12745
J. Phys. Chem. 1993,97, 12745-12751
Conformations of 1,2-Dimethoxyethane from ab Initio Electronic Structure Calculations Richard L. Jaffe' NASA Ames Research Center, Moffett Field, California 94035
Grant D. Smith Eloret Institute, 11 78 Maraschino Drive, Sunnyvale, California 94087
Do Y. Yoon IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099 Received: March 12, I993@
The conformational properties of 1,Zdimethoxyethane (DME) have been analyzed in detail using ab initio electronic structure calculations in order to better understand the influence of oxygen gauche effects on the conformation energies and populations of DME. Our calculations indicate that the energy of the gauche conformation of the 0-C-C-O bond relative to the trans conformation, which reflects the strength of the oxygen gauche effect in DME, depends strongly not only on the basis set size but also on electron correlation effects. Specifically, the energy of the tgt conformation of DME relative to the ttt conformation was determined for various basis sets at both the SCF and MP2 levels. MP2 level calculations with a D95+(2df,p) basis set, a Dunning double-tbasis set of the form (lOs6p2dlf/4slp)/[5s2p2dlf/2slp], yield an energy ofca. 0.1 kcal/mol for the gauche conformation, as compared with 0.75 kcal/mol for MP2 level calculations with the smaller D95** basis set and 1.0 kcal/mol for S C F level calculations employing the D95+(2df,p) basis set. A salient result of our investigation is the determination that the energy of the tgigF conformation lies only ca. 0.2 kcal/mol above that of the ttt conformation, apparently due to strong 0-H attractions. Finally, we find that the conformer populations of DME obtained from conformational energies determined at the MP2 level with a D95+(2df,p) basis set are in good agreement with those derived from electron diffraction experiments and can be used to successfully reproduce experimental values of N M R vicinal coupling constants and dipole moments for DME.
Introduction
Much effort has been spent on investigatingthe conformational characteristics of 1,Zdimethoxyethane (DME) as a model molecule for understanding the conformations of poly(oxyethylene) (POE). It has long been established that POE chains have a large fraction of bonds in gauche conformations.' This is a specific example of the gauche effect in which polar substituents cause the preferred conformation about a C-C bond to switch from trans to gauche.2 In ethers and polyethers, this is usually referred to as the oxygen gauche effect.' Several attempts have been made to describe polyethers using rotational isomeric state (RIS) models parameterized on the basis of molecular mechanics predictions of the conformational energies and geometries of small model molecules.3~4 Miyasaka and Yoshida? based on MM 1 calculations for 1,Zdiethoxyethane, identified three low-lying conformations of the 0-C-C-O sequence for their RIS model: ttt, tgig', and tgt, with relative energies of 0.0, 0.4, and 0.9 kcal/mol, respectively. Abe and TasakiS investigated the energy of the tgt conformer of DME relative to the ttt conformer (see Figure 1 for representative conformations of DME) using MM2 and found that by using a very high dielectricconstant they could obtain a negative gauchetrans energy difference (4.5 kcal/mol) compatible with their analysis of NMR vicinal coupling experiments. Abe and coworkers undertook additional molecular mechanics analyses of DME conformer energies which they subsequently adjusted in order to successfullyreproduce NMR vicinal coupling constants in DME solutions and neat liq~id.6,~ In their analysis they used the frameworkof a three-state RIS model for DME and concluded that the gauche state is 0.5-1 $2kcal/mol lower than the trans Abstract published in Aducmce ACS Absrracrs, October lS, 1993.
