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Articles 1 - 13 of 13
Full-Text Articles in Biological and Chemical Physics
The Schrödinger Equation With Friction From The Quantum Trajectory Perspective, Sophya V. Garashchuk, Vaibhav Dixit, Bing Gu, James Mazzuca
The Schrödinger Equation With Friction From The Quantum Trajectory Perspective, Sophya V. Garashchuk, Vaibhav Dixit, Bing Gu, James Mazzuca
Faculty Publications
Similarity of equations of motion for the classical and quantum trajectories is used to introduce afriction term dependent on the wavefunction phase into the time-dependent Schrödingerequation. The term describes irreversible energy loss by the quantum system. The force offriction is proportional to the velocity of a quantum trajectory. The resulting Schrödinger equationis nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of …
Modeling The Noble Metal/Tio2 (110) Interface With Hybrid Dft Functionals: A Periodic Electrostatic Embedded Cluster Model Study, Salai Cheettu Ammal, Andreas Heyden
Modeling The Noble Metal/Tio2 (110) Interface With Hybrid Dft Functionals: A Periodic Electrostatic Embedded Cluster Model Study, Salai Cheettu Ammal, Andreas Heyden
Faculty Publications
The interaction of Aun and Ptn (n=2,3) clusters with the stoichiometric and partially reduced rutile TiO2 (110) surfaces has been investigated using periodic slab and periodic electrostatic embedded cluster models. Compared to Au clusters, Pt clusters interact strongly with both stoichiometric and reduced TiO2 (110) surfaces and are able to enhance the reducibility of the TiO2 (110) surface, i.e., reduce the oxygen vacancy formation energy. The focus of this study is the effect of Hartree–Fock exchange on the description of the strength of chemical bonds at the interface of Au/Pt clusters and the TiO2 (110) surface. Hartree–Fock exchange helps describing …
Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk
Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk
Faculty Publications
In the de Broglie–Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant …
Geminal Model Chemistry Ii. Perturbative Corrections, V. A. Rassolov, F. Xu, Sophya V. Garashchuk
Geminal Model Chemistry Ii. Perturbative Corrections, V. A. Rassolov, F. Xu, Sophya V. Garashchuk
Faculty Publications
We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein–Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, …
Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov
Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov
Faculty Publications
We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare …
Semiclassical Application Of The Mo/Ller Operators In Reactive Scattering, Sophya V. Garashchuk, J. C. Light
Semiclassical Application Of The Mo/Ller Operators In Reactive Scattering, Sophya V. Garashchuk, J. C. Light
Faculty Publications
Mo/ller operators in the formulation of reaction probabilities in terms of wave packet correlation functions allow us to define the wave packets in the interaction region rather than in the asymptotic region of the potential surface. We combine Mo/ller operators with the semiclassical propagator of Herman and Kluk. This does not involve further approximations and can be used with any initial value representation (IVR) semiclassical propagator. Time propagation in asymptotic regions of the potential due to Mo/ller operators reduces the oscillations of the propagator integrand and improves convergence of the results with respect to the number of trajectories. The effectiveness …
Quasirandom Distributed Gaussian Bases For Bound Problems, Sophya V. Garashchuk, J. C. Light
Quasirandom Distributed Gaussian Bases For Bound Problems, Sophya V. Garashchuk, J. C. Light
Faculty Publications
We introduce quasirandom distributed Gaussian bases (QDGB) that are well suited for bound problems. The positions of the basis functions are chosen quasirandomly while their widths and density are functions of the potential. The basis function overlap and kinetic energy matrix elements are analytical. The potential energy matrix elements are accurately evaluated using few-point quadratures, since the Gaussian basis functions are localized. The resulting QDGB can be easily constructed and is shown to be accurate and efficient for eigenvalue calculation for several multidimensional model vibrational problems. As more demanding examples, we used a 2D QDGB-DVR basis to calculate the lowest …
Simplified Calculation Of The Stability Matrix For Semiclassical Propagation, Sophya V. Garashchuk, J. C. Light
Simplified Calculation Of The Stability Matrix For Semiclassical Propagation, Sophya V. Garashchuk, J. C. Light
Faculty Publications
We present a simple method of calculation of the stability (monodromy) matrix that enters the widely used semiclassical propagator of Herman and Kluk and almost all other semiclassical propagators. The method is based on the unitarity of classical propagation and does not involve any approximations. The number of auxiliary differential equations per trajectory scales linearly rather than quadratically with the system size. Just the first derivatives of the potential surface are needed. The method is illustrated on the collinear H3 system.
