Fast computation of analytical second derivatives with effective core potentials: Application to Si8C12, Ge8C12, and Sn8C12

Bode, Brett; Gordon, Mark S.

doi:10.1063/1.480225

Cited by 17 publications

(18 citation statements)

References 30 publications

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“…A slightly different approach for the analytic evaluation of semilocal ECP integrals has been proposed by Kolar26 and modified by Bode and Gordon 27. In this method (13) is evaluated using recurrence relations that are initialized by fundamental functions like the Dawson and error function.…”

Section: Ecp Integralsmentioning

confidence: 99%

Half‐numerical evaluation of pseudopotential integrals

et al. 2006

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A half-numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two-dimensional angular and one-dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l-quantum number. The radial integrals are calculated by an adaptive one-dimensional numerical quadrature. For the semilocal radial part a pretabulation scheme is used. This pretabulation simplifies the handling of radial integrals, makes their calculation much faster, and allows their easy reuse for different integrals within a given shell combination. The implementation of this new algorithm is described and its performance is analyzed.

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Section: Ecp Integralsmentioning

confidence: 99%

Half‐numerical evaluation of pseudopotential integrals

et al. 2006

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“…To evaluate the efficiency of the present ECP integral method, timings were carried out on the same Pt slab systems from section using the new method as implemented in Q-Chem 5.0, the old ECP method in Q-Chem 4.4, GAMESS (US), , and Dalton 2016 . All calculations were performed on a 2.6 GHz Intel Xeon E5-2690 v4 platform using a single CPU core.…”

Section: Resultsmentioning

confidence: 99%

“…They factor the integrals into angular and radial parts and treat the latter via asymptotic and power series expansions, which are relatively expensive to evaluate. In separate works, Kolar and Bode and Gordon developed recurrence relations (RRs) for evaluating components of the radial part of the projected integral. However, a significant number of radial components is required for each projected integral, making the method expensive.…”

Section: Introductionmentioning

confidence: 99%

Efficient Method for Calculating Effective Core Potential Integrals

et al. 2018

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Effective core potential (ECP) integrals are among the most difficult one-electron integrals to calculate due to the projection operators. The radial part of these operators may include r, r, and r terms. For the r terms, we exploit a simple analytic expression for the fundamental projected integral to derive new recurrence relations and upper bounds for ECP integrals. For the r and r terms, we present a reconstruction method that replaces these terms by a sum of r terms and show that the resulting errors are chemically insignificant for a range of molecular properties. The new algorithm is available in Q-Chem 5.0 and is significantly faster than the ECP implementations in Q-Chem 4.4, GAMESS (US) and Dalton 2016.

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“…The present ECP implementation in the LIO program follows the work by Bode and Gordon for all integrations, though we introduce a cutoff distance ( R cutoff ) so that the computational cost scales linearly with the system size. Thus, the interaction between the electrons and a pseudopotential centered on atom I is restrained by the condition , where is the distance between the origin of the basis function M and atom I , with α i being the basis exponent.…”

Section: Methodsmentioning

confidence: 99%

Role of Core Electrons in Quantum Dynamics Using TDDFT

Foglia

Morzan

Estrin

et al. 2016

J. Chem. Theory Comput.

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The explicit simulation of time dependent electronic processes requires computationally onerous routes involving the temporal integration of motion equations for the charge density. Efficiency optimization of these methods typically relies on increasing the integration time-step and on the reduction of the computational cost per step. The implicit representation of inner electrons by effective core potentials-or pseudopotentials-is a standard practice in localized-basis quantum-chemistry implementations to improve the efficiency of ground-state calculations, still preserving the quality of the output. This article presents an investigation on the impact that effective core potentials have on the overall efficiency of real time electron dynamics with TDDFT. Interestingly, the speedups achieved with the use of pseudopotentials in this kind of simulation are on average much more significant than in ground-state calculations, reaching in some cases a factor as large as 600×. This boost in performance originates from two contributions: on the one hand, the size of the density matrix, which is considerably reduced, and, on the other, the elimination of high-frequency electronic modes, responsible for limiting the maximum time-step, which vanish when the core electrons are not propagated explicitly. The latter circumstance allows for significant increases in time-step, that in certain cases may reach up to 3 orders of magnitude, without losing any relevant chemical or spectroscopic information.

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Fast computation of analytical second derivatives with effective core potentials: Application to Si8C12, Ge8C12, and Sn8C12

Cited by 17 publications

References 30 publications

Half‐numerical evaluation of pseudopotential integrals

Half‐numerical evaluation of pseudopotential integrals

Efficient Method for Calculating Effective Core Potential Integrals

Role of Core Electrons in Quantum Dynamics Using TDDFT

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