0022-3654/93/2091- 12745$04.00/0
state. Contrary to these predictions, Allinger et a1.,8 in applying the MM3 force field to DME, predict the gauche conformer to lie 0.05 kcal/mol higher in energy than the trans. The MM3 force field is purported to correct numerousdeficiencies of previous molecular mechanics models, including the need to explicitlytreat oxygen lone pairs.8 The analysis of solution experiments is complicated by the fact that the gaucheconformer population is enhanced by interactions with strongly polar solvents such as water (Andersson and KarlstrGmg estimate that water stabilizes the tgt conformer of DMEby 1.0-1.5 kcal/molmorethanthetttconformer). Inomata and Abelo have recently used gas-phase NMR measurements as a source of structural information on DME. They can reproduce the gas-phase NMR data using an RIS model where tgt conformation is preferred over the ttt conformation by 0.4 kcal/ mol. Moreover, comparison of NMR vicinal coupling in DME from gas-phase,IOneat liquid: and solution7experimentsindicates that the conformations of DME in gas-phase, neat liquid, and some polar organic solvents do not differ greatly. An analysis of gas-phase electron diffraction (ED) data for DME," which is dependent upon the relative populations of the conformations of the entire molecule (ttt, for example), yields conformer populations which differ significantly from the inferencesof the RIS model of Inomata and AbeIodiscussed above. In both cases, the ttt conformation accounts for less than 15% of the total population. However, the gas-phase RIS/NMR analysis10 yields a population of 46% for the tgt conformer and 27% for the tgfgi tg*gi conformers, while the electron diffraction study11 yields 23% for tgt and 53% for the tg*g* + tg*g'. Both studies agree that the fraction of C-C bonds in gaucheconformationsis high (75430%). However, thereis greater
+
0 1993 American Chemical Society
Jaffe et ai.
12746 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
variance in fraction of gauche C-O bonds (21% for RIS/NMR vs 36% for ED).. Prior ab initio electronic structure calculations12indicate the energy of the 0-C-C-O gauche conformation in DME is approximately0.6 kcal/mol higher than the trans conformation. These calculations utilized a 6-31G* basis set and included an estimate of the electron correlation energy using fourth order Msller-Plesset perturbation theory (MP4).I3 Very recently Hiranoand co-workers~4J~ have carried out SCF, MP2, and MP3 level calculations on all the DME conformersusing a 6-3 11+G* basis set. They find the tgt and tg*gr conformers to be nearly equal in energy and 0.5 kcal/mol higher than the ttt conformer. They also performed MP4(SDQ) level calculations using a 6-31 1++G* basis set for the ttt and tgt conformersand obtained an energy difference of 0.39 kcallmol. This work probably represents the smallest tgt to ttt energy difference obtained to date and is the first indication that the tg*gT conformer is important due to an attractive 1,5 C H 3 / 0 interaction. More ab initio studies have been published for the related molecule 1,2difluoroethane,I6lg which is similar to DME in that the C-C bond is adjacent to highly electronegativeatoms. For this system it was found that the computed relative energy of the F-C-C-F gaucheconformation is highly sensitive to the quality of the basis set used and inclusion of electron correlation effects. SCF calculations require basis sets larger than triple- f polarized to predict a gauche ground state. Electron correlation effects calculated at the MP2, MP3, and MP4 level result in a further lowering of the gauche conformer by 0.4-0.6 kcal/mol.18 Reasonable agreement with experimental values (the gauche conformer 1.&I .5 kcal/mol lower in energy than the trans) has been achieved by using a sufficiently large basis set (e.g., 6-31 I++G**, as discussed in the next section) and including electron correlation effects at the MP2 level. Including electron correlation effects beyond the MP2 level appears to have little effect on the computed gauchetrans energy difference.18 In an effort to account for discrepanciesbetween RIS, electron diffraction, and ab initio results for DME, we have undertaken a detailed ab initio analysis of the conformational energies of DME. Our aim is 2-fold: to systematicallyinvestigatethe effects of basis set size and the inclusion of electron correlation on the relative ab initio energies of the ttt and tgt conformers of DME and to compute geometriesand relative energies of all ten unique conformersof DME. The latter will allow us tocompare computed conformer populations directly with estimatesbased upon analysis of gas-phase electron diffraction studies" and to predict and compare with experimental NMR vicinal coupling constantslo for DME without invoking a particular RIS representation of the conformational energies.
