Time-dependent Formalism Research Articles

Theoretical Study of New Ruthenium-Based Dyes for Dye-Sensitized Solar Cells

Two relevant, recently reported, ruthenium-based complexes to be used as sensitizers in Grätzel photovoltaic cells are theoretically studied. The UV/vis absorption spectra have been computed within the time-dependent density functional theory formalism. The obtained excitation energies are compared with the experimental results, and the nature of the transition is analyzed in terms of the electronic density. A preliminary study on the performance of different functionals against the equation of motion coupled cluster is performed on a smaller model system.

Quantum dynamics of Renner–Teller and isotopic effects in NH(a1Δ) + D(2S) reactions

A quantum dynamics study for the NH(a(1)Δ) + D((2)S) reactions using coupled channel time dependent real wavepacket formalism is presented. Moreover, the Renner-Teller (RT) interactions between two electronic states of NHD (X[combining tilde](2)A'' and Ã(2)A') have been taken into account by means of semiempirical RT matrix elements. The introduction of RT effects opens the possibility of studying not only the adiabatic reactions [depletion (d) to N((2)D) + HD(X(1)Σ(+)) and exchange (e) to ND(a(1)Δ) + H((2)S)] but also nonadiabatic ones [quenching (q) to NH(X(3)Σ(-)) + D((2)S) and exchange-quenching (eq) to ND(X(3)Σ(-)) + H((2)S)]. Reaction probabilities, cross sections, isotopic effects, and rate constants are presented for all the before mentioned reactions. RT results are compared with Born-Oppenheimer, quasiclassical, and experimental data. Contrasting with previous NH + H results, we point out interesting RT and isotopic effects, which depend on the D and H masses and on the tunneling of the H atom. In fact, RT effects, near-threshold cross sections, and rate constants are smaller in NH + D than in NH + H, as expected from the masses of the attacking atoms. Our rate constants and quenching branching ratio agree well with previous quasiclassical and experimental data, validating the semiempirical RT coupling we employ. Some small differences between calculated and measured rate constants might be due to the theoretical approximations and to the large experimental error bars.

An exciton scattering model for carrier multiplication in semiconductor nanocrystals: Theory

The effect of carrier multiplication (CM) in semiconductor nanocrystals is systematically treated by employing an exciton scattering approach. Using projection operators, we reduce the Coulomb coupled multiexciton dynamics to scattering dynamics in the space spanning both single- and biexciton states. We derive a closed set of equations determining the scattering matrix elements. This allows us to interpret CM dynamics as a series of odd-order interband scattering events. Using the time-dependent density matrix formalism, we provide a rigorous description of the CM dynamics induced by a finite-time pump pulse. Within this approach, both processes of single- and biexciton photogeneration and the consequent population relaxation are treated on the same footing. This approach provides a framework for numerical calculations and for comparisons of the quantum efficiencies associated with each process. For applications, the limit of weak interband Coulomb coupling is considered. Finally, we demonstrate that three previously used theoretical models can be recovered as limiting cases of our exciton scattering model.

Coupling optical and electrical gating for electronic readout of quantum dot dynamics

We explore the coherent transfer of electronic signatures from a strongly correlated, optically gated nanoscale quantum dot to a weakly interacting, electrically backgated microscale channel. In this unique side-coupled ``$T$'' geometry for transport, we predict a mechanism for detecting Rabi oscillations induced in the dot through quantum, rather than electrostatic means. This detection shows up directly in the dc conductance-voltage spectrum as a field-tunable split in the Fano lineshape arising due to interference between the dipole coupled dot states and the channel continuum. The split is further modified by the Coulomb interactions within the dot that influence the detuning of the Rabi oscillations. Furthermore, time resolving the signal we see clear beats when the Rabi frequencies approach the intrinsic Bohr frequencies in the dot. Capturing these coupled dynamics requires attention to memory effects and quantum interference in the channel as well as many-body effects in the dot. We accomplish this coupling by combining a Fock-space master equation for the dot dynamics with the phase-coherent, non-Markovian time-dependent nonequilibrium Green's function transport formalism in the channel through a properly evaluated self-energy and a Coulomb integral. The strength of the interactions can further be modulated using a backgate that controls the degree of hybridization and charge polarization at the transistor surface.

