J . Phys. Chem. 1994, 98, 9072-9077
9072
Conformational Characteristics of Dimethoxymetbane Based upon ab Initio Electronic Structure Calculations Grant D. Smith' Thermosciences Institute, RTC 230-3, NASA AMES Research Center, Moffett Field, California 94035
Richard L. Jaffe NASA AMES Research Center, Moffett Field, California 94035
Do Y. Yoon IBM AImaden Research Center, 650 Harry Rd., San Jose, California 95120-6099 Received: February 8, 1994; In Final Form: May 25, 1994"
The conformational properties of dimethoxymethane (DMM) have been determined from a b initio electronic structure calculations as a critical step in the characterization of the conformational statistics of poly(oxymethylene). The preference of the gauche (g) conformation of the C*-O-C-.O bond over the trans ( t ) conformation, as denoted by the energy AEgfof the gt conformer relative to the gg conformer, was found to depend strongly on basis set size, with the energy decreasing from 4.7 kcal/mol for a 4-3 1G MP2 calculation to 2.8 kcal/mol using a D95+(2df,p) basis set, also a t the MP2 level. Electron correlation effects were also found to be important but were accounted for accurately a t the MP2 level; calculations of correlation effects beyond the MP2 level resulted in only a slight decrease in All,,. These effects led to a best estimate for Allgf of ca. 2.5 kcal/mol. Such a strong preference for the g conformation results in a very steep energy well for the DMM gg conformer relative to the remaining conformers. In terms of a rotational isomeric state (RIS) model, this necessitates the inclusion of preexponential factors for the statistical weights which deviate significantly from unity. The energies and preexponential factors which were estimated from the a b initio calculations yielded RIS conformer populations for D M M that reproduce the gas-phase dipole moment and N M R vicinal coupling constant as a function of temperature, in good agreement with experiment.
Introduction Electron diffraction studies192 of dimethoxymethane (DMM) indicate a predominance of the gauche (g) conformation of the C.-O-C-O bond in the gas phase. The lower energy of the gauche conformation relative to the trans ( t ) conformation of the bonds covalently bonded to oxygen atoms (or other electronegative atoms) is referred to as the anomeric effect and has been observed in a wide variety of compounds. The degree of stabilization of the gauche conformation in such compounds depends strongly upon the particular chemical structure (e.g., see ref 3). In this regard, the relative energies of the gauche and trans conformations of the C--O-C.-O bond in DMM remain problematic. From the magnitude and temperature dependenceof thedipole moment of DMM, Uchida and co-workers4 arrived at an energy of -1.74 kcal/mol for the gauche conformation of the C.-0C-0 bond relative to the trans. FlorySfound that a three-state rotational isomeric state ( R E ) model employing a gauche energy of -1.5 kcal/mol was consistent with the temperature dependence of the dipole moment of DMM and reproduced experimental values for the unperturbed chain dimensions, or characteristic ratio, of poly(oxymethy1ene) (POM). Abe and Mark6 found that, using a gauche energy of -1.4 kcal/mol, they could reasonably reproduce these values in a similar three-state RIS model. In a molecular mechanics study of DMM and 1,2dimethoxydimethyl ether, Miyasaka et aL7 found that a gg (denoting two gauche conformations of the same sign) sequence was about 1.5 kcal/mol lower in energy than a gt sequence. More recently, Abe and co-workers*obtained a gauche energy of -2.5 kcal/mol from the temperature dependenceof the gas phase W1HNMR vicinal coupling constant in DMM. Finally, in a recent ab initio electronic structure study of DMM, Wiberg and Murk09 Abstract published in Aduance ACS Abstracrs, July 15, 1994.
