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We present a highly efficient method for the extraction of optical properties of very large molecules via the Bethe-Salpeter equation. The crutch of this approach is the calculation of the action of the effective Coulombic interaction, $W$, through a stochastic TD Hartree propagation, which uses only 10 stochastic orbitals rather than propagating the full sea of occupied states. This leads to a scaling that is at most cubic in system size, with trivial MPI parallelization. We apply this new method to calculate the spectra and electronic density of the dominant excitons of a carbon-nanohoop bound fullerene system with 520 electrons, using less than 4000 core hours., 6 pages, 3 figures, communication

Molecular aggregates with long-range excitonic couplings have drastically different photophysical properties compared to their monomer counterparts. From Kasha's model for one-dimensional systems, positive or negative excitonic couplings lead to blue or red-shifted optical spectra with respect to the monomers, labeled H-and J-aggregates, respectively. The overall excitonic couplings in higher dimensional systems are much more complicated and cannot be simply classified from their spectral shifts alone. Here, we provide a unified classification for extended 2D aggregates using temperature dependent peak shifts, thermal broadening, and quantum yields. We discuss the examples of six 2D aggregates with J-like absorption spectra but quite drastic changes in quantum yields and superradiance. We find the origin of the differences is, in fact, a different excitonic band structure where the bright state is lower energy than the monomer but still away from the band edge. We call this an “I-aggregate.” Our results provide a description of the complex excitonic behaviors that cannot be explained solely on Kasha's model. Furthermore, such properties can be tuned with the packing geometries within the aggregates providing supramolecular pathways for controlling them. This will allow for precise optimizations of aggregate properties in their applications across the areas of optoelectronics, photonics, excitonic energy transfer, and shortwave infrared technologies.

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observable at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real-space or slicing the occupied space into energy windows, allowing for a significant reduction of the statistical fluctuations. For chemical accuracy further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as $1/\sqrt{N_\chi}$ according to the central limit theorem, where $N_\chi$ is the number of random orbitals. In this paper we combined the aforementioned embedding schemes and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground state properties such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon., Comment: The following article has been submitted to the Journal of Chemical Physics

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.

We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Moller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.

We show that a rigid scissors-like GW self-consistency approach, labeled here Δ¯GW0, can be trivially implemented at zero additional cost for large scale one-shot G0W0 calculations. The method significantly improves one-shot G0W0 and for large systems is very accurate. Δ¯GW0 is similar in spirit to evGW0 where the self-consistency is only applied on the eigenvalues entering Green’s function, while both W and the eigenvectors of Green’s function are held fixed. Δ¯GW0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G0W0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ¯GW0 increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and evGW0 to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches evGW0 quite well and both methods are in good agreement with the experiment.We show that a rigid scissors-like GW self-consistency approach, labeled here Δ¯GW0, can be trivially implemented at zero additional cost for large scale one-shot G0W0 calculations. The method significantly improves one-shot G0W0 and for large systems is very accurate. Δ¯GW0 is similar in spirit to evGW0 where the self-consistency is only applied on the eigenvalues entering Green’s function, while both W and the eigenvectors of Green’s function are held fixed. Δ¯GW0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G0W0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ¯GW0 increases with the system size. For molecules, it ...

We present a linear-response approach for time-dependent density-functional theories using time-adiabatic functionals. The resulting theory can be performed both in the time and in the frequency domain. The derivation considers an impulsive perturbation after which the Kohn-Sham orbitals develop in time autonomously. The equation describing the evolution is not strictly linear in the wave function representation. Only after going into a symplectic real-spinor representation does the linearity make itself explicit. For performing the numerical integration of the resulting equations, yielding the linear response in time, we develop a modified Chebyshev expansion approach. The frequency domain is easily accessible as well by changing the coefficients of the Chebyshev polynomial, yielding the expansion of a formal symplectic Green's operator.

The small-bias conductance of the C6 molecule, stretched between two metallic leads, is studied using time-dependent density functional theory within the adiabatic local density approximation. The leads are modeled by jellium slabs, the electronic density and the current density are described on a grid, whereas the core electrons and the highly oscillating valence orbitals are approximated using standard norm-conserving pseudopotentials. The jellium leads are supplemented by a complex absorbing potential that serves to absorb charge reaching the edge of the electrodes and hence mimic irreversible flow into the macroscopic metal. The system is rapidly exposed to a ramp potential directed along the C6 axis, which gives rise to the onset of charge and current oscillations. As time progresses, a fast redistribution of the molecular charge is observed, which translates into a direct current response. Accompanying the dc signal, alternating current fluctuations of charge and currents within the molecule and the metallic leads are observed. These form the complex impedance of the molecule and are especially strong at the plasmon frequency of the leads and the lowest excitation peak of C6. We study the molecular conductance in two limits: the strong coupling limit, where the edge atoms of the chain are submerged in the jellium and the weak coupling case, where the carbon atoms and the leads do not overlap spatially.

