J. Phys. Chem. 1993,97, 4262-4269
4262
ARTICLES Theoretical and Spectroscopic Study of Asymmetric Methyl Rotor Dynamics in Gaseous Partially Deuterated Nitrometbanes Dominique Gorse,? Dominique Cavagnat,*?$Michel Pesquer,t and Christine Lapouge+*$ Laboratoire de Physicochimie Thborique, URA503, and Laboratoire de Spectroscopie Molbculaire et Cristalline, URAl24, Universitk Bordeaux I, 351 cows de la Libbration, 33405 Talence Cedex, France Received: September 22, 1992; In Final Form: January 26, 1993
Ab-initio calculations have been performed a t the HF/6-31G** and HF/6-3 1++G(d,p) levels to study the conformational dependence of the geometry and the vibrational frequencies of three hydrogen/deuterium (do, d l , d z ) isotopomers of nitromethane. The Raman gas-phase spectra of these compounds are also presented. They compare well with the infrared ones and the theoretical prediction. The calculated overall zero-point vibrational energy of both dl and d2 isotopomers presents an angular dependence of the form VZcos(2B) V4 cos(4B). It contributes significantly to the methyl torsion potential and causes two different equilibrium positions for the d l (eclipsed) and dz (staggered) methyl groups. The vibrational origin of the VZand V4 pseudopotential terms of the rotational potential of the partially deuterated methyl groups is thus confirmed. The close correspondence between calculated and experimental results shows that theoretical calculations can be a convenient alternative to analyze the lone CH or CD stretching spectra of the partially methyl groups.
+
Introduction A great part of the considerable interest devoted to nitromethane, the simplest energetic nitro compound, is related to the understanding of the chemical mechanism of initiation of detonation. Many and experimenta13q4works have investigated the dissociation following exitation around 200 nm. The dominant process is shown to be the cleavage of the C-N bond to yield CH3 NO2 radicals (dissociation channel energy AjYo300= 60.1 kcal/mol),l indicating that the energy must flow from the initially excited NO2 moiety into the C-N bond. Recent studies of the emission5and of the resonance Raman6 spectra of this photodissociation observe dominant progressions of the symmetric stretching NO2 vibration at energy up to 15 000 cm-I (toground state C H 3 0 NO), which is approximately the lowest dissociation limit in the gas phase.] When irradiating at a higher wavelength (266 nm),’ a different photodissociatingpathway has been proposed involving the N-0 bond breaking to yield CH3NO 0 (dissociationchannel energy M o =393.5 ~ kcal/mol).I On the other hand, selective abstraction of an H atom was experimentally shown in F CH2DN02 or CHD2N02 reaction studies in an argon matrix8 although the C-H bond rupture to yield CH2N02+ H requires a relatively high energy (around 90 kcal/mol).l-9 A recent kinetic study of the H + CH3N02 reaction indicates that the principal dissociation channel leads to OH + C H 3 N 0 but that the abstraction of a methyl group hydrogen leading to H Z CH2N02 could also become a significant dissociation channel at elevated temperatures (of interest to propellant combustion).IO The importance of the nitromethyl (CH2N02) entity was further studied in an extensive series of papers which emphasize the significant role of the aci ion (CH2N02-) in the degradation chemical reactions.11-13 The presence of this ion has been advanced to explain the increased sensitivity to detonation upon UV irradiati0n.I’ It has been experimentally inferred from fast H/D exchange between the do and d3isotopomers of nitromethane induced by moderated static
+
+
+
+
+
* To whom correspondence should be addressed.
’ Laboratoire de Physicochimie Thbrique.
Laboratoire de Spectroscopie Mol6culaire et Cristalline.
pressure (2.1 GPa) and temperature (354 K) or by adding a small amount of organic base, as evidenced by spectroscopic techniques (Raman and NMR).12 The enhancement of the proton-transfer rate of D2O solvent in nitromethane solution by vibrational excitation in the C H stretch overtone (Au = 3) band at 8730 cm-I has also been related to the presence of the nitronate ion.I3 Therefore, it turnsout that a careful study of themethyl moiety, in particular that of the highly excited v(CH) vibrational states,I4 could provide some information to elucidate the initial chemical mechanism of decomposition, including means by which intramolecular energy-transfer processes can occur. Actually, one interesting peculiarity of the methyl group in nitromethane is the low value of the potential barrier to internal rotation which varies from 2.1 cm-I with 6-fold symmetry in the gas phase15 to 270 cm-l with 3-fold symmetry in the solid The motion is thus essentially free at normal temperature and remains fast, even in the solid phase ( 7 = 1 ps at 150 K).20 Its coupling with the other vibrations, especially with the CH stretching modes, could affect the vibrational energy redistribution and thus the nitromethane reactivity. The geometry of nitromethane has been determined both experimentally21-26 and theoretically.2c29 All the studies agree with a slightly more stable staggered conformation of the methyl group in the gas as well as the solid phase (Figure 1). The vibrational spectra of various isotopic derivatives of nitromethane have been investigated repeatedly in all physical state^.^^-^^ A reliable assignment of the fundamental vibrations has been done by correlation between the different 2H, l5N, and I8Oisotopomers and ab-initio calculated frequencies. However, there are some remaining ambiguities in the methyl mode assignments due partly to the presence of isotopic impurities in the dl and d2 derivatives in several studies and to the neglect of the effects of the internal motion. Indeed, the partial deuteration lowers the symmetry of the molecule such that new uconformersn which appear are spectroscopicallyobservable in spite of the very low barrier to rotation.18JOJ4 These rotamers give rise to band splittings which can be reproduced by the introduction of methyl
0022-3654/93/2097-4262$04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 . 4263
Asymmetric Methyl Rotor Dynamics
