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“…For this purpose eq 1 is rewritten as where G(n) ) (I x I y I z ) 1/2 (I R are the principal values of the inertia tensor of a given conformer) reflects the dependence of the molecular moment of inertia on conformation. It results from averaging over the dynamical variables associated with the rotational kinetic energy of the conformer as a whole; 15,16 it has only small effects on the final results. U(n,Ω) represents the total potential defined by eq 13, and D ij (n,Ω) is where θ ij denotes the angle between the internuclear vector, r ij , between the two proton spins, and the applied magnetic field.…”

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“…For this purpose eq 1 is rewritten as where G(n) ) (I x I y I z ) 1/2 (I R are the principal values of the inertia tensor of a given conformer) reflects the dependence of the molecular moment of inertia on conformation. It results from averaging over the dynamical variables associated with the rotational kinetic energy of the conformer as a whole; 15,16 it has only small effects on the final results. U(n,Ω) represents the total potential defined by eq 13, and D ij (n,Ω) is where θ ij denotes the angle between the internuclear vector, r ij , between the two proton spins, and the applied magnetic field.…”

“…However, this is not feasible if the reaction of interest has a high barrier compared to k&T, where k% is Boltzmann's constant and T is temperature, unless one employs infrequent event sampling and/or a constraint on the reaction coordinate. In such a case, one can show that it is still possible to obtain statistical information about a given reaction along a reaction coordinate by using umbrella sampling or by enforcing a constrained reaction coordinate and employing generalized normal mode analysis, thermodynamic integration, or free energy perturbation theory where the incremental charge in the reaction coordinate is the perturbation (1)(2)(3)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28). In this approach, one selects (or "distinguishes") a specific RC that most conveniently leads the system through an area of interest, for instance the transition state region.…”