Generalizations of Newton-Raphson and multiplicity independent Newton-Raphson approaches in multiconfigurational Hartree-Fock theory

The application of Newton–Raphson (second order) approaches in multiconfigurational Hartree–Fock (MCSCF) can significantly improve convergence over other MCSCF procedures. When the Hessian (second derivative) matrix has small eigenvalues, convergence of second order procedures may be slowed significantly both far from and closer to convergence. We derive techniques related to the multiplicity independent Newton–Raphson approach which are less affected by these convergence problems. We also formulate and derive generalized Newton–Raphson approaches which show quadratic, cubic, quartic, etc. convergence. We prove that certain fixed Hessian‐type Newton–Raphson iterations will show quadratic, cubic, quartic, etc. convergence and demonstrate how these approaches may be advantageously used only for a few iterations. The approaches we describe in both the energy and generalized Brillouin’s theorem formulation have about the same complexity in structure and in actual implementation on a computer as the Newton–Rap...

[1]  Hans-Joachim Werner,et al.  A quadratically convergent multiconfiguration–self‐consistent field method with simultaneous optimization of orbitals and CI coefficients , 1980 .

[2]  A. C. Wahl,et al.  Ground and excited states of the diatoms CN and AlO , 1974 .

[3]  W. Goddard,et al.  Orbital optimization in electronic wave functions; equations for quadratic and cubic convergence of general multiconfiguration wave functions , 1976 .

[4]  Poul Jo,et al.  Optimization of orbitals for multiconfigurational reference states , 1978 .

[5]  P. Jørgensen,et al.  A multiconfigurational time-dependent hartree-fock approach , 1979 .

[6]  Danny L. Yeager,et al.  Convergency studies of second and approximate second order multiconfigurational Hartree−Fock procedures , 1979 .

[7]  D. Yeager,et al.  Mode damping in multiconfigurational Hartree–Fock procedures , 1980 .

[8]  E. Dalgaard A quadratically convergent reference state optimization procedure , 1979 .

[9]  G. Das Multiconfiguration self‐consistent field (MCSCF) theory for excited states , 1973 .

[10]  P. Jørgensen,et al.  A numerical study of the convergency of second and approximate second-order multiconfiguration Hartree-Fock procedures , 1980 .

[11]  Byron H. Lengsfield,et al.  General second order MCSCF theory: A density matrix directed algorithm , 1980 .

[12]  E. Yurtsever,et al.  The orthogonal gradient method. A simple method to solve the closed‐shell, open‐shell, and multiconfiguration SCF equations , 1979 .

[13]  D. Thouless Stability conditions and nuclear rotations in the Hartree-Fock theory , 1960 .

[14]  E. Dalgaard Time‐dependent multiconfigurational Hartree–Fock theory , 1980 .

[15]  B. Roos,et al.  The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule , 1981 .

[16]  J. Linderberg,et al.  State vectors and propagators in many‐electron theory. A unified approach , 1977 .