Relations among several nuclear and electronic density functional reactivity indexes

Abstract

An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the ''Quantum Chemical le Chatelier Principle.'' Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.

Semi-Quantitatively Designing Two-Photon High-Performance Fluorescent Probes for Glutathione S-Transferases

“…The α-carbon of the arylsulfonyl group showed the maximum spin density and P + k (Figure 1), indicating the most electrophilic center lies on this very carbon, which is to be attacked by GSH, in accord with the regioselectivity revealed by previous experiments [15,17]. This result indicates that it is the electronic aspects related to electrophilicity rather than other factors such as the leaving ability of the nucleofuge related to nuclear displacement [33,34] that dominate the regioselectivity herein. Confirming P + k 's ability to reproduce the real regioselectivity led to the conclusion that the effective reactivity of a probe with GSH could be characterized by the local electrophilicity ω k of the α-carbon (refer to Equation (1)).…”

Relation between the Fukui function and the Coulomb hole

“…The positivity of both the eigenvalues implies therefore the following constraints Equation (25) in the text can be deduced by multiplying the numerator and denominator of (A11) by λ(k)/(λ(k)λ k -1), which yields and by using the explicit form of h -1 , (A8). According to (A16), when (38) is fulfilled, f k is thus equal to -∞(+ ∞) for λ(k) > 1 (λ(k) < 1) as announced in the text.…”

“…where N k is the number of electrons in fragment k (most often an atom) of the molecule. In practise, the total number of electrons N is a discontinuous variable and the derivatives in (1) and (2) must be computed by using finite difference approximations 2 or by using a continuous model of the ground-state energy E(N) which extrapolates between integer numbers N. 5,6 A large number of works have been devoted to the formulation and to practical calculations of the Fu-kui function [7][8][9][10][11][12][13][14] and in particular of the corresponding condensed (atomic) reactivity index [15][16][17][18][19][20][21][22][23][24][25] for which the possible negativity of the function is debated. The interested reader may consult the following recent reviews of the enormous literature devoted to the reactivity indexes.…”

Investigation of the role of the C-PCM solvent effect in reactivity indices

“…3 They also present set of grand canonical potential derivatives versus {Q, µ} parameters. Analysis up to second order in energy derivatives has been given by Torrent-Sucarrat et al 4 Independent approach is due to Nalewajski. 5 These approaches focus on static force as the origin of all (nuclear reactivity) indices.…”

“…First of all, the set of force constants, describe vibrational harmonic oscillations: 8 (4) and (when diagonalized) give normal mode patterns with corresponding vibrational energies. Then, nuclear reactivity index 9 is the derivative of force acting on the given atomic nuclei, with respect to the total number of electrons.…”