Kenneth Lopata

Modeling Fast Electron Dynamics with Real-Time Time-Dependent Density Functional Theory: Application to Small Molecules and Chromophores

The response of matter to external fields forms the basis for a vast wealth of fundamental physical processes ranging from light harvesting to nanoscale electron transport. Accurately modeling ultrafast electron dynamics in excited systems thus offers unparalleled insight but requires an inherently nonlinear time-resolved approach. To this end, an efficient and massively parallel real-time real-space time-dependent density functional theory (RT-TDDFT) implementation in NWChem is presented. The implementation is first validated against linear-response TDDFT and experimental results for a series of molecules subjected to small electric field perturbations. Second, nonlinear excitation of green fluorescent protein is studied, which shows a blue-shift in the spectrum with increasing perturbation, as well as a saturation in absorption. Next, the charge dynamics of optically excited zinc porphyrin is presented in real time and real space, with relevance to charge injection in photovoltaic devices. Finally, intermolecular excitation in an adenine-thymine base pair is studied using the BNL range separated functional [ Baer , R. ; Neuhauser , D. Phys. Rev. Lett. 2005 , 94 , 043002 ], demonstrating the utility of a real-time approach in capturing charge transfer processes.

Linear-Response and Real-Time Time-Dependent Density Functional Theory Studies of Core-Level Near-Edge X-Ray Absorption.

We discuss our implementation and application of time-dependent density functional theory (TDDFT) to core-level near-edge absorption spectroscopy, using both linear-response (LR) and real-time (RT) approaches. We briefly describe our restricted excitation window TDDFT (REW-TDDFT) approach for core excitations, which has also been reported by other groups. This is followed by a detailed discussion of real-time TDDFT techniques tailored to core excitations, including obtaining spectral information through delta-function excitation, postprocessing time-dependent signals, and resonant excitation through quasi-monochromatic excitation. We present results for the oxygen K-edge of water and carbon monoxide; the carbon K-edge of carbon monoxide; the ruthenium L3-edge for the hexaamminerutheium(III) ion, including scalar relativistic corrections via the zeroth order regular approximation (ZORA); and the carbon and fluorine K-edges for a series of fluorobenzenes. In all cases, the calculated spectra are found to be in reasonable agreement with experimental results, requiring only a uniform shift ranging from -4 eV to +19 eV, i.e., on the order of a few percent of the excitation energy. Real-time TDDFT visualization of excited state charge densities is used to visually examine the nature of each excitation, which gives insight into the effects of atoms bound to the absorbing center.

Excited-State Studies of Polyacenes: A Comparative Picture Using EOMCCSD, CR-EOMCCSD(T), Range-Separated (LR/RT)-TDDFT, TD-PM3, and TD-ZINDO.

The low-lying excited states (La and Lb) of polyacenes from naphthalene to heptacene (N = 2-7) are studied using various time-dependent computational approaches. We perform high-level excited-state calculations using equation of motion coupled cluster with singles and doubles (EOMCCSD) and completely renormalized equation of motion coupled cluster with singles, doubles, and perturbative triples (CR-EOMCCSD(T)) and use these results to evaluate the performance of various range-separated exchange-correlation functionals within linear-response (LR) and real-time (RT) time-dependent density functional theories (TDDFT). As has been reported recently, we find that the range-separated family of functionals addresses the well-documented TDDFT failures in describing these low-lying singlet excited states to a large extent and are as about as accurate as results from EOMCCSD on average. Real-time TDDFT visualization shows that the excited state charged densities are consistent with the predictions of the perimeter free electron orbital (PFEO) model. This corresponds to particle-on-a-ring confinement, which leads to the well-known red-shift of the excitations with acene length. We also use time-dependent semiempirical methods like TD-PM3 and TD-ZINDO, which are capable of handling very large systems. Once reparametrized to match the CR-EOMCCSD(T) results, TD-ZINDO becomes roughly as accurate as range-separated TDDFT, which opens the door to modeling systems such as large molecular assemblies.

Multiscale Maxwell-Schrodinger modeling: A split field finite-difference time-domain approach to molecular nanopolaritonics.

We present a combined finite-difference time-domain/linear response approach for modeling plasmon/molecule systems. The self-interaction of the molecule is avoided by splitting the fields and currents into two parts: those due to the molecule and those from everything else. This approach is suitable for describing surface plasmons on metal nanostructures interacting in the near field with nearby dipolar molecules or semiconductor nanostructures. The approach is applied to three collinear 5 nm diameter gold nanoparticles; the results demonstrate that a nearby molecule strongly affects surface plasmon transfer along the array. Specifically, an xy oriented molecule situated midway between the second and third nanoparticles exhibits a symmetric Fano-type inference effect. Transmission of incident x-polarized energy from the second nanoparticle to the third is enhanced over a frequency range below the molecular resonance, and partially scattered into y-polarized currents for frequencies above. At the molecules resonance frequency, the magnitude of the resulting y-current is approximately 20% of the x-current.