Results and Discussion Electronic Structure Calculations. For many molecules, ab initio electronic structure calculations have been shown to accurately predict conformational energies provided adequate atomic orbital basis sets are used.lg Furthermore, the errors incurred by using smaller basis sets and by neglect of electron correlationeffects are well ~nderstood.1~ Severalgeneral purpose computer codes are available for carrying out these calculations that utilize the determination of analytic first and second derivatives of the electronic energy to automatically determine the molecular geometries of stationary points on the potential energy surface (Le., energy minima and barriers). In the present study complete optimization of conformational geometries at the SCF level of theory was performed using the ab initio electronic structure code GRADSCFZO and additional single-point energy calculations were performed using GAUSSIAN9O2I and ACES II.22 For the study of the energy difference between the tgt and ttt conformers, geometry optimization was carried out at the MP2 level using GAUSSIAN90. Most of the
TABLE I: Difference in Energy between the tgt and ttt Conformers of DME basis set D95** D95+** D95+(2df,~)~ D95+(+)** d D95+(+)(2df,~)~ 6-31 1G* e 6-31 1G** 6-31 1+G* 6-311+G** 6-31 l+G(Zd,f,p)' a
AaSCF
AMP2
ACCSD
ACCSD(TI
1.32 1.35 0.96 1.30 0.97 1.33 1.29 1.27 1.22 0.93
0.75 0.48 0.10 0.36 0.14 0.65 0.52 0.30 0.26 0.22
0.95 0.72
0.88 0.61
0.82 0.73 0.48
0.74 0.64 0.35
Energy of the tgt conformer relative to the ttt conformer in kcal/mol.
b S e e ref 24 for details of the D95 basis set. Polarization function exponents: a d = 0.750,0.850 and ap = 1.000 for c, 0,and H atoms, respectively. Polarization function exponents for C: = 1.500,0.375, at = 0.800;for 0: a d = 1.700,0.425, a(= 1.400; and for H: ap= 1.OOO. These basis sets u t i l k a 3-1-1 hydrogen basisset anda 5d representation of the d polarization functions. See ref 23 for details of the 6-3 11G basis set. Polarization function exponents: ad = 0.626, 1.292 and ap= 0.750 for C, 0, and H atoms, respectively. /Polarization function exponents for the 6-31 1G basis sets for C: Cud = 1.252,0.313, a1 = 0.800; for 0: a d = 2.584, 0.646, a( = 1.400; and for H: ap = 0.750.
calculations were carred out on a Cray-YMP. A typical singlepoint energy calculation at the MP2 level utilizing a large basis set (e.g., D95+(2df,p)) (see below) required approximately8000 CPU s. The calculations using the ACES I1 code were carried out on a Cray C90. Calculations carried out with these codes utilize atomic orbital basis sets comprised of linear combinations of Gaussian-type functions. Previous calculations for 1,2-difluoroethane17J8have demonstrated the need to include both polarization and diffuse functions in the basis sets. The basis sets utilized in this study, 6-3 1 lG23 and D95,Z4are split valence (with three functions for the valence orbitals) and double-t, respectively. The basis sets can be further augmented by including a set of diffusesp functions (a= 0.0438 for carbon and a = 0.0845 for oxygen), denoted by "+". An additional set of diffuse sp functions (a = 0.0150 for carbon and a = 0.0290 for oxygen) yields a "+(+)" basis set. Diffuse functions are important for polar molecules and for systems in which a large portion of the valence-electrondensity is allocated to lone-pair orbitals. For basis sets with polarization functions, the notation u**n indicates a set of d functions for the heavy atoms and p functions for the hydrogen atoms. A single "*" denotes carbon and oxygen d functions without the hydrogen p functions. For basis sets with additional polarization functions, the polarization functions are written explicitly, e.g., a "(2df,p)" basis set contains two sets of d functions plus a set off functions for the heavy atoms and a set of p functions for hydrogen. Standard GAUSSIAN90 exponents were used for the polarization functions as listed in the footnote to Table I. Note that different polarization function exponents are used for the D95 and 6-3 1 1G basis sets. These basissets contain up to 264contracted Gaussian functionswhich is close to the practical limit for MP2 calculations using GAUSSIAN90 on the NASA Ames Cray-YMP. Hartree-Fock or self-consistent-field (SCF) calcualtions do not include contributions from electron correlation. For conformational energy studies, the most important contributor to electron correlation effects is the dispersion energy which can be accounted for adequately through use of second-order MallerPlesset perturbation theory (MP2).'3 As shown for 1,2-difluoroethane,l8 the inclusion of perturbation theory to higher levels does not greatly affect the trans-gauche energy difference. However, to calibrate the use of MP2 level calculations for determining the conformational energies, selected calculations were carried out at the higher level coupled cluster theory of electron correlation. Both the CCSD method,23which includes single and double excitations, and the CCSD(T) method,26 which