TABLE I: Calculated and Experimental Geometries of Gaseous CHJNOz (Bond Lengths in A and Angles in deg) 6-31G*
experimental C-N C-H I C-HI C-H3 N-01 N-02 NCHj NCH2p CNOi CNOz OiNO2
6-31G**
6-31G**
e
6-3 1+ + G ( ~ , P ) ~
gaso
solidb
stag
eclip
stag
eclip
stag
eclip
stag
eclip
1.489 (1.089) (1.089) (1.089) 1.224 1.224 107.5 107.5 117.35 117.35 125.3
1.48 1 1.093 1.092 1.092 1.223 1.227 106.4 108.1 118.2 118.0 123.7
1.478 1.os0 1.076 1.076 1.192 1.192 106.5 108.0 117.1 117.1 125.8
1.479 1.076 1.079 1.079 1.191 1.193 108.4 107.0 117.7 116.5 125.3
1.478 1.0808 1.0767 1.0766 1.1916 1.1917 106.6 107.9 117.1 117.1 1.25.7
1.478 1.0758 1.0792 1.0792 1.1907 1.1925 108.4 107.0 117.7 116.5 125.7
1.478 1.0802 1.077 1 1.0772 1.1917 1.1917 107.3 107.6 117.1 117.1 125.7
1.478 1.0765 1.0788 1.0788 1.1910 1.1923 107.8 107.3 117.7 117.5 125.7
1.48 1 1.0799 1.0770 1.0770 1.1926 1.1926 107.1 107.5 117.2 117.2 125.6
1.481 1.0765 1.0788 1.0788 1.1918 1.1934 107.7 107.2 117.8 117.6 125.6
0 References 21 and 23 (bond length, to be planar.
0.005
A; angle, *0.5').
References 24 and 26. Reference 27. Fully optimized. C-NO2 constrained n
rotor potentials of lower than 3-fold symmetry. The leading terms of these new potentials are of the form V2 cos(28) V4 cos(48).1s920~34 It was suggested that the V2 and V4 terms were actually pseudopotentials resulting from vibrational contribution rather than from the torsional kinetic energy e f f e ~ t . ] ~ ~ ~ ~ ~ ~ ~ The purpose of this paper is to calculate the zero-point vibrational energy angular variation and to analyze its effect on the rotational potential of the methyl group. The theoretical results will be compared with the empirical parameters deduced from experiment in ref 34. We have thus calculated ab-initio vibrational frequencies for the do, d l , and d2 derivatives of nitromethane for the principalconformationsof the methyl group (a) (b) and compare them with the experimental gas-phase frequencies. Figure 1. Nitromethane equilibrium conformations: (a) staggered and In order to obtain a complete experimental data set, the Raman (b) eclipsed. gas-phase spectra have been recorded for the first time in this work. gradient method of Bern~.~OVibrational frequencies were obtained by determiningsecond derivatives of energy analytically In addition, the variation of the CH bond length during the with respect to geometry distortions. methyl group rotation is particularly studied in order to verify whether it presents a precise correlation with the experimental Results and Discussion CH stretching f r e q u e n ~ i e s . ~ ~ - ~ ~ Determination of the Stable Geometry. Determination of the Experimental Section stable geometry of nitromethane concerns the orientation of the methyl group hydrogens relative to the CNOl plane and the Syntheses and Spectra. The isotopic derivatives CHzDNO2 coplanarity of the C N 0 1 0 2moiety (Figure 1). The 6-31G** and CHD2N02 were obtained by reaction of suitably labeled calculation gives the same qualitative answers as those already methyl iodide with solid silver nitrite at room temperature. The found with lower level basis sets.27-29 The theoretical fully more volatile reaction product, methyl nitrite, was removed by optimized stable configuration (total energy 243.666 887 1 fractional condensation. The compounds were then distilled under Hartrees) is found to have a methyl group hydrogen staggered partial vacuum. The isotopic purity, as checked by mass relative to the CNOl plane and presents a certain nonplanarity spectrometry, was higher than 98%. of the CNOlO2 moiety, the corresponding angle between the The Raman spectra were recorded with a 224 DILOR triple C-N bond and the NO102 plane being 1.7O, similar to that found monochromator equipped with a Hamamatsu R943-02 Peltier with the 6-31G basis.28 The energy differenceof 0.006 kcal/mol effect refrigerated photomultiplier. A Spectra Physics 171 argon between the staggered and eclipsed conformationsis lower than ion laser (514.5 nm beam at 3 W), filtered by a Photo-Physics those previously calculated with lower basis sets (0.01-0.03 kcal/ laser monochromator, was used as the exciting radiation. The gaseous compounds were transferred under vacuum into a Though this energy differenceis not significant, it can be noted that it is equal to the measured rotational barrier of cylindrical Pyrex cell equipped with two windows tilted at a nitromethane.21 Brewster angle for mutiple reflections. The resolution was 1 Geometrical parameters for both staggered and eclipsed fully cm-1. In the cell, the gas-phase pressure in equilibrium with the optimized forms are given in the column d of Table I. These liquid was 35 mmHg at 298 K. results are similar to those obtained by McKee et al.27with the The infrared spectra were recorded with a Fourier transform 6-31G* basis set (column c of Table I). In order to decrease the infrared spectrometer (Nicolet 740) and a 100-mm-path length number of optimized parameters and to keep a C, molecular gas cell equipped with CaF2 windows under a pressure of 35 symmetry, we have constrained the CNO102moiety to be planar mmHg at 298 K. (column e of Table I). Method of Calculation. The ab-initio molecular orbital Going from the6-31G** (columneofTable1) tothe6-31++Gcalculationswere performed with the GAUSSIAN 88 program3g (d,p) (column f of Table I) basis set, the C-N bond shows the using the 6-31G** basis set. In this basis, polarization functions largest change with a lengthening of 0.003 8, and comes up to are added on heavy and hydrogen atoms to the standard 6-3 1G the experimentalvalue derived from the microwave spe~trum~l-23 basis set. Polarization functionson hydrogens could improve the and from X-ray and neutron diffraction data.24,26In comparison, C-H vibrational frequency calculations. We have also used the the N-0 bonds are only lengthened by 0.001 8, and the C-H 6-3 1++G(d,p) basis set which adds diffusefunctionson all atoms bonds are not changed. The valence angles are insensitive to the of the previous basis set in order to check the effect on t h e N-0 basis set and reproduced to within 0.2O. A good agreement is vibrational frequencies. Geometry was optimized using the energy
+
4264
Gorse et al.
