Many-body localization enables iterative quantum optimization

We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that each iteration leads to a non-exponentially small probability to find a lower local energy minimum. The other key ingredient is to tailor the cycle parameters to a currently achieved optimal state (the "reference" state) and to reset them once a deeper minimum is found. We show that, if the position of the tricritical point is known, the algorithm allows to approach the absolute minimum with any given precision in a polynomial time.

Binding of HasA by its transmembrane receptor HasR follows a conformational funnel mechanism

HasR in the outer membrane of Serratia marcescens binds secreted, heme-loaded HasA and translocates the heme to the periplasm to satisfy the cell’s demand for iron. The previously published crystal structure of the wild-type complex showed HasA in a very specific binding arrangement with HasR, apt to relax the grasp on the heme and assure its directed transfer to the HasR-binding site. Here, we present a new crystal structure of the heme-loaded HasA arranged with a mutant of HasR, called double mutant (DM) in the following that seemed to mimic a precursor stage of the abovementioned final arrangement before heme transfer. To test this, we performed first molecular dynamics (MD) simulations starting at the crystal structure of the complex of HasA with the DM mutant and then targeted MD simulations of the entire binding process beginning with heme-loaded HasA in solution. When the simulation starts with the former complex, the two proteins in most simulations do not dissociate. When the mutations are reverted to the wild-type sequence, dissociation and development toward the wild-type complex occur in most simulations. This indicates that the mutations create or enhance a local energy minimum. In the targeted MD simulations, the first protein contacts depend upon the chosen starting position of HasA in solution. Subsequently, heme-loaded HasA slides on the external surface of HasR on paths that converge toward the specific arrangement apt for heme transfer. The targeted simulations end when HasR starts to relax the grasp on the heme, the subsequent events being in a time regime inaccessible to the available computing power. Interestingly, none of the ten independent simulation paths visits exactly the arrangement of HasA with HasR seen in the crystal structure of the mutant. Two factors which do not exclude each other could explain these observations: the double mutation creates a non-physiologic potential energy minimum between the two proteins and /or the target potential in the simulation pushes the system along paths deviating from the low-energy paths of the native binding processes. Our results support the former view, but do not exclude the latter possibility.

Exploring the Binding Mechanism and Dynamics of EndoMS/NucS to Mismatched dsDNA

The well-known mismatch repair (MMR) machinery, MutS/MutL, is absent in numerous Archaea and some Bacteria. Recent studies have shown that EndoMS/NucS has the ability to cleave double-stranded DNA (dsDNA) containing a mismatched base pair, which suggests a novel mismatch repair process. However, the recognition mechanism and the binding process of EndoMS/NucS in the MMR pathway remain unclear. In this study, we investigate the binding dynamics of EndoMS/NucS to mismatched dsDNA and its energy as a function of the angle between the two C-terminal domains of EndoMS/NucS, through molecular docking and extensive molecular dynamics (MD) simulations. It is found that there exists a half-open transition state corresponding to an energy barrier (at an activation angle of approximately 80 ∘ ) between the open state and the closed state, according to the energy curve. When the angle is larger than the activation angle, the C-terminal domains can move freely and tend to change to the open state (local energy minimum). Otherwise, the C-terminal domains will interact with the mismatched dsDNA directly and converge to the closed state at the global energy minimum. As such, this two-state system enables the exposed N-terminal domains of EndoMS/NucS to recognize mismatched dsDNA during the open state and then stabilize the binding of the C-terminal domains of EndoMS/NucS to the mismatched dsDNA during the closed state. We also investigate how the EndoMS/NucS recognizes and binds to mismatched dsDNA, as well as the effects of K + ions. The results provide insights into the recognition and binding mechanisms of EndoMS/NucS to mismatched dsDNA in the MMR pathway.

Chemical bond formation showing a transition from physisorption to chemisorption

Surface molecules can transition from physisorption through weak van der Waals forces to a strongly bound chemisorption state by overcoming an energy barrier. We show that a carbon monoxide (CO) molecule adsorbed to the tip of an atomic force microscope enables a controlled observation of bond formation, including its potential transition from physisorption to chemisorption. During imaging of copper (Cu) and iron (Fe) adatoms on a Cu(111) surface, the CO was not chemically inert but transited through a physisorbed local energy minimum into a chemisorbed global minimum, and an energy barrier was seen for the Fe adatom. Density functional theory reveals that the transition occurs through a hybridization of the electronic states of the CO molecule mainly with s-, pz-, and dz2-type states of the Fe and Cu adatoms, leading to chemical bonding.

