Chemical reactivity in the framework of pair density functional theories

Abstract

Chemical reactivity descriptors are derived within the framework of the pair density functional theory. These indices provide valuable information about bonding rearrangements and activating mechanisms upon electrophilic or nucleophilic reactions. Indices derived and tested in this work represent nonlocal counterparts of the local reactivity indices derived in the context of conceptual density functional theory (CDFT) and frequently used in reactivity studies; the Fukui function, the local softness and the dual descriptor. In this work, we show how these nonlocal indices provide a quantum chemical basis to explain the success of qualitative resonance models in chemical reactivity predictions. Also, local information is implicitly contained as CDFT indices are obtained by simple integration. As illustrative examples, we have considered in this work the Markovnikov's rule, the reactivity of enolate anion, the nucleophilic conjugate addition to α,β-unsaturated compounds and the electrophilic aromatic substitution of benzene derivatives. The densities used in this work were obtained with Hartree-Fock, Kohn-Sham DFT, and singles and doubles configuration interaction (CISD) approaches.

Bond fukui indices: Comparison of frozen molecular orbital and finite differences through mulliken populations

“…[23] Both studies relate second-order Fukui functions to changes in bond orders upon ionization of a molecule. In 2012, Otero and Mandado [22] introduced chemical reactivity quantities in the framework of pair densities. Essentially, all three articles rely on exchange-correlation density matrices and the derivation [35] of shared electron distribution indices [36] (variably also described as bond indices, delocalization indices, and bond orders).…”

“…Conversely, the one atom condensed Fukui function, F A can be extracted from their second-order Fukui functions through summation over all atoms B by virtue of the orthonormality of the natural orbitals. Note that both Fradera and Sola [21] and Otero and Mandado [22] base their derivations on r space-based AIM methods although they can easily be rederived using a Mulliken method, affording for a single Slater determinant theory:…”

“…(15) and for a FMO approximation as in eq. (22). Fukui matrices were obtained as described earlier, [14] expressing the density matrices for both the neutral and charged molecule in terms of the orthonormal set of molecular orbitals obtained from the neutral state calculation.…”

“…This allows for an alternative way of computing bond Fukui functions, with the added advantage that one can establish in which Fukui orbital each bond AB has the biggest contribution. Using a Mulliken reformulation of the second-order Fukui function [21][22][23] [see eq. (24)], we also computed these values for comparison.…”

“…Moreover, it should be possible to extend the Fukui functions to Fukui matrices [14,15] such that atom and bond condensed Fukui functions are the traces of the corresponding matrices. In the first section, a theoretical development of the ideas is presented, including how the presently introduced bond Fukui functions fit into derivatives of the first-order density matrix as opposed to earlier works [21][22][23] based on exchange-correlation densities and how it respects the required normalization conditions as opposed to the approach by Contreras and coworkers [24][25][26] when applied to calculations using overlapping basis functions. We also show how the newly introduced bond Fukui functions are closely related to the first-order density matrix, whereas other attempts, [21,22] in fact, require the second-order density matrix which is not always readily within reach.…”