16822
J. Phys. Chem. 1996, 100, 16822-16827
Theoretical Study of the Structure and Vibrational Spectrum of N,N-Dimethylformamide Xuefeng Zhou,* Joel A. Krauser, Dennis R. Tate, Alex S. VanBuren, Jeffrey A. Clark, Paula R. Moody, and Ruifeng Liu* Department of Chemistry, East Tennessee State UniVersity, Johnson City, Tennessee 37614-0695 ReceiVed: January 17, 1996; In Final Form: June 25, 1996X
The molecular structure and vibrational spectrum of N,N-dimethylformamide have been investigated by ab initio Hartree-Fock, MP2, and density functional theory BLYP and B3LYP methods in conjunction with basis sets ranging from 6-31G* to 6-311+G(2d,p). At all levels of theory, the heavy atom skeleton is found to be planar. The calculated CH3-N-CH3 and N-CO-H bond angles significantly differ from the results of a recent electron diffraction study, but are in reasonable agreement with early lower level theoretical results. Comparison between the calculated and electron diffraction structural parameters of many simple amides indicates that the theoretical methods employed in the present study are reliable for describing the structural features of amides. Thus, the significant difference between the recent electron diffraction structural parameters and the early theoretical results is not due to basis set incompleteness as suggested by the electron diffraction study. The calculated vibrational spectral features are in good agreement with available experimental results. On the basis of agreement between the calculated and experimental results, assignments of fundamental vibrational modes were discussed and some reassignments were proposed.
I. Introduction N,N-Dimethylformamide (DMF) is a small and simple model molecule for the peptide bond in proteins. It has been the subject of many theoretical1-6 and experimental4-11 studies. However, its structural and spectral features are still not fully understood. For example, all previous theoretical calculations on DMF predicted a planar heavy (non-hydrogen) atom skeleton,1,2,6 but a recent gas phase electron diffraction study10 concluded a pyramidal nitrogen bond configuration characterized by a 3° departure of the sum of the C-N-C angles from 360°. The authors noted10 that a deviation of several degrees from 360° is very small and may not be statistically significant in electron diffraction results; nevertheless, they concluded that there is no compelling stereochemical reason to have a rigorously planar nitrogen bond configuration in such a bonding situation. The nonplanar nitrogen bond configuration is in line with an early NMR study of DMF in a nematic solvent, which concluded that the NMR results were consistent only with rapidly inverting nonplanar conformers.11 However, the NMR results were interpreted with many assumed structural parameters, and the results may have different meaning from the gas phase electron diffraction study because the former is in the condensed phase with strong intermolecular interactions (the MP2/6-311+G** dipole moment of DMF is as high as 4.5 D) while the latter is in the gas phase with much weaker intermolecular interactions. Apart from the disagreement in planarity, there are also significant differences between the electron diffraction and theoretical CH3-N-CH3 and N-C(O)-H bond angles. The CH3-N-CH3 bond angles predicted by Hartree-Fock (HF) 3-21G and 4-31G calculations2,6 are 117.7° and 119.3°, respectively. The result of the electron diffraction study is 113.9°. The N-C(O)-H angle is predicted by HF/3-21G and HF/431G calculations to be 112.4° and 114.1°, respectively. The result of the electron diffraction study is 117.0°. In the electron diffraction study,10 these differences were attributed to the small basis sets used in the ab initio calculations. X
Abstract published in AdVance ACS Abstracts, September 15, 1996.
