Ab initio effective core potentials: Reduction of all-electron molecular structure calculations to calculations involving only valence electrons

A formalism is developed for obtaining ab initio effective core potentials from numerical Hartree–Fock wavefunctions and such potentials are presented for C, N, O, F, Cl, Fe, Br, and I. The effective core potentials enable one to eliminate the core electrons and the associated orthogonality constraints from electronic structure calculations on atoms and molecules. The effective core potentials are angular momentum dependent, basis set independent, and stable against variational collapse of their eigenfunctions to core functions. They are derived from neutral atom wavefunctions using a pseudo‐orbital transformation which is motivated by considerations of the expected accuracy of their use and of basis set economy in molecular calculations. Then the accuracy is demonstrated by multiconfiguration Hartree–Fock calculations of potential energy curves for HF, HCl, HBr, HI, F2, Cl2, Br2, and I2 and one‐electron properties for HF and HBr. The differences between valence‐electron calculations employing the present...

[1]  V. Heine,et al.  THE MODEL POTENTIAL FOR POSITIVE IONS , 1965 .

[2]  R. Berry,et al.  Pseudopotential Method for Inelastic Processes in Atoms and Molecules. I. General Method and Photodetachment of O , 1969 .

[3]  Herman Feshbach Unified theory of nuclear reactions , 1958 .

[4]  L. Szász,et al.  Atomic and Molecular Calculations with the Pseudopotential Method. I. The Binding Energy and Equilibrium Internuclear Distance of the Na2 Molecule , 1966 .

[5]  K. Freed Theoretical basis for semi-empirical pseudopotentials , 1974 .

[6]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[7]  T. H. Dunning Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms , 1970 .

[8]  V. Heine,et al.  Cancellation of kinetic and potential energy in atoms, molecules, and solids , 1961 .

[9]  D. C. Cartwright,et al.  The importance of polarization for electron scattering in the intermediate energy region , 1971 .

[10]  A. C. Roach Theoretical ground state and excited state potential energy curves for alkali diatomic molecules , 1972 .

[11]  W. Goddard,et al.  The theoretical description of an asymmetric, nonresonant charge transfer process; Li + Na+ ⇌ Li+ + Na the two-state approximation , 1972 .

[12]  A. Wachters,et al.  Gaussian Basis Set for Molecular Wavefunctions Containing Third‐Row Atoms , 1970 .

[13]  W. Goddard,et al.  Fe and Ni AB initio effective potentials for use in molecular calculations , 1974 .

[14]  J. R. Wazer,et al.  On pseudopotential and effective‐potential SCF theory and its application to compounds of heavy elements , 1975 .

[15]  G. Simons New Model Potential for Pseudopotential Calculations , 1971 .

[16]  U. Öpik THE POLARIZATION OF A CLOSED-SHELL CORE OF AN ATOMIC SYSTEM BY AN OUTER ELECTRON. II. EVALUATION OF THE POLARIZABILITIES FROM OBSERVED SPECTRA. , 1967 .

[17]  J. Bardsley Pseudopotential calculations of alkali interactions , 1970 .

[18]  S. Huzinaga,et al.  Gaussian‐Type Functions for Polyatomic Systems. II , 1970 .

[19]  L. Szász Pseudopotential Theory of Atoms and Molecules. I. A New Method for the Calculation of Correlated Pair Functions , 1968 .

[20]  Enrico Clementi,et al.  Study of the electronic structure of molecules. XXII. Correlation energy corrections as a functional of the Hartree‐Fock type density and its application to the homonuclear diatomic molecules of the second row atoms , 1974 .

[21]  D. Rapp,et al.  Wavefunctions and pseudopotential for sodium atoms , 1973 .

[22]  K. Ladányi Zur Theorie der Edelmetalle , 1956 .

[23]  G. Simons,et al.  Atomic and Molecular Pseudopotential Studies Using Gaussian Orbitals , 1970 .

[24]  Harrison Shull,et al.  NATURAL ORBITALS IN THE QUANTUM THEORY OF TWO-ELECTRON SYSTEMS , 1956 .

