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What is the lowest energy structure of the NS2 molecule?Yukio Yamaguchi, Yaoming Xie, Roger S. Grev, and Henry F. Schaefer III Citation: The Journal of Chemical Physics 92, 3683 (1990); doi: 10.1063/1.457825 View online: http://dx.doi.org/10.1063/1.457825 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/92/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Where and What are the Lowest Metallicity Stars? AIP Conf. Proc. 990, 85 (2008); 10.1063/1.2905679 Theoretical electronic structure of the lowest-lying states of the LaF molecule J. Chem. Phys. 117, 3715 (2002); 10.1063/1.1493769 Fine structure of the lowest triplet states in He2 J. Chem. Phys. 93, 983 (1990); 10.1063/1.459125 Quenching and vibrational energy transfer in the B 2Π state of the NS molecule J. Chem. Phys. 91, 5343 (1989); 10.1063/1.457665 Delocalization of electronic energy in the lowest triplet states of molecules J. Chem. Phys. 65, 2798 (1976); 10.1063/1.433427
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What is the lowest energy structure of the NS2 molecule? Yukio Yamaguchi, Yaoming Xie, Roger S. Grev, and Henry F. Schaefer III Center for Computational Quantum Chemistry. University of Georgia. Athens. Georgia 30602
(Received 29 September 1989; accepted 4 December 1989)
A paramagnetic (neutral) species, thought to be the NS2 molecule, has recently been detected by Amano using millimeter wave spectroscopy in a discharge of a mixture of N2 and CS2. Detailed theoretical studies on the possible structures of an NS2 molecule, however, had not previously been reported. This study aims to find the most probable structure for the NS2 molecule and to characterize other conceivable isomers. Among many possible structures for the NS2 species, SNS bent eAI), SNS linear enu ), NS2 ring eBI)' NSS bent eA '), and SNS bent (4A2) isomers have been investigated at the self-consistent-field (SCF) and single and double excitation configuration interaction (CISD) levels of theory with double zeta plus polarization (DZ + P) and triple zeta plus double polarization (TZ + 2P) basis sets. The SNS bent (2 A I) isomer has been found to be the lowest energy structure among the isomers studied in this research. This bent isomer has a bond angle of about ISO deg and has a shallow doubleminimum potential, the classical barrier height to linearity being 2.S (3.0) kcallmol at the TZ + 2P-CISD(Q) leveloftheory.
INTRODUCTION
In a discharge of a mixture of N2 and CS2 molecules several paramagnetic species, among a variety of compounds consisting of carbon, nitrogen, and sulfur atoms ( Cx Ny Sz ), have recently been detected by microwave spectroscopy. I Judging from the chemistry and effects of isotopic substitution, one of these paramagnetic species is thought to be the NS2 molecule. 2
To our knowledge there are to date no detailed theoretical studies on the possible structures of the NS2 molecule. NS2 is isovalent with the N02 molecule for which we recently reported theoretical predictions of the dipole moment, geometry, vibrational frequencies, and the barrier height to linearity.3 According to experiment4 and our high level theoretical studies3 the ground state of N02 molecule has a C 2v
bent structure with bond angle of 134 deg, and the barrier height to linearity is estimated to be 38 kcallmol with the zero-point vibrational energy correction.
The goal of the present research is to make a definitive prediction ofthe most stable (i.e., lowest energy) structure ofthe NS2 molecule and to elucidate other energetically lowlying electronic states. To this end, the complete geometry optimization of five isomers of the NS2 molecules have been carried out at the self-consistent-field (SCF) and configuration interaction with all single and double excitations (CISD) levels oftheory.
