Physical Chemistry The Journal of 0 Copyright 1993 by the American Chemical Society VOLUME 97, NUMBER 42, OCTOBER 21,1993 ARTICLES Polyoxymethylene: The Hessian Biased Force Field for Molecular Dynamics Simulations Siddharth Dasgupta,? Kennith A. Smith,* and William A. Goddard, III'J Materials and Molecular Simulation Center, Beckman Institute (I 39- 74), Division of Chemistry and Chemical Engineering (Contribution No. 8792), California Institute of Technology, Pasadena, California 91 125, and General Electric Central Research and Development, Schenectady, New York 12301 Received: May 28, 1993' A vibrationally accurate force field (MSXX) is developed for molecular dynamics simulations of polyoxymethylene polymers (-(-OCHr)-). This force field is developedusing the biased Hessian with singular value decomposition method (BH/SVD) applied to dimethyl ether and dimethoxymethane. The resultant force field contains parameters that are needed for molecular dynamics simulations of polyoxymethylene. Charges are derived using the electrostatic potential derived point charge calculations. The full ab initio (HF/6-3 lg**) torsional potential energy surface is fit using a Fourier series expansion to accommodate the "anomeric" effect in dimethoxymethane. The force field was applied to studies of tri- and tetramethoxymethane and is being applied to studies of the polymers. I. Introduction Polyoxymethylene (POM) is a commercially important ther- moplastic which exhibits two crystalline forms, the stable trigonal form (t-POM) and the metastable orthorhombic form (o-POM). \ CH2 yo\ CH2 /"\ Several experimental studies have been done on oriented POM, making it a good system for studies using molecular dynamics (MD). A prerequisite to careful MD studies is a force field sufficiently accurate for describing structure, energetics, and vibrations of crystallineand amorphous forms. For polyethylene? poly(viny1ene fluoride),z9 and SisN4,30 it has been shown that such vibrationally accurate force fields (MSXX) can be developed using the biased Hessian1 with singular valued decomposition2* methodology (HBFF/SVD). In this paper, we report the MSXX level of force field using a series of model compounds containing the essential chemical elements of POM. Critical to thesimulationsof the two crystalline Author to whom correspondence should be addressed. t General Electric Central Research and Development. Abstract published in Advance ACS Abstracrs, October 1, 1993. California Institute of Technology. forms as well as the amorphous form is getting an accurate description of the torsional potential, and special attention is focused on this. In section 11, we describe the HBFF methodology for using ab initio calculations and experimentaldata to extract a vibrationally accurate force field (MSXX) for dimethyl ether (CH3OCH3). Section 111 reports the application of this method to dimethoxy- methane (H2C(OCH3)2). In section IV, the accuracy of this method is tested by application to tri- and tetramethoxymethane. And finally, in section V the results are summarized. II. Dimethyl Ether Dimethoxymethane (2) is the smallest model compound containing the -(CH20)- repeating unit of polyoxymethylene. H \-/" There are some experimental data3 available on the vibrational frequencies of (2); however, not all normal modes are assigned, and a complete set of experimental frequencies for the isolated 0022-3654/93/2097-10891$04.00/0 - @ 1993 American Chemical Society
Transcript
Physical Chemistry The Journal of
0 Copyright 1993 by the American Chemical Society VOLUME 97, NUMBER 42, OCTOBER 21,1993
ARTICLES
Polyoxymethylene: The Hessian Biased Force Field for Molecular Dynamics Simulations Siddharth Dasgupta,? Kennith A. Smith,* and William A. Goddard, III'J Materials and Molecular Simulation Center, Beckman Institute ( I 39- 74), Division of Chemistry and Chemical Engineering (Contribution No. 8792), California Institute of Technology, Pasadena, California 91 125, and General Electric Central Research and Development, Schenectady, New York 12301 Received: May 28, 1993'
A vibrationally accurate force field (MSXX) is developed for molecular dynamics simulations of polyoxymethylene polymers (-(-OCHr)-). This force field is developedusing the biased Hessian with singular value decomposition method (BH/SVD) applied to dimethyl ether and dimethoxymethane. The resultant force field contains parameters that are needed for molecular dynamics simulations of polyoxymethylene. Charges are derived using the electrostatic potential derived point charge calculations. The full ab initio (HF/6-3 lg**) torsional potential energy surface is fit using a Fourier series expansion to accommodate the "anomeric" effect in dimethoxymethane. The force field was applied to studies of tri- and tetramethoxymethane and is being applied to studies of the polymers.
I. Introduction Polyoxymethylene (POM) is a commercially important ther-
moplastic which exhibits two crystalline forms, the stable trigonal form (t-POM) and the metastable orthorhombic form (o-POM).
\ CH2 yo\ CH2 /"\
Several experimental studies have been done on oriented POM, making it a good system for studies using molecular dynamics (MD). A prerequisite to careful MD studies is a force field sufficiently accurate for describing structure, energetics, and vibrations of crystalline and amorphous forms. For polyethylene? poly(viny1ene fluoride),z9 and SisN4,30 it has been shown that such vibrationally accurate force fields (MSXX) can be developed using the biased Hessian1 with singular valued decomposition2* methodology (HBFF/SVD).
In this paper, we report the MSXX level of force field using a series of model compounds containing the essential chemical elements of POM. Critical to thesimulationsof the two crystalline
Author to whom correspondence should be addressed.
t General Electric Central Research and Development. Abstract published in Advance ACS Abstracrs, October 1 , 1993.
California Institute of Technology.
forms as well as the amorphous form is getting an accurate description of the torsional potential, and special attention is focused on this.
In section 11, we describe the HBFF methodology for using ab initio calculations and experimental data to extract a vibrationally accurate force field (MSXX) for dimethyl ether (CH3OCH3). Section 111 reports the application of this method to dimethoxy- methane (H2C(OCH3)2). In section IV, the accuracy of this method is tested by application to tri- and tetramethoxymethane. And finally, in section V the results are summarized.
II. Dimethyl Ether Dimethoxymethane (2) is the smallest model compound
containing the -(CH20)- repeating unit of polyoxymethylene.
H \-/"
There are some experimental data3 available on the vibrational frequencies of (2); however, not all normal modes are assigned, and a complete set of experimental frequencies for the isolated
0022-3654/93/2097-10891$04.00/0 - @ 1993 American Chemical Society
10892 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 Dasgupta et al.
TABLE I: Geometries from HF and FF Calculations and from Experiment (p-Wave or Electron Diffraction (ED))*
molecule in the gas phase is not available. Consequently, we chose dimethyl ether (3) as the model compound for extracting scaling parameters between experiment and HartreeFock theory.
H H
For (3), all vibrational frequencies have been determined experimentally and the normal modes a~signed.~ In addition, a normal coordinate analysis has already been performed4 on this molecule, so the importance of various terms in the force field has been documented.
