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.

Articles you may be interested inSemiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems J. Chem. Phys. 134, 114103 (2011); 10.1063/1.3565425 Combining semiclassical time evolution and quantum Boltzmann operator to evaluate reactive flux correlation function for thermal rate constants of complex systems Forward-backward initial value representation for the calculation of thermal rate constants for reactions in complex molecular systems On the semiclassical description of quantum coherence in thermal rate constants J. Chem. Phys. 109, 4190 (1998); 10.1063/1.477025Mixed semiclassical-classical approaches to the dynamics of complex molecular systems Two different semiclassical approaches are presented for extending flux correlation function methodology for computing thermal reaction rate constants, which has been extremely successful for the ''direct'' calculation of rate constants in small molecule (ϳ3 -4 atoms) reactions, to complex molecular systems, i.e., those with many degrees of freedom. First is the popular mixed quantum-classical approach that has been widely used by many persons, and second is an approximate version of the semiclassical initial value representation that has recently undergone a rebirth of interest as a way for including quantum effects in molecular dynamics simulations. Both of these are applied to the widely studied system-bath model, a one-dimensional double well potential linearly coupled to an infinite bath of harmonic oscillators. The former approximation is found to be rather poor while the latter is quite good.

Polycomb group (PcG) proteins repress master regulators of development and differentiation through organization of chromatin structure. Mutation and dysregulation of PcG genes cause developmental defects and cancer. PcG proteins form condensates in the cell nucleus, and these condensates are the physical sites of PcG-targeted gene silencing via formation of facultative heterochromatin. However, the physiochemical principles underlying the formation of PcG condensates remain unknown, and their determination could shed light on how these condensates compact chromatin. Using fluorescence live-cell imaging, we observed that the Polycomb repressive complex 1 (PRC1) protein chromobox 2 (CBX2), a member of the CBX protein family, undergoes phase separation to form condensates and that the CBX2 condensates exhibit liquid-like properties. Using site-directed mutagenesis, we demonstrated that the conserved residues of CBX2 within the intrinsically disordered region (IDR), which is the region for compaction of chromatin in vitro, promote the condensate formation both in vitro and in vivo. We showed that the CBX2 condensates concentrate DNA and nucleosomes. Using genetic engineering, we report that trimethylation of Lys-27 at histone H3 (H3K27me3), a marker of heterochromatin formation produced by PRC2, had minimal effects on the CBX2 condensate formation. We further demonstrated that the CBX2 condensate formation does not require CBX2–PRC1 subunits; however, the condensate formation of CBX2–PRC1 subunits depends on CBX2, suggesting a mechanism underlying the assembly of CBX2–PRC1 condensates. In summary, our results reveal that PcG condensates assemble through liquid–liquid phase separation (LLPS) and suggest that phase-separated condensates can organize PcG-bound chromatin.

Articles you may be interested inA Cartesian classical second-quantized many-electron Hamiltonian, for use with the semiclassical initial value representation J. Chem. Phys. 137, 154107 (2012); 10.1063/1.4757935Semiclassical description of electronically nonadiabatic dynamics via the initial value representation Extremal path approach to rate constant calculations by the linearized semiclassical initial value representation A linearized approximation to the semiclassical initial value representation ͑SC-IVR͒, referred to herein as the LSC-IVR, was used by us in a recent paper ͓J. Chem. Phys. 108, 9726 ͑1998͔͒ to calculate reactive flux correlation functions for a model of a chemical reaction on a single potential energy surface. This paper shows how the LSC-IVR-which is much easier to apply than the full SC-IVR because it linearizes the phase difference between interfering classical trajectories-can be applied to electronically nonadiabatic processes, i.e., those involving transitions between different potential-energy surfaces. Applications to several model problems are presented to show its usefulness: These are the nonadiabatic scattering problems used by Tully to test surface-hopping models, and also the spin-boson model of coupled electronic states in a condensed phase environment. Though not as accurate as the full SC-IVR, the LSC-IVR does a reasonably good job for all these applications, even describing correctly Stuckelberg oscillations ͑interference between nonadiabatic transitions͒ and the transition between coherent and incoherent behavior in the spinboson example.

A method to describe the quantum dynamics of photoinduced heterogeneous electron-transfer processes at dye-semiconductor interfaces is proposed. The method is based on a model Hamiltonian, the parameters of which are determined by first-principles electronic structure calculations and a partitioning scheme to define localized donor and acceptor states as well as donor-acceptor coupling matrix elements. On the basis of this modeling procedure, accurate quantum dynamical simulations are performed employing the multilayer multiconfiguration time-dependent Hartree method. As a representative example, applications to coumarin 343 adsorbed on titanium oxide nanoparticles are presented. The results of the simulations show that the ultrafast electron-injection process in this system is accompanied by electronic coherence effects, which are partially quenched due to electronic-nuclear coupling.