Search for a density-based alternative quantum mechanics of many-electron systems

There are three reasons for seeking an alternative density-based quantum mechanics of many-electron systems, incorporating both interpretive and basic quantum mechanical aspects: (i) failure of popularad hoc chemical concepts underab initio scrutiny; (ii) failure ofab initio calculations to provide simple concepts; and (iii) highly attractive concepts and pictures generated by the electron density in three-dimensional space. At present the three interlinked pillars for such a density mechanics (in contrast to wave mechanics) are: (a) density functional theory; (b) quantum fluid dynamics; and (c) property densities in three-dimensional space. This article describes several studies dealing with these aspects. Although a density mechanics may well be an impossible ideal to realize, the search for it is indeed rejuvenating the whole of quantum chemistry.     

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.     

Conical intersections and semiclassical trajectories: comparison to accurate quantum dynamics and analyses of the trajectories

Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%-60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of approximately 32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.     

Herman-Kluk semiclassical dynamics in action-angle representation: new approaches to mapping quantum degrees of freedom

A general approach to mapping a discrete quantum mechanical problem by a continuous Hamiltonian is presented. The method is based on the representation of the quantum number by a continuous action variable that extends from -infinity to infinity. The projection of this Hilbert space onto the set of integer quantum numbers reduces the Hamiltonian to a discrete matrix of interest. The theory allows the application of the semiclassical methods to discrete quantum mechanical problems and, in particular, to problems where quantum Hamiltonians are coupled to continuous degrees of freedom. The Herman Kluk semiclassical propagation is used to calculate the nonadiabatic dynamics for a model avoided crossing system. The results demonstrate several advantages of the new theory compared to the existing mapping approaches.     

Single molecule charge transport: from a quantum mechanical to a classical description

This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.     

Full-dimensional quantum dynamics study of vinylidene-acetylene isomerization: a scheme using the normal mode Hamiltonian

Full-dimensional quantum dynamics calculations of vinylidene-acetylene isomerization are performed and the state-specific resonance decay lifetimes of vinylidene(-d(2)) are computed. The theoretical scheme is a combination of several methods: normal coordinates are chosen to describe the nuclear motion of vinylidene, with both the parity and permutation symmetry exploited; phase space optimization in combination with physical considerations is used to generate an efficient discrete variable representation; the reaction coordinate is defined by us according to the three most relevant normal coordinates, along which a kind of optimal complex absorbing potential is imposed; the preconditioned inexact spectral transform method combined with an efficient preconditioner is employed to extract the energies and lifetimes of vinylidene. The overall computation is efficient. The computed energy levels generally agree with experiment well, and several state-specific lifetimes are reported for the first time.     

Dielectrophoresis: a model to transport drugs directly into teeth

The article describes an innovative delivery system based on the principles of dielectrophoresis to transport drugs directly into site-specific intraoral targets. The hypothesis that a drug can be driven into tooth enamel during the application of an applied electrical potential difference was tested by the authors in in vitro studies comparing dielectrophoresis to diffusion to transport carbamide peroxide and fluoride. The studies showed that these agents can be transported directly into teeth using an alternating current (AC) electric field more effectively than diffusion. It was found that a 20-min bleaching treatment on human teeth with dielectrophoresis increased carbamide peroxide absorption by 104% and, on average, improved the change in shade guide unit 14 times from 0.6 SGU to 9 SGU. After applying a 1.23% acidulated phosphate fluoride gel to bovine incisors for 20 min by dielectrophoresis or diffusion, analysis with wavelength dispersive spectrometry determined that dielectrophoresis doubled fluoride uptake in the superficial layers compared to diffusion, and drove the fluoride significantly deeper into enamel with an uptake 600% higher than diffusion at 50 μm depth. Finally, dielectrophoresis promises to be a viable model that can potentially be used clinically to deliver other targeted drugs of variable molecular weight and structure.     

Application of environmental relaxation model to the transport behavior of glass-forming melts

The environmental relaxation model was applied successfully to explain the temperature dependence of viscosity, conductance, and the Walden product of molten Ca(NO₃)₂.3.91H₂O + NiCl₂ system in the non-Arrhenius region. This model was applied to pure melts, binary molten salt systems with ideal solutions marked by the absence of complex ions, and systems in which octahedral or tetrahedral complexes are formed. The values of the glass transition temperature obtained from the free volume and environmental relaxation models are in good agreement. The values of apparent activation energies for viscous and conductance flows derived from these two models are also comparable.     