S0022-3654(96)00170-0 CCC: $12.00
The vibrational spectra of DMF are not well understood either. The major problem in vibrational studies is that, due to low molecular symmetry, there are strong couplings among vibration modes. These couplings make vibrational assignments extremely difficult. Although many vibrational studies have been carried out,4-9 a complete assignment of the 30 fundamental vibrational modes is still not available. A recent combined ab initio and experimental study6 of DMF even proposed a coupling mode between the methyl umbrella vibration and the antisymmetric CN stretching to be around 2000 cm-1. This proposal was based on the results of a scaled HF/ 3-21G calculation, and a plausible explanation of this abnormally high frequency was given. However, our own HF/3-21G calculation using the Gaussian92 program package12 was unable to reproduce the reported feature. The highest non-CH stretching frequency obtained in our HF/3-21G calculation is 1876 cm-1, which is the CO stretching instead of the coupled CH3 umbrella mode. After a reduction by 0.90 to account for effects due to neglect of electron correlation and basis set incompleteness,13 the calculated CO stretching frequency, 1688 cm-1, is very close to the observed CO stretching frequency,4,6 16851725 cm-1. To better understand the structural and vibrational spectral features of DMF, we have carried out ab initio and density functional theory calculations on its structure and vibrational spectrum as a course project in our quantum chemistry class at East Tennessee State University. In agreement with previous theoretical studies, all of our calculations at different levels of theory and using different basis sets predict a planar heavy atom skeleton. Vibrational analysis based on quadratic force fields obtained by density functional theory and ab initio HF and MP2 calculations provides valuable insight into the vibrational spectra. The procedure and results of our study are reported herein. II. Computational Details The molecular structure of DMF was fully optimized by the gradient technique at the following levels of theory: HartreeFock SCF (HF), second-order Moller-Plesset perturbation © 1996 American Chemical Society
Theoretical Study of the Structure of DMF
J. Phys. Chem., Vol. 100, No. 42, 1996 16823
TABLE 1: Comparison of the Calculated and Experimental Structural Parametersa of N,N-Dimethylformamide expt
MM3
parameter
bas1b
HF bas2c
bas1b
MP2 bas2h
bas1b
BLYP bas2c
bas1b
B3LYP bas2c
GEDd
ref 1
4-31Ge
3-21Gf
RCO RNC4 RNC2 RNC3 RC4H RC2H7 RC2H8 RC3H10 RC3H11 ∠C2NC4 ∠C3NC4 ∠C2NC3 ∠NCO ∠NC4H ∠C2NCO ∠C3NCO
1.197 1.349 1.446 1.442 1.091 1.078 1.086 1.082 1.086 120.6 122.0 117.4 125.9 112.6 0.0 180.0
1.193 1.343 1.445 1.440 1.092 1.077 1.086 1.081 1.086 120.9 121.7 117.4 126.0 112.7 0.0 180.0
1.229 1.364 1.450 1.447 1.105 1.089 1.095 1.092 1.096 120.0 122.0 117.9 125.6 112.1 0.0 180.0
1.222 1.365 1.451 1.448 1.105 1.090 1.096 1.092 1.096 120.6 121.7 117.7 125.7 111.7 0.0 180.0
1.233 1.381 1.465 1.461 1.117 1.098 1.105 1.101 1.106 120.1 121.8 118.1 125.7 114.5 0.0 180.0
1.229 1.374 1.465 1.462 1.113 1.094 1.100 1.097 1.101 120.5 121.6 117.9 125.8 111.8 0.0 180.0
1.220 1.365 1.453 1.449 1.108 1.090 1.098 1.094 1.099 120.1 121.9 118.0 125.7 111.8 0.0 180.0
1.216 1.359 1.452 1.448 1.105 1.087 1.094 1.090 1.094 120.5 121.7 117.9 125.8 112.1 0.0 180.0
1.224(3) 1.391(7) 1.453(4) 1.453(4)
1.217 1.381
1.221 1.343
1.216 1.352
1.458
1.458
1.458
1.112(3)g
1.117
1.081
1.084
120.8(3) 122.3(4) 113.9(5) 123.5(6) 117.0(2.8) -16.3(4.5) -168.6(3.9)
120.8 120.3 119.0 126.6 113.7 0.0 180.0
118.5 122.2 119.3 124.8 114.1 0.0 180.0
120.1 122.2 117.7 125.5 112.4 0.0 180.0
}
HF
a Bond lengths are given in angstroms and angles are in degrees. Numbering of the atoms is given in Figure 1. b Results obtained with the 6-31G* basis set. c Results obtained with the 6-311+G(2d,p) basis set. d Results of the recent gas phase electron diffraction analysis in ref 10. e Results obtained with the 4-31G basis set; ref 2. f Results obtained with the 3-21G basis set. g Mean value. h Results obtained with the 6-311+G(d,p) basis set.
