Nonadiabatic Excited-state Molecular Dynamics Research Articles

Electronic Couplings versus Thermal Fluctuations in the Internal Conversion of Perylene Diimides: The Battle to Localize the Exciton.

Energy transfer processes among units of light-harvesting homo-oligomers impact the efficiency of these materials as components in organic optoelectronic devices such as solar cells. Perylene diimide (PDI), a prototypical dye, features exceptional light absorption and highly tunable optical and electronic properties. These properties can be modulated by varying the number of PDI units and linkers between them. Herein, atomistic nonadiabatic excited state molecular dynamics is used to explore the energy transfer during the internal conversion of acetylene and diacetylene bridged dimeric and trimeric PDIs. Our simulations reveal a significant impact of the bridge type on the transient exciton localization/delocalization between units of PDI dimers. After electronic relaxation, larger exciton delocalization occurs in the PDI dimer connected by the diacetylene bridge with respect to the one connected by the shorter acetylene bridge. These changes can be rationalized by the Frenkel exciton model. We outline a technique for deriving parameters for this model using inputs provided by nonadiabatic dynamics simulations. Frenkel exciton description reveals an interplay between the relative strengths of the diagonal and off-diagonal disorders. Moreover, atomistic simulations and the Frenkel exciton model of the PDI trimer systems corroborate in detail the localization properties of the exciton on the molecular units during the internal conversion to the lowest-energy excited state when the units become effectively decoupled. Overall, atomistic nonadiabatic simulations in combination with the Frenkel exciton model can serve as a predictive framework for analyzing and predicting desired exciton traps in PDI-based oligomers designed for organic electronics and photonic devices.

Non-adiabatic excited-state time-dependent GW molecular dynamics (TDGW) satisfying extended Koopmans' theorem: An accurate description of methane photolysis.

There is a longstanding difficulty that time-dependent density functional theory relying on adiabatic local density approximation is not applicable to the electron dynamics, for example, for an initially excited state, such as in photochemical reactions. To overcome this, we develop non-adiabatic excited-state time-dependent GW molecular dynamics (TDGW) on the basis of the extended quasiparticle theory. Replacing Kohn-Sham orbitals/energies with correlated, interacting quasiparticle orbitals/energies allows the full correspondence to the excited-state surfaces and corresponding total energies, with satisfying extended Koopmans' theorem. We demonstrate the power of TDGW using methane photolysis, CH4→CH3•+H, an important initiation reaction for combustion/pyrolysis and hydrogen production of methane. We successfully explore several possible pathways and show how this reaction dynamics is captured accurately through simultaneously time-tracing all quasiparticle levels. TDGW scales as O(NB3-4), where NB is the number of basis functions, which is distinctly advantageous to performing dynamics using configuration interaction and coupled cluster methods.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Vibrational Funnels for Energy Transfer in Organic Chromophores

Photoinduced intramolecular energy transfers in multichromophoric molecules involve nonadiabatic vibronic channels that act as energy transfer funnels. They commonly take place through specific directions of motion dictated by the nonadiabatic coupling vectors. Vibrational funnels may support persistent coherences between electronic states and sometimes delineate the presence of minor alternative energy transfer pathways. The ultimate confirmation of their role on the interchromophoric energy transfer can be achieved by performing nonadiabatic excited-state molecular dynamics simulations by selectively freezing the nuclear motions in question. Our results point out this strategy as a useful tool to identify and evaluate the impact of these vibrational funnels on the energy transfer processes and guide the in silico design of materials with tunable properties and enhanced functionalities. Our work encourages applications of this methodology to different chemical and biochemical processes such as reactive scattering and protein conformational changes, to name a few.

Infinitene: Computational Insights from Nonadiabatic Excited State Dynamics.

Progress in organic synthesis opens exploration of a rich diversity of molecules with interesting new structural topologies. This is the case of a recently synthesized helically twisted figure-eight molecule coined infinitene. The molecule belongs to a numerous family of looped polyarenes, where the degree of π-conjugation is controlled by high strain energies and steric hindrances. A particular balance of these ingredients leads to unusual optoelectronic properties potentially suitable for a range of applications in nanoelectronics and photonics. Due to its recent discovery, the photophysical properties of infinitene remain unexplored. In this Letter, atomistic nonadiabatic excited state molecular dynamics modeling unveils unique features of intramolecular electronic and vibrational energy relaxation and redistribution that take place after molecular photoexcitation. Our results detail relationships between optical and electronic properties providing useful knowledge for future molecular designs related to infinitene.

Adiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation.

We present a method to link the Nonadiabatic EXcited-state Molecular Dynamics (NEXMD) package to the SANDER package supplied by AMBERTOOLS to provide excited-state adiabatic quantum mechanics/molecular mechanics (QM/MM) simulations. NEXMD is a computational package particularly developed to perform simulations of the photoexcitation and subsequent nonadiabatic electronic and vibrational energy relaxation in large multichromophoric conjugated molecules involving several coupled electronic excited states. The NEXMD-SANDER exchange has been optimized in order to achieve excited-state adiabatic dynamics simulations of large conjugated materials in a QM/MM environment, such as an explicit solvent. Dynamics of a substituted polyphenylene vinylene oligomer (PPV3-NO2) in vacuum and different explicit solvents has been used as a test case by performing comparative analysis of changes in its optical spectrum, state-dependent conformational changes, and quantum bond orderings. The method has been tested and compared with respect to previous implicit solvent implementations. Also, the impact on the expansion of the QM region by including a variable number of solvent molecules has been analyzed. Altogether, these results encourage future implementations of NEXMD simulations using the same combination of methods.

Nonadiabatic molecular dynamics simulations based on time-dependent density functional tight-binding method.

Nonadiabatic excited state molecular dynamics underpin many photophysical and photochemical phenomena, such as exciton dynamics, and charge separation and transport. In this work, we present an efficient nonadiabatic molecular dynamics (NAMD) simulation method based on time-dependent density functional tight-binding (TDDFTB) theory. Specifically, the adiabatic electronic structure, an essential NAMD input, is described at the TDDFTB level. The nonadiabatic effects originating from the coupled motions of electrons and nuclei are treated by the trajectory surface hopping algorithm. To improve the computational efficiency, nonadiabatic couplings between excited states within the TDDFTB method are derived and implemented using an analytical approach. Furthermore, the time-dependent nonadiabatic coupling scalars are calculated based on the overlap between molecular orbitals rather than the Slater determinants to speed up the simulations. In addition, the electronic decoherence scheme and a state reassigned unavoided crossings algorithm, which has been implemented in the NEXMD software, are used to improve the accuracy of the simulated dynamics and handle trivial unavoided crossings. Finally, the photoinduced nonadiabatic dynamics of a benzene molecule are simulated to demonstrate our implementation. The results for excited state NAMD simulations of benzene molecule based on TDDFTB method compare well to those obtained with numerically expensive time-dependent density functional theory. The proposed methodology provides an attractive theoretical simulation tool for predicting the photophysical and photochemical properties of complex materials.

Vibrations Responsible for Luminescence from HJ-Aggregates of Conjugated Polymers Identified by Cryogenic Spectroscopy of Single Nanoparticles.

A single polymer chain can be thought of as a covalently bound J-aggregate, where the microscopic transition-dipole moments line up to emit in phase. Packing polymer chains into a bulk film can result in the opposite effect, inducing H-type coupling between chains. Cofacial transition-dipole moments oscillate out of phase, canceling each other out, so that the lowest-energy excited state turns dark. H-aggregates of conjugated polymers can, in principle, be coaxed into emitting light by mixing purely electronic and vibronic transitions. However, it is challenging to characterize this electron-phonon coupling experimentally. In a bulk film, many different conformations exist with varying degrees of intrachain J-type and interchain H-type coupling strengths, giving rise to broad and featureless aggregate absorption and emission spectra. Even if single nanoparticles consisting of only a few single chains are grown in a controlled fashion, the luminescence spectra remain broad, owing to the underlying molecular dynamics and structural heterogeneity at room temperature. At cryogenic temperatures, emission from H-type aggregates should be suppressed because, in the absence of thermal energy, internal conversion drives the aggregate to the lowest-energy dark state. At the same time, electronic and vibronic transitions narrow substantially, facilitating the attribution of spectral signatures to distinct vibrational modes. We demonstrate how to distinguish signatures of interchain H-type aggregate species from those of intramolecular J-type coupling. Whereas all dominant vibronic modes revealed in the photoluminescence (PL) and surface-enhanced resonance Raman scattering spectra of a single chromophore within a single polymer chain are identified in the J-type aggregate luminescence spectra, they are not all present at once in the H-type spectra. Universal spectral features are found for the luminescence from strongly HJ-coupled chains, clearly resolving the vibrations responsible for the nonadiabatic excited-state molecular dynamics that enable light emission. We discuss the possible combinations of vibrational modes responsible for H-type aggregate PL and demonstrate that only one, mainly the lowest energy one, of the three dominant vibrational modes contributes to the 0-1 transition, whereas combinations of all three are found in the 0-2 transition. From this analysis, we can distinguish between energy shifts due to either J-type intrachain coupling or H-type interchain interactions, offering a means to directly discriminate between structural and energetic disorder.