Molecular nanopolaritonics: Cross manipulation of near-field plasmons and molecules. I. Theory and application to junction control

Near-field interactions between plasmons and molecules are treated in a simple unified approach. The density matrix of a molecule is treated with linear-response random phase approximation and the plasmons are treated classically. The equations of motion for the combined system are linear, governed by a simple Liouvillian operator for the polariton (plasmon+molecule excitation) dynamics. The dynamics can be followed in time or directly in frequency space where a trace formula for the transmission is presented. A model system is studied, metal dots in a forklike arrangement, coupled to a two level system with a large transition-dipole moment. A Fano-type resonance [Phys. Rev. 103, 1202 (1956)] develops when the molecular response is narrower than the width of the absorption spectrum for the plasmons. We show that the direction of the dipole of the molecule determines the direction the polariton chooses. Further, the precise position of the molecule has a significant effect on the transfer.

Near and Above Ionization Electronic Excitations with Non-Hermitian Real-Time Time-Dependent Density Functional Theory.

We present a real-time time-dependent density functional theory (RT-TDDFT) prescription for capturing near and post-ionization excitations based on non-Hermitian von Neumann density matrix propagation with atom-centered basis sets, tuned range-separated DFT, and a phenomenological imaginary molecular orbital-based absorbing potential to mimic coupling to the continuum. The computed extreme ultraviolet absorption spectra for acetylene (C2H2), water (H2O), and Freon 12 (CF2Cl2) agree well with electron energy loss spectroscopy (EELS) data over the range of 0-50 eV. The absorbing potential removes spurious high-energy finite basis artifacts, yielding correct bound-to-bound transitions, metastable (autoionizing) resonance states, and consistent overall absorption shapes.

Nonlinear nanopolaritonics: Finite-difference time-domain Maxwell-Schrödinger simulation of molecule-assisted plasmon transfer

The effect of nonlinear excitations of a nearby two-state dipolar molecule on plasmon transfer across a pair of spherical gold nanoparticles is studied numerically using a split field finite-difference time-domain Maxwell-Schrödinger approach [K. Lopata and D. Neuhauser, J. Chem. Phys. 130, 104707 (2009)]. It is observed in the linear response regime that the molecule has a drastic effect on plasmon transfer; specifically, there is a Fano-type resonance that serves to scatter localized plasmons from x-polarization to y-polarization. With increasing nonlinearity of the molecular excitation, the scattering effect saturates due to the limited capacity of the molecule to absorb and radiate energy once the excited and ground states are equally populated.

Accelerated Broadband Spectra Using Transition Dipole Decomposition and Padé Approximants.

We present a method for accelerating the computation of UV-visible and X-ray absorption spectra in large molecular systems using real-time time-dependent density functional theory (TDDFT). This approach is based on deconvolution of the dipole into molecular orbital dipole pairs developed by Repisky, et al. [Repisky et al., J. Chem. Theory Comput. 2015, 11, 980-911] followed by Padé approximants to their Fourier transforms. By combining these two techniques, the required simulation time is reduced by a factor of 5 or more, and moreover, the transition dipoles yield the molecular orbital contributions to each transition, akin to the coefficients in linear-response TDDFT. We validate this method on valence and core-level spectra of gas-phase water and nickel porphyrin, where the results are essentially equivalent to conventional linear response. This approach makes real-time TDDFT competitive against linear response for large molecular and material systems with a high density of states.

Near-field: a finite-difference time-dependent method for simulation of electrodynamics on small scales.

We develop near-field (NF), a very efficient finite-difference time-dependent (FDTD) approach for simulating electromagnetic systems in the near-field regime. NF is essentially a time-dependent version of the quasistatic frequency-dependent Poisson algorithm. We assume that the electric field is longitudinal, and hence propagates only a set of time-dependent polarizations and currents. For near-field scales, the time step (dt) is much larger than in the usual Maxwell FDTD approach, as it is not related to the velocity of light; rather, it is determined by the rate of damping and plasma oscillations in the material, so dt = 2.5 a.u. was well converged in our simulations. The propagation in time is done via a leapfrog algorithm much like Yees method, and only a single spatial convolution is needed per time step. In conjunction, we also develop a new and very accurate 8 and 9 Drude-oscillators fit to the permittivity of gold and silver, desired here because we use a large time step. We show that NF agrees with Mie-theory in the limit of small spheres and that it also accurately describes the evolution of the spectral shape as a function of the separation between two gold or silver spheres. The NF algorithm is especially efficient for systems with small scale dynamics and makes it very simple to introduce additional effects such as embedding.

Modeling molecular effects on plasmon transport: Silver nanoparticles with tartrazine

Modulation of plasmon transport between silver nanoparticles by a yellow fluorophore, tartrazine, is studied theoretically. The system is studied by combining a finite-difference time-domain Maxwell treatment of the electric field and the plasmons with a time-dependent parameterized method number 3 simulation of the tartrazine, resulting in an effective Maxwell∕Schrödinger (i.e., classical∕quantum) method. The modeled system has three linearly arranged small silver nanoparticles with a radius of 2 nm and a center-to-center separation of 4 nm; the molecule is centered between the second and third nanoparticles. We initiate an x-polarized current on the first nanoparticle and monitor the transmission through the system. The molecule rotates much of the x-polarized current into the y-direction and greatly reduces the overall transmission of x-polarized current.