The electronic mean-field configuration interaction method. I. Theory and integral formulas

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Solving the electronic Schrodinger equation is crucial for understanding molecular behavior.
• Existing methods like mean-field configuration interaction have limitations.
• Group function theory enforces strong orthogonality, which can be restrictive.

Purpose of the Study:

• Introduce a new computational method for the electronic Schrodinger equation.
• Develop a self-consistent field approach by contracting electronic degrees of freedom.
• Enable approximation of the full configuration interaction limit without strong orthogonality constraints.

Main Methods:

• Contracting groups of electronic degrees of freedom in a mean field.
• Iterating partitions for a self-consistent field method.
• Utilizing a generalized Hopf algebra structure for matrix element derivation.
• Ensuring fermionic symmetry and group structure in wave function calculations.

Main Results:

• A novel, recursive method for solving the electronic Schrodinger equation.
• Hamiltonian and overlap matrix elements derived respecting wave function group structure and fermionic symmetry.
• Avoidance of the strong orthogonality condition typical in group function theory.
• Potential for approaching the full configuration interaction limit through coarser partitions.

Conclusions:

• The new method offers an efficient alternative for electronic structure calculations.
• It provides a flexible framework for approximating solutions to the Schrodinger equation.
• The approach is amenable to recursive computation, facilitating complex calculations.