AH and AG indicate the temperature in kelvin. Multiplicity is taken into account for the calculation of Gibbs free energies through the definitionof entropy ( c f . q 1). At273.15K. Rotamerpopulationfromthegas-phaseelectron diffraction study by Astrup (ref 12) is shown in parentheses. Sum of the GTG and GTG’ rotamers. e Sum of the TGG and TGG’ rotamers. /Sum of the GGG and GGG’ rotamers.
The sum of the populations of all rotamers which have the trans conformation for the central C 4 4 bond in the O2-C3C4-05 bond sequence is 31.2%. The sum of the population of all gauche rotamers is 68.8%. Thus, the population of T:G:G’ is about 1:1:1. The Gibbs free energy of the gauche form relative calculated from the population to that of the trans form (AG273.15) ratio68.8/31.2 i s 4 . 4 3 kcal/m01.~~ Abeand Inomata calculated the relative energy (AEBa,)from the measurement of CHz-CH2 NMRcouplingconstants in thegas phase and reported that AEgas is 4 . 3 kcal/mol with the statistical weight factor correction.I3 Our AGZ73.l5obtained from the populations of trans and gauche forms agrees with their results. It should be noted that the TGG’ rotamer having a positive AH (0.54 kcal/mol) shows negative AG ( 4 - 3 2 kcal/mol) at 273.15 K mainly due to a high multiplicity of as much as 4. A similar situation is also found for the TGT rotamer (multiplicity = 2), which shows a low plus value of AG (0.13 kcal/mol). Contributions from these TGG’ and TGT rotamers result in the preference of the gauche conformation for the central C-C bond of the O-C-C-O bond sequence,78i.e., a phenomenon called the gauche oxygen effect.16J3-24 The prevalenceof the TGG’conformation sequence has already been claimed by us for the 0-C-C-O bond sequence in the poly[(S)-oxy(1-isopropylethylene)] chain in solution from the NMR method“ as well as in the crystalline state by the X-ray and by Sakakihara et al. for the isotactic poly[oxy(l-tertbutylethylene)]chain in the crystallinestate from X-ray analysis.80 The GG’conformation sequencein the prevailing TGG’ rotamer
TOG’
GOO
GOO’
Figure 1. HG/6-311+G* geometries of the TGG’, GGG, and GGG’ rotamers.
is highly prohibited in the n-alkaline chain due to the heavy steric interaction?‘ Le., the four-bondinteraction known as the “pentane effect” or ‘1,3-diaxial interaction”. This GG’ conformation sequence is not unusual, however, for the 0-C-C-O-C bond sequence,since the bond angle for the ether linkage is more flexible than the corresponding C-C-C bond sequence. The GG’ conformation in the 04242-04 bond sequence of the TGG’ rotamer can relieve its steric strain by expanding its C-C-O (1 13.7°)andC-0-C(1 16.8°)angles82withremarkablydeviated dihedral angles from the exact gauche (Table 11). The large deviation of the bond angles and dihedral angles may relieve the steric strain associated with the GG’ conformation, but there should be some cause which disposes the 0-C-C-O-C part favorably in the GG’ conformation. Inspection of the spatial structure of the TGG’ rotamer drawn in Figure 1 suggests that some kind of interaction between the ether oxygen and one of the hydrogens of the methyl group at the 6-position (1,5 CHJO interaction) may be a candidate for that cause. Ether is known as a good solvent for nonpolar solutes. Here in Figure 1, the ether oxygen solvates intramolecularly the methyl hydrogen at the 6-position. Thus, intramolecular solvation might be a real cause to stabilize the GG’ conformation in the TGG’ rotamer unless the TGG’ rotamer should have much higher energy due to its congested GG’ structure. In the following section we will revisit the role of the 1.5 CH3/0 interaction proposed here. B. Molecular MecbanicsCdculrtionsof1,2DimetbOxyethone. In order to analyze the cause of this unexpectedly large population of the TGG’ rotamer, we calculated the relative energies of rotamers by molecular mechanics. We used the molecular mechanics parameters for ethers recently refined based on the conformationalenergies of four monoethers obtained by the MP4(SDQ)/6-31G*//HF/6-31G* level ab initio molecular orbital calculation^.^^ The torsional parameters for the 0-C-C-O bond were newly refined based on the torsional potential of this bond of 1.2-dimethoxyethane. Relative energies of trans, gauche, eclipse, and skew (saddle point between gauche and trans) rotamers for the O+2&4-O~ bond, in which the CI-Oz-C3-C4 and C3-C4-05-06 bonds were kept in the trans conformation, were calculated at the MP3/6-31 l+G//HF/6-311+G* level. Thecalculated relative energiesof these rotamers were 0.0,0.508, 9.505, and 2.403 kcal/mol, respectively. The torsional parameters of the 0-C-C-O bond were refined to reproduce these conformational energies. The thus refined VI, V2, and V3 torsional parameters are 3.964, -3.297, and 0.824 kcal/mol, respectively. The calculated relative energies of the aforementioned rotamers using these parameters