Simulating Excited State Dynamics in Systems with Multiple Avoided Crossings Using Mapping Variable Ring Polymer Molecular Dynamics

Mapping variable ring polymer molecular dynamics (MV-RPMD) is an approximate quantum dynamics method based on imaginary-time path integrals for simulating electronically nonadiabatic photochemical processes. By employing a mapping protocol to transform from a discrete electronic state basis to continuous Cartesian phase-space variables, the method captures electronic state transitions coupled to nuclear motion using only classical MD trajectories. In this work, we extend the applicability of MV-RPMD to simulations of photoinduced excited electronic state dynamics in nonadiabatic systems with multiple avoided crossings. We achieve this by deriving a new electronic state population estimator in the phase space of electronic variables that is exact at equilibrium and numerically accurate in real time. Further, we introduce an efficient constraint protocol to initialize an MV-RPMD simulation to a particular electronic state. We numerically demonstrate the accuracy of this estimator and constraint technique in describing electronic state dynamics from an initial nonequilibrium state in six model systems, three of which describe photodissociation

The Low-Lying Electronic States of Pentacene and Their Roles in Singlet Fission

We present a detailed study of pentacene monomer and dimer that serves to reconcile extant views of its singlet fission. We obtain the correct ordering of singlet excited-state energy levels in a pentacene molecule (<i>E</i> (<i>S</i>₁) < <i>E</i> (<i>D</i>)) from multireference calculations with an appropriate active orbital space and dynamical correlation being incorporated. In order to understand the mechanism of singlet fission in pentacene, we use a well-developed diabatization scheme to characterize the six low-lying singlet states of a pentacene dimer that approximates the unit cell structure of crystalline pentacene. The local, single-excitonic diabats are not directly coupled with the important multiexcitonic state but rather mix through their mutual couplings with one of the charge-transfer configurations. We analyze the mixing of diabats as a function of monomer separation and pentacene rotation. By defining an oscillator strength measure of the coherent population of the multiexcitonic diabat, essential to singlet fission, we find this population can, in principle, be increased by small compression along a specific crystal direction

Seeking Small Molecules for Singlet Fission: A Heteroatom Substitution Strategy

We design theoretically small molecule candidates for singlet fission chromophores, aiming to achieve a balance between sufficient diradical character and kinetic persistence. We develop a perturbation strategy based on the captodative effect to introduce diradical character into small π-systems. Specifically, this can be accomplished by replacing pairs of not necessarily adjacent C atoms with isoelectronic and isosteric pairs of B and N atoms. Three rules of thumb emerge from our studies to aid further design: (i) Lewis structures provide insight into likely diradical character; (ii) formal radical centers of the diradical must be well-separated; (iii) stabilization of radical centers by a donor (N) and an acceptor (B) is essential. Following the rules, we propose candidate molecules. Employing reliable multireference calculations for excited states, we identify three likely candidate molecules for SF chromophores. These include a benzene, a napthalene, and an azulene, where four C atoms are replaced by a pair of B and a pair of N atoms

Tuning Spin-States of Carbynes and Silylynes: A Long Jump with One Leg

The challenge motivating this paper is to induce, by chemical substitution, a silylyne, SiR, or a congeneric carbyne, CR, to adopt the high-spin quartet rather than the low-spin doublet as its ground state. The difficulty is seen in the preference for the doublet of the parent SiH (doublet–quartet energy difference ∼39 kcal/mol, favoring the doublet) or CH (∼17 kcal/mol). Strategies for having high-spin ground state parallel those for silylenes and carbenes: greater electropositivity (σ-donation) and π-acceptance of the single substituent favor the high-spin state. The electronegativity trend can be understood from an <i>ions in molecules</i> way of thinking already present in the literature in the works of Boldyrev and Simons, and of Mavridis and Harrison; i.e., the quartet ground state spin of some CR/SiR species is largely determined by the ground state spin of C^–/Si^–. In this study, we provide a diabatization analysis that solidly confirms the <i>ions in molecules</i> picture and explains the difference in the equilibrium internuclear distances for the two spin states. In general, electronegativity dominates the ordering of spin states. π-Acceptors also help to lower the quartet state energy of the many carbynes (silylynes) examined, whose range of doublet–quartet differences calculated is impressive, 120 (100) kcal/mol. The qualitative understanding gained leads to the prediction of some quartet-ground state carbynes (CMgH, CAlH₂, CZnH, CSiH₃, CSiF₃, etc.) and a smaller number of silylynes (SiMgH, SiMgF, SiBeH, etc.). A beginning is made on the energetics of approach geometries of the fragments in the highly exoergic dimerization of CH to acetylene; it should proceed for the ground state doublet CH through C_2<i>h</i>-like trajectories, with no activation energy