Figure 1. Numbering of the atoms of N,N-dimethylformamide.
theory (MP2), density functional theory (DFT) with BLYP functionals (Becke’s exchange functional14 and Lee-YangParr’s correlation functional15), and Becke’s three-parameter hybrid DFT/HF method16 using the Lee-Yang-Parr correlation functional (B3LYP). As previous ab initio studies2,5,6 used small basis sets without polarization functions and the results were suspected10 to be unreliable due to basis set incompleteness, we used the 6-31G*,17 6-311G(2d,p),18 and 6-311+G(2d,p) basis sets in geometry optimizations. With each method, the molecular structure of DMF was first optimized by using the 3-31G* basis set. Vibrational analysis was then carried out at the optimized structure by evaluating energy second derivatives analytically to ensure that it is an equilibrium structure with no imaginary frequencies. Geometry optimizations using the larger basis sets were started with the optimized 6-31G* structures and used the 6-31G* analytical second-derivative matrices as the initial Hessian. The energy second derivatives in Cartesian coordinates were transformed into force constants in internal coordinates and used in subsequent vibrational analysis to understand the vibrational spectral features. All of the calculations were carried out by using the Gaussian12 and TEXAS19 program packages. III. Results and Discussion Structure. Our calculated structural parameters of DMF are compared with the results of previous ab initio2,6 and MM31
calculations as well as the recent electron diffraction study10 in Table 1. In this table, bond lengths are given in angstroms and angles are in degrees. The numbering of atoms referred to in this table is given in Figure 1. It is shown that all of the calculations predicted a planar equilibrium structure. The structural parameters obtained with basis sets other than the 4-31G are in good agreement: the maximum difference is about 0.02 Å in bond lengths and about 1° in bond angles. The general trend is that the larger the basis set, the shorter the bond distance. With the same basis set, methods that recover electron correlation give slightly longer bond lengths. Except for results obtained by using the 4-31G basis set, the bond angles are only slightly affected by basis sets and theoretical methods. Some bond angles obtained with the 4-31G basis set significantly deviate (∼2°) from results obtained by all other ab initio calculations. Compared to the results of the recent electron diffraction study,10 significant differences are found for the C2-N-C3 and N-C4-H bond angles and the planarity of the nitrogen bond configuration, although the difference in planarity may be inconclusive as we are comparing the re structure with the rg structure. The latter may appear nonplanar due to thermal effects and anharmonicity of molecular vibrations. However, it is well-known that simple bond angles are predicted accurately by ab initio calculations. Experience20 from a large number of ab initio studies indicates that the HF/6-31G* bond angles are within 1.5° of reliable experimental results. However, the difference between the HF/6-31G* and the electron diffraction results is as large as 4° for the C2-N-C3 bond angle and about 5° for the N-C4-H bond angle. It is interesting to note that the calculated bond angles of C5-N-C1 and C4-N-C1 are in good agreement with the results of the electron diffraction study. This may suggest that differences between the calculated and electron diffraction results in both the planarity of the nitrogen bond configuration and the C2-N-C3 bond angle are of the same origin. If the electron diffraction C2-N-C3 angle were several degrees larger, the electron diffraction results would be consistent with the theoretical results and the nitrogen bond configuration would be planar. Since significantly larger basis sets and higher levels of theory are used in the present study, differences between the calculated and the electron diffraction results are unlikely to be due to inadequate theoretical methods as claimed in the electron diffraction study.
16824 J. Phys. Chem., Vol. 100, No. 42, 1996
Zhou et al.
Figure 2. Comparison of the calculated and gas phase electron diffraction structural parameters of simple amides (bond lengths in angstroms and angles in degrees). The first and second entries are results calculated by HF/6-31G* and B3LYP/6-31G*, respectively, and the third entry is electron diffraction structural parameters. Sources of electron diffraction structural parameters are as follows: formamide, ref 21; trans-Nmethylformamide, ref 22; N,N-dimethylformamide, ref 10; acetamide, ref 23; trans-N-methylacetamide, ref 24; dimethylcarbamyl chloride, ref 25.
