Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I<sub>2</sub>Kr<sub>17</sub> Cluster

Buchholz, M.; Goletz, Christoph-Marian; Großmann, Frank; Schmidt, Burkhard; Heyda, Jan; Jungwirth, Pavel

doi:10.1021/jp305084f

Cited by 22 publications

(20 citation statements)

References 43 publications

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“…'reduced': Reduced densities,ρ k , in each dimension k, obtained by tracing over all other degrees of freedom, see e. g. Ref [61],. shown along with corresponding purity measures, In addition to the choice of the type of graphical representation, there are many further parameters governing the details of the graphics output.…”

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confidence: 99%

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

Schmidt

Lorenz

2017

Computer Physics Communications

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WavePacket is an open-source program package for the numerical simulation of quantummechanical dynamics. It can be used to solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. The graphical capabilities allow visualization of quantum dynamics 'on the fly', including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantum mechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry. The present Part I deals with the description of closed quantum systems in terms of Schrödinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization. The upcoming Part II will focus on open quantum systems and dimension reduction; it also describes the codes for optimal control of quantum dynamics. The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found. Programming language: Matlab Supplementary material: n. a. Journal reference of previous version: n. a. Does the new version supersede the previous version?: n. a. Reasons for the new version: n. a. Summary of revisions: n. a.* Nature of problem: Schrödinger's equations are of fundamental importance in non-relativistic quantum mechanics of distinguishable particles. The solutions of the time-independent equation (TISE) are wavefunctions in coordinate space, the absolute squares of which are usually interpreted as probability density. The time-dependent equation (TDSE) describes the dynamics of a quantum system evolving in time. It plays a crucial role for the simulation, understanding, and prediction of modern experiments in atomic, molecular and optical physics where systems are driven by temporally shaped external fields. Solution method:All numerical methods compiled in WavePacket are based on discrete variable representations.Currently implemented are Gauss-Hermite, Gauss-Legendre and FFT-based schemes. The TISE is solved either by direct diagonalization or by propagation in imaginary time. For the TDSE there is a choice between second order differencing, operator splitting and Chebychev polynomial methods. Additional comments including Restrictions and Unusual features:The WavePacket program package is rather easy and intuitive to use, providing visualization of quantum dynamics 'on the fly'. It is mainly intended for low-dimensional systems, typically not exceeding three t...

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WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

Schmidt

Lorenz

2017

Computer Physics Communications

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“…Even in the case of only one additional harmonic degree of freedom, compared to full Herman-Kluk time-averaging results, the numerical effort was shown to be reduced by more than an order of magnitude. Considering different system-bath couplings and including the resonant scenario, we found peak positions to be always in very good agreement with full quantum calculations, that are still feasible in the cases considered.In the future, we are planning to apply this semiclassical method to more realistic systems, where the harmonic bath is replaced by a realistic solvent, such as rare gas matrices [50,51] In this appendix, we show that the thawed Gaussian approximation (TGA) as an exact solution of the time-dependent Schrödinger equation for the harmonic oscillator leads to the exact harmonic spectrum. The wavepacket in the TGA [13] is written as the coherent state…”

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Mixed semiclassical initial value representation time-averaging propagator for spectroscopic calculations

Buchholz

Großmann

Ceotto

2016

The Journal of Chemical Physics

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The recently introduced mixed time-averaging semiclassical initial value representation molecular dynamics method for spectroscopic calculations [M. Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 144, 094102 (2016)] is applied to systems with up to 61 dimensions, ruled by a condensed phase Caldeira-Leggett model potential. By calculating the ground state as well as the first few excited states of the system Morse oscillator, changes of both the harmonic frequency and the anhar-monicity are determined. The method faithfully reproduces blueshift and redshift effects and the importance of the counter term, as previously suggested by other methods. Differently from previous methods, the present semiclassical method does not take advantage of the specific form of the potential and it can represent a practical tool that opens the route to direct ab initio semiclassical simulation of condensed phase systems.

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“…Refs. [44,45]. Contrary to this, the HK-LSC method employs an average over bath DOFs according to the quantum-mechanically correct thermal Wigner function, see Eq.…”

Section: Anharmonic Regime At a Finite Temperaturementioning

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On computing spectral densities from classical, semiclassical, and quantum simulations

Gottwald

Ivanov

Kühn

2019

The Journal of Chemical Physics

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The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function. This simplicity has led to a variety of numerically exact quantum methods for reduced density matrix propagation. When using these methods, a spectral density has to be computed from dynamical properties of system and environment, which is commonly done using classical molecular dynamics simulations. However, there are situations, where quantum effects could play a role. Therefore, we reformulate our recently developed Fourier method in order to enable spectral density calculations from semiclassical simulations which approximately consider quantum effects. We propose two possible protocols based on either correlation functions or expectation values. These protocols are tested for the linearized semiclassical initial-value representation (LSC-IVR), the thawed Gaussian wave packet dynamics (TGWD) and hybrid schemes combining the two with the more accurate Herman-Kluk (HK) formula. Surprisingly, spectral densities from the LSC-IVR method, based on a completely classical propagation, are extremely accurate whereas those from the single-trajectory TGWD are of poor quality in the anharmonic regime. The hybrid methods provide reasonable quality when the system is close to the classical regime, although, at finite temperature, the computation protocol from expectation values turns out to be more robust. If stronger quantum effects are observed, both hybrid methods turn out as too inaccurate.

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Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I₂Kr₁₇ Cluster

Cited by 22 publications

References 43 publications

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

Mixed semiclassical initial value representation time-averaging propagator for spectroscopic calculations

On computing spectral densities from classical, semiclassical, and quantum simulations

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Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I2Kr17 Cluster

Cited by 22 publications

References 43 publications

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

Mixed semiclassical initial value representation time-averaging propagator for spectroscopic calculations

On computing spectral densities from classical, semiclassical, and quantum simulations

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Product

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Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I₂Kr₁₇ Cluster