theoretical study of the potential energy surface of diglyme

ELSEVIER

3 January 1997

Chemical Physics Letters 264 (1997) 127-133

CHEMICAL PHYSICS LETTERS

Theoretical study of the potential energy surface of diglyme

Amin Sutjianto, Larry A. Curtiss Chemical Technology Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439-4828. USA

Received 5 August 1996; in final form 23 October 1996

Abstract

The potential energy surface of diglyme has been investigated using ab initio molecular orbital theory. The all-trans conformer and 20 conformers having either one- or two-gauche conformations around C-C or C - O bonds were studied at the HF/6-31G(d) level. The four lowest energy structures were further investigated with larger basis sets and with inclusion of correlation effects. At the highest level of theory, the t g+g- t 3 conformer is 0.1 kcal/mol more stable than the all-trans conformer, while the t g t 4 and g+ g - t 4 conformers are slightly less stable than the all-trans conformer.

1. Introduct ion

Poly(ethylene oxide) (PEO) complexed with metal salts is a polymer electrolyte that exhibits ionic conductivity [1]. The conformational characteristics of the PEO chain as well as its interaction with ions play an important role in understanding ionic trans- port in the electrolytes. I t has been established that PEO chains have a large fraction of bonds in gauche conformations [2]. Torsional motions around C - C or C - O bonds that occur in the presence of polar substituents (oxygens) result in gauche conformations [3]. The conformers are usually denoted by combinations of t and g, where t refers to a trans arrangement while g refers to a gauche arrangement. If there is more than one gauche arrangement, there is a possibil i ty of having gauche arrangements with

This work was supported by the Division of Chemical Sci- ences, Office of Basic Energy Sciences, US Department of En- ergy, under Contract No. W-31-109-ENG-38.

different orientation relative to each other. These gauche arrangements are denoted by g ÷ and g - .

Recently, there have been several theoretical stud- ies reported of the energetics and rotational barriers of 1,2 dimethoxyethane (DME), H3C(OCH2CH2)- OCH 3, as a model for PEO. Ab initio molecular orbital calculations by Murcko and DiPaola [4] and by Jaffe et al. [5,6] indicate that the ail-trans conformer is more stable than the tgt conformer by a few tenths of kilocalories per mole. Jaffe et al. found that the relative energies of the conformers were quite sensitive to inclusion of correlation effects and use of large basis sets. Mueller-Plathe [7] investigated the gauche effect of DME in an aqueous solution with a given dielectric constant e and con- cluded that the gauche conformer is more stable than the all-trans conformer in the presence of a polariz- able medium. The conformations and energies of DME have also been studied using molecular mechanics and Monte Car lo / s tochas t ic dynamics simu- lations [8]. The results indicate that the gauche conformer is more stable than the all-trans conformer in

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128 A. Sutjianto, L.A. Curtiss / Chemical Physics Letters 264 (1997) 127-133

solution. The conformations of a larger model molecule than DME, namely, diglyme, H3C(OCH 2- CH2)2OCH3 have been investigated [9]. This study considered several conformers of diglyme at the HF/3-21G level and employed limited geometry optimization.

In this Letter we report ab initio molecular orbital calculations for diglyme. The purpose of this work is to characterize the rotational potential energy surface of this molecule. Diglyme should be a better model for PEO than DME because it has six internal rota- tions instead of three, and rotation about the inner C-O bond does not involve a terminal methyl group. We have carried out f u l l optimizations at the HF/6- 31G(d) level of all conformers having one- and two-gauche conformations. The lowest energy structures were further investigated with larger basis sets and with inclusion of correlation effects. In addition, the barriers to rotation between the lowest energy conformers were determined. The theoretical methods are described in section 2. The results are pre- sented and discussed in section 3, including comparison to results for DME.

2. Theoretical methods

Most of the ab initio molecular orbital calculations reported in this study were carried out at the Hartree-Fock (HF) level of theory using the 6- 31G(d) basis set [10,11]. Full optimizations were done and vibrational frequencies were calculated to determine whether the structures were local minima. The lowest energy conformers were studied at higher levels of theory, including geometry optimizations at the MP2/6-31G(d) level. At each MP2/6-31G(d) optimized geometry, single-point energy calculations at the MP2 level were carried out with larger basis sets, including the 6-311 + G(2df, p) basis [ 10-12], a double zeta basis [5s2p2dlf/2slp] referred to as D95 +(2df , p) [11,13], and a triple zeta basis [6s3p2dlf/3slp] referred to as TZP + (2dr, p) [14]. In each basis set additional functions are added to all atoms: ' + ' denotes addition of diffuse sp functions for each carbon and oxygen, and '(2df, p)' represents additional polarization functions that contain two sets of d functions plus a set of f functions for each carbon and oxygen and a set of p functions for each

hydrogen. The additional polarization functions used for the TZP + (2df,p) basis are the same as those used in the 6-311 + G(2df,p) basis [12].