for the molecular mechanics are 0.0,0.500, 9.505, and 2.408 kcal/mol, respectively. Calculated relative energies of nine rotamers by molecular mechanics are compared with the molecular orbital conformational energies as shown in Table 111. The molecular mechanics conformational energies of the first six rotamers are close to the molecular orbital conformational energies. The largest deviation is less than 0.4 kcal/mol. On the other hand, the molecular mechanics conformationalenergiesof the TGG’, GGG, and GGG’ rotamers are larger than the molecular orbital conformational energies by as much as 1.2, 2.7, and 1.4 kcal/mol, respectively. These differences can be explained by assuming that a certain intramolecular interaction, which is not considered in the molecular mechanics scheme, stabilizesthese three rotamers. The
Conformational Analysis of 1,2-Dimethoxyethane presence of such interaction is confirmed by an inspection of the calculated geometries. The gauche dihedral angles of the GGG and GGG’ rotamers having consecutive GG or GG’ bonds are different from those of the TTG and TGT rotamers having an isolated G bond. The change in these dihedral angles decreases the distancesbetween the 2-oxygen atom and the 6-methyl group in the GGG and GGG’ rotamers and also the distance between the 1-methyl group and the 5-oxygen atom in the GGG rotamer. The 2-oxygen and 6-methyl group are also close in the TGG’ rotamer, although the relevant gauche dihedral angles in the GG’ part are of similar magnitude to those in TTG and TGT rotamers (Figure 1). The distances between the 2-oxygcn atom and the nearest hydrogen atom in the 6-methyl group in the TGG’, GGG, and GGG’ rotamers are 2.569, 2.963, and 2.591 A, respectively. The distances in the TGG’ and GGG’ rotamers are smaller than the sum of the van der Waals radii of oxygen and hydrogen atoms.83 Hence, it is reasonableto assumethe presence of a kind of nonbonding attractive interaction between the oxygen atom and the methyl group. The difference between molecular mechanics and molecular orbital conformational energies in the TGG’, GGG, and GGG’ rotamers can be rationalized, if we assume that a pair of the CH3/0 attractive nonbonding interactions stabilizes these rotamers by as much as 1.2-1.4 kcal/mol. (Cf. two pairs of interactions in the GGG rotamer.) The change in the gauche dihedral angles is also observed in the TGG rotamer. However, thedistancebetween the 2-oxygen atomand thenearest hydrogen atom of the 6-methyl group in the TGG rotamer is 3.632 A, which is considerably larger than those of the former three rotamers. The stabilization, if it exists, would be little to this rotamer The consistency among the rotamer population ratios from the MP3 correlated ab initio calculations and electron diffraction measurements confirms the reliability of the ab initio molecular orbital method to estimate conformationalenergy. On the other hand, the failure of the molecular mechanics calculations shows that the neglect of weak nonbonding interactions, such as the C H 3 / 0 interaction, in the molecular mechanics scheme can be a cause of serious errors in estimating the rotamer population. The possibility of the presence of the C H 3 / 0 and CH2/0 nonbonding attractive interactions has also been pointed out by other groups.84-88 Astrup and Aomar supposed the presence of the 1,4 C H 3 / 0 attractive interaction from electron diffraction of dimethoxymethane and 2,2-dimetho~ypropanc.8~*~5 Brogen et al. mentioned the possibility of the 1,5 C H 3 / 0 interaction from the conformational analysis of 1,4,7,11- and 1,4,8,11tetraoxacyclotetradecane.86 More recently, Wiberg et al. reported the attractive CH/O interaction from X-ray crystallographic studies of nonanolactone and tridecan~lacetone.~~ Reynolds reportedthe CH/O hydrogen bond in the methyl chloride/formic acid van der Waals complex from the analysis of molecular orbital calculations.88 C. Ab Initio Molecular OrbitaJ Calculations of Intermolecular CHa/O Interaction. In order to confirm the presence of C H 3 / 0 nonbonding attractive interaction, the intermolecularinteraction energy potential of dimethyl ether dimer was calculated. The trans C-H bond of a methyl group of an ether molecule was put on the Cz axis of another ether molecule (Figure 2). Intermolecular interaction energies were calculted by MP2/6-3 1G* method with basis set superposition error correctionSoby the counterpoise method.s’ The calculatedab initio molecular orbital potential has a minimum of 4 . 9 kcal/mol at the C-0 distance of 3.6 A as shown in Figure 3. The methoxy group connected to the interacting methyl group was changed to hydroxyl, methyl, amino groups, fluoro, and hydrogen atoms to examine the effect of the adjacent groups of the interacting methyl group on the nonbonding interaction potential. The potential depth is little changed if the methoxy
.