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
TABLE II: Calculated and Experimental Gaseous Frequencies of CHJNO~(in cm-l) 6-31G*'
eclipsed 6-31G**
6-31G8
3371.4 3353.9 3249.1 1879.1 1687.9 1611.7 1586.9 1556.2 1265.1 1222.2 1050.0 736.0 702.0 524.4
3404 3369 3272 1880 1689 1620 1607 1571 1271 1233 1052 744 690 529
3404 3367 3274 1880 1688 1619 1609 1570 1270 1232 1051 736 702 527
staggered 6-31G** 3372.7 3354.1 3248.5 1879.1 1688.4 1612.1 1585.5 1557.7 1266.6 1222.0 1050.6 743.5 691.1 528.3
6-31++G(d,p)
mean freq 6-31G**
3373.6 3355.8 3249.6 1839.3 1678.1 1608.5 1582.8 1556.3 1264.5 1220.5 1042.9 737.2 688.1 525.9
3071.9 3055.5 2959.6 1569.1 1401.2 1437.9 1414.9 1388.8 1129.0 1090.1 919.0 659.8 606.0 469.5
observed freq,' cm-' infrared Raman 3080 3045 2974 1583 1397 1434 1410 1380 1131 1096 918 657 603 475
Scaled frequencies: v(CH3) X 0.91 1; v(NO2) X 0.835; v(CN) X 0.875; B,r(CH3), b,r(N02) 0 Reference 27. frequencies in the gas phase (IR, ref 33 and this work; Raman, this work).
1.079
a
v
1.078
1.077
1.076 0
I
1
I
1
45
I
1
I
I
90 teta O
I
I
I
1 135
I
I
I
180
Figure 2. Calculated C-H bond length of nitromethane ( 0 )for various torsional angles (0 in degrees) and its representation by eq 1 (-).
obtained between theoretical and experimental gaseous values. The less confident part of the theoretical geometry is the N-0 bond lengths (ArexFcalc3 0.03 A). This is not unexpected given the known difficulty in describingnitro group properties starting from a single Slater determinant d e s c r i p t i ~ n . ~ ~ ~ ~ ~ We have also studied the geometry variations as a function of the methyl group conformation. The greatest variations involved by the rotation of the methyl group concern the C-H bond length with a maximum changeof 0.0037 A going from the perpendicular to the parallel positions of this bond with respect to the NO2 plane. A similar difference (O.OO32 A) was calculated for toluene4' whereas a maximal variation of only 0.0014 A was calculated for the rotating methyl group in propane.37 This large change may be related to an effect of hyperc~njugation~~ and correlated with thevariation of the electronic chargeof the hydrogen atoms (from 0.1871 to 0.1803 for a "perpendicular" and a "parallel" C-H bond, respectively) and with the angular distortion due to the electron withdrawal by the nitro g r o ~ p . 2The ~ C-H bond length variation is well reproduced with a cosine function of the rotational angle 8 (Figure 2)
r(8) = ro + r l cos(28) + r2 cos(48) with ro = 1.0780 A, rl = -1.8 f 0.2 10-3
A.
