Resolutions of the Coulomb operator: II. The Laguerre generator
نویسندگان
چکیده
منابع مشابه
Resolutions of the Coulomb operator: II. The Laguerre generator
We discuss a resolution of the Coulomb operator, r 1 12 1⁄4 j/iih/ij, into a one-particle basis. We show that the Laguerre polynomials generate a resolution with attractive computational properties and we apply it to the calculation of Coulomb and exchange energies in hydrogenic ions, the H2 molecule, and the Be atom. Rapid convergence is observed in all cases and a theoretical reason for this ...
متن کاملResolutions of the Coulomb operator.
We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1r(12) and propose that the resulting "resolution of the Coulomb operator," r(12) (-1)=mid R:phi(i)phi(i)mid R:, may be useful for the treatment of large sys...
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We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator [T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)] and the long-range Ewald operator [T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)]) are employed in quantum chemical calcula...
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We show that the long-range Ewald operator can be resolved as erf(ωr12)/r12 = ∑k ϕk*(r1) ϕk(r2), where ϕk is proportional to the product of a spherical Bessel function and a spherical harmonic. We demonstrate the use of this new resolution by calculating the long-range Coulomb energy of the nanodiamond crystallite C84H64 and the long-range exchange energy of the graphene C96H24. The resolution ...
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Use of the resolution of Ewald operator method for computing long-range Coulomb and exchange interactions is presented. We show that the accuracy of this method can be controlled by a single parameter in a manner similar to that used by conventional algorithms that compute two-electron integrals. Significant performance advantages over conventional algorithms are observed, particularly for high...
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ژورنال
عنوان ژورنال: Chemical Physics
سال: 2009
ISSN: 0301-0104
DOI: 10.1016/j.chemphys.2008.10.047