Deeper Insights into Conformational Analysis of cis-Butene and 1-Alkenes as Monomers and Dimers : QTAIM , NCI , and DFT Approach

A few theoretical and experimental studies have been done so far about the properties and the conformational analysis of alkenes as monomers and dimers. Deeper insights into the conformational analysis of monomers and dimers of alkenes and the relation with boiling point are done in this work. In low-lying cis-butene, there is no repulsive interaction betweenmethyl groups but there is an attractive hydrogen-hydrogen bonding. In monomers of 1-alkenes, the most stable conformer has bent-inward geometry which favors the π bond interaction with methyl/methylene hydrogen/carbon atoms. Conversely, each alkene’s molecule in the corresponding most stable alkene’s dimer has a straight, zig-zag geometry. Two straight, zig-zag alkene’s molecules in the corresponding most stable dimer have only one type of intermolecular interaction (hydrogen-hydrogen bonding). As a consequence, very good linear relationships between a physical property (such as boiling point) and theoretical parameters are obtained.


Introduction
To date, there are few theoretical and experimental data about the properties of alkenes as single molecules (monoalkenes or monomers) and as complexes (dimers).From a structure-property relationship study, Nelson and Seybold [1] showed that for a large series of monoalkenes, the mass/bulk of the alkene was the most important determining factor for the most properties.Carroll and coworkers found a linear combination equation based on several structural parameters (number of the carbon atoms, number of the methyl substituents at different positions, number of the ethyl substituents at different positions, number of the propyl substituents, etc.) in order to predict the boiling points of a large range of alkenes [2].
Based on density functional theory (DFT), quantum theory of atoms in molecules (QTAIM), and generalized valence bond method (GVB), we have shown that alkyl groups are moderate electron-withdrawing groups in alkenes, whereas all undergraduate literature studies inadvertently state they are electron-donating groups [3].In that case, most probably, the alkenes' stability trend (direct relation between the increasing number of the alkyl groups attached to the vinylic carbon atoms and their stabilities) might be associated with the decreasing repulsive interaction involving π bond electrons (since the amount of shared electrons decreases as the number of alkyl groups bonded to vinylic carbon increases) and out-of-plane C-H bond electrons (as depicted in GVB analysis of methylpropene in Figure 1), plus an increasing delocalization of the π electrons through the inductive effect.
An arbitrary but extensive conformational analysis of ethene and propene complexes (or dimers) has been done by Jalkanen et al. [4] using the MP2 method where several starting geometries for each dimer were tested.e pushpull feature of tetrasubstituted alkenes (with two electron donating groups at one vinylic carbon and two electron withdrawing groups at the other vinylic carbon) were analyzed and showed strong polarized double C�C bond [5].Energy decomposition from DFT-SAPT has shown that both dispersion and electrostatic components are equally important for the intermolecular interactions in alkene dimers [6].
As to the experimental studies on alkenes, Herschbach and Krisher analyzed the conformers of propene from microwave spectroscopy [7].Holme and collaborators used photoelectron spectroscopy to find two conformers for but-1-ene and four conformers for pent-1-ene.However, for higher alkenes, no reliable information about conformers could be obtained from the photoelectron spectroscopy [8].
e electron momentum spectroscopy indicated that skew conformer of but-1-ene is more stable than its syn conformer by nearly 0.27-0.67kcal•mol −1 [9].
In this work, the DFT with dispersion correction along with QTAIM and noncovalent interaction (NCI) method was used to investigate the conformers of cis-butene, monomers (single molecules), and dimers (complexes) of 1alkenes.From this study, it was possible to obtain very good correlations between a couple of theoretical parameters and alkene's physical property, for example, boiling point.

Computational Details
e geometries of the studied species were optimized according to the Berny algorithm using energy-represented direct inversion in the iterative subspace [10,11].e optimization and frequency calculations of all dimers and cisbutene monomer were performed from the ωB97XD [12]/6-311G++(d,p) [13,14] level of theory.e optimization and frequency calculations of all monomers, except for cis-butene, were performed in the ωB97XD [12]/6-311G(d,p) level of theory.e optimized geometries were used for further QTAIM [15] and NCI [16,17]calculations.All minimum critical points at PES have no imaginary frequency.All the geometry optimization and frequency calculations were done in Gaussian 09 package [18].e accuracy of the functional ωB97XD has been proved in several performance assessments [19][20][21].All Bader's molecular graph calculations were done in AIM2000 software [22].e NCI analysis was performed on MULTIWFN program [23,24] and VMD [25].Some of the starting dimers for the optimization procedure were based on Jalkanen and collaborators' work [4].