A. Geometry. In the gas phase,s the most stable conformation of dimethyl ether is aa, Figure 1, in which each in-plane C-H bond is trans or anti to the second 0-C bond. This leads to two inequivalent types of H atoms (Hi for in plane and H, for out of plane), as indicated by the C-H bond lengths (RcH, = 1.100 A and RCHl = 1.091 A) and H-C-0 angles ( d o c & = 110.83O and d w H , = 107.23O). In addition, the C, axes of each methyl rotor are not collinear with the C-0 bond axis, subtending an angle larger than the C U C angle. For molecular dynamics simu- lations, all hydrogens of each methyl must be treated as equivalent since the dynamics might interchange them. However, for the purpose of comparison with the spectroscopic results, we allow Hi and H, to be different.
Previously,l we advocated the use of the experimental structure for determining force constants from the ab initio calculations primarily because the internuclear separations (which strongly affects the Hessian) are correct. However, the optimum theo- retical geometry for Hartree-Fock wave functions can differ significantly from experiment. In molecules such as dimethyl ether and dimethoxymethane with low-frequency torsions, this causes a noticeable rotational contamination of these modes. Since we want to use frequency scaling parameters to compare various molecules, it is better to derive the frequencies for all molecules at the ab initio minima (rather than at the experimental minimum for molecules where experimental geometries are available and the ab initio minimum for those where experimental geometries are not available). Thus, we use here the minimized Hartree- Fock structure. Table I compares the H F and experimental5 structures; the differences are quite small except the C-0-C angle, which differs by 2 . 2 O .
B. Force Field Terms. I . Valence Terms. The force field for molecular dynamics is described with a redundant set of local valence coordinates. For example, a tetrahedral center has 4 X 312 = 6 angles, but only five are independent. Similarly, a trigonal center has 3 X 212 = 3 angles, but only two are independent.
a. dimethyl ether p-wave HF(6-3 lg**) MSXX-FF
C-O C-Hi C-Ho C-0-C 0 4 - H i O-C-Ho Hi<-H H0-C-Ho
a Bond lengths in angstroms, bond anglcs in degrees. There is only one central 04-0 angle. (All ob initio calculations were performed using Gaus~ian90.~~~ All molecular mechanics calculations were per- formed using a modified version of BioGraf.31b)
Because of this redundancy, the molecular dynamics force fields are usually not unique, leading to final optimum parameters that may depend on the starting parameters. For dimethyl ether, we started with the force field (LPSFF) optimized from the experimental work of Levin et a1.,4 allowing more valid com- parisons between MSXX and LPSFF.
LPSFF allowed the H, and Hi to have different geometric parameters but required the same stretching force constants, KCH. From Badger’s rule, the force constants depend inversely on the third power of the bond length, so a difference of 8 R c ~ = 0.009 A (0.82%) implies a difference of ~ K C H = 2.4% (16 kcal/mol/ A*). Hence, we allowed different force constants for the two types of H atoms. In LPSFF, the diagonal force constants for H-C-O bending, &HI, and &&differ by about 101, but both types of H-C-H bending are described by one force constant. For MSXX, we kept the distinction between Hi and I-$, for all principal diagonal terms.
The cross-terms are harder to interpret. We have found that the bond-bond cross-terms sharing an apex atom are generally useful for bonds which are similar in nature (e.g., C-H/C-H at a methyl group and C-O/C-O at the ether oxygen). However, C-H/C-0 at the methyl group does not have much effect on the force field. This is because the splitting between equivalent terms is dominated by off-diagonal interactions whereas analogous couplings for inequivalent bonds can be built into the force field by modifying the diagonal terms. Thus, we include bond-bond cross-terms only for equivalent bonds.
The bond-angle cross-terms (involving the bonds defining the angle) are necessary for some of the splittings. However, the sign and magnitude of these terms are difficult to guess apriori. In LPSFF, the C-H/H-C-O coupling constants-differ not only
The Hessian Biased Force Field The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10893
in magnitude but also sign for H, versus Hi. On the other hand, the C-O/H-C-0 coupling only differ in magnitude. We started with thevalues of Levin and allowed the optimization todetermine both the sign and magnitude of these coupling constants. The final values often differ considerably from the starting values.
This molecule allows several types of one-center angleangle coupling terms (e.g., H-C-H/H-C-0, H-C-H/H-C-H, etc.) Levin retained only one, Hi-C-H,/Hi-C-0. The others were rejected because they either caused instabilities in the optimization or fell below the cutoff criterion for retaining cross-terms. We included such terms but find that they are often unnecessary. This particular type of cross-term has the largest effect for methyl deformation modes, primarily in the A1 and B2 blocks (that is, in the C-0-C plane), where there are several closely spaced modes. This particular cross-term may be more relevant to dimethyl ether because of the specific differences in Hiversus H,. In dimethoxymethane and higher analogs (where there is no differentiation between the Hs on the inner methylene carbons), this particular cross-term might not be relevant. After various tests, we decided to omit this class of cross-terms from the force field.
To account for methyl-methyl interactions, Levin included Ho-Ca-O/Ho-Cb-O interactions between the H, on C, and the H, on Cb when they are anti (on opposite sides of the C-0-C plane). LPSFF also includes Ca-H,/Cb-Ho interactions for both the anti and syn bonds. There is evidence from HF/4-31G calculations by Pople, et a1.6 that part of the stabilization of conformer aa over sa and ss (Figure 1) is from overlap of populations between hydrogens on the two methyl rotors. However, we left such terms out of the force field, because they represent long-range interactions that may not be transferable to larger systems and because we are not convinced that they properly describe the physics contained in the HF wave function. For long-chain molecules, we have found that two-center angle-angle cross-terms are also important. In the case of ethane and ethylene, such terms determine the splitting between rocking modes of different symmetries. In the case of polyethylene,2 they are essential in reproducing the stiffness in the chain direction. In simulations of bulk silicon, they are necessary for the mode softening of the transverse acoustic (TA) mode.' Since dimethyl ether does not have two methyl or methine groups adjacent to each other, such terms are not important and were not used in LPSFF or in MSXX. However (vide infra), the C-0-C/O- C-0 coupling will be important for dimethoxymethane.
Levin included a coupling between the adjacent C-0 torsions, even though it was barely above the cutoff criterion for retention. However, we left out such torsion-torsion cross-terms.
