A two-state rebound mechanism of alkane hydroxylation by a model active species of the enzyme cytochrome P450 is studied using density functional theoretic calculations. Theory corroborates Groves's rebound mechanism (Groves, J. T. J. Chem. Educ. 1985, 62, 928), with a key difference, namely that in the two-state rebound the reactivity and product distribution result from the interplay of two reactive states of the active ferryl-oxene (Por+•FeO) species of the enzyme:  one state is low-spin (doublet) and the other high-spin (quartet). Transition-state structures, intermediates, and product complexes are identified for the two states. The bond activation in either one of the two states involves a hydrogen abstraction-like transition structure. However, while in the high-spin state there forms a radical that has a significant barrier for rebound, in the low-spin state the rebound is virtually barrierless. Even though one cannot ignore incursion of a small amount of radicals in the low-spin state, it is clear that the radical has a significant lifetime mainly on the high-spin surface. The results are used to gain insight into puzzling experimental data which emerge from studies of ultrafast radical clocks (e.g., Toy, P. H.; Newcomb, M.; Hollenberg, P. F., J. Am. Chem. Soc. 1998, 120, 7719), vis à vis the nature the transition state, deduced from kinetic isotope effect measurements (Manchester, J. I.; Dinnocenzo, J. P.; Higgins, L. A.; Jones, J. P. J. Am. Chem. Soc. 1997, 119, 5069) and stereochemical scrambling patterns (Groves, J. T.; McClusky, G. A.; White, R. E.; Coon, M. J. Biochem. Biophys. Res. Commun. 1978, 81, 154). Understanding the electronic structure of the various species leads to a predictive structure−reactivity picture, based on the two-state reactivity scenario (Shaik, S.; Filatov, M.; Schröder, D.; Schwarz, H. Chem. Eur. J. 1998, 4, 193). The model makes it possible to predict the dependence of the relative rates of the two states, and of the corresponding steps as a function of the nature of the alkane, the resulting alkyl radical, and the binding capability of the thiolate proximal ligand of the active species.

This paper describes a reactivity paradigm called two-state reactivity (TSR) in C ± H bond activation by metal oxenoid cations (e.g., FeO). The paradigm is applied to the hydroxylation of alkanes by the active species of the enzyme cytochrome P-450, and a mechanistic scheme is proposed based on the competition between TSR pathways and single-state-reactivity (SSR) pathways. Generally, the oxide cations of the late transition metals (MO ) possess the same bonding patterns as the O 2 molecule, having a high-spin ground state and an adjacent low-spin excited state. The adjacency of the spin states, together with the poor bonding capability of the high-spin state and the good bonding capability of the low-spin state, leads to a spin crossover along the reaction coordinate and opens a low-energy TSR path for hydroxylation. The competing pathway is SSR, in which the reaction starts, occurs and ends in the same spin state. The TSR/SSR competition is modulated by the probability of spin crossover. Generally, TSR involves concerted pathways that conserve stereochemical information, while SSR results in stepwise mechanisms that scramble this information. The TSR/SSR competition is used to shed some light on recent results which are at odds with the commonly accepted mechanism of P-450 hydroxylation. The fundamental features of the paradigm are outlined and the theoretical and experimental challenges for its articulation are spelled out.

We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.

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We report a theoretical study of the photoisomerization step in the operating cycle of a prototypical fluorene-based molecular rotary motor (1). The potential energy surfaces of the ground electronic state (S0) and the first singlet excited state (S1) are explored by semiempirical quantum-chemical calculations using the orthogonalization-corrected OM2 Hamiltonian in combination with a multireference configuration interaction (MRCI) treatment. The OM2/MRCI results for the S0 and S1 minima of the relevant 1-P and 1-M isomers and for the corresponding S0 transition state are in good agreement with higher-level calculations, both with regard to geometries and energetics. The S1 surface is characterized at the OM2/MRCI level by locating two S0-S1 minimum-energy conical intersections and nearby points on the intersection seam and by computing energy profiles for pathways toward these MECIs. Semiclassical Tully-type trajectory surface hopping (TSH) simulations with on-the-fly OM2/MRCI calculations are carried out to study the excited-state dynamics after photoexcitation to the S1 state. Fast relaxation to the ground state is observed through the conical intersection regions, predominantly through the lowest-energy one with a strongly twisted central C═C double bond and pyramidalized central carbon atom. The excited-state lifetimes for the direct and inverse photoisomerization reactions (1.40 and 1.79 ps) and the photostationary state ratio (2.7:1) from the TSH-OM2 simulations are in good agreement with the available experimental data (ca. 1.7 ps and 3:1). Excited-state lifetimes, photostationary state ratio, and dynamical details of the TSH-OM2 simulations also agree with classical molecular dynamics simulations using a reparametrized optimized potentials for liquid simulations (OPLS) all-atom force field with ad-hoc surface hops at predefined conical intersection points. The latter approach allows for a more extensive statistical sampling.

