Paul M. Zimmerman

Mechanism for Singlet Fission in Pentacene and Tetracene: From Single Exciton to Two Triplets

Singlet fission (SF) could dramatically increase the efficiency of organic solar cells by producing two triplet excitons from each absorbed photon. While this process has been known for decades, most descriptions have assumed the necessity of a charge-transfer intermediate. This ab initio study characterizes the low-lying excited states in acene molecular crystals in order to describe how SF occurs in a realistic crystal environment. Intermolecular interactions are shown to localize the initially delocalized bright state onto a pair of monomers. From this localized state, nonadiabatic coupling mediated by intermolecular motion between the optically allowed exciton and a dark multi-exciton state facilitates SF without the need for a nearby low-lying charge-transfer intermediate. An estimate of the crossing rate shows that this direct quantum mechanical process occurs in well under 1 ps in pentacene. In tetracene, the dark multi-exciton state is uphill from the lowest singlet excited state, resulting in a dynamic interplay between SF and triplet-triplet annihilation.

Singlet fission in pentacene through multi-exciton quantum states

Multi-exciton generation-the creation of multiple charge carrier pairs from a single photon-has been reported for several materials and may dramatically increase solar cell efficiency. Singlet fission, its molecular analogue, may govern multi-exciton generation in a variety of materials, but a fundamental mechanism for singlet fission has yet to be described. Here, we use sophisticated ab initio calculations to show that singlet fission in pentacene proceeds through rapid internal conversion of the photoexcited state into a dark state of multi-exciton character that efficiently splits into two triplets. We show that singlet fission to produce a pair of triplet excitons must involve an intermediate state that (i) has a multi-exciton character, (ii) is energetically accessible from the optically allowed excited state, and (iii) efficiently dissociates into multiple electron-hole pairs. The rational design of photovoltaic materials that make use of singlet fission will require similar ab initio analysis of multi-exciton states such as the dark state studied here.

A Correlated Electron View of Singlet Fission

Singlet fission occurs when a single exciton splits into multiple electron-hole pairs, and could dramatically increase the efficiency of organic solar cells by converting high energy photons into multiple charge carriers. Scientists might exploit singlet fission to its full potential by first understanding the underlying mechanism of this quantum mechanical process. The pursuit of this fundamental mechanism has recently benefited from the development and application of new correlated wave function methods. These methods-called restricted active space spin flip-can capture the most important electron interactions in molecular materials, such as acene crystals, at low computational cost. It is unrealistic to use previous wave function methods due to the excessive computational cost involved in simulating realistic molecular structures at a meaningful level of electron correlation. In this Account, we describe how we use these techniques to compute single exciton and multiple exciton excited states in tetracene and pentacene crystals in order to understand how a single exciton generated from photon absorption undergoes fission to generate two triplets. Our studies indicate that an adiabatic charge transfer intermediate is unlikely to contribute significantly to the fission process because it lies too high in energy. Instead, we propose a new mechanism that involves the direct coupling of an optically allowed single exciton to an optically dark multiexciton. This coupling is facilitated by intermolecular motion of two acene monomers that drives nonadiabatic population transfer between the two states. This transfer occurs in the limit of near degeneracies between adiabatic states where the Born-Oppenheimer approximation of fixed nuclei is no longer valid. Existing theories for singlet fission have not considered this type of coupling between states and, therefore, cannot describe this mechanism. The direct mechanism through intermolecular motion describes many experimentally observed characteristics of these materials, such as the ultrafast time scale of photobleaching and triplet generation during singlet fission in pentacene. We believe this newly discovered mechanism provides fundamental insight to guide the creation of new solar materials that exhibit high efficiencies through multiple charge generation.

Oligomerization and autocatalysis of NH2BH2 with ammonia-borane.

