Mixed Quantum Classical Reaction Rates based on the Phase Space Formulation of the Hierarchical Equations of Motion

In a previous work [J. Chem. Phys. 140 , 174105 (2014)], we have shown that a mixed quantum classical (MQC) rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions. However, the method is based on the high temperature approximation of the hierarchical equation of motion (HEOM) with the Debye-Drude spectral density, and results in a multi-state Zusman type of equation. We now extend this theory to include quantum effects of the bath degrees of freedom. By writing the full HEOM into a multidimensional partial differential equation in phase space, we can define a new reaction coordinate, and the previous method can be generalized to the full quantum regime. The validity of the new method is demonstrated by using numerical examples, including the spin-Boson model, and the double well model for proton transfer reaction. The new method is found to resolve some key problems of the previous theory based on high temperature approximation, including possible numerical instability in long time simulation and wrong rate constant at low temperatures.     

Quantum dynamics calculations using symmetrized, orthogonal Weyl-Heisenberg wavelets with a phase space truncation scheme. III. Representations and calculations

In a previous paper [J. Theo. Comput. Chem. 2, 65 (2003)], one of the authors (B.P.) presented a method for solving the multidimensional Schrodinger equation, using modified Wilson-Daubechies wavelets, and a simple phase space truncation scheme. Unprecedented numerical efficiency was achieved, enabling a ten-dimensional calculation of nearly 600 eigenvalues to be performed using direct matrix diagonalization techniques. In a second paper [J. Chem. Phys. 121, 1690 (2004)], and in this paper, we extend and elaborate upon the previous work in several important ways. The second paper focuses on construction and optimization of the wavelength functions, from theoretical and numerical viewpoints, and also examines their localization. This paper deals with their use in representations and eigenproblem calculations, which are extended to 15-dimensional systems. Even higher dimensionalities are possible using more sophisticated linear algebra techniques. This approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where differential equations are involved.     

Non-Markovian stochastic Schrödinger equations in different temperature regimes: a study of the spin-boson model

Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson model. We show in this paper that two linear stochastic Schrodinger equations, derived from different perspectives by Diosi, Gisin, and Strunz [Phys. Rev. A 58, 1699 (1998)], and Gaspard and Nagaoka [J. Chem. Phys. 13, 5676 (1999)], respectively, are equivalent in the relevant order of perturbation theory. Nonlinear stochastic Schrodinger equations are in principle more efficient than linear ones, as they determine solutions with a higher weight in the ensemble average which recovers the reduced density matrix of the quantum open system. However, it will be shown in this paper that for the case of a spin-boson system and weak coupling, this improvement does only occur in the case of a bath at high temperature. For low temperatures, the sampling of realizations of the nonlinear equation is practically equivalent to the sampling of the linear ones. We study further this result by analyzing, for both temperature regimes, the driving noise of the linear equations in comparison to that of the nonlinear equations.     

High resolution electron momentum spectroscopy of dichlorodifluoromethane: unambiguous assignments of outer valence molecular orbitals

On account of controversial orbital assignment that appeared in previous works, [J. Chem. Phys. 120, 7933 (2004), and references therein] high resolution electron momentum spectroscopy (EMS) measurements on dichlorodifluoromethane has been carried out using a newly developed high resolution energy-momentum dispersive multichannel spectrometer employing asymmetric noncoplanar geometry at an impact energy of 2500 eV plus binding energy. Four resolved structures and two shoulders were obviously observed in high resolution binding energy spectrum in energy range covering eight outermost valence orbitals, whereas only two broad lobes were resolved in previous EMS studies [J. Chem. Phys. 120, 7933 (2004); Chin. Phys. 14, 2467 (2005)]. The ordering of these orbitals was reassigned unambiguously by simple comparison of experimental momentum distributions with theoretical ones.     

Rovibrational spectroscopy calculations of neon dimer using a phase space truncated Weyl-Heisenberg wavelet basis

In a series of earlier articles [B. Poirier J. Theor. Comput. Chem. 2, 65 (2003); B. Poirier and A. Salam J. Chem. Phys. 121, 1690 (2004); B. Poirier and A. Salam J. Chem. Phys. 121, 1740 (2004)], a new method was introduced for performing exact quantum dynamics calculations in a manner that formally defeats exponential scaling with system dimensionality. The method combines an optimally localized, orthogonal Weyl-Heisenberg wavelet basis set with a simple phase space truncation scheme, and has already been applied to model systems up to 17 degrees of freedom (DOF's). In this paper, the approach is applied for the first time to a real molecular system (neon dimer), necessitating the development of an efficient numerical scheme for representing arbitrary potential energy functions in the wavelet representation. All bound rovibrational energy levels of neon dimer are computed, using both one DOF radial coordinate calculations and a three DOF Cartesian coordinate calculation. Even at such low dimensionalities, the approach is found to be competitive with another state-of-the-art method applied to the same system [J. Montgomery and B. Poirier J. Chem. Phys. 119, 6609 (2003)].     

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.     

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.     