To further ensure that the theoretical methods employed in the present study are adequate for describing the structural features of amides, we have optimized the equilibrium structures of formamide, trans-N-methylformamide, acetamide, trans-Nmethylacetamide, and dimethylcarbamyl chloride by HF/6-31G* and B3LYP/6-31G* methods. The calculated results are compared with the results of gas phase electron diffraction studies21-25 in Figure 2. In this figure, all bond lengths are given in angstroms and angles are in degrees. Since reliable electron diffraction structural parameters involving hydrogen atoms are not available (in most cases they are either set at assumed values or only an average value was determined in fitting electron diffraction intensity patterns), only structural parameters of the heavy (non-hydrogen) atom skeletons are compared in Figure 2. It shows that for formamide, trans-Nmethylformamide, acetamide, and trans-N-methylacetamide, the bond angles calculated by both HF/6-31G* and B3LYP/6-312G* are in excellent agreement with the results of electron diffraction analyses; the maximum difference between the calculated and experimental results is about 1°. For dimethylcarbamyl chloride, the HF/6-31G* bond angles are in excellent agreement with the results of electron diffraction analysis, but one of the B3LYP/ 6-31G* C-N-C angles is 2.9° larger than the corresponding experimental result. The origin of this discrepancy is as yet unknown, but is probably due to the fact that B3LYP/6-31G* structural parameters of molecules involving second-row atoms are less reliable than those for molecules of the first-row atoms only.26 As HF/6-31G* and B3LYP/6-31G* are the lowest level theoretical methods employed in this study, it is clear that the theoretical methods employed in the present study are adequate for describing the structural features of DMF. To resolve the discrepancy between the experimental and theoretical results, a careful reinvestigation of the experimental structure of DMF is desirable. The nitrogen bond configuration of simple amides can be qualitatively understood by considering the following resonance forms:25,27
Form I contributes to a pyramidal nitrogen bond configuration and form II contributes to a planar bond configuration. Both formamide (R ) H) and acetamide (R ) CH3) were found by electron diffraction studies21,23 to have planar nitrogen bond configurations. Schultz and Hargittai25 asserted that substitution of the hydrogens at nitrogen by electron-donating methyl groups should decrease the positive charge on nitrogen and thus increase the relative contribution of form I. In our opinion, however, substitution of the hydrogens by electron-donating methyl groups should stabilize resonance form II and therefore increase the relative contribution of that form. This is in agreement with the results of electron diffraction studies that showed planar nitrogen bond configurations in trans-N-methylformamide22 and trans-N-methylacetamide.24 The calculated results of these molecules are also in accord with our view of substitution effects, as Figure 2 shows that from formamide to trans-Nmethylformamide and from acetamide to trans-N-methylacetamide there is a slight decrease in N-CO bond lengths coupled with a slight increase in CO bond lengths. As electron diffraction bond lengths have larger uncertainties, they may not reflect the slight differences in bond distances. Both theoretical and electron diffraction results indicate an increase in the N-CO distance from formamide or trans-N-methylformamide to DMF. This might be due to steric effects as the methyl group is bulkier than hydrogen. NMR measurements have concluded that the rotational barrier of formamide along the C-N bond is 80 kJ/ mol28 and the rotational barrier of DMF is 86-89 kJ/mol.29 The rotational barrier of both molecules should be attributed to resonance form II. The increase in the rotational barrier from formamide to DMF indeed indicates that substitution of the hydrogens on nitrogen by electron-donating methyl groups
