Fragment-based models for dissociation of strong acids in water: Electrostatic embedding minimizes the dependence on the fragmentation schemes.

Fragmentation methods such as MIM (Molecules-in-Molecules) provide a route to accurately model large systems and have been successful in predicting their structures, energies, and spectroscopic properties. However, their use is often limited to systems at equilibrium due to the inherent complications in the choice of fragments in systems away from equilibrium. Furthermore, the presence of charges resulting from any heterolytic bond breaking may increase the fragmentation error. We have previously suggested EE-MIM (Electrostatically Embedded Molecules-In-Molecules) as a method to mitigate the errors resulting from the missing long-range interactions in molecular clusters in equilibrium. Here, we show that the same method can be applied to improve the performance of MIM to solve the longstanding problem of dependency of the fragmentation energy error on the choice of the fragmentation scheme. We chose four widely used acid dissociation reactions (HCl, HClO4, HNO3, and H2SO4) as test cases due to their importance in chemical processes and complex reaction potential energy surfaces. Electrostatic embedding improves the performance at both one and two-layer MIM as shown by lower EE-MIM1 and EE-MIM2 errors. The EE-MIM errors are also demonstrated to be less dependent on the choice of the fragmentation scheme by analyzing the variation in fragmentation energy at the points with more than one possible fragmentation scheme (points where the fragmentation scheme changes). EE-MIM2 with M06-2X as the low-level resulted in a variation of less than 1 kcal/mol for all the cases and 1 kJ/mol for all but three cases, rendering our method fragmentation scheme-independent for acid dissociation processes.

EE-ONIOM-CT Method to Efficiently Account for the Missing Interactions in ONIOM: Energies and Analytic Gradients.

Hybrid methods such as ONIOM (QM:QM) are widely used for the study of local processes in large systems. However, the intrinsic need for system partitioning often leads to a less-than-desirable performance for some important chemical processes. This is due to the missing interactions in the chemically important model region (i.e., active site) of the high-level theory. The missing interactions can be categorized into two classes, viz. charge transfer (i.e., charge redistribution) and long-range electrostatic interactions. Our group presented two entirely different methods to treat these deficiencies individually. ONIOM-CT and ONIOM-EE methods have been demonstrated to improve the performance of ONIOM by incorporating charge transfer and missing electrostatic interactions, respectively. In general, the inclusion of the missing interactions separately in two different calculations may not be sufficient to reach a high accuracy. Thus, it is highly desirable to develop a method to correct both deficiencies simultaneously. In this work, we aim to connect the methods ONIOM-CT and ONIOM-EE for a more comprehensive treatment. A "stepwise" model was found to be necessary for a robust performance. This model employs a stepwise procedure by first satisfying the ONIOM-CT condition for charge balance before accounting for the electrostatic interactions from the rest of the system perturbatively. This has the advantage of easy interpretation due to the clear separation of the two effects. We demonstrate the performance of our method using embedding charges determined from a Mulliken population analysis. An efficient analytic gradient expression for this method is derived and implemented by requiring three sets of z-vector self-consistent equations. The performance of our method is assessed against full system calculations in high-level theory for a set of three proton transfer reactions representing different degrees of electrostatic embedding.

Triplet States of Cyanostar and Its Anion Complexes.

The design of advanced optical materials based on triplet states requires knowledge of the triplet energies of the molecular building blocks. To this end, we report the triplet energy of cyanostar (CS) macrocycles, which are the key structure-directing units of small-molecule ionic isolation lattices (SMILES) that have emerged as programmable optical materials. Cyanostar is a cyclic pentamer of covalently linked cyanostilbene units that form π-stacked dimers when binding anions as 2:1 complexes. The triplet energies, ET, of the parent cyanostar and its 2:1 complex around PF6- are measured to be 1.96 and 2.02 eV, respectively, using phosphorescence quenching studies at room temperature. The similarity of these triplet energies suggests that anion complexation leaves the triplet energy relatively unchanged. Similar energies (2.0 and 1.98 eV, respectively) were also obtained from phosphorescence spectra of the iodinated form, I-CS, and of complexes formed with PF6- and IO4- recorded at 85 K in an organic glass. Thus, measures of the triplet energies likely reflect geometries close to those of the ground state either directly by triplet energy transfer to the ground state or indirectly by using frozen media to inhibit relaxation. Density functional theory (DFT) and time-dependent DFT were undertaken on a cyanostar analogue, CSH, to examine the triplet state. The triplet excitation localizes on a single olefin whether in the single cyanostar or its π-stacked dimer. Restriction of the geometrical changes by forming either a dimer of macrocycles, (CSH)2, or a complex, (CSH)2·PF6-, reduces the relaxation resulting in an adiabatic energy of the triplet state of 2.0 eV. This structural constraint is also expected for solid-state SMILES materials. The obtained T1 energy of 2.0 eV is a key guide line for the design of SMILES materials for the manipulation of triplet excitons by triplet state engineering in the future.