(1)
A, and rz = 0.24 f 0.02
A similar cosine angle dependence was also evidenced for the three C-H bond lengths of the methyl group in propane, but with a much slower convergence possibly due to the less accurate calculation of the bond lengths.3* The authors noted that a more detailed analysisof the effect of methyl rotation on the vibrational spectrum is required to make the comparison with experiment
1380 1094 918 657 475
0.892; w(NO2) X 0.87. Observed
more quantitative. This quantitative study can be achieved in the CHDzNOz case as developed in the following paragraph. Indeed, the lone CH stretching mode is localized to such a degree that its frequency accuratelyreflects the subtle distinctions among the different conformations of the C-H bond. However, the calculationaccuracy isof utmost importanceas a 10-3-Avariation of the C-H length corresponds to a 10-18-cm-I variation of the stretching Vibrational Frequencies. The vibrational frequencies of CH3NO2 calculated with two different basis sets (6-31G** and 6-31++G(d,p)) are compared in Table I1 with the previously calculated ones (6-31G*)27and with the infrared and Raman gas-phase frequencies. (It can be noted that the Raman spectrum shows particularly the symmetric modes.) There is a trend toward smallerCH3modefrequenciesongoingfrom6-31G* to6-31G**, while the NO2and CN mode frequenciesare unchanged. When adding diffuse polarization functions (6-3 1++G(d,p)), the NOz and CN mode frequencies decrease, which parallels the observed bond lengthening (Table I), while the CH3 mode frequencies are not significantly changed. As we are essentially interested in the CH vibrational modes, the vibrational frequencies are only calculated in the 6-31G** basis set for the two other isotopic compounds, CHDzNOz and CHzDN02 (Tables I11 and IV). For all the isotopomers,both eclipsed and staggeredgeometries are found to be rotational transition states; Le., they have one negative eigenvalue for the torsional frequency, as expected for a quasi-free rotating methyl group. The observed spectra will thus result from an average over all torsion angles. However, the variation of the C-H bond length, as evidenced above (Table I), involves a dependence of the CH stretching frequencies on the equilibrium position of the methyl group. Some experimental proof of this effect has been given in several previous studies of partially deuterated nitromethanes not only in the solid phase where the rotation of the methyl group is hindered by a relatively high barrier essentially due to the intermolecular forcesI7J0J3 but also in gas phase where the methyl group is practically a free rotator.34 In order to examine the effects of the methyl group rotation, the vibrational frequencies have been calculated with the lone deuterium or hydrogen atom at all the different positions of the two equilibrium conformationsof the partially deuterated methyl groups (Tables I11 and IV). As usually found in ab-initio calculations, the theoretical frequencies are all too large as compared with the experimental ones (Tables 11-IV). The experimental frequencies here considered are those measured in the gas phase which are more appropriate for a comparison with calculated values than those measured in the liquid or solid phase where the effects of the intermolecular forces modify the vibrational frequencies and increase strongly the methyl group rotational barrier. 173203 Some
8
"081 1.080
X
2972 1584 1396
mode va(CH3) Js(CH3) vs(CH3) va(N02) vs(N02) 6's(CH3) Ja(CH3) 6s(CHd rl(CH3) rII(CH3) V(CN) W02) ~(N02) r(N02)
Asymmetric Methyl Rotor Dynamics
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4265
TABLE 111: Calculated (6-31C**) and Experimental Gaseous Frequencies of CHD2NO2 -
Y D
(e =
DYH D
H
D
Di
(0 = 300)
(e = 600)
(0 = 90°)
3345.8
3339.8
3320.4
2491.7 2375.7 1875.8 1687.3 1440.3 1435.7 1162.2 1096.0 1069.4 1004.7 709.1 624.9 491.7
2496.2 2376.9 1873.8 1687.3 1440.0 1427.4 1169.8 1107.7 1045.0 1005.8 719.9 619.6 494.7
2503.8 2384.1 1871.1 1687.1 1436.8 1411.1 1182.8 1116.6 1023.3 991.7 716.7 646.1 483.6
3307.8 3307.8 2508.5 2390.1 1868.8 1687.2 1436.5 1401.7 1188.6 1121.5 1022.2 976.2 710.9 661.9 480.8
00)
mean freq, cm-I
scaled freq,' cm-I
3328.4
3032.2 3013.4 2302.6 2193.6 1563.5 1408.8 1283.0 1265.7 1048.8 990.5 909.8 887.2 637.1 555.1 435.1
2500.1 2381.7 1872.4 1687.2 1438.4 1419.0 1175.8 1110.4 1039.8 994.6 714.2 638.1 487.7
observed freq,b cm-1 infrared Raman 3028.5 3013.5 2300 2194 1574 1388 1283 1264' 1057 988 895 888' 640 559 443
mode
3029 3014 2195 1572 1388 1283 1060 985 894 640 559 443
Scaled frequencies as in Table I1 (v(CD2) X 0.921). Observed frequencies in the gas phase (IR, refs 33 and 34 and this work; Raman, this work). Solid phase.
TABLE IV Calculated (6-31G**) and Experimental Gaseous Frequencies of CHzDNOz H
b
HYD H
H
(e =
00)
3353.8 3283.4 2452.2 2452.2 1873.3 1687.4 1573.7 1446.1 1419.2 1210.3 1063.1 1002.4 722.8 691.4 496.1
(0 = 30")
HgH D (0 = 6001
(e = 900)
mean freq, cm-I
scaled freq," cm-1
3358.6 3281.7
3368.2 3294.3
3371.2 3302.0
3363.0 3290.4
2446.5 1874.0 1687.1 1581.5 1449.9 1412.5 1206.2 1073.7 1008.5 723.4 680.2 500.8
243 1.4 1877.2 1687.6 1594.2 1453.3 1401.3 1193.4 1097.1 1022.5 729.8 655.7 507.7
2420.0 1878.1 1687.5 1599.9 1456.0 1396.1 1186.1 1111.4 1030.8 742.0 625.2 523.3
2437.5 1875.7 1687.4 1587.3 1451.3 1407.3 1199.0 1086.3 1016.0 729.5 663.1 507.0
3063.7 2997.5 2258.4 2245.0 1566.2 1408.9 1415.9 1294.5 1255.3 1069.5 969.0 889.0 650.7 576.9 452.2
J
H
observed freq,b cm-' infrared Raman 3071 3002 2266 1578 1387 1426 1288 1258 1068 957 898 651 579 454
mode
3004 2276 2267 1578 1388 1415 1287 1258 957 898 65 1 454
Scaled frequencies as in Table 111. Observed frequencies in the gas phase (IR, ref 35 and this work; Raman, this work).
