Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids

Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motions in liquids, typically spanning no more than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent can absorb any vibrational energy within this "band", but how is it that molecules can rid themselves of superfluous vibrational energies significantly in excess of these values? We develop a theory for such processes based on the idea that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate -- and that by far the most important of these motions are those involving what we have called the mutual nearest neighbors of the vibrating solute. Specifically, we suggest that whenever there is a single solvent molecule sufficiently close to the solute that the solvent and solute are each other's nearest neighbors, then the instantaneous scattering dynamics of the solute-solvent pair alone suffices to explain the high frequency relaxation. The many-body features of the liquid only appear in the guise of a purely equilibrium problem, that of finding the likelihood of particularly effective solvent arrangements around the solute. These results are tested numerically on model diatomic solutes dissolved in atomic fluids (including the experimentally and theoretically interesting case of I_2 in Xe). The instantaneous pair theory leads to results in quantitative agreement with those obtained from far more laborious exact molecular dynamics simulations.Comment: 55 pages, 6 figures Scheduled to appear in J. Chem. Phys., Jan, 199

Why TiSe2_2 is a band insulator

In its crystalline form, TiSe$_2$ is thought to be an insulator with a bandgap of ~0.1-0.2 eV. This materials system has attracted a much interest because of its rich array of unique properties. It forms a charge density wave (CDW) in both bulk and monolayer form, and there has been wide speculation that TiSe$_2$ is a rare realisation of an excitonic insulator. Using a self-consistent form of many body perturbation theory, we establish that TiSe$_2$ is a band insulator, but it is only nonmetallic as a consequence of fluctuations in nuclear positions about its nominally high-symmetry (P-3m1) phase. Below 200 K, TiSe$_2$ undergoes a transition to a charge density-wave (P-3c1) phase, which activates coupling between states near the Fermi level and causes a gap to form. Above 200 K the nominal P-3m1 symmetry represents only a time average of the true configuration. Dynamics in the nuclear configuration are responsible for TiSe$_2$ being nonmetallic. We demonstrate this through a combination of molecular dynamics and the Self-consistent Quasiparticle Approximation. We further establish that ladder diagrams included in the polarizability (which includes the mechanism needed to form an excitonic insulator) are of little importance

The structure of the hydrated electron. Part 2. A mixed quantum classical molecular dynamics - embedded cluster density functional theory: single-excitation configuration interaction study

Adiabatic mixed quantum/classical molecular dynamics simulations were used to generate snapshots of the hydrated electron (e-) in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the e- were extracted from these simulations and embedded in a matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory and single-excitation configuration interaction methods were then applied to these embedded clusters. The salient feature of these hybrid calculations is significant transfer (ca. 0.18) of the excess electron's charge density into the O 2p orbitals in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfc) tensors, and the IR and Raman spectra of the e-. The calculated hfc tensors were used to compute the EPR and ESEEM spectra for the e- that compared favorably to the experimental spectra of trapped e- in alkaline ice. The calculated vibrational spectra of the e- are consistent with the red-shifted bending and stretching frequencies observed in resonance Raman experiments. The model also accounts for the VIS and 190-nm absorption bands of the e-. Thus, our study suggests that to explain several important experimentally observed properties of the e-, many-electron effects must be accounted for.Comment: 68 pages, 12 figures + 16 more figures in the supplement (included) submitted to J Phys Chem

Efficient real-space configuration-interaction method for the simulation of multielectron mixed quantum and classical nonadiabatic molecular dynamics in the condensed phase

We introduce an efficient configuration interaction (CI) method for the calculation of mixed quantum and classical nonadiabatic molecular dynamics for multiple electrons. For any given realization of the classical degrees of freedom (e.g., a solvent), the method uses a novel real-space quadrature to efficiently compute the Coulomb and exchange interactions between electrons. We also introduce an approximation whereby the classical molecular dynamics is propagated for several time steps on electronic potential energy surfaces generated using only a particularly important subset of the CI basis states. By only updating the important-states subset periodically, we achieve significant reductions in the computational cost of solving the multielectron quantum problem. We test the real-space quadrature for the cases of two electrons confined in a cubic box with infinitely repulsive walls and two electrons dissolved in liquid water that occupy a single cavity, so-called hydrated dielectrons. We then demonstrate how to perform mixed quantum and classical nonadiabatic dynamics by combining these computational techniques with the mean-field with surface hopping algorithm of Prezhdo and Rossky [J. Chem. Phys. 107, 825 (1997)]. Finally, we illustrate the practicality of the approach to multielectron nonadiabatic dynamics by examining the nonadiabatic relaxation dynamics of both spin singlet and spin triplet hydrated dielectrons following excitation from the ground to the first excited state. (C) 2003 American Institute of Physics

