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The journal of physical chemistry. A 2009 Dec; 113(52)
Supersymmetric Quantum Mechanics, Excited State Energies and Wave Functions, and the Rayleigh-Ritz Variational Principle: A Proof of Principle Study (dagger).
In addition to ground state wave functions and energies, excited states and their energies are also obtained in a standard Rayleigh-Ritz variational calculation. However, their accuracy is generally much lower. Using the super-symmetric (SUSY) form o... expand abstractf quantum mechanics, we show that better accuracy and more rapid convergence can be obtained by taking advantage of calculations of the ground states of higher sector SUSY Hamiltonians, followed by application of the SUSY "charge operators". Our proof of principle study uses a general family of one-dimensional anharmonic oscillator models. We first obtain the exact, analytic ground states for a general family of anharmonic systems. We give the general, factorized form of the Hamiltonian for the hierarchy that arises in SUSY theory. The "charge" operators can then be used to convert states among the sectors. We illustrate the approach with two specific anharmonic oscillator models. Using the ground state of the second sector Hamiltonian, we show that the corresponding excited state energies and wave functions of the first sector are accurately obtained by applying the charge operators, using significantly smaller basis sets than are required in a standard variational approach applied to the original Schrodinger equation. This is a consequence of the higher accuracy of the Rayleigh-Ritz variational method when applied for ground states. collapse abstract
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The journal of physical chemistry. A 2009 Dec; 113(52)
Supersymmetric approach to excited states.
We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that M... expand abstractonte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schrodinger equation. Since the ground state of each partner potential is nodeless, we avoid any "node" problem typically associated with the Monte Carlo technique. Although we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions. collapse abstract
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The Journal of chemical physics 2009 Nov; 131(19)
Fluorescence depolarization in poly2-methoxy-5-((2-ethylhexyl)oxy)-1,4-phenylenevinylene: sites versus eigenstates hopping.
We report upon a theoretical study of singlet exciton migration and relaxation within a model conjugated polymer chain. Starting from poly[2-methoxy-5-((2-ethylhexyl)oxy)-1,4-phenylenevinylene] polymer chains, we assume that the pi-conjugation is dis... expand abstractrupted by conformational disorder of the chain itself, giving rise to a localized Frenkel exciton basis. Electronic coupling between segments as determined by the coupling between the transition densities of the localized excitons gives rise to delocalized exciton states. Using a kinetic Monte Carlo approach to compute the exciton transfer kinetics within the manifold of either the dressed chromophore site basis or dressed eigenstate basis, we find that the decay of the polarization anisotropy of the exciton is profoundly affected by the delocalization of the exciton over multiple basis segments. Two time scales emerge from the exciton migration simulations: a short, roughly 10 ps, time scale corresponding to rapid hopping about the initial excitation site followed by a slower, 180 ps, component corresponding to long range hopping. We also find that excitations can become trapped at long times when the hopping rate to lower-energy states is longer than the radiative lifetime of the exciton. collapse abstract
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Quantum initial value representations using approximate Bohmian trajectories
Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical a... expand abstractnd the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a {\em local} trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equations of motion are an infinite hierarchy, which we truncate at a given order. We show that time-correlation functions computed using these approximate quantum trajectories can be used to accurately compute the eigenvalue spectrum for various potential systems. collapse abstract
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Quantum tunneling dynamics using hydrodynamic trajectories
In this paper we compute quantum trajectories arising from Bohm's causal description of quantum mechanics. Our computational methodology is based upon a finite-element moving least-squares method (MWLS) presented recently by Wyatt and co-workers (L... expand abstractopreore and Wyatt, Phys. Rev. Lett. {\bf 82}, 5190 (1999)). This method treats the "particles" in the quantum Hamilton-Jacobi equation as Lagrangian fluid elements which carry the phase, $S$, and density, $\rho$, required to reconstruct the quantum wavefunctions. Here, we compare results obtained via the MWLS procedure to exact results obtained either analytically or by numerical solution of the time dependent Schr\"odinger equation. Two systems are considered: firstly, dynamics in a harmonic well and secondly tunneling dynamics in a double well potential. In the case of tunneling in the double well potential, the quantum potential acts to lower the barrier separating the right and left hand sides of the well permitting trajectories to pass from one side to another. However, as probability density passes from one side to the other, the effective barrier begins to rise and eventually will segregate trajectories in one side from the other. We note that the MWLS trajectories exhibited long time stability in the purely harmonic cases. However, this stability was not evident in the barrier crossing dynamics. Comparisons to exact trajectories obtained via wave packet calculations indicate that the MWLS trajectories tend to underestimate the effects of constructive and destructive interference effects. collapse abstract
