An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Spectral representation of Hartree‐Fock exchange operator

We report a new mathematical result: it is possible to construct a spectral representation of the two particles Coulomb potential in the form of | r ? r ^′|^?1 = ∑_λλg( r ) g_λ( r ^′). We call this formula λ‐decomposition. Two special nontrivial cases of λ‐decomposition are reported together with the numerical analysis of the convergence for one of them. It is shown how λ‐decomposition allows to construct a new fast algorithm for Hartree‐Fock exchange operator calculation, in which the calculation of electron repulsion integrals (ERIs) is completely avoided. The connection between the new method and the resolution of identity and Cholesky decomposition based approaches has been established. Finally, the accuracy of ERIs evaluation within the new approach has been studied numerically. The results demonstrate that it is possible to achieve the accuracy of 10^?10 for the ERIs in wide range of their orbital exponents with relatively small number of terms in λ‐decomposition. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Self-consistent field calculations using two-body density functionals for correlation energy component: I. Atomic systems

Self-consistent field calculations are done using two-body density functionals for the correlation energy. The corresponding functional derivatives are obtained and used in pseudo-eigenvalue equations analogous to the Kohn–Sham ones. The examples studied include atomic systems from He to Ar. The values obtained for ionization potentials, electron affinities, dipole polarizabilities, and virial ratios from these calculations are given, and the effect of exchange is addressed. The results obtained are in good agreement with experimental values, and are of the same quality as those given by accurate exchange-correlation functionals. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1887–1898, 1998     

Self-consistent field calculations using two-body density functionals for correlation energy component: II. Small molecules

In part I of this series, self-consistent calculations using two-body density functionals for correlation energy were done and applied to atomic systems, giving very good results. We now apply the same scheme to small molecules. The examples studied include diatomic (H₂, Li₂, B₂, C₂, N₂, O₂, F₂, HLi, HBe, HB, HF, and HCl) as well as polyatomic (H₂O, NH₃, H₂O₂, and O₃) molecules at their ground states. The values reported for equilibrium geometries, atomization energies, vibrational frequencies, and dipole moments are compared with experimental and other theoretical calculations, with good agreement in most cases. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1899–1908, 1998     

Convergence of the Rayleigh—Ritz method in self-consistent-field and multiconfiguration self-consistent-field calculations

We investigate the analytical convergence of SCF and MCSCF calculations, when the dimension of the subspaces to which the orbitals are restricted tends to infinity. We show that the completeness only inL ²(R ³;C ²) of the orbital bases does not ensure the convergence of the Ritz-energy, neither in SCF nor in MCSCF calculations, but that this convergence — as well as the convergence of the Ritz-orbitals in SCF calculations — is on the contrary guaranteed if the orbital bases are complete in the Sobolev spaceW ^1,2(R ³;C ²). Some consequences on the choice of the orbital exponents of Slater and Gauss functions are also discussed.     

Use of exchange maximization to generate starting vectors for self-consistent field calculations on metal cluster/adsorbate systems

Localized molecular orbitals (LMOs) derived from exchange maximization with respect to all atom-centered basis functions in the basis set are shown to generate a good starting electronic field for self-consistent field calculations on extended systems such as metal clusters, for which well-defined chemical bonds are not present. Examples studied are a cluster of 20 Ni atoms and the Pt(97)CO, Ag(43)/H(3)CNON, Ag(91)/H(2)CO, and vinylidene/Ni metal cluster plus adsorbate systems. It is also shown that improved starting vectors can be obtained by remixing a subset of the LMOs with the largest exchange eigenvalues through diagonalization of the Fock matrix computed with a null electronic field. Employing only a subset of the exchange-maximized LMOs in the first iterations, and then gradually expanding the space in which the diagonalizations are carried out in succeeding cycles, is shown to be an effective means of guiding the SCF procedure to the converged full-basis solution.