INTRODUCTION

Carbynes are special classes of carbon containing compounds, which are considered as reactive intermediates in various organic transformations due to their incomplete electronic state and coordinative unsaturation. Nowadays, several stable carbynes [1, 2] have been isolated and this field is becoming as an active area of research. Recent attention to carbyne organometallic complexes is due to possible involvement of these species in catalytic reactions [3–7]. Furthermore, these complexes have interesting bonding and reactivity characteristic and play significant roles in synthetic organic and polymer chemistry [8–20]. Many theoretical studies have illustrated the structures and different features of these complexes [21–27].

Cationic ruthenium(II) allenylidenes trans-[Cl(dppe)2Ru=C=C=C(CH3)R]BF4 (R = Ph,CH3) can be deprotonated to generate neutral alkenyl acetylide metal trans-[Cl(dppe)2RuC≡C–C(=CH2)R] or can be protonated with HBF4‚Et2O which leads to generating dicationic ruthenium(II) carbynes trans-[Cl(dppe)2Ru≡C–CH=C(CH3)R](BF4)2. The latter reaction was applied to transform a conjugated bis-allenylidene bridged diruthenium complex, trans-[Cl(dppe)2Ru=C=C=C(CH3)-p-C6H4–CH3)C=C= C=Ru(dppe)2Cl](BF4)2, into the first bis-alkenyl carbyne ruthenium species trans-Cl(dppe)2Ru≡C–CH=C(CH3)-p-C6H4-(CH3)C=HC–C≡Ru(dppe)2-Cl](BF4)4 [28].

The solvent plays important role in chemistry and changes the molecular behaviors by promising many variations to the interactions between solvent molecules and solute [29–31]. In order to consider the solvent effect in quantum mechanical (QM) calculations of electronic structure, several methods were developed [32]. Solvent effect on the structural and spectroscopic properties of various chemical systems has been studied [33–46]. Also, the solvent effect on the barrier height has been investigated in various systems [25, 26, 47–53].

In this study, we aimed at investigating the solvent effect on the structure, dipole moment, the energies of frontier orbitals, reactivity parameters and electronic spectrum of the trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+ complex using quantum chemical calculations.

COMPUTATIONAL METHODS

The software package of Gaussian version.09 was used for conducting all calculations [54]. The standard 6-311G(d,p) basis set [55–58] was used for main groups of elements, while the Ru element was described by the Def2-TZVPPD basis set [59]. Pseudo-potential Effective Core Potential (ECP) was applied to the Def2-TZVPPD basis set [60] to exclude direct calculation of the exchange and correlation integrals related to 28 electrons of the Ru atom. Geometry was optimized using the B3LYP* method with c3 = 0.15 [61]. A vibrational analysis was performed at each stationary point to confirm its identity as an energy minimum.

The information on MOs was evaluated by partial density of states (PDOS) using the GaussSum 3.0 software package [62]; and the Full Width at Half Maximum (FWHM) about 0.3 eV was used to convolute the spectrum. In addition, the comprehensive analysis was carried out regarding the atomic orbitals contributions to the molecular orbitals by the GaussSum 3.0 software.

In order to investigate the solvation effects, all structures were re-optimized in solution phase using the Self-Consistent Reaction Field (SCRF) approach. In this way, full optimization was carried out for the structures in a water medium that was described by Polarizable Continuum Model (PCM) [63] of solvation.

The electronic spectra for the studied compounds were calculated by TD-DFT [64] using the same hybrid functional and basis sets as used for the calculation of the optimization. The 10 lowest excitation energies were computed.

Natural Transition Orbital (NTO) analysis [65] was carried out starting from the output of TD-DFT calculations on optimized geometries. Calculated NTOs were produced using Chemissian software version 4.23 [66].