Conformations of 1,2-Dimethoxyethane adds a perturbational estimate for triple excitations, were used. Energeticsobtained using the CCSD method are generallysimilar to those obtained using MP4(SDQ). The CCSD and CCSD(T) calculations were carried out using the ACES I1 code.22 Basis Set Pad Correlation Effects on the Energy of the tgt Conformer of DME. The effects of basis set and electron correlation on the energy of the tgt conformer of DME relative to the ttt conformerwere investigated as follows. First, molecular geometriesof the tgt and ttt conformersof DME were optimized at the MP2 level using a D95** basis set. Then, these optimized geometries were used in single-point energy calculations at both the SCF and MP2 levels for the various basis sets considered. These basis sets, along with calculated SCF and MP2 energies, are given in Table I. The results of CCSD and CCSD(T) calculations carried out at these geometries are also included in Table I for selected basis sets. The zero-point vibration and thermal vibrational energy correctionsto the relative energy were found to be less than 0.1 kcal/mol at the D95** SCF level and are not considered in this analysisof the energy differencebetween the ttt and tgt conformers. Electron correlation effects were found to be quite important, as revealed in Table I. The MP2 energy differences are all at least 0.5 kcal/mol lower than the SCF values for the same basis set. The electron correlation effects increase as the size of the basis set increases. The difference between the SCF and MP2 energy differences is seen to be much larger than the difference between the MP2, CCSD, and CCSD(T) results with the order of energy differences being AE(SCF) >> AE(CCSD) > AE(CCSD(T)) > AE(MP2). MP2 energy differences are generally 0.1 kcal/mol smaller than the corresponding CCSD(T) results. The effects of basis set augmentation on the energy difference at the MP2 level are discussed in detail below. The effects of including sp diffuse functionsin the atomic orbital representation of the carbon and oxygen atoms were explored by comparing energies from the D95** and 6-31 1G** basis sets with those from the D95+** and 6-311+G** basis sets, respectively. From Table I, it is apparent that inclusion of these diffuse functions results in a 0.23-0.35 kcal/mol decrease in the gauche energy at the MP2 or CCSD(T) level. An additional set of sp diffuse functions was included for the carbon and oxygen in the D95+(+)** and D95+(+)(2df,p) basis sets. This augmentation had no significant effect on the gauche energy. Inclusion of p functions on the hydrogen atoms results in about an additional 0.1 kcal/mol lowering of the tgt conformer energy as seen from comparisonof the '*' and '* *' entries for the 6-3 11G and 6-3 11+G basis sets in Table I. The effects of polarization functions beyond the minimum representation were investigated by comparing those basis sets which have a single set of d and p polarization functions for the heavy atoms and hydrogen atoms, respectively, with (2df,p) basis sets, where additional d and f functions are included in the representation of the heavy atoms. ExaminationofTableI reveals that thegaucheenergy was reduced to a greater or lesser degree by inclusion of these additional polarization functions, depending upon the particular basis set. The effect was greater for the D95+ basis set than for the somewhat larger 6-3 11+G basis set. Our best estimate for the value of gauche energy is about 0.10.2 kcal/mol, resulting from MP2 level calculations using the largeD95+(2df,p), D95+(+)(2df,p), and 6-31 1+G(2df,p) basis sets. We believe the tendency of the MP2 method to predict too low a tgt to ttt energy difference counterbalances effects due to basis set incompleteness (e.g., using a basis set with (3df,2p) polarization functions would most likely result in an even lower gauche energy). The present result is significantly lower than the 0.4-0.6 kcal/mol obtained in previous investigations, where an estimate of the 631G** energy at the MP4 level was obtained,12 or where MP4(SDQ) calculations were carried out using the 6-31++G* basis ~ e t . ' ~However, J~ our result remains well above estimates (-0.4 to -1.2 kcal/mol) based upon the RIS
