The Response of Electronic And Energetic Properties of Two Types of The Sp-hybridised Carbon-Carbon Bonds To An External Uniform Electric Field


 The susceptibility of electronic and energetic properties of two sets of molecules to perturbation in a uniform electric field was investigated. The molecules of one set were (10)cumulenes terminated with two functional groups, R1 and R2; those of the second set were (10)polyyenes substituted with the same R1 and R2 groups. The cumulene and polyyne molecules had similar lengths of the system of conjugated bonds between the two most extreme carbon atoms. Dipole moments and polarizabilities of the molecules were used as determinants of the overall charge transfer between polar groups and their modifications due to the application of an external electric field. The field was directed along the main (longest) axis of the molecules from the negative to the positive pole. Comparison of the polarizability values revealed that they were higher in the (10)cumulenes than in the (10)polyynes. Parabolic dependence of the molecular energy as function of field strength can be interpreted in terms of the response of electron density to an electric field.


Introduction
Electric elds affect chemical reactions as the eld can signi cantly alter the potential energy curves near the transition state region governing chemical reactions [1] and consequently, in uence course and rate constants of the reactions. This way elds may also impact the biological properties of cells and their components. Impact of the external electric elds on diatomic molecules: energies, geometries, and vibrational Stark shifts is described by Sowlati-Hashjin and Matta [1]. These effects of the electric eld were investigated both theoretically and experimentally. A comprehensive and informative review of structure and reactivity control has been written by Shaik et al. [2]. Most effects can be comprehended as eld-augmented transition state stabilisation by ionic structures [2]. The interaction of molecules with external elds may result in the breaking and making of chemical bonds.
Upon variation of electric eld and polarity, it is possible to stabilise different tautomeric forms of a molecule [3]. An electric eld may also perturb molecular vibrations; the largest change in the IR spectrum induced by the eld is a linear frequency shift [4]. There are many other reports describing the impact of electric eld on the properties and reactivity of molecules [5][6][7][8][9][10].
This study is a continuation of the previous work [5] where the susceptibility of two other sets of molecules to perturbation in a uniform electric eld was investigated. The molecules of one set were deca-1,3,5,7-pentaenes terminated with two functional groups, R 1 and R 2 ; those of the second set were 4-R 1 -4'-R 2 -p-diphenylbenzenes, with R 1 and R 2 being the same as in the pentanes set. Comparison of the effect of the charge relocations in both series of the conjugated molecules revealed that the charge transfer imposed by the electric eld was more e cient in the pentanes than in the aromatic compounds. From the point of view of this study, the most interesting papers are those dealing with molecules containing chains of carbon atoms [11][12][13]. Action of an electric eld on atoms or molecules [14][15][16][17][18] can be measured and visualised with polarizability, resulting from the interaction of atoms or molecules with the eld of their interaction or an atom or molecule in electric eld. This computational study aims at gaining insight into the effect of external elds in two groups of molecules: polyynes and cumulenes with the same substituent pairs (Fig. 1). The examined cumulenes belong to class of even cumulenes, i.e. with an even number of cumulated double bonds [11].
Dipole moments were used as a measure of the overall charge transfer within the molecules, as in the case of deca-1,3,5,7-pentaenes and 4-R 1 -4'-R 2 -p-diphenylbenzenes groups. Thus, the links (linkers) connecting substituents were chains of ten sp-hybridised carbon atoms. In molecules of one type, known as cumulenes, the carbon atoms are connected with double bonds, whereas in molecules of the second type, named polyynes, there are alternating single and triple bonds. Due to polar substituents, all molecules of both types are polarised and their energies depend on the applied eld intensity. The polarizability values were calculated as slopes of the plots: dE n /dF vs F, (1) where E n stands for the energy of a molecule in an electric eld and F stands for the intensity of the applied eld.
Polarizability is believed to play an important role in intermolecular interactions of heterogenous media such as protein-ligand binding. The methods of calculation of molecular dipole moments and polarizabilities was benchmarked [18].
Electron transmission through molecules and molecular interfaces has been a subject of intensive research due to a recent interest in electron transfer phenomena underlying the operation of the scanningtunnelling microscope on one hand and in the transmission properties of molecular bridges between conducting leads on the other [19]. Most electric eld effects on molecular structures and reactions can be comprehended as the eld-induced stabilisation of ionic structures.

Calculation
Molecular geometries were optimised with and without external elds. All calculations were conducted using the Gaussian 09 program [20]. The calculations were conducted using Lee-Yang-Parr correlation functional {B3LYP} [21]. The 6-31 + G{d} basis set with the polarised and diffusion functions was employed. The values of the electric eld strength used in our calculation were taken from the interval − 0.015 to 0.015 a.u. (-7.71 × 10 9 V/m to + 7.71 × 10 9 V/m). The elds were applied along the x-axis of the coordinate system. The C-C chains were approximately parallel to the x-axis of the coordinate system therefore all elds in this study have the same direction as the x-axis along which they are aligned (Fig. 1).
The axes were oriented so that the dipole moments of all molecules without any applied electric eld were positive -that is, the dipole moments originate at the negative pole and point to the positive pole. Plots of the calculated energies against the eld intensity (F) are shown for (10) 2), which is correct in the case where the elds that are colinear with the molecular axis were applied and higher terms in F may be neglected [22].  Fig. 1, were determined according to Eq. (4). As can be seen, dipole moments in the electric eld directed along the x-axis of the molecules are larger for substituted cumulenes (Tables 1) than for polyynes (Table 2). Polarizabilities of the substituted cumulenes and polyynes, obtained from the derivative of the electronic energy (E n ) with respect to F, are given in Table 3. The data show that polarizability values of cumulenes are 7-25% higher than those of polyynes.  Figure 1 shows that the carbon atoms are linked by double bonds in cumulenes, whereas in polyynes there are alternating single and triple bonds. To verify this structure, we compared bond length values for two series of molecules with the same functional groups without the applied electric eld and with the eld of intensities + 0.01 and − 0.01 a.u. The data is shown in Table 4.

Conclusions
The reaction of cumulene and polyyne molecules with similar length of conjugation to electric eld was compared. We report that polarizability of cumulenes is 7-25% higher than that of polyynes. Standard deviation of carbon-carbon bond length is twice as large in the group of polyynes as in the group of cumulenes. It turned out that the communication between two electroactive moieties (ending groups with varying degrees of polarity) connected to two different chains of the sp carbon atoms is stronger in the group of cumulenes than in the group of polyynes.

Declarations
Funding The computing grant G44-18 from the Interdisciplinary Center for Mathematical and Computer Modelling (ICM) of Warsaw University and the nancial support from the Polish Ministry of Science and Higher Education are gratefully acknowledged.
Con icts of interest/Competing interests The authors declare no con ict of interest.
Availability of data and material Data not available.