Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Optimal Basis Set for Electron Dynamics in Strong Laser Fields: The case of Molecular Ion H2. J Chem Theory Comput 2018;14:5846-5858. [PMID: 30247900 PMCID: PMC6255052 DOI: 10.1021/acs.jctc.8b00656]

A clear understanding of the mechanisms that control the electron dynamics in a strong laser field is still a challenge that requires interpretation by advanced theory. Development of accurate theoretical and computational methods, able to provide a precise treatment of the fundamental processes generated in the strong field regime, is therefore crucial. A central aspect is the choice of the basis for the wave function expansion. Accuracy in describing multiphoton processes is strictly related to the intrinsic properties of the basis, such as numerical convergence, computational cost, and representation of the continuum. By explicitly solving the 1D and 3D time-dependent Schrödinger equation for H2+ in the presence of an intense electric field, we explore the numerical performance of using a real-space grid, a B-spline basis, and a Gaussian basis (improved by optimal Gaussian functions for the continuum). We analyze the performance of the three bases for high-harmonic generation and above-threshold ionization for H2+. In particular, for high-harmonic generation, the capability of the basis to reproduce the two-center interference and the hyper-Raman phenomena is investigated.

Kohn-Sham self-interaction correction in real time

We present a solution scheme for the time-dependent Kohn-Sham self-interaction correction. Based on the generalized optimized effective potential approach, the multiplicative Kohn-Sham potential is constructed in real time and real space for the self-interaction corrected local density approximation. Excitations of different character, including charge-transfer excitations that had been regarded as prime examples for the failure of standard time-dependent density functionals, are described correctly by this approach. We analyze the time-dependent exchange-correlation potential and density, revealing features that are decisive for the correct description of the response.

Solution of the time-dependent Schrödinger equation using time-dependent basis functions

The time-dependent Schrödinger equation is solved by using an explicitly time-dependent basis. This approach allows efficient reflection-free time propagation of the wave function. The applicability of the method is illustrated by solving various time-dependent problems including the calculation of the above threshold ionization of a model atom and the optical absorption spectrum of a sodium dimer.

REAL-TIME APPROACH TO TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY IN THE LINEAR AND NONLINEAR REGIME

The linear and nonlinear response of Si 4 and Na 4 to an external perturbation is investigated in the framework of time-dependent density-functional theory. The time-dependent Kohn–Sham equations, which are the central equations in this approach, are solved in real space and real time. A parallelized implementation to solve these nonlinear, one-particle Schrödinger equations is presented. In contrast to Na 4, Si 4 shows high-harmonic generation far beyond the cut-off predicted by the quasiclassical model and predictions for extended systems.

The charge-transfer properties of the S2 state of fucoxanthin in solution and in fucoxanthin chlorophyll-a/c2 protein (FCP) based on stark spectroscopy and molecular-orbital theory

Fucoxanthin chlorophyll-a/c 2 protein (FCP), the membrane-intrinsic light harvesting complex from the diatom Cyclotella meneghiniana, is characterized by Stark spectroscopy to obtain a quantitative measure of the excited-state dipolar properties of the constituent pigments. The electro-optical properties of the carotenoid fucoxanthin (Fx), the primary light harvester in FCP, were determined from the Stark spectrum measured in a MeTHF glass (77 K) and compared to the results from electronic-structure calculations. On photon absorption by Fx, a 17 D change in the static dipole moment (|Delta mu|exp), and a somewhat larger |Delta mu|exp at the red edge, are measured for the S 0 --> S 2 (1 (1)A g (-)-like -->1 (1)B u *+-like) transition. The large change in dipole moment indicates that Fx undergoes photoinduced charge transfer (CT), and underscores the influence of the S 2 state on the polarity-dependent excited-state dynamics of Fx that has so far been attributed to, and discussed in terms of, the S 0 and the S 1/ICT states. MNDO-PSDCI and SACCI-CISD calculations indicate that the 1 (1)B u (*+)-like state intrinsically possesses a dipole moment much smaller than the 2 (1)A g (*-)-like state, suggesting that solvent fields promote the mixing of these two states and could account for the large dipole moments measured here for the S 0 --> S 2 transition. These CT properties of the 1 (1)B u (*+)-like state of Fx are further enhanced in the protein and underpin its photosynthetic capabilities for light harvesting and energy transfer (ET). In FCP, the CT properties of the Fx's vary according to the energetic position: between 450 and 500 nm there appear to be two sets of Fx's that exhibit |Delta mu| exp values on the order of 5 and 15 D, whereas the red-most Fx's, that are very efficient in ET to chlorophyll-a (Chl-a), exhibit strikingly large |Delta mu| exp values on the order of 40 D. Such magnitudes of |Delta mu| exp suggest a mechanism that enhances Coulombic coupling to promote ET from the S 2 state of Fx to Chl-a. These three sets of Fx's, including a fourth red Fx, are identified by fitting the Stark spectrum of FCP with the Stark spectrum of Fx in MeTHF. In contrast to the Fx's in the protein, the electrostatic properties of the Chl's in FCP are comparatively much smaller. Notably, for the Q y band of Chl-a, a |Delta mu| exp of 0.92 D and a change in polarizability ( Delta alpha exp) of 20 A (3), indicate that the Chl-a's are monomeric in nature and decoupled from each other.

