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We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as $\mathcal{O}(N^3)$ for $N$ dye molecules. Our approach scales much more efficiently as $\mathcal{O}(N\log(N))$, enabling quick study of systems with a million of coupled molecules on the micron size scale. We calculate several important experimental observable including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates., Comment: 11 pages, 7 figures, as submitted to JPC

Author(s): Cytter, Y; Rabani, E; Neuhauser, D; Preising, M; Redmer, R; Baer, R | Abstract: The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense matter. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT framework, which requires knowledge only of the KS Hamiltonian but not its eigenstates and values. We show that the computational effort associated with the method scales linearly with system size and reduces in proportion to the temperature, unlike the cubic increase with traditional deterministic approaches. In addition, we find that the method allows an accurate description of the entire spectrum, including the high-frequency range, unlike the deterministic method which is compelled to introduce a high-frequency cutoff due to memory and computational time constraints. We apply the method to helium-hydrogen mixtures in the warm dense matter regime at temperatures of ∼60kK and find that the system displays two conductivity phases, where a transition from nonmetal to metal occurs when hydrogen atoms constitute ∼0.3 of the total atoms in the system.

We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band-edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian which is central for additional post-processing, for example in the stochastic Bethe-Salpeter approach., 7 pages, 3 figures

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as $O\left(N{T}^{\ensuremath{-}1}\right)$ and is compared with the high-temperature limit scaling $O\left({N}^{3}{T}^{3}\right)$ of the deterministic approach, where $N$ is the system size (number of electrons, volume, etc.) and $T$ is the temperature. The method has been implemented in a plane-waves code within the local density approximation (LDA); we demonstrate its efficiency, statistical errors, and bias in the estimation of the free energy per electron for a diamond structure silicon. The bias is small compared to the fluctuations and is independent of system size. In addition to calculating the free energy itself, one can also use the method to calculate its derivatives and obtain the equations of state.

The second-order Matsubara Green's function method (GF2) is a robust temperature dependent quantum chemistry approach, extending beyond the random-phase approximation. However, till now the scope of GF2 applications was quite limited as they require computer resources which rise steeply with system size. In each step of the self-consistent GF2 calculation there are two parts: the estimation of the self-energy from the previous step's Green's function, and updating the Green's function from the self-energy. The first part formally scales as the fifth power of the system size while the second has a much gentler cubic scaling. Here, we develop a stochastic approach to GF2 (sGF2) which reduces the fifth power scaling of the first step to merely quadratic, leaving the overall sGF2 scaling as cubic. We apply the method to linear hydrogen chains containing up to 1000 electrons, showing that the approach is numerically stable, efficient and accurate. The stochastic errors are very small, of the order of 0.1% or less of the correlation energy for large systems, with only a moderate computational effort. The first iteration of GF2 is an MP2 calculation that is done in linear scaling, hence we obtain an extremely fast stochastic MP2 (sMP2) method as a by-product. While here we consider finite systems with large band gaps where at low temperatures effects are negligible, the sGF2 formalism is temperature dependent and general and can be applied to finite or periodic systems with small gaps at finite temperatures., 9 pages

We examine the possibility of using a Metropolis algorithm for computing the exchange energy in a large molecular system. Following ideas set forth in a recent publication (Baer, Neuhauser, and Rabani, Phys. Rev. Lett. 111, 106402 (2013)) we focus on obtaining the exchange energy per particle (ExPE, as opposed to the total exchange energy) to a predefined statistical error and on determining the numerical scaling of the calculation achieving this. For this we assume that the occupied molecular orbitals (MOs) are known and given in terms of a standard Gaussian atomic basis set. The Metropolis random walk produces a sequence of pairs of three-dimensional points (x,x'), which are distributed in proportion to ρ(x,x')(2), where ρ(x,x') is the density matrix. The exchange energy per particle is then simply the average of the Coulomb repulsion energy υC(|x-x'|) over these pairs. To reduce the statistical error we separate the exchange energy into a short-range term that can be calculated deterministically in a linear scaling fashion and a long-range term that is treated by the Metropolis method. We demonstrate the method on water clusters and silicon nanocrystals showing the magnitude of the ExPE standard deviation is independent of system size. In the water clusters a longer random walk was necessary to obtain full ergodicity as Metropolis walkers tended to get stuck for a while in localized regions. We developed a diagnostic tool that can alert a user when such a situation occurs. The calculation effort scales linearly with system size if one uses an atom screening procedure that can be made numerically exact. In systems where the MOs can be localized efficiently the ExPE can even be computed with "sublinear scaling" as the MOs themselves can be screened.

