Introduction

Polyenes are hydrocarbon chains with alternating single and double bonds. Polyene polymers (polyacetylenes) have been archetypal conductive compounds whose discovery and development by Shirakawa, Heeger, and MacDiarmid was awarded the Nobel Prize in Chemistry [1]. Since then, studies on polyacetylene synthesis, structure, and properties have remained relevant [2, 3]. The long series of consecutive double bonds in the polyene chain gives rise to rich geometrical Z-E (cis-trans) isomerism, with the total number of isomers increasing with 2n, where n is the number of double bonds in the chain. The trans isomers are more stable than the cis which is destabilized by the steric repulsion between the CHCH units. However, the cis-to-trans ratio could be thermally tuned in polymerization: the cis form dominated at −78 °C, trans at above 150 °C, while a 60:40 ratio was obtained at room temperature [2].

Polyene chains are also ubiquitous in a large group of structurally diverse natural products in bacteria, fungi, plants, and marine and terrestrial organisms [4]. Some of them have significant biological activity: eicosanoids [5, 6], carotenoids [7, 8], polyene macrolides [9, 10], and a plethora of yet-unexplored natural polyenes [4]. Surprisingly, over three-fourths of known polyene natural products can be synthesized using 12 building blocks and one coupling reaction [11]. Electron transport can be stimulated in carotenoids and even four double-bond retinoids [12, 13]. Compared to an all-trans carotenoid set in a molecular junction, the other with one terminal cis double bond showed two times lower conductance [12]. Moreover, a controlled isomerization of the trans- to the -cis form, impeded using classical synthesis, can be realized for carotene-based junctions using strong external electric fields [12]. On the other hand, electron transport in 11-cis and all-trans-retinol connecting Au(111) electrodes shows a more symmetrical current-voltage curve for the former but, a molecular diode-like curve at low applied voltages for the latter [13]. This finding demonstrates that the isomeric effect may change a molecular nanowire to a diode with potential applications as field-effect transistors [13].

In this paper, we considered polyenes with one to ten double bonds, R–CnHn–R, n = 2–20, homodisubstituted at both ends with 12 functional groups of different σ- and π-electron donating and electron withdrawing properties: R = H, BeH, BH2, BF2, Br, CH3, Cl, CN, F, NH2, NO2, OH, and SiH3. We considered all-trans or all-cis geometrical isomers with the E (trans) or Z (cis) end-group position. For all isomers optimized with the B3LYP/6-31G** method, we calculated the HOMA index [13,14,15,16], which is not only the geometrical aromaticity index but also indicates the electron-delocalization properties [17,18,19,20]. Variation of HOMA values with the chain length, isomer type, and substituent is discussed. The total and Gibbs energies and the energy differences are gathered in Tables S1–S7 of the Supplementary Information file.

Computations

All structure optimizations were done with the DFT calculations using the B3LYP (Becke, 3-parameter, Lee–Yang–Parr) functional [21, 22], the 6-31G** Pople-type basis set (split-valence double-zeta polarized basis set with five d-type polarization functions on Li-Ca atoms and 2p orbitals for each H atom) [23], and Gaussian 09 software [24]. The 6-31G** basis set was chosen to enable the reproduction of the calculations in any laboratory and because this small basis set yields sufficiently good geometry, energy, and electron density data [25] to build organic physical chemistry indices. This study aims to find trends or tendencies rather than estimate the exact values. Therefore, the approximative B3LYP/6-31G** level seems to be sufficient for such an aim. It was confirmed that each structure exhibits proper symmetry and is at the energy minimum, owning all positive harmonic frequencies.

Results and discussion

The R–CnHn–R (n = 2–20) unbranched polyenes homo-disubstituted with 12 different substituents at the terminal C-atoms (R = H, BeH, BH2, BF2, Br, CH3, Cl, CN, F, NH2, NO2, OH, and SiH3) were analyzed. All-cis or all-trans geometrical isomers were considered (Schemes 1 and 2). The substituent at the terminal C = C group can be introduced in either the trans (E) or cis (Z) position. Then, for each structure, three homo-disubstituted isomers can be formed: trans-trans, trans-cis, and cis-cis, hereafter denoted as EE, EZ, and ZZ.

