Challenges to computational quantum chemistry from contemporary advances in polyatomic molecular electronic spectroscopy

Molecular electronic spectroscopy featuring intramolecular proton transfer and twisted intramolecular charge transfer poses a whole new range of problems for computational quantum chemistry. The development of the four-level laser based on the intramolecular proton-transfer focuses on the subtleties of the interaction of the singlet and triplet electronic state manifolds of the two different tautomeric species. Examples are given of the sensitive variation of proton-transfer fluorescence with chemical substitution. A competing excitation channel is shown to exist when internal molecular torsion couples with sudden polarization to yield a twisted intramolecular charge transfer configuration. In such systems, three competing fluorescences can be observed. Several electronic puzzles will be presented that can provide fertile territory for quantum chemical computations. © 1993 John Wiley & Sons, Inc.     

Dual coordinate step methods for linear network flow problems

We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of-complementary slackness, and most do not explicitly manipulate any global objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of newserial computational complexity results. We develop the basic theory of these methods and present two specific methods, the-relaxation algorithm for the minimum-cost flow problem, and theauction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N ³ logNC) and O(NA logNC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement-relaxation in a completely asynchronous, chaotic environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.Supported by Grant NSF-ECS-8217668 and by the Army Research Office under grant DAAL03-86-K-0171. Thanks are due to David Castañon, Paul Tseng, and Jim Orlin for their helpful comments.     

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas—Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special cases of the proximal point algorithm. This observation allows the unification and generalization of a variety of convex programming algorithms. By introducing a modified version of the proximal point algorithm, we derive a new,generalized alternating direction method of multipliers for convex programming. Advances of this sort illustrate the power and generality gained by adopting monotone operator theory as a conceptual framework.This paper is drawn largely from the dissertation research of the first author. The dissertation was performed at M.I.T. under the supervision of the second author, and was supported in part by the Army Research Office under grant number DAAL03-86-K-0171, and by the National Science Foundation under grant number ECS-8519058.     

Incremental proximal methods for large scale convex optimization

We consider the minimization of a sum \({\sum_{i=1}^mf_i(x)}\) consisting of a large number of convex component functions f _i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.     

Regular 4-polytopes from the Livingstone graph of Janko’s first group

The Janko group J ₁ has, up to duality, exactly two regular rank four polytopes, of respective Schl?fli types {5,3,5} and {5,6,5}. The aim of this paper is to give geometric constructions of these two polytopes, starting from the Livingstone graph.     

Tyrosine or Tryptophan? Modifying a Metalloradical Catalytic Site by Removal of the Cys–Tyr Cross-Link in the Galactose 6-Oxidase Homologue GlxA

The concerted redox action of a metal ion and an organic cofactor is a unique way to maximize the catalytic power of an enzyme. An example of such synergy is the fungal galactose 6-oxidase, which has inspired the creation of biomimetic copper oxidation catalysts. Galactose 6-oxidase and its bacterial homologue, GlxA, possess a metalloradical catalytic site that contains a free radical on a covalently linked Cys–Tyr and a copper atom. Such a catalytic site enables for the two-electron oxidation of alcohols to aldehydes. When the ability to form the Cys–Tyr in GlxA is disrupted, a radical can still be formed. Surprisingly, the radical species is not the Tyr residue but rather a copper second-coordination sphere Trp residue. This is demonstrated through the introduction of a new algorithm for Trp-radical EPR spectra simulation. Our findings suggest a new mechanism of free-radical transfer between aromatic residues and that the Cys–Tyr cross-link prevents radical migration away from the catalytic site.     

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accu-rate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward differ-ence formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical com-putations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth sub-sonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the predic-tion of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.     

Hydrogen in N-methylacetamide: positions and dynamics of the hydrogen atoms using neutron scattering

This work reports neutron diffraction and incoherent neutron scattering experiments on N-methylacetamide (NMA), which can be considered the model building block for the peptide linkage of polypeptides and proteins. Using the neutron data, we have been able to associate the onset of a striking negative thermal expansion (NTE) along the a-axis with a dynamical transition around 230 K, consistent with our calorimetric experiments. Observation of the NTE raises the question of possible proton transfer in NMA, which, from our data alone, still cannot be settled. We can only speculate that intermolecular repulsive forces increase as the O...H distance decreases upon cooling, and that around 230 K the lattice relaxes without observation of an actual proton transfer. However, the existence of a nonharmonic potential, reflected by the behavior of the phonon vibrations together with the observation of NTE, could be justified by the "vibrational" polaron theory in which a dynamic localization of the vibrational energy is created by coupling an internal molecular mode to a lattice phonon. More generally, this work shows that neutron powder diffraction techniques can be very powerful for investigating structural deformations in small peptide systems.