Using coherence to enhance function in chemical and biophysical systems.

Coherence phenomena arise from interference, or the addition, of wave-like amplitudes with fixed phase differences. Although coherence has been shown to yield transformative ways for improving function, advances have been confined to pristine matter and coherence was considered fragile. However, recent evidence of coherence in chemical and biological systems suggests that the phenomena are robust and can survive in the face of disorder and noise. Here we survey the state of recent discoveries, present viewpoints that suggest that coherence can be used in complex chemical systems, and discuss the role of coherence as a design element in realizing function.

Influence of Vibronic Coupling on Ultrafast Singlet Fission in a Linear Terrylenediimide Dimer.

Singlet fission (SF) is a photophysical process capable of boosting the efficiency of solar cells. Recent experimental investigations into the mechanism of SF provide evidence for coherent mixing between the singlet, triplet, and charge transfer basis states. Up until now, this interpretation has largely focused on electronic interactions; however, nuclear motions resulting in vibronic coupling have been suggested to support rapid and efficient SF in organic chromophore assemblies. Further information about the complex interactions between vibronic excited states is needed to understand the potential role of this coupling in SF. Here, we report mixed singlet and correlated triplet pair states giving rise to sub-50 fs SF in a terrylene-3,4:11,12-bis(dicarboximide) (TDI) dimer in which the two TDI molecules are covalently linked by a direct N-N connection at one of their imide positions, leading to a linear dimer with perpendicular TDI π systems. We observe the transfer of low-frequency coherent wavepackets between the initial predominantly singlet states to the product triplet-dominated states. This implies a non-negligible dependence of SF on nonadiabatic coupling in this dimer. We interpret our experimental results in the framework of a modified Holstein Hamiltonian, which predicts that vibronic interactions between low-frequency singlet modes and high-frequency correlated triplet pair motions lead to mixing of the pure basis states. These results highlight how nonadiabatic mixing can shape the complex potential energy landscape underlying ultrafast SF.

Tunable Symmetry-Breaking-Induced Dual Functions in Stable and Photoswitched Single-Molecule Junctions.

The aim of molecular electronics is to miniaturize active electronic devices and ultimately construct single-molecule nanocircuits using molecules with diverse structures featuring various functions, which is extremely challenging. Here, we realize a gate-controlled rectifying function (the on/off ratio reaches ∼60) and a high-performance field effect (maximum on/off ratio >100) simultaneously in an initially symmetric single-molecule photoswitch comprising a dinuclear ruthenium-diarylethene (Ru-DAE) complex sandwiched covalently between graphene electrodes. Both experimental and theoretical results consistently demonstrate that the initially degenerated frontier molecular orbitals localized at each Ru fragment in the open-ring Ru-DAE molecule can be tuned separately and shift asymmetrically under gate electric fields. This symmetric orbital shifting (AOS) lifts the degeneracy and breaks the molecular symmetry, which is not only essential to achieve a diode-like behavior with tunable rectification ratio and controlled polarity, but also enhances the field-effect on/off ratio at the rectification direction. In addition, this gate-controlled symmetry-breaking effect can be switched on/off by isomerizing the DAE unit between its open-ring and closed-ring forms with light stimulus. This new scheme offers a general and efficient strategy to build high-performance multifunctional molecular nanocircuits.

Second Linear Response Theory and the Analytic Calculation of Excited-State Properties.

We present a method based on second linear response time-dependent density functional theory (TDDFT) to calculate permanent and transition multipoles of excited states, which are required to compute excited-state absorption/emission spectra and multiphoton optical processes, among others. In previous work, we examined computations based on second linear response theory in which linear response TDDFT was employed twice. In contrast, the present methodology requires information from only a single linear response calculation to compute the excited-state properties. These are evaluated analytically through various algebraic operations involving electron repulsion integrals and excitation vectors. The present derivation focuses on full many-body wave functions instead of single orbitals, as in our previous approach. We test the proposed method by applying it to several diatomic and triatomic molecules. This shows that the computed excited-state dipoles are consistent with respect to reference equation-of-motion coupled-cluster calculations.

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences.

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

Thermodynamics and Mechanism of a Photocatalyzed Stereoselective [2 + 2] Cycloaddition on a CdSe Quantum Dot.

