J. Phys. Chem. 1985,89, 2951-2954
2951
Comparison of the Magnetic Properties and Harmonlc Force Fields of NO, and C0,- by ab Initio Calculationt Ian Carmichael* and John Bentley Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 (Received: February 7, 1985)
Ab initio calculations using a moderately large [10,6/5,4] Gaussian s,p basis set are performed on both NO2 and COz-at the UHF level to investigate the spin distribution in these radicals. The effect of spin projection on both isotropic and dipolar coupling interactions is considered. Changes due to the addition of diffuse and polarization functions to the basis set are included in the comparison with experiment. A previous UHF calculations by Almlof et al. is shown to be limited by basis set inadequacy. From conventional symmetry coordinates, a harmonic force field is derived by using the UHF procedure with the s,p basis for the symmetric stretch and bend in both species. A small CI calculation proved necessary to locate the asymmetric stretch in NO2. A comparison of the derived frequencies with experiment casts doubt on the assignment of the COT spectrum observed in a matrix.
Introduction
In an ab initio study of the spin distribution in two isoelectronic 23-electron radicals, C02-and NO2,Almlof et al.’ claimed to show that, while the isotropic hyperfine coupling constants, ab, were insensitive to the calculational procedure, at least at the unrestricted HartreeFock (UHF) level or after annihilation (AA) of the contaminating quartet spin states, the magnitudes of their anisotropic counterparts, Bi,, were not. An increase of two- to threefold in the magnitude of the principal components of the B tensor was observed upon spin annihilation. Taken together with previous R H F calculations~3they were thus able to conclude that, for such u radicals, reasonable estimates of the isotropic coupling constants only are accessible from a wide range of basis sets and computational methods. Experience4 with T and wlike radicals such as methyl and tert-butyl is quite different. In U H F calculations the spin polarization contribution represents a substantial fraction of the total spin density at a nucleus and, while the so-called ”direct” component is little affected by annihilation, the polarization term is dramatically reduced. However, since we expect that for the above u radicals the anisotropic coupling will be largely determined by the direct contribution, we were surprised to note the large annihilation effects observed by Almlof et al. In addition, for the species studied, we see no reason to expect that spin polarization should contribute to each component of the B tensor in the same algebraic sense and would, thus, expect to see both increments and decrements in the U H F values after annihilation. Here we employ a moderately large sp basis to investigate these points and consider, in addition, the differential effects on the spin distribution of augmentation with diffuse sp and (polarization) d functions. There also appears to be some question in the 1iterature5v6 concerning the assignment of the vibrational spectrum of C02-.’ Since, for NO2,the characteristic frequencies (and their harmonic com$nents) have been thoroughly documented,* we felt it worthwhile to compare the predictions of ab-initio calculations of these features for the two molecules using basis sets of uniform quality. Previous calculations by Jackels and Davidson suggest that reliable estimates of the frequency of the asymmetric stretch in NOz (v3) will not be provided at the SCF level due to the interaction of the ground state (2A1)with a nearby excited state (2B2) which is of th&same symmetry (A’) under the point group, C,, appropriate to the (vibrationally) distorted geometry. Pacansky et al.5 have, however, reported from a calculation at the S C F level a force constant for this mode in CO,. We derive here all harmonic force constants (harmonic in the symmetry ‘The research described herein was supported by the Office of Basic
Energy Sciences of the Department of Energy. This is Document No NDRL-2611 from the Notre Dame Radiation Laboratory.
0022-3654/85/2089-2951$01.50/0
tz Figure 1. Parameters and axes used. The y axis is into the plane. TABLE I: Geometry and Total Energy for COi and NO2 molecule reference re, A O,, deg EscP,hartree C02- Almlof et al.’ 1.43 134.1 -187.19587 Pacansky et aLb 1.24 135.3 -187.546626 EnglandC 1.22 136 -187.6377 1.2441 134.75 -187.568 870 present work
NO2
Almlof et al.‘ 1.188 134.1 -203.67749 Jackels and Davidsond 1.1934 134.07 -204.05075 present work 1.1902 136.22 -203.990854
“ Reference 1.
Reference 5 . Reference 6. Reference 18.
TABLE 11: Isotropic Hyperfine Coupling Constants” molecule basis method a P C ) d”O)
co;
NO2
(S2)
210.2 176.2
-14.8 -11.4
0.7969 0.7517
145.4 139.2 141.3
-31.0 -21.8 -25.0
0.7620
166.7
-32.2
a(14N) 41.8 -12.3 41.9 -9.2 50.4 -18.3 -9.4 46.2 47.6 -12.6 54.7 -20.3
0.7500
0.7661 0.7501 0.7687 0.7500
“Units are Gauss except for (S2) in au. Reference 1. Reference 28. dReference 26. coordinates, that is) consistent with the present sp basis for other modes of both molecules, and note that a C I calculation is nec(1) J. Almlof, A. Lund, and K.-A. Thuomas, Chem. Phys. Lett., 28, 179 (i9ii). (2) H. F. Schaefer I11 and S. Rothenberg, J . Chem. Phys., 54, 1423 ( 1971). ( 3 ) D. C. McCain and W. E. Palke, J . Chem. Phys., 56, 4957 (1972). (4) I. Carmichael, unpublished results.
0 1985 American Chemical Society
2952 The Journal of Physical Chemistry, Vol. 89, No. 13, 1985
Carmichael and Bentley
TABLE 111: Anisotropic Hyperfine Coupling Tensors" 1 3 c
molecule
c0,-
basis (7,3)/ 1421 (10,6)/[5,41
BXX
BYY
Bzz
Bxx
BYY
4,
-6.1 -14.2
-4.2 -12.9
10.3 27.1
5.6 12.2
5.9 12.6
-1 1.5 -24.8
0.970
UHF DIRECT PUHF
-21.1 -15.9 -17.3
-14.7 -16.6 -16.0
34.8 32.5 33.2
11.6 8.8 9.7
15.2 9.7 11.5
-26.7 -18.5 -21.2
0.982 0.973 0.977
-16.7
-11.7
28.3
10.1
8.7
-18.7
0.978
experiment' NO2
170
method UHF AA
(7,3)/[4,21
UHF AA
(10,6)/ [5,41
UHF DIRECT PUHF
experimentd
cos
c$b
-3.3 -7.5
I4N -2.7 -7.5
6.0 15.0
7.1 15.6
6.7 15.9
-13.8 -31.5
0.991
-1 1.4 -8.3 -9.3
-8.3 -9.1 -8.8
19.7 17.4 18.1
21.5 14.4 16.7
21.6 15.8 17.7
-43.0 -30.1 -34.4
0.992 0.991 0.991
-7.9
-5.4
13.3
18.6
16.0
-34.6
0.991
"Units are Gauss. bAxes are defined in Figure 1.
