A NEW GRID-FREE DENSITY-FUNCTIONAL TECHNIQUE : APPLICATION TO THE TORSIONAL ENERGY SURFACES OF ETHANE, HYDRAZINE, AND HYDROGEN PEROXIDE

We describe the implementation of a new grid-free density-functional technique for exchange-correlation potentials of ρ1/3 form (exchange-only local density-functional theory potentials). The potential is fitted to integrable functional forms by solving a set of nonlinear equations, rather than by fitting on a three-dimensional grid of points. This completely analytical method produces smooth energy surfaces and exact energy gradients. The method is found to be several times faster computationally in single-point calculations than a comparable grid-based method with a moderate number of grid points, and it is more than an order of magnitude faster for geometry optimizations. The analytical method is tested on the torsional energy surfaces of the classic isoelectronic series C2H6, N2H4, and H2O2, using the Hartree–Fock–Slater potential (α=2/3). The locations and relative energies of energy extrema, and the structural variations across the potential surfaces, are in good agreement with experimental data and...

[1]  N. Handy,et al.  Density functional theory studies of 4-π-electron systems , 1994 .

[2]  Martin,et al.  Unconstrained minimization approach for electronic computations that scales linearly with system size. , 1993, Physical review. B, Condensed matter.

[3]  T. Dunning,et al.  Theoretical Determination of the Barriers to Internal Rotation in Hydrogen Peroxide. , 1975 .

[4]  C. T. White,et al.  Local spin-density calculations of anisotropic hyperfine constants in oriented free radicals , 1988 .

[5]  D. O. Harris,et al.  On the Determination of Barriers to Internal Rotation , 1970 .

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

[7]  J. Mintmire.  Geometry optimization of molecules within an LCGTO local-density functional approach , 1990 .

[8]  Russell M. Pitzer,et al.  The barrier to internal rotation in ethane , 1983 .

[9]  J. Hougen,et al.  Analysis of the microwave spectrum of hydrazine , 1982 .

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

[11]  J. Koput.  On the r0∗ structure and the torsional potential function of hydrogen peroxide , 1986 .

[12]  J. Mrozek,et al.  Modified Gaussian functions and their use in quantum chemistry. I. Integrals , 1973 .

[13]  A. Veillard.  Distortional effects on the ethane internal rotation barrier and rotation barriers in borazane and methylsilane , 1969 .

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

[15]  R. Parr,et al.  Discontinuous approximate molecular electronic wave‐functions , 1977 .

[16]  Michael J. Frisch,et al.  Analytic second derivatives of the gradient-corrected density functional energy. Effect of quadrature weight derivatives , 1993 .

[17]  Cook,et al.  Grid-free density-functional technique with analytical energy gradients. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[18]  Brett I. Dunlap,et al.  Lcao‐Xα calculations of rotational energy barriers—prototypes of chemical reactions , 1986 .

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

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

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

[22]  K. Kuchitsu.  Comparison of Molecular Structures Determined by Electron Diffraction and Spectroscopy. Ethane and Diborane , 1968 .

[23]  L. Radom,et al.  An ab initio Investigation of the Equilibrium Structures of Hydrazine and of the Transition Structures Connecting Them , 1986 .

[24]  Ronald H. Felton,et al.  A new computational approach to Slater’s SCF–Xα equation , 1975 .

[25]  J. D. Kemp,et al.  The Entropy of Ethane and the Third Law of Thermodynamics. Hindered Rotation of Methyl Groups , 1937 .

[26]  Michael J. Frisch,et al.  Achieving Linear Scaling for the Electronic Quantum Coulomb Problem , 1996, Science.

[27]  J. Pople,et al.  Effect of electron correlation of theoretical equilibrium geometries. 2. Comparison of third-order perturbation and configuration interaction results with experiment , 1982 .

[28]  J. E. Boggs,et al.  Structural changes as a function of torsional motion studied by ab initio calculations. Part 2. X2A-AX2 (A = N, P and X = H, F, Cl) and some implications for electron diffraction analysis , 1993 .

[29]  Brett I. Dunlap.  Geometry optimization using local density functional methods , 1986 .

[30]  K. Kohata,et al.  Molecular structure of hydrazine as studied by gas electron diffraction , 1982 .

[31]  White,et al.  Proton Fermi-contact coupling constants from local-density-functional theory: Application to the soliton in polyacetylene. , 1986, Physical review letters.

[32]  T. Kasuya,et al.  Internal Motions of Hydrazine , 1963 .

[33]  H. Schaefer,et al.  SELF-CONSISTENT CHANGES OF GEOMETRICAL PARAMETERS : EXPERIMENT AND THEORY , 1994 .

[34]  Emilio San-Fabián,et al.  Automatic numerical integration techniques for polyatomic molecules , 1994 .

[35]  Z. Maksić,et al.  Explicit Formulas for Molecular Integrals over Hermite–Gaussian Functions , 1968 .

[36]  J. Mrozek,et al.  Modified Cartesian Gaussian functions and their use in quantum chemistry , 1973 .

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

[38]  R. Feynman.  Forces in Molecules , 1939 .

[39]  Jon Baker,et al.  The effect of grid quality and weight derivatives in density functional calculations , 1994 .

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

[41]  D. Cremer.  Theoretical determination of molecular structure and conformation. I. The role of basis set and correlation effects in calculations on hydrogen peroxide , 1978 .

[42]  L. B. Harding.  Theoretical studies of the hydrogen peroxide potential surface. 1. An ab initio anharmonic force field , 1989 .

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

[44]  Walter Kohn,et al.  Density functional/Wannier function theory for systems of very many atoms , 1993 .

[45]  S. L. Dixon,et al.  Semiempirical molecular orbital calculations with linear system size scaling , 1996 .

[46]  White,et al.  Hyperfine interactions in cluster models of the Pb defect center. , 1988, Physical review. B, Condensed matter.

[47]  Benny G. Johnson,et al.  A rotationally invariant procedure for density functional calculations , 1994 .

[48]  N. Rösch,et al.  On the gaussian-type orbitals approach to local density functional theory , 1989 .

[49]  S. Saito,et al.  Barrier to internal rotation in ethane from the microwave spectrum of CH3CHD2 , 1979 .

[50]  Axel D. Becke,et al.  Basis‐set‐free local density‐functional calculations of geometries of polyatomic molecules , 1993 .

[51]  R. H. Hunt,et al.  Rotational constants of the lowest torsional component (0G) of the ground state and lowest torsional component (1G) of the first excited torsional state of hydrogen peroxide , 1988 .

[52]  M. Karplus,et al.  Electron correlation and density-functional methods , 1987 .

[53]  J. D. Kemp,et al.  Hindered Rotation of the Methyl Groups in Ethane , 1936 .

[54]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

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

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

[57]  W. J. Orville-Thomas,et al.  Internal rotation in molecules , 1974 .

[58]  Weitao Yang,et al.  The divide‐and‐conquer density‐functional approach: Molecular internal rotation and density of states , 1992 .

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

[60]  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 .

[61]  R. Gáspár,et al.  Über eine Approximation des Hartree-Fockschen Potentials Durch eine Universelle Potentialfunktion , 1954 .

[62]  Jan Almlöf,et al.  Density functionals without meshes and grids , 1993 .