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Journal ArticleDOI

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

15 Nov 1976-Journal of Chemical Physics (AIP Publishing)-Vol. 65, Iss: 10, pp 3826-3853
TL;DR: In this article, 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.
Abstract: 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...
Citations
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Journal ArticleDOI
TL;DR: A description of the ab initio quantum chemistry package GAMESS, which can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication.
Abstract: A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.

18,546 citations

Journal ArticleDOI
TL;DR: In this article, the Coulomb, exchange, and core-orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg have been replaced by the ab initio effective core potentials (ECP).
Abstract: Ab initio effective core potentials (ECP’s) have been generated to replace the Coulomb, exchange, and core‐orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg. For the second and third transition series relative ECP’s have been generated which also incorporate the mass–velocity and Darwin relativistic effects into the potential. The ab initio ECP’s should facilitate valence electron calculations on molecules containing transition‐metal atoms with accuracies approaching all‐electron calculations at a fraction of the computational cost. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3d,4s,4p), (4d,5s,5p), and (5d,6s,6p) orbitals of the first, second, and third transition series atoms, respectively. All‐electron and valence‐electron atomic excitation energies are also compared for the low‐lying states of Sc–Hg, and the valence‐electron calculations are found to reproduce the all‐electron excitation energies (typically within a few tenths of an eV).

12,141 citations

Journal ArticleDOI
TL;DR: In this article, a consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn.
Abstract: A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all‐electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy‐optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all‐electron and valence‐electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent.

8,952 citations

Journal ArticleDOI
TL;DR: In this article, the angular-dependent components of these potentials are represented by compact one-and two-term Gaussian expansions obtained directly from the appropriate eigenvalue equation, and energy optimized Gaussian basis set expansions of the atomic pseudo-orbitals, which have a common set of exponents for the s and p orbitals, are also presented.
Abstract: Compact effective potentials, which replace the atomic core electrons in molecular calculations, are presented for atoms in the first and second rows of the periodic table. The angular‐dependent components of these potentials are represented by compact one‐ and two‐term Gaussian expansions obtained directly from the appropriate eigenvalue equation. Energy‐optimized Gaussian basis set expansions of the atomic pseudo‐orbitals, which have a common set of exponents (shared exponents) for the s and p orbitals, are also presented. The potentials and basis sets have been used to calculate the equilibrium structures and spectroscopic properties of several molecules. The results compare extremely favorably with corresponding all‐electron calculations.

1,952 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduce density functional theory and review recent progress in its application to transition metal chemistry, including local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and solids.
Abstract: We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

1,449 citations

References
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Book
01 Jan 1947
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

7,426 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of contraction on the energies and one-electron properties of the water and nitrogen molecules were investigated, and the authors obtained principles which can be used to predict optimal contraction schemes for other systems without the necessity of such exhaustive calculations.
Abstract: The contraction of Gaussian basis functions for use in molecular calculations is investigated by considering the effects of contraction on the energies and one‐electron properties of the water and nitrogen molecules. The emphasis is on obtaining principles which can be used to predict optimal contraction schemes for other systems without the necessity of such exhaustive calculations. Using these principles, contractions are predicted for the first‐row atoms.

4,595 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

4,525 citations

Journal ArticleDOI
TL;DR: In this article, the use of a linear combination of Gaussian type orbitals (CGTO) instead of an individual Gaussian-type orbital (GTO) as a unit of basis functions for large-scale molecular calculations is discussed.
Abstract: The use of a linear combination of Gaussian‐type orbitals (CGTO), instead of an individual Gaussian‐type orbital (GTO), as a unit of basis functions for large‐scale molecular calculations, is discussed. A systematic construction of the CGTO basis functions is attempted and the results for the atoms from Li through Ar are reported.

3,257 citations