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The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Accurate modeling of these quantum nuclear effects requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the aggressive thermostatting. Here, we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, which makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems that have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations. [ABSTRACT FROM AUTHOR]

We develop a path-integral dynamics method for water that resembles centroid molecular dynamics (CMD), except that the centroids are averages of curvilinear, rather than Cartesian, bead coordinates. The curvilinear coordinates are used explicitly only when computing the potential of mean force, the components of which are re-expressed in terms of Cartesian "quasicentroids" (so-called because they are close to the Cartesian centroids). Cartesian equations of motion are obtained by making small approximations to the quantum Boltzmann distribution. Simulations of the infrared spectra of various water models over 150–600 K show these approximations to be justified: for a two-dimensional OH-bond model, the quasicentroid molecular dynamics (QCMD) spectra lie close to the exact quantum spectra, and almost on top of the Matsubara dynamics spectra; for gas-phase water, the QCMD spectra are close to the exact quantum spectra; for liquid water and ice (using the q-TIP4P/F surface), the QCMD spectra are close to the CMD spectra at 600 K and line up with the results of thermostated ring-polymer molecular dynamics and approximate quantum calculations at 300 and 150 K. The QCMD spectra show no sign of the CMD "curvature problem" (of erroneous red shifts and broadening). In the liquid and ice simulations, the potential of mean force was evaluated on-the-fly by generalizing an adiabatic CMD algorithm to curvilinear coordinates; the full limit of adiabatic separation needed to be taken, which made the QCMD calculations 8 times more expensive than partially adiabatic CMD at 300 K, and 32 times at 150 K (and the intensities may still not be converged at this temperature). The QCMD method is probably generalizable to many other systems, provided that collective bead-coordinates can be identified that yield compact mean-field ring-polymer distributions. [ABSTRACT FROM AUTHOR]

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t4) and O(t¹), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t5) and O(t²), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions. [ABSTRACT FROM AUTHOR]

Instanton rate theory is used to study tunneling events in a wide range of systems including lowtemperature chemical reactions. Despite many successful applications, the method has never been obtained from first principles, relying instead on the "Im F" premise. In this paper, the same expression for the rate of barrier penetration at finite temperature is rederived from quantum scattering theory [W. H. Miller, S. D. Schwartz, and J.W. Tromp, J. Chem. Phys. 79, 4889 (1983)] using a semiclassical Green's function formalism. This justifies the instanton approach and provides a route to deriving the rate of other processes. [ABSTRACT FROM AUTHOR]

It is well known that path-integral methods can be used to calculate the energy splitting between the ground and the first excited state. Here we show that this approach can be generalized to give the splitting patterns between all the lowest energy levels from different symmetry blocks that lie below the first-excited totally symmetric state. We demonstrate this property numerically for some two-dimensional models. The approach is likely to be useful for computing rovibrational energy levels and tunnelling splittings in floppy molecules and gas-phase clusters. [ABSTRACT FROM AUTHOR]

We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonaldehyde yield tunnelling splittings in good overall agreement with the results of diffusion Monte Carlo calculations. [ABSTRACT FROM AUTHOR]

There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum goldenrule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems. [ABSTRACT FROM AUTHOR]

It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t → 0+ limit of a (new form of) quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we provide evidence which suggests very strongly that this QTST (≡ RPMD-TST) is unique, in the sense that the t → 0+ limit of any other flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t → 0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST. [ABSTRACT FROM AUTHOR]

We investigate the ability of the recently developed ring-polymer instanton (RPI) method [J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 134, 054109 (2011)] to treat tunneling in water clusters. We show that the RPI method is easy to extend to treat tunneling between more than two minima, using elementary graph theory. Tests of the method on water dimer and trimer yield a set of instanton periodic orbits which correspond to all known tunneling pathways in these systems. Splitting patterns obtained from the orbits are in good overall agreement with experiment. The agreement is closer for the deuterated than for the protonated clusters, almost certainly because the main approximation in the calculations is neglect of anharmonicity perpendicular to the tunneling path. All the calculations were performed on a desktop computer, which suggests that similar calculations will be possible on much larger clusters. [ABSTRACT FROM AUTHOR]

