Complete Active Space SCF (CASSCF)
and Multiconfiguration SCF (MCSCF) Wavefunctions
Dr. Yukio Yamaguchi
Center for Computational
Quantum Chemistry
School of Chemical Sciences
The University of Georgia
Athens, Georgia 30602
Spring, 1996
The MCSCF Wavefunction
The Electronic Energy
where
A Unitary Transformation Matrix, U
Molecular Orbitals Transformed by the U Matrix
In Dirac Notation
The Electronic Energy Expression to Second-Order in R
where
The Newton-Raphson Approach
Gradients for the MO space:
Hessian for the MO space:
One Step Method
Simultaneous optimization of the MO and CI coefficients
The Simultaneous Equations in a Matrix Form
Hessian for the MO space:
Hessian for the CI space:
MO-CI Interacting term:
Gradients for the MO space:
Gradients for the CI space:
An improved MO vector
An improved CI vector
Two Step Method
Suggested Procedure for Quadratically Convergent CASSCF
A core-version implementation for the two step method
- Read in parameters and SCF eigenvectors from `file30.'
- Read in MO integrals from `file52 (or file35)' and store them in core.
- Read in PDMs from `file53 (or file56)' and store them in core.
- Calculate the MCSCF energy.
- Form the Lagrangian matrix.
- Check convergence of the energy and
gradients.
- Select the non-redundant pairs and form
the gradient vector.
- Form the Hessian matrix.
- Set up the simultaneous equations.
- Solve the simultaneous equations directly (FLIN or FLINQ)
or iteratively (Pople-type algorithm).
- Test positive definiteness of the Hessian matrix.
- Test the stepsize of the R matrix elements.
- Construct the unitary transformation (rotation)
matrix, U.
- Orthonormalize the U matrix.
- Check the unitarity of the U matrix.
- Check the ordering of the MOs.
- Rotate the molecular orbitals.
- Update the SCF eigenvectors in `file30'.
This document is copyright 1996,
Mon Nov 18 12:47:18 EST 1996