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Journal ArticleDOI

Multilayer formulation of the multiconfiguration time-dependent Hartree theory

02 Jul 2003-Journal of Chemical Physics (American Institute of Physics)-Vol. 119, Iss: 3, pp 1289-1299
TL;DR: In this paper, a multilayer formulation of the multiconfiguration time-dependent Hartree (MCTDH) theory is presented, where the single-particle (SP) functions in the original MCTDH method are further expressed employing a timedependent multi-figurational expansion, and the Dirac-Frenkel variational principle is applied to optimally determine the equations of motion.
Abstract: A multilayer (ML) formulation of the multiconfiguration time-dependent Hartree (MCTDH) theory is presented. In this new approach, the single-particle (SP) functions in the original MCTDH method are further expressed employing a time-dependent multiconfigurational expansion. The Dirac–Frenkel variational principle is then applied to optimally determine the equations of motion. Following this strategy, the SP groups are built in several layers, where each top layer SP can contain many more Cartesian degrees of freedom than in the previous formulation of the MCTDH method. As a result, the ML-MCTDH method has the capability of treating substantially more physical degrees of freedom than the original MCTDH method, and thus significantly enhances the ability of carrying out quantum dynamical simulations for complex molecular systems. The efficiency of the new formulation is demonstrated by converged quantum dynamical simulations for systems with a few hundred to a thousand degrees of freedom.
Citations
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Journal ArticleDOI
TL;DR: In this paper, carbon nanoparticles were prepared by refluxing the combustion soot of natural gas in nitric acid and the resulting particles exhibited an average diameter of 4.8 ± 0.6 nm, and the crystalline lattices were consistent with graphitic carbons.
Abstract: Carbon nanoparticles were prepared by refluxing the combustion soot of natural gas in nitric acid. Transmission Electron Microscopy measurements showed that the resulting particles exhibited an average diameter of 4.8 ± 0.6 nm, and the crystalline lattices were consistent with graphitic carbons. 13C NMR and FTIR spectroscopic measurements further confirmed the presence of sp2 carbons in the form of aryl and carboxylic/carbonyl moieties. The resulting carbon nanoparticles were found to emit photoluminescence with a quantum yield of approximately 0.43%. Additionally, the emission band energy of the carbon nanoparticle was very similar to that of much smaller carbon nanoparticles obtained from candle soot, suggesting that the photoluminescence might arise from particle surface states, analogous to the behaviors of semiconductor quantum dots with an indirect bandgap. In electrochemical measurements, two pairs of well-defined voltammetric waves were observed, which might be ascribed to the peripheral functiona...

637 citations

Journal ArticleDOI
TL;DR: This survey attempts to give a literature overview of current developments in low-rank tensor approximation, with an emphasis on function-related tensors.
Abstract: During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

608 citations


Cites methods from "Multilayer formulation of the multi..."

  • ...Moreover, the so called multilayer multi-configuration time-dependent Hartree method (MLMCTDH) introduced in [265] makes use of a decomposition based on general trees instead of binary trees....

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Journal ArticleDOI
TL;DR: This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in $d=2$), and it is proved that one can find low rank (almost) best approximations in a hierarchical format ($\mathcal{H}$-Tucker) which requires only $\ mathcal{O}((d-1)k^3+dnk)$ parameters.
Abstract: We define the hierarchical singular value decomposition (SVD) for tensors of order $d\geq2$. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in $d=2$), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical format ($\mathcal{H}$-Tucker) which requires only $\mathcal{O}((d-1)k^3+dnk)$ parameters, where $d$ is the order of the tensor, $n$ the size of the modes, and $k$ the (hierarchical) rank. The $\mathcal{H}$-Tucker format is a specialization of the Tucker format and it contains as a special case all (canonical) rank $k$ tensors. Based on this new concept of a hierarchical SVD we present algorithms for hierarchical tensor calculations allowing for a rigorous error analysis. The complexity of the truncation (finding lower rank approximations to hierarchical rank $k$ tensors) is in $\mathcal{O}((d-1)k^4+dnk^2)$ and the attainable accuracy is just 2-3 digits less than machine precision.

602 citations


Cites background or methods from "Multilayer formulation of the multi..."

  • ...To our best knowledge the first successful approach to a hierarchical format has been developed by Beck & Jäckle & Worth & Meyer [1] and Wang & Thoss[18] (these references were kindly pointed out to us by Christian Lubich and Michael Griebel)....

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  • ...The hierarchical or multilayer format from [1, 18] is exactly of the H-Tucker form....

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  • ...We have defined the hierarchical singular value decomposition for tensors of order d ≥ 2 in the H-Tucker format (also known as the Φ-system representation [10] or previously the multilayer MCTDH format [18])....

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  • ...To our best knowledge the first successful approach to a hierarchical format has been developed by Beck & Jäckle & Worth & Meyer [1] and Wang & Thoss[18] (these references were kindly pointed out to us by Christian Lubich and Michael Griebel)....

    [...]

