1689
Comparison of INDO and ab Initio Methods for the Correlated Wave Functions of the Ground and Excited States of Ozone W. R. Wadtl and W. A. Goddard 111*2
Contribution No. 4742 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91109. Received August 6, 1973 Abstract: The validity of using integral approximation schemes in conjunction with correlated wave functions has been tested by performing generalized valence bond (GVB) and extensive configuration interaction (CI) calculations with INDO approximate integrals on the ground and excited states of ozone. High quality ab initio calculations have previously shown correlation effects to be extremely important for describing ozone. We find that for the CI wave functions the INDO approximation leads to vertical excitation energies within about 30z (from 0.8 eV too low to 0.6 eV too high with an RMS error of 0.5 eV), as compared to comparable ab initio calculations. We also found that the INDO-GVB wave functions lead to bond angles in good agreement with experimental and ab initio calculations but produced bond lengths that were too short. Most important was the discovery that INDO grossly favors closed geometries as opposed to open geometries, predicting the ground state of ozone to be an equilateral triangle state (even for correlated wave functions) with an energy 6 eV below the correct open state !
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n recent years significant progress has been made in developing efficient procedures for carrying out high quality ab initio calculations. 3 , 4 Extensive configuration interaction (CI) calculations with large basis sets have been reported for the ground and excited states of molecules such as C2H4,5C4H6,6,7 C6H6,80 3 , ’ COz,loetc., and for ground state potential surfaces of H * Li Hz, Hz reactions such LiH F +H HF, F, H + F HF. Despite this progress, we have a long way to go before such ab initio methods will be efficient enough (in both computer time and people time) for thorough mechanistic investigations of chemically interesting reactions (involving, perhaps, hundreds or thousands of geometries). To circumvent the feasibility restrictions of ab initio procedures, a number of approximate methods for calculating wave functions have been developed. Most of these approximations involve some empiricism, i.e., parametric fitting of experiment. Moreover, essentially all the semiempirical methods are based upon closed-shell Hartree-Fock (HF) wave functions, including (i) noninterative approaches such as extended Huckel theory (EHT), l 4 (ii) self-consistent charge gen-
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(1) NSF Graduate Fellow, 1970-1973. (2) Partially supported by grants (GP-15423 and GP-40783X) from the National Science Foundation. (3) H . F. Schaefer 111, “The Electronic Structure of Atoms and Molecules: A Survey of Rigorous Quantum Mechanical Results,” AddisonWesley, Reading, Mass., 1972. (4) W. J. Hunt, P. J. Hay, and W. A. Goddard 111, J . Chem. Phys., 57,738 (1972). ( 5 ) C. F.Bender, T. H. Dunning, Jr., H. F. Schaefer 111, W. A. Goddard 111. and W. J. Hunt. Chem. Phvs.Lett.. 15. 171 11972). (6) T. H. Dunning, Jrl, R . P. Hdsteny, and I. Shavitt, j . Amer. Chem. SOC..95. 5067 (1973). (7) G’. Levin and W. A. Goddard 111, to be submitted for publication. (8) P. J. Hay and I. Shavitt, Chem. Phys. Lett., 22, 33 (1973). (9) (a) P. J. Hay and W. A. Goddard 111, Chem. Phys. Lett., 14, 46 (1972); (b) W. A. Goddard 111, P. J. Hay, and T. H. Dunning, Jr., J. Amer. Chem. SOC.,submitted for publication; (c) P. J. Hay, T. H. Dunning, Jr., and W. A. Goddard 111, Chem. Phys. Lett., in press. (10) N. W. Winter, C. F. Bender, and W. A. Goddard 111, Chem. Phys. Lett., 20,489 (1973). (11) R . C. Ladner and W. A. Goddard 111, Theor. Chim. Acta, in press. (12) (a) C. F. Bender, P. K. Pearson, S. V. O’Neill, and H. F. Schaefer II1,J. Chem. Phys., 56,4626 (1972); (b) Science, 176, 1412 (1972). (13) S. V. O’Neill, P. K. Pearson, and H. F. Schaefer I n , J. Chem. Phys., 58,1126 (1973). (14) R . Hoffmann, J . Chem. Phys., 39,1397 (1963).
