Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Leading-order dispersion (E_disp⁽²⁰⁾) and exchange-dispersion (E_exch-disp⁽²⁰⁾) terms in symmetry-adapted perturbation theory (SAPT) exhibit slow convergence to the complete basis set limit.
• Explicitly correlated variants (E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12) were developed to accelerate convergence but were computationally inefficient due to complex integral manipulations.

Purpose of the Study:

• To develop a computationally efficient implementation of explicitly correlated dispersion and exchange-dispersion corrections in SAPT.
• To eliminate the need for manipulating various two-electron integrals by employing density fitting.
• To assess the impact of these improved corrections on the accuracy of SAPT interaction energy calculations.

Main Methods:

• Decomposition of all two-electron integrals using robust density fitting.
• Implementation of explicitly correlated dispersion (E_disp⁽²⁰⁾-F12) and exchange-dispersion (E_exch-disp⁽²⁰⁾-F12) corrections.
• Testing on the A24 database using basis sets up to aug-cc-pV5Z.

Main Results:

• The density fitting approximation introduced negligible errors with standard auxiliary bases (e.g., aug-cc-pVXZ/MP2FIT).
• The new implementation achieved vastly improved basis set convergence for E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 compared to conventional methods.
• While F12 terms did not improve low-level SAPT accuracy, they substantially enhanced the accuracy of high-level SAPT approaches (e.g., SAPT2+3(CCD)δMP2) by reducing basis set incompleteness errors.

Conclusions:

• The density-fitted, explicitly correlated F12 corrections provide a computationally efficient and accurate way to improve basis set convergence in SAPT dispersion and exchange-dispersion energies.
• These well-converged F12 values can effectively replace conventional E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾ terms in SAPT calculations.
• The F12 treatment significantly improves the accuracy of high-level SAPT methods, particularly for calculations with smaller basis sets, by mitigating basis set incompleteness errors.