# ChieMiabin

For separation calculations, phase equilibrium is most conven-ier by [c.112]

A Practical Companion to Reservoir Stimulation [c.386]

A. Campion, Ann. Rev. Phys. Chem., 36, 549 (1985). [c.326]

F. E. Karasz, W. M. Champion, and G. D. Halsey, Jr., J. Phys. Chem., 60, 376 (1956). [c.681]

Temsamani M A, Champion J-M and Oss S 1999 J. Chem. Phys. 110 2893 [c.82]

Champion P M and Albrecht A C 1981 On the modeling of absorption band shapes and resonance Raman excitation profiles Chem. Phys. Lett. 82 410-13 [c.1227]

Zhu L, Li P, Huang M, Sage J T and Champion P M 1994 Real time observation of low frequency heme protein vibrations using femtosecond coherence spectroscopy Phys. Rev. Lett. 72 301-4 [c.1998]

Zhu L, Sage J T and Champion P M 1994 Observation of coherent reaction dynamics in heme proteins Science 266 629-32 [c.1998]

Zhu L, Wang W, Sage J T and Champion P M 1995 Femtosecond time-resolved vibrational spectroscopy of heme proteins J. Raman Spectrosc. 26 527-34 [c.1998]

The question of determination of the phase of a field (classical or quantal, as of a wave function) from the modulus (absolute value) of the field along a real parameter (for which alone experimental determination is possible) is known as the phase problem [28]. (True also in crystallography.) The reciprocal relations derived in Section III represent a formal scheme for the determination of phase given the modulus, and vice versa. The physical basis of these singular integral relations was described in [147] and in several companion articles in that volume a more recent account can be found in [148]. Thus, the reciprocal relations in the time domain provide, under certain conditions of analyticity, solutions to the phase problem. For electromagnetic fields, these were derived in [120,149,150] and reviewed in [28,148]. Matter or Schrodinger waves were [c.104]

This farewell to Sartre by his life-long companion is a true labour of love (the Listener) and an extraordinary achievement (New Statesman). [c.446]

Chapter 1. COMPOaVON OF CRUDE OILS AND PETROLEUM PRODUCTS [c.13]

N. Kakuta, K. H. Park, M. F. Finlayson, A. J. Bard, A. Campion, M. A. Fox, S. E. Webber, and J. M. White, J. Phys. Chem., 89, 5028 (1985). [c.324]

A. Sobczynski, A. J. Bard, A. Campion, M. A. Fox, T. Mallouk, S. E. Webber, and J. M. White, J. Phys. Chem., 91, 3316 (1987). [c.429]

It would appear that identical particle pemuitation groups are not of help in providing distinguishing syimnetry labels on molecular energy levels as are the other groups we have considered. However, they do provide very usefiil restrictions on the way we can build up the complete molecular wavefiinction from basis fiinctions. Molecular wavefiinctions are usually built up from basis fiinctions that are products of electronic and nuclear parts. Each of these parts is fiirther built up from products of separate uncoupled coordinate (or orbital) and spin basis fiinctions. Wlien we combine these separate fiinctions, the final overall product states must confonn to the pemuitation syimnetry mles that we stated above. This leads to restrictions in the way that we can combine the uncoupled basis fiinctions. [c.173]

Kleinian V, Gordon R J, Park H and Zare R N 1998 Companion to Angular Momentum (New York Wiley) Tinkliam M 1964 Group Theory and Quantum Mechanics York McGraw-Hill) [c.183]

An essential feature of mean-field theories is that the free energy is an analytical fiinction at the critical point. Landau [100] used this assumption, and the up-down symmetry of magnetic systems at zero field, to analyse their phase behaviour and detennine the mean-field critical exponents. It also suggests a way in which mean-field theory might be modified to confonn with experiment near the critical point, leading to a scaling law, first proposed by Widom [101], which has been experimentally verified. [c.536]

Most of the theoretical predictions have now been substantially verified by a large series of experiments in a number of laboratories. Knobler and Scott and their coworkers (1977-1991) have studied a number of quasibinary mixtures, in particular ethane + (liexadecane + octadecane) for which the experimental n.2 = 17.6. Their experimental results essentially confimi the theoretical predictions shown in figure A2.5.31. [c.660]

The current frontiers for the subject of non-equilibrium thennodynamics are rich and active. Two areas dommate interest non-linear effects and molecular bioenergetics. The linearization step used in the near equilibrium regime is inappropriate far from equilibrium. Progress with a microscopic kinetic theory [38] for non-linear fluctuation phenomena has been made. Carefiil experiments [39] confinn this theory. Non-equilibrium long range correlations play an important role in some of the light scattering effects in fluids in far from equilibrium states [38, 39]. [c.713]

Overall, the Slater theory is unsuccessfiil in interpreting experiments. Many unimolecular rate constants and reaction paths are consistent with energy flowing randomly within the molecule [4,36]. If one considers the nature of classical Hamiltonians for actual molecules, it is not surprising that the Slater theory perfomis so poorly. For example, in Slater theory, the intramolecular and unimolecular dynamics of the molecule confomi to the synnnetry of the molecular vibrations. Thus, if nonnal modes of a particular synnnetry type are excited (e.g. in-plane vibrations) a decomposition path of another synnnetry type (e.g. out-of-plane dissociation) carmot occur. This path requires excitation of out-of-plane vibrations. Nonnal modes of different symmetry types for actiral molecules are coupled by Coriolis vibrational-rotational interactions [M]. Similarly, nonlmear resonance interactions couple nonnal modes of vibration, allowing transfer of energy Not [c.1025]

