On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

Electronuclear multiconfiguration time‐dependent hartree calculations on the confined H atom with mobile electron and nucleus

A multiconfiguration time‐dependent Hartree method oriented toward calculations of a non‐Born‐Oppenheimer nature has been applied to the calculation of the dynamical properties of a confined H atom. The calculation is fully six‐dimensional and does not take into account constraints arising from linear or angular momentum conservation. The orbital evolution is monitored and the energy level spectrum of the system, as well as the dependence of the results on the decomposition of the Hamiltonian and on the correlation between radial degrees of freedom, is determined. © 2012 Wiley Periodicals, Inc.     

Nonstationarity and related measures for time‐dependent hartree–fock and multiconfigurational models

Based on an earlier article (Eberly and Singh, Phys. Rev. D 1973 , 7, 359) and related works on short‐time evolution, this article proposes a many‐electron formulation for the nonstationarity degree which can be assigned to quantum system at each time point. The key measure introduced, , is a nonstationarity index that can be thought of as an inverse nominal lifetime at each instance of time. The index is directly computed from the time derivative of one‐electron density matrix and is a size‐consistent quantity. In this article, the approach is developed for the time‐dependent Hartree–Fock (TDHF), single‐excitation (TDCIS), and time‐dependent full configuration interaction (TDFCI) models. As a rule, nonstationarity effects are more pronounced in correlated electron systems, and a joint analysis of and the multiconfigurational character of wave functions apparently provide a deeper insight into dynamical molecular processes. The performed calculations on small molecules in laser fields show a preference for the TDCIS model when comparing TDCIS and TDHF with the “exact” TDFCI model. © 2013 Wiley Periodicals, Inc.     

Batch tautomer generation with MolTPC

Besides all their conformational degrees of freedom, drug‐like molecules and natural products often also undergo tautomeric interconversions. Compared to the huge efforts made in experimental investigation of tautomerism, open and free algorithmic solutions for prototropic tautomer generation are surprisingly rare. The few freely available software packages limit their output to a subset of the possible configurational space by sometimes unwanted prior assumptions and complete neglection of ring‐chain tautomerism. Here, we describe an adjustable fully automatic tautomer enumeration approach, which is freely available and also incorporates the detection of ring‐chain variants. The algorithm is implemented in the MolTPC framework and accessible on SourceForge. © 2013 Wiley Periodicals, Inc.     

Understanding the electronic energy transfer pathways in the trimeric and hexameric aggregation state of cyanobacteria phycocyanin within the framework of Förster theory

In the present study, the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria C‐phycocyanin (C‐PC) were investigated in term of the Förster theory. The corresponding excited states and transition dipole moments of phycocyanobilins (PCBs) located into C‐PC were examined by model chemistry in gas phase at time‐dependent density functional theory (TDDFT), configuration interaction‐singles (CIS), and Zerner's intermediate neglect of differential overlap (ZINDO) levels, respectively. Then, the long‐range pigment‐protein interactions were approximately taken into account by using polarizable continuum model (PCM) at TDDFT level to estimate the influence of protein environment on the preceding calculated physical quantities. The influence of the short‐range interaction caused by aspartate residue nearby PCBs was examined as well. Only when the protonation of PCBs and its long‐ and short‐range interactions were properly taken into account, the calculated energy transfer rates (1/K) in the framework of Förster model at TDDFT/B3LYP/6‐31+G* level were in good agreement with the experimental results of C‐PC monomer and trimer. Furthermore, the present calculated results suggested that the energy transfer pathway in C‐PC monomer is predominant from β‐155 to β‐84 (1/K = 13.4 ps), however, from α‐84 of one monomer to β‐84 (1/K = 0.3–0.4 ps) in a neighbor monomer in C‐PC trimer. In C‐PC hexamer, an additional energy flow was predicted to be from β‐155 (or α‐84) in top trimer to adjacent β‐155 (or α‐84) (1/K = 0.5–2.7 ps) in bottom trimer. © 2013 Wiley Periodicals, Inc.     

Synthesis and mesomorphic investigation of calamitic liquid crystalline system ethyl-[4-(4′-decyloxy)benzoyloxy]-benzoate (4-EDBB): A temperature dependent micro-Raman study and DFT calculations

A new liquid crystalline material containing diester linking group ethyl-[4-(4′-decyloxy)benzoyloxy]-benzoate (4-EDBB) was synthesized. The phase transition temperatures were noted by differential scanning calorimetry (DSC), the texture pattern were observed by polarizing optical microscopy (POM) and temperature dependent Raman study was employed to observe the transitions as well as to understand the molecular rearrangement during phase transition. The transitions were observed with all the three techniques but the Raman signature of crystal → smectic A transition is many fold and more precise and accurate. The correlation between intermolecular interaction and phase behaviour has been discussed using temperature dependence Raman data of CH in-plane bending and CO stretching vibrations. With the help of DFT method the possible dimers of 4-EDBB were optimized and the rotational isomers were also investigated. There exists weak hydrogen bonds at room temperature, which breaks as the temperature is increased causing the CH in-plane bending to shift lower and CO stretching vibrations to shift higher. The discussion of the temperature dependent Raman data reveals that at crystal → smectic A transition as a result of intra-molecular rotation the molecules transform from trans- to cis- conformer.     

Existence results of stochastic impulsive systems with expectations‐dependent nonlinear terms

In this paper, sufficient conditions are established for the existence and uniqueness of global solutions to stochastic impulsive systems with expectations in the nonlinear terms. The maximal interval and the estimate of mild solutions are also discussed. These results are obtained by using the fixed point theorem, interval partition, and Lyapunov‐like technique. Finally, examples are given to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.