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Register a new userTime-dependent density functional theory for strong electromagnetic fields in crystalline solids
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We apply the coupled dynamics of time-dependent density functional theory and Maxwell equations to the interaction of intense laser pulses with crystalline silicon. As a function of electromagnetic field intensity, we see several regions in the response. At the lowest intensities, the pulse is reflected and transmitted in accord with the dielectric response, and the characteristics of the energy deposition is consistent with two-photon absorption. The absorption process begins to deviate from that at laser intensities ~ 10^13 W/cm^2, where the energy deposited is of the order of 1 eV per atom. Changes in the reflectivity are seen as a function of intensity. When it passes a threshold of about 3 times 1012 W/cm2, there is a small decrease. At higher intensities, above 2 times 10^13 W/cm^2, the reflectivity increases strongly. This behavior can be understood qualitatively in a model treating the excited electron-hole pairs as a plasma.
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Imaginary-time time-dependent Density functional theory (it-TDDFT) has been proposed as an alternative method for obtaining the ground state within density functional theory (DFT) which avoids some of the difficulties with convergence encountered by the self-consistent-field (SCF) iterative method. It-TDDFT was previously applied to clusters of atoms where it was demonstrated to converge in select cases where SCF had difficulty with convergence. In the present work we implement it-TDDFT propagation for {it periodic systems} by modifying the Quantum ESPRESSO package, which uses a plane-wave basis with multiple $boldsymbol{k}$ points, and has the options of non-collinear and DFT+U calculations using ultra-soft or norm-conserving pseudo potentials. We demonstrate that our implementation of it-TDDFT propagation with multiple $boldsymbol{k}$ points is correct for DFT+U non-collinear calculations and for DFT+U calculations with ultra-soft pseudo potentials. Our implementation of it-TDDFT propagation converges to the exact SCF energy (up to the decimal guaranteed by double precision) in all but one case where it converged to a slightly lower value than SCF, suggesting a useful alternative for systems where SCF has difficulty to reach the Kohn-Sham ground state. In addition, we demonstrate that rapid convergence can be achieved if we use adaptive-size imaginary-time-steps for different kinetic-energy plane-waves.
The development of analytic-gradient methodology for excited states within conventional time-dependent density-functional theory (TDDFT) would seem to offer a relatively inexpensive alternative to better established quantum-chemical approaches for the modeling of photochemical reactions. However, even though TDDFT is formally exact, practical calculations involve the use of approximate functionals, in particular the TDDFT adiabatic approximation, whose use in photochemical applications must be further validated. Here, we investigate the prototypical case of the symmetric CC ring opening of oxirane. We demonstrate by direct comparison with the results of high-quality quantum Monte Carlo calculations that, far from being an approximation on TDDFT, the Tamm-Dancoff approximation (TDA) is a practical necessity for avoiding triplet instabilities and singlet near instabilities, thus helping maintain energetically reasonable excited-state potential energy surfaces during bond breaking. Other difficulties one would encounter in modeling oxirane photodynamics are pointed out but none of these is likely to prevent a qualitatively correct TDDFT/TDA description of photochemistry in this prototypical molecule.
We develop numerical methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta generalized gradient approximation (meta-GGA) proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt a predictor-corrector step for stable time-evolution. Since energy functional is not known for the TB-mBJ potential, we propose a method to evaluate electronic excitation energy without referring to the energy functional. Calculations using the HSE hybrid functional is computationally expensive due to the nonlocal Fock-like term. We develop a computational method for the operation of the Fock-like term in Fourier space, for which we employ massively parallel computers equipped with graphic processing units. To demonstrate significances of utilizing potentials providing correct band gap energies, we compare electronic excitations induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: results using TB-mBJ and HSE are close to each other, while the excitation of the LDA calculation is more intensive than the others. At high laser intensities close to a damage threshold, we have found that electronic excitation energies are similar among the three cases.
Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbour level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.
We present accurate optical spectra of semiconductors and insulators within a pure Kohn-Sham time-dependent density-functional approach. In particular, we show that the onset of the absorption is well reproduced when comparing to experiment. No empirical information nor a theory beyond Kohn-Sham density-functional theory, such as $GW$, is invoked to correct the Kohn-Sham gap. Our approach relies on the link between the exchange-correlation kernel of time-dependent density functional theory and the derivative discontinuity of ground-state density-functional theory. We show explicitly how to relate these two quantities. We illustrate the accuracy and simplicity of our approach by applying it to various semiconductors (Si, GaP, GaAs) and wide-gap insulators (C, LiF, Ar).
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