Semiclassical instanton theory gives an approximate description of deep tunneling by means of periodic orbits on the inverted potential energy surface. There are two versions of the theory, one derived by taking a semiclassical limit of the exact flux-side time-correlation function and the other by starting from the 'Im F' premise, in which the partition function is analytically continued into the complex plane. Here, we provide a derivation showing that the two versions of the theory are exactly equivalent. Unlike a previous derivation (which was restricted to a system-bath model), our derivation is completely general, and thus establishes that the 'Im F' premise, which is behind such methods as quantum transition-state theory and ring polymer molecular dynamics rate-theory, is correct in the steepest-descent limit. [ABSTRACT FROM AUTHOR]

The semiclassical instanton expression for the tunneling splitting between two symmetric wells is rederived, starting from the ring-polymer representation of the quantum partition function. This leads to simpler mathematics by replacing functional determinants with matrix determinants. By exploiting the simple Hückel-like structure of the matrices, we derive an expression for the instanton tunneling splitting in terms of a minimum on the potential surface of a linear polymer. The latter is a section cut out of a ring polymer, consisting of an infinite number of beads, which describes a periodic orbit on the inverted potential surface. The approach is straightforward to generalize to multiple dimensions, and we demonstrate that it is computationally practical by carrying out instanton calculations of tunneling splittings in HO2 and malonaldehyde in full dimensionality. [ABSTRACT FROM AUTHOR]

We extend to full dimensionality a recently developed wave packet method [M. T. Cvitasˇ and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)] for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions and also increase the computational efficiency of the method. This is done by introducing a new set of product coordinates, by applying the Crank-Nicholson approximation to the angular kinetic energy part of the split-operator propagator and by using a symmetry-adapted basis-to-grid transformation to evaluate integrals over the potential energy surface. The newly extended method is tested on the benchmark OH + H2 → H2O + H reaction, where it allows us to obtain accurately converged state-to-state reaction probabilities (on the Wu-Schatz-Fang-Lendvay-Harding potential energy surface) with modest computational effort. These methodological advances will make possible efficient calculations of state-to-state differential cross sections on this system in the near future. [ABSTRACT FROM AUTHOR]

We demonstrate that the ring-polymer molecular dynamics (RPMD) method is equivalent to an automated and approximate implementation of the “Im F” version of semiclassical instanton theory when used to calculate reaction rates in the deep-tunneling regime. This explains why the RPMD method is often reliable in this regime and also shows how it can be systematically improved. The geometry of the beads at the transition state on the ring-polymer potential surface describes a finite-difference approximation to the “instanton” trajectory (a periodic orbit in imaginary time βh on the inverted potential surface). The deep-tunneling RPMD rate is an approximation to the rate obtained by applying classical transition-state theory (TST) in ring-polymer phase-space using the optimal dividing surface; this TST rate is in turn an approximation to a free-energy version of the Im F instanton rate. The optimal dividing surface is in general a function of several modes of the ring polymer, which explains why centroid-based quantum-TSTs break down at low temperatures for asymmetric reaction barriers. Numerical tests on one-dimensional models show that the RPMD rate tends to overestimate deep-tunneling rates for asymmetric barriers and underestimate them for symmetric barriers, and we explain that this is likely to be a general trend. The ability of the RPMD method to give a dividing-surface-independent rate in the deep-tunneling regime is shown to be a consequence of setting the bead-masses equal to the physical mass. [ABSTRACT FROM AUTHOR]

A recent approach [S. C. Althorpe, J. Chem. Phys. 124, 084105 (2006)] for interpreting geometric phase (GP) effects in a nuclear wave function confined to the lower of two conically intersecting potential energy surfaces is extended to treat coupled dynamics on both surfaces. The approach is exact, and uses simple topology to separate the wave function into contributions from Feynman paths that wind different numbers of times, and in different senses, around the conical intersection. We derive the approach first, by mapping the time-dependent wave packet describing the coupled dynamics onto a double space, and second, by classifying the Feynman paths within a time-ordered expansion of the path integral. The approach is demonstrated numerically for a simple E×e Jahn–Teller system and for a model of the 1B1-S0 intersection in pyrrole. The approach allows one to investigate and interpret the effect of the GP on population transfer between the surfaces, and also to extract contributions to the coupled nuclear wave function from different reaction paths. [ABSTRACT FROM AUTHOR]

We report quantum wave packet calculations of state-to-state reaction probabilities and cross sections for the reaction H+H2(v0=0,j0=0)→H2(v,j)+H, at total energies up to 4.5 eV above the ground state potential minimum. The calculations are repeated using (i) the ground electronic state only, (ii) the ground state plus the diagonal non-Born–Oppenheimer correction, (iii) the ground state, diagonal non-Born–Oppenheimer correction and geometric phase (GP), and (iv) both electronic states including all nonadiabatic couplings, using the diabatic potential approach of Mahapatra et al. [J. Phys. Chem. A 105, 2321 (2001)]. The results for calculations (iii) and (iv) are in very close agreement, showing that the upper electronic state makes only a very small contribution to the state-to-state dynamics, even at energies much higher than the conical intersection minimum (at 2.74 eV). At total energies above 3.5 eV, many of the state-to-state reaction probabilities show strong GP effects, indicating that they are dominated by interference between one- and two-transition-state (1-TS and 2-TS) reaction paths. These effects survive the coherent sum over partial waves to produce features in the state-to-state differential cross sections which could be detected in an experiment with an angular resolution of ∼20°. Efficient dephasing of the interference between the 1-TS and 2-TS contributions causes almost complete cancellation of the GP in the integral cross sections, thus continuing a trend observed at lower energies in earlier work. [ABSTRACT FROM AUTHOR]

We have measured differential cross sections (DCSs) for the HD (v′=1,j′=2,6,10) products of the H+D2 exchange reaction at five different collision energies in the range 1.48≤=Ecoll≤=1.94 eV. The contribution from the less energetic H atoms formed upon spin-orbit excitation of Br in the photolysis of the HBr precursor is taken into account for two collision energies, Ecoll=1.84 and 1.94 eV, allowing us to disentangle the two different channels. The measured DCSs agree well with new time-dependent quantum-mechanical calculations. As the product rotational excitation increases, the DCSs shift from backward to sideward scattering, as expected. We also find that the shapes of the DCSs show only a small overall dependence on the collision energy, with a notable exception occurring for HD (v′=1,j′=2), which appears bimodal at high collision energies. We suggest that this feature results from both direct recoil and indirect scattering from the conical intersection. [ABSTRACT FROM AUTHOR]

Product rotational distributions for the reaction H+D2→HD(ν′=1,j′)+D have been measured for 16 collision energies in the range of 1.43≤Ecoll≤2.55 eV. Time-dependent quantum-mechanical calculations agree well in general with the experimental results, but they consistently yield slightly colder distributions. In terms of the average energy channeled into rotation, the differences between experiment and theory amount to approximately 10% for all collision energies sampled. No peculiarity is found for Ecoll=2.55 eV at which the system has sufficient energy to access the first HD2 electronically excited state. [ABSTRACT FROM AUTHOR]

