General orbital invariant MP2-F12 theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of molecular energies is crucial for understanding chemical phenomena.
• Explicitly correlated methods, like Moller-Plesset perturbation theory with explicitly correlated factors (MP2-F12), offer improved accuracy over traditional approaches.
• The use of resolution of the identity (RI) approximations is key to reducing the computational cost of these methods.

Purpose of the Study:

• To derive and present compact working equations for a general form of orbital invariant explicitly correlated second-order closed-shell Moller-Plesset perturbation theory (MP2-F12).
• To introduce a hierarchy of well-defined approximation levels within the MP2-F12 framework.
• To evaluate the performance of different approximations for calculating correlation energies and reaction energies.

Main Methods:

• Development of an orbital invariant explicitly correlated second-order Moller-Plesset perturbation theory (MP2-F12).
• Application of resolution of the identity (RI) approximations using the complementary auxiliary basis set approach to avoid many-electron integrals.
• Introduction of several approximation levels, including generalized Brillouin condition (GBC), extended Brillouin condition (EBC), and variations in the treatment of the exchange operator.

Main Results:

• A new approximation, MP2-F12/3C, is introduced and shown to be equivalent to MP2-F12/3B in the limit of a complete RI basis.
• Testing on 21 molecules demonstrates the convergence of correlation energies with respect to basis sets for various approximations.
• Accuracy of relative energies is confirmed for 16 chemical reactions, with approximation 3C performing comparably to the more demanding 3B.
• Orbital-variant diagonal Ansatz with localized orbitals yields the most accurate reaction energies with smaller basis sets, attributed to reduced geminal basis set superposition errors.

Conclusions:

• The developed MP2-F12 methods provide accurate and computationally efficient means for calculating molecular energies.
• Approximation 3C offers a favorable balance between accuracy and computational cost, comparable to approximation 3B.
• Careful choice of Ansatz and orbital localization can mitigate basis set superposition errors, particularly with smaller basis sets.