0022-3654/94/2098-9072%04.50/0
found the ggconformation of DMM to be 3.3 kcal/mol lower in energy than the gt Conformation. While both experimental and theoretical studies agree that the gauche conformation of the C...O-C--O bond is lower in energy that the trans, there is considerable disagreement regarding the magnitude of the energy difference. Recently,Io we have shown that with a sufficiently large basis set and inclusion of electron correlation effects, ab initio electronic structure calculations predict conformational energies for 1,2dimethoxyethane (DME) which yield conformer populations in good agreement with estimates from gas-phase electron diffraction experiments and which also reproduce the experimental dipole moment and NMR vicinal coupling constants. These DME conformationalenergies were subsequently used to develop a thirdorder RIS model for poly(oxyethy1ene) (POE) which reproduced well the experimentally measured characteristic ratio and meansquare dipole moment of the polymer.' The conformational energies and rotational energy barriers in DME were also used in developing a conformational energy force field for POE.1' Although DME is similar in structure to DMM, the conformational energetics appear to differ significantly; from ab initio calculations10 it was determined that the gauche conformation of the C-.O-C-.X torsion in DME, where X = C, is about 1.4 kcal/mol higher in energy than the trans conformation, whereas evidence (enumerated above) indicates that the gauche conformation of the C.4-C.-X torsion in DMM, where X = 0, is significantly lower in energy than the trans conformation. In an attempt to better quantify the conformational energetics of the C--O-C--O bond, we have performed a detailed ab initio electronic structure study of the conformational energetics of DMM similar to our previous study of DME. In this paper we demonstrate the ability of the conformational populations of DMM, as determined from ab intio calculations, to reproduce 0 1994 American Chemical Society
Conformational Characteristics of Dimethoxymethane
TABLE 1: Conformational Enereies of DMM energy (kcal/mol)b 4-31G conformer" type gg minimum gt minimum gt' minimum tt minimum gtg saddlepointd cisg saddlepoint gg_gt saddle point
D95+(2df,p) MP2 SCF MP2 0.00 0.00 0.00 3.10 1.99 2.81 (3.19) (2.83) 6.88 4.60 6.26 4.44 4.21 4.21 8.17 7.58 8.56 4.35 3.16 4.08
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 9073
TABLE 2: Effect of Electron Correlation Treatment on the DMM gt Conformer Energy ~~
energy (kcal/mol)"
D95**
SCF MP2 SCF 0.00 0.00 0.00 4.11 4.70 2.33 9.80 10.10 5.32 5.34 4.91 4.80 6.94 7.77 7.71 4.31 5.11 3.62
The labels g+ and g refer to gauche conformations with a + or sense, respectively. The glabel refers to a gauche conformation of either sign, but of the same sign if occurring more than once. Energies are relative to theggconformer. Numbers in parenthesesfor thegt conformer are for a D95** MP2 optimized geometry, relative to equivalent calculations for the gg conformer. d The saddle point labeled g + gis the saddle point between the g+t and tg conformers. a
experimental values of conformation-dependent properties of the molecule. In the following paper in this issue, the conformational energetics of DMM as determined in this paper are employed together with those of 1,3-dimethoxydimethyl ether to describe the conformational properties of POM chains by a revised threestate RIS model. Ab Initio Electronic Structure Calculations
Methodology. The relative energies and the geometries of the minimum-energy conformations of DMM were determined by performing ab initio electronic structure calculations similar to those performed in our study of DME.I0 In addition, energies and geometries were determined for selected saddle points, corresponding to rotational energy barriers between minimumenergy conformations. Optimized geometries were determined a t the S C F level using both a 4-31G basis set and a full doublezeta polarized basis set denoted as D95**. Energies at the S C F level and MP2 level of electron correlation were determined using a 4-3 1G basis set with the 4-3 1G optimized geometries and using D95** and D95+(2df,p) basis sets with the D95** optimized geometries. For details of the basis sets, the reader is referred to ref 10 and the references contained therein. Additionally, geometry optimizations at the MP2 level were performed for the gg and gt conformations of DMM using a D95** basis set in order to investigate the adequacy of the SCF geometry optimizations. The MP2 optimizedgeometries were utilized in calculating the relative conformational energies using a D95** basis set and D95+(2df,p) basis set a t the SCFand MP2 levels. Finally, higher levels of electron correlation treatments were investigated by comparing relative conformational energies of the gg and gt conformations of DMM calculated using MP2, CCSD, and