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Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
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Analytic Energy Gradients for Variational Two-Electron Reduced-Density Matrix Methods within the Density Fitting

J Wayne Mullinax1, Evgeny Epifanovsky2, Gergely Gidofalvi3

  • 1Department of Chemistry and Biochemistry , Florida State University , Tallahassee , Florida 32306 , United States.

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Analytic energy gradients for variational two-electron reduced-density-matrix-driven complete active space self-consistent field (v2RDM-CASSCF) calculations are presented. This method, using density fitting, enables geometry optimizations for larger chemical systems with reduced computational cost.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Complete active space self-consistent field (CASSCF) is a crucial method for accurately describing electron correlation in molecules.
  • Calculating analytic energy gradients is essential for efficient geometry optimizations and vibrational frequency analysis.
  • The computational cost of traditional CASSCF methods, especially for larger systems, can be prohibitive.

Purpose of the Study:

  • To present analytic energy gradients for a density-fitted variational two-electron reduced-density-matrix-driven CASSCF (DF-v2RDM-CASSCF) procedure.
  • To assess the computational efficiency and accuracy of DF-v2RDM-CASSCF for geometry optimizations and vibrational frequency calculations.
  • To investigate the electronic structure of linear polyacenes using the developed method.

Main Methods:

  • Development and implementation of analytic energy gradients for DF-v2RDM-CASSCF.
  • Application of the method to a set of 25 small molecules to compute equilibrium geometries and harmonic vibrational frequencies.
  • Geometry optimization of singlet and triplet states for linear polyacenes up to dodecacene.

Main Results:

  • DF approximation significantly reduces computational cost (operations and memory) for v2RDM-CASSCF gradient evaluation.
  • DF-v2RDM-CASSCF equilibrium bond lengths show excellent agreement with CI-CASSCF, with differences of 0.62 pm (PQG) and 0.05 pm (PQG+T2).
  • Quantitative agreement in harmonic vibrational frequencies between DF-v2RDM-CASSCF and CI-CASSCF requires partial three-particle N-representability conditions.
  • Optimized geometries for linear polyacenes up to dodecacene were obtained, with an active space of 50 electrons in 50 orbitals.
  • The extrapolated singlet-triplet energy gap for infinite linear acenes is 7.8 kcal/mol.

Conclusions:

  • DF-v2RDM-CASSCF provides an efficient and accurate approach for electronic structure calculations, enabling the study of larger chemical systems.
  • Consideration of partial three-particle N-representability conditions is crucial for achieving quantitative accuracy in vibrational frequencies.
  • The method is capable of describing the electronic properties of extended conjugated systems like linear polyacenes.