Ab initio density functional theory: OEP-MBPT(2). A new orbital-dependent correlation functional

Using the optimized effective potential (OEP) method in conjunction with an orbital-dependent correlation functional developed on the basis of second-order many-body perturbation theory [MBPT(2)], we perform ab initio correlated density functional calculations. Unlike other density functional methods, this offers the first correlation approximation in a converging series of approximations analogous to that in wave function theory. The OEP-MBPT(2) correlation potentials of the helium isoelectronic series and the neon atom are in excellent agreement with prior quantum Monte Carlo (QMC) results, while the widely used conventional approximate density functional theory correlation potentials have qualitatively incorrect behavior. Furthermore, the correlation energies, total energies, and the highest occupied orbital energies calculated by the OEP-MBPT(2) method are also remarkably accurate. Unlike QMC, our procedure can be applied to general molecules.

[1]  R. Dreizler,et al.  van der Waals bonds in density-functional theory , 2000 .

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

[3]  Renato Colle,et al.  Approximate calculation of the correlation energy for the closed shells , 1975 .

[4]  GRADIENT-CORRECTED CORRELATION WITH NEARLY EXACT KOHN-SHAM EXCHANGE : CALCULATIONS FOR SI AND GE , 1997 .

[5]  Görling,et al.  Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. , 1993, Physical review. B, Condensed matter.

[6]  R. Colle,et al.  Approximate calculation of the correlation energy for the closed and open shells , 1979 .

[7]  Davidson,et al.  Ground-state correlation energies for atomic ions with 3 to 18 electrons. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[8]  Per-Olof Widmark,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1990 .

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

[10]  Andreas Görling,et al.  New KS Method for Molecules Based on an Exchange Charge Density Generating the Exact Local KS Exchange Potential , 1999 .

[11]  Krieger,et al.  Construction and application of an accurate local spin-polarized Kohn-Sham potential with integer discontinuity: Exchange-only theory. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[12]  So Hirata,et al.  Can optimized effective potentials be determined uniquely , 2001 .

[13]  J. Cizek.  On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[14]  E. Keinan,et al.  Chemistry for the 21st Century , 2000 .

[15]  Krieger,et al.  Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[16]  An exact second-order expression for the density functional theory correlation potential for molecules , 2001 .

[17]  A. Szabo,et al.  Modern quantum chemistry , 1982 .

[18]  Gonze,et al.  Separation of the exchange-correlation potential into exchange plus correlation: An optimized effective potential approach. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[19]  So Hirata,et al.  Finite-basis-set optimized effective potential exchange-only method , 2002 .

[20]  Kotani,et al.  KKR-ASA method in exact exchange-potential band-structure calculations. , 1996, Physical review. B, Condensed matter.

[21]  C. Umrigar,et al.  Accurate exchange-correlation potentials and total-energy components for the helium isoelectronic series. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[22]  John C. Slater,et al.  Quantum Theory of Molecules and Solids Vol. 4: The Self‐Consistent Field for Molecules and Solids , 1974 .

[23]  Ingvar Lindgren,et al.  Atomic Many-Body Theory , 1982 .

[24]  Lévy,et al.  Excitation energies from density-functional orbital energies. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[25]  Mel Levy,et al.  Electron densities in search of Hamiltonians , 1982 .

[26]  A. Rajagopal,et al.  Theory of inhomogeneous magnetic electron gas , 1972 .

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

[28]  J. D. Talman,et al.  Optimized effective atomic central potential , 1976 .

[29]  From explicit to implicit density functionals , 1999 .

[30]  Xavier Gonze,et al.  Relationship of Kohn-Sham eigenvalues to excitation energies , 1998 .

[31]  Casida.  Generalization of the optimized-effective-potential model to include electron correlation: A variational derivation of the Sham-Schlüter equation for the exact exchange-correlation potential. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[32]  Kotani.  Exact exchange-potential band-structure calculations by the LMTO-ASA method: MgO and CaO. , 1994, Physical Review B (Condensed Matter).

[33]  E. Gross,et al.  The optimized effective potential method of density functional theory: Applications to atomic and molecular systems , 1997 .

[34]  M. Schlüter,et al.  Density-Functional Theory of the Energy Gap , 1983 .

[35]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[36]  L. Hedin,et al.  A local exchange-correlation potential for the spin polarized case. i , 1972 .

[37]  G. Iafrate,et al.  Self-consistent calculations of atomic properties using self-interaction-free exchange-only Kohn-Sham potentials. , 1993, Physical review. A, Atomic, molecular, and optical physics.

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

[39]  Davidson,et al.  Ground-state correlation energies for two- to ten-electron atomic ions. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[40]  Görling,et al.  Density-functional theory for excited states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[41]  John C. Slater,et al.  Quantum Theory of Molecules and Solids , 1951 .

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

[43]  R. T. Sharp,et al.  A Variational Approach to the Unipotential Many-Electron Problem , 1953 .