On polarization functions for Gaussian basis sets
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ORIGINAL PAPER
On polarization functions for Gaussian basis sets Milena Palhares Maringolo 1 & Ana Cristina Mora Tello 1,2 & Amanda Ribeiro Guimarães 1 & Júlia Maria Aragon Alves 1 & Francisco das Chagas Alves Lima 3 & Elson Longo 2 & Albérico Borges Ferreira da Silva 1 Received: 4 October 2019 / Accepted: 7 September 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we introduce a technique to choose polarization functions directly from the primitive set of Gaussian exponent without the necessity to optimize or even reoptimized them. For this purpose, initially, we employed Gaussian basis sets generated by using the Polynomial Generator Coordinate Hartree-Fock (PGCHF) method, and later we extended our technique to the cc-pVQZ and pc-3 Gaussian basis sets in order to show how our technique works and how good it is. Using the new polarized basis sets, from our technique, total electronic energies, equilibrium geometries, and vibrational frequencies were calculated for a set of molecules containing atoms from H(Z = 1) to Ba(Z = 56). The technique presented here can be used with any Gaussian basis set flexible (large) enough and also can be used to choose Gaussian basis set exponents from one basis set to another as polarization functions. Keywords Gaussian basis sets . Polarization functions . Polarization exponents . GBS
Introduction The Generator Coordinate Hartree-Fock (GCHF) method [1] was introduced in 1986, and since then, it was basically used in the generation of universal Slater and Gaussian basis sets [2, 3]. The main interest in the generation of universal basis sets, that time, laid on the idea that one could transfer the molecular integrals from one molecular calculation to another when using universal basis sets [4]. In fact, the idea of using universal basis set never became practical, and afterwards, it was completely abandoned. The main challenge of the GCHF method is how the integral equation of the method is discretized. Actually, this equation was always discretized
Milena Palhares Maringolo and Ana Cristina Mora Tello contributed equally to this work. * Albérico Borges Ferreira da Silva [email protected] 1
Instituto de Química de São Carlos Universidade de São Paulo, C.P. 780, São Carlos, SP 13560-970, Brazil
2
CDMF, Universidade Federal de São Carlos, P.O. Box 676, São Carlos, SP 13565-905, Brazil
3
Universidade Estadual do Piaui, C. P. 2231, Teresina, PI 64002-095, Brazil
through the Integral Discretization [5] (ID) instead of the Variational Discretization (VD) that is more commonly used. Later on, in 2003, Barbosa and da Silva [6] modified the way of discretizing the integral equation of the GCHF method with the aim to generate more flexible nonrelativistic and relativistic Gaussian basis sets [7–10] to be used in molecular calculations. There are three steps to be followed in order to attain a Gaussian basis set ready to be used in molecular calculation: (a) the construction of the primitive set of exponents, (b) the contraction of the prim
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