RESULTS AND DISCUSSION

Energetic Aspects

Figure 1 presents the structure and numbering scheme of atoms in trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+ complex. We have replaced dppe ligand in the synthesized trans-[Cl(dppe)2Ru≡C–CH=C(CH3)R](BF4)2 complex with four phosphine ligand. Table 1 reports the absolute energy and solvation energy values of this complex in the singlet state. Selected solvents are chloroform (CF), tetrahydrofuran (THF), dichloroethane (DCE), acetone, ethanol (EtOH), methanol (MeOH). As it can be seen, the stability of this complex increases in solution phase, and its stability increases in more polar solvents. Consequently, in the presence of solvent, the reacting molecule stabilizes energetically through electrostatic interaction with solvent. The solvation energies values were computed based on the variation between energetic values in gas phase and solution phase. These values were provided in Table 1. As it can be seen, these values were decreased by increasing dielectric constant of solvents. The linear relationship of solvation energies values with dielectric constants is as follow:

$${{E}_{{{\text{solv}}}}} = -1.0531\varepsilon - 146.17;\,\,{{R}^{2}} = 0.8108.$$
Fig. 1.
figure 1

Structure of complex trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+.

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Table 1.  Absolute energy (E, Hartree), solvation energy (Esolv, kcal/mol), total dipole moment (Debye, μ), the wavenumber of most intensity singlet-singlet electronic transition, frontier orbital energy, HOMO–LUMO gap, chemical potential (μ) and electrophilicity values (ω, eV) of trans-ClRu(PH3)4(≡C–CH=CMe2) complex in gas and solution phases; ε and nD are dielectric constant and refractive index of the solvent, respectively
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It can be found, that there is not good relationship between solvation energy and dielectric constant. But, fitting these values with quadratic equation revealed a good correlation between these parameters:

$$\begin{gathered} {{E}_{{{\text{solv}}}}} = {\text{ }}0.0611{\text{ }}{{\varepsilon }^{2}} - 3.2785{\text{ }}\varepsilon - 132.25; \\ {{R}^{2}} = {\text{ }}0.954. \\ \end{gathered} $$

Dipole Moment

Table 1 provides dipole moments components values of trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+ complex in vacuum phase and various solvents.

The total calculated dipole moments showed that these values were increased in solution phase rather than vacuum phase. On the other hand, these values were increased by increasing dielectric constant of solvents. Again, enhancing dielectric constants increases the solute–solvent electrostatic interactions, so, the dipole moment of solute would also increase. Linear relationship of dipole moment values with dielectric constants is as follow:

$$\mu {\text{ }} = {\text{ }}0.0358{\text{ }}\varepsilon {\text{ }} + {\text{ }}10.224;\,\,{{R}^{2}} = {\text{ }}0.844.$$

The linear correlations were investigated between ground state dipole moment of this complex and solvent polarity functions, which frequently include both the refractive index and dielectric constant of the liquid medium. In this study, we used Lippert–Mataga polarity function (called as orientation polarizability of the solvent) [67, 68] and Bakhshiev polarity function [69]. The equations related to these functions include:

Lippert–Mataga polarity function:

$$F\left( {\varepsilon ,n} \right) = ~\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} - ~\frac{{{{n}^{2}} - 1}}{{2{{n}^{2}} + 1}}.$$

Bakhshiev polarity function:

$${{F}_{1}}\left( {\varepsilon ,n} \right) = ~\frac{{2{{n}^{2}} + 1}}{{{{n}^{2}} + 2}}~\left( {\frac{{\varepsilon - 1}}{{\varepsilon + 2}} - ~\frac{{{{n}^{2}} - 1}}{{{{n}^{2}} + 2}}} \right).$$

The linear correlations between μ and these solvent polarity functions include:

$$\mu {\text{ }} = {\text{ }}6.9864F\left( {\varepsilon ,n} \right){\text{ }} + {\text{ }}9.1174;\,\,{{R}^{2}} = 0.9964,$$
$$\mu {\text{ }} = {\text{ }}2.2569{{F}_{1}}\left( {\varepsilon ,n} \right){\text{ }} + {\text{ }}9.3202;\,\,{{R}^{2}} = {\text{ }}0.9994.$$

It can be observed that there is a better correlation between ground state dipole moment with Lippert–Mataga and Bakhshiev polarity functions in the studied complex (Fig. 2).

