Aromatic aldehydes are organic chemical compounds that contain a CHO group attached to the benzene ring and they are used as precursors in the pharmaceutical and plastics industries. The simplest of aromatic aldehydes is benzaldehyde. It is used as a flavoring and as an ingredient in some dye and plastics production . Benzaldehyde and its derivatives are commonly employed for the synthesis of Schiff bases and chalcones which are found to have anti-bacterial , anti-tumor , anti-inflammatory , anti-fungal , anti-microbial and anti-oxidant properties . Substituted benzaldehydes also have chemical components that make them important in human biological functions. They can be designed to increase the oxygen affinity of human hemoglobin and to inhibit the sickle erythrocytes .
There are several reports in the literature on the changes of equilibria of conformers with solvent polarity [8, 9, 10, 11]. Conformational preference of the compounds also depends on the variety of substituents [11, 12, 13]. Previous studies showed that the substituted benzaldehydes can be defined by cis and trans conformations, relative to the oxygen atom and the substituent [14, 15, 16, 17]. Hiremath and Sundius  carried out a theoretical study with the RHF/6-311G(d), B3LYP/6-311G(d) and B3PW91/6-311G(d) methods to investigate the conformers of 2-bromo-5-fluorobenzaldehyde, and they found that the trans conformer is the more stable form. In 2015, we reported the crystal structure, vibrational spectra and theoretical simulations of 4-chloro-3-fluorobenzaldehyde (CFB)  and 4-bromo-2-fluorobenzaldehyde (BFB) . It was observed that CFB prefers the cis form, whereas the chloro (CCB) and bromo (CBB) analogs prefer the trans form in the gas phase. The conformational preference and rotational barrier remain qualitatively unaffected when HF/aug-cc-pVDZ, MP2/aug-cc-pVDZ and B3LYP/6-311+G(3df,p) methods are employed . However, in solution, it was observed that conformational energy barrier is dependent on the solvent used for CCB and CBB while it is independent for CFB . Turning to another theoretical study [B3LYP/6-311+G(3df,p)] in the gas phase, it was found that BFB, BCB and BBB compounds prefer the trans conformer .
The effects of solute–solvent interactions on the vibrational spectra are well known [17, 18, 19, 20, 21]. There are numerous examples of the solvent influence on some group frequencies [20, 21, 22, 23, 24, 25]. The carbonyl group has been extensively investigated due to its dipolarity and hydrogen bond accepting nature [20, 21, 22, 23]. In addition, several empirical approaches have characterized the solvent effects on vibrational frequencies such as Kirkwood–Bauer–Magat (KBM) [26, 27], acceptor number (AN) , Swain  and linear solvation energy relationship (LSER) .
In continuation with our interests in the characterization of the substituted benzaldehydes [15, 16, 17], the prime objective of the present study was to use density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods in conjunction with the B3LYP/6-311+G(3df,p) method to examine the solvent and halogen effects on the conformation and carbonyl stretching of BFB, BCB and BBB (Figure SI1; SI = Supplementary Information). The carbonyl stretching frequencies were correlated with the KBM, AN, Swain and LSER scales. Further, we were also interested in understanding the effect of solvent on the electronic properties such as the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO), the total, partial and overlap population density-of-states (TDOS, PDOS and OPDOS) and UV data.
2 Theoretical methods
Computations were carried out using the Gaussian 09  program. The structures were viewed using GaussView 5.0.8 . The geometrical structures of the cis and trans conformers in Cs symmetry and gas phase were optimized using the B3LYP functional, HF and MP2 levels of theory in conjunction with the aug-cc-pVDZ basis set.
Computations in solutions were performed using the B3LYP/6-311+G(3df,p) method. The polarizable continuum model (PCM) was used to evaluate the solvent effect. Harmonic vibrational frequencies were computed using the same methods and basis sets to confirm the nature of the ground-state structure. Mole fractions of the individual conformers were calculated as described earlier [17, 33]. Carbonyl frequencies were correlated using the KBM, AN, Swain and LSER scales to investigate the solvent effect, as described earlier . The KBM, AN, Swain and LSER parameters of the solvents used are given in Table SI1. HOMO, LUMO, dipole moment and DOS plots were also analyzed. In order to have more insights into electronic properties, absorption wavelengths and oscillator strengths were also computed by the TDDFT using the same method and basis set, based on the optimized structure.