Adiabatic approximation in nonperturbative time-dependent density-functional theory

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.

Electrical response of molecular systems: the power of self-interaction corrected kohn-sham theory

The accurate prediction of electronic response properties of extended molecular systems has been a challenge for conventional, explicit density functionals. We demonstrate that a self-interaction correction (SIC) implemented rigorously within Kohn-Sham theory via the optimized effective potential (OEP) yields polarizabilities close to the ones from highly accurate wave-function-based calculations and exceeding the quality of exact-change OEP. The orbital structure obtained with the OEP-SIC functional and approximations to it are discussed.

Numerical simulation of nonadiabatic electron excitation in the strong-field regime. 3. Polyacene neutrals and cations

The electron optical response for a series of linear polyacenes and their molecular ions (mono and dications) in strong laser fields was studied using time-dependent Hartree-Fock theory. The interactions of benzene, naphthalene, anthracene, and tetracene with pulsed fields at a frequency of 1.55 eV and intensities of 8.77 x 10(13), 3.07 x 10(13), 1.23 x 10(13), and 2.75 x 10(12) W/cm2, respectively, were calculated using the 6-31G(d,p) basis set. Nonadiabatic processes, including nonadiabatic time evolution of the dipole moment, Löwden charges, and occupation numbers, were studied. The nonadiabatic response increased with the length of the molecule and was greatest for the molecular monocations. The only exception was tetracene, in which the very strong response of the dication was due to a near resonance with the applied field. The intensity and frequency dependence of the dipole moment response for the monocations of naphthalene and anthracene was also calculated. As the intensity increased, the population of higher-energy excited-states increased, and as the frequency increased, the excitation volume increased in good agreement with the Dykhne approximation.

Electronic optical response of molecules in intense fields: Comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches

Time-dependent Hartree-Fock (TD-HF) and time-dependent configuration interaction (TD-CI) methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses (760 nm, 3 cycles). After the electric field of the pulse returns to zero, the molecular dipole continues to oscillate due to the coherent superposition of excited states resulting from the nonadiabatic excitation caused by the pulse. The Fourier transform of this residual dipole gives a measure of the nonadiabatic excitation. For low fields, only the lowest excited states are populated, and TD-CI simulations using singly excited states with and without perturbative corrections for double excitations [TD-CIS(D) and TD-CIS, respectively] are generally in good agreement with the TD-HF simulations. At higher field strengths, higher states are populated and the methods begin to differ significantly if the coefficients of the excited states become larger than approximately 0.1. The response of individual excited states does not grow linearly with intensity because of excited state to excited state transitions. Beyond a threshold in the field strength, there is a rapid increase in the population of many higher excited states, possibly signaling an approach to ionization. However, without continuum functions, the present TD-HF and TD-CI calculations cannot model ionization directly. The TD-HF and TD-CIS simulations are in good accord because the excitation energies obtained by linear response TD-HF [also known as random phase approximation (RPA)] agree very well with those obtained from singly excited configuration interaction (CIS) calculations. Because CIS excitation energies with the perturbative doubles corrections [CIS(D)] are on average lower than the CIS excitation energies, the TD-CIS(D) response is generally stronger than TD-CIS.