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Valence bond studies of AH2 molecules

III. A comparison of molecular orbital and valence bond calculations on CH2

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Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the3 B 1 and1 A 1 states of CH2. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the3 B 1 state gave a geometry of RC-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was −38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH2 as BeH2. The nature of the lone-pair and bonding orbitals is found to be significantly different between the3 B 1 and1 A 1 states. In the3 B 1 state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the1 A 1 state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H2O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.

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  1. 1.

    Maclagan,R.G.A.R., Schnuelle,G.W.: J. Chem. Phys.55, 5431 (1971)

  2. 2.

    Maclagan,R.G.A.R., Schnuelle,G.W.: to be published

  3. 3.

    Pitzer,R.M., Merrifield,D.P.: J. Chem. Phys.52, 4782 (1970)

  4. 4.

    Harrison,J.F., Allen,L.C.: J. Am. Chem. Soc.91, 807 (1969)

  5. 5.a

    Herzberg,G.: Proc. Roy. Soc. (Lond.) A262, 291 (1961)

  6. 5.b

    Herzberg,G., Johns,J.W.C.: Proc. Roy. Soc. (Lond.) A295, 107 (1966)

  7. 6.

    Foster,J.M., Boys,S.F.: Rev. Mod. Phys.91, 807 (1960)

  8. 7.

    Wasserman,E., Kuck,V.J., Hutton,R.S., Anderson,E.D., Jager,W.A.: J. Chem. Phys.54,4120(1971)

  9. 8.

    Herzberg,G., Johns,J.W.C.: J. Chem. Phys.54, 2276 (1971)

  10. 9.

    Bender,C.F., Schaefer,H.F.: J. Am. Chem. Soc.92, 4984 (1970)

  11. 10.a

    O'Neil,S.V., Schaefer,H.F., Bender,C.F.: J. Chem. Phys.55, 162 (1971)

  12. 10.b

    McLaughlin,D.R., Bender,C.F., Schaefer,H.F.: Theor. Chim. Acta (Berl.)25, 352 (1972)

  13. 11.

    Silverstone,H.J.: J. Chem. Phys.48, 4098 (1968)

  14. 12.

    Silverstone,H.J.: J. Chem. Phys.48, 4106 (1968)

  15. 13.

    Silverstone,H.J., Kay,K.G.: J. Chem. Phys.48, 4108 (1968)

  16. 14.

    Todd,H.D., Kay,K.G., Silverstone,H.J.: J. Chem. Phys.53, 3951 (1971)

  17. 15.

    Roothaan,C.C.J.: Rev. Mod. Phys.32, 749 (1960)

  18. 16.

    Prosser,F., Hagstrom,S.: Intern. J. Quantum Chem.2, 89 (1968)

  19. 17.

    Löwdin,P.O.: Phys. Rev.97, 1474, 1490, 1509 (1955)

  20. 18.

    Aung,S., Pitzer,R.M., Chan,S.I.: J. Chem. Phys.49, 2071 (1968)

  21. 19.

    Walsh,A.D.: J. Chem. Soc. (Lond.) 2260 (1953)

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Aided by research grants to the Johns Hopkins University from the National Science Foundation, the National Institutes of Health and the U.S. Army Research Office, Durham.

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Maclagan, R.G.A.R., Todd, H.D. Valence bond studies of AH2 molecules. Theoret. Chim. Acta 34, 19–29 (1974). https://doi.org/10.1007/BF00553228

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Key words

  • CH2
  • Valence bond calculations