Computational and Spectral Means for Characterizing the Intermolecular Interactions in Solutions and for Estimating Excited State Dipole Moment of Solute

The results obtained both in quantum chemical computation and in solvatochromic study of pyridinium di-carbethoxy methylid (PCCM) are correlated in order to estimate the electric dipole moment in the excited state of this molecule. This estimation is made by a variational method in the hypothesis that the molecular polarizability does not change in time of the absorption process. Ternary solutions of PCCM in protic binary solvents are used here, both establishing the contribution of each type of interaction to the spectral shift and to characterize the composition of the first solvation shell of PCCM. Results are compared with those obtained before for other binary solvents. The difference between the interaction energies in molecular pairs of PCCM-active solvent and PCCM-less active solvent was also estimated based on the cell statistical model of the ternary solutions.


Introduction
Knowledge about the electro-optical parameters of molecules in different electronic states obtained by experimental means is of the greatest importance for the researchers working in quantum chemistry field, either for comparison with theoretical data or for overtaking some steps of calculations based on them.
The electronic spectra (absorption or fluorescence) involve the valence electronic cloud very sensitive to the external fields. In solutions, the solute (spectrally active) molecules are under the action of the internal electrostatic field created by the solvent molecules surrounding them (named by Onsager internal reactive field [1]). The strength of the interactions between the solute and a given solvent depends both on the internal reactive field magnitude and on the electro-optical parameters of the spectrally active molecule. The ground state electric dipole moment of the studied molecule keeps its orientation, parallel to the ylid bond both in water and in ethanol, but changes its absolute value, as it results from the data of Table 1. In the same time, the molecular polarizability does not support significant change when PCCM is passed from vaporous state in solution with water or ethanol (see Table 1). A significant increase of dipole moment takes place when a PCCM molecule is solvated in water or ethanol, hydroxyl solvents in which hydrogen bond are possible between the ylid carbanion electron lone pair or the electrons of C=O groups and their hydroxyl groups. As seen from Table 1, three places are possible for a hydrogen bond addition to PCCM (three HBA counts are possible for PCCM). The aim of this study was to use the spectral data obtained for PCCM binary and ternary solutions in order to obtain information about the excited state dipole moment of ylid and the nature and the strength of the intermolecular interactions in diluted ylid solutions. The difference between the potential energies in molecular pairs achieved between the ylid and the hydroxyl solvent molecules in ternary solutions is also estimated in this study.
The inhomogeneity of the first solvation shell of ylid in ternary solutions was also evidenced, by estimating the molar fractions of the two solvents in the first solvation shell of PCCM. The results can be compared with those obtained for a pyridinium ylid with non-symmetrical carbanion, pyridinium acetyl benzoyl methylid (PABM), or for benzo-[f]-quinolinium acetyl benzoyl methylid (BQABM) published before [28,32].

Experimental and Computational Details
The studied substance was prepared as it is described in Reference [11], in the Alexandru Ioan Cuza University labs. The purity of the obtained substance was checked by spectral (NMR and IR) and chemical (elemental) means.
The spectrally grade solvents were achieved from Merck Company and Fluke (Sigma-Aldrich) and used without any purification.
The solvent parameters were taken from https://www.stenutz.eu./chem.solv26.php. The binary solvents used in this study were achieved in molar fractions from double-distilled water, ethanol, and methanol.
The visible electronic absorption band was recorded at a Specord UV-Vis Carl Zeiss Jena spectrophotometer.
Statistical analysis was made by using Origin 9.

Theoretical Notions
The optimized geometry (the arrangement of molecular atoms for which the molecular energy is minim) and some energetic, electro-optical, and QSAR parameters of the PCCM molecule in electronic ground state were established in computational estimations with Spartan'14 program.
Some of the data obtained in quantum mechanical analysis are used here for estimating, in a variational method, the excited state dipole moment of PCCM based on solvatochromic results. In this method, a relation is established between the excited dipole moment and the polarizability of PCCM, and then the excited state dipole moment is determined in the McRae [2] and Kawschi [7,34] hypothesis that the molecular polarizability does not change during of electronic transition responsible for the visible band appearance.