Scheme 1
scheme 1

Different structures of the trans isomers of 1,6-diflurohexa-1,3,5-triene (DFHT) and 1,8-difluroocta-1,3,5,7-tetraene (DFOT): first row (1E,3E,5E)-, (1Z,3E,5Z )-, and (1Z,3E,5E)-DFHT; second row (1E,3E,5E,7E)-DFOT, (1Z,3E,5E,7E)-DFOT, and (1Z,3E,5E,7Z)-DFOT

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Scheme 2
scheme 2

Different structures of the cis isomers of 1,6-diflurohexa-1,3,5-triene (DFHT) and 1,8-difluroocta-1,3,5,7-tetraene (DFOT): 1st row (1E,3Z,5E)-DFHT, (1Z,3Z,5Z)-DFHT, and (1E,3Z,5Z)-DFHT; 2nd row (1E,3Z,5Z,7E)-DFOT, (1Z,3Z,5Z,7E)-DFOT, and (1Z,3Z,5Z,7Z)-DFOT

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The unsubstituted all-trans isomers belong to the C2h group of symmetry. After the EE or ZZ disubstitution, the molecule’s symmetry remains the same, whereas the EZ isomers belong to the CS symmetry group. The symmetry does not depend on the number of the double bond in the structure (Scheme 1). The unsubstituted all-cis isomers belong to the C2v symmetry group if the number of double bonds is odd, while the C2h one if that number is even. Again, after the EE or ZZ disubstitution, the molecule’s symmetry remains the same, whereas the EZ isomers belong to the CS symmetry group (Scheme 2).

Geometry

The EE, ZZ, and EZ arrangements of the substituents at the two ends favor different substituent·HC intramolecular contacts in the all-trans and all-cis polyene chains. Moreover, various substituents have dissimilar intramolecular contacts. Instead of a detailed description of these contacts, we show them in Schemes 3, 4, 5, and 6. The contacts have an essential influence on the energetics of the studied compounds. For selected intramolecular distances, see Tables S8 and S9.

Scheme 3
scheme 3

Dominant interactions between the NO2 groups and selected hydrogen atoms in the 1,n–disubstituted cis and trans polyene isomers

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Scheme 4
scheme 4

Dominant contacts between the OH groups and selected hydrogen atoms in the 1,n–disubstituted cis and trans polyene isomers

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Scheme 5
scheme 5

Dominant contacts between the BeH groups and selected hydrogen atoms in the 1,n–disubstituted cis and trans polyene isomers. Pointed lines denote close contacts

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Scheme 6
scheme 6

Dominant interactions between the CN groups and selected hydrogen atoms in the 1,n–disubstituted cis and trans polyene isomers. Pointed lines denote close contacts

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Energetics

For all the disubstituted structures under consideration, the total energy differences between the EE, EZ, and ZZ 1,n–disubstituted trans polyene isomers have been meticulously compiled in Table 1. The structure with the lowest energy was taken as the reference point for a given chain length. The total and free Gibbs energies, crucial for understanding the energetics of these isomers, are listed in Tables S2 and S3.

Understanding changes in the energetics of the studied polyene species requires considering the interactions of the end groups: (1) with the closest H atoms and (2) the influence of the end groups on the polyene chain. The two effects depend on the polyene chain type and the end groups’ arrangements. The energetic effect of the end group’s interactions with the closest CH moieties results from an interplay between repulsive and attractive forces. Some of the substituents have free electron pair(s) and can act as proton acceptors (NO2, OH, halogens, NH2), while some others produce steric hindrances (CH3, SiH3, BH2). On the other hand, the influence of the substituent on the polyene chain and its charge delocalization can be regarded as the end groups’ σ- and π-substituent effects.

