Page 221 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

204 G. P. ARRIGHINI AND C. GUIDOTTI
The concerns we have expressed are bound to get even more acute if the problem under
study demands that we are able to adequately describe distortion effects induced in the
electron distribution by external fields. The evaluation of linear (and, still more, non
linear) response functions [1] by perturbation theory then forces one to take care also of
the nonoccupied portion of the complete orbital spectrum, which is entrusted with the
role of representing the polarization caused by the external fields in the unperturbed
electron distribution [4].
A still more outstanding role in quantum many-particle systems is assigned to the
electron density by the Hohenberg and Kohn theorem [5], a not obvious statement
affirming the existence of a rigorous theoretical framework where one is allowed to
obtain ground state properties of the system in terms of the ground state density alone.
Unfortunately, although the electron kinetic and exchange-correlation energy
contributions are shown to be universal functionals of the density the theorem does
not offer any practical guide to their actual construction. In view of the extremely
attracting perspective of treating many-electron systems at an accuracy level beyond the
HF one, without making recourse to wavefunction approaches, it is quite understandable
that many efforts have been addressed to the development of density functional theories
(DFT's) [6-8], There exists possibly general agreement that the most satisfactory DFT
approach presently implemented, suggested by Kohn and Sham [9], actually fails the
original program, because it involves a return to an orbital picture (Kohn-Sham orbitals)
as a rescue from the difficulties posed by our insufficient knowledge of the basic
universal functionals inherent of the procedure, particularly the kinetic energy one. As a
consequence, troubles met with large molecules, that we presumed to be able to leave
outdoors thanks to the novel approach, again enter home from the windows, thus
challenging to a substantial extent applications concerning most of the chemically and
technologically interesting problems.
The present (very preliminary) investigation follows a research line closer to the true
spirit of the DFT's, moving in the same direction as some recent papers where the
attention is focused on the development of a formalism able to lead to the electron
density without invoking wavefunctions, orbitals in particular [10-15]. It is right to
recall that the seminal ideas of this approach are anything but new, their origin dating
back to the atomic statistical model put forward more than sixty years ago by Thomas
and Fermi. Without pretending to review the concerned literature during such a long
period of time (but a very complete bibliography is collected in ref. [7]), we limit
ourselves to point out as particularly relevant to the present work some additional papers
[16-26] where the manifest intent of revitalizing an old subject proceeds through the
development of a general formalism that contemplates the Thomas-Fermi theory as a
low-order level of approximation.
By the present paper we intend to start to explore the possibility of generating explicit,
approximate ways for calculating the electron density of a quantum system
subjected to an external homogeneous and static electric field, without invoking, in the
construction, orbitals as basic ingredients. Although the electronic distribution of the
system is at the outset assumed to be describable in terms of (unspecified) occupied
orbitals, we immediately shirk the orbital approach in favor of an integral representation
of the electronic density involving the knowledge of the quantum mechanical
propagator (QMP) [27-30]. A drastic ansatz for the latter quantity based on the known
QMP of a particle moving in a linear potential field is the key-step of the whole
procedure, by which we attain, without any further approximations, an explicit final