THEORETICAL APPROACH
Two basis sets, labeled DZ + P and TZ + 2P, were used in this research. The double zeta basis set (DZ) was from Huzinaga5 -Dunning6 and is described as (9sSp/ 4s2p) on nitrogen and (11s7p/6s4p) on sulfur. The triple zeta basis set (TZ) was again from Huzinaga5-Dunning,6 and is described as (9sSp/Ss3p) on nitrogen and (lls7pl7sSp) on sulfur. It must be emphasized that these "triple zeta" basis sets do not literally include three distinct sets ofN ls, 2pand S 3s,
3p valence region basis functions. We use the designation TZ instead to indicate significantly increased sp flexibility relative to the more standard Huzinaga5 -Dunning6 DZ basis sets. The DZ + P basis set was the DZ basis set augmented with a single set of d functions for each atom [ad (N) = 0.80; ad (S) = O.SO]. The second basis set, TZ + 2P, was the TZ basis set augmented with two sets of d functions for each atom [ad (N) = 1.60, 0.40; ad (S) = 1.00, 0.2S].
In their classic 1976 papers Jackels and Davidson studied 12 doublet and 4 quartet states of the N02 molecule.7
•8
Following their work and using our chemical intuition, five low-lying electronic states ofNS2 molecule have been chosen and their structures determined. The first electronic configuration considered in this study has the same valence orbital occupancy as that ofthe N02 ground state ( C 2v symmetry),
2A I {core (SNS C2v )}( 6a l )2(Sb2 )2(7a I )2( 6b2)2
(1)
At the SCF level of theory, the 2AI state ofN02 molecule is known to suffer from symmetry breaking7
•8 ; the 2A I
state of N02 molecule in Cs symmetry, with two different NO bond lengths and a smaller bond angle relative to the 2A I (in the C 2v symmetry) state, is predicted to be lowerin energy. However, we have recently confirmed that this phenomena is due to an artifact of the SCF theory. 9 By employing the complete active space (CAS) SCF wave functions, the 2A' state is correctly separated to the 2 A I and 2 B2 states. The NS2
tnolecule is isovalent to N02 and therefore, may face similar problems at the SCF level of theory. The second structure considered has the same electronic configuration as Eq. (1) but is the linear structure. This linear structure is subject to a Renner-Teller splitting l
O-I3 and corresponds to case (c) in Ref. 13. Upon bending, this 2nu state splits into two components, 2AI and 2BI, the 2AI component being a transition state at linear geometries and the 2B I component a local minimum. Our specific theoretical work was carried out on the
J. Chern. Phys. 92 (6), 15 March 1990 0021-9606/90/063683-05$03.00 © 1990 American Institute of Physics 3683
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3684 Yamaguchi et al: The NS2 molecule
2 B 2u component of the 21Iu state in theD 2h subgroup of D coh
21Iu {core (SNS linear)} (50g )2( 4b,u )2( 6ag )2(5b'u)2
X (2b2u )z(2b3u )z(2b311 )z(2bzlI )z(3b2U )' (2)
With the intention of searching for a possible ring structure the following C Zv electronic configuration, which correlates with the three-membered ring, has been considered as the third isomer
ZB,{core (SNS C2V )}( 60 1 )z( 5bz)z(70 , )z( 6b2)2
(3)
The fourth electronic configuration corresponds to bent NSS (Cs symmetry) and is expressed by
2A '{core (NSS Cs )}( 1Oo')2(110')z(120,)z(130')2
X (140' )2(30" )2( 48" )z( 158')z( 168'). (4)
Finally the following quartet state has been selected as the fifth and last isomer to be investigated
4Az{core (SNS C2V )}( 60 1 )2( 5b2)2(701 )2( 6b2)2
X (80 1 )2(2b l )2(7b2) (282 )2(98,) (3b, ). (5)
In these electronic configurations the 90 I' 20z, 3b"
and 7 b2 molecular orbitals are approximately described as follows (the x and y axes being in-plane and the z axis out of plane),
(90 , )a£,N(2px) -Cz{S,(3px) +S2(3px)}
- C3{S,(3py) - Sz(3py)},
(202b~C4{S,(3pz) - Sz(3pz)},
(3b , ) e;C5N(2pz) - C6{SI(3pz) + S2(3pz)}'
(7b2) e;C7N(2Py ) - CS{SI (3px) - Sz(3px)}
- C9{SI(3py) + S2(3py)},
where the coefficients C, - C9 indicate the mixing of orbitals. The open-shell electron is localized about the N-centered p orbitals in all cases except for the quartet state, which is difficult to visualize in a simple manner.
