Acceleration of self‐consistent‐field convergence by combining conventional diagonalization and a diagonalization‐free procedure

Baldes, Alexander; Klopper, Wim; Šimunek, Ján; Noga, Jozef; Weigend, Florian

doi:10.1002/jcc.21877

Cited by 9 publications

(14 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Baldes et al found that the stability of the original algorithm strongly depended on the starting reference MOs. If the reference MOs were too distant from the solution of the SCF equation, very slow or no convergence of the SCF iterations and microiterations was observed.…”

Section: Methodsmentioning

confidence: 99%

“…If the reference MOs were too distant from the solution of the SCF equation, very slow or no convergence of the SCF iterations and microiterations was observed. To solve this problem, a hybrid scheme was suggested and implemented using the following idea: monitor the largest element

max (t)

and apply the diagonalization‐free step only if the pertinent amplitude does not exceed a threshold value set to 0.1. Otherwise, perform one diagonalization and obtain new and supposedly better reference MOs.…”

Section: Methodsmentioning

confidence: 99%

“…In contrast to conventional diagonalization, the pertinent algorithm is easily parallelizable and it provides much faster calculation as well. Moreover, it was reported that this approach can reduce the number of iterations needed to reach the SCF convergence, which would improve the efficiency of SCF approach in general, that is, even in cases when the time spent on the diagonalization step is negligible.…”

Section: Introductionmentioning

confidence: 99%

“…The main purpose of this work has been to formulate and implement the pertinent diagonalization‐free approach in the fully relativistic four‐component scheme. A modified version of this approach was successfully implemented at the one‐component and two‐component wave function levels, already . Nevertheless, it was noted that the algorithm may be unstable when one starts the calculation from a poor initial guess.…”

Section: Introductionmentioning

confidence: 99%

“…A modified version of this approach was successfully implemented at the one‐component and two‐component wave function levels, already . Nevertheless, it was noted that the algorithm may be unstable when one starts the calculation from a poor initial guess. Obtaining a good initial guess in relativistic calculations is often difficult.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

et al. 2014

Self Cite

View full text Add to dashboard Cite

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Šimunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization.

show abstract

Section: Methodsmentioning

confidence: 99%

max (t)

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

Perturbation Theory Treatment of Spin–Orbit Coupling, Part I: Double Perturbation Theory Based on a Single-Reference Initial Approximation

Desmarais

Erba

Flament

2021

J. Chem. Theory Comput.

View full text Add to dashboard Cite

We develop a perturbation theory for solving the many-body Dirac equation within a given relativistic effective-core potential approximation. Starting from a scalar-relativistic unrestricted Hartree−Fock (SR UHF) solution, we carry out a double perturbation expansion in terms of spin−orbit coupling (SOC) and the electron fluctuation potential. Computationally convenient energy expressions are derived through fourth order in SOC, second order in the electron fluctuation potential, and a total of third order in the coupling between the two. Illustrative calculations on the halogen series of neutral and singly positive diatomic molecules show that the perturbation expansion is well-converged by taking into account only the leading (nonvanishing) term at each order of the electron fluctuation potential. Our perturbation theory approach provides a computationally attractive alternative to a two-component self-consistent field treatment of SOC. In addition, it includes coupling with the fluctuation potential through third order and can be extended (in principle) to multireference calculations, when necessary for both closed-and open-shell cases, using quasi-degenerate perturbation theory.

show abstract

Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

Ballesteros

Lao

2021

J. Chem. Theory Comput.

View full text Add to dashboard Cite

The balance between cost-effective and sufficiently accurate methods represents the proverbial "promised land" for quantum chemistry calculations. The burden thus falls upon theoretical and computational chemists to provide such alternatives to mitigate the issues that arise from the employ of finite computing resources. In this paper, we attempt to demonstrate the importance of the quality of the initial guess for the self-consistent field (SCF) calculation when considering cost reduction techniques. We broach this challenge by using the many body expansion (MBE) to yield high quality density matrices (DMs) which, in turn, are applied as an SCF initial guess. The MBE-DM approaches combined with purification schemes and distance-based cutoff schemes can serve as initial guesses to reduce the SCF cycles necessary for convergence or derive energy directly through one Fock build. To this end, four unique types of clusters including water clusters, fluoride anion water clusters, sodium cation water clusters, and ammonium-bisulfate salt clusters have been used to test the performance of MBE-DM where its truncation at three-body expansion, MBE(3)-DM, shows vast improvement for those four clusters with reductions in the number of SCF cycles up to 40% as compared with the traditional superposition of atomic densities (SAD) guess. Other types of typical initial guesses, superposition of atomic potentials (SAP) and basis set projection (BSP), perform much worse than MBE-DM and SAD. In addition, the MBE-DM shows consistency across an array of fragment types irrespective of charges, size, level of theory, and basis set selection. Through MBE(3)-DM with the distance cutoff and the average purification scheme, the energy can be obtained directly with a mere 3.2 mH of the mean absolute deviation (MAD) for (H 2 O) N=6−55 which is at least 73 times better than the energy prediction using the typical initial guesses (SAD, SAP, and BSP). The corresponding MAD per monomer is only 0.14 mH which reaches the threshold of the "dynamical accuracy". The promising results of the methods outlined in this paper not only indicate two direct routes for computational cost reduction but also lay the possible foundation for composite techniques (i.e., ab initio sampling) that make best use of near converged values as their starting point.

show abstract

Acceleration of self‐consistent‐field convergence by combining conventional diagonalization and a diagonalization‐free procedure

Cited by 9 publications

References 23 publications

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

Perturbation Theory Treatment of Spin–Orbit Coupling, Part I: Double Perturbation Theory Based on a Single-Reference Initial Approximation

Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

Contact Info

Product

Resources

About