Abstract
Molecular gradients and hessians for multiconfigurational self-consistent-field wavefunctions are derived in terms of the generators of the unitary group using exponential unitary operators to describe the response of the energy to a geometrical deformation. Final expressions are cast in forms which contain reference only to the primitive non-orthogonal atomic basis set and to the final orthonormal molecular orbitals; all reference to intermediate orthogonalized orbitals is removed. All of the deformation-dependent terms in the working equations reside in the one- and two-electron integral derivatives involving the atomic basis orbitals. The deformation-independent terms, whose contributions can be partially summed, involve symmetrized density matrix elements which have the same eight-fold index permutational symmetry as the one- and two-electron integral derivatives they multiply. This separation of deformation-dependent and -independent factors allows for single-pass integral-derivative-driven implementation of the gradient and hessian expressions. 19 references.
Citation Formats
Banerjee, A, Jensen, J O, Simons, J, and Shepard, R.
MC SCF molecular gradients and hessians: computational aspects.
Netherlands: N. p.,
1984.
Web.
Banerjee, A, Jensen, J O, Simons, J, & Shepard, R.
MC SCF molecular gradients and hessians: computational aspects.
Netherlands.
Banerjee, A, Jensen, J O, Simons, J, and Shepard, R.
1984.
"MC SCF molecular gradients and hessians: computational aspects."
Netherlands.
@misc{etde_5974106,
title = {MC SCF molecular gradients and hessians: computational aspects}
author = {Banerjee, A, Jensen, J O, Simons, J, and Shepard, R}
abstractNote = {Molecular gradients and hessians for multiconfigurational self-consistent-field wavefunctions are derived in terms of the generators of the unitary group using exponential unitary operators to describe the response of the energy to a geometrical deformation. Final expressions are cast in forms which contain reference only to the primitive non-orthogonal atomic basis set and to the final orthonormal molecular orbitals; all reference to intermediate orthogonalized orbitals is removed. All of the deformation-dependent terms in the working equations reside in the one- and two-electron integral derivatives involving the atomic basis orbitals. The deformation-independent terms, whose contributions can be partially summed, involve symmetrized density matrix elements which have the same eight-fold index permutational symmetry as the one- and two-electron integral derivatives they multiply. This separation of deformation-dependent and -independent factors allows for single-pass integral-derivative-driven implementation of the gradient and hessian expressions. 19 references.}
journal = []
volume = {87}
journal type = {AC}
place = {Netherlands}
year = {1984}
month = {Jan}
}
title = {MC SCF molecular gradients and hessians: computational aspects}
author = {Banerjee, A, Jensen, J O, Simons, J, and Shepard, R}
abstractNote = {Molecular gradients and hessians for multiconfigurational self-consistent-field wavefunctions are derived in terms of the generators of the unitary group using exponential unitary operators to describe the response of the energy to a geometrical deformation. Final expressions are cast in forms which contain reference only to the primitive non-orthogonal atomic basis set and to the final orthonormal molecular orbitals; all reference to intermediate orthogonalized orbitals is removed. All of the deformation-dependent terms in the working equations reside in the one- and two-electron integral derivatives involving the atomic basis orbitals. The deformation-independent terms, whose contributions can be partially summed, involve symmetrized density matrix elements which have the same eight-fold index permutational symmetry as the one- and two-electron integral derivatives they multiply. This separation of deformation-dependent and -independent factors allows for single-pass integral-derivative-driven implementation of the gradient and hessian expressions. 19 references.}
journal = []
volume = {87}
journal type = {AC}
place = {Netherlands}
year = {1984}
month = {Jan}
}