3. Results and discussion

The local minimum of all-trans diglyme with C2v symmetry was obtained at the HF/6-31G(d) level of calculation. The all-trans conformer is denoted by t 6,

where 6 is the number of C -C and C-O torsional angles. The HF/6-31G(d) optimizations were performed for all one-gauche conformers of which there are three, namely, tgt 4, t2gt 3, and gt 5. T h e tgt 4

conformer is obtained by a rotation around one of the C-C bonds and the t2gt 3 and gt 5 conformers are obtained by rotation around the central C-O and terminal C -O bonds, respectively. The HF/6-31G(d) energies of the one-gauche conformers relative to the t 6 conformer are listed in Table 1. The structures of the all-trans and one-gauche conformers are shown in Fig. 1. The optimized gauche dihedrals range from 60-90 °. The all-trans conformer is more stable than the one-gauche conformers at the HF/6-31G(d) level by 1.2 to 1.8 kcal/mol. Single-point MP2/6-31G(d) calculations were also carried out for all HF/6- 31G(d) local minima (see Table 1). At the single- point MP2/6-31G(d) level, the tgt 4 conformer is the most stable of the one-gauche conformers, being 0.4 kcal/mol less stable than the all-trans conformer. The other conformers were less stable by more than 1 kcal/mol.

The t 6 and tgt 4 conformers were further investigated with larger basis sets and at the correlation level. The relative energies of the t 6 and tgt 4 conformers at the MP2 level using larger basis sets are listed in Table 2. The total energies of the t 6 c o n -

former are listed in Table 3. The MP2/TZP + (2df, p) calculations give the lowest total energies of conformers. At this level the tgt 4 conformer is only 0.02 kcal/mol less stable than the all-trans conformer. The results from the two other largest basis sets [6-311 + G(2df,p) and D95 + (2df,p)] also indicate that t h e t g l 4 conformer is within +0.1 kcal/mol of the 16 conformer. By comparison, the tgt conformer of DME is 0.22 and 0.14 kcal/mol higher than the energy of the t 3 conformer at the MP2/6-311G + (2df, p) and MP2/D95 + (2df, p) levels, respectively

A. Sutjianto, L.A. Curtiss / Chemical Physics Letters 264 (1997) 127-133

Table 1 Energies (in kcal /mol) of one-gauche and two-gauche conformers of diglyme relative to the all-trans conformer

129

Conformers HF/6-31G* a ZPE b MP2/6-31G* c.d

t 6 0.00 137.83 0.00(0.00)

one-gauche conformations: gt -s 1.79 137.85 1.48 tgt 4 1.24 137.86 0.43(0.45) t2gt 3 1.65 137.90 1.28

two-gauche conformations: g2t4: g +g+ t 4 / g - g - t 4 3.00 137.89 1.77

g + g t 4 / g - g+ 14 1.68 137.92 0.13( - 0.02) tg2t3: t g + g + t 3 / t g - g t 3 2.88 137.93 1.60

tg + g - t 3 / t g - g+ t 3 1.62 137.93 0.07(0.08) t2g2t~': t 2 g + g + t ~ / t 2 g - g - t 2 2.57 137.95 1.85

t2 g+g t2 / t2 g - g + t z no local minima gtgt3: g+ tg + t 3 / g - t g - t 3 3.54 137.92 2.81

g+ t g - t 3 / g tg+ t 3 3.44 137.89 2.78 gt2gt:: g+ t2 g+ t 2 / g - t ~ g - t 2 3.42 137.92 2.75

g+ t2 g - t 2 / g - t2 g + t 2 3.55 137.91 2.86 tgtgt2: tg+ tg÷ t 2 / t g - t g - t 2 2.71 137.93 1.53

tg + tg- tZ / tg - tg + t 2 3.15 137.89 1.93 gt3gt: g + t 3 g + t / g - t 3 g - t 2.98 137.88 1.84

g + t a g - t / g t3g+t 3.11 137.86 1.97 tgtZgt: t g + t 2 g + t / t g - t 2 g - t 2.49 137.87 0.85