A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and configuration-interaction with single substitution (CIS) method. This results in a time dependent Schr\"odinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the Random Phase Approximation (RPA). To solve for the optical absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of ~3000 electrons is presented and discussed., Comment: 12 pages, 5 figures

We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wavelength asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: ω(q) = q(U(q)/m)1/2, where is the bosons density and U(q) is a Fourier component of the two-body potential.

We develop a formalism for efficient iterative solutions of scattering problems involving the Maxwell equations. The methods, borrowed from recent advancements in chemical reaction dynamics, represent the scattering wavefunctions on two grids; one used for the initial wave and is one-dimensional; the other is a small three-dimensional grid padded with absorbing-potentials on which the scattered function is represented. The formalism is automatically suitable for scattering studies of transmission, reflection and scattering components of a wave. The simulations can be done with time-dependent wavepackets or direct iterative solution for the Green's function, but the results are rigorous time-independent (frequency-dependent) scattering amplitudes. Model time-dependent simulations involving up to a 100×100×100 grid for the inner wavefunction were numerically done on a simple PC.

Intermolecular kinetic-energy operators are derived (in the rigid monomer approximation) for solute–solventn clusters of the type B–An, where B is a molecule and A is either an atom or a molecule. The operators are obtained for a body-fixed frame embedded in the B moiety and parallel to the principal axes of that species. They are expressed in terms of intermolecular coordinates that represent the projection along the body-fixed axes of position vectors pointing from the center of mass of B to the centers of mass of the A species. The results are particularly useful for calculations on clusters in which A–B interactions dominate over A–A interactions in the intermolecular potential energy surface and/or there is minimal interaction between subsets of the A moieties. This utility is demonstrated in variational calculations of intermolecular states in the (1|1) isomer of anthracene–He2.

A semiclassical cellular method is proposed. Signals generated by semiclassical techniques generally deteriorate over time as trajectories become chaotic. One approach to remedy this problem has been to have each trajectory weighted by an entire cell of nearby trajectories (Filinov transform). But even in this approach the exponential part of the propagator typically becomes large and positive over time. Here the cellularization (Filinov) parameter is subject to constraints which make it time dependent and trajectory dependent. It also depends on dimensionality, so it ends up as a matrix. Physically, the Filinov transform is done differently in different directions associated with the stability matrix for the phase—essentially a more confined integration in directions where the matrix diverges and a wider integration in other directions. This squelches the contribution from any part of a trajectory that becomes excessively chaotic. A trajectory-dependent cellurized frozen Gaussian is applied here within the Herman–Kluk semiclassical approach. It is tested by looking at a single-particle three-dimensional problem, He attached to a rigid immovable naphtalene, where it is shown to be more accurate than the original HK approach, without the divergence of the correlation function common in the usual cellular dynamics (HK) formulation, and is able to separate a low-lying excited state from the ground state.

The dynamics of a chain of vibrational bonds which develop a classical solitary compression wave is simulated. A converged fully correlated quantum mechanical calculation is compared with a time dependent mean field approach (TDSCF) and with a classical simulation. The dynamics were all generated from the same Hamiltonian. The TDSCF and classical calculations show a fully developed solitary wave with the expected dependence of group velocity on amplitude. The full quantum calculations show a solitary-like wave which propagates for a while but then degrades. The robustness of the compression wave depends on the initial preparation. Evidence of partial recurrence of the wave has also been observed.

We present an approach toward the dynamically exact calculation of intermolecular states in molecule-large molecule complexes. The approach employs an intermolecular Hamiltonian specifically formulated with the case of molecule-large molecule complexes in mind. In addition, it makes use of filter diagonalization techniques to diagonalize that Hamiltonian. The approach is applied to the calculation of J=0 intermolecular states below about 110 cm−1 in the benzene–H2O complex. The results of the calculation are interpreted in terms of five internal rotation states, a doubly degenerate bending mode and a singly degenerate stretching mode, the latter two modes involving the relative translation of the monomer moieties in the complex. The internal rotation states are discussed in the context of the two-dimensional, free internal rotation/water in-plane torsion model of Pribble et al. [J. Chem. Phys. 103, 531 (1995)]. It is shown that that model is largely successful in identifying the important features of the ...

