Energy Conserving Approximations to the Quantum Potential: Dynamics with Linearized Quantum Force

Solution of the Schrödinger 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

Bohmian Dynamics on Subspaces Using Linearized Quantum Force

In the de Broglie–Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant quantum-mechanical effects in the semiclassical scattering problems of nuclear dynamics. In this paper we formulate the Bohmian dynamics on subspaces and define the energy-conserving approximate quantum potential in terms of optimized nonclassical momentum, extended to include the domain boundary functions. This generalization allows a better description of the non-Gaussian wave packets and general potentials in terms of simple fitting functions. The optimization is performed independently for each domain and each dimension. For linear fitting functions optimal parameters are expressed in terms of the first and second moments of the trajectory distribution. Examples are given for one-dimensional anharmonic systems and for the collinear hydrogen exchange reaction

Semiclassical Dynamics with Quantum Trajectories: Formulation and Comparison with the Semiclassical Initial Value Representation Propagator

We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare AQP method to the widely used semiclassical propagator of Herman and Kluk by computing energy-resolved transmission probabilities for the Eckart barrier from the wave packet time-correlation functions. We find the results obtained with the Herman–Kluk propagator to be essentially equivalent to those of AQP method with a one-Gaussian density fit for several barrier widths

Stable Long-Time Semiclassical Description of Zero-Point Energy in High-Dimensional Molecular Systems

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom

Modified Quantum Trajectory Dynamics Using a Mixed Wave Function Representation

Dynamics of quantum trajectories provides an efficient framework for description of various quantum effects in large systems, but it is unstable near the wave function density nodes where the quantum potential becomes singular. A mixed coordinate space/polar representation of the wave function is used to circumvent this problem. The resulting modified trajectory dynamics associated with the polar representation is nonsingular and smooth. The interference structure and the nodes of the wave function density are described, in principle, exactly in the coordinate representation. The approximate version of this approach is consistent with the semiclassical linearized quantum force method [S. Garashchuk and V. A. Rassolov, J. Chem. Phys. 120, 1181 (2004)]. This approach is exact for general wave functions with the density nodes in a locally quadratic potential

Semiclassical Nonadiabatic Dynamics with Quantum Trajectories

Dynamics based on quantum trajectories with approximate quantum potential is generalized to nonadiabatic systems and its semiclassical properties are discussed. The formulation uses the mixed polar-coordinate space representation of a wave function. The polar part describes the overall time evolution of the wave-function components semiclassically using the single-surface approximate quantum potential. The coordinate part represents a complex“population” amplitude, which in case of localized coupling can be solved for quantum mechanically in an efficient manner. In the high-energy regime this is accomplished by using a small basis determined by the coupling between surfaces. An illustration is given for a typical curve-crossing problem. The energy-resolved probabilities obtained from the time evolution of two wave packets for a wide range of energies are in excellent agreement with exact results for energies above the threshold of the diabatic reaction, including the case of total nonadiabatic transition

Geminal Model Chemistry II. Perturbative Corrections

We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein–Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, with dispersion interactions between the geminals being the dominant effect missing in the reference wave functions

Semiclassical Nonadiabatic Dynamics Based on Quantum Trajectories for the O(\u3csup\u3e3\u3c/sup\u3eP,\u3csup\u3e1\u3c/sup\u3eD)+H\u3csub\u3e2\u3c/sub\u3e System

The O(3P,1D)+H2→OH+H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states

Semiclassical Nonadiabatic Dynamics Using a Mixed Wave-Function Representation

Nonadiabatic effects in quantum dynamics are described using a mixed polar/coordinate space representation of the wave function. The polar part evolves on dynamically determined potential surfaces that have diabatic and adiabatic potentials as limiting cases of weak localized and strong extended diabatic couplings. The coordinate space part, generalized to a matrix form, describes transitions between the surfaces. Choice of the effective potentials for the polar part and partitioning of the wave function enables one to represent the total wave function in terms of smooth components that can be accurately propagated semiclassically using the approximate quantum potential and small basis sets. Examples are given for two-state one-dimensional problems that model chemical reactions that demonstrate the capabilities of the method for various regimes of nonadiabatic dynamics

Breaking the photoswitch speed limit

The forthcoming generation of materials, including artificial muscles, recyclable and healable systems, photochromic heterogeneous catalysts, or tailorable supercapacitors, relies on the fundamental concept of rapid switching between two or more discrete forms in the solid state. Herein, we report a breakthrough in the “speed limit” of photochromic molecules on the example of sterically-demanding spiropyran derivatives through their integration within solvent-free confined space, allowing for engineering of the photoresponsive moiety environment and tailoring their photoisomerization rates. The presented conceptual approach realized through construction of the spiropyran environment results in ~1000 times switching enhancement even in the solid state compared to its behavior in solution, setting a record in the field of photochromic compounds. Moreover, integration of two distinct photochromic moieties in the same framework provided access to a dynamic range of rates as well as complementary switching in the material’s optical profile, uncovering a previously inaccessible pathway for interstate rapid photoisomerization.</p