I. Ema

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.

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.

Master formulas for two- and three-center one-electron integrals involving Cartesian GTO, STO, and BTO

As a first application of the shift operators method we derive master formulas for the two- and three-center one-electron integrals involving Gaussians, Slater, and Bessel basis functions. All these formulas have a common structure consisting in linear combinations of polynomials of differences of nuclear coordinates. Whereas the polynomials are independent of the type (GTO, BTO, or STO) of basis functions, the coefficients depend on both the class of integral (overlap, kinetic energy, nuclear attraction) and the type of basis functions. We present the general expression of polynomials and coefficients as well as the recurrence relations for both the polynomials and the whole integrals. Finally, we remark on the formal and computational advantages of this approach.

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.

Analysis of the molecular density: STO densities

A partition of the molecular density for Slater basis sets (STO), which parallels one previously developed for Gaussian basis sets (GTO), is reported. The atomic fragments are expanded in spherical harmonics times radial factors. Each fragment contains all the one-center charge distributions centered in the atom plus the part of every two-center distribution assigned to the atom by the partition criterion. The performance of the procedure is analyzed, concluding that the analysis gives highly accurate representations of the molecular density at a very low cost. Moreover, the results of the analysis are illustrated with the study of the densities in CO and H 2 O and the comparison of the atomic densities obtained from STO and GTO molecular calculations.

DAMQT 2.1.0: A new version of the DAMQT package enabled with the topographical analysis of electron density and electrostatic potential in molecules

DAMQT‐2.1.0 is a new version of DAMQT package which includes topographical analysis of molecular electron density (MED) and molecular electrostatic potential (MESP), such as mapping of critical points (CPs), creating molecular graphs, and atomic basins. Mapping of CPs is assisted with algorithmic determination of Euler characteristic in order to provide a necessary condition for locating all possible CPs. Apart from the mapping of CPs and determination of molecular graphs, the construction of MESP‐based atomic basin is a new and exclusive feature introduced in DAMQT‐2.1.0. The GUI in DAMQT provides a user‐friendly interface to run the code and visualize the final outputs. MPI libraries have been implemented for all the tasks to develop the parallel version of the software. Almost linear scaling of computational time is achieved with the increasing number of processors while performing various aspects of topography. A brief discussion of molecular graph and atomic basin is provided in the current article highlighting their chemical importance. Appropriate example sets have been presented for demonstrating the functions and efficiency of the code.