Higher-order explicitly correlated coupled-cluster methods.

Area of Science:

• Computational Quantum Chemistry
• Theoretical Chemistry
• Electronic Structure Theory

Background:

• Conventional coupled-cluster (CC) methods require large basis sets for accurate results.
• Explicitly correlated methods (CC-R12/F12) incorporate interelectronic distances to accelerate convergence.
• Previous implementations of CC-R12 were limited in excitation levels.

Purpose of the Study:

• To implement efficient computer codes for high-level explicitly correlated coupled-cluster (CC-R12) methods, including triple and quadruple excitations.
• To demonstrate the rapid convergence and accuracy of these methods towards exact solutions of the Schrodinger equation.
• To obtain accurate absolute total energies for small molecules using CC-R12 methods with smaller basis sets.

Main Methods:

• Development of efficient computer codes for CCSDT-R12 and CCSDTQ-R12 methods using computerized symbolic algebra (SMITH).
• Incorporation of spin, Abelian point-group, and index-permutation symmetries.
• Combination of CC-R12 methods with a grid-based, numerical Hartree-Fock solver.

Main Results:

• Implemented CC-R12 hierarchy (up to CCSDTQ-R12) shows rapid convergence with respect to excitation rank and basis set size.
• CC-R12 methods achieve aug-cc-pV5Z quality results using only the aug-cc-pVTZ basis set.
• Accurate absolute total energies for Ne, BH, HF, and H2O obtained without basis set extrapolation, agreeing with experimental/computational benchmarks.

Conclusions:

• The developed CC-R12 codes provide a systematic and efficient hierarchy for accurate electronic structure calculations.
• Explicitly correlated methods significantly reduce the basis set requirements for high-accuracy quantum chemical computations.
• These advancements enable reliable prediction of molecular properties and energies for various chemical systems.