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.

Shifted contour auxiliary field Monte Carlo is implemented for molecular electronic structure using a plane-waves basis and norm conserving pseudopotentials. The merits of the method are studied by computing atomization energies of H2, BeH2, and Be2. By comparing with high correlation methods, DFT-based norm conserving pseudopotentials are evaluated for performance in fully correlated molecular computations. Pseudopotentials based on generalized gradient approximation lead to consistently better atomization energies than those based on the local density approximation, and we find there is room for designing pseudopotentials better suited for full valence correlation.

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 ...

The shifted-contour auxiliary-field Monte Carlo (SCAFMC) approach has been recently developed by Rom, Charutz and Neuhauser as an extension of the auxiliary-field Monte Carlo (AFMC) method. AFMC replaces the difficult fully interacting electrons problem by an ensemble of simpler problems where the electrons interact with a fluctuating electric field but not with each other. SCAFMC is based on shifting the auxiliary-field contour of integration to pass through the (imaginary) stationary point, leading to numerical stability at long propagation times. The new approach converges to the full CI energy in electronic structure calculations (both ground and low-lying excited states). Here we expand the application of SCAFMC from atomic to molecular problems. First, we calculate ground-state energies of a highly correlated transition-metal system (Cr2) with a moderate (12 orbitals) active space size, and demonstrate that SCAFMC is able to extract the energies accurately. In addition, we use SCAFMC to calculate a ...

We apply two hybrid methods for solving scattering problems affected by resonances, to a four-dimensional reactive surface scattering system. In each method the solution of the problem is divided into two parts: a wave packet propagation, and a resonance calculation; results of the resonance calculation are used to extrapolate the long-time behavior of the system. In the first hybrid method, the propagation is by the multistep Chebyshev method, with calculation of resonances performed by the Lanczos method. In the second, the propagation is done using an implementation of the absorbing boundary condition (ABC) evolution operator, and the resonance calculation by filter diagonalization (FDG). Each method produces accurate scattering results in much less computation time than standard long-time wave packet propagation. The Chebyshev–Lanczos approach proves most capable for the calculation of resonances, but is computationally expensive. The ABC–FDG method is much cheaper to implement, but could not be made to extract accurate data for certain broad, overlapping resonances. This was overcome by propagating longer (still much shorter than for long-time propagation) to allow the elusive resonances time to decay.

Filter-diagonalization [M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995)] is a new method for extracting frequencies and damping constants from a short-time segment of any time-dependent signal, whether of quantum origin or not. The method is efficient and able to handle signals with, e.g., millions of (possibly overlapping) frequencies, since it concentrates on specific spectral ranges. The method was shown to be a powerful tool for extracting eigenstates and normal-modes, and for reducing propagation times, in several recent works by us, by Mandelshtam and Taylor (who recently introduced the box filter) and by other groups. Here we extend the method in several directions: first, we show how it can be used with a filter of any form. Next, we show how the methodology may be extended to treat multi-dimensional signals, of the type that appears, e.g., in 2-D nuclear magnetic resonance (NMR). Finally, we exemplify the performance of the various filters for two types of signals where the time-redu...

We present quantitative results on photodissociation of CH2(X 3B1) through the coupled 2A′′ and 3A′′ states. A three-dimensional, hybrid quantum dynamical method was used, employing hyperspherical coordinates. The diabatic potential energy surfaces (PES’s) used in the dynamics were derived from ab initio calculations. A small product fraction (2.7%) was computed for the CH(A 2Δ)+H channel, in agreement with experiment and approximate dynamical calculations. The dissociation proceeds mostly on a A2-like diabatic surface, into CH(a 4Σ−)+H(93.3%) and C(3P)+H2(4.0%). Resonances of widths in the range 0.1–10 meV affect the photodissociation. Pre-exciting a vibrational mode of CH2(X 3B1) prior to photodissociation does not alter the picture, except if the antisymmetric stretch mode is excited: In this case the product fractions for the C(3P)+H2 and CH(A 2Δ)+H channels collapse to values of 1% or lower, and the resonances disappear. Model calculations show that the large product fraction found for CH(a 4Σ−)+H ...

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.

