Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Lehtola, Susi

doi:10.1021/acs.jctc.8b01089

Cited by 51 publications

(92 citation statements)

References 112 publications

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“…[4][5][6] In contrast to the Gaussian-basis approach pursued by Whitten and coworkers, where the potentials are tailored to specific chemical environments, a parameter-free variant of the SAP guess based on potentials that are a) Electronic mail: susi.lehtola@alumni.helsinki.fi b) Electronic mail: l.visscher@vu.nl determined from fully numerical 7 atomic density functional calculations at the complete basis set limit was presented in ref. 1. The resulting SAP guess proved to be the most accurate out of the seven types of initial guesses considered in ref.…”

Section: Introductionmentioning

confidence: 80%

“…orbitals, and several types of guesses have been proposed over the years. 1 The focus of the present work is the superposition of atomic potentials (SAP), which is arguably a very old idea with roots dating back at least to the late 1960s. 2,3 However, SAP was apparently forgotten for a long time, assumedly due to issues that were only recently fully resolved.…”

Section: Introductionmentioning

confidence: 99%

“…2,3 However, SAP was apparently forgotten for a long time, assumedly due to issues that were only recently fully resolved. 1 But, if one is interested only in Gaussian-basis calculations, then adopting an atomic potential arising from a spherically symmetric Gaussian expansion of a fictitious electron density (yielding error functions as is wellknown) leads to facile evaluation of the necessary matrix elements. The formation of the guess reduces to the same two-electron integrals that are used in the subsequent self-consistent field (SCF) procedure, which thus already exist in all Gaussian-basis quantum chemistry programs.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting SAP guess proved to be the most accurate out of the seven types of initial guesses considered in ref. 1, judged by the projection of the guess orbitals onto the SCF solution. An improved method for determining the atomic potentials necessary for the procedure has been recently presented in ref.…”

Section: Introductionmentioning

confidence: 99%

“…9, in which a universal atomic potential is employed as in ref. 1, but instead of real-space calculations at the basis set limit the potentials are obtained for a small Gaussian basis set and biased for molecular calculations on the lines of ref. 4.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets

Lehtola

Visscher

Engel

2020

The Journal of Chemical Physics

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The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593].Here, we study the differences between effective potentials from fully numerical density functional and optimized effective potential calculations for fixed configurations. We find that the differences are small, overall, and choose exchange-only potentials at the local density approximation level of theory computed on top of Hartree-Fock densities as a good compromise. The differences between potentials arising from different atomic configurations are also found to be small at this level of theory.Furthermore, we discuss the efficient Gaussian-basis implementation of SAP via error function fits to fully numerical atomic radial potentials. The guess obtained from the fitted potentials can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits covering the whole periodic table from H to Og are reported for non-relativistic as well as fully relativistic four-component calculations that have been carried out with fully numerical approaches.

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Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets

Lehtola

Visscher

Engel

2020

The Journal of Chemical Physics

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An improved DIIS method using a versatile residual matrix to accelerate SCF starting from a crude guess

Hu,

Sarwono,

Ding

et al. 2024

J Comput Chem

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The minimization of the commutator of the Fock and density matrices as the error matrix in the direct inversion of the iterative subspace (CDIIS) developed by Pulay is a powerful self‐consistent field (SCF) acceleration technique for the construction of optimum Fock matrix, if initiated with a fair initial guess. In this work, we present an alternative minimized error matrix to the commutator in the CDIIS, namely the residual or the gradient of the energy‐functional for a Slater determinant subject to the orthonormality constraints among orbitals, representing the search for a newly improved Fock matrix in the direction of the residual in the direct inversion of the iterative subspace (RDIIS). Implemented in the computational chemistry package GAMESS, the RDIIS is compared with the standard CDIIS and the second order SCF orbital optimization (SOSCF) for tested molecules started with a crude guess. As a result, the RDIIS stably and efficiently performs the SCF convergence acceleration. Furthermore, the RDIIS is considerably independent on the subspace size with the concentrated linear coefficients accounting proportionally for the Fock matrices close to the current iteration.

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Fully numerical Hartree‐Fock and density functional calculations. II. Diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

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We present the implementation of a variational finite element solver in the HELFEM program for benchmark calculations on diatomic systems. A basis set of the formÞ is used, where (μ, ν, φ) are transformed prolate spheroidal coordinates, B n (μ) are finite element shape functions, and Y m l are spherical harmonics. The basis set allows for an arbitrary level of accuracy in calculations on diatomic molecules, which can be performed at present with either nonrelativistic Hartree-Fock (HF) or density functional (DF) theory. Hundreds of DFs at the local spin density approximation (LDA), generalized gradient approximation (GGA), and the meta-GGA level can be used through an interface with the LIBXC library; meta-GGA and hybrid DFs are not available in other fully numerical diatomic program packages. Finite electric fields are also supported in HELFEM, enabling access to electric properties. We introduce a powerful tool for adaptively choosing the basis set by using the core Hamiltonian as a proxy for its completeness. HELFEM and the novel basis set procedure are demonstrated by reproducing the restricted open-shell HF limit energies of 68 diatomic molecules from the first to the fourth period with excellent agreement with literature values, despite requiring orders of magnitude fewer parameters for the wave function. Then, the electric properties of the BH and N 2 molecules under finite field are studied, again yielding excellent agreement with previous HF limit values for energies, dipole moments, and dipole polarizabilities, again with much more compact wave functions than what were needed for the literature references. Finally, HF, LDA, GGA, and meta-GGA calculations of the atomization energy of N 2 are performed, demonstrating the superb accuracy of the present approach. K E Y W O R D S density functional, diatomic molecule, finite element, Hartree-Fock, partial-wave expansion 1 | INTRODUCTIONIn the first part of this series, [1] we presented fully numerical Hartree-Fock (HF) and density functional calculations on atoms. The present article focuses on diatomic molecules, which may serve as even more stringent tests of ab initio as well as density functional methods than atoms, as the methods' accuracy can be probed for multiple kinds of covalent bonds, as well as for ionic bonds and dispersion effects. As reviewed at length in Ref.[2], the history of fully numerical calculations on diatomic molecules is almost as long as that on atoms, starting with the partial-wave approach of McCullough. [3,4] The partial-wave approach appears to have since fallen out of use, with the well-known programs by Heinemann, Laaksonen, Sundholm, Kobus, and coworkers [5][6][7][8] relying on grid-based approaches for the angular expansion.

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Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient

Cited by 51 publications

References 112 publications

Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets

Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets

An improved DIIS method using a versatile residual matrix to accelerate SCF starting from a crude guess

Fully numerical Hartree‐Fock and density functional calculations. II. Diatomic molecules

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