Maxim V. Ivanov

Energy Gap between the Poly-p-phenylene Bridge and Donor Groups Controls the Hole Delocalization in Donor–Bridge–Donor Wires

Poly-p-phenylene wires are critically important as charge-transfer materials in photovoltaics. A comparative analysis of a series of poly-p-phenylene (RPPn) wires, capped with isoalkyl (iAPPn), alkoxy (ROPPn), and dialkylamino (R2NPPn) groups, shows unexpected evolution of oxidation potentials, i.e., decrease (-260 mV) for iAPPn, while increase for ROPPn (+100 mV) and R2NPPn (+350 mV) with increasing number of p-phenylenes. Moreover, redox/optical properties and DFT calculations of R2NPPn/R2NPPn+• further show that the symmetric bell-shaped hole distribution distorts and shifts toward one end of the molecule with only 4 p-phenylenes in R2NPPn+•, while shifting of the hole occurs with 6 and 8 p-phenylenes in ROPPn+• and iAPPn+•, respectively. Availability of accurate experimental data on highly electron-rich dialkylamino-capped R2NPPn together with ROPPn and iAPPn allowed us to demonstrate, using our recently developed Marcus-based multistate model (MSM), that an increase of oxidation potentials in R2NPPn arises due to an interplay between the electronic coupling (Hab) and energy difference between the end-capped groups and bridging phenylenes (Δε). A comparison of the three series of RPPn with varied Δε further demonstrates that decrease/increase/no change in oxidation energies of RPPn can be predicted based on the energy gap Δε and coupling Hab, i.e., decrease if Δε < Hab (i.e., iAPPn), increase if Δε > Hab (i.e., R2NPPn), and minimal change if Δε ≈ Hab (i.e., ROPPn). MSM also reproduces the switching of the nature of electronic transition in higher homologues of R2NPPn+• (n ≥ 4). These findings will aid in the development of improved models for charge-transfer dynamics in donor-bridge-acceptor systems.

First Experimental Evidence for the Diverse Requirements of Excimer vs Hole Stabilization in π-Stacked Assemblies

Exciton formation and charge separation and transport are key dynamical events in a variety of functional polymeric materials and biological systems, including DNA. Beyond the necessary cofacial approach of a pair of aromatic molecules at van der Waals contact, the extent of overlap and necessary geometrical reorganization for optimal stabilization of an excimer vs dimer cation radical remain unresolved. Here, we compare experimentally the dynamics of excimer formation (via emission) and charge stabilization (via threshold ionization) of a novel covalently linked, cofacially stacked fluorene dimer (F2) with the unlinked van der Waals dimer of fluorene, that is, (F)2. Although the measured ionization potentials are identical, the excimeric state is stabilized by up to ∼30 kJ/mol in covalently linked F2. Supported by theory, this work demonstrates for the first time experimentally that optimal stabilization of an excimer requires a perfect sandwich-like geometry with maximal overlap, whereas hole stabilization in π-stacked aggregates is less geometrically restrictive.

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields.

Two’s Company, Three’s a Crowd: Exciton Localization in Cofacially Arrayed Polyfluorenes

Understanding the mechanisms of long-range energy transfer through polychromophoric assemblies is critically important in photovoltaics and biochemical systems. Using a set of cofacially arrayed polyfluorenes (Fn), we investigate the mechanism of (singlet) exciton delocalization in π-stacked polychromophoric assemblies. Calculations reveal that effective stabilization of an excimeric state requires an ideal sandwich-like arrangement; yet surprisingly, emission spectroscopy indicates that exciton delocalization is limited to only two fluorene units for all n. Herein, we show that delocalization is determined by the interplay between the energetic gain from delocalization, which quickly saturates beyond two units in larger Fn, and an energetic penalty associated with structural reorganization, which increases linearly with n. With these insights, we propose a hopping mechanism for exciton transfer, based upon the presence of multiple excimeric tautomers of similar energy in larger polyfluorenes (n ≥ 4) together with the anticipated low thermal barrier of their interconversion.

Strength of π-Stacking, from Neutral to Cation: Precision Measurement of Binding Energies in an Isolated π-Stacked Dimer

π-Stacking interactions are ubiquitious across chemistry and biochemistry, impacting areas from organic materials and photovoltaics to biochemistry and DNA. However, experimental data is lacking regarding the strength of π-stacking forces-an issue not settled even for the simplest model system, the isolated benzene dimer. Here, we use two-color appearance potential measurements to determine the binding energies of the isolated, π-stacked dimer of fluorene (C13H10) in ground, excited, and ionic states. Our measurements provide the first precise values for π-stacking interaction energies in these states, which are key benchmarks for theory. Indeed, theoretical predictions using ab initio and carefully benchmarked DFT methods are in excellent agreement with experiment.

