J . Phvs. Chem. 1990. 94. 7040-7055
7040
Consequently, each effect decreases the energy of the lowest lying triplet state relative to the ground singlet state. The net result is an increase in the thermal population of the paramagnetic isomer. This study represents the first example of low-spin to high-spin conversion via pressure-induced changes in molecular
geometry.
Acknowledgment. This work was supported in part by the Materials Science Division, Department of Energy, under Contract No. DE-AC02-76ER01198.
Basis Set and Gauge Dependence of ab Initio Calculations of Vibrational Rotational Strengths K. J. Jalkanen, R. W. Kawiecki, P. J. Stephens,* Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
and R. D. Amos Department of Theoretical Chemistry, Cambridge University, Cambridge CB2 1E W, U . K . (Received: August 28, 1989; In Final Form: February 20, 1990)
Calculations of vibrational rotational strengths using Stephens' equation are reported for six small chiral organic molecules: carbodiimide, and oxaziridine. Atomic hydrazine, trans-1,2-dideuteriocyclopropane,fluorohydroxylamine,propane-l,l,l-d3-2-dl, polar and axial tensors are calculated ab initio at the SCF level of approximation using analytical derivative techniques. The dependence of atomic polar and axial tensors and of dipole and rotational strengths calculated thence on the basis set and (in the case of atomic axial tensors and rotational strengths) gauge is examined. The common origin gauge leads to origin-dependent rotational strengths, while the distributed origin gauge yields origin-independent rotational strengths. The basis set dependence of the origin dependence of common origin gauge rotational strengths is also examined. Exact atomic polar and axial tensors are interconnected via a sum rule. The basis set and gauge dependence of the degree to which this sum rule is satisfied are also examined. It is found that the distributed origin gauge is substantially more accurate than the common origin gauge. The atomic polar and axial tensors obtained for cyclopropane are compared with recent RPA calculations of Lazzeretti et al. The dipole and rotational strengths obtained for trans-l,2-dideuteriocyclopropaneare compared with recent experimental spectra of Nafie and co-workers.
Introduction An a priori theory of vibrational rotational strengths, permitting the prediction of vibrational circular dichroism (VCD) spectra, has recently been developed by Stephens.',2 In addition to the molecular geometry and vibrational force field, the calculation of rotational strengths requires two sets of molecular tensors, P$ and MkR. The atomic polar tensors, Pks (A specifying a nucleus), are fundamental to the calculation of vibrational dipole strengths and absorption intensities and are ~ell-known.~The atomic axial tensors, M$, are new. This theory of vibrational rotational strengths has been implemented for a number of chiral molecules, using atomic polar and axial tensors calculated ab initio at the S C F level of appro~imation."'~ In cases where comparison to experimental VCD spectra has been p o s ~ i b l e ~ . ~ ~ ' ~ en~' couraging agreement between theory and experiment has been obtained. The accuracy of predictions of vibrational rotational strengths is a complex function of the combined accuracies of the molecular geometry, force field, and PkBand M$ tensors. For a given choice of geometry and force field, the accuracy depends on the accuracy of the f $ and M& tensors, which, when calculated ab initio and at the S C F level of approximation, in turn is a function of the basis set size. In addition, M$ tensors are gauge-dependent,* and their accuracy is a function of the gauge employed. Calculations using Stephens' theory have to date employed basis sets of inodest size almost exclusively. Two gauges have been employed, the so-called common origin (CO) and distributed origin (DO) gauges2 It is the purpose of this paper to explore the dependence of the 1314~17-19
'The work reported here was first presented at the Molecular Spectroscopy Symposium, Ohio State University, Columbus, OH, June 1987, Paper WHIO.
accuracy of P$ and MkR tensors and of rotational strengths calculated thence on the choice of basis set and of gauge. In previous publications we have reported studies of the basis set and gauge dependence of the P& and M$, tensors of HF, H20, NH3, and CH4I3and of the rotational strengths of NHDT8,9,'2using a wide range of basis sets and the CO and DO gauges. However, (1) Stephens, P. J. J . Phys. Chem. 1985, 89, 748. (2) Stephens, P. J. J. Phys. Chem. 1987, 91, 1712. (3) Person, W. B.; Newton, J. H. J. Chem. Phys. 1974, 61, 1040. (4) Lowe, M. A.; Segal, G. A.; Stephens, P. J. J . Am. Chem. SOC.1986, 108, 248. ( 5 ) Lowe, M. A.; Stephens, P. J.; Segal, G. A. Chem. Phys. Left. 1986,
123, 108. ( 6 ) Amos, R. D.; Handy, N. C.; Jalkanen, K. J.; Stephens, P. J. Chem. Phys. Lett. 1987, 133, 21. (7) Jalkanen, K. J.; Stephens, P.J.; Amos, R. D.; Handy, N. C. J . Am. Chem. SOC.1987, 109, 7193. (8) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. Chem. Phys. Left. 1987, 142, 153. (9) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Phys. Chem. 1988, 92, 1781. (10) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J. Am. Chem. SOC.1988, I IO, 201 2. ( I I ) Kawiecki, R.; Devlin, F.;Stephens, P. J.; Amos, R. D.; Handy, N. C. Chem. Phys. Lett. 1988, 145, 41 1. ( 1 2 ) Amos, R. D.; Jalkanen, K. J.; Stephens, P. J. J . Phys. Chem. 1988, 92, 5571. (13) Stephens. P. J.; Jalkanen. K. J.; Amos, R. D.; Lazzeretti. P.; Zanasi, R. J . Phys. Chem. 1990, 94, 1811. (14) Stephens, P. J . Croat. Chem. Acta 1989, 62, 429. ( I 5 ) Annamalai, A.; Jalkanen, K. J.; Narayanan, U.; Tissot, M.-C.; Keiderling, T. A.; Stephens, P. J. J . Phys. Chem. 1990, 94, 194. (16) Morokuma, K.; Sugeta, H. Chem. Phys. Lett. 1987, 134, 23. ( 1 7 ) Amos, R. D.; Handy, N. C.;Drake, A. F.; Palmieri, P. J. Chem. Phys. 1988, 89, 7287. (18) Lowe, M. A.; Alper, J . S. J. Phys. Chem. 1988, 92, 4035. (19) Dothe, H.; Lowe, M. A.; Alper, J. S. J. Phys. Chem. 1988, 92,6246.