The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 12747
TABLE II: DME Conformer Geometries, Energies, and Dipole Moments Ab
conformation (degeneracy)
92 0.0 0.0 4 . 7 106.4
0.7 118.3 0.9 104.9
0.6 97.1
4.9 6.2
93.2
0.0
116.1 131.7 97.0 106.6
93
A
D95** D95+(2d,f,p) SCF MP2 SCF MP2
0.0 0.0 -4.7 1.31 112.0 3.13 -95.8 1.63 101.3 1.89 97.2 3.94 -93.1 3.53 116.1 3.97 -98.7 3.65
0.0
0.75
0.0 1.52
2.54 1.78 2.00 2.90 4.09
1.77 0.24 1.24
2.61
3.80
1.69 4.00
1.68 -69.4 114.3 -69.8 3.82 2.53
3.89
0.0
pc
0.00
0.14d 1.52 1.51 0.23
2.67
1.65 1.43 1.93 3.13 2.44 3.08 0.00 1.64 1.49 1.86 2.10
3.85 2.41 0.09 a Torsional angles for the C-O, C-C, and 0 4 bonds, in deg, with trans defined as Oo. * A indicatesenergy relative to the ut state, in kcal/ mol. Dipole moment from theSCFwave function using the D95+(2df,p) basis set, in Debye. An energy of 0.10 kcal/mol, obtained using the MP2 optimized geometry (see Table I), was used in calculations of conformer populations. analysis of NMR vicinal coupling c~nstants.~JOThe latter discrepancy is discussed below. The effect of basis set size on the gauche energy may indicatea possible origin for the oxygen gauche effect in DME. If we consider the gauche energy to be due to an intrinsic torsinal e,nergy difference plus differences in nonbonded interactions between atoms in the gauche and trans conformations of the 0-C-C-O bond, we would expect the gauche conformation to be high in energy due to stronger electrostatic repulsion between the negatively charged oxygen atoms. However, the withdrawal of charge from the carbon atoms, which is facilitated by the use of larger basis sets, may counteract this increasein coulombic repulsion by changing the intrinsic torsional energy differencebetween the twoconformations. This difference in intrinsic torsional energy may be due to differential stabilization of the 0-C-C-H conformations, where bond-antibond orbital interactions favor the trans arrangement and hence a 0-C-C-O gauche arrar~gement.~~ This differential stabilization appears to be facilitated by a more polar C-X bond?' where here X is an oxygen atom. Initial results of ab initio investigations of other alkyl ethers indicate a correlation between the strength of the oxygen gauche effect for the 0-C-C-X bond and the degree of coulombic repulsion between the oxygen and X moiety, where X = 0, CHz(0) and CHz(CH2) have been investigated.28 The largest basis sets employed in this study, namely the D95+(2df,p), D95+(+)(2df,p), and 6-3 1 l+G(Zdf,p) basis sets, yield similar values for the gauche energy. We estimate uncertainty in the conformational energies, arising from sources such as basis set superposition (which is conformation dependent), basis set incompleteness, use of conformational geometries obtained at the SCF level with a smaller basis set (see below), and a low level treatment of electron correlation, to be about 0.2-0.3 kcal/mol. Given this uncertainty, the smallest of the three basis sets listed above, D95+(2df,p), appears adequate and was used exclusively in further analysis of DME conformer energies described below. ConformerPopulations. The ten unique low-energy conformers of DME are listed in Table I1 along with their degeneracy. Optimized geometries for the conformations were determined at the SCF level employing the D95** basis set. The optimized torsional angles for the three torsionsdefining each conformation are shown in Table 11. Also given are the SCF and MP2 singlepoint energies (using the SCF optimized geometries) for each conformer relative to the ttt conformer. The conformational energies were calculated using both the D95** and D95+(2df,p) basis sets with the D95** SCF-optimizedgeometries. Comparing SCF and MP2 results, it is apparent that inclusion of electron correlation significantly reduces the energy of all conformations relative to the ttt conformer for both basis sets. The g*g*g* and
Jaffe et al.