Table 1 The total energy differences between the EE, EZ, and ZZ 1,n–disubstituted trans polyalkene isomers (kcal/mol) where for given chain length, the lowest energy structure was assumed to be the reference point. EE, EZ, and ZZ stand for the substituent position at the chains ends. For C2 and C4, the values are equal with the cis ones (the trans and cis isomers are present for C6 or larger molecules)
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In most cases, the EE isomers are the most stable. Still, for halogens (F, Cl, Br), the ZZ isomers have the lowest energy. In the case of the CN substituent in the trans conformers, there is practically no energy difference between EE and ZZ structures, whereas in the cis conformers, the EE ones are the most stable. In the NO2 substituted structures, the O-atoms interact with the H-atoms of the CH moieties in both E and Z arrangements (Scheme 3). However, the O and H atoms are too close in the latter, and the repulsive component dominates. Finding the lowest forms of the OH-substituted isomers requires considering different cisoid and transoid conformations of the OH group (Scheme 7).

Scheme 7
scheme 7

Different CH–OH end group arrangements in various polyene chain forms: a transoidal arrangement in trans-isomers, b cisoidal arrangement in trans-isomers, c transoidal arrangement in cis isomers, d cisoidal arrangement in cis isomers. Pointed lines denote close contacts

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First, consider interactions between the end groups and the closest H-atoms. For the trans isomers disubstituted by BeH at the two ends, the energy of EE, EZ, and ZZ isomers differs: the lowest is for the former, and the highest is for the latter (Scheme 5, Table 1). Notice that the relative energy of the EZ isomer is half of the ZZ ones. The analogous relationship can be found for the substituents like BH2, BF2, CH3, NO2, NH2, and SiH3. However, the opposite inequality is found for the halogen substituents (Table 1). For CN, there are practically no differences between the energies of the three types of isomers (Scheme 6, Table 1). The slight relative energy variations are due to the imperfect optimization of the geometry of long chains. For halogens, the energy order is the opposite due to hindrance, which is present in the EE isomers but absent in the ZZ ones.

For trans isomers of the OH derivatives, the energy of the EE structures is also the lowest, EZ is intermediate, and ZZ is the highest. However, two arrangements of the end HO–CH moiety are possible: transoidal and cisoidal (Scheme 7). Therefore, consideration of OH interactions with neighboring atoms is needed. The transoidal conformation of the terminal CH–OH group (Scheme 7b) is energetically more favorable than the cisoidal one (Scheme 7a). This is due to the closer contact between O-atom and the nearest H-atom, which is 2.0 Å for transoidal while 2.2 Å for the cisoidal structure. Notice that in the former case, the nearest H-atom is attached to the same C-atom that the OH group, whereas in the latter case, the nearest H-atom is connected to the next C-atom.

Moreover, in the case of ZZ transoidal forms, destabilizing (O)H…H(C) interaction occurs. The stabilization energy in OH disubstituted trans structures is the same: energy of the ZZ isomers is the highest, that of EE is the lowest, and for EZ is intermediate. For cis isomers, the appropriate distances are equal to 2.0 Å and 2.2 Å for transoidal and cisoidal forms (Scheme 7c, d). The total Gibbs energy values and cis isomers’ Gibbs free energies are listed in Tables S4 and S5, respectively.

These observations are similar for the cis isomers, but some differences exist (Tables S1, S4, and S5). For substituents such as BeH, BH2, BF2, CH3, CN, NO2, NH2, OH, and SiH3, the lowest energy is found for EE isomers and the highest for ZZ. For halogens (Scheme 8), the situation is the opposite. For Cl, there are practically no energetic differences between the isomers; for instance, for C16, the energy differences are 0.03 and 0.05 kcal/mol for EE and ZZ isomers, respectively, while the error of calculation can be estimated as 0.05 kcal/mol, and it is impossible to differentiate which conformer (EE, EZ, or ZZ) is the most stable.

