Exchange‐correlation potentials

We describe our implementation of the Zhao, Morrison, and Parr method [Phys. Rev. A 50, 2138 (1994)] for the calculation of molecular exchange‐correlation potentials from high‐level ab initio densities. The use of conventional Gaussian basis sets demands careful consideration of the value of the Lagrange multiplier associated with the constraint that reproduces the input density. Although formally infinite, we demonstrate that a finite value should be used in finite basis set calculations. The potential has been determined for Ne, HF, N2, H2O, and N2(1.5re), and compared with popular analytic potentials. We have then examined how well the Zhao, Morrison, Parr potential can be represented using a computational neural network. Assuming vxc=vxc(ρ), we incorporate the neural network into a regular Kohn–Sham procedure [Phys. Rev. A 140, 1133 (1965)] with encouraging results. The extension of this method to include density derivatives is briefly outlined.

[1]  Peter M. W. Gill,et al.  A new gradient-corrected exchange functional , 1996 .

[2]  Parr,et al.  From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[3]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[4]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[5]  Á. Nagy Exchange energy in the exact exchange-only density functional theory , 1993 .

[6]  van Leeuwen R,et al.  Molecular Kohn-Sham exchange-correlation potential from the correlated ab initio electron density. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[7]  Á. Nagy,et al.  Correlation energy density from ab initio first‐ and second‐order density matrices: A benchmark for approximate functionals , 1995 .

[8]  Kieron Burke,et al.  Comparison shopping for a gradient-corrected density functional , 1996 .

[9]  N. Handy,et al.  Implementation of analytic derivative density functional theory codes on scalar and parallel architectures , 1995 .

[10]  C. W. Murray,et al.  Quadrature schemes for integrals of density functional theory , 1993 .

[11]  M. Delbruck,et al.  Structural Chemistry and Molecular Biology , 1968 .

[12]  Laurene V. Fausett,et al.  Fundamentals Of Neural Networks , 1994 .

[13]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[14]  George B. Bacskay,et al.  A quadratically convergent Hartree—Fock (QC-SCF) method. Application to closed shell systems , 1981 .

[15]  J. E. Harriman Orthonormal orbitals for the representation of an arbitrary density , 1981 .

[16]  A. Becke A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[17]  N. Handy,et al.  The anharmonic constants for a symmetric top , 1995 .

[18]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[19]  Chen,et al.  v-representability for systems with low degeneracy. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[20]  N. Handy,et al.  Towards accurate exchange-correlation potentials for molecules , 1996 .

[21]  Ernzerhof,et al.  Energy differences between Kohn-Sham and Hartree-Fock wave functions yielding the same electron density. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[22]  Michael J. Frisch,et al.  Gradient theory applied to the Brueckner doubles method , 1991 .

[23]  J. Perdew,et al.  Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy , 1982 .

[24]  C. Almbladh,et al.  Density-functional exchange-correlation potentials and orbital eigenvalues for light atoms , 1984 .

[25]  R. Leeuwen,et al.  Exchange-correlation potential with correct asymptotic behavior. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[26]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[27]  R. Dreizler,et al.  Density Functional Methods In Physics , 1985 .