For all five isomers mentioned in the preceding paragraph complete structural optimizations were carried out using SCFI4 and CISD I5
-17 analytic first derivative meth
ods. At the SCF level of theory harmonic vibrational frequencies were determined via analytic second derivative methods IS.19 and at the CISD level of theory via finite differences of analytic gradients. 15-17
At the CISD level of theory the eleven lowest occupied molecular orbitals [N (1s); S (ls,2s,2p)-like orbitals] were held doubly occupied (frozen cores) and the three highest lying virtual orbitals [N ( Is·); S ( Is·) -like atomic orbitals] were deleted (frozen virtuals) in all configurations. Thus the DZ + P and TZ + 2P CISD wave functions for the bent SNS isomers eAt) in C 2u symmetry include 18783 and 54843 configurations in the Hartree-Fock interacting space/O.21 respectively. These CI wave functions were determined via the shape-driven graphical group approach. Z2 In order to approximately include unlinked quadruple excitations, Davidson's correction23 was used and this type of energetic prediction is abbreviated as CISD + Q.
For the first two isomers, SNS bent eA I) and linear elIu) structures, the complete active space (CAS) SCF
method was also employed. The CASSCF method used was that developed by Werner and Knowlesz4.2s in Cambridge, England. Two sets of active spaces have been chosen as those used in our previous study of the N02 molecule3 and both are determined in conjunction with the DZ + P basis set. The smaller CASSCF involves the full CI treatment of 13 electrons in the 10 valence molecular orbitals, qualitatively constructed from 2s, 2px, 2py, 2pz-like atomic orbitals on nitrogen, and 3px, 3py, 3pz-like atomic orbitals on each sulfur. There are 3144 configurations in the DZh subgroup of D coh and 6324 configurations in C 2v symmetry with this CASSCF. The full valence CASSCF includes all configurations placing the 17 valence electrons in the 12 valence molecular orbitals. There are 13 600 configurations in D 2h symmetry and 27 199 configurations in C 2v symmetry for this choice of CAS space.
RESULTS AND DISCUSSION
The optimized geometries and physical properties for the five isomers of the NS2 molecule from SCF theory are presented in Table I (DZ + P basis set) and Table II (TZ + 2P basis set). Within SCF theory the most stable isomer is predicted to be the SNS bent structure (2A I) with the linear structure elIu) a transition state between equivalent minima (the 2A, component of the 21I u state has an imaginary bending frequency, whereas the 2BI component has a real bending frequency). The order of stability of the four minima at their respective equilibrium geometries is
SNS bentCZA , ) > SNS bent(4A2 ) > NS2 ringeB,) > NSS bent (A '). (6)
It should be realized, though, that quartet states are usually predicted to be unrealistically low in energy relative to doublet states due to the inherent limitations of SCF theory.26 This misleading effect will be corrected using correlated wave functions, as shown in the next section. It is easily seen that the NS bond lengths and the dipole moments of all isomers are predicted to be smaller with the TZ + 2P basis set relative to those predicted using the DZ + P basis set, and all isomers except the NSS bent e A ') structure were energetically raised relative to the most stable SNS isomer (2 A I) by increasing the size of the basis set.
The results from the single and double excitation configuration interaction (CISD) methods are presented in Table III (DZ + P basis set) and Table IV (TZ + 2P basis set). At the CISD level of theory the SNS bent isomer (A,) is again predicted to be the most stable and the linear isomer ell" ) to be a transition state to the bent isomer. The order of stability of the four isomers at their respective equilibrium geometries with the TZ + 2P basis set is
SNS benteA I ) >NS2 ringeBI ) > NSS benteA')
(7)
It should be noted that all isomers were destabilized relative to the most stable SNS bent isomer (z A I) in going from the DZ + P-SCF to the DZ + P-CISD level of theory, i.e., 10 kcal/mol for the NSz ring eB,), 9 kcal/mol for the NSS bent eA '), and 20 kcal/mol for the quartet SNS bent (4A 2 ),
respectively. Consequently, the NS2 ring structure e B I) becomes the second most stable isomer in the CISD level of
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Yamaguchi et a/.: The NS2 molecule 3685
TABLE I. Theoretical predictions of the physical properties of NS2 using OZ + P-SCF theory. The infrared intensities are designated I in this table, while the relative energies compared to the SNS 2 A, ground state are labeled AE.
