Overcoming systematic DFT errors for hydrocarbon reaction energies

Despite the widespread use and numerous successful applications of density functional theory, descriptions of hydrocarbon reaction energies remain problematic. Illustrative examples include large underestimation of energies associated with alkane bond separation reactions and poor general description of intramolecular dispersion in hydrocarbons (e.g., B3LYP, MAD=14.1kcalmol−1). More recent, but not readily availably functionals, along with efficient posteriori corrections, not only show considerable improvement in the energy description of hydrocarbons but also help identify the sources of error in traditional DFT. Interactions in branched alkanes and compact hydrocarbons are adequately mimicked by systems compressed below their typical van der Waals distances. At these distances, standard DFT exchange functionals are overly repulsive for non-bonded density overlaps, and significant improvement is offered by the long-range corrected exchange functionals (e.g., LC-BLYP0.33, MAD=5.5kcalmol−1). For those systems, the neglect of long-range dispersion is found to be a critical shortcoming, as well as "overlap dispersion”, for which non-negligible amounts are captured by the correlation functional. Accounting for the missing dispersion interactions is of key importance. Accordingly, most noteworthy improvements over standard functionals are obtained by using non-local van der Waals density functionals (e.g., LC-S-VV09, MAD=3.6kcalmol−1, rPW86-VV09, MAD=5.8kcalmol−1), a dispersion corrected double hybrid (B2PLYP-D, MAD=2.5kcalmol−1), or by the addition of an atom pairwise density-dependent dispersion correction to a standard functional (e.g., PBE-dDXDM, MAD=0.8kcalmol−1). To a lesser extent, the reduction of the delocalization error (e.g., MCY3, MAD=6.3kcalmol−1) or careful parameter fitting (e.g., M06-2X, MAD=5.6kcalmol−1) also lowers the error

SPAH^\mathrm{H}M: the Spectrum of Approximated Hamiltonian Matrices representations

Physics-inspired molecular representations are the cornerstone of similarity-based learning applied to solve chemical problems. Despite their conceptual and mathematical diversity, this class of descriptors shares a common underlying philosophy: they all rely on the molecular information that determines the form of the electronic Schr\"odinger equation. Existing representations take the most varied forms, from non-linear functions of atom types and positions to atom densities and potential, up to complex quantum chemical objects directly injected into the ML architecture. In this work, we present the Spectrum of Approximated Hamiltonian Matrices (SPA$^\mathrm{H}$M) as an alternative pathway to construct quantum machine learning representations through leveraging the foundation of the electronic Schr\"odinger equation itself: the electronic Hamiltonian. As the Hamiltonian encodes all quantum chemical information at once, SPA$^\mathrm{H}$M representations not only distinguish different molecules and conformations, but also different spin, charge, and electronic states. As a proof of concept, we focus here on efficient SPA$^\mathrm{H}$M representations built from the eigenvalues of a hierarchy of well-established and readily-evaluated "guess" Hamiltonians. These SPA$^\mathrm{H}$M representations are particularly compact and efficient for kernel evaluation and their complexity is independent of the number of different atom types in the database.Comment: 9 pages + SI (8 pages

A Transferable Machine-Learning Model of the Electron Density

The electronic charge density plays a central role in determining the behavior of matter at the atomic scale, but its computational evaluation requires demanding electronic-structure calculations. We introduce an atom-centered, symmetry-adapted framework to machine-learn the valence charge density based on a small number of reference calculations. The model is highly transferable, meaning it can be trained on electronic-structure data of small molecules and used to predict the charge density of larger compounds with low, linear-scaling cost. Applications are shown for various hydrocarbon molecules of increasing complexity and flexibility, and demonstrate the accuracy of the model when predicting the density on octane and octatetraene after training exclusively on butane and butadiene. This transferable, data-driven model can be used to interpret experiments, initialize electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems

SPAH^\mathrm{H}M(a,b): encoding the density information from guess Hamiltonian in quantum machine learning representations

Recently, we introduced a class of molecular representations for kernel-based regression methods -- the spectrum of approximated Hamiltonian matrices (SPA$^\mathrm{H}$M) -- that takes advantage of lightweight one-electron Hamiltonians traditionally used as an SCF initial guess. The original SPA$^\mathrm{H}$M variant is built from occupied-orbital energies (\ie, eigenvalues) and naturally contains all the information about nuclear charges, atomic positions, and symmetry requirements. Its advantages were demonstrated on datasets featuring a wide variation of charge and spin, for which traditional structure-based representations commonly fail. SPA$^\mathrm{H}$M(a,b), as introduced here, expands eigenvalue SPA$^\mathrm{H}$M into local and transferable representations. It relies upon one-electron density matrices to build fingerprints from atomic or bond density overlap contributions inspired from preceding state-of-the-art representations. The performance and efficiency of SPA$^\mathrm{H}$M(a,b) is assessed on the predictions for datasets of prototypical organic molecules (QM7) of different charges and azoheteroarene dyes in an excited state. Overall, both SPA$^\mathrm{H}$M(a) and SPA$^\mathrm{H}$M(b) outperform state-of-the-art representations on difficult prediction tasks such as the atomic properties of charged open-shell species and of $\pi$-conjugated systems.Comment: 9 pages + SI (18 pages