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J.Chem.Phys. 110 (1999), p.6645-6656
Car-Parrinello Molecular Dynamics on excited state surfaces
This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the electronic excita... expand abstracttion energy of the system, we derive coupled equations of motion for the RPA amplitudes, the single particle orbitals, and the nuclear coordinates. These equations scale linearly with basis size and can be implemented with only a single holonomic constraint. Test calculations on a model two level system give exact agreement with analytical results. Furthermore, we examined the computational efficiency of the method by modeling the excited state dynamics of a one-dimensional polyene lattice. Our results indicate that the present method offers a considerable decrease in computational effort over a straight-forward configuration interaction (singles) plus gradient calculation performed at each nuclear configuration. collapse abstract
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Decoherent Histories and Non-adiabatic Quantum Molecular Dynamics
The role of quantum coherence loss in mixed quantum-classical dynamical systems is explored in the context of the theory of quantum decoherence introduced recently by Bittner and Rossky. (J. Chem. Phys. {\bf 103}, 8130 (1995)). This theory, which i... expand abstracts based upon the consistent histories interpretation of quantum mechanics, introduces decoherence in the quantum subsystem by carefully considering the relevant time and length scales over which one must consider the effects of phase interference between alternative histories of the classical subsystem. Such alternative histories are an integral part of any quantum-classical computational scheme which employ transitions between discrete quantum states; consequently, the coherences between alternative histories have a profound effect on the transition probability between quantum states. In this paper, we review the Bittner-Rossky theory and detail a computational algorithm suitable for large-scale quantum molecular dynamics simulations which implements this theory. Application of the algorithm towards the relaxation of a photoexcited aqueous electron compare well to previous estimates of the excited state survival time as well as to the experimental measurements. collapse abstract
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Many-Body effects and resonances in universal quantum sticking of cold atoms to surfaces
The role of shape resonances and many-body effects on universal quantum sticking of ultra cold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable representation of the Dyson equation. We derive the self... expand abstract-energy renormalization of the the transition amplitude between an ultra cold scattering atom and the bound states on the surface in order to elucidate the role of virtual phonon exchanges in the limiting behavior of the sticking probability. We demonstrate that, to first order in the interactions for finite ranged atom-surface potentials, virtual phonons can only rescale the strength of the atom-surface coupling and do not rescale the range of the coupling. Thus, universal sticking behaviour at ultra-low energies is to be expected for all finite ranged potentials. We demonstrate that the onset of the universal sticking behavior depends greatly on the position of the shape resonance of the renormalized potential and for sufficiently low energy shape resonances, deviations from the universal $s(E)\propto\sqrt{E}$ can occur near these energies. We believe that this accounts for many of the low energy sticking trends observed in the scattering of sub-millikelvin H atoms from superfluid $^4$He films. collapse abstract
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Exact invariant states of the generalized squeezing operator
We explicitly construct the states that are invariant under the action of the generalized squeezing operator $\exp{(z{a^{\dagger}}^k-z^*a^k)}$ with integer $k \geq 3$. There are $k$ such states for a given value of $k$. We show that in the number r... expand abstractepresentation the states behave as $n^{-k/4}$ for large $n$'s. This implies that for any $k\geq3$ the states are normalizable. However, for a given $k$ the expectation values of operators of the form $(a^{\dagger} a)^j$ diverge for the integer $j\geq (k/2-1)$. For $k=3$ we also give an explicit form of these states in the momentum representation in terms of Bessel functions. collapse abstract
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The Journal of chemical physics 2009 Jul; 131(3)
Energy and charge-transfer dynamics using projected modes.
