Combining explicitly correlated R12 and Gaussian geminal electronic structure theories

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Standard wave function methods suffer from significant basis set errors.
• Explicitly correlated R12 methods, using a single correlation factor (F12 methods), reduce these errors but may not capture all correlation scales efficiently.
• There is a need for more general explicitly correlated methods that can efficiently describe electron correlation across various length scales.

Purpose of the Study:

• To develop and explore a more general explicitly correlated second-order Møller–Plesset perturbation theory (MP2-R12) method.
• To investigate the use of a set of contracted Gaussian-type geminals (GTGs) with optimized linear coefficients for describing electron-electron cusp conditions.
• To assess the accuracy and efficiency of this new method in calculating molecular correlation energies and atomization energies.

Main Methods:

• A generalized MP2-R12 method was developed, employing a set of GTGs with fixed exponents and linearly optimized coefficients for each electron pair.
• The method requires only two-electron integrals and uses approximations such as the resolution of the identity and the generalized Brillouin condition.
• An arbitrary number of GTGs can be used, and the method is designed for numerical stability by removing linear dependencies and ensuring a positive definite Hamiltonian matrix.

Main Results:

• Using only three GTGs and a double-zeta basis set, the method achieved valence correlation energies within 2.2% of the basis set limit for 20 small molecules.
• With seven GTGs and a double-zeta basis set, the average basis set error decreased to 1.2%, outperforming conventional MP2 calculations with much larger basis sets (quadruple, quintuple, sextuple zeta).
• The new method's accuracy in calculating correlation contributions to atomization energies matched or exceeded conventional sextuple-zeta results using only a double-zeta basis set.

Conclusions:

• The developed generalized MP2-R12 method using GTGs offers a significant reduction in basis set errors for calculating molecular correlation energies.
• This approach provides high accuracy comparable to or better than conventional methods using much larger basis sets, even with small basis sets.
• The method is computationally efficient and numerically stable, offering a promising alternative for accurate electronic structure calculations.