2. Nonbond Terms. In addition to the above valence-type terms, the MSXX FFincludes electrostatic (Q) andvan der Waals (vdW) nonbond terms that are usually eschewed from the spectroscopic force fields like LPSFF. The reason is that we require that the energy be described for all changes in geometry whereas the spectroscopic force field is needed only near equilibrium. The effect of intramolecular nonbond terms is small for these molecules, except for the torsional modes, where they make significant contributions. In spectroscopic force field, the effect of such nonbonded terms is typically absorbed into the valence parameters. In MSXX, we explicitly include the effects of nonbond terms, but the charges and vdW parameters are not modified to fit the frequencies. The vdW parameters for C and H were obtained from fitting the cell parameters, elastic constant, and phonons of graphite* and polyethylene crystals.2 The vdW parameters for 0 were obtained from a study of C02 c r y ~ t a l . ~ These are shown in Table 11. Charges were derived using the potential derived charge (PDQ) method.lO Using the electron density distribution from the HF wave function, the electrostatic potential was calculated on a set of grid points around the molecule (but excluding points within the vdW radii). The point charges
TABLE 11: van der Waals Nonbond Terms
Where p = R/R, 4 Re t
C 0.0792 3.841 13.oooO H 0.0200 3.1665 11.2000 0 0.0957 3.4046 13.482
TABLE 111: Force Field for Dimethyl Ether
Levin this work valence terms MSXX/MC MSXX/HT HTXX
C -0.038 -0.004 0 -0.3585 -0,6185 Hi 0.0875 0.1282 HO 0.0649 0.00926
2.651 D dipole moment 1.588 D 1.30 D LF'SFFuses 1/2k~($-&)~for torsion. Electrostaticpotentialderived
charges.
on the various atoms are then optimized to fit this electrostatic potential. The final charges from PDQ and from Mulliken populations are shown in Table 111. Here, we see that PDQ leads to a dipole moment in good agreement with HF and with experiment," whereas Mulliken populations lead to poor values.
C. Experimental Frequencies. The most recent experimental frequencies for dimethyl ether are those of Levin4 (1978). Their assignments agree with previous work,l2 except for two modes (al and bzmethyl symmetricdeformationat 1434and 145Ocm-1). The Levin results were obtained for solid solutions of the various isotopic species. The reported torsional modes were from polycrystalline films because they are too weak to be observed in the solid s ~ l u t i o n . ~ Hence, we chose the Levin frequencies except for torsional modes.
Two careful gas phase p-wave studies (by Durig'3) have been reported for the torsional modes of CHs-O-CHs, CDP-O-CD~, and CD3-O-CH3. The splittings between the in-phase and out- of-phase torsions from the HF frequencies (52 cm-l) were closer to the values from Durig's assignment (42 cm-l) than to those from Levin's (20 cm-1). Hence, we chose the torsional frequencies from the p-wave study. Durig found it necessary to include a
10894 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993
TABLE I V Vibrational Frequencies (cm-1) for Dimethyl Ether
Dasgupta et al.
sym mode FF expt” HFb scale avg AI T in phase 195.5 199 (248) 21 1 0.943 (1.175) BI T out of phase 269.3 241 (268) 263 0.916 (1.019) 0.9295 (1.097) Ai 6 C-0-C 406 425 443 0.959 0.959 AI C-O s-str 923 920 1042 0.883 Bz C-O a-str 1102 1095 1228 0.892 0.8875 Az CHz rock 1116 1149 1272 0.903 Bi CHz rock 1164 1179 1308 0.901 Bz CH3 rock 1165 1166 1345 0.867 A1 CHI rock 1242 1251 1395 0.897 B2 CH3 s-def 1444 1450 1597 0.908 Az CH2 a-def 1465 146W 1621 0.906 BI CHz a-def 1483 1464 1633 0.896 Bz CH3 a-def 1469 1469 1634 0.899 AI CH3 s-def 1444 1434 1634 0.878 AI CH3 a-def 1483 1487 1654 0.899 Bz CH3 s-str 2820 2825.5 3 1376 0.901 A1 CH3 s-str 2823 2816.5 3153 0.893 Az CHZ a-str 2951 2972 3192 0.931 BI CHz a-str 2952 2934 3194 0.9 18 Bz CH3 a-str 2988 2987 3278 0.91 1 Ai CH3 a-str 299 1 2992 3280 0.9 12 0.91 1 rms error 12.6d
a All frequencies from Levin, ref 4 (condensed phase), with the exception of the two torsion modes, which are from Groner and Durig (gas phase). (The Levin values are given in parentheses.) 6-31G** basis. e This frequency is not observed, but calculated using Levin’s 18-parameter force field.
Excluding the two torsional frequencies, these torsional parameters were fit to the conformation energy surface.
0.8954
coupling term of the type V33’sin(&) between the adjacent rotors to reproduce most of the observed transitions of the torsional modes. Our FF includes such couplings from Q and vdW interactions, but our current molecular mechanics program does not allow explicit torsion-torsion coupling. Our final force field leads to a splitting of 74 cm-l, which is 22 cm-* higher than HF.
Table IV lists the frequencies from HF/6-31g** and from experiment as well as the scaling factors for the ab initio frequencies.
D. Biased Hessian Fits. In the Hessian biased FF method,’ the mass-weighted Hessian from ab initio calculations, HHF, is diagonalized to obtain the vibrational frequencies U H F and the vibrational modes UHF,
where XHF is diagonal with elements (4)
( 5 ) and the columns of UHF are the modes. The uFF are about 10% higher than the experimentalvalues. We then construct the biased Hessian by
where
(7) is a diagonal matrix and where 0 is the transpose. This biased Hessian has the virtue that its eigenvalues agree with the best available information on the frequencies (from experiment) and with the best available information on the modes (from theory). The force field is then fitted to describe the biased Hessian. If the number of degrees of freedom is g = 3N-6, then fitting HBH leads tog(g+ 1)/2conditions (231 for O(CH~)z),whereasfitting just the frequencies leads to only gconditions (21 for O(CH3)2). Thus, the HBFF is severely overdetermined.
The parameters in the molecular mechanics force field (excepting the nonbond terms and the Morse well depth) were then systematically varied to match the element of the force field Hessian with the biased Hessian, while requiring zero forces at the H F structure.’*
We developed two force fields (both listed in Table 111): (i) MSXX/MC, where bond stretch is described by a Morse function,
with x = and a = d m (leading to anharmonicity and proper dissocation) and the bending terms are described with the cosine angle form,
p i y e ) = COS e - COS eel2 (9) with C = ke/sin2 8, and (ii) MSXX/HT, where the bonds are harmonic
and the bending terms are harmonic in the angle
HT is commonly employed in normal coordinate analyses using the Wilson GF matrix method. We believe that MSXX/MC is preferable for molecular dynamics simulations and use MSXX/ MC (denoted as MSXX) hereafter.
The inclusion of nonbond terms and the requirement of fitting the H F normal modes lead to force constants substantially different from LPSFF. The bond stretching force constants increase by less than 2%. However, the angle bending force constants are reduced by 10-40%. The bond-bond cross-terms remain nearly the same as those for LPSFF; however, the bond- angle cross-terms change dramatically.
E. Potential Energy Surface for Torsions. The torsional FF parameters are particularly important for describing polymers. Polymers have a distribution of conformations, and it is critical that the relativeenergiesof the minima (e.g., transversus gauche) and the barriers be properly described so that the distribution of conformations and the rates of conformational transitions be properly described. This is much more important to the simulations than the prediction of the torsional frequencies, which describe only the energies near the equilibrium conformation. Yet, experimental barrier heights are usually unavailable, as are the frequencies of the less stable rotamers of most molecules.
