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Excited states in variational Monte Carlo using a penalty method.

Shivesh Pathak1, Brian Busemeyer2, João N B Rodrigues3

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Researchers developed a variational Monte Carlo method to calculate excited states in electronic systems. This approach optimizes parameters for accurate energy calculations, achieving good agreement with established methods for the benzene molecule.

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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.