Geometry optimization with QM/MM,ONIOM, and other combined methods. I. Microiterations and constraints

Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step-size control are illustrated by calculations on bacteriorhodopsin and other systems.     

Effect of Solvation on Chemical Reactions,I. Addition of a Single Water Molecule to the H− + H2O → OH− + H2 Reaction

The gas phase chemical reaction, H^? + H₂O → H₂ + OH, and the effect of an additional water molecule on the reaction, H^?(H₂O) + H₂O → H₂ + OH(H₂O), have been investigated. The optimal structures and energies of the reactants, products, two stable intermediates, and the transition state connecting the two intermediates have been determined. The additional water molecule does not affect the potential surface congruently: it destabilizes the H(H₂O) minimum, but stabilizes the H₂ ?OH minimum and the transition state connecting the two intermediates. However, it stabilizes the products more than the H₂ ?OH^? minimum. Finally, in line with the reduction in the barrier height, the transition state for the H(H₂0) to H₂ ?OH^? isomerization moves further along the reaction path.     

Approximate solution of u′=–A2u using a relation between exp(–tA2) and exp(itA)

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u _t =–A² u. Using a representation of the semi group exp(–A² t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w _t = w _yy , with initial values v solving the initial value problem for v _y = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2^nd order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4th order equation for u to that of the 2^nd order equation for v, followed by the solution of the heat equation in one space variable.     

Metric ultraproducts of finite simple groups

Some new results on metric ultraproducts of finite simple groups are presented. Suppose that G is such a group, defined in terms of a non-principal ultrafilter ω   on N$\mathbb{N}$ and a sequence (G_i)_i∈N${(G_i)}_{i\in \mathbb{N}}$ of finite simple groups, and that G is neither finite nor a Chevalley group over an infinite field. Then G is isomorphic to an ultraproduct of alternating groups or to an ultraproduct of finite simple classical groups. The isomorphism type of G determines which of these two cases arises, and, in the latter case, the ω  -limit of the characteristics of the groups G_i$G_i$. Moreover, G is a complete path-connected group with respect to the natural metric on G.     

Parabolic finite volume element equations in nonconvex polygonal domains

We study spatially semidiscrete and fully discrete finite volume element approximations of the heat equation with homogeneous Dirichlet boundary conditions in a plane polygonal domain with one reentrant corner. We show that, as a result of the singularity in the solution near the reentrant corner, the convergence rate is reduced from optimal second order, similarly to what was shown for the finite element method in the earlier work 2 . Optimal order convergence may be restored by mesh refinement near the corners of the domain. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Angular correlations in proton-proton collisions producing a high transverse momentum π0

In an experiment at the CERN ISR, a streamer chamber detector surrounding one of the intersection regions was triggered on large transverse momentum π⁰'s by means of an array of lead-glass counters. The directions of charged particles and γ rays converted in lead-oxide plates inside the streamer chamber were measured. Data were taken at c.m. energy of √s = 53 GeV at two production angles of the high p_Tπ⁰ (90° and 53°). They indicate an enhancement of particles mostly in the hemisphere opposite to the π⁰. In the 53° data, a shift of this enhancement towards rapidities opposite to the rapidity of the π⁰ and confined to a ±30° azimuthal region around the collision plane is observed. In addition, a short-range angular correlation is evidenced between the high p_Tπ⁰ and the other collisions products (photons or charged particles). Two-particle correlations between charged particles produced in association with the high p_Tπ⁰ are found similar to those     

On symmetry breaking in BNB: real or artifactual?

The ground state of the linear BNB molecule has been examined with multireference-based ab initio methods coupled with quantitative basis sets. Previous computational studies on BNB, even those using highly correlated single reference-based methods, e.g., the CCSD(T) and BDT methods, suggested that the two BN bond lengths were unequal. In this paper, the BN(X 3Pi) + B(2Pu) potential energy curve is constructed using a state-averaged multireference-based correlated method (SA-CASSCF+PT2). The four lowest states of BN were included in the state averaging procedure. These calculations reveal no symmetry breaking along the antisymmetric stretching mode of the molecule.