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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
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Efficient Sparse Matrix Algorithm to Speed Up the Calculation of the Ladder Term in Coupled Cluster Programs.

Zoltán Pillió1, Attila Tajti1, Péter G Szalay1

  • 1Laboratory of Theoretical Chemistry, Institute of Chemistry, Eötvös University , P.O. Box 32, H-1518, Budapest 112, Hungary.

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A new algorithm improves coupled cluster calculations by efficiently partitioning atomic orbital integrals. This enhances performance on modern parallel hardware for quantum chemistry computations.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Algorithm Development

Background:

  • Coupled Cluster (CC) methods are essential for accurate electronic structure calculations.
  • Calculating the ladder-type term in Coupled Cluster Singles and Doubles (CCSD) is computationally intensive.
  • Efficient algorithms are needed to leverage modern parallel computing architectures.

Purpose of the Study:

  • To present a novel algorithm for calculating the ladder-type term in CCSD equations.
  • To optimize the use of two-electron integrals in the atomic orbital (AO) basis.
  • To enhance the performance of CCSD calculations on parallel architectures.

Main Methods:

  • Development of an orbital grouping scheme for AO integral matrices.
  • Partitioning integral matrices into sparse and dense blocks for efficient multiplication.
  • Implementation within the CFOUR quantum chemical program package.

Main Results:

  • The new algorithm demonstrates efficient matrix multiplication through optimized partitioning.
  • Numerical tests confirm the algorithm's effectiveness on highly parallel architectures.
  • The method allows for efficient utilization of modern computational devices in CCSD calculations.

Conclusions:

  • The presented algorithm offers a significant improvement for CCSD calculations.
  • The orbital grouping scheme enables efficient parallelization of integral computations.
  • This work facilitates more accessible and faster high-level quantum chemical modeling.