SF-[2]R12: a spin-adapted explicitly correlated method applicable to arbitrary electronic states

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• Basis set error is a major limitation in electronic structure calculations.
• Explicitly correlated methods, like [2](R12), reduce this error by including electron correlation explicitly.
• Existing methods may not be suitable for all electronic structure problems, especially those involving multiple electronic configurations.

Purpose of the Study:

• To develop a spin-adapted variant of the [2](R12) explicitly correlated method.
• To formulate the method using spin-free quantities for broader applicability.
• To reduce the computational cost and complexity associated with explicitly correlated corrections.

Main Methods:

• Development of a spin-adapted variant, SF-[2](R12), using spin-free quantities.
• Application of spin-free cumulant decomposition.
• Utilization of the multi-reference generalized Brillouin condition to avoid three-particle reduced density matrices.

Main Results:

• The SF-[2](R12) method is formulated entirely in terms of spin-free quantities.
• Computational complexity is found to be proportional to the sixth power of system size, comparable to MP2-R12.
• Demonstrated significant reduction in basis set error for multi-configurational wave functions.

Conclusions:

• The SF-[2](R12) method effectively reduces basis set errors in electronic structure calculations.
• It offers a computationally feasible approach for improving the accuracy of multi-configurational wave functions.
• This advancement provides a valuable tool for theoretical chemistry research.