Time-dependent auxiliary density perturbation theory

Carmona‐Espíndola, Javier; Flores‐Moreno, Roberto; Köster, Andreas M.

doi:10.1063/1.3478551

Cited by 38 publications

(39 citation statements)

References 100 publications

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“…Note that the use of auxiliary basis sets in conjunction with the Coulomb norm has a long tradition in DFT methods and is frequently used successfully in various approaches. [59][60][61][62] We now act from left with the resolution-of-the-identity (17) on Eqs. (15) and (16) and additionally insert the resolution-of-the-identity (18) before the potentials v (1) s and v (1) to obtain…”

Section: B Basic Ri-exxrpa Methodsmentioning

confidence: 99%

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Bleiziffer

Heßelmann

Görling

2012

The Journal of Chemical Physics

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Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strengthdependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N 6 to N 5 . Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Møller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.

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Section: B Basic Ri-exxrpa Methodsmentioning

confidence: 99%

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Bleiziffer

Heßelmann

Görling

2012

The Journal of Chemical Physics

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“…(5) we introduce an auxiliary basis set, the resolutionof-the-identity (RI) basis set, [67][68][69][70][71] by the unsymmetric resolutions of the identity…”

Section: A Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Efficient self-consistent treatment of electron correlation within the random phase approximation

Bleiziffer¹,

Heßelmann²,

Görling³

2013

The Journal of Chemical Physics

101

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A self-consistent Kohn-Sham (KS) method is presented that treats correlation on the basis of the adiabatic-connection dissipation-fluctuation theorem employing the direct random phase approximation (dRPA), i.e., taking into account only the Coulomb kernel while neglecting the exchangecorrelation kernel in the calculation of the Kohn-Sham correlation energy and potential. The method, denoted self-consistent dRPA method, furthermore treats exactly the exchange energy and the local multiplicative KS exchange potential. It uses Gaussian basis sets, is reasonably efficient, exhibiting a scaling of the computational effort with the forth power of the system size, and thus is generally applicable to molecules. The resulting dRPA correlation potentials in contrast to common approximate correlation potentials are in good agreement with exact reference potentials. The negatives of the eigenvalues of the highest occupied molecular orbitals are found to be in good agreement with experimental ionization potentials. Total energies from self-consistent dRPA calculations, as expected, are even poorer than non-self-consistent dRPA total energies and dRPA reaction and non-covalent binding energies do not significantly benefit from self-consistency. On the other hand, energies obtained with a recently introduced adiabatic-connection dissipation-fluctuation approach (EXXRPA+, exact-exchange random phase approximation) that takes into account, besides the Coulomb kernel, also the exact frequency-dependent exchange kernel are significantly improved if evaluated with orbitals obtained from a self-consistent dRPA calculation instead of an exact exchange-only calculation. Total energies, reaction energies, and noncovalent binding energies obtained in this way are of the same quality as those of high-level quantum chemistry methods, like the coupled cluster singles doubles method which is computationally more demanding. © 2013 AIP Publishing LLC.

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“…Wrong asymptotic behavior of the exchange functional for which local and gradient corrected density approximations are used is believed to be the reason behind the failure of DFT for conjugated systems [25,26]. Contrary to this it has been demonstrated that DFT polarizability calculations of C 60 are in good agreement with CCSD and experimental polarizabilities [27]. This suggests that DFT failures to correctly predict molecular polarizabilities and hyperpolarizabilities are not single sourced, e.g.…”

Section: Introductionmentioning

confidence: 91%

“…However, instead of calculating directly perturbed density matrix elements via the CPKS equation system, perturbed Coulomb fitting coefficients are calculated first in the here used ADPT method [27,29,34,35]. From these perturbed fitting coefficients the perturbed density matrix elements are obtained.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Therefore, it is more efficient and useful for large molecules containing up to several hundred atoms [30]. In ADFT two non-iterative approaches are possible for analytic energy derivatives namely non-iterative approximation to the CPKS method (NIA-CPKS) [31][32][33][34] and auxiliary density perturbation theory (ADPT) [27,29,33,34]. NIA-CPKS is a numericalanalytical method in which the derivative of the Kohn-Sham matrix is obtained from finite field method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Systematic comparison of DFT and CCSD dipole moments, polarizabilities and hyperpolarizabilities

Karne

Vaval

Pal

et al. 2015

Chemical Physics Letters

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Time-dependent auxiliary density perturbation theory

Cited by 38 publications

References 100 publications

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Efficient self-consistent treatment of electron correlation within the random phase approximation

Systematic comparison of DFT and CCSD dipole moments, polarizabilities and hyperpolarizabilities

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