Chiral Symmetry Versus the Lattice

After mentioning some of the difficulties arising in lattice gauge theory from chiral symmetry, I discuss one of the recent attempts to resolve these issues using fermionic surface states in an extra space-time dimension. This picture can be understood in terms of end states on a simple ladder molecule.Comment: Talk at the meeting "Computer simulations studies in condensed matter physics XIV" Athens, Georgia, Feb. 19-24, 2001. 14 page

Microcanonical cluster algorithms

I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed increases associated with multi-spin coding in the microcanonical approach. The method also provides a limited ability to tune the average cluster size.Comment: 10 page

Regularization and finiteness of the Lorentzian LQG vertices

We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of so doing, a natural regularization of the vertices is suggested. The regularized vertices are then proven to be finite. An interpretation of the regularization in terms of a gauge-fixing is also given.Comment: 16 pages; Added an appendix presenting the gauge-fixing interpretation, added three references, and made some minor change

Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

Exploring secondary-sphere interactions in Fe–N_xH_y complexes relevant to N_2 fixation

Hydrogen bonding and other types of secondary-sphere interactions are ubiquitous in metalloenzyme active sites and are critical to the transformations they mediate. Exploiting secondary sphere interactions in synthetic catalysts to study the role(s) they might play in biological systems, and to develop increasingly efficient catalysts, is an important challenge. Whereas model studies in this broad context are increasingly abundant, as yet there has been relatively little progress in the area of synthetic catalysts for nitrogen fixation that incorporate secondary sphere design elements. Herein we present our first study of Fe–NxHy complexes supported by new tris(phosphine)silyl ligands, abbreviated as [SiP^(Nme_3)] and [SiP^(iPr_2)P^(Nme)], that incorporate remote tertiary amine hydrogen-bond acceptors within a tertiary phosphine/amine 6-membered ring. These remote amine sites facilitate hydrogen-bonding interactions via a boat conformation of the 6-membered ring when certain nitrogenous substrates (e.g., NH_3 and N_2H_4) are coordinated to the apical site of a trigonal bipyramidal iron complex, and adopt a chair conformation when no H-bonding is possible (e.g., N_2). Countercation binding at the cyclic amine is also observed for anionic {Fe–N_2}− complexes. Reactivity studies in the presence of proton/electron sources show that the incorporated amine functionality leads to rapid generation of catalytically inactive Fe–H species, thereby substantiating a hydride termination pathway that we have previously proposed deactivates catalysts of the type [EP^R_3]FeN_2 (E = Si, C)

Catalytic Reduction of N_2 to NH_3 by an Fe−N_2 Complex Featuring a C‑Atom Anchor

While recent spectroscopic studies have established the presence of an interstitial carbon atom at the center of the iron–molybdenum cofactor (FeMoco) of MoFe-nitrogenase, its role is unknown. We have pursued Fe–N_2 model chemistry to explore a hypothesis whereby this C-atom (previously denoted as a light X-atom) may provide a flexible trans interaction with an Fe center to expose an Fe–N_2 binding site. In this context, we now report on Fe complexes of a new tris(phosphino)alkyl (CP^(iPr)_3) ligand featuring an axial carbon donor. It is established that the iron center in this scaffold binds dinitrogen trans to the C_(alkyl)-atom anchor in three distinct and structurally characterized oxidation states. Fe–C_(alkyl) lengthening is observed upon reduction, reflective of significant ionic character in the Fe–C_(alkyl) interaction. The anionic (CP^(iPr)_3)FeN_2^– species can be functionalized by a silyl electrophile to generate (CP^(iPr)_3)Fe–N_2SiR_3. (CP^(iPr)_3)FeN_2^– also functions as a modest catalyst for the reduction of N_2 to NH_3 when supplied with electrons and protons at −78 °C under 1 atm N_2 (4.6 equiv NH_3/Fe)

Diiron Bridged-Thiolate Complexes That Bind N_2 at the Fe^(II)Fe^(II), Fe^(II)Fe^I, and Fe^IFe^I Redox States

All known nitrogenase cofactors are rich in both sulfur and iron and are presumed capable of binding and reducing N_2. Nonetheless, synthetic examples of transition metal model complexes that bind N_2 and also feature sulfur donor ligands remain scarce. We report herein an unusual series of low-valent diiron complexes featuring thiolate and dinitrogen ligands. A new binucleating ligand scaffold is introduced that supports an Fe(μ-SAr)Fe diiron subunit that coordinates dinitrogen (N_2-Fe(μ-SAr)Fe-N_2) across at least three oxidation states (Fe^(II)Fe^(II), Fe^(II)Fe^I, and Fe^IFe^I). The (N_2-Fe(μ-SAr)Fe-N_2) system undergoes reduction of the bound N_2 to produce NH_3 (∼50% yield) and can efficiently catalyze the disproportionation of N_2H_4 to NH_3 and N_2. The present scaffold also supports dinitrogen binding concomitant with hydride as a co-ligand. Synthetic model complexes of these types are desirable to ultimately constrain hypotheses regarding Fe-mediated nitrogen fixation in synthetic and biological systems

Canonical Demon Monte Carlo Renormalization Group

We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. In contrast to the Microcanonical Renormalization Group invented by Creutz et al. our method does not suffer from systematical errors stemming from a simultaneous use of two different ensembles. We present numerical results for the $O(3)$ nonlinear $\sigma$-model.Comment: LaTeX file, 7 pages, preprints CERN TH.7330/94, MS-TPI-