Mononuclear gallium (III) complexes based on salicylaldoximes: Theoretical study of structures, topological and NBO analysis of hydrogen bonding interactions involving O–H···O bonds

3.1 Scanned and optimized geometries

In this work, to attain optimized structure, we varied the two O–H distances in (Ga–saoH) from 0.6 to 1.2 Å between the two maxima and calculated the energies at the B3LYP/6-311G(d, p) level by fixing all other parameters at their optimized equilibrium values obtained at B3LYP/6-311G(d, p). Calculated potential energy curve for two O–H bonds at B3LYP/6-311G(d, p) level (Ga–saoH) compound shows in Fig. 2. Then the structure with lower energy, was fully optimized, without symmetry restrictions, at the B3LYP/6-311G(d, p) level of theory using the Gaussian-03 program package (Frisch et al., 2004).

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Figure 2

Calculated potential energy curve for two O–H bond at B3LYP/6-311G(d, p) level (Ga–saoH) compounds.

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The optimized geometry parameters of (Ga–saoH) and (Ga–Me–saoH) are summarized in Table 1 and its geometries are shown in Fig. 3. For comparison, the X-ray diffraction results (Birnara et al., 2009) are also given in Table 1. As it is obvious from these data the calculated geometrical parameters are not very sensitive to the choice of functional or basis set at theoretical methods. The agreement between the geometrical parameters calculated on the basis of theoretical study and the experimental data is satisfactory except for H···O₁ and O–H bond lengths, which are different.

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Figure 3

Optimized geometries of (Ga–saoH) (a) and (Ga–Me–saoH) (b) at B3LYP/6-311G(d, p) level of the theory.

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By comparing two structure, the H···O₁ bond length of the (Ga–saoH) complex is longer than the (Ga–Me–saoH) complex (ca. 0.076 Å). Also the bond length of O–H is predicted to be shorter than mean 0.003 Å. Also the O–H···O₁ bond angle of (Ga–saoH) is smaller than the (Ga–Me–saoH) compounds (ca. 3 Å), (i.e., in the HF level). These geometry parameters show that intramolecular hydrogen bond of the (Ga–Me–saoH) complex is stronger than the (Ga–saoH) complex.

3.2 Calculated frequencies

The infrared band frequencies for (Ga–saoH) and (Ga–Me–saoH) in the solid phase with the calculated frequencies and their assignments are given in Tables 2 and 3, respectively. The assignments reported in Table 2 are based on the calculated intensity of the bands and on the reported polarization of Raman bands. For the high frequencies, the assignments are straightforward. For the low frequency motions, however, the assignments are less clear cut. The fundamental vibrational frequencies for (Ga–saoH) obtained at B3LYP/6-311G(d, p) and HF/6-31G(d, p) levels were compared with the experimental values, using the root mean square (RMS) error analysis. The best results are obtained with B3LYP/6-311G(d, p), resulting in RMS = 85.0.

The calculated frequencies are slightly higher than the observed values for the majority of the normal modes. Two factors may be responsible for the discrepancies between the experimental and computed spectra of (Ga–saoH) and (Ga–Me–saoH). The first is caused by the environment. The second factor for these discrepancies is the fact that the experimental value is an anharmonic frequency while the calculated value is a harmonic frequency.

Table 2 and 3 lists calculated vibrational frequencies for (Ga–saoH) and (Ga–Me–saoH) together with assignments and approximate descriptions of the motions. The calculated frequencies are compared to the experimental values reported by Giannis S. Papaefstathiou and coworkers (Birnara et al., 2009).

These tables include an approximate description base on the normal modes in terms of the stretching (ν) and bending (δ) of the bonds at the B3LYP method with 6-311G(d, p) basis set. The assignments reported are based on the calculated intensity of the bands and the RMS error. Assignment is calculated with respect to the reported data by Giannis S. Papaefstathiou and coworkers (Birnara et al., 2009). By analyzing the IR bands, the highest frequency at 3443 cm⁻¹ is assigned to the asymmetric stretching of O–H bonds with calculated intensities of ca. 1591.6 km mol⁻¹, never before reported. The two vibrational frequencies at 3427 and 3217 cm⁻¹, are assigned to the symmetric stretching of O–H and C–H_α bonds with calculated intensities of ca. 71.5 and 10.5 km mol⁻¹, respectively. Giannis S. Papaefstathiou and coworkers have assigned these modes to the stretching of O–H and C–H_α at 3064 and 3004 cm⁻¹ with medium broad and weak intensities (Birnara et al., 2009). The IR band at 1595 cm⁻¹ with stronger intensity which has been assigned to the asymmetry stretching of C⚌N bonds by Giannis S. Papaefstathiou et al., calculated at ca. 1715 cm⁻¹ with 118 km mol⁻¹ intensity. This mode is assigned to asymmetric stretching of C⚌N and bending motions of OH and CH_α bonds and in plane deformation of saoH rings exactly. The frequency of 1629 cm⁻¹ with 466.6 km mol⁻¹ intensity observed at 1530 cm⁻¹ with strong intensity, assigned to symmetric stretching of C⚌O. The observed vibration of 1586 cm⁻¹ that has been assigned to symmetric stretching of C⚌C bonds by Giannis S. Papaefstathiou et al. calculated at 1571 cm⁻¹, is assigned to in plane deformation of acac rings (Δ acac ring) with asymmetry stretching of C–CH_ά–N, stretching of C–CH_α–C, and C–CH₃ and bending motion of CH_ά, CH_α and OH. The largest difference between calculated frequencies and experimental data is about 363 cm⁻¹. This mode involves symmetric stretching of O–H bonds, with the bending motion having a larger effect on the dipole moment. Since in real systems O–H bonds engage in interactions (e.g., hydrogen bonding) that are ignored in the “gas-phase model” calculations, the vibrational frequencies seem to have increased. The other source of error may be due to the fact that the absorption band is relatively broad. However, the intensity of the peak implies that it is correctly assigned. The remaining experimental vibrations of 1517, 1465, 1440 and 1375 cm⁻¹, observed at 1511, 1496, 1483 and 1438 cm⁻¹ with strong intensity, respectively, their intensities match reported data well.

