Mean-field density matrix decompositions

Transferability of atomic energies from alchemical decomposition

We study alchemical atomic energy partitioning as a method to estimate atomization energies from atomic contributions, which are defined in physically rigorous and general ways through the use of the uniform electron gas as a joint reference. We analyze quantitatively the relation between atomic energies and their local environment using a dataset of 1325 organic molecules. The atomic energies are transferable across various molecules, enabling the prediction of atomization energies with a mean absolute error of 23 kcal/mol, comparable to simple statistical estimates but potentially more robust given their grounding in the physics-based decomposition scheme. A comparative analysis with other decomposition methods highlights its sensitivity to electrostatic variations, underlining its potential as a representation of the environment as well as in studying processes like diffusion in solids characterized by significant electrostatic shifts.

Properties of Local Electronic Structures

The simulation of intrinsic contributions to molecular properties holds the potential to allow for chemistry to be directly inferred from changes to electronic structures at the atomic level. In the present study, we demonstrate how such local properties can be readily derived from suitable molecular orbitals to yield effective fingerprints of various types of atoms in organic molecules. In contrast, corresponding inferences from schemes that instead make use of individual atomic orbitals for this purpose are generally found to fail in expressing much uniqueness in atomic environments. By further studying the extent to which entire chemical reactions may be decomposed into meaningful and continuously evolving atomic contributions, schemes based on molecular rather than atomic orbitals are once again found to be the more consistent, even allowing for intricate differences between seemingly uniform nucleophilic substitutions to be probed.

Decomposing Chemical Space: Applications to the Machine Learning of Atomic Energies

We apply a number of atomic decomposition schemes across the standard QM7 data set─a small model set of organic molecules at equilibrium geometry─to inspect the possible emergence of trends among contributions to atomization energies from distinct elements embedded within molecules. Specifically, a recent decomposition scheme of ours based on spatially localized molecular orbitals is compared to alternatives that instead partition molecular energies on account of which nuclei individual atomic orbitals are centered on. We find these partitioning schemes to expose the composition of chemical compound space in very dissimilar ways in terms of the grouping, binning, and heterogeneity of discrete atomic contributions, e.g., those associated with hydrogens bonded to different heavy atoms. Furthermore, unphysical dependencies on the one-electron basis set are found for some, but not all of these schemes. The relevance and importance of these compositional factors for training tailored neural network models based on atomic energies are next assessed. We identify both limitations and possible advantages with respect to contemporary machine learning models and discuss the design of potential counterparts based on atoms and the intrinsic energies of these as the principal decomposition units.

Quantum Alchemy Based Bonding Trends and Their Link to Hammett's Equation and Pauling's Electronegativity Model

We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, [E_AB ≈ a - bZ_AZ_B + c(Z_A^7/3 + Z_B^7/3) ]. The functional form of our expression models an alchemical atomic energy decomposition between participating atoms A and B. After calibration, reasonably accurate bond dissociation energy estimates are obtained for hydrogen-saturated diatomics composed of p-block elements coming from the same row 2 ≤ n ≤ 4 in the periodic table. Corresponding changes in bond dissociation energies due to substitution of atom B by C can be obtained via simple formulas. While being of different functional form and origin, our model is as simple and accurate as Pauling's well-known electronegativity model. Analysis indicates that the model's response in covalent bonding to variation in nuclear charge is near-linear, which is consistent with Hammett's equation.

Electronic excitations through the prism of mean-field decomposition techniques

The potential of mean-field decomposition techniques in interpreting electronic transitions in molecules is explored, in particular, the usefulness of these for offering computational signatures of different classes of such excitations. When viewed as a conceptual lens for this purpose, decomposed results are presented for ground- and excited-state energies and dipole moments of selected prototypical organic dyes, and the discrete nature of these properties as well as how they change upon transitioning from one state to another is analyzed without recourse to a discussion based on the involved molecular orbitals. On the basis of results obtained both with and without an account of continuum solvation, our work is further intended to shed new light on practical and pathological differences in between various functional approximations in orbital-optimized Kohn-Sham density functional theory for excited states, equipping practitioners and developers in the field with new probes and possible validation tools.

Decomposed Mean-Field Simulations of Local Properties in Condensed Phases

The present work demonstrates a robust protocol for probing localized electronic structure in condensed-phase systems, operating in terms of a recently proposed theory for decomposing the results of Kohn-Sham density functional theory in a basis of spatially localized molecular orbitals. In an initial application to liquid, ambient water and the assessment of the solvation energy and the embedded dipole moment of H₂O in solution, we find that both properties are amplified on average-in accordance with expectation-and that correlations are indeed observed to exist between them. However, the simulated solvent-induced shift to the dipole moment of water is found to be significantly dampened with respect to typical literature values. The local nature of our methodology has further allowed us to evaluate the convergence of bulk properties with respect to the extent of the underlying one-electron basis set, ranging from single-ζ to full (augmented) quadruple-ζ quality. Albeit a pilot example, our work paves the way toward future studies of local effects and defects in more complex phases, e.g., liquid mixtures and even solid-state crystals.