0032-3h54/90/2094-7040~02.50/0 0 1990 American Chemical Societv
Vibrational Rotational Strengths
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7041
TABLE I: Basis Set and Gauge Dependence of P $ and hf$ Tensors of trsns-1,2-Dideuteriocyclopropane(2)"
CI
STO-3Gb
6-31Gb
DZc
0.1 14 -0.177 -0.010
0.160 -0.246 0.143
0.192 -0.278 0.166
0.164 -0.161 0.155
0.161 -0.167 0.150
0.192 -0.220 0.149
0.175 -0.195 0.137
0.181 -0.209 0. I25
0.168 -0.186 0.138
0.028 0.003 -0.007 -0.040 0.005
0.097 -0.054 0.046 0.099 -0.072
0.098 -0.055 0.068 0.125 -0.083
0.074 -0.076 0.046 0.098 -0.078
0.074 -0.072 0.045 0.098 -0.075
0.080 -0.066 0.055 0.109 -0.074
0.077 -0.067 0.045 0.100 -0.068
0.075 -0.061 0.043 0.097 -0.062
0.078 -0.058 0.048 0.098 -0.065
-0.450 -0.073 -0.148 0. I64 -0.137 -0.085
-2.478
-0.354
2.478
0.105
-0.435
-0.148
-0.682
-0.170
xx YY
zz
6-31G*b 6-31G**b DZ/lpd Atomic Polar Tensors, P$
6 - 3 1 G ( e ~ t ) ~ TZ/2Pf
J?,
RPAh
H4
xx YY YZ Z Y
zz
Atomic Axial Tensors,g Mk8 CI
Z X
1
-2.154 0.113 0.065
-1.555 0.184 0.1 I8
-1.552 0.21 1 0.131
-1.238 -0.006 -0.074
-1.141 0.018 -0.049
-1.100 0.043 -0.036
-0.845 -0.094 -0.166
1.737 -0.136 -0.141
1.192 -0.242 -0.183
1.250 -0.248 -0. I80
0.822 -0.131 -0.067
0.738 -0.152 -0.090
0.710 -0.181 -0.120
0.549 -0.1 I4 -0.058
-0.312
-0.263 0.027 -0.016
-0.246 0.016 -0.027
-0.239 -0.001 -0.033
-0.180 -0.029 -0.061
-0.124 -0.082 -0.115
-0.564 0.034 0.0 I5
-0.463 -0.009 -0.075
-0.413 -0.002 -0.068
-0.400 -0.026 -0.077
-0.279 -0.043 -0.093
-0.160 -0.047 -0.082 -0.216 -0.038 -0.093
-0.122 -0.055 -0.108
-0.130 -0.074 -0.106 -0.141 -0.053 -0.104
0.475 0.009 0.005
0.374 0.137 0.145
0.362 0.074 0.096
0.325 0.150 0.148
0.250 0.164 0.164
0.213 0.123 0.131
0.168 0.159 0.160
0.170 0.150 0.153
0.435
0.204
0.403 -0.010 -0.023
0.097 -0.063 -0.069
0.129 -0.086 -0.088
0.073 -0.059 -0.070
0.003 -0.049 -0.057
0.018 -0.058 -0.061
-0.05 1 -0.053 -0.056
-0,024 -0.047 -0.048
0.682
-0.013
H4
zx
(
'Cartesian coordinates (atomic units): CI (0.000000, 1.651825, O.OOOOOO), C2 (-1.430523, -0.825913, O.OOOOOO), C3 (1.430523, -0.825913, 0.000000), H4 (0.000000, 2.727768, -I .738702), H5 (0.000000, 2.727768, 1.738702). H6 (-2.3623 15, -1.363884, -I .738702), D7 (-2.362315, -1.363884, I .738702), D8 (2.362315, -1.363884, -1.738702), and H9 (2.362315, -1.363884, 1.738702). All and M$ tensors are in atomic units. M& in imaginary. Im[MkB] is given. A more complete tabulation, including results for the 3-21G, 4-31G, and 6-311G** basis sets, is presented elsewhere.)* *Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A6 Inirio Molecular Or6ital Theory; Wiley: New York, 1986; and GAUSSIAN 82 basis set library.
