Hartree-Fock Methods: Types and Performance

This lecture covers different types of HF methods, including RHF, ROHF, and UHF, each with specific characteristics and performance evaluations. The instructor discusses the relative good and bad performance of HF in various scenarios, such as structural properties, vibrational frequencies, and transition states. Additionally, the lecture delves into electron correlation, contrasting the chemist's and physicist's views on Ecorr. Post-Hartree-Fock methods like CI, MP, and CC are introduced as ways to enhance HF results by considering electron correlation. The discussion on correlation includes topics like the Coulomb hole, correlated motion of electrons, and the construction of a basis of Slater determinants.

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Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, configuration simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), interaction means the mixing (interaction) of different electronic configurations (states).

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Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants.

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Multi-configurational self-consistent field

Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule.

Gaussian (software)

Gaussian ˈgaʊsiən is a general purpose computational chemistry software package initially released in 1970 by John Pople and his research group at Carnegie Mellon University as Gaussian 70. It has been continuously updated since then. The name originates from Pople's use of Gaussian orbitals to speed up molecular electronic structure calculations as opposed to using Slater-type orbitals, a choice made to improve performance on the limited computing capacities of then-current computer hardware for Hartree–Fock calculations.

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