Theoretical Study of the Structure of DMF
J. Phys. Chem., Vol. 100, No. 42, 1996 16825
TABLE 2: Comparison of the Calculated and Observed Vibrational Frequencies of N,N-Dimethylformamidea BLYP
B3LYP
MP2
HF freqb
sym
ν
freq
a′
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
3094 2.05 3047 18.80 2955 62.50 2941 52.79 2863 110.3 1723 331.5 1525 6.87 1495 16.36 1448 9.44 1414 6.16 1401 0.92 1375 74.81 1235 35.39 1065 116.4 1061 3.18 846 1.05 638 6.73 382 1.64 314 10.90
3181 1.08 3133 18.20 3036 57.42 3025 47.60 2970 99.04 1799 397.8 1567 14.14 1534 15.71 1491 7.66 1457 9.92 1450 16.97 1431 77.76 1292 38.61 1107 116.6 1095 2.61 882 1.46 663 7.67 393 1.67 324 11.83
3241 0.17 3407 14.03 3095 43.64 3086 44.76 3035 88.20 1802 382.8 1596 14.02 1567 14.55 1517 7.52 1482 32.96 1478 54.12 1462 30.59 1326 37.85 1131 114.1 1114 2.15 900 1.60 668 6.88 398 1.32 329 11.56
2992 2938 2861 2849 2845 1746 1502 1474 1448 1417 1413 1386 1250 1068 1056 838 634 380 313
20 21 22 23 24 25 26 27 28 29 30
2996 2981 1488 1465 1155 1108 966 330 223 190 131
3083 3072 1527 1504 1190 1141 1019 338 227 187 132
3167 3157 1560 1537 1210 1161 1025 335 233 172 92
2893 2892 1467 1448 1147 1103 1038 309 217 145 76
a′′
IIR
33.36 49.53 11.43 3.75 1.70 0.08 0.07 12.86 1.67 0.30 0.04
freq
IIR
29.49 46.97 13.70 4.06 2.28 0.05 0.51 16.58 1.83 0.23 0.06
freq
IIR
14.24 43.16 15.56 3.88 3.16 0.05 0.15 18.25 2.75 0.56 0.04
IIR
expt1c
IRA
2.44 39.33 36.16 64.16 58.59 194.4 114.5 87.23 22.63 19.53 577.0 11.57 31.07 20.92 9.10 2.94 14.01 8.28 44.14 3.03 14.00 9.71 130.9 3.81 62.20 0.62 140.0 4.67 10.54 7.59 4.73 7.82 10.63 4.25 1.71 0.38 14.12 0.66 56.73 46.23 13.54 2.31 6.60 0.06 5.87 32.34 1.63 0.28 0.03
expt2d
2928 s vs 2910 sh sh 2853 s m 2810 w w 2766 w w 1685 s 1715 s w 1512 m 1520 m w 1460 w 1480 m w 1450 m 1443 m s 1410 s 1410 m (1410) 1408 m s 1395 s 1382 s sh 1268 s 1266 s 1099 vs 1084 s s 1067 m 1062 m w 870 m 867 m s 660 s 659 s s 405 m 403 s w 319 m 318 s w
85.27 64.80 5.84 26.53 0.93 1150 3.87 4.01 2.24 350 0.37 0.25 0.20
2987 w w 2942 m sh 1464 m 1437 w 1154 w 1030 w vw 966 m 356 w 245 w w
expt3e 2987 2930 2884 2853 1715 (2000) 1480 1443 1407 1385 1266 1084 1010 866 659 404 318
mode descriptionf S11(93) S7(89) S9(41) + S10(41) S6(40) + S8(40) S2(100) S5(78) S19(49) + S24(19) + S21(11) S24(56) + S19(32) S18(79) S23(84) + S13(10) S13(61) + S18(14) + S5(10) S1(30) + S21(13) + S19(10) S3(35) + S4(24) + S26(13) + S12(10) S21(39) + S1(31) + S26(12) S26(45) + S21(28) + S3(12) S4(55) + S12(20) + S3(13) S12(34) + S3(27) + S1(16) + S17(15) S16(77) + S17(11) S17(58) + S12(27) + S16(11)
S9(50) + S10(50) S6(50) + S8(50) S25(90) S20(89) S27(47) + S22(44) S22(48) + S27(44) 966 S14(97) 355 S28(76) + S15(17) 245 S29(66) + S15(30) S30(69) + S29(15) + S15(14) S15(36) + S30(27) + S29(15) + S28(15)
2942 2910 1464 1462 1153
a Frequencies are in cm-1; the calculated IR and Raman intensities are in km/mol and Å4/amu, respectively. b The HF frequencies have been scaled by 0.89 to account for neglect of electron correlation and basis set incompleteness. c Reference 4; the intensities given are IR intensities. d Reference 5; the first entry of the intensities is IR intensity, and the second entry is Raman intensity. e Reference 6. f According to total vibrational energy decomposition analysis. Only coordinates that contribute 10% or more are listed. The definition of the internal coordinates is given in Table 3.
