Miller, Marcus

For imiltidiniensional problems, the generalization of WKB theory to the description of scattering problems is often called Miller-Marcus or classical. S-niatrix theory [ ]. The reader is refened to review articles for a more complete description of this theory [52]. 

The calculation of the time evolution operator in multidimensional systems is a fomiidable task and some results will be discussed in this section. An alternative approach is the calculation of semi-classical dynamics as demonstrated, among others, by Heller [86, 87 and 88], Marcus [89, 90], Taylor [91, 92], Metiu [93, 94] and coworkers (see also [83] as well as the review by Miller [95] for more general aspects of semiclassical dynamics). This method basically consists of replacing the 5-fimction distribution in the true classical calculation by a Gaussian distribution in coordinate space. It allows for a simulation of the vibrational... 

This reasoning was set forth by Johnston and Rapp [1961] and developed by Ovchinnikova [1979], Miller [1975b], Truhlar and Kupperman [1971], Babamov and Marcus [1981], and Babamov et al. [1983] for reactions of hydrogen transfer in the gas phase. A similar model was put forth in order to explain the transfer of light impurities in metals [Flynn and Stoneham 1970 Kagan and Klinger 1974]. Simple analytical expressions were found for an illustrative model [Benderskii et al. 1980] in which the A-B and B-C bonds were assumed to be represented by parabolic terms. 

Marcus M, Spigarelli J, Miller H. 1978. Organic compounds in organophosphoms pesticide manufacturing waste waters. Washington, DC U S. Environmental Protection Agency. NTIS PB-289821. 

An analytical theory based upon the effective medium approach (EMA) has been developed by Fishchuk et al. [70]. They consider the superposition of disorder and polaron effects and treat the elementary charge transfer process at moderate to high temperatures in terms of symmetric Marcus rates instead of Miller-Abrahams rates (see below). The predicted temperature and field dependence of the mobility is... 

J. Manz Let me add a comment on Professor W. H. Miller s remark that he would never make himself, but I can express this as the chairman of this session. In fact, Professor Miller s extension of the standard RRKM-theory allows to predict not only the statistical mean values of the rate coefficients, but also their fluctuations. This is an important achievement in the theory of chemical reaction theory over the past couple of years and it should be adequate to call it the RRKMM theory (Ramspeiger-Rice-Kassel-Marcus-Miller) [1]. 

R. A. Marcus My interests in variational microcanonical transition state theory with J conservation goes back to a J. Chem. Phys. 1965 paper [1], and perhaps I could make a few comments. First, using a variational treatment we showed with Steve Klippenstein a few years ago that the transition-state switching mentioned by Prof. Lorquet poses no major problem The calculations sometimes reveal two, instead of one, bottlenecks (transition states, position of minimum entropy along the reaction coordinate) [2], and then one can use a method described by Miller and partly anticipated by Wigner and Hirschfelder to calculate the net dux. 

R. A. Marcus Prof. Miller, has your insightful quantum mechanical flux-flux correlation expression for the rate been used to test some of the simplified quantum mechanical tunneling calculations for reactions I recall that Coltrin and I found a simple path that agreed to a factor of 2, over six or so orders of magnitude of tunneling, with the quantum mechanical results for the collinear symmetric reaction H + H2 — H2 + H [1]. Truhlar has proposed an extension for asymmetric reactions. 

Figure 2.3 Evidence for the Marcus inverted region from intramolecular electron rate constants as a function of AG° in methyltetrahydrofuran solution at 206 K. Reprinted with permission from G.L. Closs, L.T. Calcaterra, H.J. Green, K.W. Penfield and J.R. Miller, ]. Phys. Chem., 90,3673 (1986). Copyright (1986) American Chemical Society...

These tunneling concepts can be compared with the Marcus theory for electron transfer (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). In the normal regime, solvent fluctuation is required to equilibrate the reactant and... 

The theory for this intermolecular electron transfer reaction can be approached on a microscopic quantum mechanical level, as suggested above, based on a molecular orbital (filled and virtual) approach for both donor (solute) and acceptor (solvent) molecules. If the two sets of molecular orbitals can be in resonance and can physically overlap for a given cluster geometry, then the electron transfer is relatively efficient. In the cases discussed above, a barrier to electron transfer clearly exists, but the overall reaction in certainly exothermic. The barrier must be coupled to a nuclear motion and, thus, Franck-Condon factors for the electron transfer process must be small. This interaction should be modeled by Marcus inverted region electron transfer theory and is well described in the literature (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). 