CCSD(T) treatments for electron correlation for D95** optimized geometries with a double-zeta polarized basis set. All geometry optimizations except the MP2 optimizations were performed using GRADSCF.12 Calculations involving the D95+(2df,p) basis set and the MP2 geometry optimizations were performed using GAUSSIAN90 and GAUSSIAN92.13 The coupled-cluster (CC) configuration integral correlation treatments were performed using ACES II.14 All a b initio calculations were performed on a CRAY C-90 at the NASA Ames Research Center. Basis Set and Electron Correlation Effects. The relative conformational energies of the minimum-energy conformations (conformers) of DMM along with selected rotational energy barriers are shown in Table 1. Energies are reported relative to the lowest energy conformer, namely, the gg conformer. Table 2 shows the effect of different levels of electron correlation treatment on the energy of the DMM gt conformer (relative to the gg conformer). Examination of Table 1 indicates that both electron correlation and basis set size effects are important. For example, at the MP2 level, the energy of the DMM gt conformer
SCF 2.33
MP2 3.00
CCSD 2.86
CCSD(T) 2.94
Energies are relative to the gg conformer for a D95** basis set and D95** optimized geometries. The gt MP2 energy differs slightly from the D95** value given in Table 1 due to the freezing of the core electrons in the ACES I1 calculations.
(relative to the gg conformer) is about 0.6-0.8 kcal/mol greater for a given basis set than a t the S C F level. Table 2 indicates that electron correlation treatments beyond MP2 have no significant effect on the relative energies of DME gt and gg conformers. We therefore conclude that electron correlation effects are important and are adequately described by the MP2 level of theory. The effect of basis set size is seen by comparing the MP2 energies of the DMM gt conformer relative to the ggconformer as a function of basis set size. The D95** basis set, which includes polarization functions on all atoms, yields a significantly lower energy difference between the gt and gg conformers than the 4-31G basis set, which has no polarization functions. A similar result was obtained by Wiberg and murk^,^ who obtained an energy difference of 3.32 kcal/mol at the MP2 level using a 6-31+G* basis set. The D95+(2df,p) basis set, which includes diffuse functions and additional polarization functions on the heavy atoms, yields an energy for the DMM gt conformer (relative to the gg conformer) 0.3 kcal/mol lower than the D95** basis set, indicating that an accurate calculation of the conformational energies requires polarization functions beyond the minimum description. (The D95+(2df,p) basis set was successfully used in our study of DME (ref 10);a detailed description of the polarization function exponents can be found therein.) Comparing the MP2 6-31G* and 6-31+G* energies for the DMM gt conformer from ref 9 indicates that in this case the diffuse functions result in a decrease of about 0.1 kcal/mol in the energy of the gt conformer relative to gg. Basis sets larger than D95+(2df,p) were investigated for DMElO and were found to have no significant influence on the relative energies of the ttt and tgt conformers. We therefore assume that this basis set is also adequate to describe relative DMM conformer energies. Finally, a comparison of DMM gt conformer energies (relative to the gg conformer) obtained from D95** S C Foptimized geometries with those obtained from D95** MP2 optimized geometries, as shown in Table 1, indicates that use of S C F optimized geometries yields accurate relative conformational energies.
Conformational Energies and Geometries From Table 1 it can be seen that for the largest basis set considered, the D95+(2df,p) basis set, at the MP2 level, the DMM gt conformer is 2.8 kcal/mol higher in energy than the gg conformer, while the tt conformer is an additional 3.4 kcal/mol higher in energy than the gt conformer. N o true minimumenergy conformation corresponding to the g+g- sequence could be found. However, the saddle point for the transition between the g+t and tg- conformers was found to have a g+g- geometry. The torsional and valence geometries of the DMM conformers are given in Tables 3 and 4, respectively. The MP2 optimized geometries show minor differences compared to the S C F optimized geometries; the gauche torsional angle increases by about 3O for the gg conformation while the C-0-C valence angle decreases by about 3O. For the gt conformation, there is a decrease in the gauche torsional angle of about 6' in going from the 4-31G optimized geometries to the D95** optimized geometries. It can also be seen from Table 4 that while the C-0-C valence angle changes only slightly with conformation, the 04-0 valence angle varies significantly with conformation, being much more extended for the gg conformation relative to the tt conformation.