The solvent influence on the visible band of PCCM was explained both by using empirical parameters introduced by Kamlet Taft [35] and also by using Relation (2), derived by the theory of diluted solutions developed by McRae [2], Bakhshiev [3], Abe [4], and others, in the hypothesis that only long-range (universal or non-specific) interactions determine the spectral shifts. In this case, the influence of the specific interactions is taken into consideration by two empirically introduced terms in Relations (1) and (2). with The significance of the parameters in (1)-(3) is the following: v(cm −1 ) is the wavenumber in the maximum of the intramolecular charge transfer (ICT) band of PCCM; ε and n are the solvent electric permittivity and refractive index; π * is the solvent polarity/polarizability indicator; and α (HBD) and β (HBA) are the solvent abilities to donate or to accept protons in hydrogen bonds [27,36]. The empirically introduced solvent parameters [35] π * , α, and β are named Kamlet Taft parameters and are usually used in solvatochromic studies [37,38].
The correlation coefficients, C 1 and C 2 , from Relation (2) depend, as indicated by Relations (4) and (5), on molecular dipole moments, µ; polarizability, α; ionization potentials, I; and temperature, T, at which the experiments are made. The indices g and e refer to ground and excited electronic states, and u and v refer to the solute and solvent molecules, respectively.
In (4) and (5), a is the molecular radius, approximated (in the hypothesis that the molecule is a spherical entity) by using Relation (6), and ϕ is the angle between the dipole moments.
The volume, V, and the area, A, from (6) were obtained here by quantum mechanical computations (see Table 1).
The correlation coefficients, C 1 and C 2 , resulting from the solvatochromic analysis, can be used for estimating both the excited state dipole moment and the angle between the electric dipole moments in the electronic state responsible for the electronic band appearance when some electro-optical parameters of the studied molecule are obtained by other methods (for example, by computational methods). The results obtained in solvatochromic study and the molecular parameters for the PCCM ground electronic state established by Spartan'14 are used here to estimate the dipole moment in the excited state of this molecule. For the molecules showing electronic spectra both in absorption and fluorescence [3,8,34,39], the correlation coefficients, C 1 and C 2 , are usually transformed in an equations system by introducing molecular parameters of the ground electronic state obtained by quantum mechanical analysis. The excited state dipole moment, the excited state polarizability, and also the angle between the solute dipole moments in the two states of electronic transition are estimated in the limits of approximation in which the theory of liquids was developed [2][3][4][5].
There are molecules showing only absorption spectra. In their case, the values of the coefficients, C 1 and C 2 , and the electro-optical parameters theoretically obtained could offer information about the excited state dipole moment by using a variational method [40] applied with good results for other molecules [10,38].
Some relations between the excited state dipole moment, the polarizability, and angle between the dipole moments in the electronic states of the transition are established in this method. Based on these relations, the excited state and polarizability can be computed at each angle (considered as being variable) between the dipole moments. The absorption transition is supposed to be achieved when the excited state polarizability of the solute molecule equalizes the ground state polarizability, in accordance with McRae's [2] or Kawski's [7,34] approximations.
The majority of the publications [40][41][42][43][44] takes into consideration the ground electronic state parameters of the spectrally active molecules computed in quantum mechanics for isolated molecules, in their vaporous state, while in solutions, their parameters can drastically be changed by interactions. This approximation could also influence the value of the excited state dipole moment estimated by using computational and solvatochromic results.
Ternary solutions were used both to enlarge the physical parameters of the liquids used in solvatochromic study and to characterize the local structure of the diluted solutions of PCCM.
Additionally, the statistic cell model of ternary solutions [45][46][47][48][49] applied to PCCM permitted us to estimate the difference between the interaction energies in molecular pairs of the types: ylid-active solvent (1) and ylid-inactive solvent (2). This is a very important result because there are very few methods for estimating the intermolecular energy for molecular pairs in solutions.
The average statistic weight of the most active (from the interactions point of view) solvent in the first solvation shell of the solute molecule, noted by p 1 , must be defined in the statistical cell model [50,51] of the diluted ternary solutions achieved in binary homogeneous liquids, because the composition of the first solvation shell of the spectrally active molecule can differ from the composition of the liquid mixture in the bulk solution. This parameter is the average percent of the active solvent molecules in the first solvation shell of the solute molecule, which can differ by the molar concentration of this solvent in the bulk solution, noted by x 1 . Relations of the type p 1 + p 2 = 1 and x 1 + x 2 = 1 are true for the two solvents of ternary solution.
