Quantum Dynamical Approach Research Articles

The ground state dynamics of s-trans-1,3-butadiene cation: An ab initio quantum dynamical study

We used high levels of ab initio electronic structure methods and nuclear quantum dynamical approach for studying the ground state dynamics of the s-trans-1,3-butadiene cation. To benchmark the quality of the electronic structure calculations, potential energy surfaces for the energetically lowest lying doublet X2Bg, A2Au and B2Ag states along seven vibrational modes with considering mode S8 (asymmetric stretching CC bond) were calculated at the MRCI/CAS(10,7) and CAS(8,8) levels of theories. Considering contribution of S8 mode in the nuclear quantum dynamical investigation leads to a more realistic description of the ground state dynamics of s-trans-1,3-butadiene, which was not addressed before. Our calculation shows that the population transfer takes place in a time scale 50-60 fs. We also calculated the photoelectron spectrum of the molecular system under study. The excellent agreement of spectrum with the experimental one leads us the conclusion that the potential energy surfaces of three lowest cationic X2Bg, A2Au and B2Ag states and time-dependent population analysis of X2Bg were accurately determined.

Accurate and efficient DFT-based diabatization for hole and electron transfer using absolutely localized molecular orbitals.

Diabatic states and the couplings between them are important for quantifying, elucidating, and predicting the rates and mechanisms of many chemical and biochemical processes. Here, we propose and investigate approaches to accurately compute diabatic couplings from density functional theory (DFT) using absolutely localized molecular orbitals (ALMOs). ALMOs provide an appealing approach to generate variationally optimized diabatic states and obtain their associated forces, which allows for the relaxation of the donor and acceptor orbitals in a way that is internally consistent in how the method treats both the donor and acceptor states. Here, we show that one can obtain more accurate electronic couplings between ALMO-based diabats by employing the symmetrized transition density matrix to evaluate the exchange-correlation contribution. We demonstrate that this approach yields accurate results in comparison to other commonly used DFT-based diabatization methods across a wide array of electron and hole transfer processes occurring in systems ranging from conjugated organic molecules, such as thiophene and pentacene, to DNA base pairs. We also show that this approach yields accurate diabatic couplings even when combined with lower tiers of the DFT hierarchy, opening the door to combining it with quantum dynamics approaches to provide an ab initio treatment of nonadiabatic processes in the condensed phase.

Observation of the Low‐Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces

AbstractUsing the helium nanodroplet isolation setup at the ultrabright free‐electron laser source FELIX in Nijmegen (BoHeNDI@FELIX), the intermolecular modes of water dimer in the frequency region from 70 to 550 cm−1 were recorded. Observed bands were assigned to donor torsion, acceptor wag, acceptor twist, intermolecular stretch, donor torsion overtone, and in‐plane and out‐of‐plane librational modes. This experimental data set provides a sensitive test for state‐of‐the‐art water potentials and dipole moment surfaces. Theoretical calculations of the IR spectrum are presented using high‐level quantum and approximate quasiclassical molecular dynamics approaches. These calculations use the full‐dimensional ab initio WHHB potential and dipole moment surfaces. Based on the experimental data, a considerable increase of the acceptor switch and a bifurcation tunneling splitting in the librational mode is deduced, which is a consequence of the effective decrease in the tunneling barrier.

Observation of the Low-Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces.

Using the helium nanodroplet isolation setup at the ultrabright free‐electron laser source FELIX in Nijmegen (BoHeNDI@FELIX), the intermolecular modes of water dimer in the frequency region from 70 to 550 cm−1 were recorded. Observed bands were assigned to donor torsion, acceptor wag, acceptor twist, intermolecular stretch, donor torsion overtone, and in‐plane and out‐of‐plane librational modes. This experimental data set provides a sensitive test for state‐of‐the‐art water potentials and dipole moment surfaces. Theoretical calculations of the IR spectrum are presented using high‐level quantum and approximate quasiclassical molecular dynamics approaches. These calculations use the full‐dimensional ab initio WHHB potential and dipole moment surfaces. Based on the experimental data, a considerable increase of the acceptor switch and a bifurcation tunneling splitting in the librational mode is deduced, which is a consequence of the effective decrease in the tunneling barrier.