Scheme 8
scheme 8

Dominant interactions between the halogen atoms as substituents and selected hydrogen atoms in 1,n–disubstituted cis and trans polyalkene EE and ZZ isomers. Pointed lines denote close contacts

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The influence of the substituents is relatively high for small molecules like ethene and butadiene derivatives. For example, irregularities are observed for the OH and NH2 substituted ethenes: the Z isomers are more stable than the E ones. This is due to intramolecular hydrogen bonding between the substituents (OH···O or NH···N). Similar interactions are absent in the E isomers. The presence of hydrogen bonding formed by the NO2 groups in the C2 Z isomers causes high energy variations between the Z and E isomers. Deviations are also observed for the C2, C4, and, at times, C6 cis isomers of the BeH, Br, Cl, CN, and F derivatives. The energy differences between the EE, EZ, and ZZ isomers for C6–C20 isomers behave regularly.

The following homodesmotic reactions (i.e., a hypothetic reaction that has the same number and type of bonds in the reactants and in the products) were also calculated for every isomer considered:

$$C2H4\:+\:C2H2R2\;-\;H2\;\rightarrow\;C4H4R2$$
$$2\;C2H4\:+\:C2H2R2\;-\;2\;H2\;\rightarrow\;C6H6R2$$

The agreement between total and relative energies and those obtained from homodesmotic reactions is very good (Tables S6 and S7).

The disubstituted polyene stabilization/destabilization occurs, inter alia, by the chain CH–E and Z positioned substituents intramolecular interplays. The end groups are composed of electron-donating or electron-accepting atoms or both, but whether the interaction is attractive or repulsive depends on the interaction distance. If it is too small due to the structure stiffness, it may correspond to the repulsive part of the potential and be destabilizing. In contrast, if the distance is large enough but not too large, it may correspond to the attractive part of the potential and be stabilizing. The halogens destabilize the structure if they are in the E position and all the others in the Z one (Table 2). However, stronger interactions always occur for the Z-arrangement: for halogens, it is the attractive interaction (Scheme 8), and for the remaining substituents, the repulsive one (Schemes 9 and 10).

Table 2 Stabilization and destabilization of the structure by the intramolecular interactions of the chain CH groups with the substituents in the trans and cis positions
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Scheme 9
scheme 9

Dominant interactions between the substituents such as NO2, BF2, BH2, and NH2 and selected hydrogen atoms in 1,n–disubstituted cis and trans polyalkene ZZ isomers. Pointed lines denote close contacts

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Scheme 10
scheme 10

Dominant interactions between the substituents such as CH3 and SiH3 and selected hydrogen atoms in 1,n–disubstituted cis and trans polyalkene ZZ isomers. Pointed lines denote close contacts

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We expected that the polyene stabilization/destabilization would be reflected in the presence of the intramolecular bond (contacts) critical points (BCPs). Therefore, we performed the atoms-in-molecules (AIM) analysis [26, 27] and determined the electron density parameters at BCPs. The following parameters in BCPs were considered: the rho (electron density), Laplacian of rho (trace of Hessian of rho), V (Virial field = potential energy density), G (Lagrangian form of kinetic energy density), K (Hamiltonian form of kinetic energy density), H (H = G + V, total energy), L = K − G = Lagrangian density, ESP (total electrostatic potential), ESPe (electrostatic potential from electrons), and ESPn (electrostatic potential from nuclei) using AIMAll software [28]. We should obtain a trend showing the connection between an AIM parameter and stabilization energy. Surprisingly, for numerous stable systems, like the most stable conformers of the OH derivatives, no critical points indicating CH…O(H) intramolecular interaction appeared. Instead, the less stable forms revealed repulsive interactions in the conformers, enabling the CH…HO contacts. As a result, we ended up with a bunch of AIM data for only a few systems that do not correlate with stability (Tables S10 and S11).