We present a new and more efficient implementation of a hybrid approach to computing the solution of scattering problems affected by resonances. In the computationally expensive part of the calculation, wave packet propagation is used to obtain the time-dependent wave function Ψ(t) up to some time τ at which direct scattering is over. This part is made efficient by using a recently introduced modification for the absorbing boundary conditions evolution operator which allows the use of real operator algebra if the initial wave function is chosen real. In the second part of the calculation, filter diagonalization is used to efficiently obtain the energies, widths, and expansion coefficients of resonances needed to describe the long time behavior of the scattering wave function. This part is made efficient by using a recently introduced algorithm which avoids the storage of energy-dependent basis functions. We demonstrate the application of the method to a two-dimensional reactive scattering problem.

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).

Exact‐dynamics (six‐dimensional) quantum simulations of energy‐resolved initial‐state‐selected rearrangement reaction probabilities are presented for H2(v=0,1,j=0) +OH(v=0,1,j=0) →H+H2O, at J=0, using the time‐dependent reactive‐scattering formalism. A few narrow resonances appear at low reaction energies when the H2 is vibrationally excited, and are shown to be partially associated with the strong‐interaction region (in addition to the asymptotic reagents channel, where the potential has an unphysical well). Vibrational excitation of the OH bond is shown to exhibit little influence on the reaction probabilities. Together with similar results due to Zhang and Zhang (J. Chem. Phys., in press), these are the first initial‐state‐selected simulations of exact‐dynamics four‐atom molecular reactions.

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.

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.

An iterative optimization algorithm for designing laser fields to control molecular motion which utilizes laboratory input (test fields) and output (resulting product yields) information is proposed. Laboratory uncertainties such as laser field noise and limited precision in the product yield measurements are included in the simulations of the experiments. Two simulated examples of implementation of the algorithm are presented: selective electronic excitation in a model four‐state system and maximizing dissociation yield of the hydrogen fluoride molecule. Both examples demonstrate that, even with the inclusion of laboratory uncertainties, the experimental learning‐based algorithm is a potentially feasible method of controlling molecular motion and possibly manipulating chemical reactions.

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.

The possibility of controlling unimolecular–dissociation processes with multiple laser fields in the collisional regime is examined. Employing the Bloch equations to describe optical excitation and decay processes, optimal control theory is used to design amplitude modulated fields which produce the desired excited‐state products. The selectivity of the product distribution of a simple four‐state photodissociation system is shown to have a square‐root dependence on the relative value of the mean dephasing time T2 to the pulse length τ, i.e, (T2/τ)1/2. The equivalence between T2 decay and phase disruptions occurring in a random‐walk fashion is also examined. In the Appendix it is shown that the essential effect of the system temperature is to introduce a Boltzmann population factor on the product selectivity without affecting the nature of the optimal field.

A new paradigm is presented for calculation of reactive state‐to‐state transition amplitudes. The wave function is propagated in one arrangement (either reagents or the sought products, the choice being at one’s convenience); other arrangements are blocked with an absorbing potential. Reactive information is then obtained from the integral expression for the T matrix (〈ψ‖H−H0‖Ψ〉). The approach is exemplified on a collinear system, yielding accurate transition probabilities that are insensitive to the parameters of the absorbing potential. Expressions for the complete T matrix in the new reactive IOS are then derived, based solely on an IOS assumption in one of the arrangements, without a need to invoke matching procedures between different arrangements.

A precise method is presented for measuring decay fractions of metastable cluster ions with corrections concerning instrumental artifacts and ion trajectory of parents and daughters. Experimental data are used to derive the Gspann parameter and heat capacity of clusters as described in Klots' evaporative ensemble model. The model is applied to obtain binding energies of ammonia cluster ions. The deduced binding energy values are in very good agreement with both thermochemical data and Engelking's (1986) modified statistical theory.

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 (time‐independent) approach to the study of atom–diatom reactive collisions in three dimensions. The method is based on the idea of converting a reactive multiarrangement problem into an inelastic single‐arrangement problem. This conversion is done by applying optical potentials which are located at all exits of the reagents arrangement. The reactive transition probabilities are calculated applying flux formulas. The method is reminiscent of a previous time‐dependent method successfully applied for both collinear and three‐dimensional reactive collisions.

We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.

We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H2O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics.

We develop an approach for dynamical (ω > 0) embedding of mixed quantum mechanical (QM)/classical (or more precisely QM/electrodynamics) systems with a quantum sub-region, described by time-dependent density functional theory (TDDFT), within a classical sub-region, modeled here by the recently proposed near-field (NF) method. Both sub-systems are propagated simultaneously and are coupled through a common Coulomb potential. As a first step we implement the method to study the plasmonic response of a metal film which is half jellium-like QM and half classical. The resulting response is in good agreement with both full-scale TDDFT and the purely classical NF method. The embedding method is able to describe the optical response of the whole system while capturing quantum mechanical effects, so it is a promising approach for studying electrodynamics in hybrid molecules-metals nanostructures.