For electron-phonon Hamiltonians with the couplings linear in the phonon operators, we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic degrees of f... expand abstractreedom directly. The modes in the second group interact directly only with the modes in the first group but not with the electronic system. These transformations can be carried out independently for different types of phonon modes, e.g., high- versus low-frequency phonon bands. This construction generalizes recently introduced transformations for systems exhibiting a conical intersection topology. The separation of the normal modes into several groups allows one to develop new approximation schemes. We apply one of such schemes to study electronic relaxation at a semiconducting polymer interface. collapse abstract
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A Supersymmetric Approach to Excited States via Quantum Monte Carlo
We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that... expand abstract Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schr\"odinger equation. Since the ground-state of each partner potential is node-less, we avoid any ``node''-problem typically associated with the Monte Carlo technique. While we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions. collapse abstract
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Phys. Lett. A 373, 2215 (2009)
Hamiltonian approach for the wave packet dynamics: Beyond Gaussian wave functions
It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this approach... expand abstract that include non-Gausssian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion. We compare the Gaussian dynamics with these non-Gaussian extensions for a particle with the quartic potential. collapse abstract
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The journal of physical chemistry. B 2009 Jan; 113(3)
Conformational disorder and ultrafast exciton relaxation in PPV-family conjugated polymers.
We report combined experimental and theoretical studies of excitation relaxation in poly[2-methoxy,5-(2'-ethyl-hexoxy)-1,4-phenylenevinylene] (MEH-PPV), oligophenylenevinylene (OPV) molecules of varying length, and model PPV chains. We build on the p... expand abstractaradigm that the basic characteristics of conjugated polymers are decided by conformational subunits defined by conjugation breaks caused by torsional disorder along the chain. The calculations reported here indicate that for conjugated polymers like those in the PPV family, these conformational subunits electronically couple to neighboring subunits, forming subtly delocalized collective states of nanoscale excitons that determine the polymer optical properties. We find that relaxation among these exciton states can lead to a decay of anisotropy on ultrafast time scales. Unlike in Forster energy transfer, the exciton does not necessarily translate over a large distance. Nonetheless, the disorder in the polymer chain means that even small changes in the exciton size or location has a significant effect on the relaxation pathway and therefore the anisotropy decay. collapse abstract
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On the internal photorelaxation mechanism of DNA
We propose a model for the photo-deactivation mechanism for DNA based upon accurate quantum chemical and molecular dynamical evaluations of model Watson/Crick nucleoside pairs and stacked pairs. Our results corroborate recent ultrafast experimental... expand abstract studies on DNA oligonucleotides and suggest that following photo-excitation to a local $\pi-\pi^*$ state, the excitation is rapidly delocalized over several (3-4) bases on an ultrafast time-scale. However, this delocalized state is unstable with respect to the motions of the protons involved in hydrogen-bonding between Watson/Crick pairs and rapidly re-localizes to a charge-transfer state on a longer time-scale ranging from 10 to 100 ps. This state, too, is unstable and relaxes via a conical intersection with the ground state near the geometry of the enol- and imino-tautomeric form. We suggest that this internal deactivation mechanism is responsible for the intrinsic photostability of DNA. collapse abstract
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Electron transfer dynamics using projected modes
For electron-phonon Hamiltonians with the couplings linear in the phonon operators we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic degrees of ... expand abstractfreedom directly. The modes in the second group interact directly only with the modes in the first group but not with the electronic system. We show that for the $n$-level electronic system the minimum number of modes in the first group is $n_s=(n^2+n-2)/2$. The separation of the normal modes into two groups allows one to develop new approximation schemes. We apply one of such schemes to study exitonic relaxation in a model semiconducting molecular heterojuction. collapse abstract
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J. Photochem. and Photobiol. A 190, 328-334 (2007)
Frenkel Exciton Model of Ultrafast Excited State Dynamics in AT DNA Double Helices
Recent ultrafast experiments have implicated intrachain base-stacking rather than base-pairing as the crucial factor in determining the fate and transport of photoexcited species in DNA chains. An important issue that has emerged concerns whether o... expand abstractr not a Frenkel excitons is sufficient one needs charge-transfer states to fully account for the dynamics. In we present an $SU(2)\otimes SU(2)$ lattice model which incorporates both intrachain and interchain electronic interactions to study the quantum mechanical evolution of an initial excitonic state placed on either the adenosine or thymidine side of a model B DNA poly(dA).poly(dT) duplex. Our calculations indicate that over several hundred femtoseconds, the adenosine exciton remains a cohesive excitonic wave packet on the adenosine side of the chain where as the thymidine exciton rapidly decomposes into mobile electron/hole pairs along the thymidine side of the chain. In both cases, the very little transfer to the other chain is seen over the time-scale of our calculations. We attribute the difference in these dynamics to the roughly 4:1 ratio of hole vs. electron mobility along the thymidine chain. We also show that this difference is is robust even when structural fluctuations are introduced in the form of static off-diagonal disorder. collapse abstract
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Physical review letters 2008 Mar; 100(10)
Phonon-driven ultrafast exciton dissociation at donor-acceptor polymer heterojunctions.
