Energy conserving approximations to the quantum potential: dynamics with linearized quantum force

Solution of the Schrodinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.     

A Dual Threat: Redox-Activity and Electronic Structures of Well-Defined Donor–Acceptor Fulleretic Covalent-Organic Materials

The effect of donor (D)–acceptor (A) alignment on the materials electronic structure was probed for the first time using novel purely organic porous crystalline materials with covalently bound two- and three-dimensional acceptors. The first studies towards estimation of charge transfer rates as a function of acceptor stacking are in line with the experimentally observed drastic, eight-fold conductivity enhancement. The first evaluation of redox behavior of buckyball- or tetracyanoquinodimethane-integrated crystalline was conducted. In parallel with tailoring the D-A alignment responsible for “static” changes in materials properties, an external stimulus was applied for “dynamic” control of the electronic profiles. Overall, the presented D–A strategic design, with stimuli-controlled electronic behavior, redox activity, and modularity could be used as a blueprint for the development of electroactive and conductive multidimensional and multifunctional crystalline porous materials.     

Stack the Bowls: Tailoring the Electronic Structure of Corannulene‐Integrated Crystalline Materials

We report the first examples of purely organic donor–acceptor materials with integrated π‐bowls (πBs) that combine not only crystallinity and high surface areas but also exhibit tunable electronic properties, resulting in a four‐orders‐of‐magnitude conductivity enhancement in comparison with the parent framework. In addition to the first report of alkyne–azide cycloaddition utilized for corannulene immobilization in the solid state, we also probed the charge transfer rate within the Marcus theory as a function of mutual πB orientation for the first time, as well as shed light on the density of states near the Fermi edge. These studies could foreshadow new avenues for πB utilization for the development of optoelectronic devices or a route for highly efficient porous electrodes.     

Confinement-Driven Photophysics in Hydrazone-Based Hierarchical Materials

Confinement-imposed photophysics was probed for novel stimuli-responsive hydrazone-based compounds demonstrating a conceptual difference in their behavior within 2D versus 3D porous matrices for the first time. The challenges associated with photoswitch isomerization arising from host interactions with photochromic compounds in 2D scaffolds could be overcome in 3D materials. Solution-like photoisomerization rate constants were realized for sterically demanding hydrazone derivatives in the solid state through their coordinative immobilization in 3D scaffolds. According to steady-state and time-resolved photophysical measurements and theoretical modeling, this approach provides access to hydrazone-based materials with fast photoisomerization kinetics in the solid state. Fast isomerization of integrated hydrazone derivatives allows for probing and tailoring resonance energy transfer (ET) processes as a function of excitation wavelength, providing a novel pathway for ET modulation.     

Incorporation of quantum effects for selected degrees of freedom into the trajectory-based dynamics using spatial domains

The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the "quantum" degrees of freedom describing light particles such as protons, while neglecting with the quantum force for the heavy, nearly classical nuclei. The entire system comprised of light and heavy particles is described by a single wavefunction of full dimensionality. The coordinate space of heavy particles is divided into spatial domains or subspaces. The quantum force acting on the light particles is determined for each domain of similar configurations of the heavy nuclei. This approach effectively introduces parametric dependence of the reduced dimensionality quantum force, on classical degrees of freedom. This strategy improves accuracy of the quantum force and does not restrict interaction between the domains. The concept is illustrated for two-dimensional scattering systems, where the quantum force is required to reproduce vibrational energy of the quantum degree of freedom.     

Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall

Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.