Variable basis sets in perturbation theory: Numerical finite perturbation versus analytic approach

Abstract

AbstractsWe consider the problem of determining variational, external-field-dependent corrections to nonoptimal zero-field nonlinear parameters. Both a direct analytic perturbation analysis and finite perturbation methods are described in a general way and in detail for the SCF approximation. The abstract theory is illustrated by reference to the results of several explicit calculations. Also, the sensitivity of the results to the choice of zero-field values is discussed.Nous considirons le problkme de dkterminer des corrections variationnelles dkpendantes d'un champ exttrieur a des paramktres non-liniaires, non-optimalisks au champ nul. Nous dkcrivons une analyse perturbationnelle analytique directe et des mithodes de perturbations finies d'une facon gknirale et en dttail pour I'approximation SCF. La thkorie abstraite est illustrte par les risultats de plusieurs calculs explicites. Nous discutons aussi la sensibititk des risultats par rapport aux choix des valeurs correspondantes au champ nul.wir betrachten das problem von einem ausseren Feld abhangige Variationskorrekture zu nichtoptimalen, nicht-linearen Nullfeldparametern zu bestimmen. Sowohl eine direkte analytische Storungsanalyse als auch endliche Storungsmethoden werden in einer allgemeinen Weise und in Einzelheiten fur die SCF-Naherung beschrieben. Die abstrakte Theorie wird mit den Ergebnissen von mehreren expliziten Berechnungen illustriert. Auch die Empfindlichkeit der Resultate mit Rucksicht auf die Wahl von Nullfeldwerten wird diskutiert.

Analytical force constant calculation as a minimization problem

“…It has been pointed out before [22,23] that the second order contribution to the energy in the perturbation expansion is variational in the first order wave function parameters. The above development is a generalization of this earlier concept.…”

Correlation effects in externally perturbed many‐electron systems

“…In some cases also the optimization of the basis set can be carried out owing to bounding properties of certain CHF functionals [67]. In particular, this is the case of the orbital origin shift parameters for the EFV GTO bases whose value can be optimized with respect to the CHF value of the dipole polarizability [60,67,70]. A similar procedure can be to some extent applied for the optimization of orbital exponents in perturbation-independent bases.…”

“…It can be concluded from the corresponding results that the standard and relatively small GTO/CGTO bases [68] when transformed into their EFV counterparts provide highly accurate and reliable values of the dipole polarizability. Simultaneously they also lead to the improvement of molecular dipole moments [67,68,70]. Hence, the EFV GTO basis sets are suitable for the calculation of field-perturbed orbitals which can be used to compute correlation corrections to the CHF values of atomic and molecular electric properties.…”

“…According to the method of their generation, the EFV bases have the same dimension as the original GTO/CGTO basis sets and can be easily employed in calculations with standard computer programs. The optimization of a single variational parameter X can be carried out either analytically or numerically [67,70]. Relatively small EFV GTO bases can provide highly accurate values of atomic and molecular dipole polarizabilities.…”

“…The main idea behind the concept of the EFV bases follows from the consideration of the electric-field-perturbed harmonic oscillator [60,66]. The EFV GTO bases are produced from the standard GTO/CGTO basis sets by shifting the origin (R) of each GTO by the amount proportional to the field strenght (F): (57) where q denotes the GTO exponent and X is the so-called origin shift parameter whose value can be determined variationally in C H F calculations [60,66,67,70]. According to the method of their generation, the EFV bases have the same dimension as the original GTO/CGTO basis sets and can be easily employed in calculations with standard computer programs.…”