The method was developed independently by Clemens C. J. Roothaan and George G. Hall in 1951, and is thus sometimes called the Roothaan-Hall equations.[1][2][3] The Roothaan equations can be written in a form resembling generalized eigenvalue problem, although they are not a standard eigenvalue problem because they are nonlinear:
where F is the Fock matrix (which depends on the coefficients C due to electron-electron interactions), C is a matrix of coefficients, S is the overlap matrix of the basis functions, and is the (diagonal, by convention) matrix of orbital energies. In the case of an orthonormalised basis set the overlap matrix, S, reduces to the identity matrix. These equations are essentially a special case of a Galerkin method applied to the Hartree–Fock equation using a particular basis set.
In contrast to the Hartree–Fock equations - which are integro-differential equations - the Roothaan–Hall equations have a matrix-form. Therefore, they can be solved using standard techniques.
^Frank Jensen, Introduction to Computational Chemistry, John Wiley and Sons, 1999, pp. 65–69, ISBN0-471-98085-4
^Roothaan, C. C. J. (1951). "New Developments in Molecular Orbital Theory". Reviews of Modern Physics. 23 (2): 69–89. Bibcode:1951RvMP...23...69R. doi:10.1103/RevModPhys.23.69.
^Hall, G. G. (1951). "The Molecular Orbital Theory of Chemical Valency. VIII. A Method of Calculating Ionization Potentials". Proceedings of the Royal Society A. 205 (1083): 541–552. Bibcode:1951RSPSA.205..541H. doi:10.1098/rspa.1951.0048. S2CID 94393143.
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roothaan, equations, representation, hartree, fock, equation, orthonormal, basis, which, gaussian, type, slater, type, applies, closed, shell, molecules, atoms, where, molecular, orbitals, atomic, orbitals, respectively, doubly, occupied, this, generally, call. The Roothaan equations are a representation of the Hartree Fock equation in a non orthonormal basis set which can be of Gaussian type or Slater type It applies to closed shell molecules or atoms where all molecular orbitals or atomic orbitals respectively are doubly occupied This is generally called Restricted Hartree Fock theory The method was developed independently by Clemens C J Roothaan and George G Hall in 1951 and is thus sometimes called the Roothaan Hall equations 1 2 3 The Roothaan equations can be written in a form resembling generalized eigenvalue problem although they are not a standard eigenvalue problem because they are nonlinear F C S C ϵ displaystyle mathbf F mathbf C mathbf S mathbf C mathbf epsilon where F is the Fock matrix which depends on the coefficients C due to electron electron interactions C is a matrix of coefficients S is the overlap matrix of the basis functions and ϵ displaystyle epsilon is the diagonal by convention matrix of orbital energies In the case of an orthonormalised basis set the overlap matrix S reduces to the identity matrix These equations are essentially a special case of a Galerkin method applied to the Hartree Fock equation using a particular basis set In contrast to the Hartree Fock equations which are integro differential equations the Roothaan Hall equations have a matrix form Therefore they can be solved using standard techniques See also EditHartree Fock methodReferences Edit Frank Jensen Introduction to Computational Chemistry John Wiley and Sons 1999 pp 65 69 ISBN 0 471 98085 4 Roothaan C C J 1951 New Developments in Molecular Orbital Theory Reviews of Modern Physics 23 2 69 89 Bibcode 1951RvMP 23 69R doi 10 1103 RevModPhys 23 69 Hall G G 1951 The Molecular Orbital Theory of Chemical Valency VIII A Method of Calculating Ionization Potentials Proceedings of the Royal Society A 205 1083 541 552 Bibcode 1951RSPSA 205 541H doi 10 1098 rspa 1951 0048 S2CID 94393143 This quantum chemistry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Roothaan equations amp oldid 1098445673, wikipedia, wiki, book, books, library,
