Long-range/short-range separation of the electron-electron interaction in density functional theory

By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be efficiently calculated by traditional wave function methods, while the short-range part can be handled by a density functional. The analysis of this functional with respect to the range of the associated interaction reveals that, in the limit of a very short-range interaction, the short-range exchange-correlation energy can be expressed as a simple local functional of the on-top pair density and its first derivatives. This provides an explanation for the accuracy of the local density approximation (LDA) for the short-range functional. Moreover, this analysis leads also to new simple approximations for the short-range exchange and correlation energies improving the LDA.

[1]  R. D. Adamson,et al.  A family of attenuated Coulomb operators , 1996 .

[2]  Kimihiko Hirao,et al.  A density functional study of van der Waals interactions , 2002 .

[3]  Andreas Savin,et al.  Density functionals for the Yukawa electron-electron interaction , 1995 .

[4]  Burke,et al.  Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[5]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[6]  Impact of Electron-Electron Cusp on Configuration Interaction Energies , 2001, cond-mat/0102536.

[7]  Andreas Savin,et al.  Combining long-range configuration interaction with short-range density functionals , 1997 .

[8]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

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

[10]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[11]  R. O. Jones,et al.  The density functional formalism, its applications and prospects , 1989 .

[12]  Weitao Yang.  Generalized adiabatic connection in density functional theory , 1998 .

[13]  Ross D. Adamson,et al.  Efficient calculation of short‐range Coulomb energies , 1999 .

[14]  Roland Lindh,et al.  The reduced multiplication scheme of the Rys quadrature and new recurrence relations for auxiliary function based two‐electron integral evaluation , 1991 .

[15]  David Pines,et al.  Correlation Energy of a Free Electron Gas , 1958 .

[16]  Michael J. Mehl,et al.  Easily Implementable Nonlocal Exchange-Correlation Energy Functional , 1981 .

[17]  K. Burke,et al.  Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging , 1998 .

[18]  A. Savin,et al.  Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules , 2002 .

[19]  J. Perdew,et al.  Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. , 1986, Physical review. B, Condensed matter.

[20]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

[21]  M. P. Das.  RECENT ADVANCES IN THE DENSITY FUNCTIONAL THEORY , 1985 .

[22]  A. Savin,et al.  Short-Range Exchange-Correlation Energy of a Uniform Electron Gas with Modified Electron-Electron Interaction , 2004, cond-mat/0611559.

[23]  Gustavo E Scuseria,et al.  Assessment and validation of a screened Coulomb hybrid density functional. , 2004, The Journal of chemical physics.

[24]  Exchange‐correlation energies and correlation holes for some two‐ and four‐electron atoms along a nonlinear adiabatic connection in density functional theory , 2003 .

[25]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

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

[27]  San-Fabián,et al.  Density-functional formalism and the two-body problem. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[28]  M. Levy.  Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Michel Dupuis,et al.  Evaluation of molecular integrals over Gaussian basis functions , 1976 .

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

[31]  Is the local density approximation exact for short wavelength fluctuations? , 1994, Physical review letters.

[32]  O. Heinonen,et al.  Many-Particle Theory, , 1991 .

[33]  Kieron Burke,et al.  On-Top Pair-Density Interpretation of Spin Density Functional Theory, with Applications to Magnetism , 1997 .

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

[35]  A. Savin,et al.  Correlation energies for some two- and four-electron systems along the adiabatic connection in density functional theory , 1999 .

[36]  William H. Press,et al.  Numerical recipes , 1990 .

[37]  K. Hirao,et al.  A long-range correction scheme for generalized-gradient-approximation exchange functionals , 2001 .

[38]  Axel D. Becke,et al.  Hartree–Fock exchange energy of an inhomogeneous electron gas , 1983 .

[39]  P. Knowles,et al.  An efficient internally contracted multiconfiguration–reference configuration interaction method , 1988 .

[40]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[41]  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.

[42]  K. Hirao,et al.  A long-range-corrected time-dependent density functional theory. , 2004, The Journal of chemical physics.

[43]  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 .

[44]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[45]  A. Savin,et al.  Adiabatic connection approach to density functional theory of electronic systems , 2003 .

[46]  D. Langreth,et al.  Beyond the local-density approximation in calculations of ground-state electronic properties , 1983 .

[47]  S. Raimes.  Many-electron theory , 1972 .

[48]  J. Kimball.  Short-Range Correlations and Electron-Gas Response Functions , 1973 .

[49]  R. Armiento,et al.  Alternative separation of exchange and correlation in density-functional theory , 2003 .

[50]  A. Becke,et al.  Extension of the local-spin-density exchange-correlation approximation to multiplet states , 1995 .

[51]  Dmitrii E. Makarov,et al.  van der Waals Energies in Density Functional Theory , 1998 .

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