Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo.

Area of Science:

• Computational Chemistry
• Quantum Mechanics

Background:

• Variational Monte Carlo (VMC) methods are crucial for quantum mechanical calculations.
• Efficient optimization of wave functions is essential for accurate VMC results.
• Low-memory optimization techniques are needed for large-scale computations.

Purpose of the Study:

• To compare the performance of recently developed low-memory wave function optimization methods in VMC.
• To identify the complementary advantages of different optimization strategies.
• To develop a hybrid approach for enhanced wave function optimization.

Main Methods:

• Comparison of first and second derivative-based optimization methods.
• Evaluation of low-memory variants of the linear method.
• Assessment of accelerated descent approaches.
• Development and testing of a hybrid optimization strategy.

Main Results:

• Low-memory linear methods efficiently approach the energy minimum for complex wave functions.
• Accelerated descent methods refine the minimum with lower bias and statistical uncertainty.
• The hybrid approach successfully combines the strengths of both methods.
• Simultaneous optimization of determinant expansions, molecular orbitals, and Jastrow factors was achieved.

Conclusions:

• First and second derivative methods offer complementary advantages for VMC wave function optimization.
• A hybrid approach integrating linear and accelerated descent methods provides a robust and efficient optimization strategy.
• This combined methodology enables simultaneous optimization of diverse wave function components, improving computational accuracy.