Ramon Carbo

Some remarks about a generalized SCF coupling operator open shell theory

Abstract Li and He atomic systems are studied from the point of view of a general monoconfigurational Hartree-Fock coupling operator formalism. As a consequence, it is found that Lagrange multiplier hermitean conditions should be fulfilled in those electronic systems where hermiticity is not present by symmetry reasons, as in the Li ground state and the He first excited singlet. An additional condition is also needed when an excited state of the same symmetry and multiplicity of ground state should be calculated, as in He, allowing to apply the variational principle to the excited state energy functional. Without this condition, the monoconfigurational Hartree-Fock procedure will lead to unphysical energies. In semi-empirical calculations, however, the hermitean condition may be relaxed without provoking appreciable errors. The NO 2 molecule is analysed within the CNDO framework to prove this possibility, which simplifies the treatment.

Unconditional convergence in SCF theory: a general level shift technique

Abstract A level shift procedure is described in the framework of one-operator SCF formalisms. This procedure permits one to obtain in any case unconditional convergence to a stationary energy.

A general multiconfiguration paired excitation self-consistent field theory (MC PE SCF)

Abstract A multiconfigurational paired excitation SCF (MC PE SCF) framework is described, in an attempt to generalize Veillard and Clementis MC SCF theory. It is shown that a MC PE wavefunction can give a set of diagonal. Fock operators entering the variational Euler equations and, as a consequence, a recently described coupling operator technique can be used to solve the Hartee—Fock problem in this case. Monoconfigurational open or closed shells can be solved in the MC PE approach by means of a unique computational algorithm.

Electrostatic molecular potential as a static index in the study of aromatic substitutions

Abstract Electrostatic potential maps of azulene, indole and benzofuran are discussed. Theoretical results on azulene and indole fit well with the experience, while benzofuran electrostatic reactivity fails to explain the experimental facts. This anomalous behaviour may be explaned through the necessary presence of higher order terms in the activated complexs energy, which cannot be taken into account by the electrostatic potential, a first order approach, alone.

Ground and first excited states electrostatic molecular potentials of ketene and diazomethane

Abstract INDO wavefunctions for 1 A 1 , 1 A″ and 3 A″ states of ketene and diazomethane, obtained with a RHF technique, after some geometry optimization for the excited states, are used to obtain electrostatic molecular potentials under ZDO assumptions. Ground-state results agree with the experimental behaviour and also with other theoretical calculations for both molecules.

A new look on SCF theory

Abstract Hartree-Focks theory for monoconfigurational systems is analysed. A definition of a set of coulombic operators allows us to construct a set of Euler equations which has a multiconfigurational structure. A coupling operator technique is described in order to deal with the solution of these equations. Some computational examples are given to prove the practical use of the formalism. As a consequence, the unique structure of Hartree-Focks problem is evidenced.

Electronic Energy, Fock Operators and Coupling Operators

In this section the essential framework of the generalized Hartree-Fock theory will be developed. As starting point, a general energy expression and the attached operators will be discussed.

The Problem of the Helium Atom First Excited Singlet State

In an open shell monoconfigurational scheme excited states with the same symmetry and spin multiplicity as groundstate cannot be properly calculated within a SCF framework, due to the nature of Rayleigh-Ritz variational principle.

General Theory for Two and Three Electron Systems

We will study here the Fock operators formalism for two and three electron systems, in order to deal with comparatively easy cases. Fock operators for generalized situations can be found in Appendix C.

Approximate SCF Theories

It is well known that the main SCF problem, if one leaves out the SCF solution itself, lies in the calculation and handling of bielectronic integrals needed when the LCAO forms of Fock operators are constructed. The problem can be considered alleviated and solved within the present knowledge through the efficient algorithms in use. However, if one looks ahead in time, then in some cases, such as the study of huge biological molecules, the use of approximate methods can still be useful. When dealing with approximate SCF procedures one needs to divide the methodology into two separate units: non-empirical and empirical methods.