Optimizing conical intersections without derivative coupling vectors: application to multistate multireference second-order perturbation theory (MS-CASPT2)

Exploring Multiple Potential Energy Surfaces: Photochemistry of Small Carbonyl Compounds

In theoretical studies of chemical reactions involving multiple potential energy surfaces (PESs) such as photochemical reactions, seams of intersection among the PESs often complicate the analysis. In this paper, we review our recipe for exploring multiple PESs by using an automated reaction path search method which has previously been applied to single PESs. Although any such methods for single PESs can be employed in the recipe, the global reaction route mapping (GRRM) method was employed in this study. By combining GRRM with the proposed recipe, all critical regions, that is, transition states, conical intersections, intersection seams, and local minima, associated with multiple PESs, can be explored automatically. As illustrative examples, applications to photochemistry of formaldehyde and acetone are described. In these examples as well as in recent applications to other systems, the present approach led to discovery of many unexpected nonadiabatic pathways, by which some complicated experimental data have been explained very clearly.

Time-resolved photoelectron spectroscopy from first principles: excited state dynamics of benzene

We use the ab initio multiple spawning (AIMS) method to follow the dynamics of benzene after excitation to the second singlet excited state (S2). The results are validated by comparison to potential energy surfaces including dynamical electron correlation effects. Time-resolved photoelectron spectra are computed and compared to experimental results. Simulations agree with experiment that there are both short-lived and long-lived components of the excited state population. We show that these components both originate from quenching through the same S2/S1 conical intersection and that the difference between them comes from their behavior immediately after decay to S1. This is presumed to be a function of the details of the way in which the S2/S1 intersection region is accessed; for example, the momentum distribution and the topology of the seam in the relevant region.

Photoisomerization of stilbene: a spin-flip density functional theory approach

The photoisomerization process of 1,2-diphenylethylene (stilbene) is investigated using the spin-flip density functional theory (SFDFT), which has recently been shown to be a promising approach for locating conical intersection (CI) points (Minezawa, N.; Gordon, M. S. J. Phys. Chem. A2009, 113, 12749). The SFDFT method gives valuable insight into twisted stilbene to which the linear response time-dependent DFT approach cannot be applied. In contrast to the previous SFDFT study of ethylene, a distinct twisted minimum is found for stilbene. The optimized structure has a sizable pyramidalization angle and strong ionic character, indicating that a purely twisted geometry is not a true minimum. In addition, the SFDFT approach can successfully locate two CI points: the twisted-pyramidalized CI that is similar to the ethylene counterpart and another CI that possibly lies on the cyclization pathway of cis-stilbene. The mechanisms of the cis--trans isomerization reaction are discussed on the basis of the two-dimensional potential energy surface along the twisting and pyramidalization angles.

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.

Finding Minimum Structures on the Seam of Crossing in Reactions of Type A + B → X: Exploration of Nonadiabatic Ignition Pathways of Unsaturated Hydrocarbons

A new theoretical approach is proposed for finding automatically minimum structures on the seam of crossing (MSX) in reactions of type A + B → X, where the artificial-force-induced reaction (AFIR) method is combined with the seam model function (SMF) approach. Its application to reactions between triplet dioxygen and unsaturated hydrocarbons provided many MSX structures. In addition to known ignition pathways, we discovered a pathway through a new type of MSX in the reaction of dioxygen with aromatic hydrocarbons; for benzene, this new pathway requires a lower energy than those of three known ignition pathways and is likely to be the most important. This demonstrates that the AFIR-SMF approach has the ability to discover unknown/unexpected MSX structures without prejudice for presumed pathways or mechanisms.

Understanding the dynamics behind the photoisomerization of a light-driven fluorene molecular rotary motor

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.

Optimizing conical intersections by spin-flip density functional theory: application to ethylene

Conical intersections (CIs) of ethylene have been successfully determined using spin-flip density functional theory (SFDFT) combined with a penalty-constrained optimization method. We present in detail three structures, twisted-pyramidalized, hydrogen-migrated, and ethylidene CIs. In contrast to the linear response time-dependent density functional theory, which predicts a purely twisted geometry without pyramidalization as the S(1) global minimum, SFDFT gives a pyramidalized structure. Therefore, this is the first correct optimization of CI points of twisted ethylene by the DFT method. The calculated energies and geometries are in good agreement with those obtained by the multireference configuration interaction (MR-CI) method and the multistate formulation of second-order multireference perturbation theory (MS-CASPT2).