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## Area of Expertise - Quantum physics

The Hartree-Fock method is a general method for the approximate solution of the electronic Schrödinger equation of multiple electron systems (atoms, molecules) in the non-degenerate ground state or in certain excited states.

The Schrödinger equation for a two-electron system is

- $$[\underset{\xaf}{H}(\mathrm{1,2})+V(\mathrm{1,2})]\psi =\mathrm{E.}\psi \text{,}$$

because of the disturbance $V(\mathrm{1,2})$ cannot be solved exactly.

$\underset{\xaf}{H}(\mathrm{1,2})=$Hamilton operator of electrons $1$ and $2$,$V(\mathrm{1,2})=$ Operator of the potential repulsion energy of the electrons,$\psi =$ Wave function, $\mathrm{E.}=$ Total energy

Will the repulsive energy $V(\mathrm{1,2})$ neglecting the electrons, the product formulation results $\psi =\psi (1)\psi (2)$ with $\mathrm{E.}=\mathrm{E.}(1)+\mathrm{E.}(2)$ and $\underset{\xaf}{H}=\underset{\xaf}{H}(1)+\underset{\xaf}{H}(2)$ the one-electron solutions ${\psi}^{0}(1)$ and ${\psi}^{0}(2)$. With the one-electron solution ${\psi}^{0}(1)$ becomes a so-called effective potential

- $${V}_{\mathrm{eff}}(1)={\displaystyle \underset{V}{\int}{\psi}^{0}(2)\underset{\xaf}{V}(\mathrm{1,2})}{\psi}^{0}(2)dV$$

for electron $1$ calculated, with which a new one-electron function can be determined:

- $$[\underset{\xaf}{H}(1)+{V}_{\mathrm{eff}}(1)]\psi (1)=\mathrm{E.}(1)\psi (1)\text{.}$$

With this one-electron approximation, a new effective potential and, from this, another one-electron approximation is obtained. Through continued recursion, new effective potentials and electron approximations are determined until the effective potentials no longer converge (self-consistency).

See also: perturbation theory

## Learning units in which the term is dealt with

### Specialization: Ab inito procedure35 min.

#### ChemistryTheoretical chemistrydeepening

Important ab initio procedures based on the Hartree-Fock method are presented. Electron correlation and correlation energy are defined.

### Molecular modeling in drug design75 min.

#### PharmacyPharmaceutical chemistryDrug design

Molecular modeling comprises various, mostly computer-based methods and techniques for the derivation, representation and manipulation of three-dimensional chemical structures and the physicochemical molecular properties derived from them, as well as for modeling chemical reactions. Since most molecules are flexible systems that can assume different, energetically equivalent states, the modeling of individual molecules is by no means trivial and requires considerable computing power. The modeling and simulation of binding processes is even more complex, since the special features of the target as well as the investigated ligands as well as the medium or solvent in which the reaction takes place must be taken into account. For this reason, the calculated models represent a compromise between the most realistic parameters possible and necessary simplifications or approximations to the real conditions. For example, to simplify energy calculations, the molecules are visualized analogously to macroscopic bodies with a certain surface and volume and reactions are usually under the so called "ideal conditions" (eg in a vacuum) are calculated.