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994
9074
TABLE 3: DMM Conformer Torsional Geometries torsional angles (dedU 4-31G D95** conformer 41 42 41 42 113.3 113.3 112.6 112.6 (115.8) (115.8) 120.6 1.4 114.3 -1.1 (115.2) (-4.6) 98.9 -98.9 95.7 -95.4 0.0
0.0
0.0
0.0
82.2 190.3 78.6 188.9 120.5 48.2 115.4 47.3 a Values are from SCF optimized geometriesfor the basis set indicated, except for values in parentheses, which are from MP2 optimized geometries. Values are relative to t = Oo. The conformation labeled g + g is the saddle point between the g+t and tg conformers.
TABLE 4
DMM Conformer Valence Geometries valence angles (deg)' conformer OCOC OOCO OCOC gg 114.9 113.5 114.9 (1 12.0) gg (112.0) (1 13.8) gt 115.2 110.2 113.7 gt (112.3) ( 109.7) (110.9) tt 113.5 106.8 113.5 All values are from D95** SCF optimized geometries, except those in parentheses, which are from D95** MP2 optimized geometries.
lo 8
the tg- energy well. The energy well corresponding to the g+g+ conformation is narrow and deep, while the energy well corresponding to the g+t conformation is broad and shallow. Although there is no minimum-energy conformation in the g+gregion, the population of such conformations is not entirely negligible. We therefore associate a rotational isomeric state with this region of configuration space. The implications of the different shapes of the energy wells for these conformations on their relative populations are discussed below.
Conformer Populations
Free Energy. The populations of the conformers of DMM were determined from the free energy differences between the conformations. In determining the free energy differences, we treated all vibrational modes as separable and harmonic except for the two lowest frequency modes, which are associated with the backbone torsions. The latter were treated classically as described below. The harmonic contributions to the free energy differences include zero-point vibrational energy and rotational entropy differences along with thermal vibrational energy and entropy differences. The contribution of these effects to AG,, the free energy of the gt conformer relative to the gg conformer, using 4-31G a b initio frequencies (scaled by 0.9), was found to be less than fO.1 kcal/mol over the temperature range 300-500 K, and therefore these effects were neglected. These effects were assumed to be negligible for AGg+g and AG;,. In any case, the populations of the g+g- and tt conformations are relatively insignificant. The statistical weight of each conformation i ( i = gg, gt, g+g- or t t ) is therefore given by
: t
i
where gi is the degeneracy of the conformation. E(~$2,4~) is the energy of conformation 42, 41, and the integral is over the region of conformational phase space 4i associated with conformation i. Ei is the minimum energy of the conformation relative to the gg conformation. Expressing the weights relative to the gg conformation yields
-g+
0
Smith et al.
1, 280
,
,
,
,
,
, ,
,
, ,
220
,
, , ,
160
,
,
,
,
,\,l, ,
100
,
,
40
,
,I -20
torsional angle (') Figure 1. Conformational energy of the g+@conformation of DMM as a function of the torsional angle 4. The solid line is a fit of eq 1 to the abinitiodata. Division of phase space into t , g+, and g statesis indicated. The MP2 optimized D95** gauche torsional angle of 115.8' is in good agreement with values (1 14' and 117') from electron diffraction studies.192 The conformational energy of the g++l (4241) conformation of DMM as a function of torsional angle 41 is shown in Figure 1. Geometries were determined a t the S C F level using a D95** basis set with the angle $1 constrained for nonstationary points. The 62 torsional angle was optimized around the local ( g ) conformational minimum, and all other geometric parameters were optimized for each conformation; hence, the energies shown correspond to the adiabatic path for rotation about one C-O bond. The conformational energies shown in Figure 1 are D95** MP2 values. The solid curve is a least-squares fit of A
A
E ( 4 ) = a.
