Basis sets even-tempered, Gaussian primitive

Using the F ion as a prototype, the convergence of the many-body perturbation theory second-order energy component for negative ions is studied when a systematic procedure for the construction of even-tempered btisis sets of primitive Gaussian type functions is employed. Calculations are reported for sequences of even-tempered basis sets originally developed for neutral atoms and for basis sets containing supplementary diffuse functions. 

The Hartree-Fock ground state of the F anion is described by orbitals of s Emd of p symmetry. In the first part of this study, attention was restricted to the convergence of the second order many-body perturbation theory component of the correlation energy for stematically constructed even-tempered basis sets of primitive Gaussian-typ>e functions of s and p symmetry. 

EXCITED STATE SELF-CONSISTENT FIELD THEORY USING EVEN-TEMPERED PRIMITIVE GAUSSIAN BASIS SETS... 

The purpose of the present work is to investigate the convergence characteristics of calculations for solvated systems using continuum models when the solute is described by a matrix Hartree-Fock wave function and systematically constructed even-tempered basis sets of Gaussian primitive functions are employed. Specifically, no attempt has been made to achieve high accuracy but rather the emphasis has been on the trends in molecular properties with increasing basis set size. 

In Section 2 below, we give an outline of each of the continuum models used. The development of systematic sequences of primitive, even-temp>ered Gaussian functions is briefly described in section 3. In Sections 4 the results obtained in the present work are given beginning with a preliminary study using some standard basis sets and then employing sequences of even-tempered basis sets of primitive Gaussian functions. In section 5, the results are discussed and then, in section 6, the conclusions are presented. 

An efficient scheme for generating the large and flexible primitive Gaussian basis sets required for accurate calculations is provided by the even-tempered prescription in which the exponents, CkNt, are taken to form a geometric progression -... 

Systematic sequences of even-tempered basis sets of Gaussian primitive functions in calculations using continuum models... 

It has been demonstrated[81] that a sufficiently large and flexible universal even-tempered basis set of Gaussian primitive functions can support a total matrbc Hartree-Fock energy for the gas phase CO molecule of —112.7909045 Hartree for a nuclear separation of 2.132 Bohr. This differs from the finite difference Hartree-Fock energy by 2.8 jiHartree. 

The convergence behaviour observed in the present study for continuum models of solvated species using systematic sequences of even-tempered basis sets of Gaussian primitive functions of s- and p- symmetry mirrors that observed for the gas phase molecular species. Gas phase matrix Hartree-Fock calculations for the isoelectronic molecules studied in the present work which approach a suh-pHartreelevel of accuracy for the total energy have been reported elsewhere[18]-[25]. The present work demonstrates that this approach can be applied to molecules in solution by making use of continuum models. The basis set truncation error would then be 3 orders of magnitude smaller than the AE values. 

Furthermore, it was realized that the even-tempered basis of Gaussian-type geminals could also be applied in an uncontracted form. Some initial calculations were performed on He, and it was observed that the variationally determined linear parameters for the primitive Gaussian geminals were quite similar to the coefficients obtained from the fitting procedure. Results for Ne and H2O obtained from this (uncontracted) ansatz are presented in Table 9. The results show that augmentation of standard basis sets with a few explicitly correlated... 

Basis sets employed are the most diffuse (12s8p8d6/) hydrogenic orbitals constructed from 12 regularized even-tempered primitive Gaussian orbitals of each angular momentum symmetry (IS), supplemented with two additional diffuse functions having exponents of 0.02786 and 0.01156 in each case. 

Even though even-tempered basis sets are rarely used in practice for first-row atoms, they are important both conceptually and practically. Thus, an even-tempered sequence of exponents may be used as a starting point for an unconstrained optimization of the individual exponents. More important, they allow for a simple generation of sequences of Gaussian basis sets, where, by decreasing )S and increasing the number of primitives, one can approach the basis-set limit in a simple and controlled fashion. 

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