Between these parameters, a linear relation of Type (7) was established [28,32] with the slope near the unity and the cut dependent on the difference w 2 − w 1 between the interaction energies in molecular pairs ylid-active solvent (indexed by 1) and ylid-less active solvent (indexed by 2).
Relation (7) offers the possibility to estimate the difference w 2 − w 1 , which is practically impossible to be determined by other methods, except the spectral ones.
The average statistic weight of the active solvent (indexed by 1), p 1 , in the first solute solvation shell can be calculated by using the values of the wavenumbers in the maximum of the ICT band of the spectrally active molecule determined in the binary solutions realized in the two solvents and in the ternary solution, indexed with 1, 2, and t, respectively: The excess function is as follows: Reference [50] defines an indicator of the ternary solution non-homogeneity. When δ 1 < 0, the molecules of the inactive solvent (indexed by 2) are predominant in the first solvation shell of the solute. When δ 1 > 0, the molecules of the active solvent are dominant in the solute first solvation shell.

Computational Results
PCCM is a pyridinium ylid with symmetrically substituted carbanion having planar structure at the carbanion level. The ylid carbanion is sp 2 hybridized, so the two covalent simple bonds between it and the carbethoxy groups lie in the plane of the heterocycle. The lone electron pair of the carbanion is perpendicular on this plane, facilitating the heterocycle π electrons' conjugation with the electrons belonging to C=O groups of carbethoxy substituents [11].
The Spartan evaluations were made in vacuum, in water, and in ethanol. As one can see from Figure 1, the symmetry of the molecule is not changed in the two hydroxyl solvents, compared with the vacuum structure.
The ground state electric dipole moment of the studied molecule keeps its orientation, parallel to the ylid bond both in water and in ethanol, but changes its absolute value, as it results from the data of Table 1. In the same time, the molecular polarizability does not support significant change when PCCM is passed from vaporous state in solution with water or ethanol (see Table 1).
Symmetry 2020, 12, 1299 7 of 23 A significant increase of dipole moment takes place when a PCCM molecule is solvated in water or ethanol, hydroxyl solvents in which hydrogen bond are possible between the ylid carbanion electron lone pair or the electrons of C=O groups and their hydroxyl groups. As seen from Table 1, three places are possible for a hydrogen bond addition to PCCM (three HBA counts are possible for PCCM).
The changes in the E HOMO and E LUMO values listed in Table 1 at passing from vacuum to solutions in water or in ethanol are important because they show us that, in these solvents, the visible band of PCCM will be shifted to blue, which is related to its vaporous state.
The changes in area and volume of PCCM influence the dimensions of the solvation shell of this molecule. The deviation of the molecular structure at sphericity demonstrates that the theories of liquids can be applied only in some approximations, because these theories consider the spectrally active molecules as being spherical entities surrounded by solvent spherical layers.
Let us observe, in Figure 2, some change in the electronic charges near the molecular atoms of PCCM in water or ethanol, compared with vaporous state. The charges located near the atoms component of ylid bond or that al the level of C=O groups of the ylid carbanion are important for the interactions of this molecule with the hydroxyl solvent molecules, as this will result from the solvatochromic analysis. The changes in the EHOMO and ELUMO values listed in Table 1 at passing from vacuum to solutions in water or in ethanol are important because they show us that, in these solvents, the visible band of PCCM will be shifted to blue, which is related to its vaporous state.
The changes in area and volume of PCCM influence the dimensions of the solvation shell of this molecule. The deviation of the molecular structure at sphericity demonstrates that the theories of liquids can be applied only in some approximations, because these theories consider the spectrally active molecules as being spherical entities surrounded by solvent spherical layers.