Quantum dynamical simulation of intramolecular singlet fission in covalently coupled pentacene dimers.

We analyze the dynamics of intramolecular singlet fission in a series of pentacene-based dimers consisting of two pentacene-like chromophores covalently bonded to a phenylene linker in ortho, meta, and para positions. The study uses a quantum dynamical approach that employs a model vibronic Hamiltonian whose parameters are obtained using multireference perturbation theory methods. The results highlight the different role of the direct and mediated mechanism in these systems, showing that the population of the multiexcitonic state, corresponding to the first step of the intramolecular singlet fission process, occurs mainly through a superexchange-like mechanism involving doubly excited or charge transfer states that participate in the process in a virtual way. In addition, the systems investigated provide insight into the roles that built-in geometrical constraints and the electronic structure of the spacer play in the intramolecular singlet fission process.

Stochastic wave packet approach to nonadiabatic scattering of diatomic molecules from metals.

In this contribution, we present a quantum dynamical approach to study inelastic scattering of diatomic molecules from metal surfaces at normal incidence. The dissipative dynamics obeys a stochastic Schrödinger equation describing the time-evolution of the system as a piecewise deterministic process. Energy exchange between the molecular vibrational degrees of freedom and the metal electrons is represented using operators in tensor product form, which are coupled via anharmonic transition rates calculated from first-order perturbation theory. Full dimensional observables are obtained by averaging over simulations in 4D-including the internal stretch, the distance to the surface, and the orientation angles-at different surface sites. The method is applied to the state-resolved scattering of vibrationally excited NO from Au(111), revealing important channels for quantized energy relaxation.

Quantum Algorithm for Shortest Path Search in Directed Acyclic Graph

In this work, we consider a well-known “Single Source Shortest Path Search” problems for weighted directed acyclic graphs (DAGs). We suggest a quantum algorithm with time complexity $O(\sqrt {nm} \,\log \;n)$ and O(1/n) error probability, where n is a number of Vertexes, m is the number of edges. We use quantum dynamic programming approach (Khadiev, 2018) and Durr and Hoyer minimum search algorithm to speed up our search. Our algorithm is better than C. Durr and coauthors’ quantum algorithm for an undirected graph. The time complexity of C. Durr’s algorithm is $O(\sqrt {nm} \,{(\log \;n)^2})$ . The best known deterministic algorithm for the problem is based on a dynamic programming approach and its time complexity is O (n + m). At the same time, if we use algorithms for general graphs, then we do not get better results. The time complexity of best implementations of Dijkstra’s algorithm with Fibonacci heap is O (m + n log n).

The discovery of chemically produced mass independent isotope effects: The physical chemistry basis and applications to the early solar system, planetary atmospheres, and the origin of life

The discovery of chemically produced mass independent isotope effects: The physical chemistry basis and applications to the early solar system, planetary atmospheres, and the origin of life

Impurity induced renormalized phonon spectrum of cuprate superconductors

The potential problem of anharmonic lattice vibrations in high-temperature superconductors (HTS) using the most suitable Born–Mayer–Huggins (BMH) potential has been taken up to investigate the renormalized phonon density of states (RPDOS). In order to develop the suitable results, the many body theory using quantum dynamical approach of Green’s function (GF) via an almost complete Hamiltonian (without using BCS type Hamiltonian) has been incorporated which includes harmonic electron and phonon Hamiltonian, electron–phonon interaction Hamiltonian, anharmonic and defect Hamiltonian. The derivation of anharmonic phonon GF for modified form of BMH potential enables to evaluate the renormalized and perturbed mode phonon frequencies of solids. The expressions obtained for the RPDOS can be resolved into diagonal and nondiagonal parts of which the nondiagonal part chiefly depends on impurities and disappears in pure crystals. A large number of new features are investigated in the light of this formulation followed by the numerical analysis for the energy spectrum of representative cuprate HTS YBa2Cu3O[Formula: see text]. The inclusion of defects, anharmonicities and electron–phonon interactions in the cuprate superconductors substantially modifies the scenario of RPDOS and reveals a large number of unexplained peaks in the spectrum.

