Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory.

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Organic Crystal Packing Is Key to Determining the Photomechanical Response.

Organic photomechanical crystals have great promise as molecular machines, but their development has been hindered by a lack of clear theoretical design principles. While much research has focused on the choice of the molecular photochrome, density functional theory calculations here demonstrate that crystal packing has a major impact on the work densities that can be produced by a photochrome. Examination of two diarylethene molecules reveals that the predicted work densities can vary by an order of magnitude across different experimentally known crystal structures of the same species. The highest work densities occur when molecules are aligned in parallel, thereby producing a highly anisotropic photomechanical response. These results suggest that a greater emphasis on polymorph screening and/or crystal engineering could improve the work densities achieved by photomechanical engines. Finally, an inherent thermodynamic asymmetry is identified that biases photomechanical engines to exhibit higher work densities in the forward stroke direction.

Optimally controlling nutrition and propulsion force in a long distance running race.

Introduction: Runners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout the race and the propulsion force of the runner. As nutrition is an integral part of successfully running long distance races, it needs to be included in models of running strategies. Methods: We formulate a system of ordinary differential equations to represent the velocity, fat energy, glycogen energy, and nutrition for a runner competing in a long-distance race. The energy compartments represent the energy sources available in the runner's body. We allocate the energy source from which the runner draws, based on how fast the runner is moving. The food consumed during the race is a source term for the nutrition differential equation. With our model, we are investigating strategies to manage the nutrition and propulsion force in order to minimize the running time in a fixed distance race. This requires the solution of a nontrivial singular control problem. Results: As the goal of an optimal control model is to determine the optimal strategy, comparing our results against real data presents a challenge; however, in comparing our results to the world record for the marathon, our results differed by 0.4%, 31 seconds. Per each additional gel consumed, the runner is able to run 0.5 to 0.7 kilometers further in the same amount of time, resulting in a 7.75% increase in taking five 100 calorie gels vs no nutrition. Discussion: Our results confirm the belief that the most effective way to run a race is to run approximately the same pace the entire race without letting one's energies hit zero, by consuming in-race nutrition. While this model does not take all factors into account, we consider it a building block for future models, considering our novel energy representation, and in-race nutrition.

A theoretical framework for the design of molecular crystal engines.

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9-tert-butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼107 J m-3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico.

La Crosse virus spread within the mosquito population in Knox County, TN.

In Appalachia, La Crosse virus (LACV) is a leading pediatric arbovirus and public health concern for children under 16 years. LACV is transmitted via the bite of an infected Aedes mosquito. Thus, it is imperative to understand the dynamics of the local vector population in order to assess risk and transmission. Using entomological data collected from Knox County, Tennessee in 2013, we formulate an environmentally-driven system of ordinary differential equations to model mosquito population dynamics over a single season. Further, we include infected compartments to represent LACV transmission within the mosquito population. Findings suggest that the model, with dependence on degree days and accumulated precipitation, can closely describe field data. This model confirms the need to include these environmental variables when planning control strategies.

Modeling the α- and ß-resorcinol phase boundary via combination of density functional theory and density functional tight-binding.

The ability to predict not only what organic crystal structures might occur but also the thermodynamic conditions under which they are the most stable would be extremely useful for discovering and designing new organic materials. The present study takes a step in that direction by predicting the temperature- and pressure-dependent phase boundary between the α and ß polymorphs of resorcinol using density functional theory (DFT) and the quasi-harmonic approximation. To circumvent the major computational bottleneck associated with computing a well-converged phonon density of states via the supercell approach, a recently developed approximation is employed, which combines a supercell phonon density of states from dispersion-corrected third-order density functional tight binding [DFTB3-D3(BJ)] with frequency corrections derived from a smaller B86bPBE-XDM functional DFT phonon calculation on the crystallographic unit cell. This mixed DFT/DFTB quasi-harmonic approach predicts the lattice constants and unit cell volumes to within 1%-2% at lower pressures. It predicts the thermodynamic phase boundary in almost perfect agreement with the experiment, although this excellent agreement does reflect fortuitous cancellation of errors between the enthalpy and entropy of transition.

Reduced-cost supercell approach for computing accurate phonon density of states in organic crystals.

Phonon contributions to organic crystal structures and thermochemical properties can be significant, but computing a well-converged phonon density of states with lattice dynamics and periodic density functional theory (DFT) is often computationally expensive due to the need for large supercells. Using semi-empirical methods like density functional tight binding (DFTB) instead of DFT can reduce the computational costs dramatically, albeit with noticeable reductions in accuracy. This work proposes approximating the phonon density of states via a relatively inexpensive DFTB supercell treatment of the phonon dispersion that is then corrected by shifting the individual phonon modes according to the difference between the DFT and DFTB phonon frequencies at the Γ-point. The acoustic modes are then computed at the DFT level from the elastic constants. In several small-molecule crystal test cases, this combined approach reproduces DFT thermochemistry with kJ/mol accuracy and 1-2 orders of magnitude less computational effort. Finally, this approach is applied to computing the free energy differences between the five crystal polymorphs of oxalyl dihydrazide.

Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence.

Singlet fission (SF) is a photophysical process considered as a possible scheme to bypass the Shockley-Queisser limit by generating two triplet-state excitons from one high-energy photon. Polyacene crystals, such as tetracene and pentacene, have shown outstanding SF performance both theoretically and experimentally. However, their instability prevents them from being utilized in SF-based photovoltaic devices. In search of practical SF chromophores, we use many-body perturbation theory within the GW approximation and Bethe-Salpeter equation to study the excitonic properties of a family of pyrene-stabilized acenes. We propose a criterion to define the convergence of exciton wave-functions with respect to the fine k-point grid used in the BerkeleyGW code. An open-source Python code is presented to perform exciton wave-function convergence checks and streamline the double Bader analysis of exciton character. We find that the singlet excitons in pyrene-stabilized acenes have a higher degree of charge transfer character than in the corresponding acenes. The pyrene-fused tetracene and pentacene derivatives exhibit comparable excitation energies to their corresponding acenes, making them potential SF candidates. The pyrene-stabilized anthracene derivative is considered as a possible candidate for triplet-triplet annihilation because it yields a lower SF driving force than anthracene.

On the possibility of singlet fission in crystalline quaterrylene.

Singlet fission (SF), the spontaneous down-conversion of a singlet exciton into two triplet excitons residing on neighboring molecules, is a promising route to improve organic photovoltaic (OPV) device efficiencies by harvesting two charge carriers from one photon. However, only a few materials have been discovered that exhibit intermolecular SF in the solid state, most of which are acene derivatives. Recently, there has been a growing interest in rylenes as potential SF materials. We use many-body perturbation theory in the GW approximation and the Bethe-Salpeter equation to investigate the possibility of intermolecular SF in crystalline perylene and quaterrylene. A new method is presented for determining the percent charge transfer (%CT) character of an exciton wave-function from double-Bader analysis. This enables relating exciton probability distributions to crystal packing. Based on comparison to known and predicted SF materials with respect to the energy conservation criterion (ES-2ET) and %CT, crystalline quaterrylene is a promising candidate for intermolecular SF. Furthermore, quaterrylene is attractive for OPV applications, thanks to its high stability and narrow optical gap. Perylene is not expected to exhibit SF; however, it is a promising candidate for harvesting sub-gap photons by triplet-triplet annihilation.