+ z u n cos(n4) + x b nsin(n4) n=
1
(1)
n= 1
to the ab initio energies. The conformations of 4, were divided into g+, t , and g- regions, as indicated in Figure 1. For values of 41 < -96O along the adiabatic path (the g't-tg- saddle point), 42 begins to deviate significantly from g+ as the molecule enters
or gi wi = --fi exp(-AEi/kT)
(4)
gL?g
where AEi is the conformational energy relative to the gg conformation andf;: is a preexponential factor which depends on the differences in the shapes of the conformational energy wells. Conformational Energy Differences. For the purpose of determining conformer populations, D95+(2df,p) MP2 values for the conformational energies obtained from Table 1 for the gg, gt, tt, and g+g- conformations were utilized. AE, is the conformational energy difference between the gg and gt conformations or the energy of a gauche bond. From Table 1, AE, = 2.8 f 0.3 kcal/mol from the D95+(2df,p) MP2 energies. The estimated uncertainty is due to finite basis set size, electron correlation, and basis set superposition effects (ref 10). Because of the trend toward a decrease in the magnitude in gauche energy with larger basis sets (see Table l ) , we expect AE, most likely to be slightly lower in magnitude than the value from Table 1. We therefore assign AE, a value of 2.5 kcal/mol, from the low end of the uncertainty range. Accordingly, we assign AErr,the difference between the tt and gg conformer energies, a value of
Conformational Characteristics of Dimethoxymethane AElr = 5.9 kcal/mol and AEgtg,the difference between the g+gsaddle point and gg conformer energies, a value of 3.9 kcal/mol. Preexponential Factors. The preexponential factors, fn, Jr, and fgtg in eq 4 account for differences in the shapes of the energy wells for the different conformers. To first order, E(&,&) from eq 3 in the region of configuration space of conformation i can be expressed as
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 9075 ~
0 i
1
l
"
"
~
"
'
1where E l , i ( 4 1 and ) E z , ~ ( ~are z ) functions of t#q and 42 only, respectively. This approximation is quite reasonable for points up to the g+t-tg saddle point, where it was found that the optimized value of 42 was approximately independent of 41and near to the gg gauche angle. This approximation allows us to express the preexponential factors as
where fk,j results from integration of all terms dependent upon 4k. Using eq 1 to obtain estimates for ElKg(&),El8(&), and E I ~ + ~ (and & )assigning configuration space as indicated in Figure 1, we obtain fI,@ = 2.5 for temperatures in the range 300-500 K. For the g+g- conformation, we obtained a value of fi,g+g = 1.5-2. The high value for f18 is a consequence of the broad shallow character of the g+t well compared to the gg well, as illustrated in Figure 1 . This difference in shapes of the gt and gg wells is a consequence of both the large energy difference between the gt and gg conformer and the fact that the g+t-g+g+ barrier is not much higher in energy than the gt conformer. This broad, shallow nature of the t well relative to the g well for the C4-C.-0has also been observed in molecular mechanics calculations.1s It is apparent from the higher energy of the tt conformer (see Table 1) that the g+t-tt barrier will be much higher than the g+t-g+g+ barrier. The g't-g-t barrier (the cisg conformation) is also high in energy (see Table 1). Therefore, theg+t conformer will not show the same shallow, broad characteristics along the 42 (g+) coordinate that it does along the 41 (t) coordinate. We therefore approximate = 1, yielding fn = 2.5. The g+g"well" will show similar behavior to theg+t well in the 42 direction for the region of configuration space shown in Figure 1, Le.,f2,tg = 1 . However, for the region of configuration space associated with the g+g- conformation which is not shown in Figure 1, i.e., as the molecule enters that tg- well, the behavior with respect to 41 and $12 is reversed. The net result isfgtg =fiKtg2=3. Although involving several approximations, these calculations indicate that assigning fgr and fg+g > 1.0 is required for an accurate RIS representation of phase space for DMM. For the tt conformer, which is of negligible population, we chosef,, = fgJgr= 6.