High resolution vacuum ultraviolet emission spectrum of D2: the B' 1Sigmau+-->X 1Sigmag+ band system

In this work, we have extended our previous high resolution study of the vacuum ultraviolet emission spectrum of the D2 molecule [M. Roudjane, et al. J. Chem. Phys. 125, 214305 (2006)] up to 124.2 nm in order to investigate the B' 1Sigmau+-->X 1Sigmag+ band system. The analysis of the spectrum has been carried out by means of a complex spectrum visual identification code IDEN [V. I. Azarov, Phys. Scr. 44, 528 (1991); 48, 656, (1993)] and supported by theoretical calculations using ab initio data [L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995); 99, 1851 (1993); G. Staszewska and L. Wolniewicz, J. Mol. Spectrosc. 212, 208 (2002); L. Wolniewicz and G. Staszewska, 220, 45 (2003)] which provided level energies and transition probabilities. More than 1480 new emission lines have been observed and 109 bands belonging to the B' 1Sigmau+-->X 1Sigmag+ system have been identified between 84.1 and 121.6 nm. Except for the upsilon'-0 bands that were reported in absorption [I. Dabrowski and G. Herzberg, Can. J. Phys. 52, 1110 (1974)], all the upsilon'-upsilon" bands are reported here for the first time. The analysis led to the determination of 111 rovibronic energy levels in the B' 1Sigmau+ state, of which 31 with higher rotational numbers J are new. Observed perturbations are accounted for through a set of coupled equations involving the four excited electronic states B 1Sigmau+, B' 1Sigmau+, C 1Piu, and D 1Piu and including nonadiabatic couplings. The solution of this set provides the percent contribution of these four states to each of the observed rovibronic level.     

Quasielastic electron scattering from methane, methane-d4, methane-d2, ethylene, and 2-methylpropane

Quasielastic electron scattering from gaseous species at high momentum transfer was recently reported for the first time [Cooper et al., J. Electron Spectrosc. Relat. Phenom. 155, 28 (2007)]. The first results for CH(4) and CD(4) were well explained by a classical electron Compton scattering picture in which the electron scatters independently from each atom rather than the molecule as a whole. However, an alternative possible interpretation in terms of nondipole molecular vibrational excitation is suggested by previously published quantum mechanical calculations on high momentum transfer electron scattering from diatomic molecules [Bonham and de Souza, J. Chem. Phys. 79, 134 (1983)]. In order to determine which of these two interpretations best fits the experimental results, we have measured the quasielastic spectra of gaseous 2-methylpropane, ethylene, methane, and two isotopically substituted methanes, CH(2)D(2) and CD(4), at a momentum transfer of approximately 20 a.u. (2.25 keV impact energy and 100 degrees scattering angle). The experimental spectra are found to be composed of as many peaks as there are different atomic isotopes in the molecule (two for CH(4), C(2)H(4), 2-methylpropane, and CD(4) and three for CH(2)D(2)). The peak positions are predicted accurately by the independent atom electron Compton scattering model, and the relative intensities are in reasonable agreement. The experimental results thus support classical electron Compton scattering as the origin of the signal.     

Statistical mechanical theory for steady state systems. VI. Variational principles

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.     

Analysis of the phase transitions in alkyl-mica by density and pressure profiles

In a previous work [Heinz, Castelijns, and Suter, J. Am. Chem. Soc. 115, 9500 (2003)], we developed an accurate force field and simulated the phase transitions in C18-mica (octadecyltrimethylammonium-mica) as well as the absence of such transitions in 2C18-mica (dioctadecyldimethylammonium-mica) between room temperature and 100 degrees C. Here we analyze (i) average z coordinates of the carbon atoms and interdigitation of the hydrocarbon bilayers, (ii) density profiles, and (iii) pressure profiles of the structures along all Cartesian axes. In C18-mica, the standard deviation in the z coordinate for the chain atoms is high and more than doubles in the disordered phase. The order-disorder transition is accompanied by a change in the orientation of the ammonium head group, as well as decreasing tensile and shear stress in the disordered phase. In 2C18-mica, the standard deviation in the z coordinate for the chain atoms is low and does not increase remarkably on heating. The backbones display a highly regular structure, which is slightly obscured by rotations in the C18 backbones and minor head group displacements at 100 degrees C. Close contacts between the bulky head groups with sidearms cause significant local pressure which is in part not relieved at 100 degrees C. An increase of the basal-plane spacing at higher temperature is found in both systems due to larger separation between the two hydrocarbon layers and an increased z spacing between adjacent chain atoms (=decreased tilt of the chains relative to the surface normal), and, in C18-mica only, a stronger upward orientation of the C18 chain at the ammonium head group. The likelihood for chain interdigitation between the two hydrocarbon layers is 24%-30% for C18-mica, and 65%-26% for 2C18-mica (for 20-100 degrees C).     

