Sequential MC

In most cases we apply now the method—coined by Coutinho and Canuto [81,82] as sequential MC (SMC) or sequential MD (SMD)—in which an all-classical simulation is performed from which, after equilibration, a relative small number of snapshots of uncorrelated solute-solvent configurations are collected. In Ref. [81] these authors show that a relatively small number of configurations—small with respect to the total number generated in the simulation—contains all statistically relevant information. Then from QM or QM/MM calculations on the snapshots the (electronic) molecular properties in solution are obtained by averaging, or otherwise collected. In the original paper the saved solute-solvent configurations were subjected to an all-QM calculation. We apply this technique generally with only the solute as QM part for reasons already mentioned above. 

Monte Carlo/simulated annealing (MC/SA) algorithm for sequential assignment in uniformly 13C, 15N-labeled proteins [137]. The two-dimensional (2D) NCACX and NCOCX spectra measured for the fibril samples of full-length Syrian hamster prion protein (residues 23-231) have been analyzed by the MC/SA protocol, from which it has been concluded that the fibril core is formed primarily in the region of residues 173-224 [54]. 

The preceding discussion applied implicitly to what we classify as dynamical simulations — namely, those simulations in which all correlations in the final trajectory arise because each configuration is somehow generated from the previous one. This time-correlated picture applies to a broad class of algorithms MD, Langevin and Brownian dynamics, as well as traditional Monte Carlo (MC, also known as Markov-chain Monte Carlo). Even though MC may not lead to true physical dynamics, all the correlations are sequential. 

One increasingly popular method which lead to non-dynamical trajectories is replica-exchange MC or MD [11-13], which employs parallel simulations at a ladder of temperatures. The "trajectory" at any given temperature includes repeated visits from a number of (physically continuous) trajectories wandering in temperature space. Because the continuous trajectories are correlated in the usual sequential way, their intermittent — that is, non-sequential — visits to the various specific temperatures produce non-sequential correlations when one of those temperatures is considered as a separate ensemble or "trajectory" [14]. Less prominent examples of non-dynamical simulations occur in a broad class of polymer-growth algorithms (e.g., refs. 15-17). 

A reactive macrocyclic ether-urethane carbodiimide (MC-CDI), which is the key intermediate for synthesizing poly(amide-urethane) and poly(amide-imide-urethane), was prepared by the sequential self-repetitive reaction. A se-... 

Reaction of l,8-dimethoxy-9-methylenethioxanthene with 1,8-dimethoxythiopyrylium cation followed by sequential deprotonation and oxidation affords the allene 362 which shows only one methoxy signal in the 111 NMR spectrum (Scheme 84) <2005PS(180)1339>. Methylation with Mc(0 1 BF4 gives the resonance stabilized mono-methylated cation 363 which reverts to the mono cation 364 over a period of about 4 hours and which is accessible directly from the allene 362 by treatment with HBF4 (Scheme 84) <2005PS(180)1339>. 

Lim TH, Lee JS, Choi BI, Kim 10, Suh CH, Han MC, Kim CW (1987) An explanation of renal hemodynamics in acute renal failure based on sequential CT in patients with Korean hemorrhagic fever. J Comput Assist Tomogr 11 474-479... 

Gale M, Pollanen MS, Markiewicz P, Goh MC. Sequential assembly of collagen revealed by atomic force microscopy, Biophys J. 1995 68 2124-2128. 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

Figure 12.2. Microcolumn flow-through manifolds for fractionation analysis in environmental solids (ti) continuous-flow system with either fraction collection or online detection (Jj) flow-injection setup with discrete injection of extractant (c) sequential injection system as assembled for fully automated sequential or single extractions. MC microcolumn, C coil, SP syringe pump, PP peristaltic pump, R reagent, D detector, W waste, SV selection valve, IV injection valve. (Adapted from Mir6 et al., 2005a.)...

Other applications of dialkyl l-(trimethylsilyl)methylphosphonates include the reaction with dielec-trophihc reagents for the preparation of three-, four-, five-, and six-membered cycloalkylphospho-nates. Diethyl trichloromethylphosphonate is particularly well suited to this approach, and the exchange of the three halogen atoms with n-BuLi followed by sequential addition of Mc ,SiCl and (fl-dibromoalkanes results in the formation of a series of a-silylated cycloalkylphosphonates... 

The oxidation reaction in Eq. (4.1) is actually very complex. There are four major intermediates that are made during the sequential oxidations of methyl groups of pX (Figure 4.1). The conversion of each intermediate requires intervention of the MC catalyst. 

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