Consequently, we rely on the ab initio calculations to provide the torsional potential energy surface. With the 6-3 1G** basis, the single-bond rotational barriers calculated from H F wave functions generally match experimental data quite well. Thus, for dimethyl ether the calculated barrier of 2.52 kcal/mol (between aa and sa) is within 7 % of the experimental barrier14 of 2.72
The Hessian Biased Force Field The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10895
kcal/mol. Although the barrier between aa and ss has not yet been measured, our value of 4.57 kcal/mol is in reasonable agreement with the 5.19 kcal/mol calculated from the potential function derived from experimental torsional frequencies.13a In addition to the barriers, H F also provides an accurate shape for the potential surface.
The HF calculations lead to a total torsional potential function EHF(4). However, the FF includes electrostatic (EQ) and vdW (Edw) terms that also change with 4. Thus, we define a pure torsional potential, ,!?to"(@) by the equation
EHF(4) = Eva' + EQ(4) + E"dW(4) + E'"@) (12) where Ea* depends on the bond and angles but is independent of 4.
If the bonds and angles are fixed and only the torsional angle varied, then we could calculate
Eton(4) = E, + EHF(4) -I?(+) - EvdW(4) (13)
where EO is a constant (which could be adjusted so that ,!?tor($) = 0 for the lowest conformation). The problem is that rigid rotations of the CH3 about the bond axis lead in some cases to very bad contacts (e.g., for H2C(OMe)2) and are not justified even for O(Me)z since the CH3 axis does not coincide with the CO axis. Consequently, we must optimize the bonds and angles for each torsional angle. The procedure we use is to separately optimize all bonds and angles for each conformation (T~,T*) . We do a separate optimization of all bonds and angles for the H F wave function at each 4 to obtain EHF(4) and dFF(4) where the d denotes that no pure torsion terms are included. We then define the torsional potential as
E'O'(4) = E, + EHF(4) - P ( 4 ) (14)
Since dFF(4) depends on the FF for bonds and angles, this process might require iterations. Thus, to determine the nontorsional parts of the FF using HBFF, we might use approximate torsional parameters and put low weight on the torsional fit. Then after determining E'OT(4) from (14), we might redo the HBFF using ,?Pr(4) and then use the final bond and angle parameters to calculate a new dFF(4) and hence a final ,!?tor(4). In practice, we find that one such iteration is sufficient.
An alternative is to use the same geometries for the H F and FF calculations. This could be optimized either for H F or for the FF. The problem is that the H F structure is generally not optimum for the FF. Hence, fitting to (14) to determine ,!?tor(4) leads to residual forces due to bond and angle terms in the nonoptimized structure. Thus at the top of the barrier, the total forces on the molecule from either H F or FF would be nonzero so that it would not be a true maxima.
The HF wave function was calculated by restricting the dihedrals of interest (in increments of 30°) and optimizing all other bond and angle coordinates, leading to the results in Table V.
For eachdihedral point, the geometry for the FF was optimized with the dihedral of interest constrained (and a zero barrier used for this torsion). In addition to bond and angle terms, the total energy EHF(4) contains all van der Waals and charge contributions using the usual restrictions (excluding nearest-neighbor and next- nearest-neighbor contributions). This energy is subtracted from the total H F energy, (14), to give the true torsional energy EFF- (41~42). A bicubic spline is then fitted to the surface to generate a denser grid which is in turn fitted to a Fourier series of torsional terms,
Et0'(41,4J = Et0'(4J + Et0'(4& (15)
TABLE V Energies (kcal/mol) for Dimethyl Ether as Functions of the Two H-C-0-C Dihedral Angles
Table V shows EHF, dFF, and Eor(4l,4z) (and Table VI shows the final Fourier coefficients) for selected points on the surface. This fit was Boltzmann weighted, so the errors near the minima are smaller than the errors near the maxima (since the higher barrier regions will be less populated in the molecular dynamics simulations). The discrepancies are primarily due to truncation of the Fourier series to the sixth term and to the lack of explicit torsion-torsion coupling of the two adjacent rotors (which is evident in the geared and anti-geared torsional modes4). The final conformational energy is plotted in Figure S2 for H F and MSXX. (Figures and tables prefixed with an S are in the supplementary material. See the note just before the references.)
A good test of the FF is how well it predicts isotopic frequency shifts. Since well-assigned data is available for the d6 and d3 isotopomers of this molecule$ we present in Table VI1 our predicted shifts along with the experimental values. In general, the agreement with experimental data is very good. One of the biggest discrepancies is for CH3-O-CD3, where the experimental modes at 1075 (CD3, s-def') and 1102 cm-l (CD3, rock) are calculated with MSXX to be at 1038 and 1094 cm-1 and from LPSFF at 1053 and 1066.5 cm-l.
111. Dimethoxymethane
A. Geometry. For dimethoxymethane (2), there are nine conformations which have the methoxy group staggered with respect to the three other ligands to the central carbon. This leads to four distinct conformations designated by the disposition of the two C-0-C-0 dihedrals (each of which is g+, g-, or t ) : (i) g+g+, (ii) tg+, (iii) t t , and (iv) g+g-. However, g+g- leads to large steric interactions, making it high energy. The HF/6- 31g** optimized structures are reported for the first three in Table I and Figure 3. We find that g+g+ (with TI = T2 = 66.9') is most stable with tg+ at 2.67 kcal/mol, tt at 5.93 kcal/mol, and g+g- at 12.2 kcal/mol. For the polyoxymethylene simulations, we are primarily interested in the methylene unit, which has the two equivalent hydrogens for g+g+ and tt but not for tg+.
The first attempts (in 1950) to identify the structure assumed the t t configurations,lS but later (in 1954)16 theg+g+ configuration
10896 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 Dasgupta et al.
was inferred from dipole moment measurements16 to be the most populated. It is now quite clear that theg+g+ structure is stabilized over other structures because of the anomeric effect." [Consider CI-01-C2-O&. Then the A lone pair on 0 1 perpendicular to the C1-01422 plane prefers to overlap the adjacent polar bond, C r 0 2 . Similarly, the A lone pair on 02 prefers to overlap C2- O1. This leads to g+g+ or g'g, but steric effects disfavor gCg.1 The most recent experimental data on the gas-phase structure of this moleculelaarefromelectrondiffraction (ED) studies's (1973). This leads to some uncertainty (vide infra) in parameters, and it would be most valuable to carry out a new microwave determination of the structure.