SNS bent SNS linear NS2 ring NSS bent SNS bent Structure 2A, 2n. 2B, 2A' 4A2
Energy' (hartree) - 0.37554 -0.37346 - 0.36802 -0.35437 -0.37471 r.(NS) (A) 1.543 1.536 1.717 1.523 1.635 r. (SS) (A) 2.062 1.923 LSNS orLNSS (deg) 155.3 180.0 73.8 115.8 123.6 Il (Debye) 0.29 -0- 1.14 1.70 0.91 w,(a, ora') (cm-') 742 689 917 1207 703 w2(a, or a') 272 229i(381)b 585 657 291 w3(b2 or a') 1228 1273 599 344 951 I, (kmmol-') 0.9 -0- 0.3 42.8 6.3 12 2.4 - (3.5)b 1.9 102.1 0.2 13 1330.4 1288.3 25.2 25.9 9.5 ZPVE (kcal mol-') 3.20 2.80 3.00 3.16 2.78 AE (kcal mol-') 0.00 1.31 4.72 13.29 0.52 A(E +ZPVE) (kcalmol-') 0.00 0.91 4.52 13.25 0.10
• Add - 849 hartrees. bBending frequency for the 2B, component of the Renner-Teller pair of potential energy surfaces.
theory. As with the SCF theoretical predictions, shorter NS bond lengths and smaller dipole moments for all isomers have been predicted with an increase of the basis set size using the CISD method. At the TZ + 2P-CISD level of theory the difference in energy betwen the two lowest energy isomers is predicted to be 17 kcallmol. It is interesting to notice that the DZ + P-SCF and TZ + 2P-CISD levels of theory fortuitously predict very similar geometries for most isomers. Optimized geometries for the five isomers at the TZ + 2P-CISD level of theory are shown in Fig. 1.
According to Walsh's rules27 17 electron species are predicted to have bent structures for their electronic ground states. Our optimized geometries for the N02 and NS2 molecules are consistent with this prediction. On the other hand Bent's rules28
•29 predict that the N02 molecule should have
nitrogen bonding orbitals of greater p character than the NS2
molecule. Consequently the N02 molecule should be more strongly bent and show a higher barrier to linearity compared to the NS2 molecule, in agreement with our results.3
The large difference (4.8 deg) in ground state bond angles predicted from the CISD and CASSCF wave functions is noteworthy. With the smaller DZ + P basis set the angles are 150.8 (CISD) and 146.0deg (CASSCF). Under normal circumstances we would expect the CISD structural prediction to be the more reliable. However for the valence isoelectronic N02 molecule the analogous predictions3 are 134.5 (CISD) and 133.2 (CASSCF), while experiment is 133.9 deg. Since the two theoretical predictions differ from experiment by + 0.6 and - 0.7 deg, it is not possible on this basis alone to make a judgement on the relative merits of the two methods. Nevertheless we suspect that the CISD prediction is the more reliable.
TABLE II. Theoretical predictions of the physical properties of NS2 using TZ + 2P-SCF theory. The infrared intensities are designated lin this table, while the relative energies compared to the SNS 2A, ground state are labeled AE.
