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Avoiding the 4-index transformation in one-body reduced density matrix functional calculations for separable

Klaas J H Giesbertz1

  • 1Section of Theoretical Chemistry, Faculty of Exact Sciences, VU University, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands. k.j.h.giesbertz@vu.nl.

Physical Chemistry Chemical Physics : PCCP
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Computational bottlenecks in one-body reduced density matrix (1RDM) functional theory are overcome. A new algorithm enables efficient evaluation of separable 1RDM functionals, making calculations feasible for large electronic systems.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Density matrix functional theory

Background:

  • Evaluating approximate one-body reduced density matrix (1RDM) functionals is computationally intensive.
  • Advanced functionals often require a costly 4-index transformation of two-electron integrals in the natural orbital basis.

Purpose of the Study:

  • To develop a more efficient method for evaluating approximate 1RDM functionals and their derivatives.
  • To reduce the computational cost associated with 1RDM functional theory calculations.

Main Methods:

  • Introduced a novel algorithm for evaluating separable 1RDM functionals.
  • Demonstrated that a 4-index transformation is not always necessary.

Main Results:

  • The new algorithm evaluates separable functionals at cubic cost with respect to basis size.
  • This significantly reduces computational expense compared to traditional methods.

Conclusions:

  • The developed algorithm provides a substantial advancement for 1RDM functional theory.
  • Enables feasibility of 1RDM functional theory calculations for larger and more complex electronic systems.