Substituent Effect versus Aromaticity—A Curious Case of Fulvene Derivatives

A computational study on amino- and nitro-substituted penta- and heptafulvenes reveals the interplay between the aromaticity and the substituent effect (SE). Ring substitution alone has little influence on the aromaticity, but in combination with an exo substituent of opposite properties, it substantially enhances the cyclic π-electron delocalization. Despite the SE being stronger for β substitution, only γ substitution leads to higher aromaticity. An explanation is provided by the electron density of delocalized bonds (EDDB) method, which proves to be a valuable tool in analyzing both cyclic delocalization and the SE.


Table of Contents
Quantum chemical DFT calculations were performed in the Gaussian 16 program rev.A.01 1 using B3LYP functional with 6-311++G(d,p). 2 Vibrational frequencies were calculated afterwards, to confirm that the optimized geometries correspond to the minima on the potential energy surface.Two conformations have been checked in the diamine derivatives; first one corresponding to the two amino groups rotated so that their lone pairs are facing the same direction, whereas in the second one the groups are rotated by 180 degrees relative to each other -their lone pairs face opposite directions.The lower energy conformers were considered in further analyses.π-Electron delocalization was assessed using several methods: Harmonic Oscillator Model of Aromaticity (HOMA), Electron Fluctuation Index (FLU), Aromatic Stabilization Energy (ASE), Nuclear Independent Chemical Shift (NICS), and Electron Density of Delocalized Bonds (EDDB).
HOMA 3,4 is a geometry-based aromaticity index, which can be calculated from Equation 1: where n is the number of bonds taken into account when carrying out the summation, i indicates the type of bond, αj is an empirical normalization constant (for CC bond, αCC = 257.7),dopt,j is the optimal length of a given bond assumed to be realized in fully aromatic systems with HOMA = 1 (for CC bond, dopt,CC = 1.388Å), and dj,i is an actual bond length in the studied system.
FLU index is an index derived from the electronic structure of the molecule, namely the values of electron sharing indices (ESI) between pairs of atoms. 5FLU can be calculated from Equation 2, in that case the ESI used are delocalization indices between two atoms, A and B, δ(A, B). δref(A, B) is a reference value of δ(A, B); for C-C bonds it corresponds to the value for the bond in benzene.
The ring considered in Equation 2 is formed by atoms in the string {} = {A1, A2, … AN}, A0  AN and the atomic delocalization V(A) is defined by Equation 3: while  is a function that ensures that the ratio of atomic delocalizations in Eq. 2 is always greater or equal to 1 (Equation 4): The ESI used can be the delocalization index, fuzzy bond orders, or Mayer-Wiberg bond orders. 6In our particular case, FLU was calculated from fuzzy bond orders using scripts implemented in Multiwfn program. 7It should be emphasized that the FLU (Equation 2) is close to 0 in aromatic systems and increases as the molecule moves away from the aromatic reference.
EDDB is a recent method which has its roots in the orbital communication theory.It uses the natural orbital representation (NAO) of the wavefunction and several transformations to decompose the total electron density into electrons which are localized on single atoms -lone pairs and core electrons (Electron Density Localized on Atoms, EDLA), electrons localized between atomic pairs (Electron Density of Localized Bonds, EDLB), and electrons delocalized between several bonds (EDDB).The atomic populations or density of delocalized electrons can be further analyzed in order to describe delocalization quantitatively or visualize graphically.Full theory behind the EDDB method can be found in papers by Szczepanik et al. 8,9 Various variants of EDDB exist.EDDBG (G for global) evaluates the global electron delocalization, EDDBH evaluates the global electron delocalization without contribution from H atoms, EDDBF (F for fragment) evaluates delocalization in selected molecular fragment, EDDBP (P for pathway) evaluates electron delocalization for a particular cyclic delocalization pathway.In each variant contributions from electrons at σ, π, δ and φ orbitals can be dissected, for example EDDBP(π) evaluates the cyclic π-electron delocalization associated with aromaticity.
ASE is an index that goes to the very roots of aromaticity.From the beginning, high stability of benzene was observed, and later of other aromatic compounds.Thus, the idea of estimating the ASE and making it a measure of aromaticity arose.This energy used to be estimated on the basis of experimental data, nowadays on the basis of quantum-chemical calculations of the energy difference of various chemical reactions between aromatic and non-aromatic compounds. 10Unfortunately, such energy estimation is not an easy and simple task.Plenty types of chemical reactions have been proposed so far.In this work, we used probably the most efficient method for estimating ASE (only two chemical compounds are involved in the reaction), the isomerization method. 11This is based on the energy difference between the methyl derivative of the aromatic system and its nonaromatic exocyclic methylene isomer.
Unfortunately, the estimation of the aromatic stabilization energy by the isomerization method (like other methods of calculating ASE) is disturbed by many factors, such as changes in the ring stress energy (obviously not the same for the aromatic and non-aromatic derivative) or the position in the ring where the exocyclic methyl and methylene groups are located.Also, the compounds studied in this work can potentially be modified for the isomerization reactions at different places.Therefore, for the purposes of this work, the exocyclic group was always substituted in the beta position (on the opposite side of the ring from the amine or nitro groups), and the CH2 group appearing after isomerization in the ring in the adjacent alpha position.
NICS is a magnetic index of aromaticity.It was originally defined as the absolute magnetic shielding at the geometrical center of an investigated ring 12 and has had many modifications. 13One of these modifications, NICS(1)zz (where the point at which we calculate the chemical shift is one angstrom above the center of the ring, and only the component of the magnetic tensor perpendicular to the plane of the ring is taken into account), is used here. 14The calculation were carried out using the GIAO method at the B3LYP/6-311++G(d,p) computational level. 15In the case of significantly bend rings (to avoid interference due to the proximity of atomic nuclei), the NICS value was calculated on the side of the ring where the chemical shift calculation point is positioned further away from the atoms of a studied molecule.
Electronic properties of substituents were evaluated quantitatively using the charge of the substituent active region (cSAR) parameter. 16Its definition is presented in Figure S2.Positive cSAR values indicate the deficit of electrons in the substituent active region, i.e. the substituent is electron-donating.Negative values represent an excess of electrons in the active region of the substituent, indicating its electron-withdrawing properties.To allow comparison with our other results (e.g.data on benzene derivatives, presented in some figures in the Supplementary Materials), the atomic charges used to calculate cSAR were obtained by the Hirshfeld method. 17cSAR was calculated for substituents X and Y, cSAR(X) and cSAR(Y), as well as for the entire exocyclic fragment =CH-Y, cSAR(=C-Y).Substituent Effect Stabilization Energy (SESE) is the energetic substituent effect descriptor.It evaluates energy associated with interaction between two substituents and is calculated as the energy difference of reactions of type: Y-R-X + R => R-X + R-Y.AIM analysis was performed in Multiwfn program. 7igure S2.Definition of cSAR and interpretation of its value.qX is the sum of atomic charges of all atoms forming a substituent X, while qipso is the atomic charge at the ipso atom.
Supplementary Tables and Figures