Let us observe, in Figure 2, some change in the electronic charges near the molecular atoms of PCCM in water or ethanol, compared with vaporous state. The charges located near the atoms component of ylid bond or that al the level of C=O groups of the ylid carbanion are important for the interactions of this molecule with the hydroxyl solvent molecules, as this will result from the solvatochromic analysis. The similitude in the orbital aspects in hydroxyl solvents can be observed in Figure 3b,c. All three figures show that, by the visible photon absorption, the heterocycle will be enriched in electron density, thus demonstrating that intramolecular charge transfer (ICT) process takes place from the carbanion and its substituents toward the ylid heterocycle.
An electrostatic potential map (for elucidation the molecular charges distribution), local ionization potential map, and |LUMO| map of PCCM (anticipating the electrophilic and nucleophilic reactivity, respectively) in vaporous phase and in the two hydroxyl solvents are illustrated in Figure  4. Colors in these figures have the signification [28,32] specified below.
The electrostatic map corresponds to the electronic reactivity, providing a measure of the overall size and shape of the molecule. The red color corresponds to high negative potentials, while the blue color indicates high positive potentials.
The electron removing energy as a function of its location is shown by the local ionization potential map. The local ionization potentials are always positive. The blue color indicates large ionization potentials, while the red color corresponds to small ionization potentials.
The |LUMO| map displays the absolute value of LUMO onto the electron density surface. The red color indicates small absolute values of LUMO, and the blue color shows large absolute values of it.
The places of nucleophilic attack (located near carbanion and near the two oxygens of C=O groups of carbethoxy substituents) can be observed in Figure 4a-c for PCCM in vaporous phase, or in solutions in water and ethanol, respectively. The similitude in the orbital aspects in hydroxyl solvents can be observed in Figure 3b,c. All three figures show that, by the visible photon absorption, the heterocycle will be enriched in electron density, thus demonstrating that intramolecular charge transfer (ICT) process takes place from the carbanion and its substituents toward the ylid heterocycle.
An electrostatic potential map (for elucidation the molecular charges distribution), local ionization potential map, and |LUMO| map of PCCM (anticipating the electrophilic and nucleophilic reactivity, respectively) in vaporous phase and in the two hydroxyl solvents are illustrated in Figure 4. Colors in these figures have the signification [28,32] specified below.
The electrostatic map corresponds to the electronic reactivity, providing a measure of the overall size and shape of the molecule. The red color corresponds to high negative potentials, while the blue color indicates high positive potentials.
The electron removing energy as a function of its location is shown by the local ionization potential map. The local ionization potentials are always positive. The blue color indicates large ionization potentials, while the red color corresponds to small ionization potentials.  The electrostatic potential, local ionization potential and |LUMO| maps keep similar aspects for the vaporous state and also in solutions of PCCM achieved with water and ethanol. Important for our study are the orientation of the electric dipole moment of PCCM and the aspects of the HOMO and LUMO orbitals, giving information about the sense of the electronic transition in the visible light process and also about the strength of the intermolecular interactions of PCCM in solutions.
The values of the volume and molecular surface area (Table 1) were used to estimate the molecular radius in expressions of the correlation coefficients, C1 and C2, in Relations (4) and (5). The places of nucleophilic attack (located near carbanion and near the two oxygens of C=O groups of carbethoxy substituents) can be observed in Figure 4a-c for PCCM in vaporous phase, or in solutions in water and ethanol, respectively.
The electrostatic potential, local ionization potential and |LUMO| maps keep similar aspects for the vaporous state and also in solutions of PCCM achieved with water and ethanol. Important for our study are the orientation of the electric dipole moment of PCCM and the aspects of the HOMO and LUMO orbitals, giving information about the sense of the electronic transition in the visible light process and also about the strength of the intermolecular interactions of PCCM in solutions.
The values of the volume and molecular surface area (Table 1) were used to estimate the molecular radius in expressions of the correlation coefficients, C 1 and C 2 , in Relations (4) and (5).

Spectral Results
PCCM shows a UV region with an intense band attributed to π-π* transitions and a visible band of small intensity, sensitive to the solvent nature, which disappears in acid media, attributed to n-π* transition realized by electronic charge transfer from the carbanion towards the ylid heterocycle (see Figure 3 and Figure 5).
The electronic absorption spectrum in ternary solution obtained by adding sulphuric acid in the PCCM solution in ethanol is represented in Figure 5 by a dashed line. The protonated ylid shows spectral changes both in UV and in visible range, as it results from Figure 5. The visible band of PCCM disappears in the acid media in which the lone electron pair of the ylid carbanion is blocked by protonation [11,48].

Spectral Results
PCCM shows a UV region with an intense band attributed to π-π* transitions and a visible band of small intensity, sensitive to the solvent nature, which disappears in acid media, attributed to n-π* transition realized by electronic charge transfer from the carbanion towards the ylid heterocycle (see Figures 3 and 5). Symmetry 2020, 12, x FOR PEER REVIEW 10 of 23

Figure 5
Electronic absorption spectrum of PCCM in ethanol and in ethanol with addition of H2SO4.
The UV spectrum was recorded by using 0.2 cm quartz cells, and the visible range by using 5 cm glass cells.
The spectral data regarding the binary solutions of PCCM are given in Table 2. The solvent parameters are also listed in Table 2. The computed values of the wavenumbers in Table 2 were made by using Relations (10) and (11).  The electronic absorption spectrum in ternary solution obtained by adding sulphuric acid in the PCCM solution in ethanol is represented in Figure 5 by a dashed line. The protonated ylid shows spectral changes both in UV and in visible range, as it results from Figure 5. The visible band of PCCM disappears in the acid media in which the lone electron pair of the ylid carbanion is blocked by protonation [11,48].
The spectral data regarding the binary solutions of PCCM are given in Table 2. The solvent parameters are also listed in Table 2. The computed values of the wavenumbers in Table 2 were made by using Relations (10) and (11).
From the data of Table 2, we see the spectral shifts to blue of the visible electronic absorption band both in the polar and in the protic solvents, compared to the non-polar and aprotic ones. Based on the disappearance in acid solutions and on its small intensity, the visible electronic absorption band of PCCM has been attributed to intramolecular charge transfer (ICT) from the carbanion toward the heterocycle [11,24]. This attribution is sustained by the aspects of HOMO and LUMO orbitals (see Figure 3) and by other solvatochromic and computational studies made on similar structures [28,32].
As seen in Table 2, the visible ICT band is very sensitive to the solvent nature and can help us to establish the nature and the strength of interactions between the PCCM molecule and the solvents in diluted solutions.
In order to analyze the solvent effects on the visible electronic absorption band of PCCM, relations of Types (1) and (2) were used.
Based on Kamlet Taft parameters [5,35] of the used solvents (Table 2), the correlation coefficients obtained for Relation (1) in the statistical analysis are listed below. The dependence between the experimental wavenumbers in the ICT band maximum and those computed by Relation (10) values is illustrated in Figure 6.
The Kamlet Taft solvent parameters were empirically introduced, and they cannot be bonded with the electro-optical parameters of the spectrally active molecules.
For this reason, Relation (2) was also applied to the spectral data given in Table 2, because the correlation coefficients, C 1 and C 2 , are expressed as function on the molecular parameters of the spectrally active molecule [28,32] and offer the possibility to characterize the excited state of this molecule, as it results from Relations (3) and (4). The correlation coefficients obtained based on Relation (2) and the data from Table 2 are listed below. The results of statistical analysis of spectral data based on Relation (11) are illustrated in Figure 7, in which the computed values of the ICT wavenumbers are plotted vs. those experimentally obtained.   The Kamlet Taft solvent parameters were empirically introduced, and they cannot be bonded with the electro-optical parameters of the spectrally active molecules.
For this reason, Relation (2) was also applied to the spectral data given in Table 2, because the correlation coefficients, C1 and C2, are expressed as function on the molecular parameters of the spectrally active molecule [28,32] and offer the possibility to characterize the excited state of this molecule, as it results from Relations (3) and (4). The correlation coefficients obtained based on Relation (2) and the data from Table 2    The solvatochromic analysis was also made for ternary solutions realized in binary hydroxyl solvents water (1) + ethanol (2) and for water (1) + methanol (2) with the Kamlet Taft solvent parameters from [52]. The solvent parameters and the wavenumbers in the maximum of ICT visible band of PCCM are listed in Table 3 and Table 4. The data from Tables 3 and 4 demonstrate that (excess function of the active solvent) is positive, that the first solvation shell of PCCM in ternary solutions is enriched in water molecules (water was considered as being the active solvent from the interactions point of view).   Relation (12) describes, in a good manner, the dependence of the wavenumber in the maximum of the ICT band of PCCM on the solvent parameters in the binary solutions. The dependence, based on Relation (12), of the computed wavenumbers vs. those experimentally determined for the PCCM binary solutions is illustrated in Figure 7.