tg + t2 g - t / t g - t~" g + t 3.13 137.84 1.45 gt4g: g + t 4 g + / g - t 4 g 3.59 137.87 3.01

g+t4g / g t4g + 3.64 137.86 2.95

a At HF/6-31G(d) optimized geometry. All are local minima. b ZPE is the unscaled HF/6-31G(d) zero-point vibrational energy (in kcal/mol). c Single-point MP2/6-3 l G(d) calculations at the HF/6-3 l G(d) optimized geometries. d Values in parentheses are from single-point MP2/6-31G(d) calculations at the HF/6-31G(d) optimized geometries in presence of solvent using the Onsager self-consistent reaction field method (e = 80 and cavity radius = 4.42 ~.).

[5,6]. These results suggest that the gauche conformations may be favored as the chain length (CH2CH20) . is increased, although calculations on

Table 2 MP2 relative energies of diglyme conformers (in kcal/mol)

Basis set t 6 tgt 4 tg + g - t 3 g+ g - t a

6-31G(d) 0 0.39 - 0.09 0.00 6-311G(d,p) 0 0.36 -0 .21 -0 .01 6-311G(2d,p) 0 0.13 - 0 . 2 6 -0 .21 6-311 + G(2df, p) 0 0.09 0.32 0.40

D95(d) 0 - 0 . 7 3 0.11 0.13 D95(d,p) 0 0.66 0.07 0.04 D95 + (2df, p) 0 - 0 . 0 7 - 0 . 1 6 -0 .01

TZP 0 0.51 0.13 0.16 TZP + (2df, p) 0 0.02 - 0.08 0.02

l o n g e r c h a i n s a re n e e d e d to c o n f i r m th i s . J a f f e e t al.

[5 ,6] a l s o s t u d i e d t h e c o n f o r m a t i o n a l e n e r g i e s o f

D M E at a h i g h e r l eve l o f e l e c t r o n c o r r e l a t i o n u s i n g

Table 3 Total energies of all-trans conformer of digylme at the MP2 level (in hartree)

Basis set Total energy

6-31G(d) - 461.20076 6- 311G(d,p) - 46 1.50244 6-311G(2d,p) -- 461.60090 6-311 + G(2df, p) - 461.75539

D95(d) - 46 1.26810 D95(d,p) - 46 1.38573 D95 + (2df, p) - 461.66478

TZP -- 461.52745 TZP + (2df,p) - 46 1.78257


: g: g * t2g +12 [g- t2 g" t 2 g + t2 g" t2 /g" t2 g * t 2

~ tg*tg+t2/tg'tg'tZ tg*tg't2/tg'tg+t 2

g *t3 g+t/g.tJ g.t g+tS g-t/g'tS g+t tg÷g * t3 /tg'g-t3 tg ÷g- t3 /tg'g ÷ t3 ~

12g ÷g + t2A2 g-g" t2 tg * t2 g +t/l g-12g.t t g÷ t2g" t/t g" t2 g + t

g+tg+r3/g'tg-t 1 g÷tg'tl/g'tg+t 3 g*t4 g+/g-t4g" g*t4g'/g-t4 g +

Fig. 1. Optimized HF/6-31G(d) structures for all-trans, one-gauche, and two-gauche conformers of diglyme.

coupled cluster theory [5,6], including single, double, and triple excitations, CCSD(T), with smaller basis sets, e.g., D95 + (d,p) and 6-311 + G(d). They con- cluded that MP2 energy differences are generally 0.1

kcal/mol smaller than the corresponding CCSD(T) results.

Fig. 2 shows the torsional potential at the HF/6- 31G(d) level for the path from the all-trans con-

Table 4 Barriers for rotation in diglyme (in kcal /mol)

Barrier HF/6-31G(d) a MP2/6-31G(d) b MP2/6-311 +G(2df, p) c MP2/D95+(2df ,p) ¢ MP2/TZP+(2df , p) c

t 6 ~ tgt 4 3.70 2.94 2.43 2.16 2.24 t 6 ~ t2gt 3 1.99 1.93 2.07 1.84 - tgt 4 ~ tg ÷ g - t 3 1.17 1.16 1.22 1.03 1.02 tgt 4 ~ g+ g - t 4 1.30 1.29 1.36 1.24 1.16 t 2 g t 3 - ' - ~ t g + g - t 3 2.88 2.31 - - -

a HF/6-31G(d) optimized geometry. b MP2/6-31G(d) optimized geometry. c MP2/6-31G(d) geometry.

