A Bohmian total potential view to quantum effects. II: decay of temporarily trapped states

Formation, persistence and decay of temporarily trapped states, the time-dependent generalization of resonances, are analysed within the framework of Bohmian Mechanics. More specifically, the so-called Bohm’s total potential, the sum of classical plus Bohm’s quantum potential, is used. It is found that both formation and decay are triggered by the frequency in the oscillations of the total potential. These oscillations have been studied at the specific locations where the classical potential displays maxima, i.e. the ‘walls’ temporarily capturing the system’s density. Our main result is that the total potential oscillation frequency is solely dependent on the steepness of the classical potential ramp and, surprisingly, independent of the classical barrier height and width, well depth and width, collision energy or wavepacket width.     

Condensed-phase relaxation of multilevel quantum systems. I. An exactly solvable model

An analytically solvable model of multilevel condensed-phase quantum dynamics relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system characterized by nearest-neighbor hopping and off-diagonal coupling (which is linear in the bath coordinates) to a harmonic oscillator bath. We demonstrate that for N> 2 the long-time steady-state system site occupation probabilities are not the same for all sites; that is, they are distributed in a non-Boltzmann manner, which depends on the initial conditions and the number of levels in the system. Although the system-bath Hamiltonian considered here is restricted in form, the availability of an exact solution enables us to study the model in all regions of an extensive parameter space.     

Reconciling semiclassical and Bohmian mechanics. I. Stationary states

The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill behaved at caustics. In contrast, quantum trajectory methods--based on Bohmian mechanics (quantum hydrodynamics)--are characterized by divergent forces and erratic trajectories near nodes, but also well-behaved, single-valued representational functions. In this paper, we unify these two approaches into a single method that captures the best features of both, and in addition, satisfies the correspondence principle. Stationary eigenstates in one degree of freedom are the primary focus, but more general applications are also anticipated.     

Harmonic analysis of large systems. I. Methodology

Methods have been developed for the determination of vibrational frequencies and normal modes of large systems in the full conformational space (including all degrees of freedom) and in a reduced conformational space (reducing the number of degrees of freedom). The computational method, which includes Hessian generation and storage, full and iterative diagonalization techniques, and the refinement of the results, is presented. A method is given for the quasiharmonic analysis and the reduced basis quasiharmonic analysis. The underlying principle is that from the atomic fluctuations, an effective harmonic force field can be determined relative to the dynamic average structure. Normal mode analysis tools can be used to characterize quasiharmonic modes of vibration. These correspond to conventional normal modes except that anharmonic effects are included. Numerous techniques for the analyses of vibrational frequencies and normal modes are described. Criteria for the analysis of the similarity of low-frequency normal modes is presented. The approach to determining the natural frequencies and normal modes of vibration described here is general and applicable to any large system. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

A simple molecular model of adsorption chromatography. XIII. Comparison of solvation effects in liquid-solid and liquid-liquid systems

Summary R_Mvs solvent composition plots of three quinoline bases are compared for analogous liquid-liquid and liquid-solid systems. For the heptane+heptanone-2-water system for which the variation of R_M(log k′) values with concentration of heptanone-2 is due to solvation effects in the mobile phase, the slope of the plots was much smaller than in the case of the heptane + heptanone-2-silica system. This is considered as evidence that solvation in the mobile phase cannot play the decisive role in the adsorption equilibrium. On the other hand, the relationships can be interpreted in terms of competitive interactions of the solutes and polar solvent (heptanone-2) with the surface silanol groups, as the main molecular mechanism. Part XII: Ref. [1].     

Environmental effects on hydrogen bonded systems: A quantum chemical study of proton relay model systems

In this paper an application of a reaction field theory of solvent effects has been made to study proton transfer mechanisms in hydrogen bonded systems coupled to an environment. The latter is simulated with reaction fields having variable strength and direction (defined with respect to the supermolecule's total dipole moment direction), together with superposed uniform external electric fields. Changes in proton potential curves and some other properties of a model water dimer and a water trimer are reported. The results are discussed in relation to relevant phenomena in biology and biochemistry, namely proton relay systems in enzymatic catalysis.     

A simple mechanistic model to interpret the effects of narcotics

In this research we will show the advantages of using a time-independent dose metric in a mechanistic model to evaluate toxic effects for different narcotic compounds on different species. We will show how different already existing QSARs can be combined within a mechanistic framework to 1) make predictions of lethal thresholds; 2) show some limitations in the use of existing QSARs; 3) show how a mechanistic framework solves some conceptual problems in current approaches and 4) show how such a framework can be used to be of aid in an experimental setup in predicting the outcome of a survival experiment. The approach we chose is based on the simplest mechanistic model available, a scaled one-compartment model to describe uptake and elimination and hazard model to link the exposure to effects on survival. Within this theoretical framework a prediction for an internal threshold for effects on survival of 3 mmol/kg bw can be made, which should be similar for different species and independent of the partitioning characteristics of the toxicant. To demonstrate this, a threshold for 51 different species was derived, which indeed appeared to lie in a relatively small range, typically between 1 and 10 mmol/kg bw.     