Recently we presented a method for modeling a quantum system to a bath that explicitly correlates the system with the individual bath modes. We do this through representation of the bath by locally propagating Gaussians (LPG), which change in position and momentum but remain Gaussian in form. The explicit correlation of the system to the bath modes enters through the simultaneous use of a different Gaussian for each state (or grid point) of the system. In this work, we look at two possibilities for the LPG method. In the frozen LPG, the width of the Gaussians is kept constant. In the flexible LPG, we relax this condition and allow for the width to be both time dependent and complex. We present a comparative study of these two methods and compare them with both time-dependent self-consistent field calculations (TDSCF) and an exact quantum calculation. The two LPG methods, in comparison with TDSCF, more accurately describe the exact dynamics. The difference is especially noticeable in the case of weak coupling, where the averaging done in TDSCF is an oversimplification of the system.

A simple method that incorporates coupling between bath and system and between individual bath modes is proposed. In the new locally propagating gaussian (LPG) approximation, the bath is modeled by Gaussians at each system site that propagate in time. Each site couples to others by the overlap of their Gaussians. In a test case with weak but non-negligible coupling, LPG is nearly as rapid as TDSCF but more closely follows exact calculations. LPG can be extended to larger simulations. Strongly coupled system coordinates will be treated with a grid-type calculation and weakly coupled bath modes will be handled by LPG.

The filter-diagonalization method is used to find the broad and even overlapping resonances of a 1D Hamiltonian used before as a test model for new resonance theories and computational methods. Is is found that the use of several complex-scaled cross-correlation probability amplitudes from short-time propagation enables the calculation of broad overlapping resonances, which can not be resolved from the amplitude of a single complex-scaled autocorrelation calculation.

Heller’s expression for the absorption cross-section in the weak field limit is extended to cases where the total Hamiltonian contains a strong time-dependent component, supplemented by a weak field. A very similar expression to the original case then results when the (t,t) formalism is used; one only needs to construct a correlation function for the system without the weak field, and use it to extract the absorption probability for any value of the weak-field frequency (or pulse shape). In addition, a numerical approach for extracting Floquet states without full-matrix diagonalization is demonstrated, by filtering (or filter-diagonalization) a single wave function (or the correlation function) propagated under the (t,t) Hamiltonian.

A time‐independent approach to calculate scattering matrix elements using the complex coordinate method is examined. This approach is based on a combination of the expressions derived by Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] and by Kouri, Huang, Zhu, and Hoffman [J. Chem. Phys. 100, 3662 (1994)], with an analytic continuation of the Hamiltonian, while keeping the initial and final wave packets unscaled. The procedure is examined using a one dimensional Eckart barrier representing the H+H2 reaction, and a comparison between two complex scaling schemes and an optical potential one shows good convergence of the method. In addition, a one‐dimensional electron scattering from a barrier is calculated, showing an advantage here of the complex‐scaling approach over the optical potentials method when very light particles are involved in the dynamics. The complex‐scaling version enables the use of iterative techniques, hence is a promising tool for calculating dynamics in large systems of light particles.

We investigate the usefulness of a hybrid method for scattering with resonances. Wave packet propagation is used to obtain the time‐dependent wave function Ψ(t) up to some time T at which direct scattering is over. Next, Ψ(t) is extrapolated beyond T employing resonance eigenvalues and eigenfunctions obtained in a Lanczos procedure, using Ψ(T) as starting vector to achieve faster convergence. The method is tested on one two‐dimensional (2D) and one four‐dimensional (4D) reactive scattering problem, affected by resonances of widths 0.1–5 meV. Compared to long time wave packet propagation, the hybrid method allows large reductions in the number of Hamiltonian operations NH required for obtaining converged reaction probabilities: A reduction factor of 24 was achieved for the 2D problem, and a factor of 6 for the 4D problem.