Fig. 2.
figure 2

Correlation between dipole moment with Lippert–Mataga and Bakhshiev polarity functions in complex trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+.

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Molecular Orbital Analysis

Frontier orbital energy, HOMO–LUMO gap, chemical potential and electrophilicity values of the trans-ClRu(PH3)4(≡C–CH=CMe2) complex in both gas and solution phases are provided in Table 1. It can be found, that the stability of the frontier orbitals were decreased in solution phase compared to gas phase. On the other hand, the stability of these orbitals was decreased in more polar solvents. The linear correlations between frontier orbitals energy and dielectric constants are as follow:

$$E\left( {{\text{HOMO}}} \right){\text{ }} = {\text{ }}0.0373\varepsilon {\text{ }}-{\text{ }}8.0001;\,\,{{R}^{2}} = {\text{ }}0.7956;$$
$$E\left( {{\text{LUMO}}} \right){\text{ }} = {\text{ }}0.041\varepsilon {\text{ }}-{\text{ }}4.2225;\,\,{{R}^{2}} = {\text{ }}0.7961.$$

As it can be seen, there is not a good linear correlation between these parameters.

We investigated the correlation between the frontier energy values and Onsager’s reaction field parameter [70]. These correlations are as follow:

$$E\left( {{\text{HOMO}}} \right) = 9.81\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} - 11.63;~\,\,{{R}^{2}} = 0.9995,$$
$$E\left( {{\text{LUMO}}} \right) = 10.79\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} - 8.22;~\,\,{{R}^{2}} = 0.9995.$$

As it can be seen, there is not a good linear correlation between these parameters.

Plots of the frontier orbitals are presented in Fig. 3. HOMO plot shows the π*-interaction between d orbital of Ru and Cl ligand. In contrast, there is π‑interaction between d-orbital of Ru and carbon of carbyne ligand. LUMO plot shows the π*-interaction between d-orbital of Ru with Cl ligand and carbon of carbyne ligand.

Fig. 3.
figure 3

Plots of the frontier orbitals in complex trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+.

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Calculations revealed that the most value regarding the contribution percentage in the HOMO and LUMO belongs to chloride and carbyne ligands, respectively. The contribution percentage of Ru, phosphine, carbyne and Cl in HOMO are equal to 13, 4, 13 and 70%, respectively. On the other hand, the contribution percentage of Ru, phosphine, carbyne and Cl in LUMO are equal to 15, 3, 80 and 1%, respectively.

Table 1 shows that HOMO–LUMO gap values were increased in solution phase compared to gas phase. These values were increased by increasing polarity of solvents. There is not a good linear relationship between HOMO–LUMO gap and dielectric constants of solvent. However, there is a good linear relationship between HOMO–LUMO gap values and Onsager’s reaction field parameter:

$$Gap = {\text{ }}0.0037\varepsilon {\text{ }} + {\text{ }}3.7775;\,\,{{R}^{2}} = {\text{ }}0.8009;$$
$${\text{Gap}} = 0.977\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} + 3.42;~\,\,{{R}^{2}} = 0.9997.$$

Table 1 shows that chemical potential (μ) values were increased in solution phase compared to gas phase. These values were increased by increasing polarity of solvents. There is not a good linear relationship between μ and dielectric constants of solvent. But there is a good linear relationship between μ gap values and Onsager’s reaction field parameter:

$$\mu {\text{ }} = {\text{ }}0.0392\varepsilon {\text{ }}-{\text{ }}6.1113;{{R}^{2}} = {\text{ }}0.7958,$$
$${\mu } = 10.30\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} - 9.92;~{{R}^{2}} = 0.9995.$$

Table 1 shows that electrophilicity (ω) values were decreased in solution phase compared to gas phase. These values were decreased by increasing polarity of solvents. There is not a good linear relationship between electrophilicity and dielectric constants of solvent. But, there is a good linear relationship between electrophilicity values and Onsager’s reaction field parameter:

$$\omega {\text{ }} = {\text{ }}-0.1212\varepsilon {\text{ }} + {\text{ }}9.8463;\,\,{{R}^{2}} = {\text{ }}0.7674,$$
$$\omega = - 32.40\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} + 21.88;~\,\,{{R}^{2}} = 0.9964.$$