A quantum-dynamical analysis of exciton dissociation at polymer heterojunctions is presented, using a hierarchical electron-phonon model parametrized for three electronic states and 28 vibrational modes. Two representative interfacial configurations ... expand abstractare considered, both of which exhibit an ultrafast exciton decay. The efficiency of the process depends critically on the presence of intermediate bridge states, and on the dynamical interplay of high- vs low-frequency phonon modes. The ultrafast, highly nonequilibrium dynamics is consistent with time-resolved spectroscopic observations. collapse abstract
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In "General Aspects of Free Radical Chemistry", ed. Z. Alfassi, (Wiley 1997)
Numerical Simulations of Free Radical Reactions
We present an overview of the role of quantum coherence in influencing nonadiabatic processes in the condensed phase. Equations of motion for mixed quantum-classical dynamics are derived from the Consistent Histories interpretation of quantum mecha... expand abstractnics. Application of the methods toward computing the excited state lifetime of an excess electron in water and heavy water provides a unique demonstration of our method. collapse abstract
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The Journal of chemical physics 2008 Jan; 128(3)
Calculations of the exciton coupling elements between the DNA bases using the transition density cube method.
Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation ... expand abstractassociated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases. collapse abstract
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The journal of physical chemistry. B 2008 Jan; 112(2)
Phonon-driven exciton dissociation at donor-acceptor polymer heterojunctions: direct versus bridge-mediated vibronic coupling pathways.
We present a molecular-level, quantum dynamical analysis of phonon-driven exciton dissociation at polymer heterojunctions, using a linear vibronic coupling model parametrized for 3 electronic states and 24 vibrational modes. Quantum dynamical simulat... expand abstractions were carried out using the multiconfiguration time-dependent Hartree method. In this study, which significantly extends the two-state model of Tamura et al. (Tamura, H.; Bittner, E. R.; Burghardt, I. J. Chem. Phys. 2007, 126, 021103), we focus on the role of bridge states, which can mediate the decay of the photogenerated exciton and possibly interfere with the direct transition toward an interfacial charge-separated state. Both the direct and bridge-mediated pathways are found to depend critically on the dynamical interplay of high-frequency C=C stretch modes and low-frequency ring-torsional modes. The dynamical mechanism is interpreted in terms of a hierarchical electron-phonon model, leading to the identification of generalized reaction coordinates for the nonadiabatic process. Variation of the vibronic coupling model parameters in a realistic range provides evidence that the direct exciton decay pathway is not dynamically robust, and bridge-mediated pathways can become dominant. The ultrafast, coherent dynamics is of pronounced nonequilibrium character and cannot be modeled by conventional kinetic equations. The predicted femtosecond to picosecond decay times are consistent with time-resolved spectroscopic observations. collapse abstract
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The journal of physical chemistry. A 2007 Oct; 111(41)
Thermodynamics of atomic clusters using variational quantum hydrodynamics.
Small clusters of rare-gas atoms are ideal test cases for studying how quantum delocalization affects both the thermodynamics and the structure of molecular scale systems. In this paper, we use a variational quantum hydrodynamic approach to examine t... expand abstracthe structure and dynamics of (Ne)n clusters, with n up to 100 atoms, at both T = 0 K and for temperatures spanning the solid-to-liquid transition in bulk Ne. Finite temperature contributions are introduced to the grand potential in the form of an "entropy" potential. One surprising result is the prediction of a negative heat capacity for very small clusters that we attribute to the nonadditive nature of the total free-energy for very small systems. collapse abstract
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The Journal of chemical physics 2007 Jul; 127(3)
Nonadiabatic quantum dynamics based on a hierarchical electron-phonon model: exciton dissociation in semiconducting polymers.
