On the optimization of Gaussian basis sets

Petersson, George A.; Zhong, Shijun; Montgomery, John A.; Frisch, Michael J.

doi:doi:10.1063/1.1516801

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Ab initio molecular dynamics with a continuum solvation model

We present an implementation of the conductor-like screening model (COSMO) within the framework of Car–Parrinello ab initio molecular dynamics. In order to obtain the accurate forces needed for energy-conserving dynamics, analytic derivatives with respect to the atomic positions are required for all energy terms. We use a steep, but continuous surface function that effectively switches the surface charges off when they are not exposed on the molecular surface. This allows us to construct the cav...

Method for the ab initio calculation of intermolecular potentials of ionic clusters: Test on Rg–CO⁺, Rg=He, Ne, Ar

The interaction energy of a cationic complex A–B+ can be computed as the sum of the interaction energy of the neutral complex A–B and the geometry dependent difference in the ionization potentials of the complex A–B and the molecule B, with ionization potentials calculated by the outer valence Green’s function method. We test this method by computing the intermolecular potential energy of the complexes He–CO+, Ne–CO+, and Ar–CO+ for linear and T-shaped geometries. One-dimensional potential energ...

A new procedure for the optimization of the exponents, α_j, of Gaussian basis functions, Ylm(ϑ,φ)r^le^−α_jr², is proposed and evaluated. The direct optimization of the exponents is hindered by the very strong coupling between these nonlinear variational parameters. However, expansion of the logarithms of the exponents in the orthonormal Legendre polynomials, P_k, of the index, j: ln α_j = ∑k = 0k_maxA_kP_k((2j−2)/(N_prim−1)−1), yields a new set of well-conditioned parameters, A_k, and a complete sequence of well-conditioned exponent optimizations proceeding from the even-tempered basis set (k_max = 1) to a fully optimized basis set (k_max = N_prim−1). The error relative to the exact numerical self-consistent field limit for a six-term expansion is consistently no more than 25% larger than the error for the completely optimized basis set. Thus, there is no need to optimize more than six well-conditioned variational parameters, even for the largest sets of Gaussian primitives. © 2003 American Institute of Physics.

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KEYWORDS and PACS

Keywords

SCF calculations, HF calculations, Legendre polynomials, convergence, ab initio calculations, relativistic corrections, Newton-Raphson method, variational techniques

PACS

31.15.xr

Self-consistent-field methods
31.15.A-

Ab initio calculations
31.30.J-

Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
31.15.xt

Variational techniques