Chapter 3
Ab initio Electronic Structure
for Few-Body Systems
This chapter focuses on the problem of calculating the electronic structure of fewbody systems by concentrating mainly on methods based on independent particles
wavefunctions. Accordingly, we describe the variational principle, the Hartree–Fock
(HF) and self-consistent field (SCF) molecular orbital models. An overview of the use
of post HF configuration interaction (CI), multiconfiguration (MC) SCF, perturbation
methods and density functional theory (DFT) is also given. Finally, the most popular
techniques used for fitting full range potential energy surfaces suited to support the
study of chemical and more specifically reactive processes are also examined.
3.1 Structured Bodies
3.1.1 The One-Electron Wavefunction Approach
In the previous chapters, we focused our attention on the case of two interacting
particles using both a classical (Chap. 1) and a quantum (Chap. 2) treatment by making always the explicit assumption of their structureless nature. On this ground, we
worked out the ab initio bound quantum solutions of the Schrödinger equation for
the electron as a single-particle system subject to a Coulomb potential.
However, in order to generalize the ab initio treatment to molecular processes
(and, in particular, to chemical reactions in which several electrons intervene and
get redistributed around the related nuclei) some simplifying assumptions made in
Chap. 2 (such as that collision partners are spinless, do not fragment, are subject to
a central potential, etc.) have to be removed. As a consequence, the Hamiltonian of
the related Schrödinger equation has to be modified accordingly to take into account
that we deal with the problem of one or more electrons considered as independent
(or one-electron) particles. It is worth mentioning here that even when dealing with
© Springer International Publishing AG 2018
A. Laganà and G. A. Parker (eds.), Chemical Reactions, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-62356-6_3
83
Ab initio Electronic Structure
for Few-Body Systems
This chapter focuses on the problem of calculating the electronic structure of fewbody systems by concentrating mainly on methods based on independent particles
wavefunctions. Accordingly, we describe the variational principle, the Hartree–Fock
(HF) and self-consistent field (SCF) molecular orbital models. An overview of the use
of post HF configuration interaction (CI), multiconfiguration (MC) SCF, perturbation
methods and density functional theory (DFT) is also given. Finally, the most popular
techniques used for fitting full range potential energy surfaces suited to support the
study of chemical and more specifically reactive processes are also examined.
3.1 Structured Bodies
3.1.1 The One-Electron Wavefunction Approach
In the previous chapters, we focused our attention on the case of two interacting
particles using both a classical (Chap. 1) and a quantum (Chap. 2) treatment by making always the explicit assumption of their structureless nature. On this ground, we
worked out the ab initio bound quantum solutions of the Schrödinger equation for
the electron as a single-particle system subject to a Coulomb potential.
However, in order to generalize the ab initio treatment to molecular processes
(and, in particular, to chemical reactions in which several electrons intervene and
get redistributed around the related nuclei) some simplifying assumptions made in
Chap. 2 (such as that collision partners are spinless, do not fragment, are subject to
a central potential, etc.) have to be removed. As a consequence, the Hamiltonian of
the related Schrödinger equation has to be modified accordingly to take into account
that we deal with the problem of one or more electrons considered as independent
(or one-electron) particles. It is worth mentioning here that even when dealing with
© Springer International Publishing AG 2018
A. Laganà and G. A. Parker (eds.), Chemical Reactions, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-62356-6_3
83