The feasibility of some of these radical pathways has been examined using Marcus theory to obtain rate constants for comparison with the experimental data (Eberson, 1984). For some relevant anions, including hydroxide, methoxide, t-butoxide, the anion of benzaldehyde hydrate and di-2-propyl-amide, the necessary E°(RO-/RO) values are available or can be estimated with sufficient accuracy. For the reaction of t-butoxide with benzophenone in THF, or the benzaldehyde hydrate anion with benzaldehyde in aqueous dioxan, direct electron transfers between the anion and the neutral are not feasible the calculated rate constants are orders of magnitude too low to be compatible with the observed reduction rates. Any radicals observed in these reactions must arise by some other more complex mechanism. The behaviour of an aromatic aldehyde hydrate dianion has not been examined in this way, but MNDO calculation (Rzepa and Miller, 1985) suggests that such a species could easily transfer either a single electron or a hydrogen atom to an accepting aldehyde. 

The mechanism of the electrochemical cleavage of the C-X (X = F, Cl, Br and I) bond has been extensively studied (see for example, Miller and Riekena 1969 Pause et al. 2000 Costentin et al. 2003 Wang et al. 2004 Sanecki and Skital 2007) and theoretical models (Battistuzzi et al. 1993 Kuznetsov et al. 2004 Zhang et al. 2005 Golinske and Voss 2005), mostly based on the Marcus theory (Marcus 1964) for the homogeneous and heterogeneous (electrochemical) electron transfer (ET), have been formulated (Saveant 1987, 2000 Maran et al. 2001 Costentin et al. 2006a, b) and tested with the aim to predict the experimental outcomes. 

Refs. [i] Bard AJ, Faulkner LR (2001) Electrochemical methods. Wiley, New York, pp 90-94 [ii] Erdey-Gruz T (1972) Kinetics of electrode processes. Akademiai Kiadd, Budapest, pp 19-56 [iii] Gileadi E (1993) Electrode kinetics. VCH, New York, pp 106-126 [iv] Inzelt G (2002) Kinetics of electrochemical reactions. In Scholz F (ed) Electro-analytical methods. Springer, Berlin, pp 29-44 [v] Miller CJ (1995) Heterogeneous electron transfer kinetics at metallic electrodes. In Rubinstein I (ed) Physical electrochemistry. Dekker, New York, pp 27-79 [vi] Marcus RA (1965) J Chem Phys 43 679 [vii] Marcus RA (1997) In Rock PA (ed) Special topics in electrochemistry. Elsevier, p 161 ... 

Miller s approach is essentially a generalized polyatomic version of a method developed by Hofacker (227,228) and Marcus (229) for reactions of the A + BC -> AB + C type. 

Considerable use continues to be made of classical trajectory calculations in relating the experimentally determined attributes of electronically adiabatic reactions to the features in the potential energy surface that determine these properties. However, over the past 3 or 4 years, considerable progress has been made with semiclassical and quantum mechanical calculations with the result that it is now possible to predict with some degree of confidence the situations in which a purely classical approach to the collision dynamics will give acceptable results. Application of the semiclassical method, which utilises classical dynamics plus the superposition of probability amplitudes [456], has been pioneered by Marcus [457-466] and by Miller [456, 467-476],... 

Closs, G. L., Calcaterra, L. T., Green, N. J., Miller, J. R., and Penfield, K. W., 1986, Distance, Stereoelectronic Effects, and the Marcus Inverted Region in Intramolecular Electron-Transfer in Organic Radical-Anions J. Phys. Chem. 90 3673n3683. 

Marcus, S., Caldwell, G.A., Miller, D., Xue, C.B., Naider, F., and Becker, J.M. (1991). Significance of C-terminal cysteine modifications to the biological activity of the Saccharomyces cerevisiae a-factor mating pheromone. Mol Cell Biol 11 3603-3612. 

One particular example of the use of pulse radiolysis to general chemistry was the work of Miller and co-workers on the rates of electron-transfer reactions. These studies, which were begun using reactants captured in glasses, were able to show the distance dependence of the reaction of the electron with electron acceptors. Further work, where molecular frameworks were able to fix the distance between electron donors and acceptors, showed the dependence of electron-transfer rate on the energetics of the reaction. These studies were the first experimental confirmation of the electron transfer theory of Marcus. 

Gloss GL, Calcaterra LT, Green NJ, Penfield KW, Miller JR. (1986) Distance, stereoelectronic effects, and the Marcus inverted region in intramolecular electron transfer in organic radical anions. J Phys Chem 90 3673-3683. 

Marcus [17], and was confirmed experimentally by Miller and his collaborators [18], but only 24 years after its prediction. Additional aspects of the inverted region will be discussed in Section 2.5.1 which focuses on the different roles played by solvent and intrasolute modes of phonons. 

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