Conformer Populations and Dipole Moment of DMM The conformer populations as a function of temperature were determined from the relative conformational statistical weights given by eq 4. The populations of the gg conformer as function of temperature, as predicted by our model and that of Uchida and c o - ~ o r k e r s are , ~ compared in Figure 2. The RIS model of Uchida and co-workers4was parameterized to reproduce thedipole moment of DMM as a function of temperature. The models predict quite similar populations of theggconformer. Our model, with a gauche energy of -2.5 kcal/mol, indicates a greater dependence on temperature of the gg population than the model of Uchida and c o - ~ o r k e r swhere , ~ a gauche energy of -1.74 kcal/ mol was utilized. The similar populations of the gg conformer predicted by the models, despite the quite different gauche energies, are a consequence of the inclusion of preexponential factors in our model, which were neglected in the previous model. Within the RIS approximation, the mean-square dipole moment of a conformationally flexible molecule depends upon the dipole
0.2
'
0
~
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'
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_____ -
predicted, Ref. 4
,
,
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,
,
,
,
,
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,
350
400
450
,
3
' 2.0 '
1
~
4
experimental.Ref.4 predicted
0.0
300
~
,
R
0.5
0.0 500
3
temperature (K) Figure 2. Population of the gg conformer and root-mean-square dipole moment (right-side ordinate) of DMM as a function of temperature.
TABLE 5 DMM Conformer Dipole Moments conformer pa h b p (h= 1.24)' gg 0.27 0.06 g$ (0.34) (0.01) gt grd g+r tt
1.87 (2.05)
1.19
1.96
(1.24)
(2.05) 2.35
2.43 1.28 2.55 1.17 2.71 Dipole moments are in debye, from MP2 electron densities using a D95+(2df,p) basis set and D95** SCF optimized geometries. For comparison,the dipole moments for the SCF optimized geometries of the ggand rg conformers using the SCF electron densities are 0.23 and 2.00, respectively. C-obonddipolemomentwhich reproduces themagnitude of the conformer dipole moment. Conformer dipole moment computed using a C-O bond dipole of 1.24 D. From MP2 electron densities using a D95+(2df,p) basis set and D95** MP2 optimized geometries. CThe conformation labeled g + g is the saddle point between the g+r and tgconformers. moment and population of each conformer. The dipole moments for each conformation of DMM, determined a t the minimumenergy geometries (saddle point geometry for the g+g- conformation) from MP2 electron densities using the D95+(2df,p) basis set, are shown in Table 5. For the gg and gt conformers, values determined using both D95** S C F and D95** MP2 optimized geometries are shown. The dipole moments determined using the MP2 optimized geometries are slightly larger than the corresponding values determined using the S C F optimized geometries. The bond dipole ~0 required to reproduce the ab initio dipole moment for each DMM conformer, together with the dipole moment of each conformer which results from using a bond dipole of = 1.24 D, are also shown in Table 5. The rms dipole moment for DMM is shown in Figure 2, determined from the conformer populations given by eq 4 and the conformer dipole moments (from MP2 optimized geometries, where calculated) from Table 5, along with the gas-phase experimental values (open circles) measured by Uchida and cow o r k e r ~ .The ~ predicted dipole moment is in good agreement with the experimental values, indicating that the conformer populations of DMM are well represented by the RIS model. The lower value of the gauche energy determined by Uchida and co-workers4 from an RIS analysis of the DMM dipole moment is primarily a result of neglecting the preexponential factors in the weighting of the gt conformer. N M R Vicinal Coupling in DMM Within the RIS approximation it is possible to express the observed vicinal coupling c ~ n s t -a n t- ~inJ DMM ~ ~ , as8 ~ ~ ~ ~
where J,, JI, and J i are the coupling constants for the
9076 The Journal of Physical Chemistry, Vol. 98, No. 36, I994
YOCH,
h
N
6.5
8
CI *I
experimental, Ref. S
6.4
0 A
6.3
I 6.2
'
360
'
i
RIS fit, Ref. S J8 = 2.0 Hz
4
Jp=2.5Hz
"
' 380
"
"
400
"
"
"
"
420
'
440
