HartreeFocktilgangen

The Hartree-Fock approximation, also referred to as the Hartree-Fock method or simply Hartree-Fock theory, is a fundamental approach in quantum chemistry and quantum physics used to approximate the wave function of a multi-electron system. Developed independently by Douglas Hartree and Vladimir Fock in the early 20th century, this method provides a systematic way to solve the Schrödinger equation for systems with multiple interacting particles, particularly electrons in atoms and molecules.

The core idea of the Hartree-Fock method is to describe the many-body wave function as a single Slater determinant, which is a product of single-particle orbitals. Each orbital is occupied by one or two electrons with opposite spins, adhering to the Pauli exclusion principle. The method assumes that each electron moves in an average field created by all the other electrons, rather than interacting with them directly. This average field is known as the mean-field approximation.

The Hartree-Fock equations are derived by minimizing the energy of the system with respect to variations in the orbitals, subject to the constraint that the orbitals remain orthonormal. This process yields a set of coupled differential equations, which are typically solved iteratively using numerical methods. The resulting orbitals are called Hartree-Fock orbitals, and the corresponding energy is the Hartree-Fock energy.

While the Hartree-Fock method provides a reasonable approximation for many systems, it has limitations. It does not account for electron correlation, meaning it neglects instantaneous interactions between electrons beyond the mean-field approximation. This can lead to inaccuracies in predicting certain properties, such as excitation energies or reaction barriers. Despite these limitations, Hartree-Fock remains a foundational technique in computational chemistry and physics, serving as a starting point for more advanced methods that incorporate electron correlation.