eralizations of EHT,16 (iii) CND0,16 (iv) INDO” and MINDO, l8 (v) NDDO,’’ (vi) noniterative simple pseudopotential approaches (commonly used for solids), 2o (vii) Xa-type approaches (commonly used for solids).21 (The CNDO, INDO, and X a methods have also been used with unrestricted H F wave functions, which allows the lowest state of each spin to be treated approximately.) It is well known that simple H F wave functions (even when carried out exactly) generally lead to poor descriptions of the relative ordering of molecular excited states. For example, the ground , ~ ~ states, states of Cz and 0 , are k n ~ w nto~ be~ singlet but in each case the H F wave functions leads to a triplet ground ~ t a t e . ~Even ~ ~ worse ~ ~ - are ~ ~the descriptions H F wave functions usually give for potential surfaces involving bond formation or breakage.29.30This is unfortunate since it is just in the study of such excited states and reactions that reliable theoretical wave functions are so greatly needed. Consequently, in studying (15) (a) L. G. Cusachs and J. W. Reynolds, J. Chem. Phys., 43, 5160 (1965); (b) R. Rein, N. Fukuda, H. Win, G. A. Clarke, and F. E. Harris, ibid., 45,4743 (1966); (c) F. E. Harris, ibid., 48,4027 (1968). (16) (a) J. A. Pople and G. A. Segal, J. Chem. Phys., 43, 5136 (1965); (b) ibid., 44,3289 (1966). (17) J. A. Pople, D. L. Beveridge, and P. A. Dobosh, J . Chem. Phys., 47,2026 (1967). (18) (a) N. C. Baird and M. J. S. Dewar. J. Chem. Phvs.. 50. 1262 (1969); (b) M. J. S. Dewar and E. Haselbach, J. Amer.-Chem.’ SOC., 92,590 (1970). (19) J. A. Pople, D . P. Santry, and G. A. Segal, J. Chem. Phys.. 43, 5129 (1965). (20) J. C . Phillips and L. Kleinman, Phys. Rea., 116,287 (1959). (21) J. C . Slater and J. H. Wood, 1nt.J. Quantum Chem.,45,3 (1971). (22) E. A. Ballik and D. A. Ramsey, Astrophys. J., 137,84 (1963). (23) 0. R. Wulf, Proc. Nat. Acad. Sci.-Nat. Res. Couiic., Publ., 13, 744(1927). (24) G. Verhaegen, W. G. Richards, and C. M. Moser, J . Chem. Phys., 46, 160(1967). (25) The H F wave function also leads to a triplet ground state for Be0,26 while good C I calculations lead to a singlet state.*’ Although there is no definitive experimental evidence for a ground singlet state,** correlations between theoretical calculations and the available experiments point strongly toward a ground singlet state. (26) W. M. Kuo, K. J. Freed, and W. Klemperer, J. Chem. Phys., 46, 3556 (1967). (27) (a) H. F. Schaefer 111, J . Chem. Phys., 55, 176 (1971); (b) S. V. O’Neill, P. K. Pearson, and H. F. Schaefer III,.Chem. Phys. Lett., 10, 404(1971). (28) A. Lagerquist, Thesis, University of Stockholm, 1948. (29) W. A. Goddard 111,Phys. Reo., 157,81 (1967). (30) These problems of the H F wave function do not depend on whether an ab initio or an approximate method is employed. ~
Wadt, Goddard
Ground and Excited States of Ozone
1690 Table I. Vertical Excitation Energies of Ozone (Electron Volts)"
HF-------. INDO-MBS 'Ai(4T) 3B2(4A)
0.00
- 2.24
%(5n) 0.94
3Az(5.1r)
' A d 5 a)
'Bi(5T) - 1.09 4.54
3B2(6n)
Ab initio DZd
I
--GVB( 1-) --Ab iniri0-T INDO-MBS MB9 DZd
0.00 -2.16
sq
1.42 -0.52 3.72 3.85
0.00 0.51
0.00 0.51
0.00 0.68
o'88f
"04'
1'23'
o,95,
1,15,
1,34,
1.66
2.09 2.26 8.05
2.33 2.51 6.70
0.15