calibration factors are thus calculated for the groups of the same type coordinates and averaged on the three isotopomers. Agreement between scaled 6-31G** values and observed frequencies is exceptional with an average difference less than 7 cm-I. Most of the discrepancy comes from the NO2 stretches. As already pointed out, the NO2 stretching error may be due to a neglect of the second contributing c o n f i g u r a t i ~ n . ~ ~ . ~ ~ CH3N02.Compared mode for mode, the vibrational frequencies of the staggered and eclipsed conformations have nearly the same values at the same computational level. They are in good agreement with the experimental ones and confirm well the given assignments.30933J5 Somediscrepanciesbetween calculatedand experimental values for the u(CH3) and 6(CH3) modes could berelated to thedifficulty encountered in precisely localizing these modes in the gas-phase infrared spectrum owing to the complex rotation-vibration band structure. However, the assignment of the A structure band at 2974 cm-1 to the vs(CH3) mode is confirmed by theoretical calculations and by the Raman spectrum which exhibits only a strong band at 2972 cm-' (Figure 3). In addition, the oftenquoted presence of a Fermi r e s o n a n ~ e ~ Obetween , ~ ~ , ~ ~this mode and the strong infrared combination bands v,(N02) + u,(N02) and va(N02) 6,(CH3) at 2959 and 2951 cm-I is ruled out as these combination bands do not appear in the Raman spectrum (Figure 3). Several previous studies have assigned the minimum of the weak B structure band at 3080 cm-' to the u,(CH3) and the C structure band with numerous Q branches centered at 3045
+
cm-l to the v',(CH3) mode.30x33Calculations agree with these assignments (Table 11). The scaled zero-pointvibrational energy of the 3N- 7 vibrations other than the internal methyl group rotation is of 10 590 f 2 cm-1 and shows no angular dependency within calculation uncertainty. CHD2NO2. The vibrational frequencies are calculated with the lone hydrogen nucleus at all the four equilibrium positions corresponding to a rotation angle 0 of Oo, 30°, 60°, and 90° of the C-H bond with the molecular plane (Table 111). The v(CH) mode presents a maximum for the parallel position (0 = Oo) and a minimum for the perpendicular position (e = 90°) with a frequency difference of 34.6 cm-I. The scaled zero-point CH stretching energy can be written (Figure 4)
with YO = 3032 f 1 cm-1, V, = +17.5 & 1 cm-I, and V4 = -2.1 f 0.5 cm-I. The theoretical calculations agree well with the assignment of theA structureinfrared bandat 3028.5 cm-l,observedas a strong Raman band at 3029 cm-I, to the mean frequency of the u(CH) mode of the methyl group in quasi-free rotation (Figure 5 ) . It confirms that the weakC structure infrared band at 3013.5 cm-I, observed in the Raman spectrum at 3014 cm-I, corresponds to the v(CH) frequency when the C-H bond is perpendicular to the molecular ~lane.3393~
Gorse et al.
4266 The Journal of Physical Chemistry, Vol. 97,No. 17, 1993 1530
:
,
I
l
I
l
l
I
l
I
I
j 9270 9265
P
= I
9260 9255
p
9250
2
a
7
1500
45
0 3000
2980
2960
-
* 9245
90
9240 160
135
teta
2940 C M - l
Figure 4. Calculated zero-point CH stretching energy ( 0 )and overall zero-point vibrational energy (0) of CHD2N02 for various torsional angles (0 in degrees) and their representations by eq 2 (-) and eq 3 (- - -), respectively. 3029
P 0 v1
$
z
m n
I-
3100 3000 2900 ' CM-1 ' Figure 3. Infrared and Raman spectra of gas-phase CH3N02 in the CH stretching region. 3200
Comparing relations 1 and 2 leads to a frequency change of about 10 cm-I for 10-3-A change of C-H bond length which is lower than the 15 f 1 cm-I found for the C H methyl frequencies of n-alkane~,3~.38 but in good agreement with the variation found for simple organic compounds by M ~ K e a n The . ~ ~calculations predict a variation of the same type as (2) for the intensity of the u(CH) band with a minimum at 8 = ' 0 and a maximum at 8 = 90° for the Raman activity and inversely for the infrared intensity. This intensity variation is difficult to check experimentally in the case of nitromethane. However, the overall consistency of abinitio relative intensity predictions with experimental observations has been recently shown in the case of simple alcohols and thiols.,2 The v,(CD2) and v,(CD2) modes show a minimum for 8 = Oo and a maximum for 8 = 90° with a maximal frequency change of 15 and 13 cm-I, respectively. Apart from the v,(N02) and vs(N02) which are relatively pure modes, all the other modes show a conformational frequency dependence with deviations varying from 3 cm-' (6(CH)) to 41 cm-I (u(CN)), indicating that the internal rotation affects all the vibrational modes containing contributions of the methyl group motions. A further proof of this conformational dependence is given by the scaled zero-point vibrational energy of the 3N- 7 vibrations other than the internal methyl group rotation, which shows a similar cosine dependence as relations 1 and 2 (Figure 4):
E(8) = E,
+ I/*(v2 COS(~B) + v4COS(~B))
(3)
with Eo = 9256 f 1 cm-I, V2 = +22.2 f 1 cm-I, and V, = -2.4 f 0.5 cm-I. These parameter values agree with those previouslydetermined from a conventional force field calculation (Eo = 9234 cm-I, V2 = +26.7 cm-1, V4 = -3.8 ~m-I).~3They correspond to an
3050
3660
3610
3030
3010
CM-I
3020
3028.5
3200
3100
3000
2900
--
CM-1
Figure 5. Infrared and Raman (-, experimental; -,calculated from eq 4) spectra of gas-phase CHD2N02 in the CH stretching region ( V I , ~ 2 and , Y,: cf. Figure 6 ) .
