Statistical and systematic errors in Monte Carlo sampling

We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the bin length (size of the statistical sample), both at and away from a phase transition. The formalism is tested using simulations of thed=3 Ising model at the infinite-lattice transition temperature. We show that for a 96×96×96 system noticeable systematic errors (systematic underestimation of response functions) are still present for total run lengths of 10⁶ Monte Carlo steps/site (MCS) with measurements taken at regular intervals of 10 MCS.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.     

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions _AA , _AB , _BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc _v and which are strictly conserved, as are the concentrationsc _A andc _B of the two species.A-atoms may jump to vacant sites with jump rate _A , B-atoms with jump rate _B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special case _A = _B on a square lattice, considering three different choices of interactions with the same = _AB – ( _AA + _BB )/2: (i) _AB =, _AA = _BB = 0; (ii) _AA = 0, _AA = _BB ; = ; (iii) _AB = _BB = 0, _AA = –2. We obtain both the time evolution of the structure factorS(k,t) following a quench from infinite temperature to the considered temperature, and the timedependence of the mean cluster size and the various neighborhood probabilities of a vacancy. While in case (i) forc _V 0.16 the distribution of vacancies in the system stays nearly random, in case (ii) the vacancies cluster in theA-B interfacial region, and in case (iii) they get nearly completely expelled from theA-rich regions. While phase separation proceeds in case (i) only slightly faster than in case (ii), a significant slowing down of the relaxation is observed for case (iii), which shows up in a strong reduction of the effective exponents describing the growth.     

Electronic control of stereoselectivity-21 : Stereochemical parallelism between dienophilic capture and singlet oxygenation of isodicyclopentadiene derivatives

The stereochemistry and product distribution resulting from reaction of 4',5',6',7'- tetrahydrospirol[cyclopropane-1,2']-[4,7]methano[2$\text{H}$]indene(5), endo-2-methyl(6a) and 2,2-dunethyl-4,7-dihydro-4,7-methano-2$\text{H}$-indene (6b), as well as 4',5',6',7'-tetrahydrospiro[cyclopentane-1,2']-[4,7]methano-[2$\text{H}$]indene (7) with singlet oxygen have been determined. Stereochemical assignments to the diepoxide products were readily deduced by ¹³C-NMR comparison with the spectra of the parent isomcrs of established structure (X-ray). To unravel the stereochemistry of the epoxy aldehydes, recourse was made to 2D NOE experiments The observed stereosclectivity and reaction profile of each substrate are analyzed and placed in proper mechanistic and energetic perspective.     

Synthesis and Structure of a One‐Dimensional Aluminum Phosphate, [NH3(CH2)2NH2(CH2)3NH3]3+ [Al(PO4)2]3—

A one‐dimensional aluminum phosphate, [NH₃(CH₂)₂NH₂(CH₂)₃NH₃]³⁺ [Al(PO₄)₂]^3—, has been synthesized hydrothermally in the presence of N‐(2‐Aminoethyl‐)1, 3‐diaminopropane (AEDAP) and its structure determined by single crystal X‐ray diffraction. Crystal data: space group = Pbca (no. 61), a = 16.850(2), b = 8.832(1), c = 17.688(4)Å, V = 2632.4(2)ų, Z = 8, R₁ = 0.0389 [5663 observed reflections with I > 2σ(I)]. The structure consists of anionic [Al(PO₄)₂]^3— chains built up from AlO₄ and PO₄ tetrahedra, in which all the AlO₄ vertices are shared and each PO₄ tetrahedron possesses two terminal P=O linkages. The cations, which balances the negative charge of the chains, are located in between the chains and interact with the oxygen atoms through strong N—H···O hydrogen bonds. Additional characterization of the compound by powder XRD and MAS‐NMR has also been performed and described.     

Scattering from concentration fluctuations in polymer blends: A monte carlo investigation

The collective scattering function S_coll( ), which describes light (neutron-, x-ray) scattering under wavevector , is obtained from Monte Carlo simulations for a symmetrical polymer mixture. The polymers are modelled by self-avoiding walks ofN _A=N_B=N steps on a simple cubic lattice, where a fraction _V of sites is left vacant, and an attractive energy occurs if two neighboring sites are taken by the same kind of monomer. Spinodal curves are estimated from linear extrapolation of S _coll ^–1 (0) vs./k _B T, whereT is the temperature. Also the single chain structure factor is obtained and the de Gennes random phase approximation (RPA) can thus be tested. Unexpectedly, strong deviations are found if one species is very dilute. The estimation of an effective Flory-Huggins-parameter from scattering data is also discussed.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Hamburg, March 14–16, 1987.     