Electronic Spectrum Analysis

Electronic spectrum analysis of the trans-ClRu(PH3)4(≡C–CH=CMe2) complex revealed a strong peak at λmax = 354.16 nm in gas phase. The values of λmax for this complex in the studied solvents are listed in Table 1. As it can be seen, λmax values were red-shifted in solution phase compared to gas phase. On the other hand, the values were red-shifted in more polar. The linear correlation between λmax values and dielectric constants values of solvents is as follow:

$${{\lambda }_{{{\text{max}}}}} = {\text{ }}0.2812\varepsilon {\text{ }} + {\text{ }}368.29;\,\,{{R}^{2}} = {\text{ }}0.8739.$$

Kirkwood–Bauer–Magat equation (KBM). The first theoretical treatment for the solvent-induced absorption wavenumber shifts was given by Kirkwood–Bauer–Magat equation (KBM) and it is shown in the following equation [71]:

$$\frac{{\left( {{{\lambda }_{{{\text{max,gas}}}}}~ - ~{{\lambda }_{{{\text{max,solution}}}}}} \right)}}{{{{\lambda }_{{{\text{max,gas}}}}}}} = \,~\frac{{{\Delta }\lambda }}{{{{\lambda }_{{{\text{max,}}{\text{gas}}}}}}} = \frac{{C\left( {\varepsilon \,\,~ - \,\,~1} \right)}}{{\left( {2\varepsilon \,\,~ + ~\,\,1} \right)}},$$

where λmax,gas is the absorption wavenumber of a solute in the gas phase, λsolution is the absorption wavenumber of a solute in the solvent, ε is the dielectric constant of the solvent and C is a constant depending on the dimensions and electrical properties of the solute dipole.

It can be found that there is a good linear relationship between solvent-induced absorption wavenumber shifts of λmax and (ε – 1)/(2ε + 1) of the KBM equation:

$$\begin{gathered} \frac{{\left( {{{\lambda }_{{{\text{max,gas}}}}}~ - ~{{\lambda }_{{{\text{max,solution}}}}}} \right)}}{{{{\lambda }_{{{\text{max,gas}}}}}}} = - 0.198\frac{{\varepsilon - 1}}{{2\varepsilon + 1}} + 0.033;~ \\ {{R}^{2}} = 0.9909. \\ \end{gathered} $$

Therefore, KBM equation which takes into account only dielectric constant shows good correlations.

Nature of the absorption. Provided these results, we performed Natural Transition Orbital (NTO) analysis on the most intense singlet-singlet transition for the studied complex, using the optimized single geometries. NTO analysis allows a straightforward interpretation of electronic transitions in terms of a hole-particle representation. Calculated NTOs are presented in Fig. 4. As it can be found, this excitation involves mainly the promotion of one d electron of the Ru into the corresponding π* orbital of carbyne ligand. Therefore, this band was interpreted as metal-to-ligand charge transfer band (MLCT).

Fig. 4.
figure 4

Calculated NTOs of the most intensity singlet-singlet transition for complex trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+.

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CONCLUSIONS

In this study, the solvent effect on the structural, dipole moment, frontier orbital energies and electronic spectrum of carbyne complex trans-[ClRu(PH3)4(≡C–CH=CMe2)]2+ have been investigated using the B3LYP* quantum mechanics method. The findings of the computations revealed that solvation energy values indicate the increase in the stability of title complex in more polar solvents. Dipole moments values have been influenced by solvent and there was a good linear correlation between dipole moment and Bakhshiev polarity function. Frontier orbital energies, HOMO–LUMO gaps, chemical potential, and electrophilicity values have been influenced by solvent and indicate good linear correlations with Onsager’s reaction field parameter. A good association has been identified between the wavenumber of most intense singlet-singlet electronic transition and KBM solvent parameters. Electronic transition analysis shows that by increasing the solvent polarity λmax values are red-shifted. NTO analysis illustrates that this band is interpreted as metal-to-ligand charge transfer band (MLCT).