Structure of mass, momentum, and energy transfer equations under highly nonequilibrium conditions

The structure of mass, momentum, and energy transfer equations under highly non-equilibrium conditions is considered when the traditional assumption of nonequilibrium thermodynamics (the local equilibrium condition) is violated. The derived transfer equations based on particle mass, momentum, and the law of energy conservation are related to heterogeneous systems with arbitrary density, i.e., for three aggregate states and their interfaces. Fluxes of the mentioned properties are described at the atomic-molecular level by nonequilibrium discrete unary and binary distribution functions (in the lattice gas model) with regard to interparticle potential interactions of system components. It is found that the total set of local transfer equations consists of five modified mass, momentum, and energy transfer equations for each of the system sites, and of 15 new equations describing the correlated characteristics of the density, rate, and temperature for the sites of a pair. The relationship between the derived equations and previous theories is discussed.     

Numerical verification of the generalized Crooks nonequilibrium work theorem for non-Hamiltonian molecular dynamics simulations

The generalized Crooks theorem (GCT) for deterministic non-Hamiltonian molecular dynamics simulations [Phys. Rev. E 75, 050101 (2007)] connects the probabilities of nonequilibrium realizations switching the system between two thermodynamic states, to the partition functions of these states. In comparison to the "classical" Crooks nonequilibrium work theorem [J. Stat. Phys. 90, 1481 (1998)], which deals with realizations involving only mechanical work, the GCT also accounts for additional work resulting from changes of the intensive and extensive thermodynamic variables of the system. In this article we present a numerical verification of the GCT using a Lennard-Jones fluid model where two particles are subject to a time-dependent external potential. Moreover, in order to switch the system between different thermodynamic states, the temperature and the pressure (or volume), which are controlled through the Martyna-Tobias-Klein equations of motion [J. Chem. Phys. 101, 4177 (1994)], are also varied externally. The free energy difference between states characterized by different distances of the target particles is evaluated using both a standard methodology (pair radial distribution functions) and the GCT. In order to exploit the various options provided by the GCT approach, i.e., the possibility of temperature/pressure/volume changes during the realizations, the free energy difference is recovered via arbitrary thermodynamic cycles. In all tests, the GCT is quantitatively verified.     

Space-time contours to treat intense field-dressed molecular states. I. Theory

A molecular system exposed to an intense external field is considered. The strength of the field is measured by the number L of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced space-time contours [R. Baer, et al., J. Chem. Phys. 119, 6998 (2003)], to form N coupled Schrodinger equations where N相似文献   

A quantum wave-packet study of intersystem crossing effects in the O(3P2,1,0,1D2)+H2 reaction

We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1A' state [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)], the 3A' and the two degenerate 3A" states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 (2000)], and the spin-orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state Pi32 to Pi12 of the product OH was calculated to be approximately 2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.     

Rotational and spin viscosities of water: Application to nanofluidics

In this paper we evaluate the rotational viscosity and the two spin viscosities for liquid water using equilibrium molecular dynamics. Water is modeled via the flexible SPC/Fw model where the Coulomb interactions are calculated via the Wolf method which enables the long simulation times required. We find that the rotational viscosity is independent of the temperature in the range from 284 to 319 K. The two spin viscosities, on the other hand, decrease with increasing temperature and are found to be two orders of magnitude larger than that estimated by Bonthuis et al. [Phys. Rev. Lett. 103, 144503 (2009)] We apply the results from molecular dynamics simulations to the extended Navier-Stokes equations that include the coupling between intrinsic angular momentum and linear momentum. For a flow driven by an external field the coupling will reduce the flow rate significantly for nanoscale geometries. The coupling also enables conversion of rotational electrical energy into fluid linear momentum and we find that in order to obtain measurable flow rates the electrical field strength must be in the order of 0.1?MV?m(-1) and rotate with a frequency of more than 100 MHz.     

Product distributions, rate constants, and mechanisms of LiH+H reactions

We present a quantum-mechanical investigation of the LiH depletion reaction LiH+H-->Li+H2 and of the H exchange reaction LiH+H'-->LiH'+H. We report product distributions, rate constant, and mechanism of the former, and rate constant and mechanism of the latter reaction. We use the potential-energy surface by Dunne et al. [Chem. Phys. Lett. 336, 1 (2001)], the real-wave-packet method by Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)], and the J-shifting approximation. The 1H2 nuclear-spin statistics and progressions of vib-rotational states (v',j') rule both initial-state-resolved and thermal product distributions, which have saw-toothed shapes with odd j' preferred with respect to even j'. At high collision energies and temperatures, we obtain a regular 3-to-1 intensity alternation of rotational states. At low collision energies and temperatures, the degeneracy and density of many H2 levels can, however, give more irregular distributions. During the collision, the energy flows from the reactant translational mode to the product vibration and recoil ones. The rate constants of both reactions are not Arrhenius type because the reactions are barrier-less. The low-temperature, LiH depletion rate constant is larger than the H exchange one, whereas the contrary holds at high temperature. The real-time mechanisms show the nuclear rearrangements of the nonreactive channel and of the reactive ones, and point out that the LiH depletion is preferred over the H exchange at short times. This confirms the rate-constant results.     

Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations.