Overcoming positivity violations for density matrices in surface hopping.

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question of how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity while yielding improved accuracy throughout much (but not all) of parameter space.

Molecular versus Excitonic Disorder in Individual Artificial Light-Harvesting Systems.

Natural light-harvesting antennae employ a dense array of chromophores to optimize energy transport via the formation of delocalized excited states (excitons), which are critically sensitive to spatio-energetic variations of the molecular structure. Identifying the origin and impact of such variations is highly desirable for understanding and predicting functional properties yet hard to achieve due to averaging of many overlapping responses from individual systems. Here, we overcome this problem by measuring the heterogeneity of synthetic analogues of natural antennae-self-assembled molecular nanotubes-by two complementary approaches: single-nanotube photoluminescence spectroscopy and ultrafast 2D correlation. We demonstrate remarkable homogeneity of the nanotube ensemble and reveal that ultrafast (∼50 fs) modulation of the exciton frequencies governs spectral broadening. Using multiscale exciton modeling, we show that the dominance of homogeneous broadening at the exciton level results from exchange narrowing of strong static disorder found for individual molecules within the nanotube. The detailed characterization of static and dynamic disorder at the exciton as well as the molecular level presented here opens new avenues in analyzing and predicting dynamic exciton properties, such as excitation energy transport.

Exciton localization in tubular molecular aggregates: Size effects and optical response.

We study the exciton localization and resulting optical response for disordered tubular aggregates of optically active molecules. It has previously been shown that such tubular structures allow for excitons delocalized over more than a thousand molecules, owing to the combined effects of long-range dipole-dipole interactions and the higher-dimensional (not truly one-dimensional) nature of the aggregate. Such large delocalization sizes prompt the question to what extent in experimental systems the delocalization may still be determined by the aggregate size (diameter and length) and how this affects the aggregate's optical response and dynamics. We perform a systematic study of the size effects on the localization properties using numerical simulations of the exciton states in a cylindrical model structure inspired by the previously derived geometry of a cylindrical aggregate of cyanine dye molecules (C8S3). To characterize the exciton localization, we calculate the participation ratio and the autocorrelation function of the exciton wave function. We also calculate the density of states and absorption spectrum. We find strong effects of the tube's radius on the localization and optical properties in the range of parameters relevant to the experiment. In addition, surprisingly, we find that even for tubes as long as 750 nm, the localization size is limited by the tube's length for disorder values that are relevant to experimental circumstances, while observable effects of the tube's length in the absorption spectrum still occur for tube lengths up to about 150 nm. The latter may explain the changes in the optical spectra observed during the aging process of bromine-substituted C8S3 aggregates. For weak disorder, the exciton wave functions exhibit a scattered, fractal-like nature, similar to the quasi-particles in two-dimensional disordered systems.

Multiscale modeling of molecular structure and optical properties of complex supramolecular aggregates.

Supramolecular aggregates of synthetic dye molecules offer great perspectives to prepare biomimetic functional materials for light-harvesting and energy transport. The design is complicated by the fact that structure-property relationships are hard to establish, because the molecular packing results from a delicate balance of interactions and the excitonic properties that dictate the optics and excited state dynamics, in turn sensitively depend on this packing. Here we show how an iterative multiscale approach combining molecular dynamics and quantum mechanical exciton modeling can be used to obtain accurate insight into the packing of thousands of cyanine dye molecules in a complex double-walled tubular aggregate in close interaction with its solvent environment. Our approach allows us to answer open questions not only on the structure of these prototypical aggregates, but also about their molecular-scale structural and energetic heterogeneity, as well as on the microscopic origin of their photophysical properties. This opens the route to accurate predictions of energy transport and other functional properties.

Direct knock-on of desolvated ions governs strict ion selectivity in K+ channels.

The seeming contradiction that K+ channels conduct K+ ions at maximal throughput rates while not permeating slightly smaller Na+ ions has perplexed scientists for decades. Although numerous models have addressed selective permeation in K+ channels, the combination of conduction efficiency and ion selectivity has not yet been linked through a unified functional model. Here, we investigate the mechanism of ion selectivity through atomistic simulations totalling more than 400 µs in length, which include over 7,000 permeation events. Together with free-energy calculations, our simulations show that both rapid permeation of K+ and ion selectivity are ultimately based on a single principle: the direct knock-on of completely desolvated ions in the channels' selectivity filter. Herein, the strong interactions between multiple 'naked' ions in the four filter binding sites give rise to a natural exclusion of any competing ions. Our results are in excellent agreement with experimental selectivity data, measured ion interaction energies and recent two-dimensional infrared spectra of filter ion configurations.

Structural and Spectroscopic Properties of Assemblies of Self-Replicating Peptide Macrocycles.

Self-replication at the molecular level is often seen as essential to the early origins of life. Recently a mechanism of self-replication has been discovered in which replicator self-assembly drives the process. We have studied one of the examples of such self-assembling self-replicating molecules to a high level of structural detail using a combination of computational and spectroscopic techniques. Molecular Dynamics simulations of self-assembled stacks of peptide-derived replicators provide insights into the structural characteristics of the system and serve as the basis for semiempirical calculations of the UV-vis, circular dichroism (CD) and infrared (IR) absorption spectra that reflect the chiral organization and peptide secondary structure of the stacks. Two proposed structural models are tested by comparing calculated spectra to experimental data from electron microscopy, CD and IR spectroscopy, resulting in a better insight into the specific supramolecular interactions that lead to self-replication. Specifically, we find a cooperative self-assembly process in which ß-sheet formation leads to well-organized structures, while also the aromatic core of the macrocycles plays an important role in the stability of the resulting fibers.

Steering Self-Assembly of Amphiphilic Molecular Nanostructures via Halogen Exchange.

In the field of self-assembly, the quest for gaining control over the supramolecular architecture without affecting the functionality of the individual molecular building blocks is intrinsically challenging. By using a combination of synthetic chemistry, cryogenic transmission electron microscopy, optical absorption measurements, and exciton theory, we demonstrate that halogen exchange in carbocyanine dye molecules allows for fine-tuning the diameter of the self-assembled nanotubes formed by these molecules, while hardly affecting the molecular packing determined by hydrophobic/hydrophilic interactions. Our findings open a unique way to study size effects on the optical properties and exciton dynamics of self-assembled systems under well-controlled conditions.

Assessing Spectral Simulation Protocols for the Amide I Band of Proteins.

We present a benchmark study of spectral simulation protocols for the amide I band of proteins. The amide I band is widely used in infrared spectroscopy of proteins due to the large signal intensity, high sensitivity to hydrogen bonding, and secondary structural motifs. This band has, thus, proven valuable in many studies of protein structure-function relationships. We benchmark spectral simulation protocols using two common force fields in combination with several electrostatic mappings and coupling models. The results are validated against experimental linear absorption and two-dimensional infrared spectroscopy for three well-studied proteins. We find two-dimensional infrared spectroscopy to be much more sensitive to the simulation protocol than linear absorption and report on the best simulation protocols. The findings demonstrate that there is still room for ideas to improve the existing models for the amide I band of proteins.

Application of two-dimensional infrared spectroscopy to benchmark models for the amide I band of proteins.

In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinations of molecular dynamics force fields, vibrational frequency mappings, and coupling models. We find that two-dimensional infrared spectra provide a much stronger test of the models than linear absorption does. The best modelling approach in the present study still leaves significant room for future improvement. The presented benchmarking scheme, thus, provides a way of validating future protocols for modelling the amide I band in proteins.