The reactivity of NH(2)BH(2) in the presence of ammonia-borane (AB) is investigated using ab initio CCSD(T) simulations to answer the following three questions: How do AB and NH(2)BH(2) react? How do aminoborane species oligomerize apart from catalytic centers? Can the formation of experimentally observed products, especially cyclic N(2)B(2)H(7)-NH(2)BH(3), be explained through the kinetics of NH(2)BH(2) oligomerization in the presence of AB? AB is shown to react with NH(2)BH(2) by the addition of NH(3)-BH(3) across the N=B double bond, generating linear NH(3)BH(2)NH(2)BH(3). This species decomposes by surmounting a reasonable barrier to produce two NH(2)BH(2) and H(2). The generation of additional NH(2)BH(2) from NH(2)BH(2) and AB provides a pathway for autocatalytic NH(2)BH(2) production. The important intermediates along the oligomerization pathway include cyclic (NH(2)BH(2))(2) and linear NH(3)BH(2)NH(2)BH(3), both of which have been observed experimentally. Calculations show cyclic N(2)B(2)H(7)-NH(2)BH(3), an aminoborane analogue of ethylcyclobutane, to be the kinetically preferred stable intermediate resulting from oligomerization of free NH(2)BH(2) over its isomers, cyclic B(2)N(2)H(7)-BH(2)NH(3) and cyclotriborazane, cyclic (NH(2)BH(2))(3). Simulations show cyclotriborazane formation to be kinetically slower than cyclic B(2)N(2)H(7)-NH(2)BH(3) formation and imply that formation of the cyclic species cyclotriborazane and cyclopentaborazane may be catalyzed by binding of NH(2)BH(2) to a catalytic metal center. Routes that may lead to larger noncyclic oligomers are suggested to be kinetically competitive. The highly reactive N=B double bonds of NH(2)BH(2) are shown to be of central importance in understanding aminoborane oligomerization.

Automated discovery of chemically reasonable elementary reaction steps

Due to the significant human effort and chemical intuition required to locate chemical reaction pathways with quantum chemical modeling, only a small subspace of possible reactions is usually investigated for any given system. Herein, a systematic approach is proposed for locating reaction paths that bypasses the required human effort and expands the reactive search space, all while maintaining low computational cost. To achieve this, a range of intermediates are generated that represent potential single elementary steps away from a starting structure. These structures are then screened to identify those that are thermodynamically accessible, and then feasible reaction paths to the remaining structures are located. This strategy for elementary reaction path finding is independent of atomistic model whenever bond breaking and forming are properly described. The approach is demonstrated to work well for upper main group elements, but this limitation can easily be surpassed. Further extension will allow discovery of multistep reaction mechanisms in a single computation. The method is highly parallel, allowing for effective use of modern large‐scale computational clusters.

Catalytic dehydrogenation of ammonia borane at Ni monocarbene and dicarbene catalysts.

The development of ammonia borane (AB) as a promising hydrogen storage medium depends upon the ability to reversibly release H(2) from the system. We use density functional theory to investigate the mechanism of the catalytic dehydrogenation of AB by Ni N-heterocyclic carbene (NHC) complexes, which we show proceeds through Ni monocarbene and dicarbene species. Although Ni(NHC)(2) dehydrogenates AB, it competitively decomposes into a monocarbene species because AB readily displaces NHC from Ni(NHC)(2) and reaction of displaced NHC with abundant AB makes Ni monocarbene formation thermodynamically favored over the dicarbene catalyst. Prediction of NHC displacement by AB is consistent with the experimental observation of NHC-BH(3). The Ni monocarbene species Ni(NHC)(NH(2)BH(2)) competitively dehydrogenates AB with barriers consistent with the experimental temperature required to obtain reasonable reaction rates. The Ni monocarbene pathway also involves rate-limiting steps that exhibit both N-H and B-H kinetic isotope effects (KIEs), as observed experimentally. The predicted N-H and B-H KIEs are also in quantitative agreement with experiment. In contrast, AB dehydrogenation by Ni(NHC)(2) does not exhibit a B-H KIE. Activation of AB at both mono- and dicarbene catalysts proceeds through cis-carbene proton acceptance and involves transition states with significant electron delocalization over the pi-system of the carbene and its phenyl rings. NHC Ni catalysts involving carbenes with substituent groups containing steric factors that preclude planarity of the phenyl rings to the carbene aromatic system, such as the Imes and Idipp ligands, are predicted to have lower reactivity, in agreement with experiment. The addition of electron donating and withdrawing groups to the phenyl rings demonstrate the importance of pi-system electron delocalization by their influence on the barrier to cis-carbene proton acceptance.