Colloidal quantum dots (QDs) have shown promise over the last few decades for a range of applications including single photon emission, in vivo imaging, and photocatalysis. Recent experiments demonstrated that QDs impart stereoselectivity to triplet excited-state [2 + 2] cycloaddition reactions of alkenes photocatalyzed by the QD through self-assembly of the reagent molecules on the QD surface, but these experiments did not reveal the precise geometries of surface-bound molecules or their interactions with surface atoms. Here, a theoretical mechanistic approach is used to study such interactions for [2 + 2] cycloadditions of 4-vinylbenzoic acid derivatives on CdSe QDs. Spin-polarized periodic density functional theory (DFT) and nonperiodic DFT calculations are deployed to determine the origin of the selectivity for the syn diastereomer of the resultant tetrasubstituted cyclobutane product via atomistic modeling of the CdSe surface and substrates, determination of the thermodynamic energies of reactions for each step, the intermolecular interactions between the substrates, and the triplet state reaction paths. The calculations indicate that reaction selectivity arises from preferred binding of pairs through intermolecular interactions of substrate molecules on the QD surface in a syn-precursor structure followed by dimerization after triplet excitation. These mechanisms are generalizable to other metal-enriched QD surfaces that have a similar surface structure as that of CdSe, such as InSe or CdTe. Design principles for anti diastereomer derivatives are also discussed.

Domain Separated Density Functional Theory for Reaction Energy Barriers and Optical Excitations.

We recently proposed domain separated density functional theory (DS-DFT), a framework that allows for the combination of different levels of theory for the computation of the electronic structure of molecules. This work discusses the application of DS-DFT to the computation of transition-state energy barriers and optical absorption spectra. We considered several hydrogen abstraction reactions and optical spectra of molecule/metal cluster systems, including the absorption of individual species such as carbon monoxide, methane, and molecular hydrogen to a Li6 cluster. We present and discuss two domain-separated methods: (i), the screened-density approximation (SDA) and (ii) linearly weighted exchange (LWE). We find that SDA, which is applied as a hybridization based on atomic domains, could be useful to computing energy barriers, whereas LWE is suited for the analysis of electronic properties such as ground-state gaps, excitation energies, and oscillator strengths.

Light-responsive organic flashing electron ratchet.

Ratchets are nonequilibrium devices that produce directional motion of particles from nondirectional forces without using a bias, and are responsible for many types of biological transport, which occur with high yield despite strongly damped and noisy environments. Ratchets operate by breaking time-reversal and spatial symmetries in the direction of transport through application of a time-dependent potential with repeating, asymmetric features. This work demonstrates the ratcheting of electrons within a highly scattering organic bulk-heterojunction layer, and within a device architecture that enables the application of arbitrarily shaped oscillating electric potentials. Light is used to modulate the carrier density, which modifies the current with a nonmonotonic response predicted by theory. This system is driven with a single unbiased sine wave source, enabling the future use of natural oscillation sources such as electromagnetic radiation.

Quantum Interference and Substantial Property Tuning in Conjugated Z-ortho-Regio-Resistive Organic (ZORRO) Junctions.

Coherence is a significant factor in nanoscale electronic insulator technology and necessitates an understanding of the structure-property relationship between constructive and destructive quantum interference. This is particularly important in organic dielectric circuitry, which is the subject of this work. It is known that molecular wires composed of (i) meta-substituted phenylene rings, (ii) cross-conjugated double bonds (orthogonal to the molecular long axis), and (iii) single bonds can dramatically reduce electrical transmission. Here we add to these tools the use of an unexplored molecular shape to create strong and counterintuitive interference: a fully conjugated molecular wire with a structure that is forced back on itself in a Z shape, thereby exhibiting remarkably low conductance (G = 0.43 × 10-9 S) even though the phenylene arrangements are ortho- rather than meta-disposed. We call these Z-shaped molecules having ultralow conduction Z-ortho-regio-resistive organics (ZORROs). Here we analyze a series of ZORRO molecules and find them to have significant insulating properties in the coherent electron-transport regime due to interfering transmission pathways in the phenylene rings. Importantly, we find that both electron-withdrawing (fluorine) and electron-donating (methoxy) substituents enhance the transmission, which is not desirable. The former is due to the suppression of the destructive quantum interference at the F site, thereby enhancing the overall transmission, much like a Büttiker probe. The latter is due to a methoxy unit resonance additive effect, akin to oxygen doping, and positively contributes to the transmission. We then examine the effects of replacing the phenylene rings with 4,5- and 3,4-disubstituted thiophenes and how this ZORRO modification further reduces the transmission. An ultralow conductance of 0.13 × 10-9 S and a relatively high dielectric constant (εr) of ∼5 are predicted for the 3,4-thiophene ZORRO derivative, which closely resembles two cross-conjugated units, making it an intriguing candidate for a gate dielectric material.