Investigating photoinduced proton coupled electron transfer reaction using quasi diabatic dynamics propagation.

We investigate photoinduced proton-coupled electron transfer (PI-PCET) reactions through a recently developed quasi-diabatic (QD) quantum dynamics propagation scheme. This scheme enables interfacing accurate diabatic-based quantum dynamics approaches with adiabatic electronic structure calculations for on-the-fly simulations. Here, we use the QD scheme to directly propagate PI-PCET quantum dynamics with the diabatic partial linearized density matrix path-integral approach with the instantaneous adiabatic electron-proton vibronic states. Our numerical results demonstrate the importance of treating protons quantum mechanically in order to obtain accurate PI-PCET dynamics as well as the role of solvent fluctuation and vibrational relaxation on proton tunneling in various reaction regimes that exhibit different kinetic isotope effects. This work opens the possibility to study the challenging PI-PCET reactions through accurate diabatic quantum dynamics approaches combined with efficient adiabatic electronic structure calculations.

Perspective: Ring-polymer instanton theory.

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

MCTDH on-the-fly: Efficient grid-based quantum dynamics without pre-computed potential energy surfaces.

We present significant algorithmic improvements to a recently proposed direct quantum dynamics method, based upon combining well established grid-based quantum dynamics approaches and expansions of the potential energy operator in terms of a weighted sum of Gaussian functions. Specifically, using a sum of low-dimensional Gaussian functions to represent the potential energy surface (PES), combined with a secondary fitting of the PES using singular value decomposition, we show how standard grid-based quantum dynamics methods can be dramatically accelerated without loss of accuracy. This is demonstrated by on-the-fly simulations (using both standard grid-based methods and multi-configuration time-dependent Hartree) of both proton transfer on the electronic ground state of salicylaldimine and the non-adiabatic dynamics of pyrazine.

A novel quantum dynamical approach in electron microscopy combining wave-packet propagation with Bohmian trajectories.

The numerical analysis of the diffraction features rendered by transmission electron microscopy typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and any of its variants). Although numerically advantageous (relatively simple implementations and low computational costs), they involve important approximations and thus their range of applicability is limited. To overcome such limitations, an alternative, more general approach is proposed, based on an optimal combination of wave-packet propagation with the on-the-fly computation of associated Bohmian trajectories. For the sake of clarity, but without a loss of generality, the approach is used to analyze the diffraction of an electron beam by a thin aluminum slab as a function of three different incidence (working) conditions which are of interest in electron microscopy: the probe width, the tilting angle, and the beam energy. Specifically, it is shown that, because there is a dependence on particular thresholds of the beam energy, this approach provides a clear description of the diffraction process at any energy, revealing at the same time any diversion of the beam inside the material towards directions that cannot be accounted for by other conventional methods, which is of much interest when dealing with relatively low energies and/or relatively large tilting angles.

Nonequilibrium Lifshitz theory as a steady state of a full dynamical quantum system