Vibronic Photoexcitation Dynamics of Perylene Diimide: Computational Insights.

Perylene diimide (PDI) represents a prototype material for organic optoelectronic devices because of its strong optical absorbance, chemical stability, efficient energy transfer, and optical and chemical tunability. Herein, we analyze in detail the vibronic relaxation of its photoexcitation using nonadiabatic excited-state molecular dynamics simulations. We find that after the absorption of a photon, which excites the electron to the second excited state, S2, induced vibronic dynamics features persistent modulations in the spatial localization of electronic and vibrational excitations. These energy exchanges are dictated by strong vibronic couplings that overcome structural disorders and thermal fluctuations. Specifically, the electronic wavefunction periodically swaps between localizations on the right and left sides of the molecule. Within 1 ps of such dynamics, a nonradiative transition to the lowest electronic state, S1, takes place, resulting in a complete delocalization of the wavefunction. The observed vibronic dynamics emerges following the electronic energy deposition in the direction that excites a combination of two dominant vibrational normal modes. This behavior is maintained even with a chemical substitution that breaks the symmetry of the molecule. We believe that our findings elucidate the nature of the complex dynamics of the optically excited states and, therefore, contribute to the development of tunable functionalities of PDIs and their derivatives.

Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals

The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals. The nitrogencentered system ensures strong interchromophore interactions and, thus, the presence of coherences. Nevertheless, the multitude of non-deterministic photoinduced pathways during the ultrafast inter-branch migration of the excitation results in random confinement on some branches and, therefore, spatial exciton scrambling and loss of phase information at long times. We show that the vibronic coherence dynamics evolving into the incoherent scrambling mechanism on ultrafast 50 fs timescale, is accurately probed by the TRUECARS X-ray stimulated Raman signal. In combination with previous results, where the technique has revealed long-lived coherences in a rigid heterodimer, the signal is most valuable for detecting ultrafast molecular coherences or their absence. We demonstrate that X-ray Raman spectroscopy is a useful tool in the chemical design of functional molecular building blocks.

Back-and-Forth Energy Transfer during Electronic Relaxation in a Chlorin–Perylene Dyad

Donor-acceptor dyads represent a practical approach to tuning the photophysical properties of linear conjugated polymers in materials chemistry. Depending on the absorption wavelength, the acceptor and donor roles can be interchanged, and as such, the directionality of the energy transfer can be controlled. Herein, nonadiabatic excited state molecular dynamics simulations have been performed in an arylethylene-linked perylene-chlorin dyad. After an initial photoexcitation at the Soret band of chlorin, we observe an ultrafast sequential electronic relaxation to the lowest excited state. This process is accomplished through an efficient round-trip chlorin-to-perylene-to-chlorin energy transfer. It is characterized by successive intermittent localized and delocalized vibronic dynamics. Nonradiative relaxation takes place mainly through energy transfer events with perylene acting as a "heat sink" through which the nonradiative relaxation is efficiently funneled, and the excess energy is dispersed in a larger space of vibrational degrees of freedom. Thus, our findings suggest the use of donor-acceptor dyads as a useful strategy when one needs to deactivate an electronic excitation.

Excitation Energy Transfer between bodipy Dyes in a Symmetric Molecular Excitonic Seesaw.

