Journal ArticleDOI
Multilayer formulation of the multiconfiguration time-dependent Hartree theory
Haobin Wang,Michael Thoss +1 more
TLDR
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.read more
Citations
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Journal ArticleDOI
Ultrafast carbon monoxide photolysis and heme spin-crossover in myoglobin via nonadiabatic quantum dynamics
Konstantin Falahati,Hiroyuki Tamura,Irene Burghardt,Miquel Huix-Rotllant,Miquel Huix-Rotllant +4 more
TL;DR: In this article, quantum wavepacket dynamics were applied to elucidate the ultrafast photochemical mechanism for a heme-carbon monoxide (heme-CO) complex.
Journal ArticleDOI
Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
TL;DR: In this paper, a Lindblad master equation that approximates the Redfield equation without compromising the range of applicability of the Redfeld equation is presented. But this approximation only truncates terms in the redfield equation that average out over a time-scale typical of the quantum system, and it is not adaptable between its time-independent, time-dependent and Floquet form.
Journal ArticleDOI
Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force
TL;DR: This work rigorously investigates the quantum dissipative dynamics of a ratchet system described by a periodic potential model based on the Caldeira-Leggett Hamiltonian with a biharmonic force using the reduced hierarchy equations of motion in the Wigner space representation to find that at low temperature, while the quantum current is larger than the classical current in the cases of a high barrier, the opposite is true in the case of a low barrier.
Journal ArticleDOI
Renormalization of the frozen Gaussian approximation to the quantum propagator.
TL;DR: A new formula for the normalization integral is derived based on a prefactor free HK propagator which is amenable to "on the fly" computations and a new insight is provided into how the HK prefactor leads to approximate unitarity.
Book ChapterDOI
Geometric Methods on Low-Rank Matrix and Tensor Manifolds
TL;DR: This chapter presents numerical methods for low-rank matrix and Tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces, and discusses several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors.
References
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Light-Induced Redox Reactions in Nanocrystalline Systems
Anders Hagfeldt,Michael Graetzel +1 more
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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.
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Quantum Dissipative Systems
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
Journal ArticleDOI
The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets
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.
Journal ArticleDOI
Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2
John C. Tully,Richard K. Preston +1 more
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.