Density Functional Theory

The subject of quantum chemistry may have reached an impasse. Keeping the discussion to ab initio quantum chemistry we now know how to do very large SCF calculations, thanks to the introduction of the Direct methodology by Almlof[1]. We can also manage to work with good basis sets for such calculations, although I consider that 6–31G* are not good enough, and probably something nearer to TZ2P is required for definitive SCF calculations.

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

[2]  B. Delley An all‐electron numerical method for solving the local density functional for polyatomic molecules , 1990 .

[3]  J. Almlöf,et al.  Principles for a direct SCF approach to LICAO–MOab‐initio calculations , 1982 .

[4]  Benny G. Johnson,et al.  The performance of a family of density functional methods , 1993 .

[5]  Dennis R. Salahub,et al.  Analytical gradient of the linear combination of Gaussian‐type orbitals—local spin density energy , 1989 .

[6]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[7]  Nicholas C. Handy,et al.  A study of O3, S3, CH2, and Be2 using Kohn–Sham theory with accurate quadrature and large basis sets , 1993 .

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

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

[10]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[11]  D. Salahub,et al.  New algorithm for the optimization of geometries in local density functional theory , 1990 .

[12]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

[13]  Nicholas C. Handy,et al.  A general purpose exchange-correlation energy functional , 1993 .

[14]  C. W. Murray,et al.  Study of methane, acetylene, ethene, and benzene using Kohn-Sham theory , 1993 .

[15]  Erich Wimmer,et al.  Density functional Gaussian‐type‐orbital approach to molecular geometries, vibrations, and reaction energies , 1992 .

[16]  Nicholas C. Handy,et al.  Kohn—Sham bond lengths and frequencies calculated with accurate quadrature and large basis sets , 1992 .

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

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

[19]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

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

[21]  R. Parr,et al.  Long‐range behavior of natural orbitals and electron density , 1975 .

[22]  N. Handy,et al.  Structure and vibrational frequencies of diazomethylene (CNN) and diazasilene (SiNN) using nonlocal density functional theory , 1993 .

[23]  Benny G. Johnson,et al.  Preliminary results on the performance of a family of density functional methods , 1992 .

[24]  Integration points for the reduction of boundary conditions , 1973 .

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

[26]  P. Taylor,et al.  AN ACCURATE AB-INITIO QUARTIC FORCE-FIELD FOR FORMALDEHYDE AND ITS ISOTOPOMERS , 1993 .

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

[28]  Benny G. Johnson,et al.  A standard grid for density functional calculations , 1993 .

[29]  Dunlap,et al.  Local-density-functional total energy gradients in the linear combination of Gaussian-type orbitals method. , 1990, Physical review. A, Atomic, molecular, and optical physics.

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

[31]  A. Becke Thermochemical tests of a kinetic-energy dependent exchange-correlation approximation , 1994 .

[32]  Tom Ziegler,et al.  The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration , 1988 .

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

[34]  P. Dirac Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[35]  John P. Perdew,et al.  Exact differential equation for the density and ionization energy of a many-particle system , 1984 .

[36]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

[37]  Axel D. Becke,et al.  Density-functional thermochemistry. I. The effect of the exchange-only gradient correction , 1992 .

[38]  N. Handy,et al.  Structures and vibrational frequencies of FOOF and FONO using density functional theory , 1993 .

[39]  L. Curtiss,et al.  Gaussian‐1 theory: A general procedure for prediction of molecular energies , 1989 .

[40]  R. K. Nesbet,et al.  Self‐Consistent Orbitals for Radicals , 1954 .

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

[42]  Nicholas C. Handy,et al.  Analytic Second Derivatives of the Potential Energy Surface , 1993 .

[43]  R. Parr Density-functional theory of atoms and molecules , 1989 .

[44]  Axel D. Becke,et al.  Numerical solution of Schrödinger’s equation in polyatomic molecules , 1990 .

[45]  Evert Jan Baerends,et al.  Relativistic effects on bonding , 1981 .

[46]  Benny G. Johnson,et al.  Kohn—Sham density-functional theory within a finite basis set , 1992 .

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

[48]  R. O. Jones Molecular bonding in Group IIA dimers Be2–Ba2 , 1979 .

[49]  Evert Jan Baerends,et al.  Numerical integration for polyatomic systems , 1992 .

[50]  Hermann Stoll,et al.  Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr , 1989 .

[51]  A. Becke Density-functional thermochemistry. II: The effect of the Perdew-Wang generalized-gradient correlation correction , 1992 .

[52]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.