Molecular gradients and hessians implemented in density functional theory

We derive expressions for molecular gradients and hessians for the case when the energy is evaluated using density functional theory. Although derivative expressions have been proposed previously, our derivation is based on the unitary exponential parameterization of the wavefunction, and our expressions are valid for local and non–local potentials. Density functional theory, although similar in implementation to standard SCF theory, differs in that it introduces an exchange–correlation term which is density dependent. The presence of such a quantity introduces additional derivative terms which are not present in standard approaches of electronic structure theory. Expressions are derived for both the exact Coulombic repulsion, as well as the case where the density is expressed as a fitted quantity. Given these choices our final equations offer a computationally tractable expression with particular emphasis on conditions which ensure that the computed quantities are numerically correct. We show that althou...

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

[2]  R. Moccia.  Optimization of the basis functions in SCF MO calculations optimized one-center SCF MO basis set for HCL , 1967 .

[3]  T. Ziegler.  Approximate Density Functional Theory as a Practical Tool in Molecular Energetics and Dynamics , 1991 .

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

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

[6]  M. Page,et al.  Multireference CI Gradients and MCSCF Second Derivatives. , 1984 .

[7]  M. Dupuis.  Energy derivatives for configuration interaction wave functions , 1981 .

[8]  R. Bartlett,et al.  Third‐order MBPT gradients , 1985 .

[9]  P. Wormer,et al.  Conjugate gradient method for the solution of linear equations: Application to molecular electronic structure calculations , 1982 .

[10]  D. Ellis,et al.  An efficient numerical multicenter basis set for molecular orbital calculations: Application to FeCl4 , 1973 .

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

[12]  R. Stanton.  Hellmann‐Feynman Theorem and Correlation Energies , 1962 .

[13]  Leonard Kleinman,et al.  New Method for Calculating Wave Functions in Crystals and Molecules , 1959 .

[14]  Stephen W. Taylor,et al.  Modeling the potential of a charge distribution , 1992 .

[15]  P. Joergensen,et al.  Second Quantization-based Methods in Quantum Chemistry , 1981 .

[16]  J. Connolly,et al.  On first‐row diatomic molecules and local density models , 1979 .

[17]  K. Lawley.  Molecular scattering : physical and chemical applications , 1975 .

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

[19]  Peter J. Knowles,et al.  Studies using the CASSCF wavefunction , 1982 .

[20]  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.

[21]  Peter Pulay,et al.  Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules , 1969 .

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

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

[24]  Second and third derivatives of the linear combination of Gaussian type orbitals–local spin density energy , 1990 .

[25]  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.

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

[27]  Kazuhiro Ishida,et al.  Efficient determination and characterization of transition states using ab-initio methods , 1977 .

[28]  Parametrization of molecular orbital transformations , 1984 .

[29]  B. Delley,et al.  Analytic energy derivatives in the numerical local‐density‐functional approach , 1991 .

[30]  Erich Wimmer,et al.  DGauss : a density functional method for molecular and electronic structure calculations in the 1990s , 1991 .

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

[32]  B. Delley,et al.  Efficient and accurate expansion methods for molecules in local density models , 1982 .

[33]  U. V. Barth,et al.  Local-density theory of multiplet structure , 1979 .

[34]  G. G. Hall,et al.  Fitting electron densities of molecules , 1984 .

[35]  Timothy J. Lee,et al.  An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2 , 1991 .

[36]  K. P. Lawley,et al.  Ab initio methods in quantum chemistry , 1987 .

[37]  N. Handy,et al.  Higher analytic derivatives. II. The fourth derivative of self‐consistent‐field energy , 1991 .

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

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

[40]  Trygve Helgaker,et al.  Molecular Hessians for large‐scale MCSCF wave functions , 1986 .

[41]  H. Adachi,et al.  Calculations of molecular ionization energies using a self‐consistent‐charge Hartree–Fock–Slater method , 1976 .

[42]  W. Green,et al.  Ab initio prediction of fundamental, overtone and combination band infrared intensities , 1990 .

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

[44]  Willis B. Person,et al.  Dipole moment derivatives and infrared intensities. II. Polar tensors in methyl halide molecules , 1976 .

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

[46]  Poul Jo,et al.  Optimization of orbitals for multiconfigurational reference states , 1978 .

[47]  Harry F. King,et al.  Analytic computation of energy derivatives. Relationships among partial derivatives of a variationally determined function , 1986 .

[48]  Per E. M. Siegbahn,et al.  A new direct CI method for large CI expansions in a small orbital space , 1984 .

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

[50]  N. H. March,et al.  Theory of the inhomogeneous electron gas , 1983 .

[51]  Tom Ziegler,et al.  Optimization of molecular structures by self‐consistent and nonlocal density‐functional theory , 1991 .

[52]  Henry F. Schaefer,et al.  Applications of electronic structure theory , 1977 .

[53]  Magnus R. Hestenes,et al.  Conjugate Direction Methods in Optimization , 1980 .