Generation of basis sets with high degree of fulfillment of the Hellmann-Feynman theorem.

A direct relationship is established between the degree of fulfillment of the Hellman-Feynman (electrostatic) theorem, measured as the difference between energy derivatives and electrostatic forces, and the stability of the basis set, measured from the indices that characterize the distance of the space generated by the basis functions to the space of their derivatives with respect to the nuclear coordinates. On the basis of this relationship, a criterion for obtaining basis sets of moderate size with a high degree of fulfillment of the theorem is proposed. As an illustrative application, previously reported Slater basis sets are extended by using this criterion. The resulting augmented basis sets are tested on several molecules finding that the differences between energy gradient and electrostatic forces are reduced by at least one order of magnitude.

Translation of STO charge distributions.

Barnett and Coulson's zeta-function method (M. P. Barnett and C. A. Coulson, Philos. Trans. R. Soc., Lond. A 1951, 243, 221) is one of the main sources of algorithms for the solution of multicenter integrals with Slater-type orbitals. This method is extended here from single functions to two-center charge distributions, which are expanded at a third center in terms of spherical harmonics times analytical radial factors. For s-s distributions, the radial factors are given by a series of factors corresponding to the translation of s-type orbitals. For distributions with higher quantum numbers, they are obtained from those of the s-s distributions by recurrence. After analyzing the convergence of the series, a computational algorithm is proposed and its practical efficiency is tested in three-center (AB/CC) repulsion integrals. In cases of large basis sets, the procedure yields about 12 correct significant figures with a computational cost of a few microseconds per integral.

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.

Electrostatic potentials and fields from density expansions of deformed atoms in molecules.

The exact representation of the molecular density by means of atomic expansions, consisting in spherical harmonics times analytical radial factors, is employed for the calculation of electrostatic potentials, fields, and forces. The resulting procedure is equivalent to an atomic multipolar expansion in the long-range regions, but works with similar efficiency and accuracy in the short-range region, where multipolar expansions are not valid. The performances of this procedure are tested on the calculation of the electrostatic potential contour maps and electrostatic field flux lines of water and nitrobenzene, computed from high-quality molecular electron densities obtained with Slater basis sets.

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.

Drug related problems identified by European community pharmacists in patients discharged from hospital.

INTRODUCTION: Drug related problems (DRPs) are perceived to occur frequently when patients are discharged from the hospital. Community pharmacists' interventions to detect, prevent and solve DRPs in this population are scarcely studied. OBJECTIVE: To examine the nature and frequency of DRPs in community pharmacies among patients discharged from hospitals in several countries, and to examine several variables related to these drug related problems. METHOD: The study was performed in 112 community pharmacies in Europe: Austria, Denmark, Germany, The Netherlands, Portugal and Spain. Community pharmacists asked patients with a prescription after discharge from hospital between February and April 2001 to participate in the study. A patient questionnaire was used to identify drug related problems. Pharmacists documented drug related problems, pharmacy interventions, type of prescriber and patient and pharmacy variables. RESULTS: 435 patients were included in the study. Drug related problems were identified in 277 patients (63.7%). Uncertainty or lack of knowledge about the aim or function of the drug (133; 29.5%) and side effects (105; 23.3%) were the most common DRPs. Practical problems were reported 56 times (12.4%) by patients. Pharmacists revealed 108 problems (24.0%) concerning dosage, drug duplication, drug interactions and prescribing errors. Patients with more changes in their drug regimens (drugs being stopped, new drugs started or dosage modifications) and using more drugs were more likely to develop DRPs. Community pharmacists recorded 305 interventions in 205 patients with DRPs. Pharmacists intervened mostly by patient medication counselling (39.0%) and practical instruction to the patient (17.7%). In 26.2% the intervention was directed towards the prescriber. In 28 cases (9.2%) the pharmacists' intervention led to a change of the drug regimen. CONCLUSION: This study shows that a systematic intervention by community pharmacists in discharged patients, or their proxies, is able to reveal a high number of DRPs that might be relevant for patient health outcomes. There should be more initiatives to insure continuity of care, since DRPs after discharge from hospital seem to be very common.

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 H(2) or Li(2)) 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.