Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm [E. W. Dijkstra, Numer. Math. 1, 269 (1959)] to identify the "shortest" path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimized Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of various biomolecules: the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states and will be used in future discrete path sampling calculations.     

A doubly nudged elastic band method for finding transition states

A modification of the nudged elastic band (NEB) method is presented that enables stable optimizations to be run using both the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton and slow-response quenched velocity Verlet minimizers. The performance of this new "doubly nudged" DNEB method is analyzed in conjunction with both minimizers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to 2 orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.     

Nonuniform stability properties and perturbing lyapunov functions

In this paper, without assuming the conditions everywhere, we study nonuniform stability properties of differential systems by employing the method of perturbing Lyapunov functions and splitting the given system suitably     

Unusual contributions of molecular architecture to rheology and flow birefringence in hyperbranched polystyrene melts

With the increase in sophisticated synthesis methods, it appears that polymer architecture may be a tunable property. Therefore, the role of architecture in rheological and processing properties has received renewed attention, mainly because of dendrimer synthesis and metallocene‐catalyst technology. Linear polymers and hyperbranched polymers represent two ends of branching complexity. Some previous studies have suggested that hyperbranched polymers may behave like unentangled polymers, whereas others have proposed that they exhibit the properties of soft colloids. In an effort to compare the responses of linear and hyperbranched polymers, we synthesized starlike hyperbranched polystyrenes (HBPSs) of various branch lengths and numbers of branches. The HBPSs used in this study were unentangled or weakly entangled, allowing us to study the effect of branch density more readily. Two linear polystyrene (L‐PS) melts and two HBPSs were studied. Using a custom‐built rheooptical apparatus, we characterized the rheology and flow birefringence of these materials. To our knowledge, these are the first flow birefringence measurements on highly branched polymer melts. Our results suggest that the flow behavior of HBPS is significantly different from that of L‐PS: (1) HBPS shows nonterminal behavior in the low‐frequency rheological response; (2) when the stress‐optical rule (SOR) holds, the stress‐optical coefficient of HBPS is much lower than those of analogous linear polymers; and (3) when the branch density is high and the branch length is sufficiently low, the SOR fails for these homopolymer melts. A significant increase in the birefringence for a given amount of stress in the low‐frequency region suggests that there may be a soft core in these materials due to the strong preferential radial orientation of chain segments near the center of a molecule versus those near the periphery. The predominantly elastic response of the soft structures may be responsible for the enhanced form birefringence. Our preliminary results indicate that these materials may exhibit both polymeric and soft‐colloid natures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2562–2571, 2001     

Acyl pyruvates as synthons in the Biginelli reaction

Chlorotrimethylsilane-promoted Biginelli-type reaction of ethyl 2,4-dioxo-4-phenylbutanoate, benzaldehyde, and various (thio)ureas is explored. The outcome of the reaction depends on the structure of the (thio)urea used and is strongly affected by the acceptor electronic properties of the COOEt substituent in the molecule of the starting β-dicarbonyl compound. The di- and tetrahydropyrimidine derivatives obtained possess two functional groups with orthogonal reactivity, and thus represent promising building blocks for drug discovery.     

Comment on “Role of the velocity frame of reference in thermodiffusion in liquid mixtures” by M. Eslamian,C.G. Jiang and M.Z. Saghir

We analyze the material transport equations (MTE) derived by Eslamian and co-authors and address the criticism expressed regarding the approach formulated in our previous work. In doing so, we show that the MTE formulated by Eslamian and co-authors are valid only in closed stationary non-isothermal systems in combination with the restrictions on the Onsager coefficients formulated in our work which is criticized, and that for non-stationary systems the approach we took can be used.     

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.     

Isotopic substitution shifts in methane and vibrational band assignment in the 5560-6200 cm region

The absorption spectra of the ¹²CH₄ and ¹³CH₄ molecules have been recorded and assigned in the 5560-6200 cm⁻¹ region. The effects of isotopic substitution for ¹²C by ¹³C on the methane vibrational energy levels have been calculated from an ab initio potential energy surface and compared with experiment. Comparison of the results obtained for two isotopic species allows us to confirm the vibrational assignment for the strongest bands of ¹²CH₄ in this region. Good agreement of ab initio calculations with observed energy levels has been demonstrated. A list of the assigned ¹³CH₄ lines valuable in atmospheric applications is reported.