Excited states in variational Monte Carlo using a penalty method

Area of Science:

• Quantum chemistry
• Computational physics

Background:

• Calculating excited states of electronic systems is crucial for understanding molecular properties and reactions.
• Traditional methods can be computationally expensive and challenging for complex systems.

Purpose of the Study:

• To present a novel variational Monte Carlo technique for solving excited states of electronic systems.
• To demonstrate the method's efficacy by applying it to the benzene molecule.

Main Methods:

• The study employs variational Monte Carlo (VMC) with orthogonality constraints to lower energy states.
• A simple variational principle is derived for excited states, enabling energy optimization.
• Approximately 10,000 parameters were optimized for the first 12 excited states of benzene.

Main Results:

• The VMC technique successfully calculated the first 12 excited states of the benzene molecule.
• Results showed agreement within approximately 0.2 eV compared to higher-scaling coupled cluster methods.
• Minor discrepancies with experimental data were attributed to unconsidered vibrational effects.

Conclusions:

• The presented variational Monte Carlo method offers a viable approach for determining excited states in electronic systems.
• The technique demonstrates good accuracy when applied to a well-characterized molecule like benzene.
• Further refinements could improve agreement with experimental observations by incorporating vibrational dynamics.