Selective fluorination of organic semiconducting molecules is proposed as a means to achieving enhanced hole mobility. Naphthalene is examined here as a root molecular system with fluorination performed at various sites. Our quantum chemical calculations show that selective fluorination can enhance attractive intermolecular interactions while reducing charge trapping. Those observations suggest a design principle whereby fluorination is utilized for achieving high charge mobilities in the crystalline form. The utility of this design principle is demonstrated through an application to perylene, which is an important building block of organic semiconducting materials. We also show that a quantum mechanical perspective of nuclear degrees of freedom is crucial for a reliable description of charge transport.

Nonequilibrium Fermi’s golden rule (NE-FGR) describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state when the nuclear degrees of freedom start out in a nonequilibrium state. In this article, we derive a new expression for NE-FGR within the framework of the linearized semiclassical approximation. The new expression opens the door for applications of NE-FGR in complex condensed-phase molecular systems described in terms of anharmonic force fields. We show that the linearized semiclassical expression for NE-FGR yields the exact fully quantum-mechanical result for the canonical Marcus model, where the coupling between donor and acceptor is assumed constant (the Condon approximation) and the donor and acceptor potential energy surfaces are parabolic and identical except for a shift in the equilibrium energy and geometry. For this model, we also present a comprehensive comparison between the linearized semiclassical expression and a hierarchy of more approximate expressions, in both normal and inverted regions and over a wide range of initial nonequilibrium states, temperatures, and frictions.

In this article, we present a comprehensive comparison between the linearized semiclassical expression for the equilibrium Fermi’s golden rule rate constant and the progression of more approximate expressions that lead to the classical Marcus expression. We do so within the context of the canonical Marcus model, where the donor and acceptor potential energy surface are parabolic and identical except for a shift in both the free energies and equilibrium geometries, and within the Condon region. The comparison is performed for two different spectral densities and over a wide range of frictions and temperatures, thereby providing a clear test for the validity, or lack thereof, of the more approximate expressions. We also comment on the computational cost and scaling associated with numerically calculating the linearized semiclassical expression for the rate constant and its dependence on the spectral density, temperature, and friction.

The dependence of charge-transfer states on interfacial geometry at the phthalocyanine/fullerene organic photovoltaic system is investigated. The effect of deviations from the equilibrium geometry of the donor–donor–acceptor trimer on the energies of and electronic coupling between different types of interfacial electronic excited states is calculated from first-principles. Deviations from the equilibrium geometry are found to destabilize the donor-to-donor charge transfer states and to weaken their coupling to the photoexcited donor-localized states, thereby reducing their ability to serve as charge traps. At the same time, we find that the energies of donor-to-acceptor charge transfer states and their coupling to the donor-localized photoexcited states are either less sensitive to the interfacial geometry or become more favorable due to modifications relative to the equilibrium geometry, thereby enhancing their ability to serve as gateway states for charge separation. Through these findings, we eludicate how interfacial geometry modifications can play a key role in achieving charge separation in this widely studied organic photovoltaic system.

The conditions under which linear chirp can be used to control population transfer between the electronic states of a chromophore dissolved in liquid solution are investigated. To this end, we model the chromophore as a two-state system with shifted electronic potential energy surfaces and a fluctuating electronic transition frequency. The fluctuations are described as an exponentially correlated Gaussian stochastic process, which can be characterized by the average fluctuation amplitude, σ, and correlation time, τc. The time-dependent Schrödinger equation is solved numerically for an ensemble of stochastic histories, at different values of σ and τc, and under a wide range of pulse intensities and linear chirp coefficients. In the limit τc → ∞, we find that control diminishes rapidly as soon as σ exceeds the bandwidth of the pulse. However, we also find that control can be regained by reducing τc. We attribute this trend to motional narrowing, whereby decreasing τc narrows down the effective bandwidth of the solvent-induced fluctuations. The results suggest that the choice of methanol as a solvent in the actual experimental demonstration of chirp control by Cerullo et al. [ Chem. Phys. Lett. 1996, 262, 362−368] may have contributed to its success, due to the particularly short τc (∼20 fs) that the rapid librations of this hydrogen bonded liquid give rise to. The results also give rise to the rather surprising prediction that coherent control in liquid solution can be strongly dependent on the choice of solvent and be improved upon by choosing solvents that correspond to lower values of στc.

In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.

