The MC SCF theory: Method of one‐electron Hamiltonian

Abstract

AbstractsThe one-electron Hamiltonian method is developed to solve the variational equations of the MC SCF theory.The many-parameter family of the one-electron Hamiltonian is derived and conditions for parameters to provide convergence of the SCF procedure to the energy minimum are obtained. A computation scheme based on the use of the one-electron Hamiltonian is described.La mkthode d'un Hamiltonien B un klectron est dCveloppCe pour rksoudre les Cquations variationnelles de la thkorie MC SCF. On obtient une famille a plusieurs parametres de cet Hamiltonien ainsi que des conditions de convergence du procCdk SCF. On decrit un procedk numkrique base sur I'emploi de 1'Hamiltonien B un klectron.Die auf einem Einelektronenhamiltonoperator gegrundete Methode ist fur die Losung der Variationsgleichungen der Mc-scF-Theorie entwickelt. Eine Vielparameterfamilie dieses Operators wird hergeleitet und Bedingungen fur die Konvergenz des scF-Vervahrens werden erhalten. Ein auf der Anwendung des Einelektronenoperators basiertes numerisches Verfahren wird beschrieben. 7 Present address:

Modified one-electron Hamiltonian method in MC SCF theory

“…[l] and [2] the first-order OEH method was developed in which the values of x, were defined by the steepest descent minimization; the scale transformations of variables were also taken into account. In the second-order OEH method [3] the Newton-Raphson procedure was used to define the descent-step components x,.…”

On convergence guarantees for the multi-configuration self-consistent field theory

“…A recent, interesting, development is due to Kuprievich and Shramko [22] 2Q2 Downloaded by [University of Cambridge] at 23:36 15 June 2016 which attempts to amalgamate the two approaches described above by using several variable parameters. In this paper we show how it is possible to guarantee convergence of the energy to a stationary point on the energy surface within the framework of the MC-SCF theory of Veillard and Clementi [13].…”

Alternative Technique for the Constrained Variational Problem Based on an Asymptotic Projection Method: II. Applications to Open-Shell Self-Consistent Field Theory

“…Computational methods based on open-shell theory provide well-established tools which are applied routinely in modern molecular electronic structure studies (see, e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein). Today, open-shell methodology is available in many of the quantum chemical program packages, such as GAUSSIAN [23] and GAMESS [24], and is exploited in many practical applications.…”

“…This results in off-diagonal Lagrange multipliers which couple the closed-and open-shells and which cannot be eliminated by a suitably chosen unitary transformation. Many studies have been devoted to the orthogonality problem for the closed-and open-shell orbitals [1][2][3][4][5][6][7][8][9][10]. In his seminal 1960 paper, Roothaan [1] proposed the elegant coupling operator formalism to overcome this difficulty.…”

“…In his seminal 1960 paper, Roothaan [1] proposed the elegant coupling operator formalism to overcome this difficulty. Considerable progress has been made in understanding the nature of the coupling operator method (see, e.g., [2][3][4][5][6][7][8], [11]) and useful computational experience has been accumulated in solving the restricted open-shell Hartree-Fock (ROHF) equations (see, e.g., [12][13][14]). Recent investigations have made it possible to find a canonical form of the open-shell Fock operator, which leads to useful relations between the open-shell orbital energies and the ionization potentials [17].…”