We examine the redistribution of energy between electronic and vibrational degrees of freedom that takes place between a π-conjugated oligomer, a phenylene-butadiynylene, and two identical boron-dipyrromethene (bodipy) end-caps using femtosecond transient absorption spectroscopy, single-molecule spectroscopy, and nonadiabatic excited-state molecular dynamics (NEXMD) modeling techniques. The molecular structure represents an excitonic seesaw in that the excitation energy on the oligomer backbone can migrate to either one end-cap or the other, but not to both. The NEXMD simulations closely reproduce the characteristic time scale for redistribution of electronic and vibrational energy of 2.2 ps and uncover the vibrational modes contributing to the intramolecular relaxation. The calculations indicate that the dihedral angle between the bodipy dye and the oligomer change upon excitation of the oligomer. Single-molecule experiments reveal a difference in photoluminescence lifetime of the bodipy dyes depending on whether they are excited by direct absorption or by redistribution of energy from the backbone. This difference in lifetime may be attributed to the difference in dihedral angle. The simulations also suggest that a strong coupling can occur between the two end-caps, giving rise to a reversible shuttling of excitation energy between them. Strong coupling should lead to a pronounced loss in polarization memory of the fluorescence since the oligomer backbone tends to be slightly distorted and the two bodipy transition dipoles have different orientations. A sensitive single-molecule technique is presented to test for such coupling. However, although redistribution of electronic and vibrational energy between the end-caps can occur, it appears to be unidirectional and irreversible, suggesting that an additional localization mechanism is at play which is, as yet, not fully accounted for in the simulations.

Photoinduced Energy Transfer in Linear Guest-Host Chromophores: A Computational Study.

Polymer-based guest-host systems represent a promising class of materials for efficient light-emitting diodes. The energy transfer from the polymer host to the guest is the key process in light generation. Therefore, microscopic descriptions of the different mechanisms involved in the energy transfer can contribute to enlighten the basis of the highly efficient light harvesting observed in this kind of materials. Herein, the nature of intramolecular energy transfer in a dye-end-capped conjugated polymer is explored by using atomistic nonadiabatic excited-state molecular dynamics. Linear perylene end-capped (PEC) polyindenofluorenes (PIF), consisting of n (n = 2, 4, and 6) repeat units, i.e., PEC-PIFn oligomers, are considered as model systems. After photoexcitation at the oligomer absorption maximum, an initial exciton becomes self-trapped on one of the monomer units (donors). Thereafter, an efficient ultrafast through-space energy transfer from this unit to the perylene acceptor takes place. We observe that this energy transfer occurs equally well from any monomer unit on the chain. Effective specific vibronic couplings between each monomer and the acceptor are identified. These oligomer → end-cap energy transfer steps do not match with the rates predicted by Förster-type energy transfer. The through-space and through-bond mechanisms are two distinct channels of energy transfer. The former dominates the overall process, whereas the through-bond energy transfer between indenofluorene monomer units along the oligomer backbone only makes a minor contribution.

Improved algorithm for the direct dynamics variational multi-configurational Gaussian method.

The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations.

Exciton Spatial Dynamics and Self-Trapping in Carbon Nanocages.

Three-dimensional cage-shaped molecules formed from chainlike structures hold potential as unique optoelectronic materials and host compounds. Their optical, structural, and dynamical features are tunable by changes in shape and size. We perform a comparison of these properties for three sizes of strained conjugated [n.n.n]carbon nanocages composed of three paraphenylene chains (bridges) of length n = 4, 5, or 6. The exciton intramolecular redistribution occurring during nonradiative relaxation has been explored using nonadiabatic excited-state molecular dynamics. Our results provide atomistic insight into the conformational features associated with the observed red- and blue-shift trends in the absorption and fluorescence spectra, respectively, with increasing nanocage size. Their internal conversion processes involve intramolecular energy transfer that leads to exciton self-trapping on a few phenylene units at the center of a single bridge. The dependence of these dynamical features on the size of the nanocage can be used to tune their host-guest chemical properties and their use for organic electronics and catenane-like applications.

Photoinduced Dynamics with Constrained Vibrational Motion: FrozeNM Algorithm.

