Analytical calculations of molecular integrals for multielectron R-matrix methods

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Chemistry

Background:

• Ab initio molecular scattering calculations require accurate computation of electron integrals.
• Existing methods may involve complex or computationally intensive approaches.

Purpose of the Study:

• To develop closed-form analytical expressions for one- and two-electron integrals over finite spherical regions.
• To enhance the efficiency and accuracy of ab initio molecular scattering calculations.

Main Methods:

• Formulating integrals using finite summations of standard functions.
• Calculating integrals over a finite region by subtracting contributions outside the region from integrals over all space.
• Leveraging existing bound-state algorithms for integrals over all space.

Main Results:

• Accurate closed-form analytical expressions for electron integrals over finite spherical regions were derived.
• The method was validated using multidimensional Monte Carlo numerical integrations for two-electron integrals.
• The approach integrates seamlessly with current quantum chemistry software.

Conclusions:

• The developed method provides an accurate and efficient way to compute molecular integrals for scattering calculations.
• This facilitates the unification of bound- and continuum-state calculations in quantum chemistry.
• The approach is applicable to both diatomic and polyatomic molecules.