Simultaneous optimization of GTF exponents and their centers with fully variational treatment of Hartree-Fock molecular orbital calculation

The authors have proposed the fully variational molecular orbital (FVMO) method by which all parameters in the molecular orbitals are optimized under the variational principle. According to the fully variational treatment within the Hartree-Fock approximation, exponents and centers in the Gaussian-type function (GTF) basis set are determined simultaneously, as well as the linear combination of atomic orbital (LCAO) coefficients. The FBMO method gives the lowest energy under the variational principle, improves the flexibility of wave function drastically, and raises the ab initio (nonempirical) feature. In the calculation of the adiabatic potential for HeH{sup +}, the electron movement for dissociation limitation is smoothly expressed due to full optimization of GTF centers and exponents under a condition that satisfies the Hellmann-Feynman and virial theorems. Properties such as dipole and polarizability of the hydrogen and helium atoms and the LiH molecule are in good agreement with the numerical Hartree-Fock values, even if only s type GTFs are used. The authors have also applied the FVMO method to H{sub 2}O and CH{sub 4} molecules.

[1]  Hanspeter Huber.  Geometry optimization inab initio SCF calculations , 1980 .

[2]  Y. Osamura,et al.  Analytical energy gradients with respect to orbital exponents for molecular SCF wavefunctions , 1989 .

[3]  A. C. Hurley.  The computation of floating functions and their use in force constant calculations , 1988 .

[4]  J. O. Hirschfelder,et al.  Application of the Virial Theorem to Approximate Molecular and Metallic Eigenfunctions , 1937 .

[5]  Hanspeter Huber,et al.  Geometry optimization in AB initio calculations. Floating orbital geometry optimization applying the hellmann-feyman force , 1979 .

[6]  P. Mezey,et al.  The effects of optimization and scaling of AO exponents on molecular properties , 1977 .

[7]  H. Huber.  Geometry optimization inab initio SCF calculations , 1980 .

[8]  H. Schlegel,et al.  Hartree–Fock energy derivatives with respect to basis set exponents. Integral derivatives using Rys polynomials , 1987 .

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

[10]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[11]  A. A. Frost.  The Floating Spherical Gaussian Orbital Method , 1977 .

[12]  Y. Osamura,et al.  Orbital exponent optimization with the analytical gradient method for molecular self‐consistent‐field wave functions , 1991 .

[13]  R. Feynman.  Forces in Molecules , 1939 .

[14]  G. Herzberg.  Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules , 1939 .

[15]  Gradient optimization of polarization exponents inab initio MO calculations on H2SO → HSOH and CH3SH → CH2SH2 , 1990 .

[16]  J. Almlöf,et al.  Energy-optimized GTO basis sets for LCAO calculations. A gradient approach , 1986 .

[17]  G. G. Hall.  The stability of a wavefunction under a perturbation , 1961 .

[18]  Trygve Helgaker,et al.  Molecular wave functions and properties calculated using floating Gaussian orbitals , 1988 .

[19]  A. C. Hurley.  The electrostatic calculation of molecular energies - I. Methods of calculating molecular energies , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[21]  T. H. Dunning.  Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms , 1970 .

[22]  H. Huber.  Geometry optimization in ab initio scf calculations: The hydrogen clusters H+n(n = 7,9,11,13) , 1980 .