equilibrium staggered stable conformation of the methyl group with the lone C-H bond perpendicular to the NO2 plane (Figure 4). A comparison of relations 2 and 3 shows that, as suggested in previous gas study of CHD2N02,34the greatest part of angular variation of the overall zero-point vibrational energy is shown to be essentially due to the C H stretching mode, the contributions of all the other vibrations canceling each other. The V2 and V, parameter values are comparable to those estimated in ref 34 (V2 = 21 cm-1, V4 = 2 cm-I), thesignof V,being difficult todetermine experimentally. The quantum theory developed in ref 34 allows to calculate the u(CH) transitions between the effective rotational potentials in the vibrational ground state ( u = 0) and the first excited v(CH)
The Journal of Physical Chemistry, Vol. 97, No. 17. 1993 4267
Asymmetric Methyl Rotor Dynamics :
5
t
-1 -$
0
c
3 =:
5
20
o
p
= ff
-20 (a1
-40
-60
1
E -3
I
-80
1
9945
1130
h
s
1125
f
8
'1
1120 1115
P
1110
A
-20
-1 00 90
0
180
270
0
360
30
t
' ' '
'
45
' ' '
'
90
' ' '
'
' -_
9915 180
135
tera
tela (")
701
1105
T
60
20
50
10
40
O
fn
30
-10
5
20
-20
10
-30
0
-40
1
I
Figure 7. Calculated zero-point CD stretching energy ( 0 )and overall zero-point vibrational energy (0)of CH2DN02 for various torsional angles (0 in degrees) and their representations by eq 5 (-) and eq 6 (- - -), respectively.
0
f: 8' 0.
n
$
-50
10 I
0
I
90
1b o
2jO
360
tela (")
Figure 6. Calculated effective potentials of internal methyl group rotation in the ground vibrational state ( u = 0) (-) and in the first excited C H or CD stretching vibrational state ( u = 1) (- - -) in gaseous (a) CHD2NO2 and (b) CH2DN02 ( V I , v2, and vm: cf. Figures 5 and 8). The squares of the internal rotation wave functions. (e-)
vibrational state (v = 1) (Figure 6a):
= Il2v6( 1 - COS 68) + E(8) + vv,,(8)
(4)
with V , = 2 cm-I, E(0) given by (3), and u ~ ~ ( given 0 ) by (2). Assigning a Lorentzian profile to each transition allows to reproduce the isotropic v(CH) Raman spectrum. As shown in Figure 5 , a good agreement between experimental and calculated spectra is found by using the VZ and V4 ab-initio parameters values found with relations 2 and 3. This shows that the calculations of the differences in zero-point energy between rotamers are sufficientlyaccurate to provide a correct reproduction of the experimental results. CH2DN02. The vibrational frequencies are also calculated with the lone deuterium nucleus at all the four equilibrium positions corresponding to a rotation angle 8 of,'O 30°,60°, and 90' of the C-D bond with respect to the molecular plane (Table IV). The v(CD) mode presents a maximum for the parallel position (e = 0') and a minimum for the perpendicular position (0 = 90') with a frequency difference of 29.6 cm-I, the mean u(CD) frequency during the quasi-free rotation of the methyl group being 2245 cm-I. The scaled zero-point CD stretching energy can be written (Figure 7) I
/2vcD(e)
= 1/2v0+
cos(2fl) + V4 COS(48))
(5)
with v0 = 2245 f 1 cm-1, V, = +14.6 f 1 cm-I, and V4 = -1.7 f 0.5 cm-I. The Raman gas-phase spectrum exhibits two bands at 2226 and 2267 cm-I with a weak shoulder at 2276 cm-I, whereas in the infrared spectrum only one B structure band is seen at 2226 cm-l with a very weak shoulder at 2266 cm-I (Figure 8). The
2300
2240
2180
2120
2060 CM-'
--
Figure 8. Infrared and Raman (-, experimental; -,calculated from eq 7) spectra of gas-phase CH2DN02 in the CD stretching region ( V I , v2, and vm: cf. Figure6). Insert: the infraredgas-phaseCH~N02spectrum in the same spectral region.
structure of the infrared band observed at 2266 cm-I precludes its assignment to the mean frequency of the v(CD) mode of the methyl group in quasi-free rotation which should be of A type of the v(CH) band in the d2 compound. In addition, the observation of a similar band at the same frequency in the infrared CHjN02 spectrum (Figure 8) leads us to assign this infrared and Raman band to a combination band v,(NOz) + 6(N02). The Raman band at 2267 cm-I and the weak infrared feature at 2266 cm-1 are assigned to the mean frequency of the v(CD) mode (Table IV). The v,(CHz) and u,(CHz) modes show an inverse behavior with a maximum frequency change of only 18 and 16 cm-I, respectively (Table IV). These calculations agree with our observation of the v,(CH2) band at 3004 cm-l in the gas-phase Raman spectrum corresponding to the 3002-cm-l infrared band (Figure 9). They indicate that the v,(CH2) frequency value is
Gorse et al.