Reliable transition state searches integrated with the growing string method

The growing string method (GSM) is highly useful for locating reaction paths connecting two molecular intermediates. GSM has often been used in a two-step procedure to locate exact transition states (TS), where GSM creates a quality initial structure for a local TS search. This procedure and others like it, however, do not always converge to the desired transition state because the local search is sensitive to the quality of the initial guess. This article describes an integrated technique for simultaneous reaction path and exact transition state search. This is achieved by implementing an eigenvector following optimization algorithm in internal coordinates with Hessian update techniques. After partial convergence of the string, an exact saddle point search begins under the constraint that the maximized eigenmode of the TS node Hessian has significant overlap with the string tangent near the TS. Subsequent optimization maintains connectivity of the string to the TS as well as locks in the TS direction, all but eliminating the possibility that the local search leads to the wrong TS. To verify the robustness of this approach, reaction paths and TSs are found for a benchmark set of more than 100 elementary reactions.

Simultaneous Two-Hydrogen Transfer as a Mechanism for Efficient CO2 Reduction

Two-hydrogen transfer (simultaneous protic and hydridic hydrogen transfer) is examined as a potentially efficient mechanism for the selective reduction of CO(2) to methanol. High-level ab initio CCSD(T) coupled-cluster theory simulations of ammonia-borane (AB), which contains both protic and hydridic hydrogen, show the effectiveness of this mechanism. AB demonstrates how simultaneous two-hydrogen transfer is kinetically efficient because (1) two-hydrogen transfer avoids high-energy single-electron-reduced intermediates, (2) the CO(2)s HOMO is protonated while the LUMO is concurrently reduced by a hydride, and (3) complementary charge polarities around the six-membered-ring transition-state structures stabilize the transition states. This study suggests that an effective mechanism for the reduction of CO(2) to methanol proceeds through three two-hydrogen-transfer steps and that suitable catalysts should be developed that exploit two-hydrogen transfer without the use of AB.

Excited states of methylene from quantum Monte Carlo.

The ground and lowest three adiabatic excited states of methylene are computed using the variational Monte Carlo and diffusion Monte Carlo (DMC) methods using progressively larger Jastrow-Slater multideterminant complete active space (CAS) wave functions. The highest of these states has the same symmetry, (1)A(1), as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment, but single-determinant wave functions do not yield accurate DMC energies of the states of (1)A(1) symmetry, indicating that it is important to include in the wave function Slater determinants that describe static (strong) correlation. Excitation energies obtained using recently proposed pseudopotentials [Burkatzki et al., J. Chem. Phys. 126, 234105 (2007)] differ from the all-electron excitation energies by at most 0.04 eV.

Ab Initio Simulations Reveal that Reaction Dynamics Strongly Affect Product Selectivity for the Cracking of Alkanes over H-MFI

Product selectivity of alkane cracking catalysis in the H-MFI zeolite is investigated using both static and dynamic first-principles quantum mechanics/molecular mechanics simulations. These simulations account for the electrostatic- and shape-selective interactions in the zeolite and provide enthalpic barriers that are closely comparable to experiment. Cracking transition states for n-pentane lead to a metastable intermediate (a local minimum with relatively small barriers to escape to deeper minima) where the proton is shared between two hydrocarbon fragments. The zeolite strongly stabilizes these carbocations compared to the gas phase, and the conversion of this intermediate to more stable species determines the product selectivity. Static reaction pathways on the potential energy surface starting from the metastable intermediate include a variety of possible conversions into more stable products. One-picosecond quasiclassical trajectory simulations performed at 773 K indicate that dynamic paths are substantially more diverse than the potential energy paths. Vibrational motion that is dynamically sampled after the cracking transition state causes spilling of the metastable intermediate into a variety of different products. A nearly 10-fold change in the branching ratio between C2/C3 cracking channels is found upon inclusion of post-transition-state dynamics, relative to static electronic structure calculations. Agreement with experiment is improved by the same factor. Because dynamical effects occur soon after passing through the rate-limiting transition state, it is the dynamics, and not only the potential energy barriers, that determine the catalytic selectivity. This study suggests that selectivity in zeolite catalysis is determined by high temperature pathways that differ significantly from 0 K potential surfaces.