In this work we analyze the validity of Lifshitz's theory for the case of non-equilibrium scenarios from a full quantum dynamical approach. We show that Lifshitz's framework for the study of the Casimir pressure is the result of considering the long-time regime (or steady state) of a well-defined fully quantized problem, subjected to initial conditions for the electromagnetic field interacting with real materials. For this, we implement the closed time path formalism developed in previous works to study the case of two half spaces (modeled as composite environments, consisting in quantum degrees of freedom plus thermal baths) interacting with the electromagnetic field. Starting from initial uncorrelated free subsystems, we solve the full time evolution, obtaining general expressions for the different contributions to the pressure that take part on the transient stage. Using the analytic properties of the retarded Green functions, we obtain the long-time limit of these contributions to the total Casimir pressure. We show that, in the steady state, only the baths' contribute, in agreement with the results of previous works, where this was assumed without justification. We also study in detail the physics of the initial conditions' contribution and the concept of modified vacuum modes, giving insights about in which situations one would expect a non vanishing contribution at the steady state of a non-equilibrium scenario. This would be the case when considering finite width slabs instead of half-spaces.

An investigation of algebraic quantum dynamics for mesoscopic coupled electric circuits with mutual inductance

Based on the electrical charge discreteness, the Hamiltonian operator for the mutual inductance coupled quantum mesoscopic LC circuits has been found. The persistent current on two driven coupled mesoscopic electric pure L circuits (two quantum loops) has been obtained by using algebraic quantum dynamic approach. The influence of the mutual inductance on energy spectrum and quantum fluctuations of the charge and current for two coupled quantum electric mesoscopic LC circuits have been investigated.

Real-Time Quantum Dynamics Reveals Complex, Many-Body Interactions in Solvated Nanodroplets.

Electronic excitations in the liquid phase are surprisingly rich and considerably more complex than either gas-phase or solid-state systems. While the majority of physical and biological processes take place in solvent, our understanding of nonequilibrium excited-state processes in these condensed phase environments remains far from complete. A central and long-standing issue in these solvated environments is the assessment of many-body interactions, particularly when the entire system is out of equilibrium and many quantum states participate in the overall process. Here we present a microscopic picture of solute-solvent electron dynamics and solvatochromic effects, which we uncover using a new real-time quantum dynamics approach for extremely large solvated nanodroplets. In particular, we find that a complex interplay of quantum interactions underlies our observations of solute-solvent effects, and simple macroscopic solvatochromic shifts can even be qualitatively different at the microscopic molecular level in these systems. By treating both the solvent and the solute on the same footing at a quantum-mechanical level, we demonstrate that the electron dynamics in these systems are surprisingly complex, and the emergence of many-body interactions underlies the dynamics in these solvated systems.

Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane.

Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.

A Quantum Dynamical Approach to Matrix Khrushchev's Formulas

AbstractKhrushchev's formula is the cornerstone of the so‐called Khrushchev theory, a body of results which has revolutionized the theory of orthogonal polynomials on the unit circle. This formula can be understood as a factorization of the Schur function for an orthogonal polynomial modification of a measure on the unit circle. No such formula is known in the case of matrix‐valued measures. This constitutes the main obstacle to generalize Khrushchev theory to the matrix‐valued setting, which we overcome in this paper.It was recently discovered that orthogonal polynomials on the unit circle and their matrix‐valued versions play a significant role in the study of quantum walks, the quantum mechanical analogue of random walks. In particular, Schur functions turn out to be the mathematical tool which best codify the return properties of a discrete time quantum system, a topic in which Khrushchev's formula has profound and surprising implications.We will show that this connection between Schur functions and quantum walks is behind a simple proof of Khrushchev's formula via “quantum” diagrammatic techniques for CMV matrices. This does not merely give a quantum meaning to a known mathematical result, since the diagrammatic proof also works for matrix‐valued measures. Actually, this path‐counting approach is so fruitful that it provides different matrix generalizations of Khrushchev's formula, some of them new even in the case of scalar measures.Furthermore, the path‐counting approach allows us to identify the properties of CMV matrices which are responsible for Khrushchev's formula. On the one hand, this helps to formalize and unify the diagrammatic proofs using simple operator theory tools. On the other hand, this is the origin of our main result which extends Khrushchev's formula beyond the CMV case, as a factorization rule for Schur functions related to general unitary operators.© 2016 Wiley Periodicals, Inc.