TABLE 3: Definition of Internal Coordinatesa Used in the Vibrational Analysis of N,N-Dimethylformamide no.
coordinate
no.
coordinate
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15
R14 R46 R31 R21 R45 R3,11 R3,10 R3,12 R29 R28 R27 2R145 - R146 - R546 R146 - R546 δ6514 δ4321 + δ3421 + δ2431
S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30
2R312 - R413 - R412 R412 - R413 R11,3,12 + R10,3,12 + R10,3,11 - R1,3,10 - R1,3,10 - R1,3,11 - R1,3,12 2R11,3,12 - R10,3,12 - R10,3,11 R10,3,12 - R10,3,11 2R1,3,10 - R1,3,11 - R1,3,12 R1,3,11 - R1,3,12 R829 + R729 + R728 - R127 - R128 - R129 2R829 - R729 - R728 R729 - R728 2R127 - R128 - R129 R128 - R129 τ3146 + τ2146 + τ3145 + τ2145 τ11,3,1,4 + τ10,3,1,4 + τ12,3,1,4 + τ11,3,1,2 + τ10,3,1,2 + τ12,3,1,2 τ9214 + τ8214 + τ7214 + τ9213 + τ8213 + τ7213
a The internal coordinates are defined according to the recommendation of Pulay et al.31 The numbering of atoms is given in Figure 1. R 145 is the N1C4O5 bond angle, R14 is the N1-C4 bond stretching coordinate, τ3146 is the dihedral angle of C3-N1-C4-H6, and δ6514 is the angle between the H6C4 bond and the plane of C5N1C4 (out-of-plane angle).
stabilizes resonance form II, thus supporting our view of substitution effects. Vibrations. As DMF belongs to the Cs point group, its 30 fundamental vibrational modes are split into 19a′ and 11a′′ symmetry species. The calculated frequencies, together with the calculated infrared and Raman intensities, are compared with the available experimental results in Table 2. The 6-31G* basis set was used in all these calculations. The HF frequencies given in this table have been scaled by 0.89 to account for the neglect of electron correlation. The mode descriptions given in this table were obtained from total vibration energy (TED) distribution analysis30 using the BLYP/6-31G* force field. The TED
analysis was carried out in internal coordinates, which are defined according to the recommendation of Pulay et al.31 The definitions of the internal coordinates are given in Table 3. The numbering of atoms referred to in Table 3 is given in Figure 1. Since the molecular symmetry is quite low, many vibrational modes are strongly coupled and consist of contributions from many internal coordinates. Only internal coordinates contributing more than 10% to the total vibrational energy are given in Table 2. Among the calculated results, the BLYP frequencies of the non-CH stretching modes are the closest to available experimental data. The MP2 frequencies are significantly higher, and
16826 J. Phys. Chem., Vol. 100, No. 42, 1996 B3LYP frequencies are between the corresponding BLYP and MP2 results. It is well-known that raw HF frequencies are generally 10-15% higher than the observed fundamental vibrational frequencies,13 but after they are scaled by 0.89 the results are in good agreement with the observed frequencies for both non-CH stretching and CH stretching modes. Our vibrational energy analysis was carried out using the BLYP force field because this force field reproduces the observed non-CH stretching frequencies satisfactorily without any adjustments. The deviation between the BLYP and the observed CH stretching frequencies is perhaps due to significant anharmonicity of the CH stretching vibrations. In the following, we will discuss uncertainties in the vibrational assignments of DMF based on the calculated results. The most prominent discrepancy between the results of the present study and the most recent combined experimental and ab initio study6 of the vibrational spectrum is at the highest non-CH stretching mode. Our calculations indicate no evidence for the presence of a non-CH stretching fundamental mode over 1900 cm-1, but it was concluded in the previous study6 that there is a weak non-CH stretching fundamental near 2000 cm-1. A fundamental