1. VIBRATIONAL ANHARMONICITY IN ETHYLENE, METHYL FLUORIDE, AND DICHLOROMETHANE: AN EXPLORATION USING GAUSSIAN 03
NORMAN C. CRAIG, Department of Chemistry and Biochemistry, Oberlin College, Oberlin, OH 44074, USA
MARK M. LAW, Department of Chemistry, University of Aberdeen, Meston Walk, Aberdeen AB24 3UE, U. K..
DONALD C. MCKEAN, School of Chemistry, University of Edinburgh, Edinburgh EH9 3JJ, U. K.

2. Vibrational Modes of Methylene Chloridea
Symm. Species
Mode
Approx. Descript.
Wavenumber/
cm-1 a1 n1
sym. CH2 stretch n2
sym. CH2 bend
1435.0 n3
sym. CCl2 stretch
712.9 n4
sym. CCl2 bend
281.5 a2 n5
CH2 twist
1153 b1 n6
asym. CH2 stretch
3055 n7
asym. CH2 bend
898.66 b2 n8
CH2 rock n9
asym. CCl2 stretch
759.82
a Duncan, J.L.; Nivilleni, G. D.; Tullini, F. J. Mol. Spectrosc.
1986, 118, 145.

6. Comparisons of QC-Calculated Anharmonic Corrections
Di = wi – ni (cm-1) to Fundamental Frequencies for C2H4
Mode
nobsda
Ddtz+b
Ddccb
Dmtz+b
Dmccb
DCCSDc
dcc w
("obs")
(calc)
n1 Ag
3022.0
131.4
128.7
138.0
135.8
141.2
3150.7
3139.2
n5 B1g
3083.4
136.7
134.7
134.8
136.5
143.0
3218.1
3194.6
n9 B2u
3104.9
139.7
138.2
138.4
139.1
146.2
3243.1
3223.0
n11 B3u
2988.6
189.1
169.6
10.3
-74.3
160.1
3158.2
3125.5
n2 Ag
1625.4
23.1
29.0
24.4
37.8
50.4
1654.4
1693.0
n3 Ag
1343.5
24.2
25.0
35.0
27.1
28.3
1368.5
1282.2
n4 Au
1025.6
22.5
23.3
-6.9
22.1
20.8
1048.9
1067.2
n6 B1g
1222
22.6
4.4
19.5
18.8
1244.6
1246.7
n7 B1u
948.8
14.2
15.4
-50.3
17.3
17.9
964.2
979.0
n8 B2g
939.9
15.9
17.5
1015
14.0
12.4
957.4
983.4
n10 B2u
825.9
2.5
2.4
0.5
1.1
1.3
828.3
836.4
n12 B3u
1442.5
34.1
35.4
50.6
39.4
1477.9
1479.2
a Observed frequency from D. Van Lerberghe et al., J. Mol. Spectrosc. 1972, 42, 251.
b dtz+ = B3LYP/ G**; mtz+ = MP2/ G**; dcc = B3LYP/cc-pVTZ; mcc = MP2/cc-pVTZ.
c From a CCSD(T)/cc-pVTZ calculation: Martin, J.M.L.; Lee, T.J.; Taylor, P.R.; Francois, J-P. J. Chem.
Phys. 1995, 103, Mode numbers as in this reference.
Green: Fermi resonance treated specifically. Red: Fermi resonance not treated.
Blue: Anomaly ascribed to the absence of f functions in the G** basis set, when used in MP2 calculations.

7. Anomalies in Anharmonicity Constants xrs (cm-1) in C2H4
dtz+
dcc
mtz+
mcc
8 2
-5.4
-5.9
8.6
-7.1
8 3
-2.1
-2.3
-18.7
-3.2
8 4
-5.8
-6.2
47.9
-4.7
8 6
5.0
4.3
33.0
6.2
8 7
-0.7
-0.6
125.3
-0.2
8 8
1.7
1.5
465.4
3.2
7 12
-3.1
-3.5
-24.8
-4.5
7 8
11 12
-69.5
-51.6
108.8
192.3
f8888
185
181
7803
225
f1188
-179
-242
-189
f4488
131
127
407
143
f6688 25 22
140 32
Blue: ascribed to the absence of f functions.
Red: Fermi resonance not treated.

8. Methyl Fluoride
Experimental anharmonic constants exist for methyl fluoride,a but deficiencies in the G03 code for degenerate modes prevented making the intended comparison between calculations and experiment.
a M.M. Law; J.L. Duncan; I.M. Mills J. Mol. Struct. 1992, 260, 323.

9. Conclusions
The Gaussian 03 code for the option anharmonic needs substantial revision if this facility is to be generally useful. The 10-cm-1 window for recognizing resonances is too small. Molecules with degenerate modes are handled improperly. (In talk MI12, the failure to ensure use of Cartesian coordinates in the principal axis system in the vib-rot module of G03 was reported.)
B3LYP and MP2 models with triple-zeta quality basis sets can give satisfactory anharmonicity corrections, BUT MP2 calculations using bases without f functions can be quite wrong.
Differing anharmonicity corrections can be found for in-phase and out-of-phase stretching vibrations of C-H bonds. In such cases, different scale factors should be used when scaling harmonic QC force fields to reproduce observed spectra.
For 1,1-difluorocyclopropane, the G03-based anharmonic analysis of combination tones was correct for the d0 and d4 species of C2v symmetry but incorrect for the d2 species of Cs symmetry.