3.3 Hydrogen bond

3.3.1

3.3.1 AIM analysis

The ‘‘atoms in molecules’’ theory of Bader (AIM) (Bader, 1990) is a very useful method for the estimation of hydrogen bond energy (Carrol et al., 1988a; Carrol et al., 1988b; Koch and Popelier, 1995; Mo et al., 1992 and Mo et al., 1994; Raissi et al., 2007). The Bader theory is based on topological properties of the electron density (ρBCP), and Laplacian of the electron density (∇²ρBCP) at the bond critical points (BCP) of two hydrogen bonded atoms. Therefore, the analysis of bond critical points was applied to obtain the hydrogen bond energy.

Theoretical studies are able to obtain a full description of both topological and energetic properties at critical points. It is possible to calculate such energetic parameters as the local kinetic energy density, G(r), and the local electron potential energy density, V(r). Experimental studies of electron density do not provide the description of energetic properties of critical points. However, Abramov has proposed the evaluation of G(r) in terms of electron density ρ(r), its gradient ∇²ρ(r) and its Laplacian ∇²ρ(r) functions (Abramov, 1997). At the critical point, where ∇²ρ(rCP) = 0 the Abramov relation takes the form: $$\text{G}(\text{rCP})=(3/10)(3\pi 2)2/3\rho 5/3(\text{rCP})+(1/6){\nabla }^2\rho (\text{rCP})$$ All values in this relation are expressed in atomic units. The local potential energy density V(rCP) can be obtained from the virial equation (Abramov, 1997): $$2\text{G}(\text{rCP})+\text{V}(\text{rCP})=(1/4){\nabla }^2\rho (\text{rCP})$$ It was found (Espinosa et al., 1998) that V(ρBCP) correlates with the H-bond energy – E_HB (E_HB = 1/2 V(ρBCP). V(ρBCP) designates the local electron potential energy density at the H···Y BCP; Y designates the proton acceptor in X–H···Y hydrogen bond. Hence the topological theory of Bader (Carrol et al., 1988a,b) is also useful for the estimation of H-bond energy from the electron density obtained experimentally like, for example, X-ray diffraction measurement applied to the crystal structure determination (Espinosa et al., 1999).

The topological parameters (ρBCP, ∇²ρBCP) in all the BCP of (Ga–Me–saoH) and (Ga–saoH) are evaluated by means of the AIM approach at the B3LYP/6-311G(d, p) level and the results collected in Table 4. Also Fig. 4 presents the molecular graphs of the two compounds analyzed here: (Ga–saoH) and (Ga–Me–saoH). One can observe big circles corresponding to attractors which are attributed to the positions of nuclei as well as small circles which correspond to the positions of bond critical points (BCPs) and ring critical points (RCPs). It can be also observed that the density and the Laplacian of charge density at the O–H bond critical point increases from (Ga–Me–saoH) to (Ga–saoH). This increment is consistent with the contraction of the intermolecular O–O distance. Therefore, we can conclude that the hydrogen bond in (Ga–Me–saoH) is stronger than the (Ga–saoH). This conclusion is strongly supported by hydrogen bond energies (see Table 5).

Table 4 Topological parameters (in a.u.) of the (Ga–saoH) and (Ga–Me–saoH) compounds.

(Ga–saoH)	ρ	∇2ρ	(Ga–Me–saoH)	ρ	∇2ρ
O–H	0.339	0.570	O–H	0.373	0.593
H⋯O	0.040	−0.034	H⋯O	0.037	−0.028
Ga–O1	0.085	−0.093	Ga–O1	0.094	−0.131
O1–C	0.309	0.103	O1–C	0.323	0.063
Ga–N1	0.071	−0.053	Ga–N1	0.075	−0.073
SaoH ring1	0.019	−0.023	SaoH ring1	0.020	−0.024
SaoH ring2	0.014	−0.019	SaoH ring2	0.015	−0.022
Ga–O4acac	0.081	−0.086	Ga–O4acac	0.084	−0.113
acac ring	0.015	−0.020	acac ring	0.016	−0.024
BZ ring	0.020	−0.038	BZ ring	0.020	−0.041

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Figure 4

Molecular graphs of (Ga–saoH) and (Ga–Me–saoH) at B3LYP/6-311G(d, p) level of the theory.

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Table 5 Occupation number of the O–H bond of the acceptor, the lone pairs of the acceptor atom and their corresponding energies (au).

NBO	(Ga–saoH)		(Ga–Me–saoH)
	HB1	HB2	HB1	HB2
O.N (n1O)	1.94105	1.904106	1.94234	1.94233
E (n1O)	−0.43481	−0.43481	−0.41952	−0.41952
O.N (n2O)	1.81319	1.81321	1.82137	1.82136
E (n2O)	−0.54685	−0.54683	−0.52799	−0.52801
O.N (σ∗O–H)	0.0359	0.0359	0.04286	0.04287
E (σ∗O–H)	0.40741	0.40738	0.41526	0.41525