Fe(II)-Polypyridines as Chromophores in Dye-Sensitized Solar Cells: A Computational Perspective.

Over the past two decades, dye-sensitized solar cells (DSSCs) have become a viable and relatively cheap alternative to conventional crystalline silicon-based systems. At the heart of a DSSC is a wide band gap semiconductor, typically a TiO2 nanoparticle network, sensitized with a visible light absorbing chromophore. Ru(II)-polypyridines are often utilized as chromophores thanks to their chemical stability, long-lived metal-to-ligand charge transfer (MLCT) excited states, tunable redox potentials, and near perfect quantum efficiency of interfacial electron transfer (IET) into TiO2. More recently, coordination compounds based on first row transition metals, such as Fe(II)-polypyridines, gained some attention as potential sensitizers in DSSCs due to their low cost and abundance. While such complexes can in principle sensitize TiO2, they do so very inefficiently since their photoactive MLCT states undergo intersystem crossing (ISC) into low-lying metal-centered states on a subpicosecond time scale. Competition between the ultrafast ISC events and IET upon initial excitation of Fe(II)-polypyridines is the main obstacle to their utilization in DSSCs. Suitability of Fe(II)-polypyridines to serve as sensitizers could therefore be improved by adjusting relative rates of the ISC and IET processes, with the goal of making the IET more competitive with ISC. Our research program in computational inorganic chemistry utilizes a variety of tools based on density functional theory (DFT), time-dependent density functional theory (TD-DFT) and quantum dynamics to investigate structure-property relationships in Fe(II)-polypyridines, specifically focusing on their function as chromophores. One of the difficult problems is the accurate determination of energy differences between electronic states with various spin multiplicities (i.e., (1)A, (1,3)MLCT, (3)T, (5)T) in the ISC cascade. We have shown that DFT is capable of predicting the trends in the energy ordering of these electronic states in a set of structurally related complexes with the help of appropriate benchmarks, based either on experimental data or higher-level ab initio calculations. Models based on TD-DFT and quantum dynamics approaches have proven very useful in understanding IET processes in Fe(II)-polypyridine-TiO2 assemblies. For example, they helped us to elucidate the origin of "band selective" sensitization in the [Fe(bpy-dca)2(CN)2]-TiO2 assembly (bpy-dca = 2,2'-bipyridine-4,4'-dicarboxylic acid), first observed by Ferrere and Gregg [ Ferrere , S. ; Gregg , B. A. J. Am. Chem. Soc. 1998 , 120 , 843 . ]. They also shed light on the relationship between the linker group that anchors Fe(II)-polypyridines onto the TiO2 surface and the speed of IET in Fe(II)-polypyridine-TiO2 assemblies. More interestingly, our results show that the IET efficiency is strongly correlated with the amount of electron density on the linker group and that one can obtain insights into the IET in dye-semiconductor assemblies based on ground state electronic structure calculations alone. This may be useful for quick screening of a large number of complexes for use as potential sensitizers in DSSCs, especially if followed up by TD-DFT and quantum dynamics simulations for selected target compounds to confirm efficient sensitization. While our focus over the past few years has been exclusively on Fe(II)-polypyridines, the computational strategies outlined in this Account are applicable to a wide variety of sensitizers.

Геометрия релятивистского квантового хаоса: Новый подход к динамике квантовых систем в электромагнитном поле и единообразие и очарование хаоса

Work is devoted to the development of the theoretical foundations of the universal new relativistic chaos-geometric and quantum-dynamic approach that consistently includes a number of new relativistic quantum models and a number of new or improved methods of analysis (correlation integral, fractal analysis, algorithms, average mutual information, false nearest neighbors, Lyapunov exponents, surrogate data, non-linear prediction, spectral methods, etc.) to solve problems of complete modelling relativistic chaotic dynamics in an electromagnetic field. For a number of atomic systems there are firstly discovered availability of a relativistic quantum chaos and obtained the corresponding quantitative data on the chaos characteristics.