12748 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
g*g*g' conformers exhibit the largest differential correlation energy effect, and the ttg conformer has the smallest. In going from the smaller to the larger basis set, the relative energy of the tgt conformer is most significantly affected. It should be noted that the tgt MP2 energy lies 0.14 kcal/mol above the ttt energy for the D95+(2df,p) basis set using SCF optimized geometries (Table 11), little changed from 0.10 kcal/mol obtained using MP2 optimized geometries and the same basis set (Table I). Geometry optimization at the SCF level therefore appears quite adequate. Vibrational zero point energy corrections, along with thermal vibrational and rotational energy and entropy corrections (with the degeneracy considered separately) to the free energy (assuming separable harmonic oscillators for the vibrational modes), were computedfor the ttt, tgt, tg*g', and ttg conformers. The differences in these quantities are less than 0.10 kcal/mol at room temperature. These effects result in an additional stabilization of the tgt conformer relative to the other three of 0.08 kcal/mol at room temperature, which is considerablysmaller than our estimated uncertainty of 0.2-0.3 kcal/mol in the conformational energies. Thus the differences between relative electronic energies, enthalpies, and free energies are small for DME. As a result, it is acceptable approximation to use the ab initio electronic energies directly in calculating conformer populations. The energies of four conformers from Table I1 (at the D95+(2df,p) basis set MP2 level) are significantlydifferent from those predicted by simply adding the appropriate C-C and C-O gauche energies. The tg*gi, g*g*g*, and g*g*gT conformers are 1.1-1.3 kcal/mol lower in energy and the g*grg* conformer is 0.6 kcal lower in energy than expected from this additive approach. The energy of the tg*gi conformer is only 0.2 kcal/mol higher than ttt conformer, making it comparable in importance to the ttt and tgt conformer. It appears that the lower energies of these four conformers are due to a favorable electrostatic interaction between one of the oxygen atoms and the opposite terminal CH3 group. This is illustrated in Figure 2 for the tg*gT conformer, where the O.-C(methyl) and 0.-H(methy1) separations are 3.15 and 2.57 A, respectively. These are greater distances than found in typical intramolecular hydrogen bonds but are considerably shorter than seen for the other conformers (e.g., 4.70 and 4.90 A for the ttt conformer and 4.14 and 4.25 A for the tgt conformer for the O-C(methy1) and O-H(methyl) separations, respectively). Hirano and co-workers14J5have observed a similar stabilization of the tg*gT conformer, but their reported energy (at the MP3 level, relative to the ttt conformer) is higher. Statistical weights (Boltzmann populations) of each conformer are readily calculated given the relative electronic energy and degeneracy of each conformation. For simplicity, we assume preexponential factors equal to the degeneracy of each conformer. Conformer populations so determined are given in Table I11 at 0 "C. Also shown in Table I11 are the conformer populations estimated from electron diffraction studies of gas-phase DME" and from the RIS model parameterized to reproduce NMR vicinal coupling constant data for gas-phase DME.'O Our estimated populations agree quite well with the electron diffraction values11 for the most highly populated conformations, which show tg*g*+tg*gi > tgt > ttt, but differ significantly from the RIS model estimates for the tgt and tg*g* tg*gT conformers.10 Also shown for comparison are the conformer populations tabulated by Tsuzuki and~workers~5from their free energies. They predict ttt > tgt, in disagreement with the electron diffraction experiments." A discussion of the RIS representation is presented below. For a detailed discussion of the electron diffraction results the reader is referred el~ewhere.2~ Dipole Moment. The dipole moment ( N ) of each conformer is given in Table 11. The dipole moment values were computed from the SCF wave function using the D95+(2df,p) basis set. The values from the D95** SCF calculations are %IO% larger.
+
m
W
Figure 1. Representative conformations of DME. Torsional states are denoted by t for trans, g for gauche (of either sign), g+ for a gauche of positive right-hand rotation with respect to trans, and g for a state with the opposite rotation. Also shown are the conformation dependent firstorder and second-order interactions between atoms and groups in DME.
Figure2. The rpg- conformation of DME. The close approach between an oxygen and a methyl hydrogen is indicated.
TABLE HI: DME Conformer P ~ p u l a tati ~0~O C fractional population this conformer trr
rtg
z p +t g "
reg'
teg-
erg'
work 0.16 0.05 0:27 0.47 0.04 0.43 XO.01
electron" diffraction
0.13 0.03 0.23 0.53
RIS*
ref 1SC
0.12
0.25 0.06 0.20
0.08 0.51
0.25 0.16 0.09 0.01 0.03
0.47
0.02 0.45
gt&+ + 0.05
