Nuclear reactivity indices within regional density functional theory

Barrier Height Prediction by Machine Learning Correction of Semiempirical Calculations

Different machine learning (ML) models are proposed in the present work to predict density functional theory-quality barrier heights (BHs) from semiempirical quantum mechanical (SQM) calculations. The ML models include a multitask deep neural network, gradient-boosted trees by means of the XGBoost interface, and Gaussian process regression. The obtained mean absolute errors are similar to those of previous models considering the same number of data points. The ML corrections proposed in this paper could be useful for rapid screening of the large reaction networks that appear in combustion chemistry or in astrochemistry. Finally, our results show that 70% of the features with the highest impact on model output are bespoke predictors. This custom-made set of predictors could be employed by future Δ-ML models to improve the quantitative prediction of other reaction properties.

The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds

The concept of a connectivity matrix, essential for the reaction fragility (RF) spectra technique for monitoring electron density evolution in a chemical reaction, has been supported with a novel formulation for the diagonal matrix elements; their direct link to the electron density function ρ(r) has been demonstrated. By combining the concept with the atomization energy of a system, the separation of the potential energy into atomic and/or bond contributions has been achieved. The energy derivative diagrams for atoms and bonds that are variable along a reaction path provide new insight into the reaction mechanism. Diagonalization of the connectivity matrix resulted in the eigenvectors that provide information on a role of individual atoms in the development of structural changes along a reaction path.

Bond Softening Indices Studied by the Fragility Spectra for Proton Migration in Formamide and Related Structures

Computational scheme to obtain bond softening index λ, defined within the conceptual DFT, has been obtained with the use of the reaction fragility (RF) concept. Numerical results were obtained with the RF spectra for the proton transfer reaction in formamide molecule (H₂NCHO) and the water assisted proton migration in H₂NCHO·H₂O complex. Double proton transfer reaction in the formamide dimer, (H₂NCHO)₂, and its analogues, (H₂NCHS)₂ and (H₂NCHO)·(H₂NCHS), have also been studied. The atomic and bond RF spectra clearly describe the density reorganization in the backbone of each molecule, resulting from proton displacement in the systems. The obtained softening indices have been calculated for hydrogen atoms in the reactant state (RS) and product state (PS) configuration. These indices provide fine characteristics for the local sensitivity of the reacting system to a disturbance of the position of a chosen atom.

Bond Fragility Spectra for the Double Proton-Transfer Reaction in the Formic Acid-Type Dimers

The newly developed method of fragility spectra for observation of bond breaking and formation upon a reaction has been applied to the canonical reaction series of the double proton transfer (DPT). Formic acid and its thio-analogues HCXYH (X, Y = O, S) have been chosen for the analysis. Very accurate linear correlations have been determined between the nondiagonal elements of the connectivity matrix, essential for the method, and the Wiberg bond orders for the corresponding bonds. Relation of the slope of this correlation to the global softness and to the atomic numbers of the bonded atoms has been proved, thus corroborating the c-DFT formula describing the fragility spectra. The electron density changes in bonds, as observed by the fragility spectra, are in harmony with the curvature diagrams reported by other authors.

Evolution of the atomic valence observed by the reaction fragility spectra on the reaction path

The computational fragility spectra of atoms on the reaction path are presented for a selection of canonical processes represented by an amino group rotation around the (X)HC-NH(Y) bond (X = O, S; Y=H, CH₃). Calculated spectra are found to very accurately describe the variation of atomic valence. Significant linear correlation is also demonstrated between the Wiberg bond indices and the corresponding elements of the connectivity matrix, instrumental for calculation of the spectra. Demonstrated atomic fragility spectra contain rich and subtle information on the variation of the bonding status of all atoms, including the weak interacting individual hydrogens. Correlation with the atomic valences confirm the earlier finding that the spectra contain a picture of the electron density flow upon a reaction.

Conceptual DFT analysis of the fragility spectra of atoms along the minimum energy reaction coordinate

Theoretical justification has been provided to the method for monitoring the sequence of chemical bonds' rearrangement along a reaction path, by tracing the evolution of the diagonal elements of the Hessian matrix. Relations between the divergences of Hellman-Feynman forces and the energy and electron density derivatives have been demonstrated. By the proof presented on the grounds of the conceptual density functional theory formalism, the spectral amplitude observed on the atomic fragility spectra [L. Komorowski et al., Phys. Chem. Chem. Phys. 18, 32658 (2016)] reflects selectively the electron density modifications in bonds of an atom. In fact the spectral peaks for an atom reveal changes of the electron density occurring with bonds creation, breaking, or varying with the reaction progress.

Atomic Resolution for the Energy Derivatives on the Reaction Path

Definite algorithms for calculation of the atomic contributions to the reaction force Fξ and the reaction force constant kξ (the first and the second derivatives of the energy over the reaction path step) are presented. The electronic part in the atomic and group contributions has been separated, and this opened the way to identification of the reactive molecule fragments on the consecutive stages of the reaction path. Properties have been studied for the two canonical test reactions: CO + HF → HCOF and HONS → ONSH.

The reaction fragility spectrum

We report an original method that provides a new insight into the reaction mechanism by direct observation of bond breaking and formation. Example: HONS → ONSH.

Variation of the electronic dipole polarizability on the reaction path

The reaction force and the electronic flux, first proposed by Toro-Labbé et al. (J Phys Chem A 103:4398, 1999) have been expressed by the existing conceptual DFT apparatus. The critical points (extremes) of the chemical potential, global hardness and softness have been identified by means of the existing and computable energy derivatives: the Hellman-Feynman force, nuclear reactivity and nuclear stiffness. Specific role of atoms at the reaction center has been unveiled by indicating an alternative method of calculation of the reaction force and the reaction electronic flux. The electron dipole polarizability on the IRC has been analyzed for the model reaction HF + CO→HCOF. The electron polarizability determined on the IRC α_e(ξ) was found to be reasonably parallel to the global softness curve S(ξ). The softest state on the IRC (not TS) coincides with zero electronic flux.

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Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: A new formula for the energy third derivative γ

Nuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground state hardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons (N), but is so within constant chemical potential (mu) constraint. The authors apply this feature to evaluate an energy third derivative (gamma). MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model. 11, 312 (2005); J. Chem. Sci. 117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energy-density [A. Tachibana, J. Mol. Mod. 11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.