Excited states in auxiliary field quantum Monte Carlo

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Calculating excited states is crucial for understanding molecular properties and reactions.
• Traditional methods like equation of motion coupled cluster (EOM-CCSD) can be computationally expensive and may lack accuracy for certain systems.
• Auxiliary field quantum Monte Carlo (AFQMC) is an emerging method for electronic structure calculations.

Purpose of the Study:

• To systematically investigate the accuracy and scalability of AFQMC for calculating low-lying excited states.
• To compare AFQMC performance against established methods like EOM-CCSD.
• To identify optimal trial states for AFQMC calculations of excited states.

Main Methods:

• Utilizing symmetry to target triplet excited states as ground-state problems in AFQMC.
• Employing truncated equation of motion coupled cluster with single and double excitations (EOM-CCSD) as trial states for open-shell singlet excited states.
• Benchmarking AFQMC calculations on small to medium molecules and polyacenes.

Main Results:

• AFQMC successfully calculates triplet excited states using restricted open-shell determinants.
• EOM-CCSD trial states improve accuracy for open-shell singlet excited states compared to active space methods.
• AFQMC results show systematically higher accuracy than EOM-CCSD, reducing excitation energy errors by approximately half for open-shell singlets.
• AFQMC achieves a per-sample cost scaling of O(N^6).

Conclusions:

• AFQMC is a viable and accurate method for calculating low-lying excited states, particularly when EOM-CC triples are computationally prohibitive.
• AFQMC offers a scalable and more accurate alternative to EOM-CCSD for excited-state calculations.
• The choice of trial state significantly impacts AFQMC accuracy for open-shell singlet states.