Counterintuitive Coulomb hole around the bond midplane.

The Coulomb hole does not have its largest depth around an electron in or near the bond midplane. It splits into two parts, localized on both nuclear sites forming the bond. Even counterintuitive positive values of the "hole" around such a position may be observed. This happens when the Fermi hole is deeper than the total exchange-correlation hole at the reference electron position. This Coulomb "heap" is shown to arise from correlation effects on the one-electron density rather than correlation effects in the pair density. Left-right correlation tends to enhance the effect of the nuclear attraction, contracting the electron density around the nuclear positions and depleting the bond center region. Possible alternative definitions of the Coulomb hole are discussed, including one based on the exact Kohn-Sham exchange hole. Approximate density functional theory methods (generalized gradient approximation) are not accurate enough to realize the advantages of this definition.

[1]  D. Ellis.  Density Functional Theory of Molecules, Clusters, and Solids , 2012 .

[2]  Manolo C Per,et al.  Anisotropic intracule densities and electron correlation in H2: a quantum Monte Carlo study. , 2009, The Journal of chemical physics.

[3]  Yu Wang,et al.  Electron correlation in the GK state of the hydrogen molecule. , 2007, The Journal of chemical physics.

[4]  Jian Wang,et al.  Counterintuitive effects of the electron correlation in the first-excited 1Σ+g state of the hydrogen molecule , 2006 .

[5]  Ting-Kuo Lee,et al.  Exchange-correlation energy in molecules: A variational quantum Monte Carlo study , 2006 .

[6]  P. Gori-Giorgi,et al.  Simple model for the spherically and system-averaged pair density: Results for two-electron atoms , 2004, cond-mat/0411179.

[7]  R. Bartlett,et al.  Short-range corrections to the correlation hole , 2004 .

[8]  S. Moroni,et al.  Pair distribution functions of the two-dimensional electron gas with two symmetric valleys , 2004, 0902.0155.

[9]  Xiaoyin Pan,et al.  Quantal density functional theory of the hydrogen molecule. , 2003, The Journal of chemical physics.

[10]  D. Salahub,et al.  Metal-ligand interactions : molecular, nano-, micro-, and macro-systems in complex environments , 2003 .

[11]  P. Gori-Giorgi,et al.  Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities , 2002, cond-mat/0206147.

[12]  R. Bartlett,et al.  Time-dependent density functional theory employing optimized effective potentials , 2002 .

[13]  Evert Jan Baerends,et al.  An approximate exchange-correlation hole density as a functional of the natural orbitals , 2002 .

[14]  Frank Jensen,et al.  Polarization consistent basis sets: Principles , 2001 .

[15]  R. Q. Hood,et al.  Comparative study of density-functional theories of the exchange-correlation hole and energy in silicon , 2001, cond-mat/0101363.

[16]  M Nekovee,et al.  Quantum Monte Carlo analysis of exchange and correlation in the strongly inhomogeneous electron gas. , 2000, Physical review letters.

[17]  M. Ratner,et al.  Reply to ``Comment on `Correlation holes in a spin-polarized dense electron gas' '' , 2000 .

[18]  C. Y. Fong,et al.  Exchange-correlation hole of the Si atom: A quantum Monte Carlo study , 2000, physics/0004073.

[19]  Debashis Mukherjee,et al.  Cumulant expansion of the reduced density matrices , 1999 .

[20]  M. Ratner,et al.  Correlation holes in a spin-polarized dense electron gas , 1999 .

[21]  John P. Perdew,et al.  Generalized gradient approximation to the angle- and system-averaged exchange hole , 1998 .

[22]  A. J. Williamson,et al.  Exchange and correlation in silicon , 1998 .

[23]  G. Ortiz,et al.  Erratum: Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas [Phys. Rev. B50, 1391 (1994)] , 1997 .

[24]  E. Baerends,et al.  Exchange and correlation energy in density functional theory. Comparison of accurate DFT quantities with traditional Hartree-Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2. , 1997 .

[25]  Evert Jan Baerends,et al.  A Quantum Chemical View of Density Functional Theory , 1997 .

[26]  Nicholas C. Handy,et al.  Exchange‐correlation potentials , 1996 .

[27]  Baerends,et al.  Effect of molecular dissociation on the exchange-correlation Kohn-Sham potential. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[28]  R. Leeuwen,et al.  Molecular exchange‐correlation Kohn–Sham potential and energy density from ab initio first‐ and second‐order density matrices: Examples for XH (X=Li, B, F) , 1996 .

[29]  R. Needs,et al.  Monte Carlo Investigation of Exchange and Correlation in Silicon , 1996 .

[30]  Jorge M. Seminario,et al.  Recent developments and applications of modern density functional theory , 1996 .

[31]  M. Levy.  Elementary Concepts in Density Functional Theory , 1996 .

[32]  K. Burke,et al.  Real‐space analysis of the exchange‐correlation energy , 1995 .

[33]  Y. Takada,et al.  Coulomb Hole in a He Atom , 1995 .