We investigate the performance of a scattering algorithm which uses purely real algebra for the major part of the wave function calculation, while incorporating automatically the appropriate boundary conditions. The algorithm falls in the category of time‐independent wave packet methods ([R. Kosloff, J. Phys. Chem. 92, 2087 (1988)], and, more specifically for scattering [Y. Huang, W. Zhu, D. J. Kouri, and D. K. Hoffman, Chem. Phys. Lett. 206, 96 (1993)]), and combines two previous approaches: A method [V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 103, 2903 (1995)] in which the action of the absorbing potentials is implicitly inserted in a polynomial expansion of the Green’s function, and a real initial wave function approach, in which zero initial momenta are avoided. Compared to the conventional, multiple time‐step Chebyshev method, the new algorithm required three times less Hamiltonian evaluations for a model problem involving direct scattering. The new method also showed faster convergence for a problem involving resonances. Both methods showed convergence problems in the vicinity of a very narrow resonance.

This article has a few goals. First, a new highly accurate and anomaly free time‐independent approach to reactive scattering is presented, based on the use of very‐short‐range imaginary potentials. The range of the imaginary potentials is extremely short—in successful one‐dimensional simulations they cover only two grid points. The savings are incurred by limiting the role of the imaginary potentials to shifting the eigenvalues of the Hamiltonian away from the real axis, thereby avoiding anomalies; the imaginary potentials are not required to impose outgoing boundary conditions. Another goal is a rigorous derivation of a flux‐amplitude (FA) expression, whereby (for any scattering approach, whether using negative imaginary potentials or not) reactive S‐matrix amplitudes are extracted from the wavefunction at a single surface of any desired ‘‘internal’’ coordinate system—there is no need to project the wave function to the asymptotic products coordinates before determining its flux. With the FA expression, expensive volume integrals in state‐to‐state scattering are reduced to simple surface integrals. The FA expression also leads to a rigorous derivation of various alternate expressions for the scattering matrix which are useful whenever negative imaginary potentials are utilized. Finally, a new expression is presented for estimating the errors in absorbing potentials single‐column calculations due to imperfections in the absorbing potentials.

In a previous paper we developed a method, Filter‐Diagonalization, for extracting eigenvalues and eigenstates of a given operator at any desired energy range. In essence, the method eliminates correlation between distant eigenstates through a short‐time filter while correlations between closely lying states are eliminated by diagonalization. Here we extend Filter‐Diagonalization. When used to extract eigenvalues for a given operator H, we show that all eigenvalue information is directly extracted from a short segment of the correlation functionC(t)=(ψ(0)‖e −iHt ‖ψ(0)), or alternately from a small number of residues (ψ(0)‖R n (H)‖ψ(0)), where ψ(0) is a random initial function and R n (H) is any desired polynomial expansion in H. The implications of this feature are twofold. First, in contrast to the previous version the wave packet needs only to be propagated once (to prepare C(t)), and eigenstates at all desired energy windows can then be extracted with negligible extra computation time (and negligible storage requirements). In a simulation presented here, accurate eigenvalues are extracted using propagation times which are only a 0.0041 fraction of the ‘‘natural’’ time, i.e., the time by which the relative phase of the two closest eigenstates reaches 2π. The second and more important feature is that the method is automatically suitable for extracting eigenvalues (or normal modes) using a short‐time segment of any signal C(t) which is a sum of (unknown) Fourier components (C(t)=∑ nd ne −ie nt ) regardless of its origin. In addition to its use for determining eigenvalues of known operators, the method may also be utilized to extract normal modes from classical‐dynamics simulations, eigenstates from real‐time Quantum Monte‐Carlo studies, frequencies from experimental optical or electrical signals, or be utilized in any other circumstance where a correlation function or general signal is only known for short times (or expensive to generate at long times).

Auxiliary‐field Monte Carlo (AFMC) is an exact approach for calculating the ground state of a system of fermions (or bosons) interacting by pair‐potentials. The method uses the Hubbard–Stratonovich transformation to replace the exact imaginary‐time propagator by an average over an ensemble of propagators for independent particles in the presence of a varying external field, so that the calculation of the exact energy is reduced to multiple independent calculations, each of which costs essentially the same as one Hartree–Fock iteration. Here we consider the application of AFMC to calculate molecular structure, and present preliminary simulations on He and Be. We develop two simple methods to partially alleviate a ‘‘sign‐problem’’ in AFMC through restriction of the length of the imaginary‐time propagation, by either a simultaneous propagation of several initial states followed by subspace‐diagonalization or by incorporation of information from all propagated time steps. The first method is tested and found to yield significant improvement in accuracy. For the present simulations, the single‐particle orbitals are expanded in a given set of primitive orbitals. The resulting spectral‐AFMC method yields, for sufficiently converged ensembles, the full‐CI energy associated with a given basis. The developments reported here, and in particular the demonstration of subspace‐diagonalization, have however general validity independent of whether a basis set or a grid representation is used for the single‐particle orbitals (in the first case a full‐CI result is obtained in the given basis, while a converged grid representation would yield the exact result).

