Density- and density-matrix-based coupled Kohn–Sham methods for dynamic polarizabilities and excitation energies of molecules

Görling, Andreas; Heinze, H.; Ruzankin, Sergey Ph.; Staufer, Markus; Rösch, Notker

doi:10.1063/1.477922

Cited by 121 publications

(92 citation statements)

References 37 publications

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“…The recent success of the time-dependent density functional perturbation theory ͑TDDFPT͒ [1][2][3][4] in calculations of electron excitations [5][6][7][8][9][10][11][12] and other molecular response properties [13][14][15][16][17] is due to its efficient treatment of electron exchange and correlation. The exchange-correlation ͑xc͒ effects in the ground state are represented with the local, state independent exchange-correlation potential v xc in the oneelectron Kohn-Sham ͑KS͒ equations ͕Ϫ 1 2 ٌ 2 ϩv ext ͑ r͒ϩv H ͑ r͒ϩv xc ͑ r͖͒ i ͑ r͒ϭ⑀ i i ͑ r͒.…”

Section: Introductionmentioning

confidence: 99%

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Grüning

Gritsenko

Gisbergen

et al. 2001

The Journal of Chemical Physics

360

315

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Shape corrections to the standard approximate Kohn-Sham exchange-correlation ͑xc͒ potentials are considered with the aim to improve the excitation energies ͑especially for higher excitations͒ calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection ͑GRAC͒ of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends ͑LB͒ are seamlessly connected to the ͑shifted͒ xc potential of Becke and Perdew ͑BP͒ with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N 2 , CO, CH 2 O, C 2 H 4 , C 5 NH 5 , C 6 H 6 , Li 2 , Na 2 , K 2 . The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of ͑model͒ orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine ''local'' density functional with an analytical representation.

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Section: Introductionmentioning

confidence: 99%

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Grüning

Gritsenko

Gisbergen

et al. 2001

The Journal of Chemical Physics

360

315

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“…13,14 Perhaps the most popular application of time-dependent density functional theory (TD-DFT) in the molecular regime has been the calculation of excitation energies, in which many groups have, by now, been involved. 5,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] The equations from which the excitation energies are obtained are well-established. 18,20,25 They are formally quite similar to the time-dependent Hartree-Fock (TDHF) equations (TDHF is also known as random phase approximation (RPA)) and can be solved efficiently 25 by using iterative techniques, such as the Davidson algorithm.…”

Section: Introductionmentioning

confidence: 99%

Excitation Energies for Transition Metal Compounds from Time-Dependent Density Functional Theory. Applications to MnO₄^-, Ni(CO)₄, and Mn₂(CO)₁₀

et al. 1999

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The first time-dependent density functional theory (TDDFT) calculations on the spectra of molecules containing transition metals are reported. Three prototype systems are considered, of which the assignments are controversial: MnO 4 -, Ni(CO) 4 , and Mn 2 (CO) 10 . The TDDFT results are shown to be comparable in accuracy to the most elaborate ab initio calculations and lead to new insights in the spectra of these molecules. In some cases, the presented TDDFT results differ substantially, in both the ordering and the values for the excitation energies, from the older DFT method for the calculation of excitation energies: the ∆SCF approach. For the Mn 2 (CO) 10 molecule, the presented results are the highest-level theoretical results published so far. Over all, the results show that TDDFT can be a very useful tool in the calculation and interpretation of the spectra of transition metal compounds.

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“…54 Both methods start from the same expression for the uncoupled response function, (2) and then take higher order electron-electron interactions into account through the solution of a Dyson-type equation that can be solved in several ways. 55 In Eq. (2), indices i, (j, k, .…”

Section: Dispersion Interactions From Approximate Single-particlementioning

confidence: 99%

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

Heßelmann

2012

The Journal of Chemical Physics

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Long-range correlation energies are calculated using an approximation of the single-particle densitydensity response function of the system that leads to an expression requiring only occupied orbitals and eigenvalues. Dipole-dipole polarisabilities and isotropic leading-order dispersion coefficients obtained from this approximation are shown to be in a reasonable agreement with corresponding values from the experiment or dipole oscillator strength distributions. The localised polarisabilities were used to calculate a long-range correlation correction to a hybrid-generalised gradient approximation functional using a proper damping function at short ranges. It was found that the hybrid density-functional theory+dispersion method obtained in this way has a comparable accuracy than high-level ab initio wave function methods at a much lower computational cost. This has been analysed for a number of systems from the GMTKN30 database including subsets for noncovalently bound complexes, relative energies for sugar conformers and reaction energies and barrier heights of pericyclic reactions of some medium sized organic molecules.

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Density- and density-matrix-based coupled Kohn–Sham methods for dynamic polarizabilities and excitation energies of molecules

Cited by 121 publications

References 37 publications

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Excitation Energies for Transition Metal Compounds from Time-Dependent Density Functional Theory. Applications to MnO₄^-, Ni(CO)₄, and Mn₂(CO)₁₀

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

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Density- and density-matrix-based coupled Kohn–Sham methods for dynamic polarizabilities and excitation energies of molecules

Cited by 121 publications

References 37 publications

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Excitation Energies for Transition Metal Compounds from Time-Dependent Density Functional Theory. Applications to MnO4-, Ni(CO)4, and Mn2(CO)10

Long-range correlation energies from frequency-dependent weighted exchange-hole dipole polarisabilities

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Excitation Energies for Transition Metal Compounds from Time-Dependent Density Functional Theory. Applications to MnO₄^-, Ni(CO)₄, and Mn₂(CO)₁₀