Calculations of canonical averages from the grand canonical ensemble

Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in canonical ensemble based on calculations of the expectation values in grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble

Angular momentum dependent friction slows down rotational relaxation under non-equilibrium conditions

It has recently been shown that relaxation of the rotational energy of hot non-equlibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby breakdown of the linear response description [Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial non-equilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium

Exact quantum master equation for a molecular aggregate coupled to a harmonic bath

We consider a molecular aggregate consisting of $N$ identical monomers. Each monomer comprises two electronic levels and a single harmonic mode. The monomers interact with each other via dipole-dipole forces. The monomer vibrational modes are bilinearly coupled to a bath of harmonic oscillators. This is a prototypical model for the description of coherent exciton transport, from quantum dots to photosynthetic antennae. We derive an exact quantum master equation for such systems. Computationally, the master equation may be useful for the testing of various approximations employed in theories of quantum transport. Physically, it offers a plausible explanation of the origins of long-lived coherent optical responses of molecular aggregates in dissipative environments

What can be learned about molecular reorientation from single molecule polarization microscopy?

We have developed a general approach for the calculation of the single molecule polarization correlation function C(t), which delivers a correlation of the emission dichroisms at time 0 and t. The approach is model independent and valid for general asymmetric top molecules. The key dynamic quantities of our analysis are the even-rank orientational correlation functions, the weighted sum of which yields C(t). We have demonstrated that the use of non-orthogonal schemes for the detection of the single molecule polarization responses makes it possible to manipulate the weighting coefficients in the expansion of C(t). Thus valuable information about the orientational correlation functions of the rank higher than second can be extracted from C(t)

Manifestation of nonequilibrium initial conditions in molecular rotation: the generalized J-diffusion model

In order to adequately describe molecular rotation far from equilibrium, we have generalized the J-diffusion model by allowing the rotational relaxation rate to be angular momentum dependent. The calculated nonequilibrium rotational correlation functions (CFs) are shown to decay much slower than their equilibrium counterparts, and orientational CFs of hot molecules exhibit coherent behavior, which persists for several rotational periods. As distinct from the results of standard theories, rotational and orientational CFs are found to dependent strongly on the nonequilibrium preparation of the molecular ensemble. We predict the Arrhenius energy dependence of rotational relaxation times and violation of the Hubbard relations for orientational relaxation times. The standard and generalized J-diffusion models are shown to be almost indistinguishable under equilibrium conditions. Far from equilibrium, their predictions may differ dramatically

Cluster Expansion by Transfer Learning from Empirical Potentials

Cluster expansions provide effective representations of the potential energy landscape of multicomponent crystalline solids. Notwithstanding major advances in cluster expansion implementations, it remains computationally demanding to construct these expansions for systems of low dimension or with a large number of components, such as clusters, interfaces, and multimetallic alloys. We address these challenges by employing transfer learning to accelerate the computationally demanding step of generating configurational data from first principles. The proposed approach exploits Bayesian inference to incorporate prior knowledge from physics-based or machine-learning empirical potentials, enabling one to identify the most informative configurations within a dataset. The efficacy of the method is tested on face-centered cubic Pt:Ni binaries, yielding a two- to three-fold reduction in the number of first-principles calculations, while ensuring robust convergence of the energies with low statistical fluctuations

Genetic and Biochemical Characterization of Human AP Endonuclease 1 Mutants Deficient in Nucleotide Incision Repair Activity

Background: Human apurinic/apyrimidinic endonuclease 1 (APE1) is a key DNA repair enzyme involved in both base excision repair (BER) and nucleotide incision repair (NIR) pathways. In the BER pathway, APE1 cleaves DNA at AP sites and 39-blocking moieties generated by DNA glycosylases. In the NIR pathway, APE1 incises DNA 59 to a number of oxidatively damaged bases. At present, physiological relevance of the NIR pathway is fairly well established in E. coli, but has yet to be elucidated in human cells. Methodology/Principal Finding: We identified amino acid residues in the APE1 protein that affect its function in either the BER or NIR pathway. Biochemical characterization of APE1 carrying single K98A, R185A, D308A and double K98A/R185A amino acid substitutions revealed that all mutants exhibited greatly reduced NIR and 39R59 exonuclease activities, but were capable of performing BER functions to some extent. Expression of the APE1 mutants deficient in the NIR and exonuclease activities reduced the sensitivity of AP endonuclease-deficient E. coli xth nfo strain to an alkylating agent, methylmethanesulfonate, suggesting that our APE1 mutants are able to repair AP sites. Finally, the human NIR pathway was fully reconstituted in vitro using the purified APE1, human flap endonuclease 1, DNA polymerase b and DNA ligase I proteins, thus establishing the minimal set of proteins required for a functional NIR pathway in human cells. Conclusion/Significance: Taken together, these data further substantiate the role of NIR as a distinct and separable functio

3,6-Dimethyl-1-phenyl-1H,4H-pyrano[2,3-c]pyrazol-4-one

The title compound, C14H12N2O2, is almost planar with an r.m.s. deviation for all non-H atoms of 0.038 Å. The observed planarity is rationalized in terms of a close intra­molecular C—H⋯O inter­action. Supra­molecular layers, two mol­ecules thick and with a step topology, are formed in the crystal packing via C—H⋯O contacts involving the carbonyl O atom, which accepts two such bonds, and π–π inter­actions between the components of the fused ring system and the phenyl ring of inversion-related mol­ecules [centroid–centroid distances = 3.6819 (13) and 3.6759 (12) Å]