We investigate the molecular structure of the solvated complex, [(NC)6Fe–Pt(NH3)4–Fe(CN)6]4–, and related dinuclear and mononuclear model complexes using first-principles calculations. Mixed nuclear complexes in both solution and crystal phases were widely studied as models for charge transfer (CT) reactions using advanced spectroscopical and electrochemical tools. In contrast to earlier interpretations, we find that the most stable gas phase and solvated geometries are substantially different from the crystal phase geometry, mainly due to variance in the underlying oxidation numbers of the metal centers. Specifically, in the crystal phase a Pt(IV) metal center resulting from Fe ← Pt backward electron transfers is stabilized by an octahedral ligand field, whereas in the solution phase a Pt(II) metal complex that prefers a square planar ligand field forms a CT salt by bridging to the iron complexes through long-range electrostatic interactions. The different geometry is shown to be consistent with spectroscopical data and measured CT rates of the solvated complex. Interestingly, we find that the experimentally indicated photoinduced process in the solvated complex is of backward CT (Fe ← Pt).

•Thin film orbital gaps are misleadlingly reproduced by gas-phase traditional KS-DFT.•OT-RSH functionals correct the orbital gap failures in traditional KS-DFT.•We show OT-RSH gas phase orbital energies reproduce gas phase experimental values.•Including a PCM correction accounts for solid-state effects in thin-film measurements.•OT-RSH functionals give molecular-level insight for developing OPV design principles.Ionization potentials (IP) and electron affinities (EA) of organic molecules with applications in photovoltaic devices are calculated using modern density functional theory (DFT). Calculated frontier orbital energies are compared to experimentally determined IPs and EAs at gas phase and thin film environments. Gas phase frontier orbital energies calculated with widely-used DFT functionals accidentally coincide with thin film measurements, reproducing condensed phase results for the wrong reasons. Recently developed range separated hybrid (RSH) functionals, on the other hand, provide gas phase frontier orbital energies that correspond properly to measured IPs and EAs. We also employ a polarizable continuum model to address the effects of the electrostatic environment in the solid state. We find that the environmentally-corrected RSH orbital energies compare well with thin film experimental measurements.

Charge transfer (CT) states formed at the donor/acceptor heterointerface are key for photocurrent generation in organic photovoltaics (OPV). Our calculations show that interfacial donor-to-donor CT states in the phthalocyanine–fullerene OPV system may be more stable than donor-to-acceptor CT states and that they may rapidly recombine, thereby constituting a potentially critical and thus far overlooked loss mechanism. Our results provide new insight into processes that may compete with charge separation, and suggest that the efficiency for charge separation may be improved by destabilizing donor-to-donor CT states or decoupling them from other states.Keywords: charge transfer; constrained density functional theory (C-DFT); Fermi’s golden rule; organic photovoltaics; range separated hybrid functional;

The rates of interfacial charge transfer and recombination between the donor and acceptor layers play a key role in determining the performance of organic photovoltaic cells. The time scale and mechanism of these processes are expected to be impacted by the structure of the interface. In this paper we model the kinetics of those processes within the framework of a subphthalocyanine/fullerene donor/acceptor dimer model. Two likely configurations (on-top and hollow) in which the interfacial charge transfer and recombination may occur are studied. The corresponding rate constants are calculated within the fully quantum-mechanical framework of Fermi’s golden rule. All the input parameters (excitation energies, electronic coupling coefficients, normal-mode frequencies and coordinates, and Huang–Rhys factors) are obtained from density functional theory calculations with density functionals designed to yield accurate results in the case of noncovalently bound systems and charge transfer states. Multiple π–π* and charge-transfer excited states are identified and assigned. The kinetics of photoinduced charge transfer is obtained by solving a master equation using Fermi’s golden rule rate constants for the electronic transitions between the various excited states. Our results suggest that the hollow configuration may be superior to the on-top configuration and that maximizing its prevalence may improve the performance of subphthalocyanine/fullerene-based photovoltaic cells.