A. Sutjianto, L.A. Curtiss / Chemical Physics Letters 264 (1997) 127-133 131

1 2 . . . . t . . . . I . . . . i , , r , , ¸ . . . . . i ' ~

10

8

0 60 120 180 240 300 360

Torsional angles

Fig. 2. Potential energy surface for the torsional path of the

all-trans conformer to each of the one-gauche conformers with the barriers for ( ) t 6 ~ tgt 4, ( - - - ) t 6 --~ gt 5, and ( - • - - ) t 6 _~ t2gt 3.

former to each of the one-gauche conformers obtained by optimizing the structure of each one-gauche conformation at different torsional angles in the range from 0 to 360 degrees. The barriers from t 6 tO tgt 4 and from t 6 t o t2gt 3 are denoted by t 6 --+ tgt 4 and t 6 ~ t 2 g t 3, respectively. The geometries at the barriers were also reoptimized at the MP2/6-31G(d) level. Single-point calculations of the barriers at the MP2/6-311 + G(2df,p), and MP2/D95 + (2df,p) levels were subsequently performed; the t 6---~ tgt 4 barrier was also calculated at the MP2/TZP + (2df,p) level. The barriers are listed in Table 4 are about 2 kcal/mol. At the MP2/D95 + (2df,p) level, the bar- tiers of t 6 ~ tgt 4 and t 6 ~ t2 gt 3 are only slightly lower (0.2 kcal /mol) than the corresponding barriers ( t 3 ~ t g t and t 3 ~ t t g ) for DME [5,6].

The two-gauche conformers of diglyme were optimized at the HF/6-31G(d) level. In the two-gauche conformers, the gauche conformations are denoted by g+ or g - . There are 36 possible conformers having the two-gauche conformations. Some of the conformers are equivalent, i.e., two-gauche arrangements having the same orientation denoted by either g+g+ or g g and those with different orientation denoted by g+g- or g-g+. Also, we did not find a local minimum for the t 2g+g- t 2 conformer; it col- lapsed to the t2gt 3 conformer. Thus, the total number of conformers with two-gauche conformers is reduced to 17. The two-gauche conformers are shown in Fig. 1. Similar to the case of the one-gauche

conformers, we have performed single-point MP2/6-31G(d) calculations at the HF/6-31G(d) optimized geometries. The energies with respect to the all-trans conformer are listed in Table 1. Except for the g + g - t 4 and t g+g- t 3 conformers, the energies of the two-gauche conformations at the MP2 level are higher by more than 0.9 kcal /mol than the all-trans conformer. Based on single-point MP2/6- 31G(d) calculations, the g+ g - t 4 and tg+ g - t 3 conformers are more stable than the t g t 4 conformer, but higher than the all-trans conformer by about 0.1 kcal/mol. Thus, higher level calculations were done on the g+ g - t 4 and tg+ g - t 3 conformers.

The g + g - t 4 and tg + g - t 3 conformers were further reoptimized at the MP2/6-31G(d) level, and single-point MP2 calculations using larger basis sets were carried out. The g + g - t 4 conformer is obtained from the tgt 4 conformer by rotating around one of the terminal C - O bonds (next to the C - C bond that forms the gauche arrangement) in the opposite direction to its gauche neighbor. The t g+g- t 3 conformer is formed from either t h e tgt 4 o r t 2 g t 3 conformer by rotating one of the internal C - O bonds or one of the C - C bonds, respectively, in the opposite direction to the next gauche arrangement. The relative energies are listed in Table 2. At the MP2/TZP + (2df, p) level, the t g+g- t 3 conformer is more stable than the all-trans conformer by 0.08 kcal/mol, while the g + g - t 4 conformer is 0.02 kcal /mol less stable.

Several pathways to the g + g - t 4 a n d tg+g- t 3 conformers have been considered. The torsional po- tentials for the path from t h e t g t 4 conformer to the g+ g - t 4 and tg + g - t 3 conformers and from the t2 gt 3 conformer to the t g+g- t 3 conformer have been calculated in a similar manner as for the one-gauche conformers. The barriers are denoted by l g t 4"-~

g+ g - t 4, tgt a ~ tg+ g - t 3, and t2gt 3 --+ tg+ g - t 3, respectively. The results are listed in Table 4. The barriers for t g t 4 ~ tg + g - t 3 and t g t 4 ~ g + g - t 4 at the MP2/D95 + (2df,p) and MP2/TZP + (2df, p) levels are about 1 kcal /mol , which is about 1 kca l /mol less than for the t 6 ~ t g t 4 barrier.