A Direct Mechanism of Ultrafast Intramolecular Singlet Fission in Pentacene Dimers

Interest in materials that undergo singlet fission (SF) has been catalyzed by the potential to exceed the Shockley–Queisser limit of solar power conversion efficiency. In conventional materials, the mechanism of SF is an intermolecular process (xSF), which is mediated by charge transfer (CT) states and depends sensitively on crystal packing or molecular collisions. In contrast, recently reported covalently coupled pentacenes yield ∼2 triplets per photon absorbed in individual molecules: the hallmark of intramolecular singlet fission (iSF). However, the mechanism of iSF is unclear. Here, using multireference electronic structure calculations and transient absorption spectroscopy, we establish that iSF can occur via a direct coupling mechanism that is independent of CT states. We show that a near-degeneracy in electronic state energies induced by vibronic coupling to intramolecular modes of the covalent dimer allows for strong mixing between the correlated triplet pair state and the local excitonic state, despite weak direct coupling

Tuning Singlet Fission in π‑Bridge‑π Chromophores

We have designed a series of pentacene dimers separated by homoconjugated or nonconjugated bridges that exhibit fast and efficient intramolecular singlet exciton fission (iSF). These materials are distinctive among reported iSF compounds because they exist in the unexplored regime of close spatial proximity but weak electronic coupling between the singlet exciton and triplet pair states. Using transient absorption spectroscopy to investigate photophysics in these molecules, we find that homoconjugated dimers display desirable excited-state dynamics, with significantly reduced recombination rates as compared to conjugated dimers with similar singlet fission rates. In addition, unlike conjugated dimers, the time constants for singlet fission are relatively insensitive to the interplanar angle between chromophores, since rotation about σ bonds negligibly affects the orbital overlap within the π-bonding network. In the nonconjugated dimer, where the iSF occurs with a time constant >10 ns, comparable to the fluorescence lifetime, we used electron spin resonance spectroscopy to unequivocally establish the formation of triplet–triplet multiexcitons and uncoupled triplet excitons through singlet fission. Together, these studies enable us to articulate the role of the conjugation motif in iSF

Tuning Singlet Fission in π‑Bridge‑π Chromophores

We have designed a series of pentacene dimers separated by homoconjugated or nonconjugated bridges that exhibit fast and efficient intramolecular singlet exciton fission (iSF). These materials are distinctive among reported iSF compounds because they exist in the unexplored regime of close spatial proximity but weak electronic coupling between the singlet exciton and triplet pair states. Using transient absorption spectroscopy to investigate photophysics in these molecules, we find that homoconjugated dimers display desirable excited-state dynamics, with significantly reduced recombination rates as compared to conjugated dimers with similar singlet fission rates. In addition, unlike conjugated dimers, the time constants for singlet fission are relatively insensitive to the interplanar angle between chromophores, since rotation about σ bonds negligibly affects the orbital overlap within the π-bonding network. In the nonconjugated dimer, where the iSF occurs with a time constant >10 ns, comparable to the fluorescence lifetime, we used electron spin resonance spectroscopy to unequivocally establish the formation of triplet–triplet multiexcitons and uncoupled triplet excitons through singlet fission. Together, these studies enable us to articulate the role of the conjugation motif in iSF