Plenary 7 7. P M Champion et al, e-mail address champ neu.edu (TRRRS). Femtosecond impulsive preparation and timing of ground and excited state Raman coherences in heme proteins. Discovery of coherence transfer along a de-ligation coordinate. See above for fiirther connnent. [c.1219]

Zhu I, Wdom A and Champion P M 1997 A multidimensional Landau-Zener description of chemical reaction dynamics and vibrational coherence J. Chem. Phys. 107 2859-71 [c.1227]

Champion P M, Rosea F, Chang W, Kumar A, Christian J and Demidov A 1998 Femtosecond coherence spectroscopy of heme proteins XVith int. Conf on Raman Spectroscopy ed A M Heyns (New York Wley) pp 73-6 [c.1227]

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In all of these stmctures the atomic positions are fixed by the space group syimnetry and it is only necessary to detennine which of a small set of choices of positions best fits the data. According to the theory of space groups, all stmctures composed of identical unit cells repeated hi three dimensions must confomi to one of 230 groups tliat are fomied by coinbinmg one of 14 distinct Bmvais lattices with other syimnetry operations. [c.1372]

Surface reconstructions have been observed by STM in many systems, and the teclmique has, indeed, been used to confmn the missing row structure in the 1 x 2 reconstruction of Au(l 10) [28]. As the temperature was increased within 10 K of the transition to the disordered 1 1 phase (700 K), a drastic reduction in domain size to -20-40 A (i.e. less than the coherence width of LEED) was observed. In this way, the STM has been used to help explain and extend many observations previously made by diffraction methods. [c.1682]

Kambhampati P, Child C M, Foster M C and Campion A 1998 On the ohemioal meohanism of surfaoe enhanoed Raman soattering experiment and theory J. Chem. Rhys. 108 5013-26 [c.1797]

Since silicon is tire most important semiconductor material, clusters of silicon have been most extensively studied, botli tlieoretically and experimentally. The electronic stmcture [101, 102, 103 and 104], geometrical stmcture [105, 106, 107, 108, 109 and 110] and chemical reactivity [111] of silicon clusters have been investigated. The stmctures of small silicon clusters assume tlrree-dimensional stmctures different from botli tliat of tire bulk crystal and tliat of its group IV neighbour, carbon. Ion mobility experiments have been very effective in providing experimental stmctural infonnation for silicon clusters, and confinn tliat many stmctural isomers exist for silicon clusters because of tlieir strong covalent bonding and relatively open stmctures [106, 110]. Ion mobility results show tliat silicon clusters up to 27 atoms follow a prolate growtli sequence, resulting in geometries witli an aspect ratio of 3 [106]. Larger clusters appear to assume more spherical geometries. The stmctures of medium-sized silicon clusters witli 12-26 atoms have been studied recently by tlieoretical calculations using density functional tlieory in combination witli ion mobility experiments [110]. Figure Cl. 1.6 shows tlie calculated stmctures of silicon clusters containing 12-20 atoms. The clusters witli less tlian 18 atoms can be visualized as stacked Sig tricapped trigonal prisms, whereas global minima of Si g and Si,g assume more spherical stmctures. [c.2396]

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo [c.2537]

The appropriate quantum mechanical operator fomi of the phase has been the subject of numerous efforts. At present, one can only speak of the best approximate operator, and this also is the subject of debate. A personal historical account by Nieto of various operator definitions for the phase (and of its probability distribution) is in [27] and in companion articles, for example, [130-132] and others, that have appeared in Volume 48 of Physica Scripta T (1993), which is devoted to this subject. (For an introduction to the unitarity requirements placed on a phase operator, one can refer to [133]). In 1927, Dirac proposed a quantum mechanical operator tf), defined in terms of the creation and destruction operators [134], but London [135] showed that this is not Hermitean. (A further source is [136].) Another candidate, e is not unitary. [c.103]

We begin by considering a three-atom system, the allyl radical. A two anchor loop applies in this case as illush ated in Figure 12 The phase change takes place at the allyl anchor, and the phase-inverting coordinate is the asymmetric stretch C3 mode of the allyl radical. Quantum chemical calculations confiiin this qualitative view [24,56]. In this particular case only one photochemical product is expected. [c.349]

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.) [c.379]

Th is discussion focuses on th e individual compon en ts of a typical molecular mechanics force field. It illustrates the mathematical functions used, wdi y those functions are chosen, and the circiim -Stan ces u n der wh ich the fun ction s become poor approxirn atiori s. Part 2 of th is book, Theory and Melhadx, includes details on the implementation of the MM+,. AM BHR, RlO-g and OPl.S force fields in HyperChem. [c.22]

The relative sizes ofthe poten tial barriers in dicate that the AF force con Stan t is larger th an the V con stan t. fh e ph ase sh ift is 180 degrees for th e Fourier compoiien t with a two-fold barrier. Minima occur at 180, 0, and I 80 degrees and maxima at 90 and 90 [c.25]

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**ChieMiabin**:

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Organic syntheses based on name reactions and unnamed reactions (1994) -- [ c.39 ]