vibrational frequency of ∼2000 cm-1 is unusually high for a non-CH(D) stretching mode of DMF. The only evidence for this surprising result was that, in their HF/3-21G calculation of DMF, Steele and Quatermain found a methyl umbrella mode coupled with antisymmetric CN stretching at around 2000 cm-1. We have carried out HF/3-21G calculations on DMF, and the highest mode of substantial CH bending character obtained in our calculations is only 1707 cm-1 (unscaled). At the HF/6-31G* level, this mode is at 1688 cm-1 (unscaled). The same mode calculated by BLYP, B3LYP, and MP2 is even lower. Thus, we concluded that the unusually high methyl umbrella frequency of the previous study is due to errors in their HF calculations.32 The BLYP/6-31G* frequency of the highest CH3 umbrella mode is 1525 cm-1, which is in good agreement with the early experimental assignments4,5 of a medium to weak band at 1512-1520 cm-1. With the help of the measured polarization ratios of the Raman bands and the contours of the absorption bands, the other a′ modes of DMF have been confidently assigned. These experimental assignments are in good agreement with the calculated results. However, the experimental assignment of the a′′ modes is not as well established. For example, the lowest observed frequency is 245 cm-1, which was assigned to the lowest a′′ mode, ν30, by Steele and Quatermain.6 Our calculations, however, indicated that there are two modes below 200 cm-1. One is at 190 cm-1 and the other is at 131 cm-1. Both of them have very low infrared and Raman intensities and are therefore expected to give very weak infrared and Raman bands. As a result, they are not likely to be observed with infrared and Raman techniques. A discrepancy between our calculated results and the experimental assignments of the a′′ modes is found for ν25. According to our calculation, this mode should give a very weak infrared band at around 1100 cm-1. Experimentally, a weak infrared band of the type C contour was found at 1030 cm-1 with a very weak Raman counterpart. It was assigned to the CH3 wagging on the basis of results of a HF/ STO-3G calculation. The deviation between our calculated results and this frequency appears too large. Since our calculations predict this mode to have nearly zero infrared intensity, and since it is very close to the strong infrared band due to ν15, it is highly probable that the band due to ν25 was obscured.
Zhou et al. IV. Summary Results of ab initio calculations at the HF and MP2 levels of theory and density functional theory calculations using the BLYP and B3LYP functionals indicate that the equilibrium structure of DMF has Cs symmetry with a planar nitrogen bond configuration. This is in agreement with the results of previous lower level theoretical studies, but is at variance with the conclusion of a recent gas phase electron diffraction study. The calculated CH3-N-CH3 and N-CO-H bond angles also significantly differ from the electron diffraction results. Comparison between the calculated and electron diffraction structures of many other amides indicates that the theoretical methods employed in the present study are adequate for describing the structural features of DMF. Analysis of substitution effects suggests that replacement of the hydrogens on nitrogen by methyl groups contributes to a planar nitrogen bond configuration in DMF. In view of the role DMF plays as a model compound containing the peptide bond, a careful reinvestigation of its electron diffraction structure is desirable. The calculated vibrational spectral features of DMF are in satisfactory agreement with available experimental results. On the basis of agreement between the calculated and observed spectral features, assignments of the fundamental vibrational modes were examined. The calculations strongly support the early