Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo

Area of Science:

• Computational chemistry
• Quantum mechanics
• Electronic structure theory

Background:

• Selected configuration interaction methods are increasingly using multi-Slater trial wave functions in quantum Monte Carlo (QMC) methods.
• Efficient calculation of local energy is crucial for QMC simulations.

Purpose of the Study:

• To present a novel algorithm for calculating the local energy of a multi-Slater wave function in orbital space.
• To improve the computational scaling compared to existing orbital space algorithms.

Main Methods:

• Developed an algorithm for calculating local energy in orbital space for multi-Slater wave functions.
• Algorithm cost scaling is O(n⁵ + n_c), an improvement over the O(n⁴n_c) of previous methods.
• Applied the method using variational Monte Carlo (VMC) with a Jastrow multi-Slater wave function.

Main Results:

• The new algorithm demonstrates significantly improved computational efficiency.
• Achieved a cost scaling of O(n⁵ + n_c) for ab initio Hamiltonians.
• Successfully applied to polyacetylene, enabling the use of a larger number of configurations.

Conclusions:

• The presented algorithm offers a more efficient approach for QMC calculations involving multi-Slater wave functions.
• This advancement facilitates the use of more complex wave functions, potentially leading to more accurate results in electronic structure studies.
• The method's applicability extends to various QMC techniques, including auxiliary field QMC.