An Improved Penalty-Based Excited-State Variational Monte Carlo Approach with Deep-Learning Ansatzes

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Variational Quantum Monte Carlo (VMC) is a powerful method for calculating electronic excited states.
• Existing VMC methods face challenges in accuracy and computational efficiency for certain systems.
• Improvements are needed to enhance the reliability and applicability of VMC for excited-state calculations.

Purpose of the Study:

• To introduce significant improvements to the penalty-based VMC algorithm for computing electronic excited states.
• To demonstrate the competitive accuracy of the updated method compared to existing excited-state VMC approaches.
• To enable selective computation of states with specific spin properties.

Main Methods:

• Implemented an automatic tuning mechanism for penalty term scales.
• Introduced an updated overlap penalty with proven convergence properties.
• Developed a novel spin-penalty term for selective state computation.
• Utilized a self-attention-based ansatz for improved accuracy.

Main Results:

• Achieved a mean absolute error below 1 kcal/mol for vertical excitation energies of 26 atoms and molecules.
• Demonstrated accuracy on par with natural-excited-state (NES) VMC for carbon dimer dissociation excited states.
• Provided results for previously inaccessible regions of the carbon dimer potential energy surface.
• Improved accuracy for ethylene's conical intersection, matching NES-VMC and multireference configuration interaction.

Conclusions:

• The improved penalty-based VMC method offers competitive accuracy for electronic excited states.
• The enhancements allow for selective computation of states with desired spin.
• This method provides valuable insights into molecular excited states, including dissociation pathways and conical intersections.