Efficient and accurate density-based prediction of macromolecular polarizabilities

Reaction rate constant: a theoretical description from local temperature

Application of various descriptors based on electron density and its associated quantities to quantify chemical reactivity within the conceptual density functional theory has recently come into spotlight. Among others and particularly relevant to our study, local temperature based on electron density as well as kinetic energy density, as a measure of the kinetic energy of an electron moving in the Kohn-Sham potential of systems, should be mentioned. In this work, we propose to use the local temperature for describing the reaction rate constant, where our main idea originates from the point that the smaller the local temperature at the reaction center, the easier the electron removal, leading to a larger rate constant. On the basis of theoretical considerations, it is proved that the rate constant variations caused by the substituent effects can well be proportional to the local temperature at the reaction center. In order to numerically validate our proposed approach, we have taken the phenol derivatives with the available experimental rate constants of their O-methylation reaction as working models. The reason for this choice is that one of the most versatile approaches for labeling biologically active compounds with the 11C nuclide for positron emission tomography (PET) is methylation by methyl iodide including 11C nuclide, [11C]MeI, where methylation of phenolic oxygen with [11C]MeI is utilized to label some important tracers for PET studies. Our results unveil that the local temperature changes at the reaction center of the aforementioned reaction are reasonably correlated with the rate constant variations. Hopefully, incorporating the proposed correlations between the local temperature and the kinetics data into a computer control algorithm not only provides a simple tool for predicting the rate constant of the O-methylation reaction for other substituted phenols, but also, as a part of the chemical artificial intelligence, the optimum [11C]MeI labeling conditions for a wide variety of phenol derivatives can be controlled.

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Some Recent Advances in Density-Based Reactivity Theory

Establishing a chemical reactivity theory in density functional theory (DFT) language has been our intense research interest in the past two decades, exemplified by the determination of steric effect and stereoselectivity, evaluation of electrophilicity and nucleophilicity, identification of strong and weak interactions, and formulation of cooperativity, frustration, and principle of chirality hierarchy. In this Featured Article, we first overview the four density-based frameworks in DFT to appreciate chemical understanding, including conceptual DFT, use of density associated quantities, information-theoretic approach, and orbital-free DFT, and then present a few recent advances of these frameworks as well as new applications from our studies. To that end, we will introduce the relationship among these frameworks, determining the entire spectrum of interactions with Pauli energy derivatives, performing topological analyses with information-theoretic quantities, and extending the density-based frameworks to excited states. Applications to examine physiochemical properties in external electric fields and to evaluate polarizability for proteins and crystals are discussed. A few possible directions for future development are followed, with the special emphasis on its merger with machine learning.

Directionality and additivity effects of molecular acidity and aromaticity for substituted benzoic acids under external electric fields

Our recent study [M. Li et al.Phys. Chem. Chem. Phys., 2023, 25, 2595-2605] unveiled that the impact of an external electric field on molecular acidity and aromaticity for benzoic acid is directional, which can be understood using changes in frontier orbitals and partial charges. However, it is unclear if the effect will disappear when substituting groups are present and whether new patterns of changes will show up. In this work, as a continuation of our efforts to appreciate the impact of external electric fields on physiochemical properties, we find that the directionality effect is still in place for substituted benzoic acid derivatives and that there exists the additivity effect with respect to the number of substituent groups, regardless of the direction of the applied field and the type of substituting groups. We confirm the findings using electron-donating and electron-accepting groups with the electric field applied either parallelly or perpendicularly to the carboxyl group along the benzene ring. The directionality and additivity effects uncovered from this work should enrich the body of our knowledge about the impact of external electric fields on physiochemical properties and could be applicable to other systems and properties as well.

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study

Accurate and efficient determination of excited-state polarizabilities (α) is an open problem both experimentally and computationally. Following our previous work, (Phys. Chem. Chem. Phys. 2023, 25, 2131−2141), in which we employed simple ground-state (S0) density-related functions from the information-theoretic approach (ITA) to accurately and efficiently evaluate the macromolecular polarizabilities, in this work we aimed to predict the lowest excited-state (S1) polarizabilities. The philosophy is to use density-based functions to depict excited-state polarizabilities. As a proof-of-principle application, employing 2-(2′-hydroxyphenyl)benzimidazole (HBI), its substituents, and some other commonly used ESIPT (excited-state intramolecular proton transfer) fluorophores as model systems, we verified that either with S0 or S1 densities as an input, ITA quantities can be strongly correlated with the excited-state polarizabilities. When transition densities are considered, both S0 and S1 polarizabilities are in good relationships with some ITA quantities. The transferability of the linear regression model is further verified for a series of molecules with little or no similarity to those molecules in the training set. Furthermore, the excitation energies can be predicted based on multivariant linear regression equations of ITA quantities. This study also found that the nature of both the ground-state and excited-state polarizabilities of these species are due to the spatial delocalization of the electron density.