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Basis set (chemistry) - Wikipedia

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In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals | 𝜓 𝑖 ⟩ are expanded within the basis set as a linear combination of the basis functions | 𝜓 𝑖 ⟩ ≈ ∑ 𝜇 𝑐 𝜇 𝑖 | 𝜇 ⟩ , where the expansion coefficients 𝑐 𝜇 𝑖 are given by 𝑐 𝜇 𝑖 = ∑ 𝜈 ⟨ 𝜇 | 𝜈 ⟩ − 1 ⟨ 𝜈 | 𝜓 𝑖 ⟩ . The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quantum chemistry community; plane waves which are typically used within the solid state community, or real-space approaches. Several types of at

Basis set (chemistry) - Wikipedia Jump to content From Wikipedia, the free encyclopedia Set of functions used to represent the electronic wave function In theoretical and computational chemistry , a basis set is a set of functions (called basis functions ) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identi

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