Conformers of cis-butene.
e cis-butene has three conformers: one minimum at the potential energy surface (the lowest in Gibbs free energy), one first-order transition state, and one second-order transition state (the highest in Gibbs free energy).
e most stable conformer has two methyl hydrogen atoms (from opposing methyl groups) at the closest interatomic distance (2.102 Å) which enables an attractive intramolecular interaction called hydrogenhydrogen bond according to the molecular graph in Figure 2(a).e most unstable conformer has the longest interatomic distance between methyl hydrogens (2.597 Å), while the intermediate conformer in stability has also intermediate interatomic distance between methyl hydrogens (2.513 Å).
Opposing all undergraduate literature, the methyl groups attached to the vinylic carbon atoms do not promote repulsive interaction in the most stable conformer of cisbutene rather than an attractive interaction with the highest intensity (of all conformers) according to NCI plot (the S function or reduced density gradient isosurface at 0.5 isovalue at the left and the S function versus sign (λ 2 )ρ plot at the right) in Figure 2(a).Conversely, when the methyl hydrogen atoms have the highest interatomic distance (in the second-order TS conformer), there appears the lowest intensity of attractive interaction and the highest intensity of repulsive interaction (Figure 2(c)).
Although having an attractive interaction between methyl groups, cis-butene has 1 kcal•mol −1 higher energy than its trans isomer.From Figure 2(d), one can see that C-C(sp 2 )-C bond angle in trans-butene is closer to 120 °than that in cis-butene.en, in trans-butene, there is smaller angle strain in their vinylic carbon atoms than in cis-butene.

Intermolecular Interactions in Alkene Complexes/Dimers.
In a previous work, we have showed that alkanes and branched alkanes have only hydrogen-hydrogen bond as intermolecular or intramolecular interaction [26].Nonetheless, the alkenes might have three different types of intermolecular interactions: (1) the so-called hydrogenhydrogen bond; (2) hydrogen-carbon interaction; and (3) carbon-carbon interaction.e QTAIM molecular graphs of the most stable complex (after conformation analysis shown in Figures 3(a) and 3(b)) for cis-butene and transbutene indicate have these three types of intermolecular interactions (Figures 3(c) and 3(d)).Not necessarily all of these intermolecular interactions exist in one alkene complex/dimer.
Since each pair of bonded interaction (chemical bond or intermolecular interaction) has a specific range of charge density and delocalization index and since we intend to  Journal of Chemistry obtain linear relations between two properties (a physical and a theoretical property), the analysis of intermolecular interactions from the bimolecular model in alkenes (having two or more distinguished types of intermolecular interaction) is more complex than that in alkanes.In alkenes, all three types of intermolecular interactions (H-H bond, C--H intermolecular interaction and/or C--C intermolecular interaction) might be present or just one or two of them, while in alkanes, only hydrogen-hydrogen bonds are present.en, the use of the bimolecular model to analyze an alkene's physical property (e.g., boiling point) in order to obtain linear relation with the number of intermolecular interactions, for instance, has to be limited to a certain type of alkenes.For example, 1-alkenes have only one type of intermolecular interaction, and then it is possible to obtain a linear relation with a physical property.On the contrary, when taking several types of alkenes (1-alkenes plus its cis/ trans isomers), no linear relation between the boiling point and the number intermolecular interactions or energy of complex formation exists.

