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

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

Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real and in reciprocal space, and (iii) accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

A density functional theory based analysis of photoinduced electron transfer in a triazacryptand based K+ sensor

The electronic structure and photoinduced electron transfer processes in a K+ fluorescent sensor that comprises a 4-amino-naphthalimide derived fluorophore with a triazacryptand lig- and is investigated using density functional theory (DFT) and time-dependent density functional theory (TDDFT) in order to rationalise the function of the sensor. The absorption and emission energies of the intense electronic excitation localised on the fluorophore are accurately described using a ∆SCF Kohn-Sham DFT approach, which gives excitation energies closer to experiment than TDDFT. Analysis of the molecular orbital diagram arising from DFT calculations for the isolated molecule or with implicit solvent cannot account for the function of the sensor and it is necessary to consider the relative energies of the electronic states formed from the local excitation on the fluorophore and the lowest fluorophore→chelator charge transfer state. The inclusion of solvent in these calculations is critical since the strong interaction of the charge transfer state with the solvent lowers it energy below the local fluorophore excited state making a reductive photoinduced electron transfer possible in the absence of K+, while no such process is possible when the sensor is bound to K+. The rate of electron transfer is quantified using Marcus theory, which gives a rate of electron transfer of k_ET=5.98 x 10^6 s−1

Geometric and Electronic Structures of the NiI and Methyl−NiIII Intermediates of Methyl-Coenzyme M Reductase†

ABSTRACT: Methyl-coenzyme M reductase (MCR) catalyzes the terminal step in the formation of biological methane from methyl-coenzyme M (Me-SCoM) and coenzyme B (CoBSH). The active site in MCR contains a Ni-F430 cofactor, which can exist in different oxidation states. The catalytic mechanism of methane formation has remained elusive despite intense spectroscopic and theoretical investigations. On the basis of spectroscopic and crystallographic data, the first step of the mechanism is proposed to involve a nucleophilic attack of the NiI active state (MCRred1) on Me-SCoM to form a NiIII-methyl intermediate, while computational studies indicate that the first step involves the attack of NiI on the sulfur of Me-SCoM, forming a CH3 radical and a NiII-thiolate species. In this study, a combination of Ni K-edge X-ray absorption spectroscopic (XAS) studies and density functional theory (DFT) calculations have been performed on the NiI (MCRred1), NiII (MCRred1-silent), and NiIII-methyl (MCRMe) states of MCR to elucidate the geometric and electronic structures of the different redox states. Ni K-edge EXAFS data are used to reveal a five-coordinate active site with an open upper axial coordination site in MCRred1. Ni K-pre-edge and EXAFS data and time-dependent DFT calculations unambiguously demonstrate the presence of a long Ni-C bond (∼2.04 Å) in the NiIII-methyl state of MCR. The formation and stability of this species support mechanism I, and the Ni-C bond length suggests a homolytic cleavage of the NiIII-methyl bon

Does Compound I Vary Significantly between Isoforms of Cytochrome P450?

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New Strategies in Modeling Electronic Structures and Properties with Applications to Actinides

This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic Hamiltonians that are frequently applied to account for relativistic effects. Then, we scrutinize various quantum chemistry methods that approximate the $N$-electron wave function. In this respect, we will review the most popular single- and multi-reference approaches that have been developed to model the multi-reference nature of heavy element compounds and their ground- and excited-state electronic structures. Specifically, we introduce various flavors of post-Hartree--Fock methods and optimization schemes like the complete active space self-consistent field method, the configuration interaction approach, the Fock-space coupled cluster model, the pair-coupled cluster doubles ansatz, also known as the antisymmetric product of 1 reference orbital geminal, and the density matrix renormalization group algorithm. Furthermore, we will illustrate how concepts of quantum information theory provide us with a qualitative understanding of complex electronic structures using the picture of interacting orbitals. While modern quantum chemistry facilitates a quantitative description of atoms and molecules as well as their properties, concepts of quantum information theory offer new strategies for a qualitative interpretation that can shed new light onto the chemistry of complex molecular compounds.Comment: 43 pages, 3 figures, Version of Recor