Communication: Explicitly correlated formalism for second-order single-particle Green's function.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical chemistry

Background:

• The second-order single-particle Green's function (GF2) method is widely used for electronic structure calculations.
• Basis set incompleteness is a major source of error in GF2 calculations, particularly for ionization potentials.
• Existing methods often employ approximations, such as the diagonal approximation, which can limit accuracy.

Purpose of the Study:

• To develop an explicitly correlated formalism for the GF2 method (GF2-F12) that overcomes limitations of previous approaches.
• To improve the accuracy of ionization potential calculations by reducing basis set errors.
• To provide a more cost-effective method for high-accuracy electronic structure predictions.

Main Methods:

• Development of an explicitly correlated formalism for the GF2 method, termed GF2-F12.
• The GF2-F12 method explicitly accounts for electron correlation without the diagonal approximation.
• The energy dependence of explicitly correlated terms is incorporated into the formalism.

Main Results:

• GF2-F12 demonstrates radically improved basis set convergence for ionization potentials compared to the standard GF2 method.
• For small and medium organic molecules, GF2-F12 achieves accuracy comparable to higher-level basis sets at a lower computational cost.
• Specifically, GF2-F12 with the aug-cc-pVDZ basis set outperforms GF2 with the aug-cc-pVQZ basis set.

Conclusions:

• The GF2-F12 method offers a significant advancement in the accurate and efficient calculation of ionization potentials.
• This approach provides a more reliable and computationally feasible alternative for studying electronic properties of organic molecules.
• The developed formalism paves the way for more accurate quantum chemical calculations with reduced basis set dependence.