A quantum model of the solvated electron in simple media

The interaction of a slow electron with a medium is modeled by the Fermi pseudopotential and image force potential. A quantum model of the solvated electron in simple media is constructed. The model can be used to analyze the lifetime of the solvated electron, its mobility in an electric field, and its absorption spectrum depending on pressure and temperature.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

Transient-state transport in some finite systems. Part I. A simple (two-stage) cascade

Some formal theory of transport in and through a simple (two-stage) cascade is presented. The treatment relates to a constant diffusion coefficient with solution or sorption obeying Henry's law. Detailed consideration is given to the time-dependence of the pressure of diffusant in the intermediate volume of the cascade. Time-lags associated with transport through the cascade have been evaluated and some of their properties indicated. The separation of binary gas mixtures is considered.     

Valency. I. A quantum chemical definition and properties

A quantum chemical definition of the valency of an atom in a molecule is proposed. It is defined as the sum of the squares of the appropriate offdiagonal elements of the first-order density matrix of the system in an orthogonal basis. It is a measure of the degree of electron sharing of the given atom with the other atoms. Its properties such as invariance to rotation of the coordinate system, its limiting values as well as its relation to natural hybrids and bond orbitals are discussed.     

A simple Hill-series approach to the linear potential

A simple Hill-series method is shown to yield accurate energy levels and expectation values for the linear potential for any angular momentum L and confinement radius R. The numerical results are verified by comparison with those from two hypervirial perturbation methods which are specially constructed to give accurate results at L = 0 for small R values and at L >?1 for R =?∞.     

A simple model to explain the complex kinetic behavior of epoxy/anhydride systems

A survey of the literature dealing with the kinetics of epoxy/anhydride polymerizations initiated by tertiary amines, shows inconsistencies in results reported by several authors. Both first-order and autocatalytic expressions have been used to fit experimental results. In the former case, significantly different values of apparent activation energies were found in isothermal and nonisothermal experiments. A simple kinetic model is proposed to explain these inconsistencies, based on the following steps: (a) a reversible reaction transforming an inactive initiator species into an active one, (b) a propagation step, and (c) a chain transfer step regenerating the active initiator (step not relevant to the kinetic analysis). The simple model explains both the first-order and autocatalytic behaviors reported in the literature. It also leads to the experimental values of the apparent activation energies obtained under different conditions. It is also shown that isoconversional methods should not be applied to obtain fundamental kinetic parameters in systems where the reaction rate depends on the concentration of an active species that varies independently of the conversion of functional groups. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2799–2805, 1999     

Hypervirial analysis of enclosed quantum mechanical systems. I. Dirichlet boundary conditions

Diagonal hypervirial relations are applied to enclosed one-dimensional systems when wave functions obey Dirichlet boundary conditions. A general formula for the energy is derived and it shows a striking difference with the usual formulas through an “extra” term. It constitutes a generalization of previous ones for the virial theorem when there exist nonusual boundary conditions. The values obtained are compared with other approximate methods. Several extensions are proposed.     

A simple model for the Slater exchange potential and its performance for solids

A simple local model for the Slater exchange potential is determined by least square fit procedure from Hartree–Fock (HF) atomic data. Since the Slater potential is the exact exchange potential yielding HF electron density from Levy‐Perdew‐Sahni density functional formalism (Levy et al., Phys. Rev. A 1984, 30, 2745), the derived local potential is significantly more negative than the conventional local density approximation. On the set of 22 ionic, covalent and van der Waals solids including strongly correlated transition metal oxides, it has been demonstrated, that this simple model potential is capable of reproducing the band gaps nearly as good as popular meta GGA potentials in close agreement with experimental values.     

Large amplitude quantum mechanics in polyatomic hydrides. I. A particles-on-a-sphere model for XH(n)

A framework is presented for converged quantum mechanical calculations on large amplitude dynamics in polyatomic hydrides (XH(n)) based on a relatively simple, but computationally tractable, "particles-on-a-sphere" (POS) model for the intramolecular motion of the light atoms. The model assumes independent two-dimensional (2D) angular motion of H atoms imbedded on the surface of a sphere with an arbitrary interatomic angular potential. This assumption permits systematic evolution from "free rotor" to "tunneling" to "quasi-rigid" polyatomic molecule behavior for small, but finite, values of total angular momentum J. This work focuses on simple triatom (n=2) and tetratom (n=3) systems as a function of interatomic potential stiffness, with explicit consideration of H2O, NH3, and H3O+ as limiting test cases. The POS model also establishes the necessary mathematical groundwork for calculations on dynamically much more challenging XH(n) species with n>3 (e.g., models of CH5+) where such a reduced dimensionality approach offers prospects for being quantum mechanically tractable at low J values (i.e., J=0, 1, 2) characteristic of supersonic jet expansion conditions.