The lifetimes of the first vibrational state of 12C14N– and 13C15N– dissolved in H2O or D2O were calculated. The calculations were based on the Landau–Teller formula that puts the vibrational lifetimes in terms of the autocorrelation function of the force exerted on the C–N stretch by the remaining degrees of freedom. The force autocorrelation functions were calculated from classical molecular dynamics simulations of the four cyanide/water isotopomer combinations (12C14N–/H2O, 12C14N–/D2O, 13C15N–/H2O, 13C15N–/D2O). The cyanide ion was described by a polarizable force field, and the water was described by either the rigid SPC/E model or the flexible SPC/Fw model, in order to compare two different types of accepting modes, namely, (1) intermolecular (translational and rotational) solvent accepting modes (rigid SPC/E water) and (2) intramolecular (vibrational) solvent accepting modes (flexible SPC/Fw water). Since quantum effects are expected to increase in size with increasing frequency mismatch between relaxing and accepting modes, different quantum correction factors were employed depending on the identity of the accepting modes, more specifically, the harmonic/Schofield quantum correction factor in the case of intermolecular accepting modes and the standard quantum correction factor in the case of intramolecular accepting modes. The lifetimes with either the rigid SPC/E or flexible SPC/Fw water models were found to be in good quantitative agreement with the experimentally measured values for all isotopomer combinations. Our results suggest that taking into account quantum effects on the vibrational energy relaxation of cyanide in aqueous solution can make the intermolecular pathway at least as likely as the intramolecular pathway.

We benchmark several protocols for evaluating the energies of excited charge transfer (CT) states of organic molecules dissolved in polar liquids. The protocols combine time-dependent density functional theory using range-separated hybrid functionals, constrained density functional theory, dispersion corrected functional, and a dielectric continuum model for representing the solvent. We compare the different protocols against well-established experimental measured charge transfer state energies in solvated dimers of functionalized anthracene and tetracyanoethylene. We find that using the range-separated hybrid functional for the charge-transfer state energies and the combination of constrained density functional theory with the recently improved switching Gaussian polarizable continuum model (PCM) provide good agreement with the experimental values of the solvated CT states. We also find that using dispersion corrected solvated geometries for the weakly coupled donor–acceptor dimers considered here leads to improved agreement with experimental measured values.

The feasibility of calculating photoinduced intramolecular electron transfer rate constants in realistic molecular donor–acceptor systems via Fermi’s golden rule, using inputs obtained from state-of-the-art electronic structure techniques, is demonstrated and tested. To this end, calculations of photoinduced electron transfer rate constants were performed on two benchmark systems: (1) phenylacetylene-bridged carbazole-naphthalimide (meta and para) and (2) C60-(N,N-dimethylaniline). Intramolecular input parameters such as normal-mode frequencies, Huang–Rhys factors, and electronic coupling coefficients were obtained via ground state, time-dependent, and constrained density functional theory. Good agreement between the intramolecular Fermi’s golden rule rate constants and the experimental rate constants is found for both systems without accounting for the solvent reorganization. The relative roles of intramolecular vs intermolecular modes at promoting electron transfer and the validity of several limits of Fermi’s golden rule for describing intramolecular electron transfer are discussed.

The intramolecular hydrogen-bond structure of stereoselectively synthesized syn-tetrol and anti-tetrol dissolved in deuterated chloroform is investigated via a mixed quantum-classical molecular dynamics simulation. An extensive conformational analysis is performed in order to determine the dominant conformations, the distributions among them, and their sensitivity to the method for assigning partial charges (RESP vs AM1-BCC). The signature of the conformational distribution and method of assigning partial charges on the infrared absorption spectra is analyzed in detail. The relationship between the spectra and the underlying hydrogen-bond structure is elucidated.

The effect of vibrational excitation and relaxation of the hydroxyl stretch on the hydrogen-bond structure and dynamics of stereoselectively synthesized syn-tetrol and anti-tetrol dissolved in deuterated chloroform are investigated via a mixed quantum-classical molecular dynamics simulation. Emphasis is placed on the changes in hydrogen-bond structure upon photoexcitation and the nonequilibrium hydrogen-bond dynamics that follows the subsequent relaxation from the excited to the ground vibrational state. The propensity to form hydrogen bonds is shown to increase upon photoexcitation of the hydroxyl stretch, thereby leading to a sizable red-shift of the infrared emission spectra relative to the corresponding absorption spectra. The vibrational excited state lifetimes are calculated within the framework of Fermi’s golden rule and the harmonic-Schofield quantum correction factor, and found to be sensitive reporters of the underlying hydrogen-bond structure. The energy released during the relaxation from the excited to the ground state is shown to break hydrogen bonds involving the relaxing hydroxyl. The spectral signature of this nonequilibrium relaxation process is analyzed in detail.

The solvation dynamics of formylperylene in methanol/acetonitrile liquid mixtures have been experimentally observed to slow down with increasing concentration of methanol. We present results from equilibrium and nonequilibrium molecular dynamics simulations that relate the slowdown to the formation of a hydrogen-bonded methanol oligomer, which is hydrogen-bonded to the carbonyl group of formylperylene.

