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9
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84951365870
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Translator, University of Ottawa, Ontario, Canada
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Boshko, O.1
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24
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0011823298
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(b) In Alexandrov et al. [Ref. 16(a)] the electron transfer between the bipheny1 anion and napthalene had a [formula omitted] of [formula omitted] and that between the same anion and phenylethylene had [formula omitted] In another study [J. R. Miller (private communication)] the β for the same anion reacting with acridine was [formula omitted] Electron transfer between tetramethylenediamine with a pyrine cation and with a biphenyl cation each had a β of [formula omitted]
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(1981)
J. Chem. Phys
, vol.74
, pp. 6746
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Miller, J.R.1
Beitz, J.V.2
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25
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0015144078
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The β inferred from conduction between two metals separated by monolayers of fatty acid salts of varying chain lengths varied between 1.0 and 1.5
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(1971)
J. Appl. Phys
, vol.42
, pp. 4398
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Mann, B.1
Kuhn, H.2
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36
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0021388505
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In such models the transfer rate varies approximately as a power [formula omitted]where n is the total number of orbitals in the shortest path from donor to acceptor which includes the donor, acceptor, and all intervening atomic or molecular centers, and [formula omitted]
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(1984)
J. Am. Chem. Soc
, vol.106
, pp. 1584
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Beratan, D.N.1
Hopfield, J.J.2
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38
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0021388505
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If each orbital occupies a length a, such a model yields a rate which is proportional to [formula omitted] In Thus, these “exchange” models yield an exponential dependence of the rate on r. In such theories there will be differences of rate with exchange path, according as the paths are assumed to be composed of bonded species or of solvent molecules.
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(1984)
J. Am. Chem. Soc
, vol.106
, pp. 1584
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-
Beratan, D.N.1
Hopfield, J.J.2
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46
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84987142620
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Newton has performed ab initio calculations of the thermal matrix element for the [formula omitted] self-exchange reaction for Fe-Fe separation distances up to 10 Å.
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(1980)
Int. J. Quantum Chem. Symp
, vol.14
, pp. 363
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Newton, M.D.1
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50
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85034730724
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In all cases, energies were obtained iteratively and are accurate to not fewer than five digits.
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58
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85034730388
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Let the x axes of the two wells both be in the plane of Fig. 6. Rotation of an eigenfunction in well A, [formula omitted] by an angle [formula omitted] about the fixed z axis yields a rotated function [formula omitted] A rotated [formula omitted] may be obtained analogously and one obtains for [formula omitted] [formula omitted] Introducing the addition formulas for [formula omitted] and [formula omitted] into this expression and using Eq. (11) one sees that due to symmetry, only terms involving [formula omitted] and [formula omitted] are nonzero. Then, [formula omitted] becomes [formula omitted] is as given in the second half of Eq. (11).
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61
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84951365833
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The eigenvalues [formula omitted] were obtained using Hodge’s algorithm, trivially modified as follows: The set [formula omitted] contains the eigenvalues of a matrix that is, in principle, of infinite dimension. Hodge (Ref. 34) presents a prescription for constructing the elements of the matrix so that the matrix eigenvalues are the eigenvalues of Eqs. (13) and (14). In practice, the matrix must be truncated. The eigenvalues of the truncated matrix are not, in general, equal to the eigenvalues [formula omitted] of the differential equations. In order to obtain a finite set [formula omitted] of true eigenvalues (i.e., eigenvalues of the differential equations), a larger set [formula omitted] of approximate eigenvalues [formula omitted] was constructed, where [formula omitted] and [formula omitted] is an eigenvalue of the [formula omitted] truncated matrix. [formula omitted] was then increased until every element of the subset [formula omitted] was constant to 11 significant digits upon successive increases of [formula omitted] At that point it was assumed that the first N true eigenvalues [formula omitted] had been obtained.
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62
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85034725856
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In cases when the expansions did not yield satisfactory convergence the functions were obtained by numerical integration of the appropriate differential equations, for example, Eq. (13) for [formula omitted]
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65
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0003758310
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For spherical wells, the method of solution for the single-site wave functions may be found in 3rd ed. (McGraw-Hill, New York
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(1968)
Quantum Mechanics
, pp. 83-88
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Schiff, L.I.1
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71
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84951365837
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Ph.D. thesis, California Institute of Technology, Pasadena, California,Chap. 5, Appendix A. Available from University Microfilms, Ann Arbor, MI, No. 83-22, 674.
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(1983)
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Siders, P.D.1
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