A semiclassical model for the vibrational excitation of spherical-top molecules in collisions with ions

A simple theory is presented to explain the previously observed single-mode vibrational excitation of the spherical-top molecules CH₄, CF₄ and SF₆ in collisions with H⁺ and Li⁺. The theory is based on a three-dimensional forced-oscillator model which has been modified to take account of many independent harmonic oscillators. For small-angle collisions the linear driving forces are the dipole-, polarizability- and quadrupole-derivatives taken from IR, Raman spectroscopy and simple estimates, respectively. To explain the results at larger angles near and beyond the rainbow it has been necessary to introduce short-range repulsive forces between the ions and the outer atoms of the molecule. For small angles both the predicted first moment of the energy transfer and the time-of-flight spectra agree quantitatively with the experimental results. At large angles, for which only the first moment of the energy is available, good qualitative agreement is obtained after a slight adjustment of the potential parameters. The energy transfer as a function of time is calculated and shows a different oscillatory behavior for the proton and Li⁺-ion systems. Also the effect of intra-mode coupling is investigated and shown to have only a small effect on the overall energy transfer. The paper closes with a discussion of the implications of these experiments and the possible role of rotational excitation. The field strengths in these ion scattering experiments are shown to be greater than in the strongest focused Q-switched laser pulses.     

New method for the direct calculation of electron density in many-electron systems. I. Application to closed-shell atoms

Analytical properties of hydrogen-like atomic orbitals (HAO ) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.     

Dynamics of electronic states and spin-flip for photodissociation of dihalogens in matrices: experiment and semiclassical surface-hopping and quantum model simulations for F2 and ClF in solid Ar

Three approaches are combined to study the electronic states' dynamics in the photodissociation of F(2) and ClF in solid argon. These include (a) semiclassical surface-hopping simulations of the nonadiabatic processes involved. These simulations are carried out for the F(2) molecule in a slab of 255 argon atoms with periodic boundary conditions at the ends. The full manifold of 36 electronic states relevant to the process is included. (b) The second approach involves quantum mechanical reduced-dimensionality models for the initial processes induced by a pump laser pulse, which involve wavepacket propagation for the preoriented ClF in the frozen argon lattice and incorporate the important electronic states. The focus is on the study of quantum coherence effects. (c) The final approach is femtosecond laser pump-probe experiments for ClF in Ar. The combined results for the different systems shed light on general properties of the nonadiabatic processes involved, including the singlet to triplet and intertriplet transition dynamics. The main findings are (1) that the system remains in the initially excited-state only for a very brief, subpicosecond, time period. Thereafter, most of the population is transferred by nonadiabatic transitions to other states, with different time constants depending on the systems. (2) Another finding is that the dynamics is selective with regard to the electronic quantum numbers, including the Lambda and Omega quantum numbers, and the spin of the states. (3) The semiclassical simulations show that prior to the first "collision" of the photodissociated F atom with an Ar atom, the argon atoms can be held frozen, without affecting the process. This justifies the rigid-lattice reduced-dimensionality quantum model for a brief initial time interval. (4) Finally, degeneracies between triplets and singlets are fairly localized, but intertriplet degeneracies and near degeneracies can span an extensive range. The importance of quantum effects in photochemistry of matrix-isolated molecules is discussed in light of the results.     

Coupling quantum Monte Carlo to a nonlinear polarizable continuum model for spherical solutes

Starting from the nonlinear dielectric response model of Sandberg and Edholm, we derive an analytical expression of the polarization contribution to the solvation free energy in terms of the electronic density of the solute and the dielectric properties of the solvent. The solvent inhomogeneity is taken into account with the use of a smooth switching function whose spacial variation is established on the basis of how the solvent is arranged around the solute. An explicit form of a local potential representing the solvent effect on the solute is thus obtained by functional analysis. This effective potential can be combined with density functional or quantum chemical methods for the quantum mechanical treatment of the solute. Here, we use quantum Monte Carlo techniques for the solute and apply the method to the hydration of atomic ions finding very good agreement with experimental data.