Light-driven molecular rotary motors derived from chiral overcrowded alkenes represent a broad class of compounds for which photochemical rearrangements lead to large scale motion of one part of the molecule with respect to another. It is this motion/change in molecular shape that is employed in many of their applications. A key group in this class are the molecular rotary motors that undergo unidirectional light-driven rotation about a double bond through a series of photochemical and thermal steps. In the present contribution we report a combined quantum chemical and molecular dynamics study of the mechanism of the rotational cycle of the fluorene-based molecular rotary motor 9-(2,4,7-trimethyl-2,3-dihydro-1H-inden-1-ylidene)-9H-fluorene (1). The potential energy surfaces of the ground and excited singlet states of 1 were calculated, and it was found that conical intersections play a central role in the mechanism of photo conversion between the stable conformer of 1 and its metastable conformer. Molecular dynamics simulations indicate that the average lifetime of the fluorene motor in the excited state is 1.40 +/- 0.10 ps when starting from the stable conformer, which increases to 1.77 +/- 0.13 ps for the reverse photoisomerization. These simulations indicate that the quantum yield of photoisomerization of the stable conformer is 0.92, whereas it is only 0.40 for the reverse photoisomerization. For the first time, a theoretical understanding of the experimentally observed photostationary state of 1 is reported that provides a detailed picture of the photoisomerization dynamics in overcrowded alkene-based molecular motor 1. The analysis of the electronic structure of the fluorene molecular motor holds considerable implications for the design of molecular motors. Importantly, the role of pyramidalization and conical intersections offer new insight into the factors that dominate the photostationary state achieved in these systems.

Unrestricted density functional theory (UDFT) can be used for the description of open-shell singlet (OSS) biradicals provided a number of precautions are considered. Biradicals that require a two-determinantal wave function (e.g. OSS state of carbenes) cannot be described by UDFT for principal reasons. However, if the overlap between the open-shell orbitals is small (the single electrons are located at different atomic centers) errors become small and, then, the principal failure of UDFT in these cases is not apparent and may even be disguised by the fact that UDFT has the advantage of describing spin polarization better than any restricted open shell DFT method. In the case of OSS biradicals with two-or multiconfigurational character (but a onedeterminantal form of the leading configuration), reasonable results can be obtained by broken-symmetry (BS)-UDFT, however in each case this has to be checked. In no case is it reasonable to lower the symmetry of a molecule to get a suitable UDFT description. Hybrid functionals such as B3LYP perform better than pure DFT functionals in BS-UDFT calculations because the former reduce the self-interaction error of DFT exchange functionals, which mimics unspecified static electron correlation effects, so that the inclusion of specific static electron correlation effects via the form of the wavefunction becomes more effective.

In the past, the design of light-driven single molecule rotary motors has been mainly guided by the modification of their ground-state conformational properties. Further progress in this field is thus likely to be achieved through a detailed understanding of light-induced dynamics of the system and the ways of modulating it by introducing chemical modifications. In the present theoretical work, the analysis of model organic chromophores and synthesized rotary motors is used for rationalizing the effect of electron-withdrawing heteroatoms (such as a cationic nitrogen) on the topography and branching plane of mechanistically relevant conical intersections. Such an analysis reveals how the character of rotary motion could be changed from a precessional motion to an axial rotational motion. These concepts are then used to design and build quantum chemical models of three distinct types of Schiff base rotary motors. One of these models, featuring the synthetically viable indanylidenepyrroline framework, has conical intersection structures consistent with an axial rotation not hindered by ground-state conformational barriers. It is expected that this type of motor should be capable of funneling the photon energy into specific rotary modes, thus achieving photoisomerization quantum efficiencies comparable to those seen in visual pigments.