SNS bent SNS linear NS2 ring NSS bent SNS bent Structure 2A, 2n. 2B, 2A' 4A2
Energy' (hartree) -0.390 83 -0.38835 -0.38150 -0.37699 -0.38854 r.(NS) (A) 1.530 1.523 1.707 1.508 1.619 r.(SS) (A) 2.059 1.905 LSNS or LNSS (deg) 154.5 180.0 74.2 116.2 122.9 Il (Oebye) 0.25 -0- 1.05 1.38 0.69 w,(a, ora') (cm-') 745 688 908 1218 706 w2(a, or a') 286 247i(378)b 570 674 303 w3(b2 or a') 1210 1245 579 352 935 I, (kmmol-') 0.9 -0- 0.1 37.6 6.6 12 2.5 _ (3.6)b 2.0 100.3 0.3 13 1410.0 1318.0 19.1 22.0 3.0 ZPVE (kcal mol-') 3.20 2.76 2.94 3.21 2.78 AE (kcal mol-') 0.00 1.56 5.86 8.69 1.44 A(E + ZPVE) (kcal mol-') 0.00 1.12 5.60 8.70 1.02
• Add - 849 hartrees. b Bending frequency for the 2 B, component of the Renner-Teller pair of potential energy surfaces.
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3686 Yamaguchi et al.: The NS2 molecule
TABLE III. Theoretical predictions of the physical properties ofNS, using DZ + P-CISD theory. The infrared intensities are designated I in this table, while the relative energies compared to the SNS ' A I ground state are labeled I!..E.
SNS bent SNS linear NS2 ring NSS bent SNS bent Structure 2A, 2IIu 'B, 'A' 4A2
Energy' (hartree) - 0.777 07 - 0.773 09 - 0.753 62 -0.74228 -0.74379 (CISD+Q) ( - 0.833 25) ( - 0.82832) (-0.806 81) (-0.79818) (- 0.79172) r,(NS) (A) 1.562 1.550 1.728 1.550 1.632 r,(SS) (A) 2.088 1.934 LSNS or LNSS (deg) 150.8 180.0 74.3 116.2 124.2 f.l (Debye) 0.45 -0- 1.20 1.48 0.90 w,(a , ora') (em-I) 730 672 871 1072 730 w2(a , or 0') 300 271i(359)b 550 665 282 w3(b, or a') 1299 1361 539 297 876 I, (kmmol- I) 2.8 -0- 1.8 26.6 7.6 I, 3.5 _ (5.4)b 0.5 51.9 0.4 13 632.0 649.7 29.8 20.4 1.8 I!..E (kcal mol-I) 0.00 2.50 14.72 21.83 20.88 I!..E(CISD+Q) (0.00) (3.09) (16.59) (22.01) (26.06) ZPVE (kcal mol-I) 3.33 2.91 2.80 2.91 2.70 I!..E(CISD+ZPVE) (kcalmol- I) 0.00 2.08 14.19 21.41 20.25 I!..E (CISD + Q + ZPVE) (0.00) (2.67) (16.06) (21.59) (25.43 )
• Add - 849 hartrees. bBending frequency for the 2B, component of the Renner-Teller pair of potential energy surfaces.
TABLE IV. Theoretical predictions of the physical properties of NS2 using TZ + 2P-CISD theory. The relative energies compared to the SNS 2 A I ground state are labeled I!..E.
SNS bent SNS linear NS2 ring NSS bent SNS bent Structure 2A, 2IIu 'B, 2A' 4A2
Energy' (hartree) - 0.82180 - 0.817 76 - 0.79519 - 0.79121 -0.78827 (CISD + Q) ( - 0.884 56) (-0.87976) ( - 0.854 92) ( - 0.852 53) ( - 0.842 86) r,(NS) (A) 1.546 1.536 1.716 1.528 1.613 r, (SS) (A) 2.091 1.921 LSNS or LNSS (deg) 151.3 180.0 75.1 116.8 124.2 f.l (Debye) 0.37 -0- 1.13 1.30 0.70 I!..E (kcal mol-I) 0.00 2.54 16.70 19.20 21.04 I!..E(CISD+Q) (0.00) (3.01) (18.60) (20.10) (26.17)
• Add - 849 hartrees.
TABLE V. Theoretical predictions of the physical properties of the most stable NS2 isomer, SNS (2A I ). The infrared intensities are designated I in this table.