Temperature (K) Figurel W-IH NMR vicinal couplingconstants in DMM as a function of temperature. Gas-phase experimental values are shown. Calculated values for different values of Jg are shown. The J, + J i coupling values were adjusted to give the best fit for each Jg (see text). arrangements illustrated in Figure 3 andf, is the fraction of trans C.-O-C--O bonds, which is easily determined from the conformer populations. Following Abe and co-workers: we initially assumed a standard value of Jg= 2.0 Hz. Experimental gas-phase coupling constants as a function of temperature8 are shown in Figure 4. Also shown are the calculated gas-phase values8 from an RIS model with a gauche energy of -2.5 kcal/mol and J, J; = 13.4 Hz, the best agreement between eq 7 and the experimental data. In this RIS model preexponential factors were not considered nor was the g+g conformation included. The best fit to the gasphase coupling constants for conformer populations determined from eq 4 corresponds to a value of J, + J i = 13.9 Hz. The resulting coupling constants are shown in Figure 4. Agreement with experiment is fair. Some improvement is seen when a value of J, = 2.5 Hz is used, yieldingJ, + Jgl = 13.8 Hz. We consider agreement between calculated and experimental values for the NMR vicinal coupling constants acceptable given the uncertainties in J,and J, + Jgl,which depend upon the conformational geometry. It is worth noting that a model using a gauche energy of -2.5 kcal/mol and neglecting preexponential factors, as in ref 8, will not reproduce the experimental dipole moment of DMM as a function of temperature.
+
Smith et al. approximation. When used to predict the dipole moment and N M R vicinal coupling in DMM, such a model is consistent with the experimental data. The model of Uchida and co-workers! utilizing a gauche energy of -1.74 kcal/mol while neglecting preexponential factors, tends toslightly underestimate the temperature dependence of the dipole moment when a nonzero value of wgg is utilized, while our model slightly overestimates the temperature dependence, both models resulting in about the same goodness of fit. It was found that the Uchida model reproduces the experimental gas-phase N M R vicinal coupling constant data as well as our model. From these results one would be tempted to assume that, in determining the conformer population for the C--.O-C-.C bond in DMM over the temperature range of the experimental data, preexponential factors can be neglected if the gauche energy is subsequently adjusted. However, such an "adjusted" gauche energy should be taken with caution in developing a molecular mechanics force field. This can be seen in ref 15, where a molecular mechanics force field, parameterized to reproduce the gauche energy of -1.74 kcal/mol determined by Uchida et a1.,4 is employed. The ggwell is narrow and deep, while the gt well is shallow and broad, as was found in our ab initio calculations. This is a result of the large gauche energy and relatively low barrier relative to the gt conformer. Subsequently, an analysis of the energy profile of the gg and gt would result in a value offfl > 1.O,as was found in our analysis. However, for a gauche energy of -1.74 kcal/mol, a value off@ = 1.0 is required to give accurate conformational populations. Therefore, a gauche energy of about -2.5 kcal/ mol, as determined from a b initio calculations, should be utilized in parameterizing a conformational force field for DMM. A final comment on the applicability of the conformer energies and populations of DMM presented here is warranted. The ab initio calculations were performed on isolated DMM molecules and do not take into account possible effects of intermolecular interactions on conformer energies in condensed phases. Experimentally, it has been observed that both the dipole moment4 and l3C N M R vicinal coupling8in DMM solutions with nonpolar solvents are consistent with values observed in the gas phase. However, analysis of l3C NMRvicinal coupling in DMM solutions with polar solvents appears to indicate a stabilization of the trans conformation of the C.4-C-0 bond.8 This is consistent with interactions of DMM with the polar environment stabilizing the gt conformer, which has a much larger dipole moment than the lowest energy gg conformer. Therefore, the conformer energies and populations derived in this work do not appear to be directly applicable to polar condensed systems.