In a previous paper [J. Chem. Phys. 93, 2611 (1990)] a new method, filter diagonalization, was introduced for extracting highly excited rovibrational states from an arbitrary Hamiltonian, in any desired energy range. In the method, an arbitrary initial wave packet is propagated for a short time and during the propagation a ‘‘short time filter’’ of the wave packet is accumulated at various energies in any desired ‘‘window,’’ yielding a small set of functions which span the eigenfunctions of the Hamiltonian in the desired range. A small Hamiltonian matrix is then evaluated in the filtered‐functions basis, to yield the eigenvalues in the desired range. The combination of the time‐dependent (TD) propagation with the small matrix diagonalization eliminates the uncertainty‐relation limitation associated with a pure TD approach and the large‐matrix diagonalization necessary in a purely time‐independent approach. In this paper we give the first demonstration of the power of filter diagonalization for a molecular Hamiltonian exhibiting accidental near degeneracies, thereby supplying a stringent test of our approach. A two‐dimensional model of LiCN (J=0) is used. Good agreement is established with previous results for high‐energy states. For a further check of consistency, we perform a large‐scale direct diagonalization of the Hamiltonian, and verify a very‐high accuracy even for nearly degenerate levels. Extraction of these levels by a purely TD approach would have necessitated ≊700‐fold increase in propagation time.

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 Yee's 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.

An optimization procedure for producing selective excitation of molecules undergoing stochastic dephasing collisions is presented. The collisional effects are incorporated by propagating the Schrodinger equation with random perturbations. The optimization procedure utilizes gradients of the perturbation‐averaged physical objective with respect to the laser field parameters; we demonstrate on a model problem that very few averages over collisional events suffice to yield converged results. Therefore, this method is computationally efficient because large averaging of dynamical simulations is not necessary. These results show the viability of the optimal control procedure for application to controlling chemical reactions in solution.

Controlling curve‐crossing dynamics of a model diatomic system between two dissociative electronic states through radiative coupling with a third bound state is examined. Starting with an initial wave packet on one of the crossing surfaces, optimal control theory is used to design the radiative field to either enhance or eliminate (at our choice) selectivity of one product channel over another. A new optimization procedure is introduced which filters out dc and low frequency components from the optimal field, but still allows for resonant transitions to a third bound state. This procedure forces the fields to employ interesting physical mechanisms involving the bound state in order to control the electronic branching ratios rather than directly negating or enhancing the diabatic coupling term in the Hamiltonian. A new propagation scheme for a multisurface Hamiltonian using Pauli matrices is also presented.

In this work is presented a time‐independent treatment of a reactive system employing negative imaginary decoupling potentials. We discuss two aspects: (a) we show how with the help of these potentials a reactive scattering problem is converted into a bound‐type problem, and (b) we show that a reactive treatment can be carried out entirely in the products arrangement channel without the use of the reagents arrangement channel. By doing that we are able to obtain exact reactive state‐to‐state S matrix elements or transition probabilities.

Time‐dependent scattering is extended to systems possessing narrow resonances. At short times the wave function is integrated directly, and at late times the wave function is expanded in terms of the slowly decaying (complex) resonance eigenfunctions of the Hamiltonian, Ψ(X,t)≂Σn ane−ient−Γ nt/2Φn(X). The slowly decaying eigenfunctions are easily found via a short‐time filterization approach adapted from bound‐state studies, in which a random wave packet is filtered at various energies and the resulting vectors are then diagonalized. The method is exemplified for collinear reactions of H+H2, where it halves the propagation time.

A method for performing reactive scattering calculations using mixed quantum/classical dynamics is described. The wavefunction is decomposed into a time-dependent SCF product form. Reactive degrees of freedom are treated quantum mechanically and the rest are treated classically. The wave packet in the quantum degree of freedom is only followed in one arrangement channel to minimize the size of the numerical grid. Parts of the packet that move into other arrangement channels are absorbed using negative imaginary optical potentials. Two variants of the method are tested on the collinear T + HT → TH + T reaction where they give qualitatively correct predictions of tunneling probabilities near threshold.

