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# What is a Hartree-Fock state?

## What is a Hartree-Fock state?

In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state. A solution of these equations yields the Hartree–Fock wave function and energy of the system.

What is a Hartree Orbital?

Hartree-Fock theory is fundamental to much of electronic structure theory. It is the basis of molecular orbital (MO) theory, which posits that each electron’s motion can be described by a single-particle function (orbital) which does not depend explicitly on the instantaneous motions of the other electrons.

What is Hartree-Fock exchange?

Hartree Fock theory is one the simplest approximate theories for solving the many-body Hamiltonian. It is based on a simple approximation to the true many-body wavefunction: that the wavefunction is given by a single Slater determinant of spin-orbitals.

### What is the major limitation of Hartree-Fock theory?

There are two factors that limit the accuracy of the Hartree-Fock method. One is the accuracy with which one actually solves the HF equations and the second is the intrinsic limitation of the model. The accuracy with which on solves the HF equations is determined by the completeness of the expansion basis.

What is Hartree-Fock limit?

This limiting energy is the lowest that can be obtained with a single determinant wavefunction. This limit is called the Hartree-Fock limit, the energy is the Hartree-Fock energy, the molecular orbitals producing this limit are called Hartree-Fock orbitals, and the determinant is the Hartree-Fock wavefunction.

Is Hartree Fock size consistent?

Hartree–Fock, coupled cluster, many-body perturbation theory (to any order), and full configuration interaction (CI) are size extensive but not always size consistent.

## What can DFT do?

Classical DFT allows the calculation of the equilibrium particle density and prediction of thermodynamic properties and behavior of a many-body system on the basis of model interactions between particles. The spatially dependent density determines the local structure and composition of the material.

Why is size consistency important?

In quantum chemistry, size consistency and size extensivity are concepts relating to how the behaviour of quantum chemistry calculations changes with size. This property of size consistency is of particular importance to obtain correctly behaving dissociation curves.

How does Hartree Fock theory relate to molecular structure?

Hartree-Fock theory is fundamental to much of electronic structure theory. It is the basis of molecular orbital (MO) theory, which posits that each electron’s motion can be described by a single-particle function (orbital) which does not depend explicitly on the instantaneous motions of the other electrons.

### What is the variational theorem of Hartree Fock?

Relaxation of the last two approximations give rise to many so-called post-Hartree–Fock methods. The variational theorem states that for a time-independent Hamiltonian operator, any trial wave function will have an energy expectation value that is greater than or equal to the true ground-state wave function corresponding to the given Hamiltonian.

When did Slater and Fock discover the Pauli exclusion principle?

In 1930, Slater and V. A. Fock independently pointed out that the Hartree method did not respect the principle of antisymmetry of the wave function. The Hartree method used the Pauli exclusion principle in its older formulation, forbidding the presence of two electrons in the same quantum state.

How does the Hartree method relate to Pauli exclusion?

The Hartree method used the Pauli exclusion principle in its older formulation, forbidding the presence of two electrons in the same quantum state. However, this was shown to be fundamentally incomplete in its neglect of quantum statistics .