Publisher’s Note: Time-dependent internal density functional theory formalism and Kohn-Sham scheme for self-bound systems [Phys. Rev. C80, 054614 (2009)

Publisher’s Note: Time-dependent internal density functional theory formalism and Kohn-Sham scheme for self-bound systems [Phys. Rev. C<b>80</b>, 054614 (2009)

Analysis of the excited-state absorption spectral bandshape of oligofluorenes

We present ultrafast transient absorption spectra of two oligofluorene derivatives in dilute solution. These spectra display a photoinduced absorption band with clear vibronic structure, which we analyze rigorously using a time-dependent formalism of absorption to extract the principal excited-state vibrational normal-mode frequencies that couple to the electronic transition, the configurational displacement of the higher-lying excited state, and the reorganization energies. We can model the excited-state absorption spectrum using two totally symmetric vibrational modes with frequencies 450 (dimer) or 400 cm(-1) (trimer), and 1666 cm(-1). The reorganization energy of the ground-state absorption is rather insensitive to the oligomer length at 230 meV. However, that of the excited-state absorption evolves from 58 to 166 meV between the oligofluorene dimer and trimer. Based on previous theoretical work [A. Shukla et al., Phys. Rev. B 67, 245203 (2003)], we assign the absorption spectra to a transition from the 1B(u) excited state to a higher-lying mA(g) state, and find that the energy of the excited-state transition with respect to the ground-state transition energy is in excellent agreement with the theoretical predictions for both oligomers studied here. These results and analysis permit profound understanding of the nature of excited-state absorption in pi-conjugated polymers, which are the subject of general interest as organic semiconductors in the solid state.

A Subsystem TDDFT Approach for Solvent Screening Effects on Excitation Energy Transfer Couplings.

We present a QM/QM approach for the calculation of solvent screening effects on excitation-energy transfer (EET) couplings. The method employs a subsystem time-dependent density-functional theory formalism [J. Chem. Phys. 2007, 126, 134116] and explicitly includes solvent excited states to account for the environmental response. It is investigated how the efficiency of these calculations can be enhanced in order to treat systems with very large solvation shells while fully including the environmental response. In particular, we introduce a criterion to select solvent excited states according to their approximate contribution weight to the environmental polarization. As a model system, we investigate the perylene diimide dimer in a water cluster in comparison to a recent polarizable QM/MM method for EET couplings in the condensed phase [J. Chem. Theory Comput. 2009, 5, 1838]. A good overall agreement in the description of the solvent screening is found. Deviations can be observed for the effect of the closest water molecules, whereas the screening introduced by outer solvation shells is very similar in both methods. Our results can thus be helpful to determine at which distance from a chromophore environmental response effects may safely be approximated by classical models.

First step towards a non-adiabatic description of the fission process based on the Generator Coordinate Method

Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238U [1]. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn’t seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238U and 239U for an excitation energy of 2.3 MeV above the barrier [2–4]. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.

Time-dependent internal density functional theory formalism and Kohn-Sham scheme for self-bound systems

We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all defined by the internal one-body density and the initial state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way to compute the internal density. The main difference with the traditional DFT / Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the functional.

An ab-initio study of photoabsorption spectrum of ultra small CdS clusters

An ab-initio calculation of photoabsorption, and absorption threshold has been performed for (CdS) n , n=1–8, atomic clusters using time-dependent density functional formalism. We used both time-propagation method as well as the Casida's linear theory formalism to compute photoabsorption spectrum for energies up to 15 eV. The photoabsorption exhibits prominent peaks for energies between 0 and 15 eV, and validity too of our methodology is not under any kind of question mark, in this energy range. The computed results from both time-propagation method as well as the Casida's formalism are found in good agreement with each other as well as with recently reported photoabsorption experimental data on (CdS) n , atomic clusters, for UV frequency range. Our results show that the absorption thresholds lie in between 2.08 and 6.29 eV, and first ionization energies of clusters varies from 3.14 to 8.92 eV for all (CdS) n clusters.

Atomic photoionization in weak and strong two-color radiation fields

Two-color photoionization processes in rare gases have been studied using the combination of XUV pulses from the Free Electron Laser in Hamburg (FLASH) and intense femtosecond pulses from an external synchronized near infrared laser. In the low field regime of the NIR dressing laser (<1011 W/cm2), the partial cross sections of the two-photon ionization were determined by measuring the polarization dependence of the Above Threshold Ionization (ATI). In the high field regime (>1111 W/cm2), multi-photon processes are dominant and theoretical descriptions beyond time-dependent second order perturbation formalism have to be applied.

Quantum Study of a Trapped Dipolar Fermi Gas

Using the time-dependent Hartree–Fock theory (TDHF), we study the ground states of dipolar fermion gases in a spherical trap. It is found that deformed configurations which have prolate shape both in real and momentum space are energetically favored and that when the dipolar interaction is not very strong, the deformation of the gases shows a prominent shell structure at closed oscillator-shell configurations. The quadrupole and breathing modes are also studied in TDHF and it is found that these modes are little affected by the dipolar interaction when the gases have the closed-shell configurations. The effects of the two-body correlations on the ground-state properties and also on the damping of the quadrupole mode are also investigated using a time-dependent density-matrix formalism. It is found that the effects of the two-body correlations are not significant for the closed-shell configurations.

