M. Berrondo

The algebraic approach to the Morse oscillator

The discrete spectrum for a Morse oscillator is found using an SO(2, 1) algebra. Since this algebra does not prove to be appropriate to compute matrix elements for the oscillator eigenfunctions, the author construct a B1-type algebra with the aid of an auxiliary angle variable. Matrix elements and recurrence relations are found for several useful operators using the algebra. The limit in which the anharmonicity tends to zero is studied.

Convergence of multibody expansions for alkaline earth metals. Contrast between magnesium and beryllium clusters

An ab anitio SCF–LCAO–MO study of nonadditive three‐ and four‐body interaction energies in Mg3 (equilateral and linear) and Mg4 (tetrahedral) clusters is presented. The relative importance of these few‐body terms to the interaction energy is at most 39% for three‐ and 8% for four‐body terms. This lies in marked contrast with the case of Be clusters where these terms can have a relative weight of up to 76%, and 31.6%, respectively. The reason for such radically different nonadditive effects is discussed. Some new results for Be3, Be4, and Be5 clusters are presented confirming this is a case where multibody expansions are expected to be very slowly convergent. Finally these results provide an explanation for the poor convergence of the chemisorption energy of an H atom as a function of the size of Ben clusters.

Narrow resonances as an eigenvalue problem and applications to high energy magnetic resonances: An exactly soluble model

We formulate the problem of finding the narrow positive energy resonances in a deep potential well as an eigenvalue problem (thereby extending the scope of the discrete spectrum problem). We determine the number of resonances in an exactly soluble case. The method is then applied to a nonperturbative treatment of the magnetic resonances occurring in charge‐dipole interactions, and the existence of the previously conjectured high mass narrow resonances in this model is proved.

Use of pseudopotentials for the analysis of the non-additivity of short-range intermolecular interactions

Abstract The pseudopotential method of Barthelat . is shown to be quite adequate for obtaining short-range intermolecular potentials between closed-shell structures through the study of argon clusters. Not only the all-electron SCF pair interactions for the Ar 2 system are well reproduced but the more rigorous test of obtaining the non-additive few-body terms for small Ar clusters (e.g. Ar 3 and Ar 4 ) is also met by this approach giving quite good agreement with previous modified effective electorn studies for the same system.

Automated Aufbau of antibody structures from given sequences using Macromoltek's SmrtMolAntibody

This study was a part of the second antibody modeling assessment. The assessment is a blind study of the performance of multiple software programs used for antibody homology modeling. In the study, research groups were given sequences for 11 antibodies and asked to predict their corresponding structures. The results were measured using root‐mean‐square deviation (rmsd) between the submitted models and X‐ray crystal structures. In 10 of 11 cases, the results using SmrtMolAntibody show good agreement between the submitted models and X‐ray crystal structures. In the first stage, the average rmsd was 1.4 Å. Average rmsd values for the framework was 1.2 Å and for the H3 loop was 3.0 Å. In stage two, there was a slight improvement with an rmsd for the H3 loop of 2.9 Å. Proteins 2014; 82:1636–1645.

DVDSON: A subroutine to evaluate selected sets of eigenvalues and eigenvectors of large symmetric matrices

Abstract Program HYMAT, originally written by Weber, Lacroix and Wanner, has been improved in efficiency and generalized to evaluate any selected set of eigenvalues and eigenvectors of large sparse real symmetric matrices. The time-consuming steps are expressed as calls to subroutines which may exploit a vector architecture. A novel way to improve speed of convergence is discussed.

The coulomb hole and the correlation energy for the electron gas at intermediate densities

Abstract An approximation for the correlation energy of the electron gas is derived (employing a direct modelling of the Coulomb hole) for the pair distribution function: ϵ c ( r s ) = −0.303/( r s + 1.108) rydberg. It is of the same form as the expressions of Wigner and of McWeeny.

Local exchange potential for atomic systems

Abstract An approximate local potential for the exchange term is found for atomic systems. A functional form for the density matrix as a real exponential is assumed, in order to account for the nuclear attraction. The potential is obtained as the functional derivative of the exchange energy, imposing the idempotency condition on the density matrix. The resulting local potential has the correct asymptotic behaviour without the need of ad-hoc cut-off procedures, or additional assumptions.

Cluster models of ionic crystals: Band gaps

The authors performed electronic ab initio calculations of ion clusters simulating a piece of ionic crystal. The main interest here is to estimate the (direct) energy band gap from the cluster energy levels. The model consists of a central cation surrounded by four shells of ions, with additional point charges embedding the cluster. The authors present results for the series of alkali halides with rock-salt structure. 16 refs., 1 tab.

Vibration-translation energy transfer in a collision between an atom and a Morse oscillator

We study the vibration-translation energy transfer in an atom-Morse oscillator collision. We obtain the interaction picture Hamiltonian ℋI(t) corresponding to an atom-molecule interaction potential linear in the ladder operators J +, J -. The time evolution operators corresponding to several different approximations to ℋI(t) are constructed with Lie algebraic methods. We evaluate the vibrational transition probability as a function of the total collision energy, and also as a function of the strength of the Morse potential.