Recent experimental advances in the ability to tune the optical properties of silsesquioxanes by functionalizing them with photoactive ligands have made these compounds attractive candidates for building blocks of photovoltaic materials. We employ state-of-the-art ab initio methodologies to determine the nature of the excited charge-transfer (CT) states that give rise to a large red-shift between absorption and emission in these molecules, in comparison to the corresponding red-shift in the individual ligand. The calculations are based on time-dependent density functional theory and employ the recently developed Baer–Neuhauser–Livshits range-separated hybrid (RSH) functional. Solvent effects are accounted for via a combination of charge-constrained density functional theory and the polarizable continuum model. We find that the experimentally observed red-shift is consistent with identifying the emissive state as a ligand-to-ligand, rather than a ligand-to-silsesquioxane, CT state. We also find that the enhanced red-shift cannot be explained without accounting for solvation effects, and we demonstrate the importance of using a RSH functional to obtain reliable predictions regarding the emissive state.

Time-dependent density functional theory with range-separated hybrid functionals is used to calculate off-site excitations involving transitions between spatially separated orbitals in weakly coupled systems. Although such off-site excitations involve charge transfer, orbital degeneracy in symmetrical systems results in linear combinations of off-site excitations with equal weights and therefore zero net charge-transfer character. Like other types of off-site excitations, such “hidden” charge-transfer excitations are not accurately captured by conventional density functionals. We show that the recently introduced Baer–Neuhauser–Livshitz range-separated hybrid functional accurately characterizes such hidden off-site excitation energies via applications to the ethene dimer model system and to dye-functionalized silsesquioxanes.

We present a mixed quantum-classical molecular dynamics study of the hydrogen-bonding structure and dynamics of a vibrationally excited hydroxyl stretch in methanol/carbon-tetrachloride mixtures. The adiabatic Hamiltonian of the quantum-mechanical hydroxyl is diagonalized on-the-fly to obtain the ground and first-excited adiabatic energy levels and wave functions which depend parametrically on the instantaneous configuration of the classical degrees of freedom. The dynamics of the classical degrees of freedom are determined by Hellmann–Feynman forces obtained by taking the expectation value of the force with respect to the ground or excited vibrational wave functions. Polarizable force fields are used which were previously shown to reproduce the experimental infrared absorption spectrum rather well, for different isotopomers and over a wide composition range [Kwac, K.; Geva, E. J. Phys. Chem. B2011, 115, 9184]. We show that the agreement of the absorption spectra with experiment can be further improved by accounting for the dependence of the dipole moment derivatives on the configuration of the classical degrees of freedom. We find that the propensity of a methanol molecule to form hydrogen bonds increases upon photoexcitation of its hydroxyl stretch, thereby leading to a sizable red-shift of the corresponding emission spectrum relative to the absorption spectrum. Treating the relaxation from the first excited to the ground state as a nonadiabatic process, and calculating its rate within the framework of Fermi’s golden rule and the harmonic-Schofield quantum correction factor, we were able to predict a lifetime which is of the same order of magnitude as the experimental value. The experimental dependence of the lifetime on the transition frequency is also reproduced. Nonlinear mapping relations between the hydroxyl transition frequency and bond length in the excited state and the electric field along the hydroxyl bond axis are established. These mapping relations make it possible to reduce the computational cost of the mixed quantum-classical treatment to that of a fully classical treatment.

We present a general and comprehensive theoretical and computational framework for modeling ultrafast multidimensional infrared spectra of a vibrational excitonic system in liquid solution. Within this framework, we describe the dynamics of the system in terms of a quantum master equation that can account for population relaxation, dephasing, coherence-to-coherence transfer, and coherence-to-population transfer. A unique feature of our approach is that, in principle, it does not rely on any adjustable fitting parameters. More specifically, the anharmonic vibrational Hamiltonian is derived from ab initio electronic structure theory, and the system−bath coupling is expressed explicitly in terms of liquid degrees of freedom whose dynamics can be obtained via molecular dynamics simulations. The applicability of the new approach is demonstrated by employing it to model the recently observed signatures of coherence transfer in the two-dimensional spectra of dimanganese decacarbonyl in liquid cyclohexane. The results agree well with experiment and shed new light on the nature of the molecular interactions and dynamics underlying the spectra and the interplay between dark and bright states, their level of degeneracy, and the nature of their interactions with the solvent.