In recent generalized Kohn-Sham (GKS) schemes for density functional theory (DFT) Hartree-Fock type exchange is important. In plane waves and grid approaches the high cost of exchange energy calculations makes these GKS considerably more expensive than Kohn-Sham DFT calculations. We develop a stochastic approach for speeding up the calculation of exchange for large systems. We show that stochastic error per particle does not grow and can even decrease with system size (at a given number of iterations). We discuss several alternative approaches and explain how these ideas can be included in the GKS framework.

We extend the recently developed near-field (NF) method to include an arbitrary number of dielectrics. NF assumes that the dipoles and fields respond instantaneously to the density, without retardation. The central task in NF is the solution of the Poisson equation for every time step, which is here done by a conjugate gradient method which handles any dielectric distribution. The optical response of any metal-dielectric system can now be studied very efficiently in the near field region. The improved NF method is first applied to simple benchmark systems: a gold nanoparticle in vacuum and embedded in silica. The surface plasmons in these systems and their dependence on the dielectrics are reproduced in the new NF approach. As a further application, we study a silver nanoparticle-based structure for the optical detection of a "lipid" (i.e., dielectric) layer in water, where the layer is wrapping around part of the metallic nanostructure. We show the ~0.1-0.15 eV shift in the spectrum due to the presence of the layer, for both spherical and non-spherical (sphere+rod) systems with various polarizations.

We study a time-dependent semiempirical method to determine excitation energies, TD-PM3. This semiempirical method allows large molecules to be treated. A Linear-response Chebyshev approach yields the TD-PM3 spectrum very efficiently. Spectra and excitation energies were tested by comparing it with the results obtained using TD-DFT (Time Dependent-Density Functional Theory), using both small and large basis sets. They were also compared to PM3-CI, Time Dependent-Hartree Fock using the STO-3G basis set, and to experiment. TD-PM3 results generally match better the large-basis set calculations than the small-basis TD-DFT do; excitation energies are almost always accurate to within about 20% or less, except for a few small molecules. Accuracy improves as the molecules get larger.

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.

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-field scanning microscopy and nonlinear spectroscopy on a molecular scale involve weakly interacting subsystems that dynamically exchange electrons and electromagnetic energy. The theoretical description of such processes requires unified approach to the electron-near-field dynamics. By considering electronic structure and dynamics of two distant clusters or atoms we show that adiabatic local spin-density approximation (ALSDA) fails to describe (even qualitatively) essential details of electron dynamics in weakly interacting systems. A recently developed functional addresses these ailments within a time-dependent setting. With this method we study the spectroscopy of a composite system, namely, two weakly coupled metallic clusters. The near-field (dipole-dipole) coupling and electron transfer display an interesting interplay, producing exponential sensitivity of emission yield to the intercomponent distance.

Calculations are presented for the glycine-(H(2)O)(n) (-) (n=0-2) anionic clusters with excess electron, with the glycine core in the canonical or zwitterion form. A variety of conformers are predicted, and their relative energy is examined to estimate thermodynamic stability. The dynamic (proton transfer) pathways between the anionic clusters with the canonical and the zwitterion glycine core are examined. Small barrier heights for isomerization from the zwitterion glycine-(H(2)O)(2) (-) anion to those with canonical glycine core suggest that the former conformers may be kinetically unstable and unfavorable for detection of neutral glycine zwitterion-(H(2)O)(n) (n=1,2) clusters by photodetachment, in accordance with the photoelectron spectroscopic experiments by Bowen and co-workers [Xu et al., J. Chem. Phys. 119, 10696 (2003)]. The calculated stability of the glycine-(H(2)O)(n) (-) anion clusters with canonical glycine core relative to those with zwitterion core indicates that the observation of the anionic conformers with the canonical glycine core would be much more feasible, as revealed by Johnson and co-workers [Diken et al. J. Chem. Phys. 120, 9902 (2004)].

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.

The first successful application of the three-dimensional quantum body frame wave packet approach to reactive scattering is reported for the H + H2 exchange reaction on the LSTH potential surface. The method used is based on a procedure for calculating total reaction probabilities from wave packets. It is found that converged, vibrationally resolved reactive probabilities can be calculated with a grid that is not much larger than required for the pure inelastic calculation. Tabular results are presented for several energies.