The structural parameters from the ED data were obtained by fitting various models to the experimental radial distribution curve.18 In this fitting, the correlation between the two C-0 bond lengths and their vibrational amplitudes (U-value) makes the bond lengths highly dependent on the amplitudes, which have some uncertainty. The final ED geometry leads to 0-CH3 and 0-CH2 bond distances differing by 0.05 A, whereas the H F calculations lead to a difference of 0.018 A. As mentioned in ref 18, the ED does not prove unequivocally that the inner and outer C-0 bonds are of different lengths, and we believe that the theoretical value is much more reliable. Also, the experiments found significant correlation between the 0-C-O and C-0-C angles. Here the final ED structure has a difference of 0.3' in
these angles whereas the ab initio value is 1.5'. In addition, the ED did not distinguish the various C-H bond lengths. (HF indicates that they vary by 0.01 A.)
From HF, the largest change going from g+g+ to t t is in the 0-C-O angle (which decreases by 6.8O), whereas the C - 0 - C angles decrease only by 0.9'. Most of the bond length changes are negligibly small. The C-042-0 dihedral calculated for g+g+ is 66.9O. This is larger than the electron diffraction valuel8 of 63.3'; however, it is considerably smaller than the experimental dihedral angle (77.0' or 78.0°) for t-POM20 and close to the value (63.0') for o - P O M . ~ ~
The difference between the 73.2' for (17) and the value of 77-78' for t-POM may be due to packing of chains (BoydZ2 calculates a dihedral in the isolated helix of 71.9' but 78.3' and 77.9O for t-POM). To investigate the origin of this effect, we performed ab initio calculations (HF/6-31G**) on the methyl- capped tetramer of formaldehyde
CH,-O-CH2-0-CH,-O-CH,-O-CH, (1 7) Here, the -0CH20CH20CH20- unit has a dihedral value of 73.2' while the terminal dihedrals (CH3-0-CH+), which are similar to those of dimethoxymethane, have a 67.0' dihedral. Thus, it appears that long-range electrostatic interactions between the oxygens cause the dihedral to open up from 67' to 73' and that the difference between this and 77O is due to chain packing. This implies that the best model for the long-range interactions for POM is (17) rather than (2).
B. Force Field Terms. 1 . Valence Terms. The FF for dimethoxymethane contains all terms used in dimethyl ether plus two additional terms. These are the two-center angleangle coupling (e.g., C-O-C with 0-C-0 of C-0-C-0) and two- center bond-bond coupling (e.g., C-O with C-O of C-O-C- 0). Such terms are quite critical in dimethoxymethane because of the near degeneracies but were not important in dimethyl ether because the H-C bonds and H-C-O angles are well separated from the C-0 bonds and 0-C-O angle, respectively. The force field for dimethyl ether was used as a starting parameter with suitable modifications (the initial value of the 0-C-O angle term was set equal to the C - O C term, and methylene C-H was initially the same as the methyl C-H from dimethyl ether). The initial values and sign of the new terms were chosen from past experience with skeletal deformation fits in other molecules and were optimized with2s HBFF/SVD. The results are reported in Table VIII.
The discussion of the torsional parameters is deferred to section 1II.D.
2. Nonbond Terms. The van der Waals parameters are unchanged from those used for dimethyl ether. The charges are quite different, and we used the PDQ procedure to determine these charges for the various conformations. Thus, the valence force field of Table VI11 was derived for the g+g+ conformation which used the PDQ charges from HFcalculations. The problem here is that dimethoxymethane exists in three different confor- mations, each of which leads to different PDQ charges (see Table VIII). For molecular dynamics, we need to fix the charges since the molecule will sample various conformations. In the MSXX FF, we fix the charges at the values from g+g+ and build into the torsional terms any effects resulting from changes in charge withconformation. Use of the covalent shell model29 or explicit atomic polarizabilities might mediate this problem.
A potential difficulty is the convergence of the charges for larger molecules. We calculated the PDQ charges (from HF/ 6-31G** wave functions) for a series of polyoxymethylene polymers up to
CH,-O-CH2-O-CH2-O-CH,-O-CH,-O-CHZ-O-CH,
(18) Theresults (TableIX) show that thechargeson thecentral-CHI
The Hessian Biased Force Field The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10897
TABLE VIIk Force Field for Dimethoxymethane dimethoxymethane MSXX/MC
0 -0,3845 -0.4305 -0.2997 -0.4298 methylene C +0.1275 +0.3053 (+0.3053)' +0.4997 H +0.1039 +0.0544 +0.0295 -0.0083 methyl C +0.0093 +0.0404 -0.1691 +0.0328 Hi +0.0691 +0.0745 +0.1241 +0.0940
+0.0691 +0.0404 +0.0867 +0.0307 +0.0442 +0.0839
Ho dipole 0.28 D 2.08 D 2.79 D 0.67 D (298 K)
moment 1.08 D (472 K)
"Only one value. b See section 1II.D for detailed discussion on experimental dipole moment data. unit change from QC = +0.13 for C3 to QC = +0.40 for Cs and Cs to Qc = +0.42 for C7. Thus, the end methyl caps significantly affect the charge transfer between the methylene CHI unit and the adjacent 0 atoms. This suggests that (1 7) would be the best model for obtaining FF parameters of POM.
The charge calculations from Table IX suggest that for infinite helical chains the charges should be Qc = 0.42, QH = 0.04, and Qo = -0.50. However, since the (2-0-C-O torsions werederived for dimethyoxymethane, we have used charges from this molecule with slight modifications. The oxygen charge is the same (QH = -0.38) while the carbon and hydrogen charges were slightly modified to maintain charge neutrality for the OCHz group (Qc
C. Vibrational Frequencies. The only available vibrational data in the literture are the 1980 determination of Raman and
= 0.14, QH = 0.12).
TABLE IX a. Force Field for Polyoxymethylene
bonds C32-0 K, 920.78 1.355 685.32
RQ C32-H Kr
1.083 122.18
Re angles C32-32 Ka e, 108.90
K# -17.56 K d 24.73
0 4 2 3 2 - 0 K8 229.32 0, 113.86 K?O -3.94 K d -0.60
04232-H K8 63.55 6, 109.8 K# 29.28
H-C32-H K8 55.09 KZO -1.29
0, 122.14 K# 3.37 K d 7.99
b. Variation of Charges for CH3-O-(CH&).CH3' N = l N - 3 N = 4 N = 5
Cmctbyl u p +0.01 +0.01 -0.02 -0.03 Hmcthyl cap +0.07 +0.06 +0.07 +0.07 dipole 0.28 D 0.00 D 1.45 D 0.38 D
moment a Theg+conformationisusedfor eachdihedral. Startingfromccnter.