Following the reviewer’s suggestion, we performed the non-covalent interactions analysis, NCI [29, 30], using the MULTIWFN program [31]. The example of an NCI analysis visualizing the end group’s intramolecular interactions and interchain C–H···H–C contacts is shown in Fig. 1, and some other systems are presented in Figs. S1–S4. The NCI analysis confirms the identification of intramolecular interactions and contacts found using AIM analysis and reveals areas of the substituent-chain dispersion interactions. However, NCI analysis does not provide a unique descriptor of the substituent-chain dispersion interactions. Thus, neither AIM nor NCI analysis takes us any closer to quantifying the effect of the substituent on the polyene chain with an unequivocal parameter, which could be correlated with the structure stability.

Fig. 1
figure 1

The non-covalent interactions (NCI) and reduced density gradient (RDG) scatter graphs for the dinitro (a, c) and disilane (b, d) octatetraenes in all-trans (a, b), and all-cis (c, d) configurations, and the EZ arrangement of the end groups. Green NCI surfaces show only intramolecular interactions. RDG peaks appear at ρ ≈ −0.05 − −0.015  a.u. for hydrogen bonds at ρ ≈ 0.01 a.u. for van der Waals interactions

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It is vital that intramolecular interactions shown in Schemes 8, 9, and 10 and characterized in Table 2 are specific for polyene “bristling” with CH in the all-trans and all-cis arrangements and different from both (i) the group electronegativity acting through the σ-electrons of the polyene skeleton and (ii) resonance effect, i.e., the substituent action on the π-electron system of the polyene chain (Fig. 2). Indeed, no correlation is observed between the energetic stabilization or destabilization and substituent effect descriptors sEDA and pEDA [32] (Fig. 2a and b). Instead, the substituent intramolecular interaction with CH moieties in the trans and cis positions is similar but not exactly the same (Fig. 2c). The interaction in all-cis polyenes is always more destabilizing. One reason is the interaction of the central CH groups, as revealed in the non-covalent interactions NCI analysis (Fig. 1c and d).

Fig. 2
figure 2

The juxtaposition of the substituent effect descriptors sEDA and pEDA [32] with the energetic stabilization or destabilization in the trans and cis polyenes a sEDA(e) and ΔEtrans; b pEDA(e) and ΔEtrans; c ΔEtrans and ΔEcis

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Lengthening the structure

Consider the effects of lengthening the substituted polyene structures using the HOMA (Harmonic Oscillator Model of Aromaticity) index [14,15,16] calculated for the entire polyene chain. The index was initially defined to measure the geometrical aromaticity of the carbo- [33,34,35] and then heterocyclic rings [36,37,38], and some derivative indices better reflecting some heterocyclic systems, like HOMED (Harmonic Oscillator Model of Electron Delocalization), appeared [38].

For carbocyclic rings, the HOMA index is defined as follows:

$$\mathrm{HOMA}=1-\frac\alpha n\sum\nolimits_{i=1}^n\left(R_i-R_{\mathrm{opt}}\right)^2$$
(1)

where Ri and Ropt (Å) stand for the ith CC bond length in the analyzed ring and the reference benzene ring (Ropt=RB) for which HOMA = 1, n is number of CC bonds in the ring, and α = 257.7 Å−2 normalizes the index to be unitless and equal to 0 for a hypothetical perfectly alternating Kekulé cyclohexatriene ring.

However, the HOMA was also recognized as possessing the ability to be used as a general chemical index applicable to aromatic and non-aromatic, cyclic and linear, or branched structures, with and without multiple bonds [16,17,18,19,20]. In particular, the HOMA index adopted to polyene systems without any change of definition parameters, i.e., optimal bond in benzene Ropt treated as a reference standard, and the α parameter being a normalization factor zeroing the HOMA index for an elusive non-aromatic cyclohexatriene structure, is a parameter showing the degree of electron delocalization [18].