Conformers in Gas
Phase of 1-Alkene Monomers.In the gas phase, any molecule has high translational and rotational motions which prevent intermolecular interactions in most cases.Hence, the conformational analysis of monoalkenes might be relevant for the analysis of their properties in the gas phase.Conformational analysis was done by changing the dihedral angles from vicinal carbon atoms as usually done in alkane's conformational analysis.Except for propene and but-1-ene, our conformational analysis was focused solely on the minimum at the potential energy surface, PES.
In propene, there are two conformers where the lowlying conformer (minimum at the PES) has one methyl hydrogen and one vinylic hydrogen (from C1) at the same plane, and the TS conformer has no methyl hydrogen coplanar with C1 vinylic hydrogen.But-1-ene has also three conformers where one is the TS at the PES and the other two are minima at the PES: the most stable conformer (skew conformer) has the methyl group in C4 in an inward position (Figure 4(a)), while in the least stable conformer (syn conformer), this methyl group is outwards (Figure 4(b)), which is in accord with the experimental data [9].
e pent-1-ene has three conformers as minima at the PES (Figure 4(c)), but none of them is in a straight, zig-zag conformation.According to the analysis of its photoelectron spectrum, it has four conformers but one of the proposed conformers is indeed a straight, zig-zag conformer [8].All of the three conformers are bent inwards to the double bond.Even when the starting, arbitrary geometry is a straight, zigzag main chain, its final, optimized geometry has a bentinward conformation (Figure 4(d)).e most stable bentinward conformer of pent-1-ene has intramolecular attractive interaction between π bond and methyl hydrogen/ carbon according to its reduced density gradient surface at 0.5 isovalue (Figure 4(e)).
e hex-1-ene has five optimized conformers as minima at the PES where two conformers are very close in energy (Figure 5(a)).e reduced density gradient surface at 0.5 isovalue of the most stable conformer of hex-1-ene indicates three regions of intramolecular interactions involving methyl hydrogen and π bond, vinylic carbon and methylene hydrogen, plus hydrogen-hydrogen bond (Figure 5(b)).No straight, zig-zag conformer of hex-1-ene exists.Likewise, no straight, zig-zag conformer of hep-1-ene was found.In hep-1-ene, there are seven conformers as minima at the PES, all of them having a bent-inward geometry (Figure S1).One can see that as the chain length of 1-alkene increases, the number of conformers also increases, as expected.en, we can state that single molecules of 1-alkenes in the gas phase have several bent-inward conformations but no straight, zig-zag conformer (as in the case of alkanes).
In all cases of monomers of 1-alkenes, the bent-inward geometry favors π bond interaction with methyl/methylene hydrogen/carbon atoms according to NCI.All monomers of 1-alkenes being minima at the PES have the propene moiety (whose similar structure of its molecule is the minimum at the PES) where the (C3)-methylene hydrogen is coplanar with (C1)-vinylic hydrogen [27].One exception is the syn conformer of but-1-ene.
Figure 6 shows the plots of electronic energy versus C-C-C-C dihedral angle for but-1-ene and pent-1-ene.One can see that the rotational barrier ranges from 2.2 to 4.9 kcal•mol −1 .
e rotational barriers in the