Figure S5 .
Figure S5.Differences in absolute values of cSAR(Y) for the β and γ heptafulvene derivatives.

Figure S8 .
Figure S8.Dependences between HOMA of the hepta-and pentafulvene ring and C=C bond length.

Figure S9 .
Figure S9.Dependence between exocyclic C=C bond parameters -its length and electron density at bond critical point, ρBCP.

Table S1 .
Relative stability of hepta-and pentafulvene derivatives and calculated values of aromaticity indices for fulvene ring.ΔE(cis,trans) compares the stability of cis and trans diastereoisomers of given compound; ΔE compares the stability of all configurational isomers with the same chemical formula (each group is separated by double borders).FLU*/FLU is the value of FLU for unsubstituted hepta-or pentafulvene divided by the value for given system.

Table S2 .
Collected data generated in this study.Electronic properties of groups X, Y and exocyclic fragment =CH-Y, evaluated by cSAR.Values of aromaticity indices, lengths of C-X (dCX) C-Y (dCY) and exocyclic C=C (dC=C) bonds (in Å), electron density at C=C bond critical point (ρBCP, in e•B -3 ), corresponding laplacian of electron density (∇²ρBCP, in e•B-5) and C=C bond ellipticity (ε).Planarity of fulvene rings in studied compounds is color coded in the first column: green -planar, orange -bent.Systems are sorted by decreasing HOMA value.