Finite expansion of the inverse matrix in the polarization propagator method

 An alternative theoretical approach to the polarization propagator based on a new finite expansion of a finite-dimensional matrix is presented. The general equations for such an expansion are derived and the validity conditions stated. This method is used to accomplish an approximate scheme for the self-energy of the particle–hole propagator within the superoperator formalism. Within this scheme each contribution includes corrections to infinite order in electronic interaction and so describes collective effects in a natural way. Individual contributions can be interpreted as describing the propagation of the interaction through a particular subset of electronic excitations. Comparison with other known approximation levels, such as the random-phase approximation, is also analyzed. Received: 14 February 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

Path integral ground state with a fourth-order propagator: application to condensed helium

Ground state properties of condensed helium are calculated using the path integral ground state (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other quantum Monte Carlo (QMC) techniques and different propagators. For this particular application, we find that the fourth-order propagator performs comparably to the pair product approximation, and is far superior to the primitive approximation. Results obtained for the equation of state of condensed helium show that PIGS compares favorably to other QMC methods traditionally utilized for this type of calculation.     

On the properties of a primitive semiclassical surface hopping propagator for nonadiabatic quantum dynamics

A previously developed nonadiabatic semiclassical surface hopping propagator [M. F. Herman J. Chem. Phys. 103, 8081 (1995)] is further studied. The propagator has been shown to satisfy the time-dependent Schrodinger equation (TDSE) through order h, and the O(h2) terms are treated as small errors, consistent with standard semiclassical analysis. Energy is conserved at each hopping point and the change in momentum accompanying each hop is parallel to the direction of the nonadiabatic coupling vector resulting in both transmission and reflection types of hops. Quantum mechanical analysis and numerical calculations presented in this paper show that the h2 terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the h2 terms are analyzed for the nonadiabatic semiclassical propagator. It is shown that the propagator can satisfy the TDSE for multidimensional systems by including another type of nonclassical trajectories that reflect on the same surfaces. This h2 analysis gives three conditions for these three types of trajectories so that their coefficients are uniquely determined. Besides the nonadiabatic semiclassical propagator, a numerically useful quantum propagator in the adiabatic representation is developed to describe nonadiabatic transitions.     

Finite temperature string method for the study of rare events

A method is presented for the study of rare events such as conformational changes arising in activated processes whose reaction coordinate is not known beforehand and for which the assumptions of transition state theory are invalid. The method samples the energy landscape adaptively and determines the isoprobability surfaces for the transition: by definition the trajectories initiated anywhere on one of these surfaces has equal probability to reach first one metastable set rather than the other. Upon weighting these surfaces by the equilibrium probability distribution, one obtains an effective transition pathway, i.e., a tube in configuration space inside which conformational changes occur with high probability, and the associated rate. The method is first validated on a simple two-dimensional example; then it is applied to a model of solid-solid transformation of a condensed system.     

Statistical temperature molecular dynamics: application to coarse-grained beta-barrel-forming protein models

Recently the authors proposed a novel sampling algorithm, "statistical temperature molecular dynamics" (STMD) [J. Kim et al., Phys. Rev. Lett. 97, 050601 (2006)], which combines ingredients of multicanonical molecular dynamics and Wang-Landau sampling. Exploiting the relation between the statistical temperature and the density of states, STMD generates a flat energy distribution and efficient sampling with a dynamic update of the statistical temperature, transforming an initial constant estimate to the true statistical temperature T(U), with U being the potential energy. Here, the performance of STMD is examined in the Lennard-Jones fluid with diverse simulation conditions, and in the coarse-grained, off-lattice BLN 46-mer and 69-mer protein models, exhibiting rugged potential energy landscapes with a high degree of frustration. STMD simulations combined with inherent structure (IS) analysis allow an accurate determination of protein thermodynamics down to very low temperatures, overcoming quasiergodicity, and illuminate the transitions occurring in folding in terms of the energy landscape. It is found that a thermodynamic signature of folding is significantly suppressed by accurate sampling, due to an incoherent contribution from low-lying non-native IS in multifunneled landscapes. It is also shown that preferred accessibility to such IS during the collapse transition is intimately related to misfolding or poor foldability.     

Molecular dynamics study to identify the reactive sites of a liquid squalane surface

Molecular dynamics simulations of liquid squalane, C30H62, were performed, focusing in particular on the liquid-vacuum interface. These theoretical studies were aimed at identifying potentially reactive sites on the surface, knowledge of which is important for a number of inelastic and reactive scattering experiments. A united atom force field (Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1999, 103, 4508-4517) was used, and the simulations were analyzed with respect to their interfacial properties. A modest but clearly identifiable preference for methyl groups to protrude into the vacuum has been found at lower temperatures. This effect decreases when going to higher temperatures. Additional simulations tracking the flight paths of projectiles directed at a number of randomly chosen surfaces extracted from the molecular dynamics simulations were performed. The geometrical parameters for these calculations were chosen to imitate a typical abstraction reaction, such as the reaction between ground-state oxygen atoms and hydrocarbons. Despite the preference for methyl groups to protrude further into the vacuum, Monte Carlo tracking simulations suggest, on geometric grounds, that primary and secondary hydrogen atoms are roughly equally likely to react with incoming gas-phase atoms. These geometric simulations also indicate that a substantial fraction of the scattered products is likely to undergo at least one secondary collision with hydrocarbon side chains. These results help to interpret the outcome of previous measurements of the internal and external energy distribution of the gas-phase OH products of the interfacial reaction between oxygen atoms and liquid squalane.     