Acknowledgment. The authors acknowledge Professors R. H. Boyd and A. Abe for helpful discussions. G.D.S. is grateful for support provided by NASA through Eloret Contract NAS214031.
Discussion
References and Notes
Accurate conformational energies for DMM can be obtained from a b initio electronic structure calculations provided an adequate basis set (e.g., D95+(2df,p)) and electron correlation (MP2) treatment are considered. In order to predict DMM conformer populations which reproduce the experimental dipole moment and N M R coupling constants as a function of temperature, the differences in shapes of the energy wells for the low-energy gg and gt conformations must be considered. Because of the broad, shallow nature of the well for the gt conformation compared to the low-energy gg well, a preexponential factor of around 2.5 for the gt conformer is required in order to describe the relative populations of these conformers in terms of an RIS
(1) Astrup, E. E. Acra Chem. Scand. 1971, 25, 1494. (2) Astrup, E. E. Acra Chem. Scand. 1973, 27, 3271. (3) Smith, G. D.; Yoon, D. Y.; Jaffe, R. L. Macromolecules 1993, 26, 5213. (4) Uchida, T.; Kurita, Y.; Kubo, M. J . Polym. Sci. 1956, 19, 365. (5) Flory, P.J. Srarisrical Mechanics of Chain Molecules; Interscience: New York, 1969. (6) Abe, A,; Mark, J. E. J. Am. Chem. SOC.1976, 98, 6468. (7) Miyasaka, T.; Kinai, Y . ;Imamura, Y .Makromol. Chem. 1981,182, 3533. (8) A h , A.; Inomata, K.; Tanisawa, E.; Ando, I. J. Mol. Strucr. 1990, 238, 315. (9) Wiberg, K.B.; Murcko, M. A. J . Am. Chem. SOC.1989,111,4821. (10) Jaffe, R. L.; Smith, G. D.; Yoon, D.Y . J . Phys. Chem. 1993, 97, 12745.
Conformational Characteristics of Dimethoxymethane (11) Smith, G.D.; Jaffe, R. L.; Yoon, D. Y. J . Phys. Chem. 1993, 97, 12752. (12) GRADSCF is an ab initio gradient program system designed and written by A. Komornicki at Polyatomics Research Institute, Inc., supported by grants through NASA. (13) Frisch, M. J.; Head-Gordon, M.; Trucks, G.W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.;Robb, M.A.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Steward, J. J. P.; Topiol, S.; Pople, J. A. GAUSSIAN 90, Reuision J; Gaussian, Inc.: Pittsburgh, PA, 1990. Frisch, M. J.; Trucks, G.W.; Head-Gordon, M.; Gill, P. M. W.; Wong. M. W.; Foresman, J. B.; Johnson, B. G.;Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez,
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 9077 C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Steward, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision E.2.; Gaussian, Inc.: Pittsburgh, PA, 1992. (14) ACES I1 is a computational chemistry package especially designed for coupled cluster and many-body perturbation calculations. The SCF, trasformation, correlation energy, and gradient codes were written by J. F. Stanton, J. Gauss, J. D. Watts, W. J. Lauderdale, and R. J. Bartlett. The two-electron integrals are taken from the vectorized MOLECULE code of J. ABACUS Alml6fandP. R.Taylor. ACESIIincludesamodifiedversionofthe integral derivativesprogram, written by T. Halgaker, H. J. Jensen, P. Jerensen, J. Olsen, and P. R. Taylor, and the geometry optimization and vibrational analysis package written by J. F. Stanton and D. E. Bernholt. (15) Boyd, R. H.; Phillips, P. J. The Science of Polymer Molecules; Cambridge University Press: New York, 1994.