DZ+P DZ+P Basis set DZ+P TZ+2P DZ+P TZ+2P CASSCF CASSCF Level SCF SCF CISD CISD (13e- /10 MO) (17e- /12 MO)
Energy' (hartree) - 0.37554 - 0.390 83 - 0.777 07 -0.82180 -0.51795 - 0.52310 r,(NS) (A) 1.543 1.530 1.562 1.546 1.601 1.602 r.(NS)b (A) 1.536 1.523 1.550 1.536 1.579 1.580 LSNS (deg) 155.3 154.5 150.8 151.3 145.8 146.0 f.l (Debye) 0.29 0.25 0.45 0.37 0.48 0.49 w,(a , ) (em-I) 742 745 730 728 658 656 w2(a , ) 272 286 300 307 320 318 w3 (b2) 1228 1210 1299 1296 1172 1162 I, (km mol-I) 0.9 0.9 2.8 2.6 2.6 2.7 12 2.4 2.5 3.5 3.5 2.5 2.6 13 1330.4 1410.0 632.0 630.9 281.6 300.7 ZPVE (kcal mol- I ) 3.20 3.20 3.33 3.33 3.07 3.05 I!..E c (kcal mol-I) 1.31 1.56 2.50 2.54 5.03 4.91 I!..E(CISD + Q)C (3.09) (3.01)
• Add - 849 hartrees. b Bond length at linear geometry. C Barrier height to linearity.
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Yamaguchi Bt al: The NS2 molecule 3687
/~1.546A / 15~~ ~
S S
s;--------N--~1~.~~6~A--S
A1.71 / \6A
S S 2.091 A
l1~):A ---i-n-:S
N 1.52aA
N ~1.613A
/ 124.2" ~ S S
O.OkcaVmol
2.5 kcaVmol
16.7 kcaVmol
19.2 kcaVmol
21.0 kcaVmol
FIG. 1. Optimized geometries and relative energies for the five isomers at the TZ + 2P-CISD level of theory.
According to our theoretical study the NS2 molecule observed in the microwave spectrum is, therefore, likely to be the SNS bent isomer e A I) whose equilibrium bond angle is predicted to be about 150 deg. This bent isomer appears to form a shallow double-minimum potential, the barrier to linearity being only 3 kcallmol, and its microwave spectrum might therefore be a challenge to interpret. On the other hand its isovalent relative, N02, has a reasonable large barrier height to linearity, 38 kcallmol and its microwave spectra is much easier to interpret.30-
32 Table V summarizes theoretical predictions ofthe physical properties of the most stable isomer, i.e., the SNS bent eA I) structure at the various levels of theory.
CONCLUDING REMARKS
The work presented in this study involves complete geometry optimizations and harmonic vibrational analyses for five low-lying NS2 molecular structures at the SCF and CISD levels of theory. The theoretical results reveal that the most stable isomer of the NS2 molecule has a bent structure with a bond angle of about 150 deg. The classical barrier to linearity is predicted to be 2.5 and 3.0 kcallmol at the TZ + 2P-CISD and CISD + Q23 levels of theory, respectively.
ACKNOWLEDGMENTS
We thank Dr. Takayoshi Amano and Dr. Takako Amano at National Research Council of Canada, Ottawa, Canada for their very informative discussions and suggestions. We also thank Dr. Randall D. Davy for his very helpful comments on the paper. This research was supported by U.S. National Science Foundation, Grant No. CHE-8718469. Contribution CCQC No. 71.
'T. Amano and T. Amano, Abstract RFI, 44th Symposium on Molecular Spectroscopy, June 12-16, 1989, Columbus, Ohio.
2T. Amano and T. Amano (private communication, April-June, 1989). 3y. Xie, R. D. Davy, B. F. Yates, C. P. Blahous, Y. Yamaguchi, and H. F. Schaefer, Chern. Phys. 135, 179 (1989).
'Y. Morino, M. Tanimoto, S. Saito, E. Hirota, and T. Tanaka, J. Mol. Spectrosc. 98, 331 (1983).
