G. Ramírez

Reference program for molecular calculations with Slater-type orbitals

A program for computing all the integrals appearing in molecular calculation with Slater‐type orbitals is reported. The program is mainly intended as a reference for testing and comparing other algorithms and techniques. An analysis of the performance of the program is presented, paying special attention to the computational cost and the accuracy of the results. Results are also compared with others obtained with Gaussian basis sets of similar quality. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1284–1293, 1998

New program for molecular calculations with Slater‐type orbitals

A new program for computing all the integrals appearing in molecular calculations with Slater-type orbitals (STO) is reported. This program follows the same philosophy as the reference pogram previously reported but introduces two main changes: Local symmetry is profited to compute all the two-electron integrals from a minimal set of seed integrals, and a new algorithm recently developed is used for computing the seed integrals. The new code reduces between one and two orders of magnitude the computational cost in most polyatomic systems.

Molecular integrals with Slater basis. I: General approach

A method for the calculation of many‐center integrals involving Slater‐type orbitals (STOs) is reported. The method is based on the separation of the short‐ and long‐range terms of the potentials generated by charge distributions. The calculation of three‐center nuclear attraction integrals and many‐center electron repulsion integrals, when the short‐range contributions are negligible, is formulated in terms of multipolar moments of charge distributions. Recurrence relations for obtaining the multipolar moments, which enable us to reduce their calculations to the evaluation of some basic integrals, are reported.

Polarized basis sets of Slater‐type orbitals: H to Ne atoms

We present three Slater‐type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree–Fock (HF) and frozen‐core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H2 or Li2) plus the ground‐state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core‐valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.

Calculation of many-centre two-electron molecular integrals with STO

Abstract A program for the calculation of two-electron molecular integrals between real Slater-type orbitals (STO) is reported.The program is mainly intended for comparison purposes, to analyze and test the results provided by other algorithms. However, it can be used in actual molecular calculations of small systems. The integrals are obtained by means of Gaussian expansions of the STO. Expansions that enable to attain an accuracy of at least ten decimal places in the integrals are included.

Efficiency of the algorithms for the calculation of Slater molecular integrals in polyatomic molecules.

The performances of the algorithms employed in a previously reported program for the calculation of integrals with Slater‐type orbitals are examined. The integrals are classified in types and the efficiency (in terms of the ratio accuracy/cost) of the algorithm selected for each type is analyzed. These algorithms yield all the one‐ and two‐center integrals (both one‐ and two‐electron) with an accuracy of at least 12 decimal places and an average computational time of very few microseconds per integral. The algorithms for three‐ and four‐center electron repulsion integrals, based on the discrete Gauss transform, have a computational cost that depends on the local symmetry of the molecule and the accuracy of the integrals, standard efficiency being in the range of eight decimal places in hundreds of microseconds.

Analytical method for the representation of atoms-in-molecules densities

We present analytic refinements and applications of the deformed atomic densities method [Fernández Rico, J.; López, R.; Ramírez, G. J Chem Phys 1999, 110, 4213–4220]. In this method the molecular electron density is partitioned into atomic contributions, using a minimal deformation criterion for every two‐center distributions, and the atomic contributions are expanded in spherical harmonics times radial factors. Recurrence relations are introduced for the partition of the two‐center distributions, and the final radial factors are expressed in terms of exponential functions multiplied by polynomials. Algorithms for the practical implementation are developed and tested, showing excellent performances. The usefulness of the present approach is illustrated by examining its ability to describe the deformation of atoms in different molecular environments and the relationship between these atomic densities and some chemical properties of molecules.

Analysis of the molecular density

The minimal deformation criterion, previously proposed for the partition of the molecular density into atomic contributions, is updated and extended. For any Gaussian basis set, these atomic contributions are expanded in a series of real spherical harmonics by radial factors. The terms with l=0 determine the spherical parts of the atomic clouds and the remaining ones, their deformations. This detailed description is complemented with a simplified representation of the molecular density in terms of atomic charges and multipoles. Moreover, these descriptions give a simple way to calculate the electrostatic potential of the molecule as well as the electrostatic interaction between molecules.

Molecular integrals with Slater basis. II. Fast computational algorithms

A new algorithm for the calculation of molecular integrals involving STOs is reported. The algorithm enables us to obtain every two‐center one‐electron integral and the long‐range many‐center one‐ and two‐electron integrals. The efficient implementation of the algorithm is discussed and its performance is thoroughly tested. The analysis on the stability of the relations employed in the calculation of multipolar moments is included. Futhermore, the computer time required to carry out each step (construction of basic matrices, calculation of multipolar moments, and calculation of two‐electron integrals) has also been analyzed. The range of validity of this approach is shown in several molecular integrals.

Molecular calculations with B functions

A program for molecular calculations with B functions is reported and its performance is analyzed. All the one- and two-center integrals and the three-center nuclear attraction integrals are computed by direct procedures, using previously developed algorithms. The three- and four-center electron repulsion integrals are computed by means of Gaussian expansions of the B functions. A new procedure for obtaining these expansions is also reported. Some results on full molecular calculations are included to show the capabilities of the program and the quality of the B functions to represent the electronic functions in molecules.