Calculation of the molecular integrals with the range-separated correlation factor.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Explicitly correlated quantum chemical calculations necessitate the computation of five types of two-electron integrals beyond standard electron repulsion integrals.
• Accurate calculation of these integrals is crucial for high-precision quantum chemical methods.

Purpose of the Study:

• To present a novel computational scheme for calculating specific two-electron integrals required in explicitly correlated quantum chemistry.
• To implement a "range-separated" correlation factor that combines short-range and long-range behaviors.

Main Methods:

• Utilizes general ideas of the McMurchie-Davidson technique.
• Employs a "range-separated" correlation factor, merging short-range electronic cusp behavior with helium atom long-range asymptotics.
• Formulates almost all computational steps recursively for efficiency and precision control.

Main Results:

• A novel and efficient scheme for computing challenging two-electron integrals is presented.
• The recursive formulation allows for efficient implementation and precise control over calculations.
• The method is flexible and general, accommodating arbitrary correlation factors.

Conclusions:

• The developed method provides an efficient and flexible way to compute necessary integrals for explicitly correlated quantum chemical calculations.
• The recursive approach ensures computational efficiency and precision.
• This work facilitates the application of advanced correlation factors in electronic structure studies.