Cumulative Reaction Probability In Terms Of Reactant-Product Wave Packet Correlation Functions, Sophya V. Garashchuk, D. J. Tannor
Cumulative Reaction Probability In Terms Of Reactant-Product Wave Packet Correlation Functions, Sophya V. Garashchuk, D. J. Tannor
Faculty Publications
We present new expressions for the cumulative reaction probability (N(E)), cast in terms of time-correlation functions of reactant and product wave packets. The derivation begins with a standard trace expression for the cumulative reaction probability, expressed in terms of the reactive scattering matrix elements in an asymptotic internal basis. By combining the property of invariance of the trace with a wave packet correlation function formulation of reactive scattering, we obtain an expression for N(E) in terms of the correlation matrices of incoming and outgoing wave packets which are arbitrary in the internal coordinates. This formulation, like other recent formulations of …
Correlation Function Formulation For The State Selected Total Reaction Probability, Sophya V. Garashchuk, D. J. Tannor
Correlation Function Formulation For The State Selected Total Reaction Probability, Sophya V. Garashchuk, D. J. Tannor
Faculty Publications
A correlation function formulation for the state-selected total reaction probability, Nα(E), is suggested. A wave packet, correlating with a specific set of internal reactant quantum numbers, α, is propagated forward in time until bifurcation is complete at which time the nonreactive portion of the amplitude is discarded. The autocorrelation function of the remaining amplitude is then computed and Fourier transformed to obtain a reactivity spectrum. Dividing by the corresponding spectrum of the original, unfiltered, wave packet normalizes the reactivity spectrum, yielding the total reaction probability from the internal state, α. The procedure requires negligible storage and just one time-energy Fourier …
Π-Systems As Lithium/Hydrogen Bond Acceptors: Some Theoretical Observations, Salai Cheettu Ammal, P. Venuvanalingam
Π-Systems As Lithium/Hydrogen Bond Acceptors: Some Theoretical Observations, Salai Cheettu Ammal, P. Venuvanalingam
Faculty Publications
Ab initio calculations at the Hartree–Fock and correlated levels and density functional theory calculations have been performed with 6-31++G(d,p) and 6-311++G(d,p)basis sets on LiF and HF complexes of benzene, ethylene, and acetylene. Complex binding energies have been corrected for basis set superposition error, and zero point energy corrections have been done on Hartree–Fock binding energies. Computed results indicate that the complexes exist in different conformations and among them those with π-lithium and π-hydrogen bonds are the most stable. π-lithium bonds are stronger than π-hydrogen bonds. The computed binding energies and geometry of HF complexes correlate well with the available experimental …
Semiclassical Approach To The Hydrogen-Exchange Reaction Reactive And Transition-State Dynamics, Sophya V. Garashchuk, F. Grossmann, D. Tannor
Semiclassical Approach To The Hydrogen-Exchange Reaction Reactive And Transition-State Dynamics, Sophya V. Garashchuk, F. Grossmann, D. Tannor
Faculty Publications
Scattering matrix elements and symmetric transition-state resonances for the collinear H 2 + H → H + H 2 reaction are obtained using a time-dependent approach. The correlation function between reactant channel wavepackets and product channel wavepackets is used to determine the S-matrix elements. In a similar fashion, autocorrelation functions are used to extract the positions and widths of transition-state resonances. The time propagation of the wavepackets is performed by the improved semiclassical frozen Gaussian method of Herman and Kluk, which is an initial value, uniformly converged method. The agreement between the quantum and semiclassical results is far better …
Lithium Bonding Interaction In H2Cy⋯Lif (Y=O,S) Complexes: A Theoretical Probe, Salai Cheettu Ammal, P. Venuvanalingam, S. Pal
Lithium Bonding Interaction In H2Cy⋯Lif (Y=O,S) Complexes: A Theoretical Probe, Salai Cheettu Ammal, P. Venuvanalingam, S. Pal
Faculty Publications
Ab initio calculations at 6-31++G(d,p) level have been done on H2CY⋯LiF (Y=O,S) complexes choosing ten possible orientations in each complex. The effect of correlation on complex binding energies has been studied via single point MP2 (full) calculations done on 6-31++G(d,p) geometry. Binding energies have been corrected for basis set superposition error. Frequency calculations confirm that H2CO⋯LiF and H2CS⋯LiF complexes have three and two stable forms, respectively. The most stable form in each complex has been found to have a strong lithium bonding interaction and a secondary hydrogen bondinginteraction. NBO analysis has revealed that in this form oxygen donates nσ lone …