Initial Excited-State Structural Dynamics of Uracil from Resonance Raman Spectroscopy Are Different from Those of Thymine (5-Methyluracil)

To explore the origin of the differences in UV photochemistry of uracil (RNA) and thymine (DNA) nucleobases, we have measured the UV resonance Raman spectra of uracil in aqueous solution at wavelengths throughout the lowest-energy absorption band and analyzed the resulting resonance Raman excitation profiles and absorption spectra using a time-dependent wave-packet formalism to obtain the initial excited-state structural changes. In contrast to thymine, which differs from uracil only by the presence of a methyl group at C(5), most of the resonance Raman intensity and resulting initial excited-state structural dynamics for uracil occur along in-plane hydrogen-bond angle deformation, ring stretching, and carbonyl vibrational modes. Weaker intensities and less significant structural dynamics are observed along the C=C stretching mode. These results suggest that the initial excited-state structural dynamics of uracil occur along a carbon pyramidalization coordinate. These dynamics are different from those of thymine, which distorts primarily along a C(5)=C(6) bond lengthening coordinate. These differences in initial excited-state structural dynamics can explain the different primary photoproducts observed for these two pyrimidine nucleobases.

LOCAL LINEAR ANALYSIS OF INTERACTION BETWEEN A PLANET AND VISCOUS DISK AND AN IMPLICATION ON TYPE I PLANETARY MIGRATION

We investigate the effects of viscosity on disk-planet interaction and discuss how type I migration of planets is modified. We have performed a linear calculation using shearing-sheet approximation and obtained the detailed, high resolution density structure around the planet embedded in a viscous disk with a wide range of viscous coefficients. We use a time-dependent formalism that is useful in investigating the effects of various physical processes on disk-planet interaction. We find that the density structure in the vicinity of the planet is modified and the main contribution to the torque comes from this region, in contrast to inviscid case. Although it is not possible to derive total torque acting on the planet within the shearing-sheet approximation, the one-sided torque can be very different from the inviscid case, depending on the Reynolds number. This effect has been neglected so far but our results indicate that the interaction between a viscous disk and a planet can be qualitatively different from an inviscid case and the details of the density structure in the vicinity of the planet is critically important.

Semiclassical formulation of non-Markovian quantum Brownian motion

Recently it was shown [W. Koch, F. Grossmann, J.T. Stockburger, J. Ankerhold, Phys. Rev. Lett. 100 (2008) 230402] that a combination of an exact stochastic decomposition of non-Markovian dissipative quantum dynamics with the time-dependent semiclassical initial value formalism offers a powerful tool to describe quantum Brownian motion in domains of parameter space where other approaches fail. In particular, low temperatures, stronger friction, a wide range of spectral bath densities, and continuous nonlinear systems can be treated. Details of this formulation including its numerical implementation and the impact of non-Markovian phenomena are discussed for the exactly solvable case of a harmonic oscillator.

Kinematic vortex-antivortex lines in strongly driven superconducting stripes

In the framework of the time-dependent Ginzburg-Landau formalism, we study the ``resistive'' state of a submicron superconducting stripe in the presence of a longitudinal current. Sufficiently strong current leads to phase slippage between the leads, which is manifested as oppositely charged kinematic vortices moving in opposite directions perpendicular to applied drive. Depending on the distribution of superconducting current density the vortex-antivortex either nucleate in the middle of the stripe and are expelled laterally or enter on opposite sides of the sample and are driven together to annihilation. We distinguish between the two scenarios as a function of relevant parameters and show how the creation/annihilation point of the vortex-antivortex and their individual velocity can be manipulated by applied magnetic field and current.

Application of time-dependent density-functional theory to molecules and nanostructures

We present ab initio time-dependent density-functional calculations for the optical properties of molecules, atomic clusters, functionalized carbon nanotubes, and metal-nanotube heterostructures. Our calculations are carried out in the framework of a real-space higher-order finite difference method combined with the pseudopotential approximation. In this method, the Kohn–Sham equations for electronic states are solved self-consistently on a real-space three-dimensional Cartesian grid without the use of explicit basis functions. The time-dependent density-functional linear response formalism is applied to calculate the excited-state properties of the water molecule, analyze the optical spectra of potassium atoms and clusters adsorbed on graphene and carbon nanotubes, study the assembly of organic molecules to carbon nanotubes and compute the Stokes shifts in hydrogenated silicon clusters. The results of our calculations show that the time-dependent density-functional computational approach is flexible and can be successfully applied to a variety of different physical problems.

