Basis set

Basis Set is a set of functions (usually mathematical or computational) used in quantum mechanics to describe the wave function of a system in the context of the Schrodinger equation. The choice of basis set can significantly affect the accuracy and efficiency of quantum mechanical calculations, making it a key concept in computational chemistry and physics.

Overview

A basis set is used to represent the electronic wave function in the Hartree-Fock method and post-Hartree-Fock methods. It is a set of functions, often atomic orbitals, which are used to construct the molecular orbitals. These functions can be simple atomic orbitals, or they can be more complex functions such as Gaussian orbitals.

Types of Basis Sets

There are several types of basis sets used in quantum mechanical calculations:

• Minimal Basis Sets: These are the smallest possible basis sets. They include only one function for each atomic orbital in the atom. An example of a minimal basis set is the STO-3G basis set.

• Split-Valence Basis Sets: These basis sets include more than one basis function for each atomic orbital. They are designed to provide a more accurate description of the electron distribution. Examples include the 6-31G and 6-311G basis sets.

• Correlation-Consistent Basis Sets: These basis sets are designed to systematically converge to the complete basis set limit as the size of the basis set increases. Examples include the cc-pVXZ basis sets.

• Plane Wave Basis Sets: These basis sets use plane waves as basis functions and are often used in calculations involving periodic systems.

Selection of Basis Sets

The selection of a basis set for a particular calculation depends on a variety of factors, including the type of system being studied, the level of theory being used, and the computational resources available. In general, larger basis sets provide more accurate results, but at a higher computational cost.

See Also

• Quantum Chemistry
• Computational Chemistry
• Molecular Orbital Theory
• Hartree-Fock Method