Computational Studies of Electronic Structures and Hyperfine Interactions of Muonium in Tetraphenylgermane

The equilibrium structure of muoniatedtetraphenylgermane (GePh4Mu) was studied using the first principle Density Functional Theory (DFT) method. Three muonium (Mu) trapping sites were considered, namelyortho,meta, andparapositions on one of the phenyl rings. Geometry optimization procedure was utilized to determine the local energy minimum for all the systems. The total energies corresponding to Mu at the three positions are very similar to each other. For themetacase, the corresponding energy is higher than the other two sites by only about 0.03 eV. The hyperfine parameters of Mu were also calculated. The Mu isotropic hyperfine coupling constants were found to be 441.85 MHz, 449.80 MHz, and 439.01 MHz for theortho,meta, andparacases, respectively. The anisotropic value was calculated to be very small.

p-WAVE PAIRING IN FERMI SYSTEMS WITH UNEQUAL POPULATION NEAR FESHBACH RESONANCE

We explore p-wave pairing in a single-channel two-component Fermi system with unequal population near Feshbach resonance. Our analytical and numerical study reveal a rich superfluid (SF) ground state structure as a function of imbalance. In addition to the state Δ±1 ∝ Y1±1, a multitude of “mixed” SF states formed of linear combinations of Y1m's give global energy minimum under a phase stability condition; these states exhibit variation in energy with the relative phase between the constituent gap amplitudes. States with local energy minimum are also obtained. We provide a geometric representation of the states. A T = 0 polarization vs. p-wave coupling phase diagram is constructed across the BEC-BCS regimes. With increased polarization, the global minimum SF state may undergo a quantum phase transition to the local minimum SF state.

Circumspect descent prevails in solving random constraint satisfaction problems

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios α; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.

Low-temperature enantiotropic k2 phase transition in the ionic 222-cryptand complex with LiClO4

Crystallographic analyses at 100 and 200 K are reported for the macrobicyclic polyether 4,7,13,16,21,24-hexaoxa-1,10-diaza-bicyclo[8.8.8]hexacosane (denoted as 222-cryptand) that encapsulates a Li+ cation and then forms a complex (I) with ClO_4^-. Compound (I) undergoes a reversible second-order k phase transition at 253 (2) K from an almost ordered structure [space group P212121] at 100 K to a more disordered structure that exhibits a different unit cell [P21212 (2c′ = c)] above 253 (2) K. At 295 K the Li+ cation and five atoms of the perchlorate anion are each disordered over at least two positions about a crystallographic twofold axis [Chekhlov (2003). Russ. J. Coord. Chem. 29, 828–832]; as the temperature decreases the dynamic positional disorder is slowly frozen out, but is still observed for lithium even at 100 K. Based upon DFT computations, it seems that in the solid state the position of the Li+ cation in the cavity of the 222-cryptand below 253 (2) K likely corresponds to a local energy minimum; the global minimum in the gas phase corresponds to a near D 3 symmetrical conformation of the 222-cryptand with the undersized Li+ cation residing in the center of its cavity.

Regime Switching Issues and Criteria for Coupled Static-Dynamic Atomistic Methods

Coupled static-dynamic atomistic method may be used for coarse graining time in temporal multi-scale atomistic modeling of nano-mechanical problems. This approach can be especially effective for mechanical processes that consist of two distinct phases: the slow phase when the system resides in one local energy minimum and the fast phase associated with a rapid transition from one meta-stable state to another. In this case, the slow phase can be effectively modeled using static energy minimization technique, while the fast phase corresponding to the state transition event may be modeled dynamically. In this case, dynamic modeling is necessary to capture the dynamic effects, such as thermal and inertial, that can not be accounted for in static modeling. One of the major issues of this type of method is to determine when the transitions between the two regimes have to be done. In this presentation, issues of switching between the static and dynamic regimes are outlined and criteria that can be used for effective switching between the two regimes are proposed. In particular, a dynamic-to-static switch based on the kinetic energy and static-to-dynamic switch based on the potential energy are discussed.

STRUCTURES, ABSORPTION SPECTRA, AND ELECTRONIC PROPERTIES OF POLYFLUORENE AND ITS DERIVATIVES: A THEORETICAL STUDY

The structural and energetic properties of polyfluorene and its derivatives were investigated, using quantum chemical calculations. Conformational analysis of bifluorene was performed by using ab initio (HF/6-31G* and MP2/6-31G*) and density functional theory (B3LYP/6-31G*) calculations. The results showed that the local energy minimum of bifluorene lies between the coplanar and perpendicular conformation, and the B3LYP/6-31G* calculations led to the overestimation of the stability of the planar pi systems. The HOMO-LUMO energy differences of fluorene oligomers and its derivatives — 9,9-dihexylfluorene (DHPF), 9,9-dioctylfluorene (PFO), and bis(2-ethylhexyl)fluorene (BEHPF) — were calculated at the B3LYP/6-31G* level. Energy gaps and effective conjugation lengths of the corresponding polymers were obtained by extrapolating HOMO-LUMO energy differences and the lowest excitation energies to infinite chain length. The lowest excitation energies and the maximum absorption wavelength of polyfluorene were also performed, employing the time-dependent density functional theory (TDDFT) and ZINDO methods. The extrapolations, based on TDDFT and ZINDO calculations, agree well with experimental results. These theoretical methods can be useful for the design of new polymeric structures with a reducing energy gap.