Electronic correlation

An overview of electronic correlation in quantum chemistry

Electronic correlation refers to the interaction between electrons in a quantum system that cannot be described by a single Slater determinant or Hartree-Fock method. It is a crucial concept in quantum chemistry and solid-state physics as it accounts for the complex interactions that arise due to the Pauli exclusion principle and the Coulomb interaction.

Overview

Illustration of electron correlation in a two-electron system.

In quantum mechanics, the behavior of electrons in atoms and molecules is often approximated using the Hartree-Fock method, which assumes that each electron moves independently in the average field created by all other electrons. However, this approximation neglects the instantaneous interactions between electrons, known as electronic correlation.

Electronic correlation is essential for accurately describing the electronic structure of systems, especially those with strong electron-electron interactions. It is responsible for phenomena such as dispersion forces, magnetism, and the band gap in semiconductors.

Types of Electronic Correlation

Electronic correlation can be broadly classified into two types:

Dynamic Correlation

Dynamic correlation arises from the rapid, small-scale fluctuations in the positions of electrons. It is typically well-described by methods such as Møller-Plesset perturbation theory and coupled cluster theory. Dynamic correlation is important for accurately predicting the energies of molecular systems.

Static Correlation

Static correlation occurs in systems where multiple electronic configurations are nearly degenerate, such as in transition metal complexes or conjugated systems. It is often addressed using methods like multiconfigurational self-consistent field (MCSCF) and complete active space self-consistent field (CASSCF).

Methods to Account for Electronic Correlation

Several computational methods have been developed to account for electronic correlation:

• Configuration Interaction (CI): A method that considers a linear combination of multiple Slater determinants to describe the wavefunction.
• Coupled Cluster (CC): A highly accurate method that includes correlations by considering excitations of electrons from occupied to virtual orbitals.
• Density Functional Theory (DFT): A widely used approach that incorporates correlation effects through exchange-correlation functionals.

Applications

Understanding electronic correlation is vital for predicting the properties of materials and molecules. It plays a key role in:

• Designing new materials with specific electronic properties.
• Understanding chemical reactions and reaction mechanisms.
• Developing quantum computing technologies.

Challenges

Despite advances in computational methods, accurately capturing electronic correlation remains challenging, especially for large systems. The computational cost of methods that include correlation effects can be significant, limiting their application to small or medium-sized systems.

Related pages

• Quantum chemistry
• Hartree-Fock method
• Density functional theory
• Møller-Plesset perturbation theory