SIMONA 1.0: An efficient and versatile framework for stochastic simulations of molecular and nanoscale systems

Molecular simulation methods have increasingly contributed to our understanding of molecular and nanoscale systems. However, the family of Monte Carlo techniques has taken a backseat to molecular dynamics based methods, which is also reflected in the number of available simulation packages. Here, we report the development of a generic, versatile simulation package for stochastic simulations and demonstrate its application to protein conformational change, protein–protein association, small-molecule protein docking, and simulation of the growth of nanoscale clusters of organic molecules. Simulation of molecular and nanoscale systems (SIMONA) is easy to use for standard simulations via a graphical user interface and highly parallel both via MPI and the use of graphical processors. It is also extendable to many additional simulations types. Being freely available to academic users, we hope it will enable a large community of researchers in the life- and materials-sciences to use and extend SIMONA in the future. SIMONA is available for download under http://int.kit.edu/nanosim/simona . © 2012 Wiley Periodicals, Inc.     

Parametric Presburger arithmetic: complexity of counting and quantifier elimination

We consider an expansion of Presburger arithmetic which allows multiplication by k parameters $t_1,\dots ,t_k$. A formula in this language defines a parametric set $S_{\mathbf{t}}?{\mathbb{Z}}^d$ as $\mathbf{t}$ varies in ${\mathbb{Z}}^k$, and we examine the counting function $|S_{\mathbf{t}}|$ as a function of t . For a single parameter, it is known that $|S_t|$ can be expressed as an eventual quasi‐polynomial (there is a period m such that, for sufficiently large t, the function is polynomial on each of the residue classes mod m). We show that such a nice expression is impossible with 2 or more parameters. Indeed (assuming $\mathbf{P}\ne \mathbf{NP}$) we construct a parametric set $S_{t_1,t_2}$ such that $|S_{t_1,t_2}|$ is not even polynomial‐time computable on input $(t_1,t_2)$. In contrast, for parametric sets $S_{\mathbf{t}}?{\mathbb{Z}}^d$ with arbitrarily many parameters, defined in a similar language without the ordering relation, we show that $|S_{\mathbf{t}}|$ is always polynomial‐time computable in the size of t , and in fact can be represented using the gcd and similar functions.     

Syntheses and structures of magnesium and zinc boraamidinates: EPR and DFT investigations of Li, Mg, Zn, B, and In complexes of the [PhB(NtBu)2].- anion radical

The first magnesium and zinc boraamidinate (bam) complexes have been synthesized via metathetical reactions between dilithio bams and Grignard reagents or MCl2 (M = Mg, Zn). The following new classes of bam complexes have been structurally characterized: heterobimetallic spirocycles {(L)mu-Li[PhB(mu-NtBu)2]}2M (6a,b, M = Mg, L = Et2O, THF; 6c, M = Zn, L = Et(2)O); bis(organomagnesium) complexes {[PhB(mu3-NtBu)2](MgtBu)2(mu3-Cl)Li(OEt2)3} (8) and {[PhB(mu3-NtBu)2](MgR)2(THF)2} (9a, R = iPr; 9b, R = Ph); mononuclear complex {[PhB(mu-NDipp)2]Mg(OEt2)2} (10). Oxidation of 6a or 6c with iodine produces persistent pink (16a, M = Mg) or purple (16b, M = Zn) neutral radicals {Lx-mu-Li[PhB(mu-NtBu)2]2M}. (L = solvent molecule), which are shown by EPR spectra supported by DFT calculations to be Cs-symmetric species with spin density localized on one of the bam ligands. In contrast, characterization of the intensely colored neutral radicals {[PhB(mu-NtBu)2]2M}. (5c, M = In, dark green; 5d, M = B, dark purple) reveals that the spin density is equally delocalized over all four nitrogen atoms in these D2d-symmetric spirocyclic systems. Oxidation of the dimeric dilithio complex {Li2[PhB(mu4-NtBu)2]}2 with iodine produces the monomeric neutral radical {[PhB(mu-NtBu)2]Li(OEt2)x}. (17), characterized by EPR spectra and DFT calculations. These findings establish that the bam anionic radical [PhB(NtBu)2].- can be stabilized by coordination to a variety of early main-group metal centers to give neutral radicals whose relative stabilities are compared and discussed.     

Syntheses and X-ray structures of monocyclic,bicyclic, and spirocyclic gallium and indium boraamidinates

