The absorption of one photon by a semiconductor material usually creates one electron-hole pair. However, this general rule breaks down in a few organic semiconductors, such as pentacene and tetracene, where one photon absorption may result in two electron-hole pairs. This process, where a singlet exciton transforms to two triplet excitons, can have quantum yields as high as 200%. Singlet fission may be useful to solar cell technologies to increase the power conversion efficiency beyond the so-called Shockley-Queisser limit. Through time-resolved two-photon photoemission (TR-2PPE) spectroscopy in crystalline pentacene and tetracene, our lab has recently provided the first spectroscopic signatures in singlet fission of a critical intermediate known as the multiexciton state (also called a correlated triplet pair). More importantly, we found that population of the multiexciton state rises at the same time as the singlet state on the ultrafast time scale upon photoexcitation. This observation does not fit with the traditional view of singlet fission involving the incoherent conversion of a singlet to a triplet pair. However, it provides an experimental foundation for a quantum coherent mechanism in which the electronic coupling creates a quantum superposition of the singlet and the multiexciton state immediately after optical excitation. In this Account, we review key experimental findings from TR-2PPE experiments and present a theoretical analysis of the quantum coherent mechanism based on electronic structural and density matrix calculations for crystalline tetracene lattices. Using multistate density functional theory, we find that the direct electronic coupling between singlet and multiexciton states is too weak to explain the experimental observation. Instead, indirect coupling via charge transfer intermediate states is two orders of magnitude stronger, and dominates the dynamics for ultrafast multiexciton formation. Density matrix calculation for the crystalline tetracene lattice satisfactorily accounts for the experimental observations. It also reveals the critical roles of the charge transfer states and the high dephasing rates in ensuring the ultrafast formation of multiexciton states. In addition, we address the origins of microscopic relaxation and dephasing rates, and adopt these rates in a quantum master equation description. We show the need to take the theoretical effort one step further in the near future by combining high-level electronic structure calculations with accurate quantum relaxation dynamics for large systems.

Real-time time-dependent functional theory (RT-TDDFT) directly propagates the electron density in the time domain by integrating the time-dependent Kohn-Sham equations. This is in contrast to the popular linear response TDDFT matrix formulation that computes transition frequencies from a ground state reference. RT-TDDFT is, therefore, a potentially powerful technique for modeling atto-to picosecond electron dynamics, including charge transfer pathways, the response to a specific applied field, and frequency dependent linear and nonlinear properties. However, qualitatively incorrect electron dynamics and time-dependent resonant frequencies can occur when perturbing the density away from the ground state due to the common adiabatic approximation. An overview of the RT-TDDFT method is provided here, including examples of some cases that lead to this qualitatively incorrect behavior.

Mixed quantum mechanical (QM)/classical methods provide a computationally efficient approach to modeling both ground and excited states in the condensed phase. To accurately model short-range interactions, some amount of the environment can be included in the QM region, whereas a classical model can treat long-range interactions to maintain computational affordability. The best computational protocol for these mixed QM/classical methods can be determined by examining convergence of molecular properties. Here, we compare molecular mechanical (MM) fixed point charges to a polarizable continuum model (PCM) for computing electronic excitations in solution. We computed the excitation energy of three pairs of neutral/anionic molecules in aqueous solvent, including up to 250 water molecules in the QM region. Interestingly, the convergence is similar for MM point charges and a PCM, with convergence achieved when at least one full solvation shell is treated with QM. Although the van der Waals (VDW) definition of the PCM cavity is adequate with small amounts of QM solvent, larger QM solvent layers had gaps in the VDW PCM cavity, leading to asymptotically incorrect excitation energies. Given that the VDW cavity leads to unphysical solute-solvent interactions, we advise using a solvent-excluded surface cavity for QM/PCM calculations that include QM solvent.

Time-dependent density functional theory (TDDFT) calculations are employed to examine the optical absorption and circular dichroism (CD) spectra of undecagold Au(11)L(4)X(2)(+) (X = Cl, Br) complexes and their Au(2)X(2)L precursors, where L is either 2,2'-bis(diphenylphosphino)-1,1'-binaphtyl (BINAP) or 1,4-diphosphino-1,3-butadiene (dpb). These systems exhibit intense and mirror-image Cotton effects in their CD spectra. Experimental peak positions are well reproduced in the calculations. The low energy peaks of Au(11)L(4)X(2)(+) arise primarily from transitions between delocalized metal superatom orbitals. Bidentate phosphine ligands have both a structural and electronic impact on the system. The lowest energy structure of Au(11)L(4)X(2)(+) has a chiral C(2) geometry, whereas monodentate phosphine ligands lead to a C(1) structure. In addition, the chiral core structure of Au(11)L(4)X(2)(+) is not sufficient to explain the strong Cotton effects, and the intensity of the CD spectrum is increased by the presence of the bidentate phosphine ligands.

ConspectusMolecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantum mechanics rather than only using quantum mechanical results to fit analytic force fields. In this spirit, this approach is called a quantum mechanical force field (QMFF).X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems (“fragments”) to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantum mechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantum mechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples involving water clusters (which show the power of two-body corrections), ethylmethylimidazolium acetate ionic liquids (which reveal that the amount of charge transfer between anion and cation is much smaller than what has been assumed in some classical simulations), and a solvated protein in aqueous solution (which shows that the average charge distribution of carbonyl groups along the polypeptide chain depends strongly on their position in the sequence, whereas they are fixed in most classical force fields). The development of QMFFs also offers an opportunity to extend the accuracy of biochemical simulations to areas where classical force fields are often insufficient, especially in the areas of spectroscopy, reactivity, and enzyme catalysis.

Multistate density functional theory (MSDFT) is presented to estimate the effective transfer integral associated with electron and hole transfer reactions. In this approach, the charge-localized diabatic states are defined by block localization of Kohn–Sham orbitals, which constrain the electron density for each diabatic state in orbital space. This differs from the procedure used in constrained density functional theory that partitions the density within specific spatial regions. For a series of model systems, the computed transfer integrals are consistent with experimental data and show the expected exponential attenuation with the donor–acceptor separation. The present method can be used to model charge transfer reactions including processes involving coupled electron and proton transfer.

For reliable condensed phase simulations, an accurate model that includes both short- and long-range interactions is required. Short- and long-range interactions can be particularly strong in aqueous solution, where hydrogen-bonding may play a large role at short range and polarization may play a large role at long range. Although short-range solute-solvent interactions such as charge transfer, hydrogen bonding, and solute-solvent polarization can be taken into account with a quantum mechanical (QM) treatment of the solvent, it is unclear how much QM solvent is necessary to accurately model interactions with different solutes. In this work, we investigate the effect of explicit QM solvent on absorption spectra computed for a series of solutes with decreasing polarity. By adjusting the boundary between QM and classical molecular mechanical solvent to include up to 400 QM water molecules, convergence of the calculated absorption spectra with respect to the size of the QM region is achieved. We find that the rate of convergence does not correlate with solute polarity when excitation energies are calculated using time-dependent density functional theory with a range-separated hybrid functional, but it does correlate with solute polarity when using configuration interaction singles. We also find that larger basis sets converge the computed spectrum with fewer QM solvent molecules. To optimize the computational cost with respect to convergence, we test a mixed basis set with more basis functions for atoms of the chromophore and the solvent molecules that are nearest to it and fewer basis functions for the atoms of the remaining solvent molecules in the QM region. Our results show that using a mixed basis set is a potentially effective way to significantly lower the computational cost while reproducing the results computed with larger basis sets.

A critical element in theoretical characterization of the mechanism of proton-coupled electron transfer (PCET) reactions, including hydrogen atom transfer (HAT), is the formulation of the electron and proton localized diabatic states, based on which a More O’Ferrall-Jencks diagram can be represented to determine the step-wise and concerted nature of the reaction. Although the More O’Ferrall-Jencks diabatic states have often been used empirically to develop theoretical models for PCET reactions, the potential energy surfaces for these states have never been determined directly based on first principles calculations using electronic structure theory. The difficulty is due to a lack of practical method to constrain electron and proton localized diabatic states in wave function or density functional theory calculations. Employing a multistate density functional theory (MSDFT), in which the electron and proton localized diabatic configurations are constructed through block-localization of Kohn-Sham orbitals, we show that distinction between concerted proton-electron transfer (CPET) and HAT, which are not distinguishable experimentally from phenomenological kinetic data, can be made by examining the third dimension of a More O’Ferrall-Jencks diagram that includes both the ground and excited state potential surfaces. In addition, we formulate a pair of effective two-state valence bond models to represent the CPET and HAT mechanisms. We found that the lower energy of the CPET and HAT effective diabatic states at the intersection point can be used as an energetic criterion to distinguish the two mechanisms. In the isoelectronic series of hydrogen exchange reaction in (PhX)2H•, where X = O, NH, and CH2, there is a continuous transition from a CPET mechanism for the phenoxy radical-phenol pair to a HAT process for benzyl radical and toluene, while the reaction between PhNH2 and PhNH• has a mechanism intermediate of CPET and HAT. The electronically nonadiabatic nature of the CPET mechanism in the phenol system can be attributed to the overlap interactions between the ground and excited state surfaces, resulting in roughly orthogonal minimum energy paths on the adiabatic ground and excited state potential energy surfaces. On the other hand, the minimum energy path on the adiabatic ground state for the HAT mechanism coincides with that on the excited state, producing a large electronic coupling that separates the two surfaces by more than 120 kcal/mol.