It has already been demonstrated for unsubstituted polyenes that the HOMA values of both trans and cis polyenes increase as the number of C-atoms increases and approach a horizontal asymptote [18]. However, the asymptote for the trans polyenes is higher than that for the cis ones. This has been interpreted as an indication that delocalization in the trans polyenes is more prominent than in the cis ones. The same applies to disubstituted polyenes regardless of the (EE, EZ, ZZ) ending and the substituent (Fig. 3). Indeed, for the given chain type, the HOMA values for EE-, EZ-, and ZZ-ended structures show a small difference (points of different colors almost overlap). Moreover, although short chains ended with the BH2 and Br substituents differ a lot (Fig. 3) for the chains composed of 50 atoms, the trans polyenes converge to ca. HOMA = 0.8 while the cis ones converge to ca. HOMA = 0.7.

Fig. 3
figure 3

Examples of correlation between the HOMA index of the disubstituted trans and cis polyenes with different (EE, EZ, ZZ) ending and the number of C-atoms in the chain: a BH2, b BeH, c F, and d NH2 isomers

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It is clear why it is so: the substituent effect is significant on short chains. The short-range influence of substituent on the σ-orbital system (group electronegativity expressed by the sEDA descriptor) cooperates with the long-range impact of substituent on the π-orbital system (resonance effect described by the pEDA descriptor). However, the former is negligible at moderate distances, while the latter becomes insignificant at sufficiently large distances of ca. 20–30 C-atoms.

Let us look at this effect in more detail. Correlations of the HOMA index with the number of carbon atoms for the trans- and cis-type of EZ isomers (Fig. 4) show that in both cases, for a low number of carbon atoms, the lowest HOMA values are observed for the F-substituted structures and the highest for the BH2-substituted ones. BH2 is a strong σ-electron donor and strong π-electron acceptor substituent, while F is a strong σ-electron acceptor and moderate π-electron donor substituent [32]. Both substituents show opposite effects. Judging whether the σ- or π-electron effect affects the delocalization is difficult.

Fig. 4
figure 4

The asymptotic increase of the HOMA index with the number of carbon atoms in the a trans and b cis isomers of the EZ-type

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Moreover, the σ- and π-electron systems are not entirely separated, and a hyperconjugation may occur. However, it should be noted that the H-substituent with null σ- and π-effects acts almost like an F-substituent (Fig. 4). This indicates that the strong σ-electron-withdrawing ability of fluorine is not decisive. Therefore, the π-electron substituent effect plays a key role. Again, the π-electron properties of BH2- and F-substituents are opposite. Thus, strong π-electron withdrawal of the BH2-group increases the delocalization in the polyene chain, while π-electron donation of the F group decreases it. The same trend occurs for a large number of C-atoms, but it weakens as the chain increases (Fig. 4).

In addition, we analyzed changes of ellipticity in bond critical points (BCP) averaged over the single and double CC bonds as the all-trans and all-cis chains increased (Fig. 5). The unitless ellipticity, ε = (λ1/λ2 − 1), where λ1 and λ2, λ1 < λ2 < 0, are the negative eigenvalues of the Hessian of the electron density at the BCP, describes the degree of the electron density distortion in directions 1 and 2 perpendicular in BCP to the bond axis. Large ε denotes a significant π-double bond character, and ε approaching zero denotes a cylindrical electron density shape characterizing either σ-single or triple bond. We expected that due to charge delocalization, with the increase of the all-trans or all-cis polyene chain, the average ellipticity of the single bonds would increase, and the double bond would decrease [39]. The electron density distortion of the former would become greater with an increase of the double bond character, and the opposite would be valid for the latter, for which the double bond character decreases. The ellipticity values averaged over single and double bonds make it possible to integrate the changes as the chain lengthens. Indeed, for the π-electron donating NH2 and F substituents [32], the graphs in Fig. 5 approach the ellipticity value of ca. 0.21 (as in benzene) from the larger value side, while for the π-electron withdrawing BH2 and BeH substituents approaches that value from the smaller value side. The graph of averaged ellipticity changes in the unsubstituted polyenes runs between systems substituted with groups of π-electron donating and π-electron withdrawing (Fig. 5). Observe that the averaged ellipticity values of the all-trans polyenes are always a bit larger than those of the all-cis ones. The substituent effect on single and double bonds alone provides a slightly more complex picture (Fig. S5).