5S. Huzinaga, J. Chern. Phys. 42, 1293 (1965); S. Huzinaga and Y. Sakai, ibid. 50, 1371 (1969).
"T. H. Dunning, J. Chern. Phys. 53, 2823 (1970); T. H. Dunning and P. J. Hay, in Modern Theoretical Chemistry, edited by H. F. Schaefer (Plenum, New York, 1977), Vol. 3, pp. 1-27.
1C. F. Jackels and E. R. Davidson, J. Chern. Phys. 64, 2908 (1976). "C. F. Jackels and E. R. Davidson, J. Chern. Phys. 65, 2941 (1976). 9C. P. Blahous, B. F. Yates, and H. F. Schaefer Theor. Chim. Acta. (submitted).
,oG. Herzberg, Electronic Spectra of Polyatomic Molecules (Van Nostrand Reinhold, New York, 1966).
"Ch. Jungen and A. J. Merer, in Molecular Spectroscopy: Modern Research, edited by K. N. Rao (Academic, New York, 1976), Vol. 2, p. 127.
'2J. M. Brown and F. J0rgensen, Adv. Chern. Phys. 52,117 (1983). 13T. J. Lee, D. J. Fox, H. F. Schaefer, and R. M. Pitzer, J. Chern. Phys. 81,
356 (1984). 14J. D. Goddard, N. C. Handy, and H. F. Schaefer, J. Chern. Phys. 71,1525
(1979). 15B. R. Brooks, W. D. Laidig, P. Saxe, J. D. Goddard, Y. Yamaguchi, and
H. F. Schaefer, J. Chern. Phys. 72, 4652 (1981). 16y' Osamura, Y. Yamaguchi, and H. F. Schaefer, J. Chern. Phys. 77,383
( 1982). I7J. E. Rice, R. D. Amos, N. C. Handy, T. J. Lee, and H. F. Schaefer, J.
Chern. Phys. 85, 963 (1986). '"Y. Osamura, Y. Yamaguchi, P. Saxe, M. A. Vincent, J. F. Gaw, and H. F.
Schaefer, Chern. Phys. 72, 131 (1982). I"y. Osamura, Y. Yamaguchi, P. Saxe, D. J. Fox, M. A. Vincent, and H. F.
Schaefer, J. Mol. Spectrosc. 103,183 (1983). 2°A. Bunge, J. Chern. Phys. 53, 20 (1970). 21c. F. Bender and H. F. Schaefer, J. Chern. Phys. 55, 4789 (1971). 22p. Saxe, D. J. Fox, H. F. Schaefer, and N. C. Handy, J. Chern. Phys. 77,
5584 (1982). BE. R. Davidson, in The World of Quantum Chemistry, edited by R. Dau-
del and B. Pullman (Reidel, Dordrecht, Holland, 1974), p. 17-30. 2.p. J. Knowles and H. J. Werner, Chern. Phys. Lett. 119,259 (1985). 25H. J. Werner and P. J. Knowles, J. Chern. Phys. 82, 5053 (1985). 26N. C. Handy, J. D. Goddard, and H. F. Schaefer, J. Chern. Phys. 71, 426
(1979). 21A. D. Walsh, J. Chern. Soc. 1953, 2266. 2"H. A. Bent, J. Chern. Ed. 37, 616 (1960). 29H. A. Bent, Chern. Rev. 61, 275 (1961). 3"0. K. Hsu, D. L. Monts, and R. N. Zare, Spectral Atlas of Nitrogen Diox
ide 5530 to 6680 A (Academic, New York, 1978). 31K. Uehara and H. Sasada, High Resolution Spectral Atlas of Nitrogen
Dioxide 559-597 nm, Springer Series in Chemical Physics, Vol. 41 (Springer, Berlin, 1985).
32G. Hirsch and R. J. Buenker, Can. J. Chern. 63, 1542 (1985).
J. Chern. Phys., Vol. 92, No.6, 15 March 1990 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
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