Experimental measurements of rovibrational product state distributions for the inelastic scattering process H+D2(ν=0,j)→H+D2(ν′=1,2,j′) are presented and compared with the results of quasiclassical and quantum mechanical calculations. Agreement between theory and experiment is almost quantitative. Two subtle trends are found: the relative amount of energy in product rotational excitation decreases slightly with increasing collision energy and increases slightly with increasing product vibrational excitation. These trends are the reverse of what has been found for reactive scattering in which the opposite trends are much more pronounced. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We recently interpreted several reactive scattering experiments using a plane wave packet (PWP) formulation of quantum scattering theory [see, e.g., S. C. Althorpe, F. Fernández-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper presents the first derivation of this formulation for atom-plus-diatom reactive scattering, and explains its relation to conventional time-independent reactive scattering. We generalize recent results for spherical-particle scattering [S. C. Althorpe, Phys. Rev. A 69, 042702 (2004)] to atom-rigid-rotor scattering in the space-fixed frame, atom-rigid-rotor scattering in the body-fixed frame, and finally A+BC rearrangement scattering. The reactive scattering is initiated by a plane wave packet, describing the A+BC reagents in center-of-mass scattering coordinates, and is detected by projecting onto a series of AC+B (or AB+C) plane wave “probe” packets. The plane wave packets are localized at the closest distance from the scattering center at which the interaction potential can be neglected. The time evolution of the initial plane wave packet provides a clear visualization of the scattering into space of the reaction products. The projection onto the probe packets yields the time-independent, state-to-state scattering amplitude, and hence the differential cross section. We explain how best to implement the PWP approach in a numerical computation, and illustrate this with a detailed application to the H+D2 reaction. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present experimental rotational distributions for the reaction H+D[sub 2]→HD(ν[sup ′]=3,j[sup ′])+D at eight different collision energies between 1.49 and 1.85 eV. We combine a previous measurement of the state-resolved excitation function for this reaction [Ayers et al., J. Chem. Phys. 119, 4662 (2003)] with the current data to produce a map of the relative reactive cross section as a function of both collision energy and rotational quantum number (an E–j[sup ′] plot). To compare with the experimental data, we also present E–j[sup ′] plots resulting from both time-dependent and time-independent quantum mechanical calculations carried out on the BKMP2 surface. The two calculations agree well with each other, but they produce rotational distributions significantly colder than the experiment, with the difference being more pronounced at higher collision energies. Disagreement between theory and experiment might be regarded as surprising considering the simplicity of this system; potential causes of this discrepancy are discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An experimental and theoretical investigation of the collision energy dependence of the HD(ν[sup ′]=2,j[sup ′]) rotational product state distribution for the H+D[sub 2] reaction in the collision energy range of E[sub col]=1.30–1.89 eV has been carried out. Theoretical results based on time-dependent and time-independent quantum mechanical methods agree nearly perfectly with each other, and the agreement with the experiment is good at low collision energies and very good at high collision energies. This behavior is in marked contrast to a previous report on the HD(ν[sup ′]=3,j[sup ′]) product state rotational distribution [Pomerantz et al., J. Chem. Phys. 120, 3244 (2004)] where a systematic difference between experiment and theory was observed, especially at the highest collision energies. The reason for this different behavior is not yet understood. In addition, this study employs Doppler-free spectroscopy to resolve an ambiguity in the E, F–X resonantly enhanced multiphoton ionization transition originating from the HD(ν[sup ′]=2,j[sup ′]=1) state, which is found to be caused by an accidental blending with the transition coming from the HD(ν[sup ′]=1,j[sup ′]=14) state. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We outline a new time-dependent wave packet formulation of quantum scattering theory. The theory obtains the differential cross section directly from the time-evolution of a plane wave packet, bypassing the usual S-matrix formulas. We introduce the theory for potential scattering, generalize it to reactive scattering, then explain how the theory was used recently to interpret the H[sup +]D[sub 2] →HD (υ=3j=0)+D reaction in collaboration with experiment IS. C. Althorpe, F. Fernández-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. We also present new findings of quantum interference in the H+D[sub 2] reaction. [ABSTRACT FROM AUTHOR]

