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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Equations of explicitly-correlated coupled-cluster methods.

Toru Shiozaki1, Muneaki Kamiya, So Hirata

  • 1Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435, USA.

Physical Chemistry Chemical Physics : PCCP
|June 7, 2008
PubMed
Summary

This study introduces a new symbolic algebra tool, smith, for deriving coupled-cluster (CC) calculations that explicitly include interelectronic distances (CC-R12). smith automates complex tensor contractions and algebraic steps, enabling efficient computation of high-rank CC-R12 energies and wave functions.

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Area of Science:

  • Computational Quantum Chemistry
  • Theoretical Chemistry
  • Electronic Structure Theory

Background:

  • High-rank coupled-cluster (CC) methods are essential for accurate electronic structure calculations.
  • Explicitly including interelectronic distances (r12) in CC methods (CC-R12) improves accuracy but introduces significant computational complexity.
  • Automating the derivation and implementation of these complex methods is crucial for practical application.

Purpose of the Study:

  • To derive tensor contraction expressions for high-rank CC-R12 energies and wave functions.
  • To develop efficient computational sequences for these CC-R12 methods.
  • To automate algebraic transformations specific to R12 methods using a symbolic algebra tool.

Main Methods:

  • Development and application of a symbolic algebra tool (smith) for deriving tensor contractions.
  • Identification and automation of algebraic steps, including resolution-of-the-identity insertions.
  • Derivation of expressions for ground state, excited states (EOM-CC-R12), and analytical gradients (Lambda-CC-R12).

Main Results:

  • Successfully derived CC-R12 tensor contraction expressions, including up to connected quadruple excitations (CCSDTQ-R12).
  • Proposed efficient computational sequences and identified reusable intermediate tensors.
  • Analyzed the computational scaling of geminal amplitude equations, showing they are often less demanding than standard amplitude equations for high-rank CC-R12.

Conclusions:

  • The symbolic algebra tool (smith) effectively automates complex derivations for CC-R12 methods.
  • Efficient computational strategies are proposed for various CC-R12 formalisms.
  • Solving unabridged geminal amplitude equations is feasible and recommended for benchmark accuracy in high-rank CC-R12 calculations.