Independent trajectory implementation of the semiclassical Liouville method: application to multidimensional reaction dynamics

We describe an independent trajectory implementation of semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, a single ensemble of trajectories describes all semiclassical density matrix elements of a coupled electronic state problem, with the ensemble evolving classically under a single reference Hamiltonian chosen on the basis of physical grounds. In this paper, we introduce an additional uncoupled trajectory approximation, allowing the members of the ensemble to evolve independently of one another and eliminating the major computational costs of our previous coupled trajectory implementation. The accuracy of the method is demonstrated for model one-dimensional problems. In addition, the approach is applied to the chemical reaction dynamics of a collinear triatomic system, yielding excellent agreement with exact calculations. This method allows molecular dynamics involving coupled electronic surfaces to be modeled with essentially the same effort as classical molecular dynamics and ensemble averaging.     

Hybrid coupled cluster and molecular dynamics approach: application to the excitation spectrum of cytosine in the native DNA environment

Evolution of the excited state energies of cytosine base in the native DNA environment was investigated using a hybrid coupled cluster and classical molecular dynamics approach. The time averaged excitation energies obtained with the variant of the completely renormalized equation-of-motion with singles, doubles, and non-iterative triples approach that includes a bulk of the correlation effects for excited states, are compared with the analogous calculations in the gas phase. Significant blue shifts for the two lowest singlet excitation energies can be observed as a result of the interaction of the quantum system with the surrounding environment.     

Proton transfer reactions in model condensed-phase environments: Accurate quantum dynamics using the multilayer multiconfiguration time-dependent Hartree approach

The recently proposed multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) approach to evaluating reactive quantum dynamics is applied to two model condensed-phase proton transfer reactions. The models consist of a one-dimensional double-well "system" that is bilinearly coupled to a "bath" of harmonic oscillators parameterized to represent a condensed-phase environment. Numerically exact quantum-mechanical flux correlation functions and thermal rate constants are obtained for a broad range of temperatures and system-bath coupling strengths, thus demonstrating the efficacy of the ML-MCTDH approach. Particular attention is focused on the regime where low temperatures are combined with weak system-bath coupling. Under such conditions it is found that long propagation times are often required and that quantum coherence effects may prevent a rigorous determination of the rate constant.     

Modeling the sorption dynamics of NaH using a reactive force field

We have parametrized a reactive force field for NaH, ReaxFF(NaH), against a training set of ab initio derived data. To ascertain that ReaxFF(NaH) is properly parametrized, a comparison between ab initio heats of formation of small representative NaH clusters with ReaxFF(NaH) was done. The results and trend of ReaxFF(NaH) are found to be consistent with ab initio values. Further validation includes comparing the equations of state of condensed phases of Na and NaH as calculated from ab initio and ReaxFF(NaH). There is a good match between the two results, showing that ReaxFF(NaH) is correctly parametrized by the ab initio training set. ReaxFF(NaH) has been used to study the dynamics of hydrogen desorption in NaH particles. We find that ReaxFF(NaH) properly describes the surface molecular hydrogen charge transfer during the abstraction process. Results on heat of desorption versus cluster size shows that there is a strong dependence on the heat of desorption on the particle size, which implies that nanostructuring enhances desorption process. To gain more insight into the structural transformations of NaH during thermal decomposition, we performed a heating run in a molecular dynamics simulation. These runs exhibit a series of drops in potential energy, associated with cluster fragmentation and desorption of molecular hydrogen. This is consistent with experimental evidence that NaH dissociates at its melting point into smaller fragments.     

A new method for solving the quantum hydrodynamic equations of motion: application to two-dimensional reactive scattering

The de Broglie-Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian-Eulerian frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.     