Germanium Fluoride Nanocages as Optically Transparent n-Type Materials and Their Endohedral Metallofullerene Derivatives.

Carbon- and silicon-based n-type materials tend to suffer from instability of the corresponding radical anions. With DFT calculations, we explore a promising route to overcome such challenges with molecular nanocages which utilize the heavier element Ge. The addition of fluorine substituents creates large electron affinities in the range 2.5-5.5 eV and HOMO-LUMO gaps between 1.6 and 3.2 eV. The LUMOs envelop the surfaces of these structures, suggesting extensive delocalization of injected electrons, analogous to fullerene acceptors. Moreover, these Ge nF n inorganic cages are found to be transparent in the UV-visible region as probed with their excited states. Their capacitance, linear polarizabilities, and dielectric constants are computed and found to be on the same order of magnitude as saturated oligomers and some extended π-organics (azobenzenes). Furthermore, we explore fullerene-type endohedral isomers, i.e., cages with internal substituents or guest atoms, and find them to be more stable than the parent exohedral isomers by up to -206.45 kcal mol-1. We also consider the addition of Li, He, Cs, and Bi, to probe the utility of the exo/ endo cages as host-guest systems. The endohedral He/Li@F8@Ge60F52 cages are significantly more stable than their parent exohedral isomers He/Li@Ge60F52 by -182.46 and -49.22 kcal mol-1, respectively. The energy of formation of endohedral He@F8@Ge60F52 is exothermic by -10.4 kcal mol-1, while Cs and Bi guests are too large to be accommodated but are stable in the exohedral parent cages. Conceivable applications of these materials include n-type semiconductors and transparent electrodes, with potential for novel energy storage modalities.

Domain Separation in Density Functional Theory.

Research within density functional theory (DFT) has led to a large set of conceptual and computational methodologies to explore and understand the electronic structure of molecules and solids. Among the most commonly employed techniques in DFT are those of hybrid functionals, which are capable of producing accurate results for diverse properties, with notable exceptions. However, other techniques have been proposed to address limitations in the application of conventional hybrid functional techniques, especially to cases where a single reference is insufficient to achieve a proper description of the system of interest. In this paper we consider several previous developments in the field for the combination of local and nonlocal potentials and show that they can be formalized within the constrained-search Levy formalism, offering routes and ideas for the development of (nontraditional) density functionals, especially for treating strongly correlated regions of a molecule. The proposed formalism is centered around the idea of decomposing into domains the differential volume elements that are present in the definition of the electronic repulsion operator, which is contained in the electronic Hamiltonian, but this can also be applied to other operators as well. We show that the domain decomposition leads to a formulation that allows for the combination of different theories: DFT, correlated wave function theory, and Hartree-Fock, among others. This combination could accelerate the computation of electronic properties and allow for explicit inclusion, at the wave function level, of correlation effects, as in configuration-interaction theory. Our discussion covers both single- and multideterminantal methods. We demonstrate the approach through a simple application to the electronic structure of the methane and ethylene molecules, in which nonlocal exchange is applied to a given set of atoms, or domains, with the remaining atoms modeled with the local density approximation.

Charge transport network dynamics in molecular aggregates.

Due to the nonperiodic nature of charge transport in disordered systems, generating insight into static charge transport networks, as well as analyzing the network dynamics, can be challenging. Here, we apply time-dependent network analysis to scrutinize the charge transport networks of two representative molecular semiconductors: a rigid n-type molecule, perylenediimide, and a flexible p-type molecule, [Formula: see text] Simulations reveal the relevant timescale for local transfer integral decorrelation to be [Formula: see text]100 fs, which is shown to be faster than that of a crystalline morphology of the same molecule. Using a simple graph metric, global network changes are observed over timescales competitive with charge carrier lifetimes. These insights demonstrate that static charge transport networks are qualitatively inadequate, whereas average networks often overestimate network connectivity. Finally, a simple methodology for tracking dynamic charge transport properties is proposed.

Photoinduced Anomalous Coulomb Blockade and the Role of Triplet States in Electron Transport through an Irradiated Molecular Transistor.