The paper reports converged quantum total integral reactive cross sections for the reaction F + H2 yielding HF + H, for initial rotational states j sub i = 0 and 1, using a time-dependent method. The results are compared to classical results and to the experimental results of Neumark et al. (1985). Strong quantum effects are found in the threshold region for both initial states (i.e., in the dependence of the reaction on initial state for low energies). The classical results agree better with experiment than do the quantum results; this appears to be due to errors in the potential used.

Friction is a desired property in quantum dynamics as it allows for localization, prevents backscattering, and is essential in the description of multistage transfer. Practical approaches for friction generally involve memory functionals or interactions with system baths. Here, we start by requiring that a friction term will always reduce the energy of the system; we show that this is automatically true once the Hamiltonian is augmented by a term of the form integral a(q;n(0)) x [partial differential j(q,t)/partial differential t] x J(q)dq, which includes the current operator times the derivative of its expectation value with respect to time, times a local coefficient; the local coefficient will be fitted to experiment, to more sophisticated theories of electron-electron interaction and interaction with nuclear vibrations and the nuclear background, or alternately, will be artificially constructed to prevent backscattering of energy. We relate this term to previous results and to optimal control studies, and generalize it to further operators, i.e., any operator of the form integral a(q;n(0))[partial differential c(q,t)/partial differential t] x C(q)dq (or a discrete sum) will yield friction. Simulations of a small jellium cluster, both in the linear and highly nonlinear excitation regime, demonstrate that the friction always reduces energy. The energy damping is essentially double exponential; the long-time decay is almost an order of magnitude slower than the rapid short-time decay. The friction term stabilizes the propagation (split-operator propagator here), therefore increasing the time-step needed for convergence, i.e., reducing the overall computational cost. The local friction also allows the simulation of a metal cluster in a uniform jellium as the energy loss in the excitation due to the underlying corrugation is accounted for by the friction. We also relate the friction to models of coupling to damped harmonic oscillators, which can be used for a more sophisticated description of the coupling, and to memory functionals. Our results open the way to very simple finite grid description of scattering and multistage conductance using time-dependent density functional theory away from the linear regime, just as absorbing potentials and self-energies are useful for noninteracting systems and leads.

We present a method to obtain bound‐state eigenfunctions in any arbitrary range of energies, by a Fourier resolution (from time to energy) of a real‐time wave packet. The resolution is done simultaneously at a number of energies within the sought range, and the resulting vectors yield, after diagonalization, all bound‐state eigenvalues and eigenfunctions within that range. The method is exemplified on a Morse potential: eigenfunctions for 18 high‐lying states (n∼200) are obtained from resolution at 25 energies.

This paper describes a new approach to the study of atom–diatom reactive collisions in three dimensions employing wave packets and the time‐dependent Schrodinger equation. The method uses a projection operator approach to couple the inelastic and reactive portions of the total wave function and optical potentials to circumvent the necessity of using product arrangement coordinates. Reactive transition probabilities are calculated from the state resolved flux of the wave packet as it leaves the interaction region in the direction of the reactive arrangement channel. The wave packet does not need to be propagated into the asymptotic reactive region in order to determine accurate vibrationally resolved, but rotationally summed reaction probabilities. The present approach is used to obtain such vibrationally resolved reaction probabilities for the three‐dimensional H+H2 (J=0) hydrogen exchange reaction, using a body‐fixed system of coordinates.

This work describes a new approach for the study of atom-diatom reactive collisions. The method is reminiscent of a time-dependent approach presented earlier but is formulated within the time-independent framework. As before, the method makes use of the projection operator formalism to form a coupled system of Schroedinger equations and of optical potentials, to reduce the reactive multiarrangement system to a (single arrangement) nonreactive system. However, in contrast to the time-dependent approach, here the optical potentials impose outgoing boundary conditions, reducing significantly the numerical effort required to solve the Schroedinger equations. The reactive probabilities are obtained by calculating the fluxes at the exit region of each reactive channel. As an example, the method is applied to the collinear reactive H + H{sub 2} system. The extension of this method, to three dimensions like in the time-dependent approach, is straightforward.