Journal ArticleDOI
John C. Tully1
TL;DR: This Perspective examines the most significant theoretical and computational obstacles to achieving nonadiabatic dynamics realism, and suggests some possible strategies that may prove fruitful.
Abstract: Nonadiabatic dynamics—nuclear motion evolving on multiple potential energy surfaces—has captivated the interest of chemists for decades. Exciting advances in experimentation and theory have combined to greatly enhance our understanding of the rates and pathways of nonadiabatic chemical transformations. Nevertheless, there is a growing urgency for further development of theories that are practical and yet capable of reliable predictions, driven by fields such as solar energy, interstellar and atmospheric chemistry, photochemistry, vision, single molecule electronics, radiation damage, and many more. This Perspective examines the most significant theoretical and computational obstacles to achieving this goal, and suggests some possible strategies that may prove fruitful.

524 citations

Journal ArticleDOI
TL;DR: The theory and fundamental principles of the spin-vibronic mechanism for ISC are presented, followed by empirical rules to estimate the rate of ISC within this regime.
Abstract: Intersystem crossing (ISC), formally forbidden within nonrelativistic quantum theory, is the mechanism by which a molecule changes its spin state. It plays an important role in the excited state decay dynamics of many molecular systems and not just those containing heavy elements. In the simplest case, ISC is driven by direct spin–orbit coupling between two states of different multiplicities. This coupling is usually assumed to remain unchanged by vibrational motion. It is also often presumed that spin-allowed radiationless transitions, i.e. internal conversion, and the nonadiabatic coupling that drives them, can be considered separately from ISC and spin–orbit coupling owing to the vastly different time scales upon which these processes are assumed to occur. However, these assumptions are too restrictive. Indeed, the strong mixing brought about by the simultaneous presence of nonadiabatic and spin–orbit coupling means that often the spin, electronic, and vibrational dynamics cannot be described independe...

505 citations

References
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Journal ArticleDOI
TL;DR: A review with 156 refs on interfacial electron transfer reactions in colloidal semiconductor solns and thin films and their application for solar light energy conversion and photocatalytic water purifn is presented in this paper.
Abstract: A review with 156 refs. on interfacial electron transfer reactions in colloidal semiconductor solns. and thin films and their application for solar light energy conversion and photocatalytic water purifn. Some of the topics discussed include; optical and electronic properties of colloidal semiconductor particles, quantum size effects in the photoluminescence of colloidal semiconductors, light-induced charge sepn., dynamics of interfacial charge transfer processes, properties and prepn. of nanocryst. semiconductor electrodes, energetics and operations of the nanoporous solar cell.

5,065 citations

Journal ArticleDOI
TL;DR: In this article, a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment is presented, and an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of dissipative environments to the spin-boson problem is given.
Abstract: This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For $sl1$ the system is localized at zero temperature, and at finite $T$ relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For $sg2$ it undergoes underdamped coherent oscillations for all relevant temperatures, while for $1lsl2$ there is a crossover from coherent oscillation to overdamped relaxation as $T$ increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case, $s=1$, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature $T$: over most of the ($\ensuremath{\alpha}$,$T$) plane (including the whole region $\ensuremath{\alpha}g1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low $T$ and $0l\ensuremath{\alpha}l\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.

4,047 citations

Book
15 Dec 1999
TL;DR: In this paper, the authors present a survey of the various approaches to Quantum-Statistical metastability, including Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational
Abstract: Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-Ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational Approach and Effective Potential Method Unified Approach to Quantum-Statistical Metastability: From Thermal Activation to Quantum Tunneling Electron Transfer and Incoherent Tunneling Macroscopic Quantum Effects in Josephson Systems Spin-Boson Model and Qubit Dissipative Two-State System: Thermodynamics and Dynamics Single-Charge and Cooper-Pair Tunneling Magnetic and Spin Tunneling Driven Quantum Tunneling Nonequilibrium Quantum Transport Full Counting Statistics Charge Transport in Quantum Impurity Systems Duality and Self-Duality.

3,777 citations

Journal ArticleDOI
TL;DR: In this article, a review of the multiconfiguration time-dependent Hartree (MCTDH) method for propagating wavepackets is given, and the formal derivation, numerical implementation, and performance of the method are detailed.

2,053 citations

Journal ArticleDOI
TL;DR: In this article, an extension of the classical trajectory approach is proposed that may be useful in treating many types of nonadiabatic molecular collisions, where nuclei are assumed to move classically on a single potential energy surface until an avoided surface crossing or other region of large NDE coupling is reached.
Abstract: An extension of the classical trajectory approach is proposed that may be useful in treating many types of nonadiabatic molecular collisions. Nuclei are assumed to move classically on a single potential energy surface until an avoided surface crossing or other region of large nonadiabatic coupling is reached. At such points the trajectory is split into two branches, each of which follows a different potential surface. The validity of this model as applied to the HD2+ system is assessed by numerical integration of the appropriate semiclassical equations. A 3d “trajectory surface hopping” treatment of the reaction of H+ with D2 at a collision energy of 4 eV is reported. The excellent agreement with experiment is an encouraging indication of the potential usefulness of this approach.

1,416 citations