Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules

Wang, Sanwu

doi:10.1103/physreva.60.262

Cited by 64 publications

(50 citation statements)

References 20 publications

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“…7͑c͒ converges only linearly in this range and time steps down to ⌬t =1-2 as must be used in order to obtain accurate results. The f-sum rule ͑or ThomasReiche-Kuhn sum rule͒, 47 ͐S ij ͑͒d = N␦ ij , where N is the number of electrons, is fulfilled within a few percent in the present calculations. Note that care must be taken when constructing the PAW-projectors, because, if pseudo-wavefunctions represented in the grid cannot be accurately transformed to the atomic basis by the PAW-projectors, the f-sum becomes incomplete.…”

Section: B Time-propagationmentioning

confidence: 75%

Time-dependent density-functional theory in the projector augmented-wave method

Walter

Häkkinen

Lehtovaara

et al. 2008

The Journal of Chemical Physics

211

221

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Articles you may be interested inMixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry J. Chem. Phys. 129, 124108 (2008) We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.

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Section: B Time-propagationmentioning

confidence: 75%

Time-dependent density-functional theory in the projector augmented-wave method

Walter

Häkkinen

Lehtovaara

et al. 2008

The Journal of Chemical Physics

211

221

View full text Add to dashboard Cite

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“…Of course, in principle, the absorption spectrum of any system extends up to infinite frequency. In practice, however, it is bounded from above by the f-sum rule, 65 so that a finite ͑and usually fairly small, as seen͒ number of Lanczos iterations suffices to capture it. We believe that, from the algorithmic point of view, the new method is close to optimal in its application range and that it opens thus the way to the simulation of the dynamical properties of large and very large molecular and condensed-matter systems.…”

Section: Discussionmentioning

confidence: 99%

Turbo charging time-dependent density-functional theory with Lanczos chains

Rocca

Gebauer

Saad

et al. 2008

The Journal of Chemical Physics

251

309

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We introduce a new implementation of time-dependent density-functional theory which allows the entire spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a single standard ground-state calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a super-operator formulation of linearized timedependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian super-operator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the non-symmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn-Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C60 fullerene, and of chlorofyll a.

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“…The Thomas-Reiche-Kuhn (TRK) sum rule 25 relates the oscillator strengths of the ground-to-excited-state transitions:…”

Section: Computation Of the Infrared Intensitymentioning

confidence: 99%

Effect of hydrogen bonding on the infrared absorption intensity of OH stretch vibrations

2017

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We consider how the infrared intensity of an O-H stretch in a hydrogen bonded complex varies as the strength of the H-bond varies from weak to strong. We obtain trends for the fundamental and overtone transitions as a function of donor-acceptor distance R, which is a common measure of H-bond strength. Our calculations use a simple two-diabatic state model that permits symmetric and asymmetric bonds, i.e. where the proton affinity of the donor and acceptor are equal and unequal, respectively. The dipole moment function uses a Mecke form for the free OH dipole moment, associated with the diabatic states. The transition dipole moment is calculated using one-dimensional vibrational eigenstates associated with the H-atom transfer coordinate on the ground state adiabatic surface of our model. Over 20-fold intensity enhancements for the fundamental are found for strong H-bonds, where there are significant non-Condon effects. The isotope effect on the intensity yields a nonmonotonic H/D intensity ratio as a function of R, and is enhanced by the secondary geometric isotope effect. The first overtone intensity is found to vary non-monotonically with H-bond strength; strong enhancements are possible for strong H-bonds. Modifying the dipole moment through the Mecke parameters is found to have a stronger effect on the overtone than the fundamental. We compare our findings with those for specific molecular systems analysed through experiments and theory in earlier works. Our model results compare favourably for strong and medium strength symmetric H-bonds. However, for weak asymmetric bonds we find much smaller effects than in earlier work.

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Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules

Cited by 64 publications

References 20 publications

Time-dependent density-functional theory in the projector augmented-wave method

Time-dependent density-functional theory in the projector augmented-wave method

Turbo charging time-dependent density-functional theory with Lanczos chains

Effect of hydrogen bonding on the infrared absorption intensity of OH stretch vibrations

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