Poly-p-hydroquinone Ethers: Isoenergetic Molecular Wires with Length-Invariant Oxidation Potentials and Cation Radical Excitation Energies

Typical poly-p-phenylene wires are characterized by strong interchromophoric electronic coupling with redox and optical properties being highly length-dependent. Herein we show that an incorporation of a pair of para-methoxy groups at each p-phenylene unit in poly-p-phenylene wires (i.e., PHEn) changes the nodal structure of HOMO that leads to length-invariant oxidation potentials and cation radical excitation energies. As such, PHEn represents a unique class of isoenergetic wires where hole delocalization mainly occurs via dynamic hopping and thus may serve as an efficient medium for long-range charge transfer. Availability of these wires will allow demonstration of long-range electron transfer via incoherent hopping using donor-bridge-acceptor systems with isoenergetic PHEn-based wires as bridges.

Cofacially Arrayed Polyfluorenes: Spontaneous Formation of π-Stacked Assemblies in the Gas Phase

Understanding geometrical and size dependencies of through-space charge delocalization in multichromophoric systems is critical to model electron transfer and transport in materials and biomolecules. In this work, we examine the size evolution of hole delocalization in van der Waals clusters of fluorene (i.e., (F)n), where a range of geometries are possible, reflecting both π-stacking and C-H/π interactions. Using mass-selected two-color resonant two-photon ionization spectroscopy (2CR2PI), we measure electronic spectra and vertical ionization potentials (IPs) in the gas phase. Results are compared with model covalently linked assemblies (denoted Fn), exhibiting a sterically enforced cofacial (i.e., π-stacked) orientation of chromophores. For both systems, an inverse size dependence (i.e., 1/n) of IP vs cluster size is found. Surprisingly, the values for the two sets fall on the same line! This trend is examined via theory, which emphasizes the important role of π-stacking, and its geometrical dependencies, in the process of hole delocalization in multichromophoric assemblies.

When Substituents Do Not Matter: Frontier Orbitals Explain the Unusually High and Invariant Oxidation Potential in Alkoxy-, Alkyl-, and H-Substituted Iptycenes

Frontier molecular orbitals (FMOs) have played a critical role in predicting reactivity/selectivity of pericyclic reactions. Here we show that the structurally similar iptycene-based hydroquinone ether (HE), that is, MeOIpt and BOHE/BHHE, molecules have drastically different ordering of bisallylic and quinoidal FMOs. They are almost degenerate in BOHE/BHHE, while in MeOIpt, the bisallylic orbital lies far below the quinoidal HOMO. Oxidation of BOHE/BHHE induces coplanarization of the methoxy group and destabilizes the bisallylic HOMO, leading to a relatively low oxidation potential. In MeOIpt, considerable energy must be invested in coplanarization of the methoxy group to bring about orbital swapping, resulting in an oxidation potential higher than that in structurally similar BOHE/BHHE. As the quinoidal HOMO density does not extend to the substituent-bearing carbon in H-, alkyl-, and alkoxy-substituted iptycenes, their redox potentials remain invariant. This case study involving a simple visual inspection of the nodal arrangement as well as energetics of the FMOs and Walsh analysis could serve as a tool for the design of organic molecules with a desired redox potential.

The Role of Torsional Dynamics on Hole and Exciton Stabilization in π‐Stacked Assemblies: Design of Rigid Torsionomers of a Cofacial Bifluorene

Exciton and charge delocalization across π-stacked assemblies is of importance in biological systems and functional polymeric materials. To examine the requirements for exciton and hole stabilization, cofacial bifluorene (F2) torsionomers were designed, synthesized, and characterized: unhindered (model) Me F2, sterically hindered tBu F2, and cyclophane-like C F2, where fluorenes are locked in a perfect sandwich orientation via two methylene linkers. This set of bichromophores with varied torsional rigidity and orbital overlap shows that exciton stabilization requires a perfect sandwich-like arrangement, as seen by strong excimeric-like emission only in C F2 and Me F2. In contrast, hole delocalization is less geometrically restrictive and occurs even in sterically hindered tBu F2, as judged by 160 mV hole stabilization and a near-IR band in the spectrum of its cation radical. These findings underscore the diverse requirements for charge and energy delocalization across π-stacked assemblies.

Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

Atom-centered point charge (PC) model of the molecular electrostatics-a major workhorse of the atomistic biomolecular simulations-is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field.