[34]  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.

[35]  Sahni,et al.  Coulomb holes and correlation potentials in the helium atom. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[36]  Ortiz,et al.  Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas. , 1994, Physical review. B, Condensed matter.

[37]  Görling,et al.  Exact Kohn-Sham scheme based on perturbation theory. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[38]  Kirk A. Peterson,et al.  Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction , 1994 .

[39]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[40]  K. E. Banyard,et al.  Momentum space and Coulomb correlation: A two‐particle density analysis for the H2(1Σ+g) molecule , 1993 .

[41]  L. Wolniewicz,et al.  Relativistic energies of the ground state of the hydrogen molecule , 1993 .

[42]  E. Krotscheck,et al.  Electron correlations in atomic systems , 1992 .

[43]  Wang,et al.  Pair-distribution function and its coupling-constant average for the spin-polarized electron gas. , 1992, Physical review. B, Condensed matter.

[44]  K. E. Banyard,et al.  Coulomb correlation in the H2 molecule: A two‐particle density analysis , 1992 .

[45]  Wang,et al.  Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. , 1991, Physical review. B, Condensed matter.

[46]  V. Tschinke,et al.  On the different representations of the hole‐correlation functions in the Hartree–Fock and the Hartree–Fock–Slater methods and their influence on bond energy calculations , 1990 .

[47]  Wang,et al.  Pair-correlation function and single-particle occupation numbers in diamond and silicon. , 1990, Physical review letters.

[48]  E. Krotscheck,et al.  Local structure of electron correlations in atomic systems , 1989 .

[49]  A. Becke,et al.  Exchange holes in inhomogeneous systems: A coordinate-space model. , 1989, Physical review. A, General physics.

[50]  D. Ceperley,et al.  Ground state of the two-dimensional electron gas. , 1989, Physical review. B, Condensed matter.

[51]  V. Tschinke,et al.  On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems , 1989 .

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

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

[54]  R. J. Boyd,et al.  Intracule densities and electron correlation in the hydrogen molecule , 1988 .

[55]  A. Becke.  Correlation energy of an inhomogeneous electron gas: A coordinate‐space model , 1988 .

[56]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[57]  Ajit J. Thakkar,et al.  Extracules, Intracules, Correlation Holes, Potentials, Coefficients and All That , 1987 .

[58]  M. Levy.  Correlation Energy Functionals of One-Matrices and Hartree-Fock Densities , 1987 .

[59]  Robert Erdahl,et al.  Density Matrices and Density Functionals , 1987 .

[60]  J. Perdew,et al.  Accurate density functional for the energy: Real-space cutoff of the gradient expansion for the exchange hole. , 1985, Physical review letters.

[61]  A. Thakkar,et al.  Anisotropy of the Coulomb hole in H2 , 1984 .

[62]  James S. Harris,et al.  Adiabatic-connection approach to Kohn-Sham theory , 1984 .

[63]  John P. Perdew,et al.  Study of the density-gradient expansion for the exchange energy , 1982 .

[64]  R. J. Boyd,et al.  Angular aspects of electron correlation and the Coulomb hole , 1982 .

[65]  Mats Jonson,et al.  Descriptions of exchange and correlation effects in inhomogeneous electron systems , 1979 .

[66]  John P. Perdew,et al.  Exchange-correlation energy of a metallic surface: Wave-vector analysis , 1977 .

[67]  B. Lundqvist,et al.  Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism , 1976 .

[68]  John P. Perdew,et al.  The exchange-correlation energy of a metallic surface , 1975 .

[69]  B. Lundqvist,et al.  Contribution to the cohesive energy of simple metals: Spin-dependent effect , 1974 .

[70]  R O Jones,et al.  The surface energy of a bounded electron gas , 1974 .

[71]  J. C. Slater,et al.  Self-Consistent-Field X α Cluster Method for Polyatomic Molecules and Solids , 1972 .

[72]  W. Kutzelnigg,et al.  Correlation Coefficients for Electronic Wave Functions , 1968 .

[73]  L. Hedin.  NEW METHOD FOR CALCULATING THE ONE-PARTICLE GREEN'S FUNCTION WITH APPLICATION TO THE ELECTRON-GAS PROBLEM , 1965 .

[74]  C. Coulson,et al.  Electron Correlation in the Ground State of Helium , 1961 .

[75]  R. Mcweeny.  Some Recent Advances in Density Matrix Theory , 1960 .

[76]  V W Maslen,et al.  The Fermi, or Exchange, Hole in Atoms , 1956 .

[77]  Per-Olov Löwdin,et al.  Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock Approximation , 1955 .

[78]  P. Löwdin.  Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction , 1955 .

[79]  J. C. Slater.  A Simplification of the Hartree-Fock Method , 1951 .

[80]  E. Wigner.  On the Interaction of Electrons in Metals , 1934 .

[81]  E. Wigner,et al.  On the Constitution of Metallic Sodium. II , 1933 .