The solvatochromic analysis was also made for ternary solutions realized in binary hydroxyl solvents water (1) + ethanol (2) and for water (1) + methanol (2) with the Kamlet Taft solvent parameters from [51]. The solvent parameters and the wavenumbers in the maximum of ICT visible band of PCCM are listed in Tables 3 and 4. The data from Tables 3 and 4 demonstrate that δ 1 (excess function of the active solvent) is positive, that the first solvation shell of PCCM in ternary solutions is enriched in water molecules (water was considered as being the active solvent from the interactions point of view). Table 3. Binary solvent water (1) + ethanol (2): molar composition (x 1 ) and Kamlet Taft solvent parameters (π*, α, β); wavenumbers, ν (cm −1 ), in the maximum of the PCCM visible ICT band and p 1 .
No.  The dependence of Type (1) was observed for the ternary PCCM solutions in both pairs of binary solvents. The correlation coefficients obtained using Relation (1) and the data from Tables 3 and 4 for the two types of solutions are given in Relations (13) and (14). The dependence between the computed, v calc (cm −1 ) and the experimental wavenumber, v exp (cm −1 ), and for PCCM in water (1) + ethanol (2) and in water (1) + methanol (2) is illustrated in Figures 8 and 9.
Adj. R-square =0.992 . = (180 ± 445) + (0.993 ± 0.018) . , with: Adj. R-square = 0.993, SD = 100      The presence of some aberrant points for high water content in Figure 8 could be explained [52] by the increased ability of water to make some cages around the hydrocarbon part of superior alcohols. This ability increases with the length of hydrocarbon chain from the alcohol molecules, and it was emphasized for water + ethanol mixtures [51].
Results or ternary solution PCCM in water (1) + ethanol (2): The universal interactions of the orientation-induction type are dominant in aprotic solvents, while, in the hydroxyl solvents, a great contribution to the spectral shift of ICT visible band of PCCM is given by specific interactions between the ylid and the hydroxyl groups of these solvents (see Tables 5  and 6).
The dependence of the type ln p 1 p 2 vs.
x 1 x 2 , where p 1 and x 1 are the statistic average weight of the active solvent (considered by us as being water) in the first solvation shell of PCCM and the molar fraction of the same solvent in the bulk solution, respectively, for PCCM ternary solutions is illustrated in Figures 10 and 11. The index 2 shows the same parameters for the second solvent, considered as being a few active from the interactions point of view. Table 5. Contribution of each type of intermolecular interactions (in binary solutions) to the spectral shifts of PCCM visible ICT band.

No.
Solvent   Table 6. Contribution (in percents) of each type of intermolecular interaction to the spectral shift in PCCM ternary solutions.

No. x 1
Water + Ethanol Water + Methanol ∆ν (cm −1 )     From Figure 10 and Figure 11, it results a linear dependence between the points corresponding to both types of the binary hydroxyl solvents, proving the applicability of the statistic cell model of ternary solutions to the studied mixtures.
The difference between the interaction energies in the molecular pairs of the types PCCM-water (1) and PCCM-ethanol (2) and, respectively, PCCM-Water (1) and PCCM-Methanol (2) was estimated based on the significance of the cut at origin of the corresponding lines (see Figure 10 and Figure 11).
The difference − , determined using the cut of line (7) for the ternary solution PCCM + water (1) + ethanol (2), has the value − = (0.574 ± 0.013)10 , and for solution PCCM + water (1) + methanol (2) has the value − = (0.475 ± 0.010) 10 . These values demonstrate (by their positive signs) that the interaction energy of ylid molecule with a water molecule is higher From Figures 10 and 11, it results a linear dependence between the points corresponding to both types of the binary hydroxyl solvents, proving the applicability of the statistic cell model of ternary solutions to the studied mixtures.
