Nonrelativistic Hamiltonian for a Molecular System

Historically, the nonrelativistic many-electron theory was developed and computationally tested first. For molecules containing only light atoms, this approach turned out to be remarkably successful in chemistry. Consequently, we are well advised to be inspired by this success if we look for a relativistic theory that is to be computationally as feasible as its nonrelativistic relative. 

A feature of the nonrelativistic external-field-free many-particle Hamiltonian is that its principles of construction are simple. First of all, kinetic energy operators for each particle in the system, i.e., for each electron and each atomic nucleus, are summed. Since the elementary particles can be well described as point-like particles, it is not necessary to consider electrostatic multipole 

The nonrelativistic many-particle Hamiltonian of a collection of electrons and nuclei in the absence of additional external electromagnetic fields can be written (in Gaussian units) as. 

It is important to be aware of the fact that we have largely simplified all interactions present within a molecule or a molecular aggregate. For instance, apart from retardation effects on the electron-electron, electron-nucleus, and nucleus-nucleus interactions, the effect of the weak magnetic field associated with a nuclear spin is completely neglected at this stage. This procedure fea- 

We thus exploit the fact that electrostatic (monopole) interactions dominate all other interactions. It also allows us to treat all other interactions as small perturbations, an issue which then leads to the calculation of molecular properties in the framework of response theory in chapter 15. 

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