experimental assignment of the highest mode of substantial CH3 bending character at 1520 cm-1. The recent reassignment of this mode by Steele and Quatermain to a frequency at ∼2000 cm-1 is at variance with the calculated results. The difference is due to an error in their ab initio calculations. This study shows that molecular orbital calculation is becoming an effective tool for both research and teaching, and it is a promising approach to understand the structural and spectral features not easily amenable to experimental studies. Acknowledgment. This study was partially supported by the Research and Development Committee of East Tennessee State University. We are grateful to Mr. David Sean for technical assistance. References and Notes (1) Lii, J.-H.; Allinger, N. L. J. Comput. Chem. 1991, 12, 186. (2) Dimitrov, V. S.; Ladd, J. A. J. Mol. Struct. 1987, 159, 107. (3) Kaufman, G.; Leroy, M. J. F. Bull. Soc. Chim. Fr. 1967, 402. (4) Durgaprasad, G.; Sathyanarayana, D. N.; Patel, C. C. Bull. Chem. Soc. Jpn. 1971, 44, 316. (5) Jao, T. C.; Scott, I.; Steele, D. J. Mol. Spectrosc. 1982, 92, 1. (6) Steele, D.; Quatermain, A. Spectrochim. Acta 1987, 43A, 781. (7) Jones, R. L. J. Mol. Spectrosc. 1963, 11, 411. (8) Randall, E. W.; Yoder, C. M. S.; Zuckerman, J. J. Inorg. Chem. 1966, 5, 2240. (9) Chalapathi, V. V.; Ramaiah, K. V. Proc. Indian Acad. Sci. 1968, 68A, 109. (10) Schultz, G.; Hargittai, I. J. Phys. Chem. 1993, 97, 4966. (11) Bopp, T. T.; Balakrishnan, N. S. Mol. Cryst. Liq. Cryst. 1977, 41, 47. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, ReVision B.1; Gaussian, Inc.: Pittsburgh, PA, 1995. (13) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; Defrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Int. J. Quant. Chem., Symp. 1981, 15, 269. (14) Becke, A. D. Phys. ReV. 1988, A38, 3098. (15) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1988, 157, 200. (16) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
Theoretical Study of the Structure of DMF (17) Hehre, W. J.; Ditchfield, R. D.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (18) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (19) Pulay, P. Theor. Chim. Acta 1979, 50, 299. (20) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (21) Kitano, M.; Kuchitsu, K. Bull. Chem. Soc. Jpn. 1974, 47, 67. Hirota, E.; Sugisaki, R.; Nielsen, C. J.; Sorensen, G. O. J. Mol. Spectrosc. 1974, 49, 251. (22) Kitano, M.; Kuchitsu, K. Bull. Chem. Soc. Jpn. 1974, 47, 631. (23) Kitano, M.; Kuchitsu, K. Bull. Chem. Soc. Jpn. 1973, 46, 3048. (24) Kitano, M.; Fukuyama, T.; Kuchitsu, K. Bull. Chem. Soc. Jpn. 1973, 46, 384. (25) Schultz, G.; Hargittai, I. J. Phys. Chem. 1995, 99, 11412. (26) Ma, B.; Lii, J.-H.; Schaefer, H. F., III; Allinger, N. L. J. Phys. Chem. 1996, 100, 8763.
J. Phys. Chem., Vol. 100, No. 42, 1996 16827 (27) Wiberg, K. B.; Laiding, K. E. J. Am. Chem. Soc. 1987, 109, 5935. (28) Drakenberg, T.; Forsen, S. J. Phys. Chem. 1970, 74, 1. (29) Drakenberg, T.; Dahlqvist, K.; Forsen, S. J. Phys. Chem. 1972, 76, 2178. (30) Pulay, P.; Torok, F. Acta Chim. Hung. 1965, 44, 287. Keresztury, G.; Jalsovszky, G. J. Mol. Struct. 1971, 10, 304. (31) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J. Am. Chem. Soc. 1979, 101, 2550. Fogarasi, G.; Zhou, X.; Taylor, P.; Pulay, P. J. Am. Chem. Soc. 1992, 114, 8191. (32) As a referee of this paper, Prof. D. Steele kindly pointed out that he has recognized an error in his work (ref 6). The cause arose from the need at the time to compute the force field by finite perturbations of the structure. The two N-methyl bonds were cross-labeled, with drastic results on the mode mixing and severe perturbations of certain N-C/methyl deformation modes. He is grateful to Prof. G. Fogarasi, who located this elusive error.
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