*Introduction to Computational Chemistry* - Third Edition*Frank Jensen*
*Department of Chemistry, Aarhus University, Denmark*

## Introduction

Chemistry is the science dealing with

construction,transformationandpropertiesofmolecules.

### Overview

#### “**many-body problem**”

**many-body problem**

Systems composed of more than two particles cannot be solved by analytical methods, but Computational methods.

#### the *Breit* term

$$ \begin{equation} \mathbf{V}_{\text {elec }}\left(\mathbf{r}_{12}\right)=\frac{1}{r_{12}}\left[1-\frac{1}{2}\left(\boldsymbol{\alpha}_{1} \cdot \boldsymbol{\alpha}_{2}+\frac{\left(\boldsymbol{\alpha}_{1} \cdot \mathbf{r}_{12}\right)\left(\boldsymbol{\alpha}_{2} \cdot \mathbf{r}_{12}\right)}{r_{12}^{2}}\right)\right] \end{equation} $$

The first-order correction is known as the Breit term, and α1 and α2 represent velocity operators. The first term in Equation (1.4) can be considered as a magnetic interaction between two electrons, but the whole Breit correction describes a “retardation” effect, since the interaction between distant particles is “delayed” relative to interactions between close particles, owing to the finite value of c (in atomic units, c ∼ 137).

#### Dimains of dynamical equations

#### potential energy surface (PES)

one of the major problems is calculating the electronic energy for a given nuclear configuration to give a potential energy surface.

## Force Field Methods

also referred to as molecular mechanics (MM) methods.