3 Results and discussion
3.1 Structural studies
Recently, some of us have found that BFB crystallizes in orthorhombic space group P212121 with the trans conformation and BFB, BCB and BBB in the gas phase prefer the trans form. Further, although the free energy difference between the cis and trans forms is less than 2.5 kcal/mol, the free energy rotational barrier is at least 7.4 kcal/mol by B3LYP/6-311+G(3df,p) . To ensure the B3LYP/6-311+G(3df,p) level in the gas phase, we optimized these structures using more refined methods such as HF/aug-cc-pVDZ, MP2/aug-cc-pVDZ and B3LYP/aug-cc-pVDZ. The relative free energy and dipole moment are included in Table 1. Analysis of the free energy data shows that the qualitative results remain unaffected, although there are insignificant changes in the values. In view of this analysis, the highly demanding MP2/aug-cc-pVDZ and B3LYP/6-311+G(3df,p) can be used as compromise methods to investigate the conformational preference.
Free energy and mole fraction for the optimized geometries of the conformers of 4-bromo-2-halogenobenzaldehydes in solutions are listed in Table 2. Solvent-induced carbonyl frequency versus energy and the solvent dielectric constant versus energy plots for the compounds are depicted in Figures 1, SI2 and SI3. There is a linear correlation noticed between the carbonyl frequency and energy values (R2= 0.99829, 0.99857 and 0.99820 for BFB, BCB and BBB, respectively). In the cases of the solution of BFB, BCB and BBB, the trans form is more stable than cis (Table 2). According to the calculations of mole fractions of the individual conformers, BFB, BCB and BBB prefer trans and cis conformers in the solutions with approximate probabilities of 95–78 % and 22–25 %, 96–89 % and 11–14 %, and, 97–90 % and 10–13 %, respectively. It is observed that the most stable conformation of all compounds is independent of the medium and halogen. Also, the stability of the conformers decreases with increase in the polarity or dielectric constant of the solvents while it increases with the size of the halogen atom.
The carbonyl bond length and dipole moment of the compounds are listed in Table 3 together with C=O frequency. It is observed that the carbonyl bond length indicates a linear correlation with the carbonyl frequency (R2 = 0.99820, 0.99847 and 0.99827 for BFB, BCB and BBB, respectively). The carbonyl bond length increases with the increase of the dielectric constant of the solvent and with the decrease of the carbonyl frequency. It is known that the conformer with larger dipole moment is less stable [15, 16]. Therefore, the conformational preference for all compounds can be explained on the basis of their large dipole moments (Table 1). The dipole moment is expected to be larger in solution than in the gas phase (Table 1 and Table 3). In solutions, BFB, BCB and BBB have 2.4–3.0, 2.3–2.8 and 2.2–2.7 Debye dipole moments correspondingly. There is a good and linear correlation between the carbonyl frequency and dipole moment (R2 = 0.99849, 0.99874 and 0.99848 for BFB, BCB and BBB, respectively). The dipole moment increases with the increase of the dielectric constant and with the decrease of the carbonyl frequency.
3.2 Carbonyl stretching
The computed carbonyl vibrations of the compounds are listed in Table 3. In n-hexane, the carbonyl frequencies are calculated at higher frequencies. It belongs to the free monomer state of carbonyl as no remarkable solute–solvent interactions occur in the inert solvent n-hexane. Interestingly, these bands were found at lower frequencies in polar solvents such as dimethylsulfoxide and methanol.
As observed from Table 4, Figures 1, SI2 and SI3, there is a linear correlation between the ν(C=O) and f(ε) for the KBM equation. The negative slope shows that the frequency is red-shifted by the increase in dielectric constant of the solvent. Even though both the specific and non-specific solvent effects contribute to solute–solvent interactions, the KBM only takes notice of the dielectric constant. Further, the carbonyl frequencies computed are inversely proportional to the dielectric constant of the solvent. These facts result in a good relationship between the KBM parameter and ν(C=O) (R2 = 0.99737, 0.99734 and 0.99631 for BFB, BCB and BBB, respectively). The present theoretical values show that the PCM model is suitable to determine the dielectric-induced solvent effect on the vibrational frequencies. Similar results were reported for the KBM equation [17, 25, 34]. For the AN equation, however, there are poor correlations (Table 4, Figures 1, SI2 and SI3). Analysis of these data indicates that this equation has no major role in the determination of vibrational frequency shift in solution.
Solvent effects are divided into two species by Swain, the anion-solvating tendency of the solvent (acidity) and the cation-solvating tendency of the solvent (basicity). Hence, the specific solute–solvent interactions are only considered. The Swain equations are also listed in Table 4. Although the correlations of the Swain equations are poor, it is better than those found with AN. Both the Lewis acidity and basicity of the solvent are considered in Swain equation, whereas the AN only takes into consideration the Lewis acidity of the solvent. The negative sign for Aj and Bj means that hydrogen-bond donor (HBD) acidity and hydrogen-bond acceptor (HBA) basicity of the solvent lead to red-shift of the ν(C=O). The ratio of these two is equal to about 2. It suggests that the red-shift of the carbonyl band induced by the solvent acidity is larger than the one induced by the solvent basicity.
