Contracted auxiliary Gaussian basis integral and derivative evaluation

Giese, Timothy J.; York, Darrin M.

doi:10.1063/1.2821745

Cited by 25 publications

(44 citation statements)

References 54 publications

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“…So, to convince those readers, and to more clearly demonstrate how our method is a generalization, let us insert Eq. (11) into (10) (33) and now, upon comparing this to (34) we see that χ i (r)χ j (r) ≈ S ij φ a (r − R a ), for one-center AO products; and …”

Section: Generalization Of the Auxiliary Basismentioning

confidence: 99%

Density-functional expansion methods: grand challenges

Giese¹,

York²

2012

Highlights in Theoretical Chemistry

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We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one-and two-body treatment of the coreHamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

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Section: Generalization Of the Auxiliary Basismentioning

confidence: 99%

Density-functional expansion methods: grand challenges

Giese¹,

York²

2012

Highlights in Theoretical Chemistry

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“…Furthermore, we may use more than one GME on an atom, e.g., 3D, which indicates that there are three GMEs with l max = 2 and each corresponding to one of three Slater exponents. The idea of using more than one GME may initially seem daunting to the reader; however, it has previously been shown 55 that the GME integrals can be computed very efficiently, and the calculation of the Coulomb energy [Eq. (17)] is greatly simplified merely from the fact that an atom will appear as a single point multipole expansion to all nonoverlapping atoms.…”

Section: Functional Form Of the Auxiliary Basismentioning

confidence: 99%

“…55; the algorithm used here is a direct implementation of what has previously been described. We note that the 1D Slater-like functions are twice as slow as the 1S timings; however, the Fock matrix must be diagaonlized at every iteration as well, and so a doubling of times in Table V does not mean that the SCF cycles will halve their net speed.…”

Section: E Computational Effortmentioning

confidence: 99%

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Density-functional expansion methods: Generalization of the auxiliary basis

Giese¹,

York²

2011

The Journal of Chemical Physics

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The formulation of density-functional expansion methods is extended to treat the second and higherorder terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the selfconsistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

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“…34 The evaluation of interaction energies and forces between permanent multipoles using the particle mesh Ewald (PME) 35 method has been, and remains, an active area of research. 21,[36][37][38][39][40][41][42][43][44][45][46] In 1996, Hättig introduced 47 a quasi-internal (QI) coordinate system, in which the local z-axis is aligned with the internuclear axis for each pair. The QI coordinate system allows orthogonality to be exploited when spherical harmonic multipole moments are used and vastly simplifies the evaluation of forces and torques.…”

Section: Introductionmentioning

confidence: 99%

Efficient treatment of induced dipoles

Simmonett

Pickard

Shao

et al. 2015

The Journal of Chemical Physics

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Most existing treatments of induced dipoles in polarizable molecular mechanics force field calculations use either the self-consistent variational method, which is solved iteratively, or the "direct" approximation that is non-iterative as a result of neglecting coupling between induced dipoles. The variational method is usually implemented using assumptions that are only strictly valid under tight convergence of the induced dipoles, which can be computationally demanding to enforce. In this work, we discuss the nature of the errors that result from insufficient convergence and suggest a strategy that avoids such problems. Using perturbation theory to reintroduce the mutual coupling into the direct algorithm, we present a computationally efficient method that combines the precision of the direct approach with the accuracy of the variational approach. By analyzing the convergence of this perturbation series, we derive a simple extrapolation formula that delivers a very accurate approximation to the infinite order solution at the cost of only a few iterations. We refer to the new method as extrapolated perturbation theory. Finally, we draw connections to our previously published permanent multipole algorithm to develop an efficient implementation of the electric field and Thole terms and also derive some necessary, but not sufficient, criteria that force field parameters must obey. [http://dx

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Contracted auxiliary Gaussian basis integral and derivative evaluation

Cited by 25 publications

References 54 publications

Density-functional expansion methods: grand challenges

Density-functional expansion methods: grand challenges

Density-functional expansion methods: Generalization of the auxiliary basis

Efficient treatment of induced dipoles

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