Leveraging DFT and Molecular Fragmentation for Chemically Accurate pKa Prediction Using Machine Learning.

We present a quantum mechanical/machine learning (ML) framework based on random forest to accurately predict the pKas of complex organic molecules using inexpensive density functional theory (DFT) calculations. By including physics-based features from low-level DFT calculations and structural features from our connectivity-based hierarchy (CBH) fragmentation protocol, we can correct the systematic error associated with DFT. The generalizability and performance of our model are evaluated on two benchmark sets (SAMPL6 and Novartis). We believe the carefully curated input of physics-based features lessens the model's data dependence and need for complex deep learning architectures, without compromising the accuracy of the test sets. As a point of novelty, our work extends the applicability of CBH, employing it for the generation of viable molecular descriptors for ML.

Vibrational Analysis of Constrained Molecular Systems.

Vibrational spectroscopy, including infrared (IR), Raman spectroscopy, and vibrational circular dichroism, is instrumental in determining the structure and composition of molecules. These techniques are highly sensitive to molecular conformations. However, full molecular optimization, necessary for theoretical vibrational spectra, can lead to unintended conformational changes, especially in large biomolecules like polypeptides. To address this, dihedral angle constraints can be imposed during optimization to preserve the molecule's native conformation. Constraint-optimized molecular geometries, not being true stationary points in the full configurational space, pose challenges for traditional vibrational analysis. We address this by considering such geometries as subspace minima, reformulating vibrational analysis to incorporate constraints. Normal modes and spectra consistent with these constraints are obtained by projecting the force constant matrix onto a space orthogonal to the constrained coordinates. This method, illustrated by the example of enkephalin, yields 3N - 6 - m nonzero frequencies after constraint projection, demonstrating its applicability to biomolecules with flexible conformations. Our approach offers a comprehensive mathematical framework to compute vibrational spectra of molecules with conformationally flexible subunits under environmental constraints.

Accelerated Computer-Aided Screening of Optical Materials: Investigating the Potential of Δ-SCF Methods to Predict Emission Maxima of Large Dye Molecules.

Accurate simulation of electronic excited states of large chromophores is often difficult due to the computationally expensive nature of existing methods. Common approximations such as fragmentation methods that are routinely applied to ground-state calculations of large molecules are not easily applicable to excited states due to the delocalized nature of electronic excitations in most practical chromophores. Thus, special techniques specific to excited states are needed. Δ-SCF methods are one such approximation that treats excited states in a manner analogous to that for ground-state calculations, accelerating the simulation of excited states. In this work, we employed the popular initial maximum overlap method (IMOM) to avoid the variational collapse of the electronic excited state orbitals to the ground state. We demonstrate that it is possible to obtain emission energies from the first singlet (S1) excited state of many thousands of dye molecules without any external intervention. Spin correction was found to be necessary to obtain accurate excitation and emission energies. Using thousands of dye-like chromophores and various solvents (12,318 combinations), we show that the spin-corrected initial maximum overlap method accurately predicts emission maxima with a mean absolute error of only 0.27 eV. We further improved the predictive accuracy using linear fit-based corrections from individual dye classes to achieve an impressive performance of 0.17 eV. Additionally, we demonstrate that IMOM spin density can be used to identify the dye class of chromophores, enabling improved prediction accuracy for complex dye molecules, such as dyads (chromophores containing moieties from two different dye classes). Finally, the convergence behavior of IMOM excited state SCF calculations is analyzed briefly to identify the chemical space, where IMOM is more likely to fail.

Cooperativity in Photofoldamer Chloride Double Helices Turned On with Sequences and Solvents, Around with Guests, and Off with Light.

Photofoldamers are sequence-defined receptors capable of switching guest binding on and off. When two foldamer strands wrap around the guest into 2:1 double helical complexes, cooperativity emerges, and with it comes the possibility to switch cooperativity with light and other stimuli. We use lessons from nonswitchable sequence isomers of aryl-triazole foldamers to guide how to vary the sequence location of azobenzenes from the end (FEND) to the interior (FIN) and report their impact on the cooperative formation of 2:1 complexes with Cl-. This sequence change produces a 125-fold increase from anti-cooperative (α = 0.008) for FEND to non-cooperative with FIN (α = 1.0). Density functional theory (DFT) studies show greater H-bonding and a more relaxed double helix for FIN. The solvent and guest complement the synthetic designs. Use of acetonitrile to enhance solvophobicity further enhances cooperativity in FIN (α = 126) but lowers the difference in cooperativity between sequences. Surprisingly, the impact of the sequence on cooperativity is inverted when the guest size is increased from Cl- (3.4 Å) to BF4- (4.1 Å). While photoconversion of interior azobenzenes was poor, the cis-cis isomer forms 1:1 complexes around chloride consistent with switching cooperativity. The effect of the guest, solvent, and light on the double-helix cooperativity depends on the sequence.