Exploring the role of decoherence in condensed-phase nonadiabatic dynamics: a comparison of different mixed quantum/classical simulation algorithms for the excited hydrated electron

Mixed quantum/classical (MQC) molecular dynamics simulation has become the method of choice for simulating the dynamics of quantum mechanical objects that interact with condensed-phase systems. There are many MQC algorithms available, however, and in cases where nonadiabatic coupling is important, different algorithms may lead to different results. Thus, it has been difficult to reach definitive conclusions about relaxation dynamics using nonadiabatic MQC methods because one is never certain whether any given algorithm includes enough of the necessary physics. In this paper, we explore the physics underlying different nonadiabatic MQC algorithms by comparing and contrasting the excited-state relaxation dynamics of the prototypical condensed-phase MQC system, the hydrated electron, calculated using different algorithms, including: fewest-switches surface hopping, stationary-phase surface hopping, and mean-field dynamics with surface hopping. We also describe in detail how a new nonadiabatic algorithm, mean-field dynamics with stochastic decoherence (MF-SD), is to be implemented for condensed-phase problems, and we apply MF-SD to the excited-state relaxation of the hydrated electron. Our discussion emphasizes the different ways quantum decoherence is treated in each algorithm and the resulting implications for hydrated-electron relaxation dynamics. We find that for three MQC methods that use Tully's fewest-switches criterion to determine surface hopping probabilities, the excited-state lifetime of the electron is the same. Moreover, the nonequilibrium solvent response function of the excited hydrated electron is the same with all of the nonadiabatic MQC algorithms discussed here, so that all of the algorithms would produce similar agreement with experiment. Despite the identical solvent response predicted by each MQC algorithm, we find that MF-SD allows much more mixing of multiple basis states into the quantum wave function than do other methods. This leads to an excited-state lifetime that is longer with MF-SD than with any method that incorporates nonadiabatic effects with the fewest-switches surface hopping criterion.     

Renormalization of the frozen Gaussian approximation to the quantum propagator

The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining "on the fly" quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to "on the fly" computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable "on the fly"; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.     

Influence of temperature and headgroup size on condensed-phase patterns in langmuir monolayers of some oxyethylenated nonionic surfactants

The surface phase behavior in Langmuir monolayers of some oxyethylenated nonionic surfactants of the general formula C16En, with n = 1, 2, 3, and 4, at the air-water interface has been studied by film balance and Brewster angle microscopy (BAM) over a wide range of temperatures. The C16E4 monolayers cannot show any indicative features of phase transition because of strong dipolar as well as hydration-induced repulsive interactions between the bulky headgroups. On the other hand, the monolayers of C16E1, C16E2, and C16E3 show a sharp cusp point followed by a pronounced plateau region in their respective isotherms with subsequent formation of a variety of structures in the two-phase coexistence region between the liquid expanded (LE) and liquid condensed (LC) phases at different temperatures. As usually observed, the domains of C16E1, which bears only one ethylene oxide (EO) unit in the headgroup, are circular at lower temperatures while fractal at higher temperatures. On the other hand, those for C16E2 and C16E3 are initially found to be irregular structures, which attain increasingly compact shape with increasing temperature, and finally become circular when the subphase temperature is 26 and 15 degrees C for C16E2 and C16E3, respectively. It is concluded that a higher degree of dehydration around the headgroup region appreciably reduces the headgroup size, which imparts to the molecules an increase in hydrophobicity, thereby a closer molecular packing. Consequently, the line tension of the interface increases, showing compact structures at higher temperatures. Since C16E1 bears only one EO unit in its headgroup, the dehydration effect cannot appreciably raise its hydrophobicity to overcome the increases in thermal motion and chain flexibility of the molecules. Rather, increases in subphase temperature result in a decrease in the line tension of the interface, giving fractal structures at higher temperatures.     

Computer simulation of quantum dynamics in a classical spin environment

In this paper, a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric phases in the evolution of the density matrix. It is shown that such geometric phases must also be considered in the quantum–classical Liouville equation for a classical bath with canonical phase space coordinates; this occurs whenever the adiabatics basis is complex (as in the case of a magnetic field coupled to the quantum subsystem). When the quantum subsystem is weakly coupled to the spin environment, non-adiabatic transitions can be neglected and one can construct an effective non-Markovian computer simulation scheme for open quantum system dynamics in classical spin environments. In order to tackle this case, integration algorithms based on the symmetric Trotter factorization of the classical-like spin propagator are derived. Such algorithms are applied to a model comprising a quantum two-level system coupled to a single classical spin in an external magnetic field. Starting from an excited state, the population difference and the coherences of this two-state model are simulated in time while the dynamics of the classical spin is monitored in detail. It is the author’s opinion that the numerical evidence provided in this paper is a first step toward developing the simulation of quantum dynamics in classical spin environments into an effective tool. In turn, the ability to simulate such a dynamics can have a positive impact on various fields, among which, for example, nanoscience.     

Effect of temperature on the retention of ionizable compounds in reversed-phase liquid chromatography: application to method development

The analysis of pharmaceutical compounds is often a difficult challenge which requires mathematical tools to improve the quality of the separation method. This work is an attempt to rationalize the anomalous variation of the logarithm of the retention factor with temperature in case of ionizable compounds. The effect of temperature on ionizable compounds was studied within a large range of temperature, ranging from 30 to 130 degrees C. The determination of the so-called chromatographic pKa and the study of its variation with temperature allow to explain why the forms of the van't Hoff curves are so different depending on the type of solute, the type of buffer and the type of the mobile phase. A retention model along with a computation procedure is proposed to optimize both temperature and mobile phase composition and to provide good and robust conditions as shown by illustrative examples.