IR spectra in the gas, liquid, and crystalline phase3 (only the experimental frequencies are reported even though a normal coordinate analysis was performed). The experimental frequen- cies do not form a complete set (no C-H modes are reported), and many modes are missing. Also, some modes are assigned to the fg+ conformation, presumably based on the normal coordinate analysis. Because of these difficulties, we have chosen to derive the experimental frequencies from scaling of the theoretical frequencies (from HF/6-3 1G** calculations) where the scaling factors were derived from comparing experiment and theory for dimethyl ether. The H F frequencies are reported with the scaled frequencies in Table X. Also given are the experimental frequencies for all three phases from the work of Sakakibara et ~ 1 . ~ We have taken values from the gas phase where available and the crystalline solid phase elsewhere. Excluding CH modes (no experimental values), the scaled H F and experimental values agree to 12 cm-1.
The normal mode descriptions are quite complex, and without a proper potential energy decomposition (PED) it is difficult to assign any particular mode to a specific description like CH3 ip-rock, CH3 op-rock, or CHI wag, etc. The initial assignments oftheHF/6-3 1G** frequencies for dimethoxymethanewerebased on clustering of group frequencies. In dimethyl ether, the lowest two modes are the two C-0 torsions (1 99 and 24 1 cm-I), followed by an angle bending mode (425 cm-l), two C-O stretching modes (920 and 1095 cm-l), and then the methyl deformation modes (starting at 1145 cm-1). On the basis of this scheme, the dimethoxymethane HF/6-3 1G** frequencies were originally assigned as follows: the first four are C-O torsions, then three skeletal angle bending modes, followed by four C-O stretching modes, and then the CH deformation modes. This is the scheme we used for scaling the ab initio frequencies with group scaling constants. A closer examination of the PED for the H F modes reveals that the B mode at 1198.2 cm-l actually has a larger CH2 rocking component while the B mode at 13 19.5 cm-l has a larger C-O stretching component. However, even allowing for this
1089% The Journal of Physical Chemistry, Vol, 97, No, 42, 1993
TABLE X: V i b n t i d Fr uencies (cm-1) for Mmethoxymethane (%%) HF/6-31C**, Scnled HF/631C**, Force Field, and Experiment for ImtopicaUy%mtituted Species and from MM3
Dasgupta et al.
force field SYm mode H Fa scaledb exptc parent -"CHr '80 MM3
A B A B A B A A B B A B A A B B A B A B A B B A A A B A B A B B A RE'
T(--O--CHr) d-O-CHz-1 d-O-CH3) f(-O-CJ33) C-O-C-O-C def. C-O-C-O-C def. C-O-C-O-C def. C-O str. C-O str. C-O str. C-O str. CH2 rock CH2 twist CH3 def. CHI def. CH3 def.
CHI def. CH3 def.
CH3 def.
CH3 def. CH3 def. CH3 def. C-H str. C-H str. C-H str. C-H str. C-H str. C-H str. C-H str. C-H str.
,I 6-31G** basis. Using scale factors from Table IV (dimethyl ether). Experimental data from Sakakibara er al. (g = gas, s = solid, 1 = liquid). d Excluding C-H modes (for which no exoerimental numbers are available) and torsion modes, which were fitted to the HF/6-31G** PES rather than the torsional frequencies: * RMS error, from experiment.
particular misassignment, the scaling factor for the C-O stretching modes (0.8875) is only 0.88% different from the CH deformation group scale factor (0.8954), and this leads to little error. Since we use the normal mode description from the H F wave function to provide constraints on the force field optimization, the normal mode description will be similar to the H F normal modes.
The HF/6-3 1G** frequencies for the tg' and tt conformations are listed in Tables XI and XIIS (in supplementary material), respectively, along with the scaled frequencies, the frequencies from the optimized force field, and the few experimental frequencies available for these less populated conformer^.^ In applying the scaling derived from dimethyl ether, we assumed that the scale factors are independent of the conformation of the molecule. This is not rigorously true, as evidenced by large changes in the normal mode couplings of various C-O stretching vs CH deformation modes. However, for dimethoxymethane there is insufficient experimental data available to allow scale factors to depend on conformation. Sakakibara et ul.3 assigned three modes to the tg+ conformation, each of which is in reasonable agreement with our scaled frequencies. However, we obtain a different assignment (e.g., the experimental band at 965 cm-l was assigned to the lowest C-O stretching mode by Sakakibara while we find it to be CH2 rocking mode).
force constants are varied systematically to fit both frequencies and modes while obtaining zero forces at the given structures. For dimethoxy- methane, the residual forces are 1.377 kcal/mol/rh, which leads to bonds within 0.003 A and angles within 0 . 8 O of the target geometries. (Table I, Figure 3).
The overall fit of the vibrational frequencies is quite good, as can be seen from Table X. The modes showing the largest
D. Fits. In the HBFF/SVD fitting
deviation are the A skeletal deformation mode calculated at 649 cm-I and the B CH2 rocking mode at 883 cm-1. The overall error in the fit to experiment is 20 cm-I. Including more complicated cross-terms could have yielded a more accurate fit to the frequencies, but there is little justification for this incremental improvement. The MM3 frequencies23 (also listed in Table X) lead to an rms error of 69 cm-*.
The C-O stretching modes strongly mix with some of the lower frequency CH deformation modes (CHI rocking and twisting and also the CH2 degenerate deformation mode which is equivalent to CH2 twisting in the methyl groups). The potential energy decomposition provides some guide as to the principal character of most modes, but in these cases, the contributions from the two types of force constants (C-O stretching and H-C-H, C-C-H bending) are almost equal, and hence the dominant character cannot be unambiguously assigned. Hence, we report in Tables X and XIIIS (in supplementary material) the frequencies for 13C, l8O, and D isotopes (calculated with the MSXX force field) as a guide for assigning future experimental results and for testing our FF. E. Torsional Potential Ewrgy Surface. Wiberg and Murckolg
(WM) published a careful study of the torsional potential energy (PES) surface of dimethoxymethane using 6-31G* (and larger) basis set and a selected set of points for geometry optimizations. We used the 6-31G** basis set (with polarization functions on the H's) and optimized the geometry at a larger number of points with closer grid spacings to cover the entire potential energy surface (Table XIVa). The global minimum occurs for $1 = 42 = 66.9' (g+g+), and the relative energies of the other surface points are tabulated in Table XIVa. The contour plots of this potential energy surface are shown in Figure 4. The differences
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TABLE XI: Vibrational Frequencies (cm-1) for Dimethoxymethane, tg+ Conformer sym mode HF scaled expt force field A T(-O-CH~) 88.3 A d-O-CHr) 130.0 A 7(-O-CH3) 189.0 A r ( a H 3 ) 235.3 A C-O-C-O-Cdcf. 350.3 A C-0-C-O-C dcf. 405.0 A C-O-C-O-Cdef. 607.2
1107.5 A C-O str. A C-O str. A C-Ostr. A C-Ostr. A CHzrock A CHztwist A CH3def. A CH3def. A CH3def. A CH3dtf. A CH3dtf. A CH3def. A CH3def. A CH3def. A CH3def. A CH3def. A CH~def. A CH3def. A C-H str. A C-H str. A C-H str. A C-H str. A C-H str. A C-H str. A C-H str. A C-H str.
between the PES from WM (HF/6-31G*) and our study (HF/ 6-31G**) are slight. The energies of the stationary points are listed in Table XIVb.
