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See e.g., ref 6 in ref 5d
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The point of view of the present perspective is that when the quantum proton does not tunnel, it is in the quantum proton adiabatic regime, as described in length in section 1, as opposed to the traditional view where it is instead motion of a classical proton over the proton barrier. For calculations in which the latter is taken as the reference situation for the rate and tunneling effects provide a quantum modification of this picture, see (a) Alhambra, C.; Corchado, J.C.; Sánchez, M.L.; Gao, J.; Truhlar, D.G. J. Am. Chem. Soc. 2000, 122, 8197.
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note
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This statement needs qualification in some circumstances related to intramolecular coordinates in the reacting solute system, see II.
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note
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The PT reaction rate of interest does not include formation of the hydrogen-bonded complex or separation of the contact ion pair. In this work, we define the PT reaction asymmetry within the hydrogen-bonded complex; a difference in certain work terms would need to be incorporated to connect to the free energy difference for the separated species. See for example ref 2c. Because this plays no essential role in the analysis, we do not incorporate it here.
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0011108125
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note
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35 it adds complexity in the present context without changing any conclusions made throughout this paper.
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The literature here is quite extensive. Some reviews include (a) Bagchi, B. Annu. Rev. Phys. Chem. 1989, 40, 115.
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The eigenstates and eigenenergies in eq 2.13 are obtained using a discrete variable representation basis. See for example (a) Light, J.C.; Hamilton, I.P.; Lill, J.V. J. Chem. Phys. 1985, 82, 1400.
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0011090697
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note
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12 However, the extra parameters so introduced would add unnecessary complexity to the model without changing its basic structure. Sample calculations have shown that the single Morse model gives results similar to those of the composite two potential models.
-
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-
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111
-
-
0011155775
-
-
note
-
min and ZPE in Sec. 5. Nonetheless, our preliminary investigations including intrinsic asymmetry indicate that the FER and its underlying physical picture are not significantly altered. The inclusion of intrinsic asymmetry will be presented in future work.
-
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112
-
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0011089075
-
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note
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12,44.
-
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113
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0003466709
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Holt, Rinehart, and Winston: New York
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118
-
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0011148224
-
-
note
-
Although the latter PT is in an O⋯N hydrogen bond, the dipole moments for PT within an O⋯O hydrogen bond are not expected to differ significantly. We also note that although the selected reactant diabatic dipole moment is zero (which emphasizes the expected difference from the diabatic product dipole moment in an H-bonded PT system), the resulting electronically adiabatic dipole moment eq 2.5 for the neutral reactant is actually nonzero: ∼1 D. The magnitude of the diabatic dipole moments will not affect the resulting theory and FER.; only the numerical value of the latter's ingredients will be altered.
-
-
-
-
119
-
-
0011125772
-
-
note
-
vac = 91-108 kcal/mol values bracketing the symmetric reaction.
-
-
-
-
120
-
-
0011088985
-
-
note
-
eq, the R and P partition functions for the fluctuating ΔE coordinate and momentum also enter in principle. However, for the systems described within, those contributions are identical for R and P and cancel out, leaving the definition in the text. These issues, which are discussed for other reactions in refs 37a and 37b, arise in connection with what we term intrinsic asymmetry, and are treated elsewhere.
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-
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122
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0031587575
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Pines, E.; Magnes, B.-Z.; Lang, M.J.; Fleming, G.R. Chem. Phys. Lett 1997, 281, 413.
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123
-
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0011141748
-
-
note
-
We will return to the issue of the small activation barrier in II, where we will discuss certain difficulties found in some treatments.
-
-
-
-
124
-
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0011141749
-
-
note
-
Here, the rate of PT is defined as the interconversion of the reactant and product H-bond complexes which are separated by a barrier (See Figure 3), and thus, no diffusional rate of formation of these complexes is included in the PT rate. For extreme asymmetric reactions the harrier is wiped out, and PT is then limited by diffusion. Hence, no inverted regime is expected for adiabatic PT, a point also noted by Marcus.
-
-
-
-
127
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0011122706
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For "abnormal" or "anomalous" PT Brønsted behavior, see the following, and references therein: (a) Pross, A. Adv. Phys. Org. Chem. 1985, 21, 166.
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0000053815
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(b) Baksic, D.; Bertran, J.; Lluch, J.M.; Hynes, J.T. J. Phys. Chem. A 1998, 102, 3977. This behavior likely involves the necessity of more than two VB states in the description, and so is not governed by the present theory.
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Baksic, D.1
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129
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0011148226
-
-
note
-
E = 13.6 kcal/mol, a constant independent of the reaction asymmetry via eq 5.15.
-
-
-
-
130
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85056020425
-
-
note
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‡.
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