There are a variety of methods for including nuclear quantum effects in dynamics simulations by combining quantum Boltzmann statistics with classical dynamics. Among them are thermostatted ring-polymer molecular dynamics (TRPMD), centroid molecular dynamics (CMD), quasi-centroid molecular dynamics (QCMD), and the linearised semi-classical initial value representation (LSC-IVR). Here we make a systematic comparison of these methods by calculating the infrared spectrum of water in the gas phase, and in the liquid and ice phases (using the q-TIP4P/F model potential). Some of these results are taken from previous work, and some of them are new (including the LSC-IVR calculations for ice, and extensions of all the spectra into the near-infrared region dominated by overtone and combination bands). Our results suggest that QCMD is the best method for reproducing fundamental transitions in the spectrum, and that LSC-IVR gives the best overall description of the spectrum (albeit with large errors in the bend fundamental band caused by zero-point-energy leakage). The TRPMD method gives damped spectra that line up with the QCMD spectra, and is by far the cheapest method. [ABSTRACT FROM AUTHOR]

Studies the reactant-produced decoupling (RPD) equations of state-to-state reactive scattering. Introduction of the RPD equations; Solution for the time-independent wave packet (TIW) form of the RPD equations; Derivation of the TIW RPD equations; Application of the extended Chebyshev propagator to the TIW RPD equations.

Discusses a Chebyshev method for calculating state-to-state reaction probabilities from the time-independent wavepacket reactant-product decoupling equations. Derivation of the extended Chebyshev propagator; Comparison of the extended Chebyshev propagator with related methods.

Studies the ability of time-resolved photoelectron angular distributions to provide information regarding the alignment of wave packets and a view on excited state dynamics. Pump-probe equations; Photoionization dynamics; Application to nitric oxide; Implementation of the theory; Excitation dynamics.

Rovibrational quantum nuclear motion computations, with J = 0, 1, and 2, are reported for the intermolecular degrees of freedom of the methane–water dimer, where J is the quantum number describing the overall rotation of the complex. The computations provide the first explanation of the far-infrared spectrum of this complex published in J. Chem. Phys., 1994, 100, 863. All experimentally reported rovibrational transitions, up to J = 2, can be assigned to transitions between the theoretically computed levels. The deviation of the experimental and computed rovibrational transitions is 0.5 cm−1 for the ortho and 2 cm−1 for the para species with a variance of 0.005 cm−1. In addition to a lower systematic error, the overall agreement of theory and experiment is also better for the ortho species (involving ortho-H2O). Most importantly, for this species all levels of the 24-fold tunneling splitting manifold corresponding to the zero-point vibration (ZPV) are involved in at least one experimentally reported transition. For the para species there are a few energy levels in the computed ZPV manifold that are not involved in the reported experimental transitions. Furthermore, computed energy levels are identified that correspond to the ZPV tunneling splitting manifold of the secondary minimum structure of the dimer, which presumably appear in rovibrational transitions in the same energy regime as the observed transitions, but have not been experimentally reported. [ABSTRACT FROM AUTHOR]

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a “planetary” model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the “planet”). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The “planetary” fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid. [ABSTRACT FROM AUTHOR]

Author(s): Stuart C. Althorpe (corresponding author) [1, 2]; Félix Fernández-Alonso [3]; Brian D. Bean [4]; James D. Ayers [4]; Andrew E. Pomerantz [4]; Richard N. Zare [4]; Eckart Wrede [1] [...]

Modern computational methods have become so powerful for predicting the outcome for the H + H2 → H2 + H bimolecular exchange reaction that it might seem further experiments are not needed. Nevertheless, experiments have led the way to cause theorists to look more deeply into this simplest of all chemical reactions. The findings are less simple. [ABSTRACT FROM AUTHOR]

The de Broglie-Bohm "pilot-wave" theory replaces the paradoxical wave-particle duality of ordinary quantum theory with a more mundane and literal kind of duality: each individual photon or electron comprises a quantum wave (evolving in accordance with the usual quantum mechanical wave equation) and a particle that, under the influence of the wave, traces out a definite trajectory. The definite particle trajectory allows the theory to account for the results of experiments without the usual recourse to additional dynamical axioms about measurements. Instead, one need simply assume that particle detectors click when particles arrive at them. This alternative understanding of quantum phenomena is illustrated here for two elementary textbook examples of one-dimensional scattering and tunneling. We introduce a novel approach to reconcile standard textbook calculations (made using unphysical plane-wave states) with the need to treat such phenomena in terms of normalizable wave packets. This approach allows for a simple but illuminating analysis of the pilot-wave theory's particle trajectories and an explicit demonstration of the equivalence of the pilot-wave theory predictions with those of ordinary quantum theory. [ABSTRACT FROM AUTHOR]