The difference between the interaction energies in the molecular pairs of the types PCCM-water (1) and PCCM-ethanol (2) and, respectively, PCCM-Water (1) and PCCM-Methanol (2) was estimated based on the significance of the cut at origin of the corresponding lines (see Figures 10 and 11).
The difference w 2 − w 1 , determined using the cut of line (7) for the ternary solution PCCM + water (1) + ethanol (2), has the value w 2 − w 1 = (0.574 ± 0.013)10 −20 J, and for solution PCCM + water (1) + methanol (2) has the value w 2 − w 1 = (0.475 ± 0.010)10 −20 J. These values demonstrate (by their positive signs) that the interaction energy of ylid molecule with a water molecule is higher in modulus compared with those between the ylid and one alcohol molecule (either ethanol or methanol).
The difference w 2 − w 1 is higher for the case of ternary solutions in water + ethanol, proving that the interaction energy in molecular pairs: ylid-ethanol is smaller compared with that corresponding to pairs: ylid-methanol.
A study of the protic solvent influence on the visible ICT band of pyridinium di-carbethoxy methylid and of iso-quinolinium di-carbethoxy methylid was also accomplished in Reference [27]. The difference w 2 − w 1 was estimated for the binary solvents containing one protic and one aprotic solvent. The w 2 − w 1 values obtained in Reference [27] for pyridinium di-carbethoxy methylid were 0.289 10 −20 J for the binary solvent octanol (1) + dichloroethane (2) and 0.190 10 −20 J for the binary solvent methanol (1) + benzene (2).
The higher values obtained in this paper for binary solvents containing water and ethanol or methanol, compared with those obtained in Reference [27], could be explained by the action of the orientation-induction forces on the complexes formed by ylid with hydroxyl molecule, having in view the high value of the water electric permittivity. A study of the orientation-induction interactions in ternary solutions pyridinium ylids + water + ethanol has been made in Reference [53,54] and emphasized the great contribution of the orientation interactions on the ylid complexes realized by hydrogen bonds.
The experimental data regarding the interactions between two molecules are important for the researchers who study the interactions in liquids, because there are few methods in which these types of data can be obtained (any of the devices introduced in liquids for measurements disturb the internal equilibrium in this state of matter). Only spectrally active molecules are used as probes able to estimate, by spectra modifications, the strength of the reactive internal field in liquids.
Information about the excited states of the spectrally active molecules, especially about their excited electric dipole moment and its orientation relative to the ground state dipole moment are important for quantum chemistry and can serve to develop the calculations in the molecular excited states.
The dipole moment of PCCM in its first excited state (corresponding to the ICT process caused by the visible photon absorption) is estimated here by using the variational method proposed in Reference [28,32,41] and the data of PCCM in the ground state obtained in quantum chemical estimation (Table 1).
With the values of the correlation coefficients, C 1 and C 2 , obtained in (11) based on Relations (3) and (4) and using the computed by Spartan'14 values of the ground state electric dipole moment and polarizability of PCCM, the variational method proposed in Reference [41] permitted us to estimate the excited state dipole moment of PCCM and the angle between the dipole moments in the electronic state between which the absorption transition takes place, in the approximation that the molecular polarizability does not vary in the electronic transition time [2,34].
Let us apply this method for the PCCM by using the data from Table 1, the values of the coefficients, C 1 and C 2 , from Relation (11), and the molecular radius computed by using the surface area and volume in Formula (6).
The estimation is made in some approximations, having in view the ovality of PCCM molecule obtained by Spartan (see Table 1) and the hypothesis of the cell model regarding the solute and solvation shell sphericity. Using Definitions (4) and (5) and the values of the coefficients, C 1 and C 2 , one obtains the following: 0.0143µ 2 e −12.56 µ e cos ϕ + 72.1007 = 0 Equations (15) and (16) where obtained by using the values for the sum C 1 + C 2 and C 1 regression coefficients from Relation (11) and the ground state dipole moment of PCCM computed in water (Table 1).
Equation (16) has real solutions in the hypothesis that its discriminator is a positive quantity. A limitation for the angle, ϕ, between the dipole moments results in this condition.
