Atomic <i>C</i> <sub>6</sub> dispersion coefficients: a four-component relativistic Kohn–Sham study

Sulzer, David; Norman, Patrick; Saue, Trond

doi:10.1080/00268976.2012.709283

Cited by 15 publications

(9 citation statements)

References 68 publications

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“…The reference values for the polarizabilities and C 6 coefficients of the rare-gas and alkaline-earth-metal atoms considered here are taken from Derevianko et al [56] and were obtained from accurate many-body calculations and/or experimental data. The contributions from relativistic effects on the value of the C 6 coefficients can be neglected for the atoms considered here, being at most 2% for Ca [13].…”

Section: Computational Detailsmentioning

confidence: 99%

“…The C 6 dispersion coefficients are conveniently expressed by the Casimir-Polder formula [2,3] involving imaginary-frequency dynamic dipole polarizabilities, and can be efficiently calculated from linear-response time-dependent density-functional theory (TDDFT) [4]. In such TDDFT calculations of C 6 coefficients, a number of approximations have been used for the Kohn-Sham exchange-correlation potential v xc and the corresponding response kernel f xc , including the local-density approximation (LDA) [4][5][6][7], generalized-gradient approximations (GGA) [8,9], hybrid approximations [10][11][12][13][14] and optimized effective potential (OEP) approaches [15][16][17][18][19][20]. Using the generalized Casimir-Polder formula [3], non-expanded dispersion energies can also be calculated from TDDFT [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we investigate the impact of long-range HF exchange on these C 6 coefficients. To the best of our knowledge, the only rangeseparated TDDFT method that had been applied so far to the calculation of van der Waals dispersion coefficients was the one based on CAM-B3LYP [13,14,53,54], but the different results were inconclusive on whether or not long-range HF exchange brings any improvement. Hartree atomic units (a.u.)…”

Section: Introductionmentioning

confidence: 99%

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Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Toulouse¹,

Rebolini²,

Gould³

et al. 2013

The Journal of Chemical Physics

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We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of rangeseparated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

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Section: Computational Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Toulouse¹,

Rebolini²,

Gould³

et al. 2013

The Journal of Chemical Physics

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“…The computational cost is similar to the eigenvalue response equation and DFT kernels are required also in this case. In the context of relativistic theories with variational SO interaction, the methodology has been developed in the spin-orbit ZORA 42 , and 4c 43,44 framework and applied to the calculation of frequency-dependent dipole polarizabilities 45 , electronic absorption spectra in valence and X-ray regions 46,47 , and electric dipole dispersion interaction coefficients 48 . An extensive list of review texts on eigenvalue and damped response theory can be found in Table 1 in Ref.…”

Section: Please Cite This Article As Doi:101063/15128564mentioning

confidence: 99%

Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations

Konecny

Repiský

Ruud

et al. 2019

The Journal of Chemical Physics

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We present a detailed theory, implementation, and a benchmark study of a linear damped response time-dependent density functional theory (TDDFT) based on the relativistic four-component (4c) Dirac-Kohn-Sham formalism using the restricted kinetic balance condition for the small-component basis and a non-collinear exchangecorrelation kernel. The damped response equations are solved by means of a multifrequency iterative subspace solver utilizing decomposition of the equations according to hermitian and time-reversal symmetry. This partitioning leads to robust convergence and the detailed algorithm of the solver for relativistic multicomponent wavefunctions is also presented. The solutions are then used to calculate the linear electricand magnetic-dipole responses of molecular systems to an electric perturbation, leading to frequency-dependent dipole polarizabilities, electronic absorption and circular dichroism (ECD), and optical rotatory dispersion (ORD) spectra. The methodology has been implemented in the relativistic spectroscopy DFT program ReSpect, and its performance assessed on a model series of dimethylchalcogeniranes, C 4 H 8 X (X = O, S, Se, Te, Po, Lv) and on larger transition metal complexes that have been studied experimentally, [M(phen) 3 ] 3+ (M = Fe, Ru, Os). These are the first 4c damped linear response TDDFT calculations of ECD and ORD presented in the literature.

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“…This approach has been successfully applied for a plethora of different molecular properties, e.g., Raman scattering, 48,49 circular dichroism, [50][51][52] optical rotatory dispersion, 53 X-ray absorption spectroscopy, 54,55 and C 6 dispersion coefficients. 55,56 As our main focus is to demonstrate the virtues of the four-component CPP/DFT approach as well as to investigate trends due to metal-substitution, we determine only the electronic responses and merely refer to studies dedicated to vibrational effects 27,57 and we also adopt established assignments of spectral features. 34 For the valence spectra, measurements on H 2 P and related compounds were initially rationalized using Gouterman's four-orbital model, [58][59][60] where the relative intensity of the weak, low-energy (500−650 nm) Q-band in comparison to the strong, high-energy (350−400 nm) B-band, or Soret band, is understood as arising from transitions from the two highest occupied (HOMO and HOMO-1) to the two lowest unoccupied molecular orbitals (LUMO and LUMO+1).…”

Section: Introductionmentioning

confidence: 99%

Four-Component Damped Density Functional Response Theory Study of UV/Vis Absorption Spectra and Phosphorescence Parameters of Group 12 Metal-Substituted Porphyrins

Fransson

Saue

Norman

2016

J. Chem. Theory Comput.

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The influences of group 12 (Zn, Cd, Hg) metal-substitution on the valence spectra and phosphorescence parameters of porphyrins (P) have been investigated in a relativistic setting. In order to obtain valence spectra, this study reports the first application of the damped linear response function, or complex polarization propagator, in the four-component density functional theory framework [as formulated in Villaume et al. J. Chem. Phys. 2010 , 133 , 064105 ]. It is shown that the steep increase in the density of states as due to the inclusion of spin-orbit coupling yields only minor changes in overall computational costs involved with the solution of the set of linear response equations. Comparing single-frequency to multifrequency spectral calculations, it is noted that the number of iterations in the iterative linear equation solver per frequency grid-point decreases monotonously from 30 to 0.74 as the number of frequency points goes from one to 19. The main heavy-atom effect on the UV/vis-absorption spectra is indirect and attributed to the change of point group symmetry due to metal-substitution, and it is noted that substitutions using heavier atoms yield small red-shifts of the intense Soret-band. Concerning phosphorescence parameters, the adoption of a four-component relativistic setting enables the calculation of such properties at a linear order of response theory, and any higher-order response functions do not need to be considered-a real, conventional, form of linear response theory has been used for the calculation of these parameters. For the substituted porphyrins, electronic coupling between the lowest triplet states is strong and results in theoretical estimates of lifetimes that are sensitive to the wave function and electron density parametrization. With this in mind, we report our best estimates of the phosphorescence lifetimes to be 460, 13.8, 11.2, and 0.00155 s for H2P, ZnP, CdP, and HgP, respectively, with the corresponding transition energies being equal to 1.46, 1.50, 1.38, and 0.89 eV.

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Atomic C ₆ dispersion coefficients: a four-component relativistic Kohn–Sham study

Cited by 15 publications

References 68 publications

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations

Four-Component Damped Density Functional Response Theory Study of UV/Vis Absorption Spectra and Phosphorescence Parameters of Group 12 Metal-Substituted Porphyrins

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Atomic C 6 dispersion coefficients: a four-component relativistic Kohn–Sham study

Cited by 15 publications

References 68 publications

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations

Four-Component Damped Density Functional Response Theory Study of UV/Vis Absorption Spectra and Phosphorescence Parameters of Group 12 Metal-Substituted Porphyrins

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Atomic C ₆ dispersion coefficients: a four-component relativistic Kohn–Sham study