Kubo measured24 the dipole moment of dimethoxymethane as a function of temperature in the gaseous state161 and at 292 K in n-hexane. He reports a value of 0.67 D at room temperature. On the other hand, in the electron diffraction paper** Astrup reports unpublished results from Kane's group that the dipole moment of dimethoxymethane measured in benzene is 0.99 D. The temperature of measurement is not mentioned by Astrup. The calculated dipole moments (from HF/6-31G** wave func- tions) of the g+g+, tg+ and tt conformers are reported in Table VIII. The ground-state g+g+ leads to 0.28 D, while the tg+ and tt conformations lead to 2.08 and 2.79 D, respectively. Since tg+ is 2.67 kcal/mol above g+g+, it should contribute only 1.13% at room temperature. More significant is how the dipole moment changes with conformation near g+g+. There should be an increase, but it is not clear that it would change to 0.67 D. A low-temperature study would be valuable. On the basis of dimethyl ether, the calculated dipole moment should be slightly larger (10%) than the experimental value.
Kubo" approximated the difference between the g+g+ and rg+ as AE and the difference between g+g+ and tt as 2AE, in reasonable agreement with our calculations, which lead to 2.25hE. Using the measured dipole moment of dimethoxymethane as a function of temperature and an approximate formula for the dipole moment of a helicalchain polyoxymethylene, Kubodeduced that the energy difference between the g+g+ and the tg+ states was 1.74 kcal/
considerably lower than our calculated energy difference of 2.67 kcal/mol. However, it is relevant to point out (as already done by WM19) that the relative populations of the various conformers will be dependent on the dielectric constant of the solvent or medium. In this light, it is surprising that Kubo's original measurement of the dipole moment of dimethoxymethane in the gaseous state agrees so well with his later measurements in n-hexane. This is also counter to the reported measurement
360.
0.0 360.
360.
0.0 360. Figure 4. (a, top) PES for dimethoxymethane using the force field. Contours are spaced at 1 kcal/mol. (b, bottom) PES from the HF/6- 31g** calculations. Contours are spaced at 1 kcal/mol. of Kane, but since the temperature of the latter work is unclear, it is difficult tosay unequivocally whether the0.99-D measurement is in disagreement with Kubo's data. This clearly points to the need for a more careful measurement of the dipole moment of dimethoxymethane in the gaseous state as well as in solvents of differing dielectric constant. In the absence of such data, we have proceeded on the assumption that the calculated differences (from HF/6-31G**) between the g+g+, (tg+, and tt structures are reasonable and that the rest of the H F PES surface is also accurate. We should mention that we disagree with the Boyd parameterization22 of the C-O-C-0 torsional barrier. They were able to reproduce the temperature variation of the dipole moment by incorporating an inductive effect, but the analysis is flawed because a single conformer was used, ignoring the other two conformers. Also, WM19 pointed out that thefortuitious estimate of the anomeric effect in the work of Deslongchamps17 and of Allinger25 does not take the entropic factor into account. In the case of 2-methoxytetrahydropyran (THP), low-temperature NMR experiments26 indicate that the anomeric effect in this case is primarily due to the entropic factor and that the enthalpic
10900 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993
TABLE XIV Calculated Energies of Dimethoxymethane Conformers from HF/6-31G**
difference between the two conformers is negligible. However, in contrast to the NMR results WM19 calculated (at the 3-21G level) a negligible entropic difference (0.06 kcal/mol) between the axial and equatorial forms of THP.
In order to parametrize the explicit torsional potential For- (&,@z), we followed the same strategy as for dimethyl ether. The molecular mechanics energies were calculated for each of the conformers minimized with the optimized valence force field. The two C-0-C-O dihedrals were constrained to the values used in the H F calculation, and the barriers for these two dihedrals were set to zero. The barriers for the remaining H-C-0-C torsions were used from the parametrization of the H F PES in dimethyl ether. This energy, 6(41,42), has the contributions to the -C-O- barrier from the electrostatic, van der Waals, and other dihedrals but is missing the C-O-C-O dihedral term. We then defined
4 " l , 4 2 ) = EHF(41,42) - 6FF(4142) and fitted Pr(41,42) with a sum of C - 0 4 - 0 torsions as in (1 5) and (16).
The resulting torsional barriers are reported in Table VI, and the final potential energy surface for MSXX is compared with H F in Figure 4.
The agreement with the H F PES is excellent (Table XIV), except for the high-energy conformers. This is not a serious discrepancy since these high-energy conformers are less frequently sampled in molecular dynamics calculations. This torsional potential leads to torsional modes 20-30% higher than experi- mental values and may affect the lower frequency skeletal modes (since these have significant contributions from the torsional coordinate). As discussed earlier, we consider the fit to the global PES to be more important than the torsional frequencies.
The experimental data are sparse for the two other conformers of dimethoxymethane. Hence, we report their scaled ab initio frequencies in Tables XI and XIIS. The components of the FF energy for various configurations are given in Table XV.
IV. Tri- and Tetramethoxymethane To check the validity of our force field, we calculate the
structures and properties of the next two higher analogs. The structure of (1 9) is given in Table XVI, and the vibrational
frequencies are in Table XVIIS. The vibrational frequencies of (20) are given in Table XIXS. There are no structural data
energy 0.00 0.36 2.95 3.25 73 -53.91 56.35 56.20 53.14
H I
59.93 154.44 -2.18 154.50 -59.69 154.50 6.03 8.62
Me Me Me 0
available, but Lee and Wilmshurst reported a complete study27 of the IR and Raman spectra of these two molecules in (i) the vapour phase, (ii) as solutions in CS2 and CC14, and (iii) in the solid state.
A. Trimethoxymethaw. According to the analysis of Lee and Wilmshurst, the three X-0- dihedrals of (19) can adopt either the t, g, or g'conformations (note that the dihedral in question is H-C-O-C (H on the central C), whereas in dimethoxymethane it is the C-0-C-O dihedral). Also, they point out that steric
The Hessian Biased Force Field The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10901
Qgg (E=2.95 kcaVmol) ttg (E=3,25kcaVmol)
P
Figure 5. Optimum structures for trimcthoxymethane (from force field).