Divergent Electronic Structures of Isoelectronic Metalloclusters: Tungsten(II) Halides and Rhenium(III) Chalcogenide Halides

Same but different: DFT calculations on hexanuclear tungsten(II) halide clusters [W(6)X(8)X'(6)](2-) (X, X'=Cl, Br, I) indicate a breakdown in the isoelectronic analogy between themselves and the isostructural rhenium(III) chalcogenide clusters [Re(6)S(8)X(6)](4-) (see figure).The hexanuclear tungsten(II) halide clusters and the sulfido-halide clusters of rhenium(III) are subsets of a broad system of 24-electron metal-metal bonded assemblies that share a common structure. Tungsten(II) halide clusters and rhenium(III) sulfide clusters luminesce from triplet excited states upon ultraviolet or visible excitation; emission from both cluster series has been extensively characterized elsewhere. Reported here are density-functional theory studies of the nine permutations of [W(6)X(8)X'(6)](2-) (X, X'=Cl, Br, I). Ground-state properties including geometries, harmonic vibrational frequencies, and orbital energy-level diagrams, have been calculated. Comparison is made to the sulfide clusters of rhenium(III), of which [Re(6)S(8)Cl(6)](4-) is representative. [W(6)X(8)X'(6)](2-) and [Re(6)S(8)Cl(6)](4-) possess disparate electronic structures owing to the greater covalency of the metal-sulfur bond and hence of the [Re(6)S(8)](2+) core. Low-lying virtual orbitals are raised in energy in [Re(6)S(8)Cl(6)](4-) with the result that the LUMO+7 (or LUMO+8 in some cases) of tungsten(II) halide clusters is the LUMO of [Re(6)S(8)Cl(6)](4-) species. An inversion of the HOMO and HOMO-1 between the two cluster series also occurs. Time-dependent density-functional calculations using asymptotically correct functionals do not recapture the experimentally observed periodic trend in [W(6)X(14)](2-) luminescence (E(em) increasing in the order [W(6)Cl(14)](2-) < [W(6)Br(14)](2-) < [W(6)I(14)](2-)), predicting instead that emission energies decrease with incorporation of the heavier halides. This circumstance is either a gross failure of the time-dependent formalism of DFT or it indicates extensive multistate emission in [W(6)X(8)X'(6)](2-) clusters. The inapplicability of isoelectronic analogies between clusters of Group 6 and Group 7 is emphasized.

Computational Delineation of the Bioenergetics of Protein-Mediated Orchestration of Membrane Vesiculation in Clathrin-Dependent Endocytosis

Internalization of extracellular cargo by eukaryotic cells via the clathrin-dependent endocytosis (CDE) is an important regulatory process prominent in several cellular functions. Subsequent to receptor activation, a sequence of molecular events in CDE is responsible for the recruitment of various accessory proteins such as AP-2, epsin, AP180, eps15, dynamin, amphiphysin, endophilin, and clathrin to the plasma membrane to orchestrate membrane vesiculation. While the involvement of these proteins have been established and their roles in membrane deformation, cargo recognition, and vesicle scission have been identified, current conceptual understanding falls short of a mechanistic description of the cooperativity and the bioenergetics of the underlying vesicle nucleation event which we address here using theoretical models based on an elastic continuum representation for the membrane and atomistic to coarse-grained representations for the proteins. We employ the surface evolution approach to describe membrane geometries by minimizing the Helfrich Hamiltonian in a curvilinear coordinate system and address how the energetics of vesicle formation in a membrane is impacted by the presence of a growing clathrin coat. We consider two limiting scenarios: (1) the clathrin assembly model in which the clathrin coat induces membrane curvature by forming a curvilinear scaffold; (2) the accessory curvature-inducing protein assembly model, in which the clathrin lattice merely serves as a template to spatially pattern curvature inducing proteins such as epsin which collectively induce membrane curvature. Analyzing the energy required for vesicle formation from a planar bilayer, we demonstrate the role of the CDE protein assembly in driving membrane vesiculation. Furthermore, using a time-dependent Ginzburg-Landau formalism along with the thermodynamic method of free energy perturbation, we calculate the free energy the nucleated vesicle and quantify the finite-temperature corrections to the energy landscape of vesicle nucleation in CDE.

Electronic-structure and quantum dynamical study of the photochromism of the aromatic Schiff base salicylideneaniline

The ultrafast proton transfer dynamics of salicylideneaniline has been theoretically analyzed in the ground and first singlet excited electronic states using density functional theory (DFT) and time-dependent DFT calculations, which predict a (pi,pi( *)) barrierless excited state intramolecular proton transfer (ESIPT). In addition to this, the photochemistry of salicylideneaniline is experimentally known to present fast depopulation processes of the photoexcited species before and after the proton transfer reaction. Such processes are explained by means of conical intersections between the ground and first singlet (pi,pi( *)) excited electronic states. The electronic energies obtained by the time-dependent density functional theory formalism have been fitted to a monodimensional potential energy surface in order to perform quantum dynamics study of the processes. Our results show that the proton transfer and deactivation of the photoexcited species before the ESIPT processes are completed within 49.6 and 37.7 fs, respectively, which is in remarkable good agreement with experiments.