The role of exchange and correlation in time-dependent density-functional theory for photoionization

Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom

We explore the merits of linear-response range-separated time-dependent density-functional theory (TDDFT) for the calculation of photoionization spectra. We consider two variants of range-separated TDDFT, namely, the time-dependent range-separated hybrid (TDRSH) scheme, which uses a global range-separation parameter, and the time-dependent locally range-separated hybrid (TDLRSH), which uses a local range-separation parameter, and compare with standard time-dependent local-density approximation (TDLDA) and time-dependent Hartree-Fock (TDHF). We show how to calculate photoionization spectra with these methods using the Sternheimer approach formulated in a non-orthogonal B-spline basis set with appropriate frequency-dependent boundary conditions. We illustrate these methods on the photoionization spectrum of the Be atom, focusing, in particular, on the core resonances. Both the TDRSH and TDLRSH photoionization spectra are found to constitute a large improvement over the TDLDA photoionization spectrum and a more modest improvement over the TDHF photoionization spectrum.

Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, H2O, and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.

Time-dependent density functional theory calculations for core-excited states: Assessment of standard exchange-correlation functionals and development of a novel hybrid functional

A new hybrid functional for accurate descriptions of core and valence excitations, the core-valence Becke's three-parameter exchange (B3)+Lee-Yang-Paar (LYP) correlation functional (CV-B3LYP), is proposed. The construction of the new hybrid functional is based on the assessment that B3LYP performs well for properties concerning valence electrons and Becke's half-and-half exchange+LYP functional (BHHLYP), which includes 50% portion of Hartree-Fock exchange, performs well for core excitations. By using the appropriate portions of Hartree-Fock exchange for core and valence regions separately, CV-B3LYP overcomes the disadvantages of BHHLYP and B3LYP, which give inferior descriptions of valence and core excitations, respectively. Density functional theory (DFT) calculations with the CV-B3LYP functional reproduce core- and valence-orbital energies close to those of BHHLYP and B3LYP, respectively. Time-dependent DFT calculations with the CV-B3LYP functional yield both core- and valence-excitation energies with reasonable accuracy.

Accurate Rydberg excitations from the local density approximation

Despite the incorrect asymptotic behavior of its potential, the time-dependent local density approximation can yield accurate optical spectra. The oscillator strengths of Rydberg excitations appear in the calculated spectrum as continuum contributions with excellent optical intensity. We explain why, illustrate this for the neon and helium atoms, and also discuss when such calculations of the optical response will be inaccurate.