On the models for deuterium long-range isotope effects in13C NMR spectroscopy

The long-range deuterium isotope effects on13C nuclear shielding are physically not yet completely understood. Two existing models for explaining these effects, vibrational and substituent, are compared here. The vibrational model is based on the Born-Oppenheimer approximation, but it can explain only one-bond deuterium effects. To the contrary, the substituent model may explain many long-range isotope effects, but it is controversial due to the assumption of some distinct electronic properties of isotopes. We explain how long-range deuterium isotope effects may be rationalized by the subtle electronic changes induced by isotope substitution, which does not violate the Born-Oppenheimer approximation.

Models for spin-state transitions in solids

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

A Deterministic Optimization Approach to Protein Sequence Design Using Continuous Models

Determining the sequence of amino acid residues in a heteropolymer chain of a protein with a given conformation is a discrete combinatorial problem that is not generally amenable for gradient-based continuous optimization algorithms. In this paper we present a new approach to this problem using continuous models. In this modeling, continuous "state functions" are proposed to designate the type of each residue in the chain. Such a continuous model helps define a continuous sequence space in which a chosen criterion is optimized to find the most appropriate sequence. Searching a continuous sequence space using a deterministic optimization algorithm makes it possible to find the optimal sequences with much less computation than many other approaches. The computational efficiency of this method is further improved by combining it with a graph spectral method, which explicitly takes into account the topology of the desired conformation and also helps make the combined method more robust. The continuous modeling used here appears to have additional advantages in mimicking the folding pathways and in creating the energy landscapes that help find sequences with high stability and kinetic accessibility. To illustrate the new approach, a widely used simplifying assumption is made by considering only two types of residues: hydrophobic (H) and polar (P). Self-avoiding compact lattice models are used to validate the method with known results in the literature and data that can be practically obtained by exhaustive enumeration on a desktop computer. We also present examples of sequence design for the HP models of some real proteins, which are solved in less than five minutes on a single-processor desktop computer Some open issues and future extensions are noted.

A divisive scheme for constructing minimal spanning trees in coordinate space

An algorithm to generate a minimal spanning tree is presented when the nodes with their coordinates in some m-dimensional Euclidean space and the corresponding metric are given. This algorithm is tested on manually generated data sets. The worst case time complexity of this algorithm is O(n log2n) for a collection of n data samples.

An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csiszar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner bases method to compute an implicit representation of minimum KL-divergence models.

Models of the proton spin structure

A phenomenological model of spin sharing by the constituents of a proton is constructed, based on the recent EMC measurement of the spin dependent structure function and knowledge of the unpolarized parton densities.

Minimal three-component SU(2) gadget for polarization optics

Two identities involving quarter-wave plates and half-wave plates are established. These are used to improve on an earlier gadget involving four wave plates leading to a new gadget involving just three plates, a half-wave plate and two quarter-wave plates, which can realize all SU(2) polarization transformations. This gadget is shown to involve the minimum number of quarter-wave and half-wave plates. The analysis leads to a decomposition theorem for SU (2) matrices in terms of factors which are symmetric fourth and eighth roots of the identity.

Mean-field theories of Hubbard and t-J models

We report novel results obtained for the Hubbard and t-J models by various mean-field approximations.

Approximate VB-MO schemes for excitation gaps in Hubbard models

The excitation gaps in the singlet and triplet manifolds for finite Hubbard models in one, two and three dimensions have been obtained using different approximate configuration interaction (CI) schemes, as a function of the correlation strength, by using valence bond (VB) functions constructed over the molecular orbital (MO) basis. These are compared with numerically exact results and it is found that the scheme in which all particle hole excitations below a given threshold are included is the method of choice. The excitation energies are well reproduced, in trend as well as magnitude, particularly when the threshold equals the bandwidth of the corresponding noninteracting system.

Direct versus kinetic exchange in multiband models for organic ferromagnetism

Multiband Hubbard and Pariser-Parr-Pople calculations have been carried out on mixed donor-acceptor (DA) stacks with doubly degenerate acceptor orbitals and nondegenerate donor orbitals at two-thirds filling. Model exact results for 2, 3, and 4 DA units show that McConnell's prediction of high-spin ground states in these systems is, in general, incorrect. The larger phase space available for the low-spin states leads to their kinetic stabilization in preference to high-spin states. However, for large electron-correlation strengths, the direct exchange dominates over the kinetic exchange resulting in a high-spin ground state