More than a cognitive experience: unfamiliarity, invalidation, and emotion in organizational learning

Literature on organizational learning (OL) lacks an integrative framework that captures the emotions involved as OL proceeds. Drawing on personal construct theory, we suggest that organizations learn where their members reconstrue meaning around questions of strategic significance for the organization. In this 5-year study of an electronics company, we explore the way in which emotions change as members perceive progress or a lack of progress around strategic themes. Our framework also takes into account whether OL involves experiences that are familiar or unfamiliar and the implications for emotions. We detected similar patterns of emotion arising over time for three different themes in our data, thereby adding to OL perspectives that are predominantly cognitive in orientation

The role of electronic symmetry in charge-transfer-to-solvent reactions: Quantum nonadiabatic computer simulation of photoexcited sodium anions

Since charge-transfer-to-solvent (CTTS) reactions represent the simplest class of solvent-driven electron transfer reactions, there has been considerable interest in understanding the solvent motions responsible for electron ejection. The major question that we explore in this paper is what role the symmetry of the electronic states plays in determining the solvent motions that account for CTTS. To this end, we have performed a series of one-electron mixed quantum/classical nonadiabatic molecular dynamics simulations of the CTTS dynamics of sodide, Na-, which has its ground-state electron in an s orbital and solvent-supported CTTS excited states of p-like symmetry. We compare our simulations to previous theoretical work on the CTTS dynamics of the aqueous halides, in which the ground state has the electron in a p orbital and the CTTS excited state has s-like symmetry. We find that the key motions for Na- relaxation involve translations of solvent molecules into the node of the p-like CTTS excited state. This solvation of the electronic node leads to migration of the excited CTTS electron, leaving one of the p-like lobes pinned to the sodium atom core and the other extended into the solvent; this nodal migration causes a breakdown of linear response. Most importantly, for the nonadiabatic transition out of the CTTS excited state and the subsequent return to equilibrium, we find dramatic differences between the relaxation dynamics of sodide and the halides that result directly from differences in electronic symmetry. Since the ground state of the ejected electron is s-like, detachment from the s-like CTTS excited state of the halides occurs directly, but detachment cannot occur from the p-like CTTS excited state of Na- without a nonadiabatic transition to remove the node. Thus, unlike the halides, CTTS electron detachment from sodide occurs only after relaxation to the ground state and is a relatively rare event. In addition, the fact that the electronic symmetry of sodide is the same as for the hydrated electron enables us to directly study the effect of a stabilizing atomic core on the properties and solvation dynamics of solvent-supported electronic states. All the results are compared to experimental work on Na- CTTS dynamics, and a unified picture for the electronic relaxation for solvent-supported excited states of any symmetry is presented. (C) 2003 American Institute of Physics

Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrodinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems. (c) 2005 American Institute of Physics

Alpha-Vacua, Black Holes, and AdS/CFT

The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola-Allen transform on the modes associated with the Hartle-Hawking, or Euclidean, vacuum. These vacua are the `alpha'-vacua for these black holes. The causal structure of a typical black hole may ameliorate certain difficulties which are encountered in the case of de Sitter alpha-vacua. For Schwarzschild-AdS black holes, a Bogoliubov transformation which mixes operators of the two boundary CFT's provides a construction of the dual CFT alpha-states. Finally, we analyze the thermal properties of these vacua.Comment: 40 pages REVTeX and AMSLaTeX, 17 black&white eps figures. v3: references added. v4: details of the pinch singularity avoidance for the string quantization of the Rindler space toy model have been added in both the body of the paper and in a new 7 page appendix. Other clarifications and references added. This is the version accepted for publication in Class. Quant. Gra