Conformers in Liquid Phase Using 1-Alkene Dimers.
In the liquid phase, the molecules have slower translational and rotational motions in comparison with the gas phase.
en, all types of intermolecular interactions (as many as possible depending on the molecular system) exist in the liquid phase.In order to analyze theoretically these intermolecular interactions, the simplest model is the bimolecular model-the same model we have used in alkanes to obtain linear relations of the number of hydrogenhydrogen bonds with their corresponding boiling point  [26].By using the bimolecular model for 1-alkenes, we have found eight conformers for but-1-ene complex/dimer (Figure S2), seven conformers for pent-1-ene complex/ dimer (Figure 7), and nine conformers for hex-1-ene complex/dimer (Figure 8).e dimers with very small number of intermolecular interactions (according to the bond paths from QTAIM) were not taken into account, and they are not depicted in the following figures because they have the highest electronic energy of complex formation, ΔE.
Unlike 1-alkenes monomers, there is no direct relation between the increase of the hydrocarbon chain and the number of conformers in the bimolecular model.Our conformational analysis for 1-alkene complex was done by changing the position of 1-alkene molecule according to the position of its π bond in relation with the π bond (or methyl/methylene group) of the other molecule.For all 1-alkenes, some of the initial geometries gave the same complex conformer.
Surprisingly, unlike the 1-alkenes in the gas phase where the most stable conformation is associated with bent-inward geometry, the conformation of each 1-alkene in the most stable dimer is nearly straight zig-zag conformation (similar to linear alkanes) when not taking for granted the double bond at one terminal of their chain.For example, the complex conformers of pent-1-ene are depicted in Figure 7 where in the most stable complex conformer, each single pent-1-ene has nearly straight zig-zag conformation.Similar trend occurs with hex-1-ene where bent-inwards geometries are 0.44 kcal•mol −1 higher in energy than the straight zig-zag geometry (Figure 8).en, although 1-alkenes monomers 6 Journal of Chemistry have lowest energy in the bent-inward geometry, when they are interacting with each other as dimers, in the most stable complex conformer, each 1-alkene molecule has the straight, zig-zag geometry.
In addition, 1-alkene complexes have nearly only one type of intermolecular interaction (out of the three possible intermolecular interactions as abovementioned in the previous subsection), except for propene (two C--H intermolecular interactions) and but-1-ene with two C--H intermolecular interaction.e most stable conformation of the 1-alkenes dimers have nearly only hydrogen-hydrogen bonds (Figure 9), which enables linear relations with boiling point, for example.Likewise in alkanes, the number of intermolecular interactions-according to the bond paths of    the QTAIM molecular graphs-of alkene complexes increases as the number of their hydrocarbon chain increases.Propene complex has 2 intermolecular interactions; but-1ene complex has 6 intermolecular interactions; pent-1-ene complex has 8 intermolecular interactions; hex-1-ene complex has 10 intermolecular interactions and so on (Figure 9).Table 1 shows the boiling point of some 1-alkenes along with the electronic energy of complex formation of the corresponding 1-alkenes based on the bimolecular model plus the number of hydrogen-hydrogen bonding (H-H bonds) in the corresponding complex.As the carbon chain increases, the boiling point of the corresponding alkene also increases because the number of H-H bonds increases proportionally.As the number of H-H bonds increase in the complex, the electronic energy of the complex formation decreases because the sum of all interactions increases (the whole intermolecular interaction strength increases).All of these three properties give three linear relations (depicted in Figure 10) with coefficient of determination higher than 0.91 (which corresponds to very good linear relations).It is important to highlight the  excellent correlation between the boiling points of 1-alkenes and the number of H-H bonds of the corresponding dimers (which is even better than that for alkanes in our previous work).

Conclusions
e methyl groups in cis-butene on the ground state lead to attractive interaction by means of hydrogen-hydrogen bond instead of repulsive interaction.e trans-butene is more stable probably due to smaller angle strain.
In gas phase, 1-alkenes monomers have several bentinward conformations but no straight, zig-zag geometry as it is found in linear alkanes.eir bent-inward geometry favors π bond interaction with methyl/methylene hydrogen/ carbon atoms.Conversely, in liquid phase, by considering the bimolecular model, the conformation of each 1-alkene in the most stable complex conformation is nearly straight, zigzag geometry.In addition, this most stable complex conformation of 1-alkenes has only one type of intermolecular interaction, hydrogen-hydrogen bond, whereas other alkene complexes might have up three different types of intermolecular interaction.erefore, it is possible to obtain very good linear relations between 1-alkene's boiling points and the number of hydrogen-hydrogen bonds or the energy of complex formation of the corresponding dimers.

Figure 1 :
Figure 1: GVB mono-occupied orbitals of π bond and carbon localized σ C-H bond in the plane and out of the plane of vinylic carbons along with their corresponding overlap integrals.

Figure 2 :
Figure 2: e S function or reduced density gradient (RDG) surface at 0.5 isovalue at the left and the S function versus function versus sign (λ 2 )ρ plot at the right of cis-butene in its (a) most stable conformer, along with its molecular graph; (b) second most stable conformer; and (c) most unstable conformer.e optimized geometries of trans-and cis-butene along with C-C-C bond angle in degrees.

Figure 3 :
Figure 3: Optimized complex conformers of (a) cis-butene and (b) trans-butene along with their molecular graphs in (c) and (d), respectively.

Figure 6 :
Figure 6: Electronic energy, in kcal•mol −1 , versus C-C-C-C dihedral angle, in degrees, for (a) but-1-ene and (b) pent-1-ene as indicated by the curved arrow of the corresponding molecule.e calculated values are in red points in each plot.