Investigating the Stacking Interactions Responsible for Driving 3D Self-Association of Tricarb Macrocycles.

We have investigated the noncovalent forces that play a crucial role in the three-dimensional (3D) self-association of the tricarb macrocycle (composed of alternating triazoles and carbazoles) to understand the multilayer stacks observed through electron microscopy. To explore this idea quantitatively, we have investigated a stacked dimer model of tricarb, where we consider homochiral as well as heterochiral forms of the dimer. We have computed the rotational potential energy surface of the dimer by conducting an angle-dependent scan between the two macrocycles using different levels of theory including the RI-MP2 ab initio method. We observe that dimers oriented at an angle of 60° exhibit the highest stability, while a secondary minimum is observed at an angle of 30°. While density functional theory (DFT) describes the behavior of both minima very close to that obtained with RI-MP2, semiempirical and MM models appear to obtain only a shoulder instead of the second minimum. To further understand the underlying interactions responsible for stabilizing the self-assembly of the macrocycles, we employed energy decomposition analysis (EDA) using SAPT0. This quantitative assessment allowed us to identify the major contributing noncovalent interactions, including electrostatic, exchange-repulsion, dispersion, and induction. Finally, we expanded our study to evaluate the accuracy of the MIM (molecules-in-molecules) fragmentation methodology in capturing the crucial π-stacking interactions. Our benchmarking results using the MIM method accurately replicated the angle-dependent PES results. This shows the efficacy of MIM in predicting the noncovalent interactions responsible for the construction of 3D and other higher-order nanoarchitectures for tricarb and related compounds.

Quantitative Prediction of Vertical Ionization Potentials from DFT via a Graph-Network-Based Delta Machine Learning Model Incorporating Electronic Descriptors.

While accurate wave function theories like CCSD(T) are capable of modeling molecular chemical processes, the associated steep computational scaling renders them intractable for treating large systems or extensive databases. In contrast, density functional theory (DFT) is much more computationally feasible yet often fails to quantitatively describe electronic changes in chemical processes. Herein, we report an efficient delta machine learning (ΔML) model that builds on the Connectivity-Based Hierarchy (CBH) scheme─an error correction approach based on systematic molecular fragmentation protocols─and achieves coupled cluster accuracy on vertical ionization potentials by correcting for deficiencies in DFT. The present study integrates concepts from molecular fragmentation, systematic error cancellation, and machine learning. First, we show that by using an electron population difference map, ionization sites within a molecule may be readily identified, and CBH correction schemes for ionization processes may be automated. As a central feature of our work, we employ a graph-based QM/ML model, which embeds atom-centered features describing CBH fragments into a computational graph to further increase accuracy for the prediction of vertical ionization potentials. In addition, we show that the incorporation of electronic descriptors from DFT, namely electron population difference features, improves model performance well beyond chemical accuracy (1 kcal/mol) to approach benchmark accuracy. While the raw DFT results are strongly dependent on the underlying functional used, for our best models, the performance is robust and much less dependent on the functional.

Tautomerization of H+KPGG: Entropic Consequences of Strong Hydrogen-Bond Networks in Peptides.

Ion mobility spectrometry-mass spectrometry and quantum chemical calculations are used to determine the structures and stabilities of the singly protonated peptide H+KPGG. The two peaks making up the IMS distribution are shown to be tautomers differing by the location of the extra proton on either the lysine side chain or the N-terminus. The lysine-protonated tautomer is strongly preferred entropically while being disfavored in terms of the electronic energy and enthalpy. This relationship is shown, through comparison of all low-lying conformers of both tautomers, to be related to the strong hydrogen-bond network of the N-terminally protonated tautomer. A general relationship is demonstrated wherein stronger cross-peptide hydrogen-bond networks result in entropically disfavored conformers. Further effects of the H+KPGG hydrogen-bond network are probed by computationally examining singly and doubly methylated analogues. These results demonstrate the importance of the entropic consequences of hydrogen bonds to peptide stability as well as techniques for perturbing the hydrogen-bond network and folding preferences of peptides via minimal chemical modification.

Structure Dependence of CO2 Reduction Electrocatalyzed by Metal-Nanographene Complexes: A Computational Study.

Improving the energy efficiency of electrocatalytic reduction of CO2 requires tuning of redox properties of electrocatalysts to match redox potentials of the substrate. Recently, we introduced nanographenes as ligands for metal complexes for such purposes by taking advantage of size-dependent properties of the conjugated systems. Here, we use computations to investigate the structure dependence of the electrocatalysis at Re(diimine)(CO)3Cl complexes with nanographene ligands that contain a polycyclic aromatic hydrocarbon moiety through a pyrazinyl linkage. We show that the reduction potentials of the complexes depend not only on conjugation size but also on shape and geometry of the ligands, revealing another parameter in tuning the redox properties of the electrocatalysts. In addition, our work reveals a compromise between reduction potentials and activation of this class of electrocatalysts.

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.

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.