Turning to the multiparameter equation LSER, there are not only the specific interaction parameters such as α and β, but also the non-specific interaction parameter as π*. The negative π* coefficients inform that red-shift of the frequency is observed by non-specific solvent effects. The π* or δ coefficients having the biggest absolute values among the others prove that non-specific solvent effects are dominant in the interactions. The coefficients α and β are also negative, in agreement with the case of Aj and Bj in Swain equation (Table 4). This states the same influence with regard to the red-shift of the carbonyl stretching frequencies by the solvent HBD acidity and HBA basicity. The α coefficients are bigger than the β values. The carbonyl stretching vibrations of the compounds are more susceptible to the HBD acidity than the HBA basicity. The poor correlations derived by the LSER and Swain equations verify that the PCM model neglects specific solvent effects.
3.3 Electronic properties
Absorption wavelength, excitation energy and oscillator strength of the compounds are collected in Table 5 together with the contribution of the transition. From the UV data, the absorption bands are assigned at 274.3, 288.4 and 294.4 nm in the gas phase for F-, Cl- and Br-compounds, respectively, due to their higher HOMO\gtLUMO contribution. As the dielectric constant is increased, the area of these absorption bands also increases gradually. It is observed that the absorption bands, optical band gaps and transitions are dependent on the both solvent and halogen effects.
The energy values of HOMO and LUMO are presented in Table 6. The optical band gap is, in general, smaller than the electrical band gap, which is known as the energy gap between HOMO and LUMO, due to the Coulombic interaction. This situation is clearly observed in Table 5 and Table 6. The energy of HOMO–LUMO gap decreases gradually by getting from the gas phase to the polar solvent for all compounds. The density plots and energy values for HOMO and LUMO are shown in Figure 2. These diagrams are plotted by a contour value of 0.02. HOMO and LUMO of the compounds in the gas phase and solutions are delocalized on almost all atoms. The values of chemical hardness, electronegativity, chemical potential and electrophilicity index of the compounds are also given in Table 6. The values of the chemical hardness of the compounds show same trends with the energy gaps.
TDOS, PDOS and OPDOS spectra of the compounds are illustrated in Figures 3, SI4 and SI5. These plots were created by convoluting the molecular orbital information with Gaussian curves of unit height and full width at half maximum (FWHM) of 0.3 eV. These plots demonstrate the molecular orbital compositions and their contributions to the chemical bonding. In Figure SI4, TDOS plots show population analysis per orbital. According to PDOS plots of BFB, HOMO and LUMO orbitals in the gas phase and benzene are fairly localized on halogen atom, ring and formyl groups, while these orbitals in methanol are localized on formyl and ring groups, and there is no contribution of halogen atom to these orbitals. As can be seen from Figure 3, there are solvent effect on PDOS plots for BFB. Turning to BCB, there is a different contribution ranking as halogen atom, formyl and ring groups in the all medium for both orbitals. Moving to the computed contribution energies for groups of BBB in the gas phase and methanol, the sequence is halogen atom, ring and formyl groups whereas it is halogen atom, formyl and ring groups in benzene. Hence, there are halogen and solvent effects on PDOS plots of all compounds and F- and Br-compounds, respectively. OPDOS spectra show that the formyl ↔ ring, formyl ↔ halogen and ring ↔ halogen groups have significant bonding, anti-bonding or non-bonding states in the related range of the energy windows (Figure SI5). The interactions between the formyl ↔ ring, formyl ↔ halogen and ring ↔ halogen groups of BCB, BFB and BBB, respectively, are positive values (bonding interaction) in the gas phase and solvents. For all medium, other interactions have anti-bonding characters, which are negative data. The solvent effect is not observed on OPDOS spectra, but there is halogen effect.
We have undertaken a theoretical research to understand the effects of halogen and solvent on the conformational stability, vibrational and electronic properties of the investigated disubstituted benzaldehydes. The results can be useful for analysis of the structures involving these moieties. To summarize, the salient features of this work are:
The minimum energies of the optimized structures decrease with the dielectric constant of the solvent and the size of halogen. Conformational energy barrier is independent on the solvent for all compounds. Further, there is no halogen effect on the conformation.
The carbonyl stretching vibrations increases gradually on lowering the carbonyl bond length, dipole moment and dielectric constant. However, it can be said that there is no halogen effect on the carbonyl frequency, although there are insignificant changes in the values.
It is worth to note that the compounds in solutions have large dipole moments, and this is an essential criterion for drug–receptor interaction .
The Swain and LSER parameters have poor correlations, while the KBM model shows a good correlation since it only considers the dielectric constant.
The HOMO–LUMO gap is about 4.8 eV which is sufficiently large to meet the viability criterion suggested by Hoffmann et al. .
There is no solvent effect on OPDOS of all compounds and PDOS of Cl-compound, whereas the solvent effect is observed on PDOS of F- and Br-compounds, electrical band gaps and UV data of all compounds.
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