A hierarchical electron-phonon coupling model is applied to describe the ultrafast decay of a photogenerated exciton at a donor-acceptor polymer heterojunction, via a vibronic coupling mechanism by which a charge-localized interfacial state is create... expand abstractd. Expanding upon an earlier Communication [H. Tamura et al., J. Chem. Phys. 126, 021103 (2007)], we present a quantum dynamical analysis based on a two-state linear vibronic coupling model, which accounts for a two-band phonon bath including high-frequency C[Double Bond]C stretch modes and low-frequency ring torsional modes. Building upon this model, an analysis in terms of a hierarchical chain of effective modes is carried out, whose construction is detailed in the present paper. Truncation of this chain at the order n (i.e., 3n+3 modes) conserves the Hamiltonian moments (cumulants) up to the (2n+3)rd order. The effective-mode analysis highlights (i) the dominance of the high-frequency modes in the coupling to the electronic subsystem and (ii) the key role of the low-frequency modes in the intramolecular vibrational redistribution process that is essential in mediating the decay to the charge-localized state. Due to this dynamical interplay, the effective-mode hierarchy has to be carried beyond the first order in order to obtain a qualitatively correct picture of the nonadiabatic process. A reduced model of the dynamics, including a Markovian closure of the hierarchy, is presented. Dynamical calculations were carried out using the multiconfiguration time-dependent Hartree method. collapse abstract
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Energy relaxation dynamics and universal scaling laws in organic light emitting diodes
Electron-hole (e-h) capture in luminescent conjugated polymers (LCPs) is modeled by the dissipative dynamics of a multilevel electronic system coupled to a phonon bath. Electroinjected e-h pairs are simulated by a mixed quantum state, which relaxes... expand abstract via phonon-driven internal conversions to low-lying charge-transfer (CT) and excitonic (XT) states. The underlying two-band polymer model reflects PPV and spans monoexcited configuration interaction singlets (S) and triplets (T), coupled to Franck-Condon active C=C stretches and ring-torsions. Focusing entirely upon long PPV chains, we consider the recombination kinetics of an initially separated CT pair. Our model calculations indicated that S and T recombination proceeds according to a branched, two-step mechanism dictated by near e-h symmetry. The initial relaxation occurs rapidly with nearly half of the population going into excitons ($S_{XT}$ or $T_{XT}$), while the remaining portion remains locked in metastable CT states. While formation rates of $S_{CT}$ and $T_{CT}$ are nearly equal, $S_{XT}$ is formed about twice as fast $T_{XT}$ in concurrence with experimental observations of these systems. Furthermore, breaking e-h symmetry suppresses the XT to CT branching ratio for triplets and opens a slow CT$\to$ XT conversion channel exclusively for singlets due to dipole-dipole interactions between geminate and non-geminate configurations. Finally, our calculations yield a remarkable linear relation between chain length and singlet/triplet branching ratio which can be explained in terms of the binding energies of the respective final excitonic states and the scaling of singlet-triplet energy gap with chain length. collapse abstract
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Interplay between the repulsive and attractive interaction and the spacial dimensionality of an excess electron in a simple fluid
The behavior of an excess electron in a one, two and three dimensional classical liquid has been studied with the aid of Chandler, Singh and Richardson (CSR) theory [J. Chem. Phys. {\bf 81} 1975 (1984)] . The size or dispersion of the wavepacket as... expand abstractsociated with the solvated electron is very sensitive to the interaction between the electron and fluid atoms, and exhibits complicated behavior in its density dependence. The behavior is interpreted in terms of an interplay among four causes: the excluded volume effect due to solvent, the pair attractive interaction between the electron and a solvent atom, the thermal wavelength of the electron ($\lambda_e$), a balance of the attractive interactions from different solvent atoms and the range of repulsive interaction between electron and solvent atom. Electron self-trapping behavior in all the dimensions has been studied for the same solvent-solvent and electron-solvent interaction potential and the results are presented for the same parameter in every dimension to show the comparison between the various dimensions. collapse abstract
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Current producing states in molecular semiconductors: photo-current from a molecular wire
We present a methodology for computing photocurrent production in molecular semiconducting molecules. Our model combines a single-configuration interaction picture with the Schwinger-Keldysh non-equilibrium Greens function approach to compute the c... expand abstracturrent response of a molecular semi-conducting wire following excitation. We give detailed analysis of the essential excitonic, charge-transfer, and dipole states for poly-(phenylenevinylene) chains of length 32 and 48 repeat units under an electric field bias and use this to develop a reduced dimensional tunneling model which accounts for chain-length and field-dependent behavior. collapse abstract
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