In this study, we explore photoinduced electron transport through a molecule weakly coupled to two electrodes by combining first-principles quantum chemistry calculations with a Pauli master equation approach that accounts for many-electron states. In the incoherent limit, we demonstrate that energy-level alignment of triplet and charged states plays a crucial role, even when the rate of intersystem crossing is much smaller than the rate of fluorescence. Furthermore, the field intensity dependence and an upper bound to the photoinduced electric current can be analytically derived in our model. Under an optical field, the conductance spectra (charge stability diagrams) exhibit unusual Coulomb diamonds, which are associated with molecular excited states, and their widths can be expressed in terms of energies of the molecular electronic states. This study offers new directions for exploring optoelectronic response in nanoelectronics.

Detecting and Visualizing Reaction Intermediates of Anisotropic Nanoparticle Growth.

This paper describes a correlative approach to detect, visualize, and characterize intermediate species during a seedless, anisotropic nanoparticle synthesis. Changes in radical concentration as a function of time were correlated in situ to the optical properties and morphology of the particles. Depending on type and concentration of reaction precursors, either one or two increases in radical production occurred, corresponding to initial particle formation and increased branch length, respectively. Thus, changes in radical intensity can be considered as an indicator of nanoparticle structure and properties.

Photoinduced Plasmon-Driven Chemistry in trans-1,2-Bis(4-pyridyl)ethylene Gold Nanosphere Oligomers.

Continuous wave (CW) pump-probe surface-enhanced Raman spectroscopy (SERS) is used to examine a range of plasmon-driven chemical behavior in the molecular SERS signal of trans-1,2-bis(4-pyridyl)ethylene (BPE) adsorbed on individual Au nanosphere oligomers (viz., dimers, trimers, tetramers, etc.). Well-defined new transient modes are caused by high fluence CW pumping at 532 nm and are monitored on the seconds time scale using a low intensity CW probe field at 785 nm. Comparison of time-dependent density functional theory (TD-DFT) calculations with the experimental data leads to the conclusion that three independent chemical processes are operative: (1) plasmon-driven electron transfer to form the BPE anion radical; (2) BPE hopping between two adsorption sites; and (3) trans-to- cis-BPE isomerization. Resonance Raman and electron paramagnetic resonance (EPR) spectroscopy measurements provide further substantiation for the observation of an anion radical species formed via a plasmon-driven electron transfer reaction. Applications of these findings will greatly impact the design of novel plasmonic devices with the future ability to harness new and efficient energetic pathways for both chemical transformation and photocatalysis at the nanoscale level.

Benchmarking Semiempirical Methods To Compute Electrochemical Formal Potentials.

Computational methods to predict and tune electrochemical redox potentials are important for the development of energy technologies. Here, we benchmark several semiempirical models to compute reduction potentials of organic molecules, comparing approaches based on (1) energy differences between the S0 and one-electron-reduced D0 states of the isolated molecules and (2) an orbital energy shift approach based on tuning the charge-transfer triplet energy of the Ag20-molecule complex; the second model enables explicit modeling of electrode-molecule interactions. For molecules in solution, the two models yield nearly identical results. Both PM7 and PM6 predict formal potentials with only a slight loss of accuracy compared to standard density functional theory models, and the results are robust across several choices of geometries and implicit solvent models. PM6 and PM7 show dramatically improved accuracy over older semiempirical Hamiltonians (MNDO, AM1, PM3, and INDO/S). However, our recently developed INDO parameters model the electronic properties of our Ag20 model electrode much more accurately than does PM7. These results demonstrate the need for further development of semiempirical models to accurately model molecules on surfaces.

Locally coupled open subsystems: A formalism for affordable electronic structure calculations featuring fractional charges and size consistency.

This manuscript introduces a methodology (within the Born-Oppenheimer picture) to compute electronic ground-state properties of molecules and solids/surfaces with fractionally occupied components. Given a user-defined division of the molecule into subsystems, our theory uses an auxiliary global Hamiltonian that is defined as the sum of subsystem Hamiltonians, plus the spatial integral of a second-quantized local operator that allows the electrons to be transferred between subsystems. This electron transfer operator depends on a local potential that can be determined using density functional approximations and/or other techniques such as machine learning. The present framework employs superpositions of tensor-product wave functions, which can satisfy size consistency and avoid spurious fractional charges at large bond distances. The electronic population of each subsystem is in general a positive real number and is obtained from wave-function amplitudes, which are calculated by means of ground-state matrix diagonalization (or matrix propagation in the time-dependent case). Our method can provide pathways to explore charge-transfer effects in environments where dividing the molecule into subsystems is convenient and to develop computationally affordable electronic structure algorithms.