Fig. 5
figure 5

The asymptotic convergence of the average ellipticity in bond critical points (BCP) of the single and double bonds with the number of carbon atoms in the all-trans and all-cis isomers disubstituted by BH2 and BeH π-electron withdrawing, F and NH2 π-electron donating substituents, and unsubstituted systems

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Conclusions

The all-trans and all-cis polyenes homodisubstituted at the ends composed of up to 50 carbon atoms were calculated at the B3LYP/6-31G** level. Twelve substituents were considered: H, BeH, BH2, BF2, Br, CH3, Cl, CN, F, NH2, NO2, OH, and SiH3 for their diversified σ- and π-electron-donating and electron-withdrawing properties. The studied structures, basically planar if only non-H-atoms are considered, reveal many possible arrangements due to three ending possibilities. At the end of the first and last double bonds, the substituent can be in either trans or cis position, and thus, trans-trans, trans-cis, and cis-cis arrangements (denoted as EE, EZ, and ZZ) are possible. In the case of all-trans isomers, the subtypes are independent of the parity of the number of the double bonds in the chain. In contrast, for an even number of double bonds in the all-cis isomers, the EE and ZZ isomers have the C2V symmetry, while the EZ ones exhibit the CS symmetry. In contrast, for an odd number of double bonds, the EE and ZZ isomers have the C2h symmetry, and the EZ ones exhibit the CS symmetry.

Unexpectedly, we found that the substituent electron donor-acceptor characteristics are not the most crucial for the properties of studied systems. Instead, the intramolecular interactions between the substituents and the neighboring chain CH groups appeared more decisive. The disubstituted polyene stabilization/destabilization occurs, inter alia, by the chain CH–E and Z-positioned substituents intramolecular interplays. The end groups are composed of electron-donating or electron-accepting atoms, and depending on the interaction distance, the chain-substituent interaction is attractive or repulsive. The halogens destabilize the structure if they are in the E position and all the other substituents in the Z one. The substituent-chain interplay is consonant in the all-trans and all-cis polyenes. Still, they are always more destabilizing in the latter than in all-trans isomers. The non-covalent interactions and atoms in molecules analyses confirmed the identification of intramolecular interactions, contacts, and substituent-chain dispersion interactions. However, neither of those analyses had taken us any closer to quantifying the effect of the substituent on the polyene chain, which could be correlated with the structure stability.

Using the HOMA index, we demonstrated that for disubstituted polyenes, the electron delocalization increases as the number of C-atoms increases and approaches a horizontal asymptote regardless of the (EE, EZ, ZZ) ending and the substituent. For the trans polyenes, the asymptote is higher than that for the cis ones, which means that the delocalization in the former is more prominent than in the latter. For the chains composed of 50 atoms, the trans polyenes converge to ca. HOMA = 0.8 while the cis ones converge to ca. HOMA = 0.7. Expectedly, the π-electron substituent effect plays a key role: the strong π-electron withdrawal of the BH2 group increases the delocalization in the polyene chain, while π electron donation of the F group decreases it. The same trend is observed for a large number of carbon atoms, but it weakens as the chain increases. The ellipticity changes in bond critical points averaged over the single and double CC bonds with increased polyene chains confirmed delocalization in the chains shown by HOMA changes. Interestingly, the convergence of the ellipticity values for the π-electron donating and withdrawing substituents to the value similar to that in fully delocalized benzene occurred from the larger value side for the former while from the smaller value side for the latter.

This study may have implications for using polyenes as organic molecular nanowires conducting electric current: those constituted up to ca. 20 carbon atoms can exhibit a significant influence on the molecular composition of materials to which they are attached. In contrast, the conductivity of longer polyenes can be independent of the chemical composition of the end connector groups. Moreover, the π-electron donating and withdrawing character of the end (connector) groups matter for the shorter polyenes, and differently acting substituents play significantly different roles. Our study also indicates that the electric conductivity of the all-cis polyenes would be weaker than that of all-trans isomers.