Many methods for correcting harmonic partition functions for the presence of torsional motions employ some form of one-dimensional torsional treatment to replace the harmonic contribution of a specific normal mode. However, torsions are often strongly coupled to other degrees of freedom, especially other torsions and low-frequency bending motions, and this coupling can make assigning torsions to specific normal modes problematic. Here, we present a new class of methods, called multi-structural (MS) methods, that circumvents the need for such assignments by instead adjusting the harmonic results by torsional correction factors that are determined using internal coordinates. We present three versions of the MS method: (i) MS-AS based on including all structures (AS), i.e., all conformers generated by internal rotations; (ii) MS-ASCB based on all structures augmented with explicit conformational barrier (CB) information, i.e., including explicit calculations of all barrier heights for internal-rotation barriers between the conformers; and (iii) MS-RS based on including all conformers generated from a reference structure (RS) by independent torsions. In the MS-AS scheme, one has two options for obtaining the local periodicity parameters, one based on consideration of the nearly separable limit and one based on strongly coupled torsions. The latter involves assigning the local periodicities on the basis of Voronoi volumes. The methods are illustrated with calculations for ethanol, 1-butanol, and 1-pentyl radical as well as two one-dimensional torsional potentials. The MS-AS method is particularly interesting because it does not require any information about conformational barriers or about the paths that connect the various structures.

We present a new formulation of variational transition state theory (VTST) called multi-structural VTST (MS-VTST) and the use of this to calculate the rate constant for the 1,4-hydrogen shift isomerization reaction of 1-pentyl radical and that for the reverse reaction. MS-VTST uses a multi-faceted dividing surface and provides a convenient way to include the contributions of many structures (typically conformers) of the reactant and the transition state in rate constant calculations. In this particular application, we also account for the torsional anharmonicity. We used the multi-configuration Shepard interpolation method to efficiently generate a semi-global portion of the potential energy surface from a small number of high-level electronic structure calculations using the M06 density functional in order to compute the energies and Hessians of Shepard points along a reaction path. The M06-2X density functional was used to calculate the multi-structural anharmonicity effect, including all of the structures of the reactant, product and transition state. To predict the thermal rate constant, VTST calculations were performed to obtain the canonical variational rate constant over the temperature range 200–2000 K. A transmission coefficient is calculated by the multidimensional small-curvature tunneling (SCT) approximation. The final MS-CVT/SCT thermal rate constant was determined by combining a reaction rate calculation in the single-structural harmonic oscillator approximation (including tunneling) with the multi-structural anharmonicity torsional factor. The calculated forward rate constant agrees very well with experimentally-based evaluations of the high-pressure limit for the temperature range 300–1300 K, although it is a factor of 2.5–3.0 lower than the single-structural harmonic oscillator approximation over this temperature range. We anticipate that MS-VTST will be generally useful for calculating the reaction rates of complex molecules with multiple torsions.

In enzymatic C–H activation by hydrogen tunneling, reduced barrier width is important for efficient hydrogen wave function overlap during catalysis. For native enzymes displaying nonadiabatic tunneling, the dominant reactive hydrogen donor–acceptor distance (DAD) is typically ca. 2.7 Å, considerably shorter than normal van der Waals distances. Without a ground state substrate-bound structure for the prototypical nonadiabatic tunneling system, soybean lipoxygenase (SLO), it has remained unclear whether the requisite close tunneling distance occurs through an unusual ground state active site arrangement or by thermally sampling conformational substates. Herein, we introduce Mn²⁺ as a spin-probe surrogate for the SLO Fe ion; X-ray diffraction shows Mn-SLO is structurally faithful to the native enzyme. ¹³C ENDOR then reveals the locations of ¹³C10 and reactive ¹³C11 of linoleic acid relative to the metal; ¹H ENDOR and molecular dynamics simulations of the fully solvated SLO model using ENDOR-derived restraints give additional metrical information. The resulting three-dimensional representation of the SLO active site ground state contains a reactive (a) conformer with hydrogen DAD of ∼3.1 Å, approximately van der Waals contact, plus an inactive (b) conformer with even longer DAD, establishing that stochastic conformational sampling is required to achieve reactive tunneling geometries. Tunneling-impaired SLO variants show increased DADs and variations in substrate positioning and rigidity, confirming previous kinetic and theoretical predictions of such behavior. Overall, this investigation highlights the (i) predictive power of nonadiabatic quantum treatments of proton-coupled electron transfer in SLO and (ii) sensitivity of ENDOR probes to test, detect, and corroborate kinetically predicted trends in active site reactivity and to reveal unexpected features of active site architecture.