Multidimensional Classical Liouville Dynamics with Quantum Initial Conditions

A simple and numerically efficient approach to Wigner transforms and classical Liouville dynamics in phase-space is presented. The Wigner transform can be obtained with a given accuracy by optimal decomposition of an initial quantum-mechanical wavefunction in terms of a minimal set of Gaussian wavepackets. The solution of the classical Liouville equation within the locally quadratic approximation of the potential energy function requires a representation of the density in terms of an ensemble of narrow Gaussian phase-space packets. The corresponding equations of motion can be efficiently solved by a modified Leap-Frog integrator. For both problems the use of Monte-Carlo based techniques allows numerical calculation in multidimensional cases where grid-based methods such as fast Fourier transforms are prohibitive. In total, the proposed strategy provides a practical and efficient tool for classical Liouville dynamics with quantum-mechanical initial states

Nonadiabatic Effects on Peptide Vibrational Dynamics Induced by Conformational Changes

Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH3-CO-NH-CH2-CO-NH-CH3). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (B3LYP/6-31+G(d)) level. The ordering of the energetically most stable isomers (C7 and C5) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C7 and C5 minimum energy structures occur on a sub-picosecond timescale (700 ... 800 fs). Vibrationally non-adiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly non-adiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a timescale of 200 ... 500 fs with population transfer of more than 50 % between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy

Dimension reduction by balanced truncation: Application to light-induced control of open quantum systems

In linear control, balanced truncation is known as a powerful technique to reduce the state-space dimension of a system. Its basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace without changing the overall response of the system. This work deals with a first application of balanced truncation to the control of open quantum systems which are modeled by the Liouville-von Neumann equation within the Lindblad formalism. Generalization of the linear theory have been proposed to cope with the bilinear terms arising from the coupling between the control field and the quantum system. As an example we choose the dissipative quantum dynamics of a particle in an asymmetric double well potential driven by an external control field, monitoring population transfer between the potential wells as a control target. The accuracy of dimension reduction is investigated by comparing the populations obtained for the truncated system versus those for the original system. The dimension of the model system can be reduced very efficiently where the degree of reduction depends on temperature and relaxation rate

Fully Adaptive Propagation of the Quantum-Classical Liouville Equation

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The trapezoidal rule for adaptive integration of Liouville dynamics (TRAIL) [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for non-adiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac delta-like trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-like trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multi-dimensional problems with deterministic treatment of non-adiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Non-adiabatic effects occuring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results

Quantum-Classical Liouville Approach to Molecular Dynamics: Surface Hopping Gaussian Phase-Space Packets

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a molecular system are modeled quantum-mechanically while the remaining degrees of freedom are treated within the classical approximation. Such models can be systematically derived as a first order approximation to the partial Wigner transform of the quantum Liouville-von Neumann equation. The resulting adiabatic quantum-classical Liouville equation (QCLE) can be decomposed into three individual propagators by means of a Trotter splitting: Phase oscillations of the coherences resulting from the time evolution of the quantum-mechanical subsystem. Exchange of densities and coherences reflecting non-adiabatic effects in quantum-classical dynamics. Classical Liouvillian transport of densities and coherences along adiabatic potential energy surfaces or arithmetic means thereof. A novel stochastic implementation of the QCLE is proposed in the present work. In order to substantially improve the traditional algorithm based on surface hopping trajectories [J. C. Tully, J. Chem. Phys. 93 (2), 1061 (1990)], we model the evolution of densities and coherences by a set of surface hopping Gaussian phase-space packets (GPPs) with variable width and with adjustable real or complex amplitudes, respectively. The dense sampling of phase-space offers two main advantages over other numerical schemes to solve the QCLE. First, it allows to perform a quantum-classical simulation employing a constant number of particles, i. e. the generation of new trajectories at each surface hop is avoided. Second, the effect of non-local operators in the exchange of densities and coherences can be treated without having to invoke the momentum jump approximation. For the example of a single avoided crossing we demonstrate that convergence towards fully quantum-mechanical dynamics is much faster for surface hopping GPPs than for trajectory-based methods. For dual avoided crossings the Gaussian-based dynamics correctly reproduces the quantum-mechanical result even when trajectory-based methods not accounting for the transport of coherences fail qualitatively

Tracing Electron-Ion Recombination in Nanoplasmas Produced by Extreme- Ultraviolet Irradiation of Rare-Gas Clusters

We investigate electron-ion recombination in nanoplasmas produced by the ionization of rare-gas clusters with intense femtosecond extreme-ultraviolet (XUV) pulses. The relaxation dynamics following XUV irradiation is studied using time-delayed 790-nm pulses, revealing the generation of a large number of excited atoms resulting from electron-ion recombination. In medium-sized Ar-Xe clusters, these atoms are preferentially created in the Xe core within 10 ps after the cluster ionization. The ionization of excited atoms serves as a sensitive probe for monitoring the cluster expansion dynamics up to the ns time scale

Cancer Precision Medicine: Why More Is More and DNA Is Not Enough

Every tumour is different. They arise in patients with different genomes, from cells with different epigenetic modifications, and by random processes affecting the genome and/or epigenome of a somatic cell, allowing it to escape the usual controls on its growth. Tumours and patients therefore often respond very differently to the drugs they receive. Cancer precision medicine aims to characterise the tumour (and often also the patient) to be able to predict, with high accuracy, its response to different treatments, with options ranging from the selective characterisation of a few genomic variants considered particularly important to predict the response of the tumour to specific drugs, to deep genome analysis of both tumour and patient, combined with deep transcriptome analysis of the tumour. Here, we compare the expected results of carrying out such analyses at different levels, from different size panels to a comprehensive analysis incorporating both patient and tumour at the DNA and RNA levels. In doing so, we illustrate the additional power gained by this unusually deep analysis strategy, a potential basis for a future precision medicine first strategy in cancer drug therapy. However, this is only a step along the way of increasingly detailed molecular characterisation, which in our view will, in the future, introduce additional molecular characterisation techniques, including systematic analysis of proteins and protein modification states and different types of metabolites in the tumour, systematic analysis of circulating tumour cells and nucleic acids, the use of spatially resolved analysis techniques to address the problem of tumour heterogeneity as well as the deep analyses of the immune system of the patient to, e.g., predict the response of the patient to different types of immunotherapy. Such analyses will generate data sets of even greater complexity, requiring mechanistic modelling approaches to capture enough of the complex situation in the real patient to be able to accurately predict his/her responses to all available therapies