The excited state dipole moment, obtained as the real solution of Equation (16), is used for estimating the excited state polarizability of PCCM based on Relation (15).
In variational method, the angle between the molecular dipole moments in the electronic states participating to the absorption process is varied until the polarizability in the excited state of the spectrally active molecule equalizes the ground state polarizability. In conformity with the supposition of McRae [2], the electronic transition takes place for the corresponding value of the angle, ϕ. The data are listed in Table 7. In Table 7, only some of the estimations are listed, because for ϕ = 8.5 • , the value of the excited state polarizability equalizes the ground state polarizability, and one can appreciate that the electronic transition with ICT takes place at this angle. The results obtained when the dipole moments triangle ( Figure 12) was solved are µ e = 5.84D, ∆µ = 1D, ϕ = 8.5 • , for initial values µ g = 6.28D, computed by Spartan for PCCM in water; I u = 5.58 eV and I v = 9.96 eV (for cyclohexane); and C 1 = 1642 cm −1 and C 2 = −261 cm −1 . In Figure 12, the angle between the ground state dipole moment and the vector ∆µ is 59.72 degrees, and the angle between the excited state dipole moment and the vector ∆µ is 111.78 degrees. In Table 7, only some of the estimations are listed, because for φ = 8.5°, the value of the excited state polarizability equalizes the ground state polarizability, and one can appreciate that the electronic transition with ICT takes place at this angle. The results obtained when the dipole moments triangle (Figure 12) was solved are μ = 5.84 , Δµ=1D, φ = 8.5°, for initial values μ = 6.28 , computed by Spartan for PCCM in water; = 5.58 and = 9.96 (for cyclohexane); and C1 = 1642 cm and C2 = −261 . In Figure 12, the angle between the ground state dipole moment and the vector Δµ is 59.72 degrees, and the angle between the excited state dipole moment and the vector Δµ is 111.78 degrees. In the case when only ( ) and α influence the wavenumber in the maximum of the ICT band (see Relation (12')), the correlation coefficients are C1 = 1731 cm and C2 = 0 cm . A system of equations of the Types ( 18) and ( 19) is obtained in this case. In the case when only f (ε) and α influence the wavenumber in the maximum of the ICT band (see Relation (12')), the correlation coefficients are C 1 = 1731 cm −1 and C 2 = 0 cm −1 . A system of equations of the Types (18) and (19) is obtained in this case.
Equations (18) and (19) have the solutions as it follows. The real solutions are obtained for ϕ ∈ [0, 80.71) ∪ (99. 28,180] • , but the condition that the excited state polarizability is the same as in the ground electronic state imposes the following solutions: ϕ = 0 • , µ e = 5.75D, and ∆µ = 0.53D. The parallelism between the ground and excited dipole moments of the molecule in the time of ICT can be admitted with good precision, having in view the approximation in which the theory regarding the solvent influence on the wavenumbers of the electronic transitions in the absorption process has been developed.
In the case of symmetrically substituted carbanion, the angle between the dipole moments process is small, and the excited state dipole moment is smaller than the ground state dipole moment. This fact determines the hypsochromic shift of the ICT band in polar solvents, because the solvation energy of the orientation induction type is higher in the ground state of PCCM molecule, compared with that in its excited state.

Conclusions
The experimental data obtained in solvatochromic study and quantum mechanical parameters computed by Spartan can be used in order to characterize the excited electronic state of a spectrally active molecule without fluorescence spectrum.
The excited state dipole moment of PCCM in the excited state of the ICT transition, estimated here by the variational method, is smaller than the ground state dipole moment, and it makes a small angle with this.
The long-range (universal) interactions of the dipolar types of PCCM with the solvents are stronger in the ground electronic state, as compared with the excited state.
The universal interactions are predominant in PCCM solutions achieved in aprotic solvents, while in the protic ones, the specific interactions of the hydrogen types in which the ylid molecules accept protons significantly influence the position of the visible ICT band of ylid.
A part of experimental data obtained in this research could be used by researchers in the quantum chemistry field for developing quantum chemical computations for the excited state parameters of the ylid molecules in different liquids.