crowding makes ttt, ttg, ggg’, and tg’g unfavorable, and only the ggg (C, point group), tgg, and tgg’groups will be populated at the lower temperatures. On the basis of the change of relative intensities between the vapor-phase spectrum and the spectrum taken in a rapidly cooled glassy state, they concluded that two different conformers existed in the vapor phase. Using band contour analysis, they were able to assign the modes to those of the more and less stable conformers. Since all bands were depolarized in the Raman spectrum, this indicated that tgg and tgg’ were the two rotamers present, with the tgg’ being more stable by 0.6 1 kcal/mol as deduced from the temperature variation of the 912/929-cm-l marker bands. The IR spectrum of the solid state was substantially different, with closely spaced doublets, hinting that this must be due to the ggg conformer whose degenerate e modes would be split because of lowered crystal site symmetry. One important point to note is that Lee and Wilmshurst state2’ that their assignment of specific fundamentals to specific modes in the tgg and tgg’ conformers is somewhat arbitrary since it is based on rough estimation of band contours calculated from models and moments of intertia. Hence, we only report the observed gggfrequencies in Table XVIIS. The overall agreement between the calculated and observed frequencies is within the expected accuracy (based on dimethoxymethane fits), with the exception of the lowest energy skeletal modes. The lowest energy skeletal COC bending mode in dimethyl ether is predicted (using scaled HF/6-31G**) at 425, at 329.5 cm-l for g+g+,at 335.9cm-1 for tg+,andat 225.4cm-l for thettconformers. MSXX predicts the lowest energy mode for trimethoxymethane at 284.4 cm-l (e doublet) (190.1 cm-l for tgg‘, 285.3 cm-l for tgg). Differences between isolated gas-phase frequencies and solid-state frequencies cannot explain this discrepancy. In this light, we think the assignment of the lowest frequency skeletal mode in the ggg conformer at 543 cm-l is incorrect.
TABLE XVIII: Comparison of Individual Energy Terms for Various Rotamen of Trimethoxymehne
tgg’ tgg ggg t tg R C ~ ttr total 15.12 15.48 18.07 18.37 21.15 23.74 bond 0.57 0.63 0.47 0.95 0.40 1.36 angle 11.62 9.65 10.18 11.31 12.74 16.54 torsion 1.27 3.01 3.83 4.15 3.74 3.69 VdW 4.25 5.24 4.64 5.30 3.13 4.38
F i p e 6 . Optimum structure for tetramethoxymethane (from force field).
We find (Table XVIII) that the tgg’is indeed the lowest energy conformer (as speculated by Lee and Wilmshurstz’), but it is stable over the tgg conformer by only 0.36 kcal/mol. The ggg conformer is 3 kcal/mol higher and the ttganother 0.3 kcal/mol higher. The gg’ conformation (of two H-C-O-C dihedrals) corresponds to the tt conformation of the dimethoxymethane. Lee and Wilmshurst speculate that in those conformations where two adjacent 0 lone pairs are eclipsed (as in the t t structure for dimethoxymethane and tgg’ for trimethoxymethane) the lone- pair repulsions will force the methyl groups on these two oxygens to twist away in opposite directions. In the tgg’conformer, this leads to a loss of the symmetry plane of the molecule. In our calculations, we do not find evidence for this lone-pair repulsion. While most of our HF calculations were performed with constrained dihedrals for the grid search, we allowed full optimizations of all the coordinates for the tt and tg+ conformers of dimethoxymethane. Interestingly, for the tt conformation of dimethoxymethane the two C-0-C-0 dihedrals are not skewed away from 180’. The dihedral potentials of MSXX reflect this, and hence the tgg’ structure does not have the methyls twisted in opposite directions to break the plane of symmetry. However, in the tggconformer the twodihedrals differ slightly in magnitude (Figure 5). The ggg conformer is quite symmetrical, with all three dihedrals very similar. The trg conformer shows one trans dihedral quite far from the expected trans value. The tg’g conformer was unstable and minimized to the tggconformer. But the biggest surprise was that the ggg’conformer minimized to a stable but relatively high energy gcg’conformer where one of the dihedrals was cis. The highest energy conformer was the ttt, but the dihedrals were slightly skewed away from the trans value.
B. Tetramethoxymethane. The calculations on tetramethoxy- methane indicate again the absence of the distortion due to the lonepair interactions, and the minimum structure has the idealized DU geometry (Figure 6). The frequencies are reported also in Table XIXS. The assigned frequencies from Lee and Wilm- shurst27 agree remarkably for most cases but do not always match the calculated frequencies. We should point out that the experimental assignments are tentative, and more careful ex-
10902 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 Dasgupta et al.
perimental studies may need to be performed on these two molecules to settle the vibrational spectrum.
V. Summary and Conclusions The Hessian biased methodology is quite useful for extracting
vibrationally accurate force fields. Since it combines theoretical mode descriptions with experimental frequencies, it provides sufficient constraints for force field development. In cases where complete experimental data are unavailable (either or both geometries and vibrational frequencies), the method circumvents this problem by using scale factors. This is aptly demonstrated with the molecules of interest in this paper.
The lowest member of the polyoxymethylene series, meth- oxymethane (or dimethyl ether), has both well-characterized structure and frequencies. From this, we were able to extract scaling factors for the ab initio (HF/6-3 1G**) frequencies for each class of vibrational modes. We also extracted the H-C- 0-C torsional parameter by fitting it to the full PES.
The next member of the series, dimethoxymethane, has incomplete experimental data available. Using the ab initio geometry and applying the group scale factors, we were able to generate a complete “experimental” spectrum. The force field parameters were fitted with these constraints. This molecule has two adjacent C-042-0 dihedrals which are key to the full force field for POM. These dihedrals were fit to reproduce the complete ab initio PES for these two degrees of freedom. The energy differences between the most stable g+g+ and the less stable tg+ and tr conformers are quite similar to the ab initio energy differences. However, this gives a population ratio which does not agree with that inferred from measurements of dipole moment as a function of temperature. However, the data on this are not fully consistent between various reports and need to be carefully remeasured.
The force field extracted for dimethoxymethane was used to predict structure and properties of tri- and tetramethoxymethanes. For trimethoxymethane, the three lowest conformers agree with those deduced experimentally. Among the various high-energy conformers, we find one which has a cis dihedral even though this individual interaction is quite unfavorable. For the lowest energy tgg conformer, we find no evidence for breaking the plane of symmetry due to repulsion of the lone pairs on oxygens, as concluded from the experiments. Similarly, we could not detect the distortion inferred from the experiment for tetramethoxy- methane.
We will report simulations of cyclic and crystalline POM in a subsequent paper.
Acknowledgment. The research was funded by the NSF (CHE 90-100289). The facilities of the MSC are also supported by a grant from DOE-AICD, NSF-DMR-MRG, NSF-ACR, Allied- Signal Corp., Asahi Chemical, Asahi Glass, BP America, Chevron, BF Goodrich, Xerox, and Beckman Institute.
Supplementary Material Available: Tables XIIS (vibrational frequencies for tr conformers of dimethoxymethane), XIIIS
(isotopic shifts for g+g+ conformer of dimethoxymethane), XVIIS (calculated frequencies for all conformations of trimethoxy- methane), andXIXS (frequencies for tetramethoxymethane) and Figure 2s (potential energy surface for dimethyl ether) (6 pages). Ordering information is given on any current masthead page.
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