Improved one-centre wave functions for the hydrogen and methane molecules

Corrections are made to the Joy-Parr hydrogen and the Saturno-Parr methane one-centre wave functions and the functions are accurately reminimized with respect to the energy. The electronic wave functions and total molecular energies are obtained for various internuclear distances and the equilibrium internuclear distance and the breathing force constant determined. Three methods for calculating the force constant are given and compared. The equilibrium bond length for hydrogen is found to be 1·38 a.u. (experimental, 1·40 a.u.) and the force constant 6·33 md/a (experimental, 5·75 md/a). For methane the equilibrium C-H distance is found to be 2·014 a.u. (experimental, 2·05 a.u. and the force constant 25·8 md/a (experimental, 23·5 md/a). The total computed molecular energies for the equilibrium configurations of hydrogen and methane are -1·1605 a.u. (experimental, -1·175 a.u.) and -39·8444 a.u. (experimental, -40·51 a.u.) respectively.

[1]  L. Bartell,et al.  Mean and Equilibrium Molecular Structures of Methane and Deuteromethane as Determined by Electron Diffraction , 1961 .

[2]  E. L. Albasiny,et al.  A one-centre S.C.F. wave function for the methane molecule , 1961 .

[3]  R. Parr,et al.  On the Introduction of Arbitrary Angular Peakedness into Atomic Orbitals , 1961 .

[4]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[5]  W. L. Clinton.  Forces in Molecules. I. Application of the Virial Theorem , 1960 .

[6]  R. Parr,et al.  A One‐Center Wave Function for the Methane Molecule , 1960 .

[7]  A. D. McLean,et al.  Configuration Interaction in the Hydrogen Molecule—The Ground State , 1960 .

[8]  G. Herzberg,et al.  THE LYMAN BANDS OF MOLECULAR HYDROGEN , 1959 .

[9]  L. H. Jones,et al.  Force constants of methane. Infrared spectra and thermodynamic functions of isotopic methanes , 1959 .

[10]  R. Parr,et al.  A One‐Center Wave Function for the Hydrogen Molecule , 1958 .

[11]  B. Stoicheff.  HIGH RESOLUTION RAMAN SPECTROSCOPY OF GASES: IX. SPECTRA OF H2, HD, AND D2 , 1957 .

[12]  C. Carter.  Molecular orbital wave functions for methane and silane , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  H. C. Longuet-Higgins,et al.  The dynamics of binary hydrides , 1955 .

[14]  H. Massey,et al.  A self-consistent field for methane and its applications , 1941, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  J. C. Slater.  The Virial and Molecular Structure , 1933 .