Page 220 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

Electronic Charge Density of Quantum Systems in the Presence of an Electric Field:
a Search for Alternative Approaches

G.P. ARRIGHINI and C. GUIDOTTI
Dipartimento di Chimica e Chimica Industriale. Università di Pisa
Via Risorgimento 35, 56126 Pisa, Italy

1. Introduction

Many fundamental properties of atoms and molecules could come within our reach
through the "simple" knowledge of the electronic distribution density Among these
properties we limit ourselves to quote as particularly significant the various multipole
moments of the distribution itself, electric potential and field generated by it in the
surrounding space. The list of properties that we could master grows longer if we were in
a position to establish how the electronic distribution density is polarized under the action
of external electric and magnetic fields, inasmuch as one might evaluate also various
kinds of (generally nonlinear) response parameters of matter, a piece of information that
is nowadays of utmost importance for a vast series of research programs endowed with
prominent technological significance (for instance, oriented toward the very ambitious
goal of "designing" molecularly-thought materials in such strategic fields as photonics,
optoelectronics, etc. [1-3]). Although the electronic density is physically defined in
a space of lowdimensionality according to the proper modeling adopted
for the system under investigation), the canonical approach to the computation of such
fundamental quantity involves the preliminary obtainment of the electronic
wavefunction, a solution to the Schrodinger equation depending on the totality of the
DN e space coordinates associated with the N e present electrons. Without going into the
slightest detail, we simply restrict our comments on this point to re-emphasize what is
well known even to quantum chemistry students, the fact that the usually accepted
descriptions of the quantum behaviour of many-electron systems correspond to
approximate solutions to the Schrödinger equation, most frequently built up in terms of
one-electron wavefunctions, i.e. orbitals. Hartree-Fock (HF) orbitals constitute almost
invariably the output of ab initio molecular calculations carried out by today's computer
program packages up to and lead obviously to an orbital picture of the
electronic distribution as a sum of contributions from each of the occupied orbitals.
Overcoming the HF accuracy so as to take into account effects beyond the mean-field
approximation (electron correlation) is permitted at the cost of handling much smaller
molecules, while for systems containing a very large number of electrons even the HF
level of description becomes untenable and one has to turn to empirical or semiempirical
models.
203
Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 203–218.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.