The reactions of [Li(2)[PhB(N(t)Bu)(2)]](2) with GaCl(3) in various stoichiometries yield [Li(thf)(4)][PhB(mu-N(t)Bu)(2)GaCl(2) x GaCl(3)] (1), [PhB(mu-N(t)Bu)(2)GaCl](2) (2), and [mu-Li(OEt(2))[PhB(N(t)Bu)(2)]Ga] (3a), a series of complexes in which the three chloride ligands are successively replaced by the dianion [PhB(N(t)Bu)(2)](2-). The X-ray structures of 1, 2, and 3a show that the boraamidinate ligand adopts an N,N'-chelating mode. In the ion-separated complex 1, one of the nitrogen atoms is coordinated to a GaCl(3) molecule. The related indium complexes [mu-LiCl(thf)(2)][PhB(mu-N(t)Bu)(2)InCl](2) (4) and [mu-Li(OEt(2))[PhB(mu-N(t)Bu)(2)]In] (3b) were obtained in a similar manner. Complex 4 is the indium analogue of 2 with the incorporation of a bissolvated LiCl molecule. In 3a and 3b the spirocyclic [[PhB(mu-N(t)Bu)(2)](2)M](-) (M = Ga, In) anions are N,N'-chelated to the [Li(OEt(2))](+) counterion. Prolonged reactions result in the formation of [PhB(mu-N(t)Bu)(2)GaCl][(t)BuN(H)GaCl(2)] (5) and [[PhB(mu-N(t)Bu)(2)InCl][(t)BuN(H)InCl(2)][mu-LiCl(OEt(2))(2)]] (6), respectively. The X-ray structures of 5 and 6 reveal bicyclic structures which formally involve the entrapment of the monomers (t)BuN(H)MCl(2) by a four-membered BN(2)M ring (M = Ga, In). The synthesis and X-ray structure of Cl(2)Ga[mu-N(H)(t)Bu](2)GaCl(2) are also reported.     

Coinage Metal Complexes of a Tellurium Diimide: cis→trans Isomerization and Metal–Metal Interactions

The different coordination behavior of the ligand tBuN=Te(μ-NtBu)₂Te=NtBu (L) towards Cu⁺ and Ag⁺ results from a cis→trans isomerization. The two Cu⁺ ions in [Cu₂L₃]²⁺ (shown schematically) bridge trans and cis isomers of the ligand, whereas the Ag⁺ ions in [Ag₂L₂]²⁺ link two trans ligands and exhibit a weak Ag⋅⋅⋅Ag interaction.     

Syntheses, X-ray structures and AACVD studies of group 11 ditelluroimidodiphosphinate complexes

Reactions of Na(tmeda)[N((i)Pr(2)PTe)(2)] with CuCl, AgI or AuCl (in the presence of PPh(3)) in THF produced the coinage metal ditelluroimidodiphosphinate complexes {Cu[N((i)Pr(2)PTe)(2)]}(3), (5), {Ag[N((i)Pr(2)PTe)(2)]}(6) (6) and Au(PPh(3))[N((i)Pr(2)PTe)(2)] (7), respectively. Complexes 5, 6 and 7 were characterized in the solid state by X-ray crystallography. Complex 5 is trimeric and exhibits a highly distorted Cu(3)Te(3) ring. In contrast, the Ag(I) complex 6 is a hexamer, and forms a twelve-membered Ag(6)Te(6) ring. The replacement of the (i)Pr groups on phosphorus by Ph results in an intriguing structural change to a tetramer with a boat-shaped Ag(4)Te(4) ring in {Ag[N(Ph(2)PTe)(2)}(4).2THF (8). The gold(I) complex 7 is monomeric. Aerosol-assisted chemical vapour deposition (AACVD) of compounds 5, 6 and 7 yields CuTe, Ag(7)Te(4), AuTe(2) and Au films, respectively. The films were grown at temperatures of 300-500 degrees C and characterized by X-ray powder diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive analysis of X-rays (EDAX).     

A square‐planar tellurium(II) complex with Te,Te′‐chelating ligands

While exploring the chemistry of tellurium‐containing dichalcogenidoimidodiphosphinate ligands, the first all‐tellurium member of a series of related square‐planar E^II(E′)₄ complexes (E and E′ are group 16 elements), namely bis(P,P,P′,P′‐tetraphenylditelluridoimidodiphosphinato‐κ²Te,Te′)tellurium(II) (systematic name: 2,2,4,4,8,8,10,10‐octaphenyl‐1λ³,5,6λ⁴,7λ³,11‐pentatellura‐3,9‐diaza‐2λ⁵,4λ⁵,8λ⁵,10λ⁵‐tetraphosphaspiro[5.5]undeca‐1,3,7,9‐tetraene), C₄₈H₄₀N₂P₄Te₅, was obtained unexpectedly. The formally Te^II centre is situated on a crystallographic inversion centre and is Te,Te′‐chelated to two anionic [(TePPh₂)₂N]⁻ ligands in an anti conformation. The central Te^II(Te)₄ unit is approximately square planar [Te—Te—Te = 93.51 (3) and 86.49 (3)°], with Te—Te bond lengths of 2.9806 (6) and 2.9978 (9) Å.     

Estimation of critical and viscous frequencies for Biot theory in cancellous bone

The use of Biot theory for modelling ultrasonic wave propagation in porous media involves the definition of a "critical frequency" above which both fast and slow compressional waves will, in principle, propagate. Critical frequencies have been evaluated for healthy and osteoporotic cancellous bone filled with water or marrow, using data from the literature. The range of pore sizes in bone gives rise to a critical frequency band rather than a single critical frequency, the mean of which is lower for osteoporotic bone than normal bone. However, the critical frequency is a theoretical concept and previous researchers considered a more realistic "viscous frequency" above which both fast and slow waves may be experimentally observed. Viscous frequencies in bone are found to be several orders of magnitude greater than calculated critical frequencies. Whereas two waves may well be observed at all ultrasonic frequencies for water-filled cancellous bone at 20 degrees C, it is probable megahertz frequencies would be needed for observation of two waves in vivo.