The Journal of Physical Chemistry, Vol. 97, No. 7, 1993 1349
Me’
F/
H’
Figure 2. Orientations of dimethyl ether dimer and related complexes used for intermolecular interaction energy calculation. 0.5
R=OCH3 0
0.0
R=NH2 R=CH3
0
E
I
E t
-0.5
w
-1.o
-1.5, I
3.5
Distance
4.0
4.5
(A)
Figure 3. Nonbonding interaction energies (E) of dimethyl ether dimer andrelatedcomplexescalculated at the MP2/6-31G* level. Orientations of complexes are shown in Figure 2.
group is replaced by the hydroxyl group or the fluoro atom. On theother hand, thedepth ofthepotentialissubstantiallydecreased, if the methoxy group is replaced by the methyl or amino group or the hydrogen atom. This difference shows that an electronegative substituent connected to the methyl group enhances the nonbonding attractive interaction.
IV. Conclusion The calculations of conformational energies of nine rotamers of 1,Zdimethoxyethane by the ab initio molecular orbital method support the results of Astrup’s electron diffraction measurement that 1,Zdimethoxyethane exists as a rotamer mixture in the gas phase, and the TGG’ rotamer has the largest population. We have found from the comparison of the conformational energies obtained by the molecular orbital and molecular mechanics calculations that the TGG’ rotamer is stabilized by the 1,s CHJO nonbonding attractive interaction. These interactions are exclusively found in the TGG’, GGG, and GGG’ rotamers. The stabilization energy associated with a pair of these nonbonding interactions is 1.2-1.4 kcal/mol. The calculation of the nonbonding interaction potential of dimethyl ether dimer also supports the presence of this attractive interaction. A comparison with the interaction potentials of related complexesshows that this attractiveinteractionis activated by the electronegativeoxygen atom connected to the interacting methyl group.
1350 The Journal of Physical Chemistry, Vol. 97, No. 7, 1993
It should be noted that the 1,5 CH3/0 interaction gives a drastic effect on the rotamer ratio of 1,2-dimethoxyethane. It follows that the neglect of weak nonbonding interactions, such as the C H 3 / 0nonbonding interaction, in conventional molecular mechanics scheme can cause serious errors in estimating rotamer populations.
Supplementary Material Available: Table of bond distances and valence angles of nine rotamers of 1,2-dimethoxyethane calculated at the HF/6-311+G* level (1 page). Ordering information is given on any current masthead page. References and Notes (1) Miyake, A. J . Am. Chem. SOC.1960.82, 3040.
(2) (3) (4) (5) (6)
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(72) Sato, A.; Hirano, T.; Tsuruta, T. Makromol. Chem. 1975,176,1187. (73) Sato, A.; Hirano, T.; Tsuruta, T. Makromol. Chem. 1976,177,3059. (74) Ohsaku, M.; Imamura, A. Macromolecules 1978, I ! , 970. (75) Brunck, T. K.; Weinhold, F. J . Am. Chem. Soc. 1979, 101, 1700. (76) Anderson and KarlstrcTm reported that they found no minima for the GG'G rotamer (ref 17). (77) The predicted populations of rotamers are slightly different from those from electron diffraction. The populations of rotamers 'ITT and TGT are inverted. The cause of this slight disagreement is not certain. Astrup analyzed rotamer populations from the measurement of electron diffraction by assuming that dihedral angles 4 (OCCO) trans, 4 (OCCO) gauche, 4 (COCC) trans, and $ (COCC) gauche are q u a l in all rotamers. Calculated geometries of rotamers show that this assumption is not appropriate. This defect can be the cause of the slight disagreement of the predicted and experimental rotamer populations. (78) When G and G'are differentially counted, the AG for theG (and also G') rotamer at 273.15 K is 4 . 0 5 kcal/mol relative to that for the T rotamer, indicating that the relative populations of T, G, and G' are almost 1:l:l. (79) Takahashi, Y.; Tadokoro, H.; Hirano, T.; Sato, A.; Tsuruta, T. J . Polym. Sci., Polym. Phys. Ed. 1975, 13, 285. (80) Sakakihara, H.; Takahashi, Y.; Tadokoro, H.; Oguni, N.; Tani, H. Macromolecules 1973, 6, 205. (81) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience Publishers: New York, 1969. (82) The C-C-0 and C-0-C angles in the TTT rotamer calculated at HF/6-311+G8 level are 107.9O and 1 14.S0, respectively. (83) Bondi, A. J . Phys. Chem. 1964.68.441. (84) Astrup, E. E. Acta Chem. Scand. 1973, 27, 3271. (85) Astrup, E. E.;Aomar, A. M. Acra Chem. Scand. 1975, A29, 794. (86) Borgen, G.; Dale, J.; Teien, G. Acra Chem. Scand. 1979, 833, 15. (87) Wiberg, K. B.; Waldron, R. F.; Schultc, G.; Saunders, M. J. Am. Chem. Soc. 1991, 113, 971. (88) Reynolds, C. H. J . Am. Chem. SOC.1990, 112, 7903.