4268 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 3004
vibrational state presents a lower barrier and a changed equilibrium position comparedto the groundvibrational state potential (Figure 6b). The isotropic u(CD) Raman spectrum calculated by using the ab-initio Vz an V4 parameters values found with relations 5 and 6 shows again a good agreement with the experimental one (Figure 8). These calculations show that the transitions 10,O) ll,O), and l0,l) 11,2), coming from the two lowest internal rotational levels with wave functions localized around 8 = Oo, are responsible for the weak shoulder observed at 2276 cm-I in the Raman spectrum. This feature can thus be assigned to the mean v(CD) frequency when the C-D bond is around a position parallel to the molecular plane. As already noted in several previous these calculations show that, in gaseous nitromethane, the hindering potential of the methyl group internal rotator has essentially an electronic origin, the overall zero-point vibrational energy effect on the barrier being very small in the case of symmetric rotor as shown by the only slight difference measured between CH3N02 and CD3N02 compounds (V, = 2.1 and 1.8 cm-I, respectively).23 However, when the dynamic symmetry of the methyl group is reduced by substitution of one or two deuteriums for hydrogens, additional lower symmetry terms Vz and V4 must be introduced into the effective hindering potential. The vibrational origin of these terms is confirmed by the calculations, the effect of the isotope dependence of the kinetic energy or of the torsionalrotational coupling being negligible4H6as concluded in a recent theoretical study of the partially deuterated acetophenone~.~6 The overall zero-point vibrational energy variation becomes then the principal term of the effective potential, leading to different equilibrium conformations for each isotopomer, a staggered one for the d2 compound and an eclipsed one for the dl compound (Figure 6). In addition, the calculations corroborate the previously developed theory34 relating the u(CH) splitting observed in the gaseous CHDzNOz spectra to the nonlocal character of the methyl group torsion which gives rise to dependence on the torsional angle of the zero-point energy of modes other than the torsion and more particularly that of the CH stretching mode. It permits a more accurate assignment of the CH2DNO2 spectra, in particular in the u(CD) region.
-
3050
3000
2950
CM-l
5
3200
3000
3100
2950
CM-l
Figure 9. Infrared and Raman spectra of gas-phase CHzDNOz in the CH stretching region.
rather of about 3071 cm-I than 31 15 cm-I as assigned in ref 35. Apart from the u,(NO2) and us(N02) which are relatively pure modes, all the other modes show a conformational frequency dependence with deviations varying from 9 cm-I (w(CH2)) to 57 cm-' ( ~ ( N O Z ) )indicating , that the internal rotation affects all the vibrationalmodes containing contributionsof the methyl group motions. The scaled zero-point vibrational energy variation of the 3N - 7 vibrations other than the internal methyl group rotation shows again a similar cosine dependence as found for the d~ derivative (3) (Figure 7):
E(8) = E,
+
v,COS(B) + v4 COS(^^))
(6)
with EO = 9927 f 1 cm-I, V2 = -24.8 f 1 cm-I, and V4 = 2.1 f 0.5 cm-I. Comparison of relations 3 and 6 shows that the V, and V, parameters found for CH2DNO2 are nearly equal and of opposite sign to those calculated for CHD2N02, in good agreement with symmetry considerations, and correspond to an equilibrium eclipsed stable conformation of the methyl group with the lone C-D bond in the NO2 plane (Figure 6). If the Raman spectrum of the lone u(CD) is analyzed as that of the lone u(CH) in CHDzN02, the effective rotational potentials in the vibrational ground state ( u = 0) and in the first excited u(CD) state can also be written (Figure 6b)
v,(e)= 1 / 2 ~ 6 (-COS 1
68)
+ E(8) + D u c D ( e )
(7) with V6 = 2 cm-I, E(8) given by (6),and ucD(8)given by (5). Contrary to what happens for CHDzNOz (relation 4), the V2 and V4 parameters of E(0) and uco(8) have opposite signs so that the effective rotational potential of the first excited u(CD)
-
Conclusion
Ab-initio results predict the methyl group staggered conformation lightly more stable than the eclipsed one in nitromethane (0.006 kcal/mol). Vibrational frequencies of -the different conformershave been calculated for the do, d ~and , d2 isotopomers. They are in good agreement with the infrared and Raman gaseous values and allow a precise assignment of the spectra. The overall zero-point vibrational energy differences between the rotational conformers have been calculated. Calculations confirm the vibrational origin of the V2 and V4 pseudopotential terms which must be added to the rotational potential of the partially deuterated methyl group. The so-determined pseudopotential terms lead to different equilibrium conformers for the dl and dz isotopomers and to a good reproduction of the lone u(CH) and u(CD) isotropic Raman spectra. The close correspondence between calculated and experimental results suggests that the calculations are reasonably accurate. For the d2 compound,the u(CH) frequency variation is shown to represent the greatest part of the zero-point vibrational energy differences between the rotamers. The correlation found between C-H bond length and calculated frequency shift as a function of the internal rotation angle agrees qualitatively and quantitatively with the experiments. Acknowledgment. The authors are grateful to R. Cavagnat for assisting with the Raman measurements and to M. F. Lautie for her help in the deuterated compounds synthesis. They also thank the CIRCE/CNRS for calculation facilities.