Ab initio molecular dynamics (AIMD) simulation, analyzed in terms of vibrational normal modes, is a widely used technique that facilitates understanding of complex structural motions and coupling between electronic and nuclear degrees of freedom. Usually, only a subset of vibrations is directly involved in the process of interest. The impact of these vibrations can be evaluated by performing AIMD simulations by selectively freezing certain motions. Herein, we present frozen normal mode (FrozeNM), a new algorithm to apply normal-mode constraints in AIMD simulations, as implemented in the nonadiabatic excited state molecular dynamics code. We further illustrate its capacity by analyzing the impact of normal-mode constraints on the photoinduced energy transfer between polyphenylene ethynylene dendrimer building blocks. Our results show that the electronic relaxation can be significantly slowed down by freezing a well-selected small subset of active normal modes characterized by their contributions in the direction of energy transfer. The application of these constraints reduces the nonadiabatic coupling between electronic excited states during the entire dynamical simulations. Furthermore, we validate reduced dimensionality models by freezing all the vibrations, except a few active modes. Altogether, we consider FrozeNM as a useful tool that can be broadly used to underpin the role of vibrational motion in a studied process and to formulate reduced models that describe essential physical phenomena.

NEXMD Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present a versatile new code released for open community use, the nonadiabatic excited state molecular dynamics (NEXMD) package. This software aims to simulate nonadiabatic excited state molecular dynamics using several semiempirical Hamiltonian models. To model such dynamics of a molecular system, the NEXMD uses the fewest-switches surface hopping algorithm, where the probability of transition from one state to another depends on the strength of the derivative nonadiabatic coupling. In addition, there are a number of algorithmic improvements such as empirical decoherence corrections and tracking trivial crossings of electronic states. While the primary intent behind the NEXMD was to simulate nonadiabatic molecular dynamics, the code can also perform geometry optimizations, adiabatic excited state dynamics, and single-point calculations all in vacuum or in a simulated solvent. In this report, first, we lay out the basic theoretical framework underlying the code. Then we present the code's structure and workflow. To demonstrate the functionality of NEXMD in detail, we analyze the photoexcited dynamics of a polyphenylene ethynylene dendrimer (PPE, C30H18) in vacuum and in a continuum solvent. Furthermore, the PPE molecule example serves to highlight the utility of the getexcited.py helper script to form a streamlined workflow. This script, provided with the package, can both set up NEXMD calculations and analyze the results, including, but not limited to, collecting populations, generating an average optical spectrum, and restarting unfinished calculations.

Electronic Energy Relaxation in a Photoexcited Fully Fused Edge-Sharing Carbon Nanobelt.

Carbon nanobelts are cylindrical molecules composed of fully fused edge-sharing arene rings. Because of their aesthetically appealing structures, they acquire unusual optoelectronic properties that are potentially suitable for a range of applications in nanoelectronics and photonics. Nevertheless, the very limited success of their synthesis has led to their photophysical properties remaining largely unknown. Compared to that of carbon nanorings (arenes linked by single bonds), the strong structural rigidity of nanobelts prevents significant deformations away from the original high-symmetry conformation and, therefore, impacts their photophysical properties. Herein, we study the photoinduced dynamics of a successfully synthesized belt segment of (6,6)CNT (carbon nanotube). Modeling this process with nonadiabatic excited state molecular dynamics simulations uncovers the critical role played by the changes in excited state wave function localization on the different types of carbon atoms. This allows a detailed description of the excited state dynamics and spatial exciton evolution throughout the nanobelt scaffold. Our results provide detailed information about the excited state electronic properties and internal conversion rates that is potentially useful for designing nanobelts for nanoelectronic and photonic applications.

Vibronic Quantum Beating between Electronic Excited States in a Heterodimer.

Energy transfer in multichromophoric molecules can be affected by coherences that are induced by the electronic and vibrational couplings between chromophore units. Coherent electron-vibrational dynamics can persist at the subpicosecond time scale even at room temperature. Furthermore, wave-like localized-delocalized motions of the electronic wave function can be modulated by vibrations that actively participate in the intermolecular energy transfer process. Herein, nonadiabatic excited state molecular dynamics simulations have been performed on a rigid synthetic heterodimer that has been proposed as a simplified model for investigating the role and mechanism of coherent energy transfer in multichromophoric systems. Both surface hopping (SH) and Ehrenfest approaches (EHR) have been considered. After photoexcitation of the system at room temperature, EHR simulations reveal an ultrafast beating of electronic populations between the two lowest electronic states. These oscillations are not observed at low temperature and have vibrational origins. Furthermore, they cannot be reproduced using SH approach. This periodic behavior of electronic populations induces oscillations in the spatial localization of the electronic transition density between monomers. Vibrations whose frequencies are near-resonant with energy difference between the two lowest electronic excited states are in the range of the electronic population beating, and they are the ones that contribute the most to the coherent dynamics of these electronic transitions.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials.

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.