Hydrogenation of CO to Methanol on Ni(110) through Subsurface Hydrogen.

We present a combined theoretical and experimental study of CO hydrogenation on a Ni(110) surface, including studies of the role of gas-phase atomic hydrogen, surface hydrogen, and subsurface hydrogen reacting with adsorbed CO. Reaction mechanisms leading both to methane and methanol are considered. In the reaction involving surface or subsurface hydrogen, we investigate four possible pathways, using density functional theory to characterize the relative energetics of each intermediate, including the importance of further hydrogenation versus C-O bond breaking, where the latter may lead to methane production. The most energetically favorable outcome is the production of methanol along a pathway involving the sequential hydrogenation of CO to a H3CO* intermediate, followed by a final hydrogenation to give methanol. In addition, we find that subsurface hydrogen noticeably alters reaction barriers, both passively and through the energy released by diffusion to the surface. Indeed, the effective reaction barriers are even lower than for CO methanolation on Cu(211) and Cu(111) than for Ni(110). In studies of gas-phase H atoms impinging on a CO-adsorbed Ni(110) surface, Born-Oppenheimer molecular dynamics simulations show that direct impact of H is unlikely to result in hydrogenation of CO. This means that Eley-Rideal or hot-atom mechanisms are not important; thus, thermal reactions involving subsurface hydrogen are the primary reaction mechanisms leading to methanol. Finally, we demonstrate experimentally for the first time the production of methanol and formaldehyde from CO hydrogenation on Ni(110) and confirm the role of subsurface hydrogen in the mechanism of this reaction.

Exciton Absorption Spectra by Linear Response Methods: Application to Conjugated Polymers.

The theoretical description of the time-evolution of excitons requires, as an initial step, the calculation of their spectra, which has been inaccessible to most users due to the high computational scaling of conventional algorithms and accuracy issues caused by common density functionals. Previously (J. Chem. Phys. 2016, 144, 204105), we developed a simple method that resolves these issues. Our scheme is based on a two-step calculation in which a linear-response TDDFT calculation is used to generate orbitals perturbed by the excitonic state, and then a second linear-response TDDFT calculation is used to determine the spectrum of excitations relative to the excitonic state. Herein, we apply this theory to study near-infrared absorption spectra of excitons in oligomers of the ubiquitous conjugated polymers poly(3-hexylthiophene) (P3HT), poly(2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV), and poly(benzodithiophene-thieno[3,4-b]thiophene) (PTB7). For P3HT and MEH-PPV oligomers, the calculated intense absorption bands converge at the longest wavelengths for 10 monomer units, and show strong consistency with experimental measurements. The calculations confirm that the exciton spectral features in MEH-PPV overlap with those of the bipolaron formation. In addition, our calculations identify the exciton absorption bands in transient absorption spectra measured by our group for oligomers (1, 2, and 3 units) of PTB7. For all of the cases studied, we report the dominant orbital excitations contributing to the optically active excited state-excited state transitions, and suggest a simple rule to identify absorption peaks at the longest wavelengths. We suggest our methodology could be considered for further developments in theoretical transient spectroscopy to include nonadiabatic effects, coherences, and to describe the formation of species such as charge-transfer states and polaron pairs.

Spin-Selective Photoreduction of a Stable Radical within a Covalent Donor-Acceptor-Radical Triad.

Controlling spin-spin interactions in multispin molecular assemblies is important for developing new approaches to quantum information processing. In this work, a covalent electron donor-acceptor-radical triad is used to probe spin-selective reduction of the stable radical to its diamagnetic anion. The molecule consists of a perylene electron donor chromophore (D) bound to a pyromellitimide acceptor (A), which is, in turn, linked to a stable α,γ-bisdiphenylene-ß-phenylallyl radical (R•) to produce D-A-R•. Selective photoexcitation of D within D-A-R• results in ultrafast electron transfer to form the D+•-A-•-R• triradical, where D+•-A-• is a singlet spin-correlated radical pair (SCRP), in which both SCRP spins are uncorrelated relative to the R• spin. Subsequent ultrafast electron transfer within the triradical forms D+•-A-R-, but its yield is controlled by spin statistics of the uncorrelated A-•-R• radical pair, where the initial charge separation yields a 3:1 statistical mixture of D+•-3(A-•-R•) and D+•-1(A-•-R•), and subsequent reduction of R• only occurs in D+•-1(A-•-R•). These findings inform the design of multispin systems to transfer spin coherence between molecules targeting quantum information processing using the agency of SCRPs.