ONIOM Method with Charge Transfer Corrections (ONIOM-CT): Analytic Gradients and Benchmarking.

Hybrid methods such as ONIOM that treat different regions of a large molecule using different methods are widely used to investigate chemical reactions in a variety of materials and biological systems. However, there are inherent sources of significant errors due to the standard treatment of the boundary between the regions using hydrogen link atoms. In particular, an unbalanced charge distribution in the chemically important model region is a potential source of such problems. We have previously suggested ONIOM-CT (ONIOM with charge transfer corrections) which addresses this issue by applying a potential in the form of point charges to obtain a desired charge redistribution. The metric for charge redistribution relies on the type of population analysis used to obtain the charges. ONIOM-CT has been implemented using Mulliken and Löwdin population analyses and has been shown to improve computed reaction energies for illustrative chemical reactions. In this work, we derive and implement the analytic gradients for ONIOM-CT that requires solving two sets of coupled-perturbed self-consistent equations, one each for the model system and the full system. However, both are needed only at the low level of theory, allowing for an efficient formulation and implementation for both Mulliken and Löwdin population analyses. Benchmarking and illustrative geometry optimizations have been carried out for a previously studied set of reactions involving a single link atom between regions. Additionally, we have generalized our method for the treatment of model systems involving multiple link atoms to enable applications for a broader set of problems. The generalized methods are illustrated for both charge models. Furthermore, we have studied a set of three proton transfer reactions and demonstrate that significant improvement is achieved by ONIOM-CT over ONIOM using both Mulliken and Löwdin population analyses.

Photosensitized [2+2]-Cycloadditions of Alkenylboronates and Alkenes.

A new strategy for the synthesis of highly versatile cyclobutylboronates via the photosensitized [2+2]-cycloaddition of alkenylboronates and alkenes is presented. The process is mechanistically different from other processes in that energy transfer occurs with the alkenylboronate as opposed to the other alkene. This strategy allows for the synthesis of an array of diverse cyclobutylboronates. The conversion of these adducts to other compounds as well as their utility in the synthesis of melicodenine C is demonstrated.

Electrostatically embedded molecules-in-molecules approach and its application to molecular clusters.

We report the application of our fragment-based quantum chemistry model MIM (Molecules-In-Molecules) with electrostatic embedding. The method is termed "EE-MIM (Electrostatically Embedded Molecules-In-Molecules)" and accounts for the missing electrostatic interactions in the subsystems resulting from fragmentation. Point charges placed at the atomic positions are used to represent the interaction of each subsystem with the rest of the molecule with minimal increase in the computational cost. We have carefully calibrated this model on a range of different sizes of clusters containing up to 57 water molecules. The fragmentation methods have been applied with the goal of reproducing the unfragmented total energy at the MP2/6-311G(d,p) level. Comparative analysis has been carried out between MIM and EE-MIM to gauge the impact of electrostatic embedding. Performance of several different parameters such as the type of charge and levels of fragmentation are analyzed for the prediction of absolute energies. The use of background charges in subsystem calculations improves the performance of both one- and two-layer MIM while it is noticeably important in the case of one-layer MIM. Embedded charges for two-layer MIM are obtained from a full system calculation at the low-level. For one-layer MIM, in the absence of a full system calculation, two different types of embedded charges, namely, Geometry dependent (GD) and geometry independent (GI) charges, are used. A self-consistent procedure is employed to obtain GD charges. We have further tested our method on challenging charged systems with stronger intermolecular interactions, namely, protonated ammonia clusters (containing up to 30 ammonia molecules). The observations are similar to water clusters with improved performance using embedded charges. Overall, the performance of NPA charges as embedded charges is found to be the best.