CHANGE IN SULFHYDRYL GROUP MICROENVIRONMENT OF CALF LENS α-CRYSTALLIN BY 300 nm LIGHT

Abstract— The effect of 300 nm irradiation on the sulfhydryl groups of calf lens a-crystallin has been investigated by using specific, covalently bound fluorescent sulfhydryl probes 4–(N-iodoacetoxy)ethyl-N-methylamino-7-n-itrobenz-2-o-xa-1,3-d-iazole (IANBD), N-iodoacetyl-N'-(5-s-ulfo-l-naphthyl) ethylene-diamine (1,5 IAEDANS) and 5-i-odoacetamidofluorescein (IAF). The decrease in tryptophan fluorescence with time of irradiation of a-crystallin, is accompanied by a decrease in the fluorescence of the hydrophobic sulfhydryl label IANBD. In addition, the fluorescence of the surface-sulfhydryl label IAF increased in the irradiated a-crystallin. These results indicate that the sulfhydryl groups are in a more exposed (hydrophilic) environment in the irradiated protein than in the control, possibly because of partial unfolding of the protein. This result is confirmed by fluorescence lifetime measurements with IAEDANS. The decay curve of IAEDANS-α-crystallin has a major lifetime of 15.7 ns and a minor one of 24.6 ns. Upon irradiation, the lifetime of the major component decreases to 10.2 ns and that of the minor component to 21.7 ns. Denatured IAEDANS-α-crystallin has a single lifetime of 10.4 ns. These results show that the photoinduced damage to the tryptophan residues of α-crystallin alters the environment of the sulfhydryl groups and induces a change in the tertiary structure of the protein. Proximity of the cysteine residues to tryptophan in the tertiary structure of the protein may be an important determinant of their susceptibility to photoinduced change.     

Structures and relative energies of gas-phase [C2H7N]+˙ radical cations

Ab initio molecular orbital calculations with split-valence plus polarization basis sets and incorporating electron correlation and zero-point energy corrections have been used to examine possible equilibrium structures on the [C₂H₇N]⁺˙ surface. In addition to the radical cations of ethylamine and dimethylamine, three other isomers were found which have comparable energy, but which have no stable neutral counterparts. These are \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm }, $\end{document} with calculated energies relative to the ethylamine radical cation of ?33, ?28 and 4 kJ mol^?1, respectively. Substantial barriers for rearrangement among the various isomers and significant binding energies with respect to possible fragmentation products are found. The predictions for \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^ + {\rm H}_{\rm 3} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3}$\end{document} are consistent with their recent observation in the gas phase. The remaining isomer, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm },$\end{document}is also predicted to be experimentally observable.     

The stability constants of some metal chelates of triethylenetetraminehexaacetic acid (ttha)

Stability constants for Al(III), Cd(II), Co(II), Cu(II), Fe(III), Hg(II), La(III), Nd(III), Er(III), Mg(II). Mn(II), Ni(II), Pb(II), Th(IV) and Zn(II) complexes of triethylenetetraminehexaacetic acid (TTHA) have been evaluated from data obtained by pH and pM measurements. The pM method based on measurements with the mercury electrode and the redox system Fe(III)/Fe(II) proved to be very useful when binuclear complexes are formed.     

Unravelling the composition of very complex samples by comprehensive gas chromatography coupled to time-of-flight mass spectrometry. Cigarette smoke

The potential and current limitations of comprehensive two-dimensional gas chromatography coupled to time-of-flight mass spectrometry (GC x GC-TOF-MS) for the analysis of very complex samples were studied with the separation of cigarette smoke as an example. Because of the large number of peaks in such a GC x GC chromatogram it was not possible to perform manual data processing. Instead, the GC-TOF-MS software was used to perform peak finding, deconvolution and library search in an automated fashion; this resulted in a peak table containing some 30000 peaks. Mass spectral match factors were used to evaluate the library search results. The additional use of retention indices and information from second-dimension retention times can substantially improve the identification. The combined separation power of the GC x GC-TOF-MS system and the deconvolution algorithm provide a system with a most impressive separation power.