Recently, the possibility of transporting electromagnetic energy as local-plasmon-polariton waves along arrays of silver nanoparticles was demonstrated experimentally [S. A. Maier et al., Nat. Mater. 2, 229 (2003)]. It was shown that dipole coupling facilitates phase-coherent excitation waves, which propagate while competing against decoherence effects occurring within each dot. In this article the authors study the ideal coherent shuttling in such a system, leaving decoherence for future investigation. In the weak field limit, the waves obey a Schrodinger equation, to be solved using either time-dependent wave-packet or energy resolved scattering techniques. The authors study some dynamical characteristics of these waves, emphasizing intuition and insight. Scattering from barriers, longitudinal-transverse coupling and acceleration methods are studied in detail. The authors also discuss briefly two-dimensional arrays and a simple decoherence model.

We describe a simple approach and present a straightforward numerical algorithm to compute the best fit shot-noise limited proximity ratio histogram (PRH) in single-molecule fluorescence resonant energy transfer diffusion experiments. The key ingredient is the use of the experimental burst size distribution, as obtained after burst search through the photon data streams. We show how the use of an alternated laser excitation scheme and a correspondingly optimized burst search algorithm eliminates several potential artifacts affecting the calculation of the best fit shot-noise limited PRH. This algorithm is tested extensively on simulations and simple experimental systems. We find that dsDNA data exhibit a wider PRH than expected from shot noise only and hypothetically account for it by assuming a small Gaussian distribution of distances with an average standard deviation of 1.6 A. Finally, we briefly mention the results of a future publication and illustrate them with a simple two-state model system (DNA hairpin), for which the kinetic transition rates between the open and closed conformations are extracted.

Excited state mixed valence (ESMV) occurs in molecules in which the ground state has a symmetrical charge distribution but the excited state possesses two or more interchangeably equivalent sites that have different formal oxidation states. Although mixed valence excited states are relatively common in both organic and inorganic molecules, their properties have only recently been explored, primarily because their spectroscopic features are usually overlapped or obscured by other transitions in the molecule. The mixed valence excited state absorption bands of 2,3-di-p-anisyl-2,3-diazabicyclo[2.2.2]octane radical cation are well-separated from others in the absorption spectrum and are particularly well-suited for detailed analysis using the ESMV model. Excited state coupling splits the absorption band into two components. The lower energy component is broader and more intense than the higher energy component. The absorption bandwidths are caused by progressions in totally symmetric modes, and the difference in bandwidths is caused by the coordinate dependence of the excited state coupling. The Raman intensities obtained in resonance with the high and low energy components differ significantly from those expected based on the oscillator strengths of the bands. This unexpected observation is a result of the excited state coupling and is explained by both the averaging of the transition dipole moment orientation over all angles for the two types of spectroscopies and the coordinate-dependent coupling. The absorption spectrum is fit using a coupled two-state model in which both symmetric and asymmetric coordinates are included. The physical meaning of the observed resonance Raman intensity trends is discussed along with the origin of the coordinate-dependent coupling. The well-separated mixed valence excited state spectroscopic components enable detailed electronic and resonance Raman data to be obtained from which the model can be more fully developed and tested.

One-dimensional and two-dimensional conductivity calculations are done for a set of several closely spaced quantum silicon rings, following the development of bottom-up approaches for producing silicon rings. The transmission is easily influenced by electric and magnetic gatings and has band features even for two or three rings, showing its potential usefulness for logical devices. Analysis on different gatings shows that the electric-field gating would be as effective as the Aharonov-Bohm magnetic gating.

An alternative time-dependent wave-packet method for treating three-dimensional gas phase reactive atom-diatom collisions is presented. The method employs a nonreactive body-frame wave packet propagation procedure, made possible by judicious use of absorbing optical potentials, a novel scheme for interpolating the wave function from coordinates in one arrangement to those in another and the fact that the time-dependent Schroedinger equation is an initial-value problem. The last feature makes possible a computationally viable and accurate procedure for changing from one arrangement's coordinates to another. In addition, the method allows the determination of S-matrix elements over a wide range of energies from a single wave-packet propagation. The method is illustrated by carrying out detailed calculations of inelastic and reactive scattering in the H + H2 system using the Liu-Siegbahn-Truhlar-Horowitz potential surface.

This work describes a new approach for the study of atom–diatom reactive collision employing the time‐dependent wave packet Schrodinger equation. The method makes use of the projection operator formalism to form a coupled system of time dependent Schrodinger equations and of optical potentials to circumvent the necessary use of products coordinates. Two versions are presented. As an example we applied the method to the collinear reactive H+H2 system for which are calculated both transition probabilities and rate constants.