A. López Piñeiro

Matrix elements for rotating Morse oscillators using the Elsum and Gordon approximations

In this paper, formulas and recursion relations for the matrix elements of the operators {1−exp[−a(r−re)]}n, exp[−a(r−re)]n, and (r−re){exp[−a(r−re)]}n are derived for a rotating Morse oscillator within the Elsum and Gordon approximation. These equations can be used to calculate the diagonal (v=v’, J=J’) and off‐diagonal (v≠v’, J≠J’) matrix elements.

HYDMATEL: a code to calculate matrix elements for hydrogen-like atoms

Abstract Recursion relations for determining radial matrix elements of r -dependent operators between hydrogenic wavefunctions are derived using a technique based on the hypervirial theorem along with a second quantization formalism. These expressions have been included in the program HYDMATEL, and this code is valid for both diagonal and off-diagonal matrix element calculations with no limitation on the values of the n and l quantum numbers or on the power of the operator.

Accurate closed-form approximations to partition functions

We develop a method for obtaining accurate closed‐form approximations to partition functions for all values of the temperature. The method is based on an alternative application of the Euler–Maclaurin summation formula and is therefore restricted to those partition functions which can be treated by such an approach. As an illustrative example we discuss the rigid rotor and show analytic expressions for the partition functions obtained by summing over all states, even states, and odd states.

Influence of the solvent on the conformational-dependent properties of random coil polypeptides: II. Mean square optical anisotropies and Kerr constants

Mean square optical anisotropies and molar Kerr constants were calculated for homopolypeptides of the 20 natural amino acids and of several enzymes and proteins in the random-coil state. The effect of hydration was taken into account in constructing the molecular potential that gives the conformational energies as a function of the rotational angles phi and psi of the backbone and chi(1) of the side chain. The Rotational Isomeric State model was used in calculated energies, the Valence Optical Scheme and the matrix calculus technique of Flory being employed in the evaluation of the optical properties. The results are compared with calculations for the same substances that were performed without taking into account the solvent, as well as with other similar studies. The Kerr constant is confirmed as being one of the most sensitive properties of a given polypeptide to the residue class and to the sequence of those residues.

Perturbed morse oscillator in diatomic molecules: an hypervirial treatment

Abstract The rovibrational behavior problem of diatomic molecules is solved by an hypervirial perturbed treatment, by using as potential a perturbed Morse oscillator (PMO). Formulae have been derived from spectral data in order to calculate the PMO parameters, and numerical calculations have been made with the RbH molecule in its electronic ground state, comparing our results with those obtained by others authors.

Calculation of the absolute infrared frequencies and intensities of a diatomic molecule or of local diatomic groups

Abstract In this paper we present a computer program (in FORTRAN IV) for calculating the absolute infrared intensities (or frequencies) of a diatomic molecule or of local diatomic groups using a theoretical dipole (and/or potential) function. The formalism is based in the perturbation theory and take into account four cases:(1) the electrical and mechanical harmonicity, (2) the electrical harmonicity and mechanical anharmonicity, (3) the mechanical harmonicity and electrical anharmonicity and (4) the electrical and mechanical anharmonicity.

Recursion relations for matrix elements and Franck-Condon factors of rotating Morse oscillators

Abstract Several recursion relations connecting matrix elements of two displaced Morse oscillators of arbitrary D e are derived using the hypervirial theorem along with a set of ladder (raising and lowering) operators. These operators are obtained when we factorize the Schrodinger equation, for the Morse oscillator, following the method proposed by Infeld and Hull. The recursion relations obtained can be used to calculate either matrix elements of x α =exp [− a α( r - r e )] operators or Franck-Condon factors between the vibrational-rotational states belonging to two distinctly separated Morse oscillators of different dissociation energies. The results are valid for any value of v and J of both oscillators.

Hypervirial treatment of centrifugal distortion of 2Π energy levels

Abstract An analytical perturbation has been carried out, using a hypervirial scheme, of the wave equation with Morse potential and additional perturbations involving powers of [1-exp(-aq)]. The centrifugal distortion contributions to rovibrational energies are derived for diatomic molecules and compact formulae are obtained for successive radial derivatives of the spin-orbit function. Numerical applications are described to the X 2 Π states of several molecules.