The Linear Response Kernel: Inductive and Resonance Effects Quantified

Abstract

Calculations of conceptual density functional theory (DFT) reactivity indices are mainly restricted to global quantities and local functions, whereas values for the nonlocal kernels are rarely presented. We used a molecular orbitalbased expression to calculate the atom-condensed linear response kernel. The results are the first published values of this quantity that have been obtained through a direct and generally applicable methodology. This letter focuses on the off-diagonal elements, which provide insight into the nonlocal contributions to chemical reactivity. A detailed study of a set of eight functionalized alkane and polyalkene derivatives enabled us to quantify inductive and resonance effects. SECTION Molecular Structure, Quantum Chemistry, General Theory S everal authors 1-4 have recently been paying attention to higher order derivatives and functional derivatives of the electronic energy E within the context of conceptual or chemical density functional theory (DFT). [5][6][7][8][9] The linear response function or polarizability kernel χ(r,r 0 ), which is defined as

Theoretical Investigation on Nearsightedness of Finite Model and Molecular Systems Based on Linear Response Function Analysis

“…During the past decades, LRFs of molecules has been computed in relation to the chemical reactivities [15][16][17][18][19][20][21][22]. In particular, an important relation is the Berkowitz-Parr relation [17] as given by:…”

“…Of course, the reactivities of molecules are closely related to the issue of nearsightedness of molecules. In particular, the substituent effects such as inductive and resonance effects are not localized on the few sites, for which NEM does not holds [19]. Our study is to examine NEM of finite systems on the basis of LRF analyses of both model systems and molecular systems.…”

Linear Response Function of Bond-Order

“…Next, we calculated the LRF-BOs of the saturated and unsaturated (conjugated) molecules, which has been one of the standard systems for testing of the applicability of the linear response function of density (LRF-D) to inductive and resonance effects of organic molecules [9,14]. For this purpose, we picked out hexan-1-ol and hexa-1,3,5-trien-1-ol, the molecular structures of which are illustrated in Figure 5a,b.…”

“…One of the well-established properties is the Fukui functions, which are defined as the left (−) and right (+) side derivatives of density with respect to the number of electrons, N, i.e., $f^{\pm }(r)\equiv {(\partial \rho (r)/\partial N)}_{\mathrm{normalv}}^{\pm }$, and are known to be typical indicators for nucleophilic and electrophilic attacking sites, respectively [3,4,5]. Also, a derivative of density with respect to external potential ($\mathrm{normalv}$) with fixing the number of electrons (N), ${(\partial \rho (r)/\partial \mathrm{v}(r^{\prime }))}_{\mathrm{normalN}}$, called the linear response function (LRF), has been found to be a measure of electron delocalization properties such as induced and resonating effects of conjugated systems [4,5,6,7,8,9,10,11,12,13,14,15,16]. Also, the LRF is reported to have maximum values at transition states for several Diels-Alder reactions, being another important descriptor of chemical reactions [13].…”

The polarisability of atoms and molecules: a comparison between a conceptual density functional theory approach and time-dependent density functional theory

“…In recent years, some of the present authors have used the linear response function to investigate inductive, mesomeric and hyperconjugative effects, aromaticity and antiaromaticity, opting for an atom condensation scheme in order to reduce the computational effort required [16][17][18][19][20][21][22]. Specifically, the object under study was given by…”