Nuclear Subspace Research Articles

Factorized Electron-Nuclear Dynamics with an Effective Complex Potential.

We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.

Polaron formation: Ehrenfest dynamics vs. exact results

We use a one-dimensional tight binding model with an impurity site characterized by electron-vibration coupling, to describe electron transfer and localization at zero temperature, aiming to examine the process of polaron formation in this system. In particular we focus on comparing a semiclassical approach that describes nuclear motion in this many vibronic-states system on the Ehrenfest dynamics level to a numerically exact fully quantum calculation based on the Bonca-Trugman method [J. Bonča and S. A. Trugman, Phys. Rev. Lett. 75, 2566 (1995)]. In both approaches, thermal relaxation in the nuclear subspace is implemented in equivalent approximate ways: In the Ehrenfest calculation the uncoupled (to the electronic subsystem) motion of the classical (harmonic) oscillator is simply damped as would be implied by coupling to a Markovian zero temperature bath. In the quantum calculation, thermal relaxation is implemented by augmenting the Liouville equation for the oscillator density matrix with kinetic terms that account for the same relaxation. In both cases we calculate the probability to trap the electron by forming a polaron and the probability that it escapes to infinity. Comparing these calculations, we find that while both result in similar long time yields for these processes, the Ehrenfest-dynamics based calculation fails to account for the correct time scale for the polaron formation. This failure results, as usual, from the fact that at the early stage of polaron formation the classical nuclear dynamics takes place on an unphysical average potential surface that reflects the distributed electronic population in the system, while the quantum calculation accounts fully for correlations between the electronic and vibrational subsystems.

General and efficient simulation of pulse EPR spectra

We present a rather general and efficient method of simulating electron-spin echo spectra for spin systems where the microwave frequency does not simultaneously excite EPR transitions that share a common level. The approach can handle arbitrary pulse sequences with microwave pulses of arbitrary length and strength. The signal is computed as a sum over signals from the electron coherence transfer pathways contributing to the detected echo. For each pathway, amplitudes and frequencies of the signal components are computed and used to construct a spectral histogram from which the time-domain signal is obtained. For multinuclear spin systems, the nuclear subspace is factorized to accelerate the computation. The method is also applicable to high electron spin systems with significant zero-field splitting and to pulse electron-nuclear double resonance experiments. The method is implemented in the software package EasySpin, and several illustrative calculations are shown.

The Role of Charge Localization in Current‐Driven Dynamics

AbstractWe explore the role of charge localization in current‐triggered, resonance‐mediated, dynamical events in molecular junctions. To that end we use a simple model for a molecular rattle, a Li+C9H−9 zwitterion attached between two metal clusters. By varying the size of the metal clusters we systematically vary the degree of delocalization of the electronic orbitals underlying the resonant current, and thus can draw general conclusions regarding the effect of delocalization on dynamical processes induced by resonance inelastic current in molecular electronics.In the small cluster limit, we find interesting quantum dynamics in the nuclear subspace, corresponding to coherent tunneling of the wave packet through the barrier of an asymmetric double‐well potential. These dynamics are rapidly damped with increasing charge delocalization in extended systems.

Theory of current-induced dynamics in molecular-scale devices

We develop a theoretical framework for the study of inelastic resonant transport and current-driven dynamics in molecular nanodevices. Our approach combines a Born-Oppenheimer solution of the coordinate-, energy-, and voltage-dependent self-energy with a time-dependent scattering solution of the vibrational dynamics. The formalism is applied to two classic problems in current-triggered dynamics. As a simple example of bound-bound events in the nuclear subspace we study the problem of current-induced oscillations in Au-C60-Au heterojunctions. As a well-studied example of bound-free events in the nuclear subspace we revisit the problem of scanning-tunneling-microscopy-triggered H-atom desorption from a Si(100) surface. Our numerical results are supported by a simple analytically soluble model.

Nonadiabatic vibronic dynamics as a tool. From surface nanochemistry to coherently driven molecular machines

AbstractResonances are ubiquitous in molecular heterojunctions and in scanning tunneling microscopy (STM) experiments. In the former environment, resonance tunneling is essential for favorable wire‐length‐dependence of the conductance and is often the mechanism underlying conductance enhancement through application of a gate voltage. In the latter environment, resonance tunneling has served to develop a powerful vibrational spectroscopy.Resonance conductance is often strongly nonadiabatic; in the course of the tunneling event, electron energy is channelled into vibrational modes and triggers molecular dynamics. The qualitative physics underlying current‐driven, resonance‐mediated dynamics in molecular electronics is very simple, and is familiar from related phenomena such as gas phase electron‐molecule scattering and photochemistry on conducting surfaces. Equilibrium displacement between the initial and resonant states translates into vibronic coupling in the language of the Marcus theory of electron transfer; it produces a nonstationary superposition in the nuclear subspace that evolves during the resonance lifetime. Upon relaxation the system is internally excited and interesting dynamics is likely to ensue.While the underlying physics is very general, the single‐molecule STM and molecular heterojunction environments open unique and exciting opportunities. The former introduces the possibility of determining resonance lifetimes through fit of experimental voltage dependencies to a quantum mechanical theory. The latter introduces the possibility of developing coherently driven molecular machines, a new form of nanolithography, and a new means of manipulating the conductivity of molecular‐scale devices.We briefly review the theory of current‐driven dynamics in molecular‐scale devices, discuss the results of ongoing research on surface nanochemistry and molecular machines, and sketch a variety of potential applications.

Nuclear subspace of L0 and the Kernel of a linear measure

Let E be a locally convex space. Then E is nuclear metrizable if and only if there exists a σ-additive measure μ on E′ such that L: E → L 0( E′, μ), L( x) = 〈 x, ·〉, is an isomorphism. Let E be quasi-complete or barrelled. Suppose that there exists a σ-additive measure ν on E satisfying ( E′, τ ν )′ ⊃ E. Then E′ b is an isomorphic subspace of L 0( E, ν) and nuclear, where b is the strong dual topology and τ ν is the L 0( E, ν) topology. In the case where E is an LF space, for a random linear functional L: E → L 0(Ω, U , P), the next conditions are equivalent: (a) The cylinder set measure μ on E′ determined by L is σ-additive and (b) x n → 0 in E implies that L( x n ) → 0, P-a.s.