Asymmetric Methyl Rotor Dynamics
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4269
References and Notes ( I ) Butler, L. J.; Krajnovich, Q.; Lee, Y. T.; Ondrey, G.; Bersohn, R. J . Chem. Phys. 1983, 79, 1708. (2) Roszak, S.; Kaufman, J. J. J . Chem. Phys. 1991, 94, 6030 and references therein. (3) Blais, N. C. J . Chem. Phys. 1983, 79, 1723. (4) Moss, D. B.;Trentelman, K. A,; Houston, P. L.J. Chem. Phys. 1992, 96, 237. (5) Lao, K. Q.; Jensen, E.; Kash, P. W.; Butler, L. J. J. Chem. Phys. 1990, 93, 3958. (6) Phillips, D. L.; Myers, A. B. J . Phys. Chem. 1991, 95, 7164. (7) Zabarnick, K. S.; Fleming, J. W.; Baronauski, A. P. J . Chem. Phys. 1986,85, 3395. (8) Jacox, M. E. J . Phys. Chem. 1983,87, 3126. (9) McKee, M. L. J . Am. Chem. SOC.1986, 108, 5784. (10) KO,T.; Flaherty, W. F.; Fontijn, A. J . Chem. Phys. 1991, 95,6967. (1 1) Engelke, R.; Earl, W. L.; Rohlfing, McM. C. J . Phys. Chem. 1986, 90, 545 and references therein. (12) Engelke, R.; Shifferl, D.; Storm, C. B.; Earl, W. L. J. Phys. Chem. 1988, 92, 6815. (13) Goodhall, D. M.; Chetwood, I. Chem. Phys. Lett. 1986, 129, 291. (14) Cavagnat, D.; Lespade, L. To be published. (15) Tannenbaum, E.; Myers, R. J.; Gwinn, W . D. J . Chem. Phys. 1956, 25, 42. (16) Cavagnat, D.; Lascombe, J.; Lassegues, J. C.; Horsewill, A. J.; Heidemann, A.; Suck, J. B. J. Phys. (Paris) 1984, 45, 97. (17) Cavagnat, D.; Magerl, A.; Vettier, C.; Anderson, I. S.;Trevino, S. F. Phys. Reu. Lett. 1985, 54, 193. (18) Cavagnat, D.; Brom, H.; Nugteren, P. R. J . Chem. Phys. 1987,87, 801. (19) Rice, B. M.; Trevino, S.F. J . Chem. Phys. 1991, 94, 7478. (20) Cavagnat, D.; Lascombe, J. J . Phys. (Paris) 1983,44, 67. (21) Cox, A. P.; Waring, S.J . Chem. SOC.,Faraday Trans. 2 1972, 1060. (22) Cox, A. P. J. Mol. Struct. 1983, 97, 61. (23) Sorensen, G. 0.;Pedersen, T.; Dreizler, H.; Guarnieri, A.; Cox, A. P. J. Mol. Struct. 1983, 97, 77. (24) Trevino, S.F.; Prince, E.; Hubbard, C. R. J . Chem. Phys. 1980, 73, 2996. (25) Cromer, D. T.; Ryan, R. R.; Schifferl, D. J . Phys. Chem. 1985,89, 2315. (26) Jeffrey, G. A,; Ruble, J. R.; Wingert, L.M.; Yates, J. H.; McMullan, R. K. J. Am. Chem. SOC.1985, 107, 6227.
,
(27) McKee, M. L. J . Am. Chem. SOC.1985. 107. 1900. (28) Bock, C. W.; Krasnoshchiokov, S.V.;Khristenko, L. V.;Panchenko, Yu. N.; Pentin, Yu. A. J . Mol. Strucr. (THEOCHEM)1987, 149, 201. (29) Engelke, R.;Schifferl, D.; Earl, W. L. J. Mol. Stmct. (THEOCHEM) 1988, 180, 141. (30) Jones, W. J.; Sheppard, N. Proc. R. SOC.London 1968, ,4304, 135. Sheppard, N.; Woodman, F. R. S. and C. M. Proc. R. SOC.London 1969, A313, 149. (31) Verderame, F. D.; Lannon, J. A.; Harris, L. E.; Thomas, W. G.; Lucia, E. A. J. Chem. Phys. 1972, 56, 2638. (32) Trinquecoste, C.; Rey-Lafon, M.; Forel, M. T. Spectrochim. Acta 1974, A30, 813. (33) McKean, D. C.; Watt, R. A. J. Mol. Spectrosc. 1976, 61, 184. (34) Cavagnat, D.; Lascombe, J. J . Mol. Spectrosc. 1982, 92, 141. (35) Hill, J. R.; Moore, D. S.; Schmidt, S. C.; Storm, C. B. J . Phys. Chem. 1991, 95, 3037 and references therein. (36) McKean, D. C. J . Mol. Struct. 1984, 113, 251. (37) Snyder, R. G.; Aljibury, A. L.; Straws, H. L.; Casal, H. L.;Gough, K. M.; Murphy, W. F. J. Chem. Phys. 1984,81, 53. (38) Aljibury, A. L.; Snyder, R.G.; Straws, H. L.; Raghavachari, K. J . Chem. Phys. 1986, 84, 6872. (39) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A. GAUSSIAN 88; Gaussian Inc., Pittsburgh, PA, 1988. (40) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem. Symp. 1979, 13, 225. Schlegel, H. B. J. Compur. Chem. 1982, 3, 214. (41) Pang, F.; Boggs, J. E.; Pulay, P.; Fogarasi, G. J . Mol. Srrucr. 1980, 66, 281. (42) Williams, G. A.; MacDonald, J. N.; Dunn, K. M.; Boggs, J. E. Spectrochim. Acta 1992, 48A, 783. (43) Cavagnat, D.; Lautie, M. F. J . Raman Spectrosc. 1990, 21, 185. (44) Chang, T. L.; Quade, C. R. J. Mol. Spectrosc. 1985, 111, 398. (45) Chun Fu Su;Liu, M.; Quade, C. R. J . Mol. Spectrosc. 1991, 146, 264. (46) Siebrand, W.; Zgierski, M. Z.; Zerbetto, F.; Lim, E. C. J . Chem. Phys. 1992, 96, 7973.