The mixed quantum-classical Liouville equation provides a unified and self-consistent platform for modeling the spectral signatures of nonequilibrium solvation dynamics, non-Condon effects, and nonadiabatic transitions. These features are demonstrated in this paper in the context of the pump−probe infrared spectra of the hydrogen stretch in a moderately strong hydrogen-bonded complex dissolved in a polar solvent. Particular emphasis is put on incorporating nonadiabatic transitions and accounting for their unique spectral signature.

Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute−solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore’s quantum state during the various time intervals separating light−matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system’s dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore’s ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward−backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.

We present a first-principles study of the 2D carbonyl stretch infrared spectra of dimanganese decacarbonyl, Mn2(CO)10, and its photoproducts, Mn2(CO)9 and Mn(CO)5. The corresponding multidimensional anharmonic potential energy surfaces are computed via density functional theory up to fourth-order in the normal mode coordinates. The anharmonic shifts are computed using vibrational perturbation theory and benchmarked against results obtained by diagonalizing the vibrational Hamiltonian in the case of Mn(CO)5. The importance of accounting for couplings between the photoactive and photoinactive CO stretches as well as for contributions that arise from fourth-order force constants is demonstrated. The 2D spectra are compared with experiment in the case of Mn2(CO)10.The reasonable agreement between theory and experiment suggests that an approach combining density functional theory with vibrational perturbation theory can provide a useful route for computing 2D infrared spectra, particularly in cases where direct diagonalization of the vibrational Hamiltonian is not feasible.

The accuracy and robustness of several approximate methods for computing linear and nonlinear optical spectra are considered. The analysis is performed in the context of a benchmark model that consists of a two-state chromophore with shifted harmonic potential surfaces that differ in frequency. The exact one- and two-dimensional spectra for this system are calculated and compared to spectra calculated via the following approximate methods: (1) The semiclassical forward−backward initial-value representation (FB-IVR) method; (2) the linearized semiclassical (LSC) method; (3) the standard second-order cumulant approximation which is based on the ground-state equilibrium frequency−frequency correlation function (2OC); (4) an alternative second-order cumulant approximation which is able to account for nonequilibrium dynamics on the excited-state potential surface (2OCa). All four approximate methods can be shown to reproduce the exact results when the frequencies of the ground and excited harmonic surfaces are identical. However, allowing for the ground and excited surfaces to differ in frequency leads to a more meaningful benchmark model for which none of the four approximate methods is exact. We present a comparison of one- and two-dimensional spectra calculated via the above-mentioned approximate methods to the corresponding exact spectra, as a function of the following parameters: (1) The ratio of excited state to ground-state frequencies; (2) Temperature; (3) The horizontal displacement of the excited-state potential relative to the ground-state potential; (4) The waiting time between the coherence periods in the case of two-dimensional spectra. The FB-IVR method is found to predict spectra which are practically indistinguishable from the exact ones over a wide region of parameter space. The LSC method is found to predict spectra which are in good agreement with the exact ones over the same region of parameter space. The 2OC and 2OCa are found to be highly inaccurate unless the frequencies of the ground and excited states are very similar. These observations give credence to the use of the LSC method for modeling spectra in complex systems, where exact or even FB-IVR-based calculations are prohibitively expensive.

The effect of the commonly employed Condon and second-order cumulant approximations on one- and two-dimensional infrared spectra is examined in the case of a vibrational mode which is strongly coupled to its environment. The analysis is performed within the context of the hydrogen stretch of a moderately strong hydrogen-bonded complex dissolved in a dipolar liquid. The IR spectra are calculated using an adiabatic mixed quantum−classical approach that treats the hydrogen quantum-mechanically, while the remaining degrees of freedom are treated classically. While the cumulant and Condon treatments are seen to produce extremely broad and rather structureless spectra, the non-Condon spectra are found to consist of several relatively narrow bands that can be traced back to subsets of bath configurations with large transition dipole moments. Thus, although the cumulant and Condon approximations can capture some general qualitative spectral trends and are able to reproduce some highly averaged quantities such as the photon-echo peak shift, they fail to reproduce many important features of the spectra. We show that the great sensitivity of the transition dipole moment to the bath configuration provides new means for decongesting the spectra, probing statistically unfavorable bath configurations, and obtaining unique information regarding the dynamics of individual subsets of bath configurations and of the rates of transitions between them.