The Plane Wave Packet (PWP) approach is a new formulation of quantum scattering theory which interprets the results of (energy-domain) scattering experiments in terms of time-evolving wave packets. The wave packets allow one to visualize the scattering of the collision products in space, and thus link the dynamics on the potential surface with the angular distributions measured in experiments. Here we review the theoretical basis of the PWP approach, its connection with conventional quantum scattering theory, and the applications that have been made of it to date. These include calculations on simple model systems, and on the H + H 2 , H + D 2 and F + HD reactions. We give a thorough explanation of the theoretical basis of the PWP approach, which includes a review of the relevant parts of the literature on time-independent reactive scattering. We explain in detail how the PWP approach can be used to separate out different scattering mechanisms, and how such interpretations complement those of time-independent scattering theory. We also suggest possible future developments of the approach. [ABSTRACT FROM AUTHOR]

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described. [ABSTRACT FROM AUTHOR]

Investigates the formation of functional surface layers on ceramics. Incorporation of selected low-molecular-mass additives into the precursor polymer; Stabilization of compositionally changed surface region by calcination; Impact of thermal treatment on the additives.

We present a 3D quantum wavepacket method for calculating state-to-state reactive cross sections for the A+BC→AC+B reaction. The method avoids the coordinate problem (of A+BC arrangements being difficult to represent by AC+B coordinates, and vice versa) by solving the reactant-product decoupling (RPD) equations [T. Peng and J. Z. H. Zhang, J. Chem. Phys. 105, 6072 (1996)] in their further partitioned form [S. C. Althorpe, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 107, 7816 (1997)]. These equations decouple the nuclear dynamics Schro¨dinger equation into separate reactant, strong-interaction, and product regions, permitting different coordinates to be used in each region. We solve the equations using A+BC Jacobi coordinates in the reactant region, and AC+B Jacobi coordinates in the strong-interaction and product regions. In test calculations on the J=0 H+H[sub 2] reaction, we show that this partitioning of coordinate systems is much more efficient than using A+BC coordinates in the strong-interaction region (as was done in all previous applications of the RPD equations). We apply the method to the H+H[sub 2] reaction (for J=0-24), and obtain the first state-to-state differential cross sections to be calculated by an exact quantum wavepacket method. The method will allow state-to-state cross sections to be calculated for the same reactions for which wavepacket methods can currently calculate total cross sections. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We investigate the physical origin of direct reflection of rotation-vibration coupling in time-resolved photoelectron angular distributions. The theory is developed for a general rotation-vibration coupling mechanism in a polyatomic system and applied to the simplest instance of such interaction, namely centrifugal coupling in a diatomic molecule. Our results suggest the possibility of determining coupling strengths from the observed time dependence of the ionization asymmetry parameters. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A solvable molecular collision model that predicts Aharonov–Bohm (AB) like scattering in the adiabatic approximation is introduced. For it, we propagate coupled channel wave packets without resorting to a Born–Oppenheimer (BO) approximation. In those, exact, solutions we find evidence of topological phase dislocation lines that are independent of the collision energy and provide definitive signatures of AB-like scattering. The results of these simulations contrast with the conclusions of a recent study that suggests survival of the molecular Aharonov–Bohm effect only in the adiabatic limit in which the nuclear reduced mass . We discuss generalizations of this model and consider possible screening of the Mead–Truhlar vector potential by the presence of multiple conical intersections (CI). We demonstrate that the Wilson loop phase integral has the value −1 if it encloses an odd-number of CI's, and takes the value +1 for an even number. Within the scope of this model, we investigate the ultra-cold limit of scattering solutions in the presence of a conical intersection and comment on the relevance of Wigner threshold behavior for s-wave scattering. [ABSTRACT FROM AUTHOR]