Gejji et al. [9] reported results for the diglyme obtained for single-point MP2/6-311 + +G(d,p) calculations at HF/3-21G optimized structures for the t g t 4, t2gt 3, and all-trans conformers. The gauche conformers were not fully optimized. The energies of the t g t 4 and t2gt 3 conformers were -0 .02 and 1.05


kcal /mol relative to the all-trans conformer, respectively. The t 6 ~ tgt 4 and t 6 ~ t2gt 3 barriers were 2.29 and 1.79 kcal /mol , respectively. Our results, which are based on full optimization and higher levels of theory, are consistent with the results of Gejji et al., indicating that the tgt 4 conformer is nearly equal in energy to the all-trans conformer. Gejji et al. did not investigate any two-gauche conformations, for which we have found two conformers to be very close in energy to the all-trans conformer.

Mueller-Plathe [7] found that the gauche (tgt) conformer of DME is more stable than the all-trans ( / 3 ) conformer, in the presence of an aqueous solution using the Onsager self-consistent reaction field method [15,16] with a dielectric constant s = 80 and cavity radius of 4 A. The stabilization of tgt relative to t 3 of about 0.5 kca l /mol is due to the presence of a dipole in the tgt conformer, while the t 3 conformer has no dipole moment. Unlike DME, the all-trans (t 6) conformer of diglyme has a dipole of 1.58 debye, while t h e lgt 4, tg÷g- t 3, and g+g- t 4 conformers have dipoles of 1.32, 1.39, and 1.62 debye, respectively. The relative stability of these conformers in aqueous solution with a dielectric constant

= 80 and cavity radius of 4.42 ,~, (a recommended value for diglyme obtained from molecular volume calculations) obtained from single-point MP/6 - 31G(d) calculations at the HF/6-31G(d) geometry are included in Table 1, The results indicate that in the presence of the reaction field the g÷g- t 4 conformer is stabilized by 0.15 kcal /mol relative to the all-trans conformer while the other conformers are slightly destabilized relative to the all-trans conformer. Therefore, there is little stabilization of the gauche conformers of diglyme relative to the all-trans conformer, in the presence of a polar solvent. We note that the solvation model that we used accounts for bulk dielectric effects. There may be local so- lute-solvent interactions such as hydrogen bonding which are not well represented by the Onsager model and could be affected by conformational changes. A recent molecular dynamics study of liquid DME by Smith et al. [17] indicated a decreased population of tg +-g ~ relative to tgt even though tg +-g ~ has a significant dipole moment. They suggested hydrogen bonding between DME molecules could account for the decrease in population of the tg ±g ~ conformer. Local hydrogen bonding interactions could also play

a role in the relative stability of diglyme conformers in an aqueous solution.

We have not fully investigated conformers con- taining the three-, four-, five-, and all-gauche conformations. There are 40, 72, 48, and 32 possible conformers, respectively. At the HF/6-31G(d) level, we have investigated several of these conformers. The g+t3g÷ g - , g+ g g g t 2, g - g - g - g - g - t , a n d g÷g+g+g+g-g- conformers are 3.46, 4.66, 7.21, and 7.19 kcal /mol higher in energy than the all-trans conformer, respectively.

4. Conclusions

We have studied diglyme conformers at the HF and MP2 level of calculations. The inclusion of electron correlation effects and larger basis sets is important in the relative stabilities. The calculations show that several one-gauche and two-gauche conformers (tgt 4, g+ g - t 4, and tg+ g - t 3) are very close in energy to the all-trans conformer. At the M P 2 / T Z P + ( 2 d f , p) level, the tg+g- t 3 conformer is 0.1 kca l /mol more stable than the all-trans conformer. The tgt 4 and g+g- t 4 conformers are only slightly less stable 0.02 kcal /mol than the all-trans conformer. Inclusion of a solvent reaction field has little effect on the relative energies. The barrier for t 6---~ tgt 4 is about 2.0 kcal /mol, while the tgl 4---~ tg+ g - t 3 and tgt4-'* g+ g - t 4 barriers are about 1.0 kcal/mol.

Acknowledgements

This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, US Department of Energy, under Contract No. W- 31-109-ENG-38, We acknowledge a grant of computer time at the National Energy Research Super- computer Center.

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theoretical study of the potential energy surface of diglyme

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