Multilayer formulation of the multiconfiguration time-dependent Hartree theory

Wang, Haobin; Thoss, Michael

doi:10.1063/1.1580111

Cited by 865 publications

(826 citation statements)

References 62 publications

Supporting

Mentioning

822

Contrasting

Unclassified

Order By: Relevance

“…Combining such precious information with quantum dynamics simulations could hopefully open new routes for improving our knowledge on radiationless transitions, which control many biochemical and technological processes. Although powerful methodologies capable of handling molecular systems with a large number of degrees of freedom and complex molecular Hamiltonians have been developed [3][4][5][6] their use, is often limited by their algorithmic complexity and high computational costs. There are two possible ways out: i) to employ model Hamiltonians with a small number of 'active' nuclear degrees of freedom, i.e.…”

Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Borrelli

Peluso

2015

J. Chem. Theory Comput.

View full text Add to dashboard Cite

This is the author's final version of the contribution published as:Borrelli, Raffaele; Peluso, Andrea. Quantum dynamics of radiationless electronic transitions including normal modes displacements and duschinsky rotations: A second-order cumulant approach. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. 11 (2) AbstractAn analytical expression for the population dynamics of electronic radiationless transitions has been derived from the second order expansion of the quantum evolution operator in the Liouville space and the cumulant theory. The expression includes the effect of both normal mode displacements and Duschinsky rotations and allows to take into account both equilibrium and non-equilibrium initial conditions. The methodology has been applied to model the electron-transfer process between the accessory bacteriochlorophyll and the bacteriopheophytine in bacterial reactions centers, providing a rate in good agreement with experimental findings.

show abstract

Section: Introductionmentioning

confidence: 99%

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Borrelli

Peluso

2015

J. Chem. Theory Comput.

View full text Add to dashboard Cite

show abstract

“…[121] However, the necessity to know a priori the full multidimensional PES is a severe bottleneck of the method, rendering quantum dynamics in full dimensionality unfeasible for systems with many degrees of freedom. There exist a number of approximations that allow treating an increasing number of degrees of freedom, for example, the "multiconfigurational time-dependent Hartree" method (MCDTH), [121] its variants "Gaussian-based MCTDH," [123] "multilayer MCTDH," [124] and "variational multiconfigurational Gaussians," [125] and the unrelated "full multiple spawning" method. [126] Alternatively, the dimensionality problem can be tackled with trajectory surface hopping nonadiabatic dynamics.…”

Section: Dynamics Simulations Of Intersystem Crossingmentioning

confidence: 99%

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Mai

Marquetand

González

2015

Int J of Quantum Chemistry

270

406

View full text Add to dashboard Cite

Intersystem crossing is a radiationless process that can take place in a molecule irradiated by UV‐Vis light, thereby playing an important role in many environmental, biological and technological processes. This paper reviews different methods to describe intersystem crossing dynamics, paying attention to semiclassical trajectory theories, which are especially interesting because they can be applied to large systems with many degrees of freedom. In particular, a general trajectory surface hopping methodology recently developed by the authors, which is able to include nonadiabatic and spin‐orbit couplings in excited‐state dynamics simulations, is explained in detail. This method, termed SHARC, can in principle include any arbitrary coupling, what makes it generally applicable to photophysical and photochemical problems, also those including explicit laser fields. A step‐by‐step derivation of the main equations of motion employed in surface hopping based on the fewest‐switches method of Tully, adapted for the inclusion of spin‐orbit interactions, is provided. Special emphasis is put on describing the different possible choices of the electronic bases in which spin‐orbit can be included in surface hopping, highlighting the advantages and inconsistencies of the different approaches. © 2015 Wiley Periodicals, Inc.

show abstract

“…Methods based on the so-called matrix product states factorization were introduced in density matrix renormalization group (DMRG) theory in [100] (see also [97] for the algebra of MPS formats). In computational molecular dynamics such methods are known for longer time as hierarchical or binary cascadic multi-configuration methods (MCTDH) used in combination with the Tucker tensor format (see [2,99,68] for further details). In the quantum information theory the concept of MPS was also introduced as the state decomposition of slightly entangled systems [98].…”

Section: Advances Of Tensor Methods In the Recent Decadementioning

confidence: 99%

Tensors-structured numerical methods in scientific computing: Survey on recent advances

Khoromskij¹

2012

Chemometrics and Intelligent Laboratory Systems

161

153

View full text Add to dashboard Cite

In the present paper, we give a survey of the recent results and outline future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientific computing. The guiding principle of the tensor methods is an approximation of multivariate functions and operators relying on certain separation of variables. Along with the traditional canonical and Tucker models, we focus on the recent quantics-TT tensor approximation method that allows to represent N -d tensors with log-volume complexity, O(d log N ). We outline how these methods can be applied in the framework of tensor truncated iteration for the solution of the high-dimensional elliptic/parabolic equations and parametric PDEs. Numerical examples demonstrate that the tensor-structured methods have proved their value in application to various computational problems arising in quantum chemistry and in the multi-dimensional/parametric FEM/BEM modeling-the tool apparently works and gives the promise for future use in challenging high-dimensional applications.

show abstract

Multilayer formulation of the multiconfiguration time-dependent Hartree theory

Cited by 865 publications

References 62 publications

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

A general method to describe intersystem crossing dynamics in trajectory surface hopping

Tensors-structured numerical methods in scientific computing: Survey on recent advances

Contact Info

Product

Resources

About