Overcoming systematic DFT errors for hydrocarbon reaction energies

Despite the widespread use and numerous successful applications of density functional theory, descriptions of hydrocarbon reaction energies remain problematic. Illustrative examples include large underestimation of energies associated with alkane bond separation reactions and poor general description of intramolecular dispersion in hydrocarbons (e.g., B3LYP, MAD = 14.1 kcal mol-1). More recent, but not readily availably functionals, along with efficient posteriori corrections, not only show considerable improvement in the energy description of hydrocarbons but also help identify the sources of error in traditional DFT. Interactions in branched alkanes and compact hydrocarbons are adequately mimicked by systems compressed below their typical van der Waals distances. At these distances, standard DFT exchange functionals are overly repulsive for non-bonded density overlaps, and significant improvement is offered by the long-range corrected exchange functionals (e.g., LC-BLYP0.33, MAD = 5.5 kcal mol-1). For those systems, the neglect of long-range dispersion is found to be a critical shortcoming, as well as ‘‘overlap dispersion’’, for which non-negligible amounts are captured by the correlation functional. Accounting for the missing dispersion interactions is of key importance. Accordingly, most noteworthy improvements over standard functionals are obtained by using non-local van der Waals density functionals (e.g., LC-S-VV09, MAD = 3.6 kcal mol-1, rPW86-VV09, MAD = 5.8 kcal mol-1), a dispersion corrected double hybrid (B2PLYP-D, MAD = 2.5 kcal mol-1), or by the addition of an atom pairwise densitydependent dispersion correction to a standard functional (e.g., PBE-dDXDM, MAD = 0.8 kcal mol-1). To a lesser extent, the reduction of the delocalization error (e.g., MCY3, MAD = 6.3 kcal mol-1) or careful parameter fitting (e.g., M06-2X, MAD = 5.6 kcal mol-1) also lowers the errors

Learning on-top: regressing the on-top pair density for real-space visualization of electron correlation

The on-top pair density [$\Pi(\mathrm{\mathbf{r}})$] is a local quantum-chemical property that reflects the probability of two electrons of any spin to occupy the same position in space. Being the simplest quantity related to the two-particle density matrix, the on-top pair density is a powerful indicator of electron correlation effects, and as such, it has been extensively used to combine density functional theory and multireference wavefunction theory. The widespread application of $\Pi(\mathrm{\mathbf{r}})$ is currently hindered by the need for post-Hartree--Fock or multireference computations for its accurate evaluation. In this work, we propose the construction of a machine learning model capable of predicting the CASSCF-quality on-top pair density of a molecule only from its structure and composition. Our model, trained on the GDB11-AD-3165 database, is able to predict with minimal error the on-top pair density of organic molecules, bypassing completely the need for $\textit{ab initio}$ computations. The accuracy of the regression is demonstrated using the on-top ratio as a visual metric of electron correlation effects and bond-breaking in real-space. In addition, we report the construction of a specialized basis set, built to fit the on-top pair density in a single atom-centered expansion. This basis, cornerstone of the regression, could be potentially used also in the same spirit of the resolution-of-the-identity approximation for the electron density.Comment: Article and Supporting Informatio

Genetic Algorithms for the Discovery of Homogeneous Catalysts

In this account, we discuss the use of genetic algorithms in the inverse design process of homogeneous catalysts for chemical transformations. We describe the main components of evolutionary experiments, specifically the nature of the fitness function to optimize, the library of molecular fragments from which potential catalysts are assembled, and the settings of the genetic algorithm itself. While not exhaustive, this review summarizes the key challenges and characteristics of our own (i.e., NaviCatGA) and other GAs for the discovery of new catalysts

Nickel pincer model of the active site of lactate racemase involves ligand participation in hydride transfer

Pincer complexes are widely applied in homogeneous catalysis. However, only very recently has the first pincer complex been discovered in the active site of a metalloenzyme, namely, lactate racemase. Here, we report a synthetic model of the active site of lactate racemase. The nickel pincer model not only reproduces some key structural features of the active site, but also mediates the dehydrogenation of alcohols, a reaction relevant to lactate racemization. Our work suggests a mechanism in which the unique pyridinium-derived SCS pincer ligand actively participates in the hydride transfer. This work not only represents a successful biomimetic study of this enzyme but also lays the foundation for the development of new bioinspired pincer ligands

Toward in silico Catalyst Optimization

In this minireview, we overview a computational pipeline developed within the framework of NCCR Catalysis that can be used to successfully reproduce the enantiomeric ratios of homogeneous catalytic reactions. At the core of this pipeline is the SCINE Molassembler module, a graph-based software that provides algorithms for molecular construction of all periodic table elements. With this pipeline, we are able to simultaneously functionalizenand generate ensembles of transition state conformers, which permits facile exploration of the influencenof various substituents on the overall enantiomeric ratio. This allows preconceived back-of-the-envelope designnmodels to be tested and subsequently refined by providing quick and reliable access to energetically low-lyingntransition states, which represents a key step in undertaking in silico catalyst optimization