Optimization of quantum Monte Carlo wave functions by energy minimization

Area of Science:

• Computational Chemistry
• Quantum Monte Carlo Methods

Background:

• Variational Monte Carlo (VMC) is a key quantum chemistry method.
• Efficient wave function optimization is crucial for accurate electronic structure calculations.
• Minimizing energy in VMC requires robust optimization techniques.

Purpose of the Study:

• To investigate and compare three energy minimization methods within VMC.
• To assess the efficiency of Newton, linear, and perturbative optimization approaches.
• To evaluate the impact of wave function parameter optimization on Diffusion Monte Carlo (DMC) energies.

Main Methods:

• Newton method: Uses energy gradient and Hessian with reduced variance estimator.
• Linear method: Diagonalizes Hamiltonian matrix estimator using the zero-variance principle.
• Perturbative method: Approximates linear method's eigenvalue equation via perturbation theory.
• Application to C2 molecule wave function optimization (Jastrow-Configuration State Functions).

Main Results:

• Newton and linear methods show high efficiency for Jastrow, CSF, and orbital parameters.
• Perturbative method is suitable for optimizing CSF and orbital parameters.
• Monotonic improvement in DMC total energy observed with increased parameter optimization in VMC.
• Implies monotonic improvement of the nodal hypersurface with parameter optimization.

Conclusions:

• The studied VMC optimization methods offer distinct advantages for different parameter sets.
• Effective wave function optimization in VMC leads to improved DMC energies.
• The findings contribute to advancing accurate quantum mechanical calculations for molecular systems.