# I Hartree Fock v.s. Configuration Interaction

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1. Nov 6, 2016

### Jan Hidding

Hey everyone,

For my studies I have to read a part about approximation methods in Quantum Mechanics. Unfortunately I'm having difficulties understanding some concepts.

If I'm correct, for describing a multi fermionic system of n electrons, the Hartree Fock (HF) method uses a Slater determinant consisting of spin-orbitals to approximate the system wave function.
$$\psi=(n!)^{-1/2} det|\phi_a(1) \phi_b(2) ...\phi_z(n)|$$
The Slater determinant is used to obey anti symmetry and thus the Pauli Exclusion Principle. Then the Hartree Fock equation is used to obtain the spin-orbitals. By means of a Self Consisting Field approach the spin-orbitals are then optimized until the wave functions do not change anymore. The HF ground state is then found by constructing a Slater Determinant of the n energetically lowest orbitals.

For the Configuration Interaction (CI) method the electronic wave function is constructed of a linear combination of several Slater determinants. These determinants correspond to different singly, doubly, triply, etc. excited states.

Does this mean that you do not take into account any excited states for constructing your electronic wave function using the Hartree Fock method and that you are only able to find the ground state wave function?

I really have a hard time understanding any of this so if you would be able to explain it simply it is much appreciated :)

2. Nov 6, 2016

### A. Neumaier

Usually yes; the electronic ground state is the state most important for chemistry. Finding excited states is already an extension of the basic method.

3. Nov 9, 2016

### DrDu

There are some excited states which can be described by a single Slater determinant. These are often states of lowest energy of a different symmetry than that of the ground state. But sometimes it is also symmetry which demands looking for a solution consisting of more than one Slater determinant. It is then often possible to represent the state by only a hand full of Slater determinants and optimize the orbitals. This is called multiconfiguration SCF.