[25]  W. Fink Approach to Partially Predetermining Molecular Electronic Structure. The Li He Interaction Potential , 1972 .

[26]  H. Preuss Untersuchungen zum kombinierten Näherungsverfahren , 1955 .

[27]  William A. Goddard,et al.  Self‐Consistent Procedures for Generalized Valence Bond Wavefunctions. Applications H3, BH, H2O, C2H6, and O2 , 1972 .

[28]  L. Szász,et al.  Pseudopotential Theory of Atoms and Molecules. II. Hylleraas‐Type Correlated Pair Functions for Atoms with Two Valence Electrons , 1972 .

[29]  B. Pittel,et al.  Accuracy and limitations of the pseudopotential method , 1974 .

[30]  H. A. Pohl,et al.  An improved Hellmann-type pseudopotential for atoms and molecules , 1974 .

[31]  P. Gombás Über eine vereinfachte Methode des self-consistent field für Atome , 1966 .

[32]  W. Goddard,et al.  Use of Ab Initio G1 Effective Potentials for Calculations of Molecular Excited States , 1972 .

[33]  R. Sternheimer Effect of the Atomic Core on the Nuclear Quadrupole Coupling , 1954 .

[34]  H. Hellmann,et al.  A New Approximation Method in the Problem of Many Electrons , 1935 .

[35]  W. E. Baylis Semiempirical, Pseudopotential Calculation of Alkali–Noble-Gas Interatomic Potentials , 1969 .

[36]  N. Sabelli,et al.  Frozen core approximation, a pseudopotential method tested on six states of NaH , 1975 .

[37]  R. Koch,et al.  Simulation of the influence of core electrons by a pseudopotential II , 1969 .

[38]  A. Veillard,et al.  Gaussian basis sets for molecular wavefunctions containing third-row atoms , 1971 .

[39]  C. Bender,et al.  The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvectors of very large symmetric matrices , 1973 .

[40]  James S. Cohen,et al.  Modified statistical method for intermolecular potentials. Combining rules for higher van der Waals coefficients , 1974 .

[41]  J. Callaway,et al.  Application of the Pseudopotential Method to Atomic Scattering. , 1969 .

[42]  C. Fischer Iterative solution of the Hartree-Fock equations with improved stability , 1972 .

[43]  A. C. Wahl,et al.  The Method of Optimized Valence Configurations: A Reasonable Application of the Multiconfiguration Self-Consistent-Field Technique to the Quantitative Description of Chemical Bonding* , 1970 .

[44]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[45]  W. Goddard New Foundation for the Use of Pseudopotentials in Metals , 1968 .

[46]  S. Rice,et al.  Use of Pseudopotentials in Atomic‐Structure Calculations , 1968 .

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

[48]  G. Hart,et al.  Hellmann Pseudopotential Parameters for Atoms with One Valence Electron , 1970 .

[49]  C. T. Fike Computer Evaluation of Mathematical Functions , 1970 .

[50]  S. Rice,et al.  Pseudopotential theory of atomic and molecular rydberg states , 1966 .

[51]  R. Mcweeny,et al.  Valence-electron-only calculations of electronic structure , 1973 .

[52]  V. McKoy,et al.  Rydberg States of Diatomic and Polyatomic Molecules Using Model Potentials , 1971 .

[53]  H. Nussbaumer,et al.  A programme for calculating atomic structures , 1969 .

[54]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[55]  J. Weisheit,et al.  Spin-orbit and core-polarization effects in potassium , 1971 .

[56]  W. Struve Semi-empirical pseudopotential calculations of alkali dimer-ion dissociation energies , 1970 .

[57]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[58]  B. Schneider,et al.  AB-initio effective potentials derived from many-body green's function theory: Application to Li , 1973 .

[59]  R. Dixon,et al.  A general pseudopotential model for molecules with many valence electrons , 1975 .

[60]  P. Stone,et al.  CESIUM OSCILLATOR STRENGTHS , 1962 .

[61]  W. Schwarz Gombás pseudopotential SCF calculations for atoms , 1972 .