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Updated: Jul 4, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: applications to
Marcin Ziółkowski1, Ville Weijo, Poul Jorgensen
1The Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Arhus C, Denmark. marcin@chem.au.dk
Abstract:
The conjugate residual with optimal trial vectors (CROP) algorithm is developed. In this algorithm, the optimal trial vectors of the iterations are used as basis vectors in the iterative subspace. For linear equations and nonlinear equations with a small-to-medium nonlinearity, the iterative subspace may be truncated to a three-dimensional subspace with no or little loss of convergence rate, and the norm of the residual decreases in each iteration. The efficiency of the algorithm is demonstrated by solving the equations of coupled-cluster theory with single and double excitations in the atomic orbital basis. By performing calculations on H(2)O with various bond lengths, the algorithm is tested for varying degrees of nonlinearity. In general, the CROP algorithm with a three-dimensional subspace exhibits fast and stable convergence and outperforms the standard direct inversion in iterative subspace method.
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