Theoretical investigation of the interaction between the metal phthalocyanine [MPc]a(M = Sc, Ti, and V; a = –1, 0, and +1) complexes and formaldehyde

Formaldehyde (FA, CH2O) is one of the toxic volatile organic compounds that cause harmful effects on the human body. In this work, the interaction of FA gas with metal phthalocyanine (MPc) molecules was studied by employing density functional theory calculations. A variety of [MPc]a (M = Sc, Ti, and V; a = –1, 0, and +1) complexes were studied, and the electronic properties, interaction energies, and charge transfer properties of all of the studied molecules were systematically discussed. Among the studied complexes, the Sc and Ti phthalocyanines were more reactive toward the adsorption of FA gas. Moreover, it was revealed that the interaction of the [ScPc]+1 and [TiPc]0 complexes with the CH2O molecule was stronger, in which the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy gap of 46% and 36% decreased after FA adsorption. The results indicated that the MPc-based materials may be a promising candidate for the detection of FA gas.

a systematic study of the ability of the porous sheet of MPcs (Sc to Zn) toward hydrogen storage. They concluded that the ScPc sheet was able to store 4.6% hydrogen and might be a promising material for H 2 storage. However, there are a few studies on the application of MPc complexes (M = Sc, Ti, and V).
The ability of transition MPcs in the interaction with different gases, on one side, and the existence of the CH 2 O molecule in ambient air as a pollutant, on the other side, provided the motivated herein to study the interaction of MPc (M = Sc, Ti, and V) complexes with FA gas. Arokiyanathan et al. [30] showed that the substitution of functional groups did not affect the properties of the MPc ring (Sc and Mg). Accordingly, to reduce the computational cost, the effect of the axial groups, functional groups, and substrates that were present in many synthesized MPc complexes were not considered herein. All in all, in the current work, the electronic properties and adsorption behaviors of the [MPc] a (M = Sc, Ti, and V; a = -1, 0, 1) complexes toward the FA molecule were studied. The interaction of H 2 CO with the three considered forms of the [MPc] a (-1, 0, and +1) complexes was investigated based on analyses of the preferable orientations, electronic properties, and corresponding binding energies within the density functional theory (DFT) framework.

Computational details
All of the calculations performed herein were conducted using the Kohn-Sham DFT with the Becke three-parameter hybrid, non-local exchange, and correlation functional, known as B3LYP [31,32], in conjunction with the split-valence basis set 6-31G* for the H, N, C, and O atoms, and the LANL2DZ basis set for the transition metals, as implemented in the Gaussian 09 program (Gaussian, Inc., Wallingford, CT, USA) [33]. Moreover, previous studies revealed that the use of the B3LYP functional performs reasonably well to predict ground-state properties and gas adsorption on the MPc complexes [34][35][36][37][38]. The validity of the global minimum was determined using the calculation of the vibrational frequencies, in which the absence of vibrational modes with imaginary frequencies demonstrated that the optimized molecular geometry was found at the lowest energy structure. The values of the atomic charges were estimated by employing natural bond orbital (NBO) analysis with the same geometry optimization level. In addition, to obtain accurate results for adsorption of the gases over the MPcs, and taking into account the Van der Waals forces, the results were obtained by considering the longrange correction scheme introduced by Grimme (i.e. the D3-DFT method) [39].
The zero-point energy (ZPE) corrected interaction energy (E int ) for the complexes were calculated by employing the following formula: (1) Here, E Gas-PMc is the total energy of [Gas/MPc] complex, and E PMc and E Gas are the calculated energies for the pure MPc complex and the gas molecule, respectively. Based on the obtained results, a negative value of E int showed that the adsorption process had an exothermic character. Furthermore, the basis set superposition error was eliminated by taking into account the standard counterpoise correction method of Boys and Bernardi [40].
the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy gap (HOMO-LUMO) (E g ) was obtained using the following equation: (2) where ε LUMO and ε HOMO are the corresponding energies of the LUMO and HOMO, respectively.
The change in the HOMO-LUMO energy gap (ΔE g ) was calculated as in Eq. (3) for the [MPc] a (M = Sc, Ti, and V; a = -1, 0, and +1) complexes toward the FA adsorption.

Electronic structure of the [ScPc] a (a = -1, 0, and +1) complexes
The optimized structures of the [ScPc] a (a = -1, 0, and +1) complexes are shown in Figure 1a. The data analyses showed that the ScPc in all three of the oxidized, neutral, and reduced states had a nonplanar geometric structure with C 2v symmetry. Moreover, the Sc atom was projected by about 1.115, 1.002, and 0.774 Å out of the molecular planes of the [ScPc] +1 , [ScPc] 0 , and [ScPc] −1 complexes, respectively. It was found that increasing the negative charge on the ScPc complex reduced the out-of-plane projection of the Sc atom. The calculated Sc-N bond lengths were 2.086, 2.080, and 2.082 Å for the [ScPc] +1 , [ScPc] 0 , and [ScPc] −1 complexes, respectively. These data also showed an increase of 0.006 and 0.002 Å in the Sc-N bond length in the oxidized and reduced states, which showed that these bonds were weaker than that of neutral state. Moreover, the calculated bond orders for the Sc-N bond were 0.73 and 0.45 for the [ScPc] −1 and [ScPc] 0 states, respectively, which demonstrated that this bond order decreased by inducing the positive charge on the ScPc complexes. Furthermore, increasing the positive charge on the ScPcs prevented the bond between the Sc and N atoms. In this regard, [ScPc] +1 may be an unstable and more reactive complex.
Metal coordination is an important feature of the MPcs toward gas adsorption. In these structures the positivelycharged M atoms coordinated to the four isoindole nitrogens of the phthalocyanine ring through covalent and electrostatic interactions. According to the NBO population analysis (see Table 1), the Sc atom presented a positive charge, with values of 1.89, 1.81, and 1.75 e for the [ScPc] +1 , [ScPc] 0 , and [ScPc] −1 complexes, respectively. The values of the charge on the Sc atom revealed that, when the ScPc complex was reduced, a part of the induced charge remained close to the Sc atom.
Frontier molecular orbitals (FMOs) are important descriptors used to better understand the stability and reactivity of the complexes. In the electrophilic attack, the ionization potential was related to the HOMO. In the nucleophilic reactions, electronic affinity, and susceptibility were directly related to the LUMO. Moreover, the HOMO-LUMO energy gap (E g ) can be utilized to estimate the chemical stability and reactivity of the complexes. The spatial distribution of the FMOs of the ScPcs are presented in Figure 1b, where it can be seen that the electron density of the HOMO and LUMO orbitals was uniformly distributed over the surfaces of the [ScPc] −1 and [ScPc] 0 complexes. However, the HOMO of the [ScPc] +1 complex was mainly localized on the phthalocyanine ring, without any contribution by the Sc atom. The E g values of the [ScPc] +1 , [ScPc] 0 , and [ScPc] −1 complexes were 1.82, 1.18, and 1.26 eV, respectively. Therefore, as a result of the narrow HOMO-LUMO gap, the [ScPc] 0 complex was more reactive than its counterparts toward FA adsorption.
A map of electrostatic potential (MEP) is a physical descriptor to predict the active site of complexes upon nucleophilic and electrophilic attacks, where the positive and negative electrostatic potential regions are represented by the suitable part of a complex in electrophilic and nucleophilic attacks, respectively. The MEP of the ScPcs is shown in Figure 1c, which demonstrates the distribution of negative and positive electrostatic potential regions on the ScPcs. Moreover, in all of the complexes, the positive region (in blue) is mainly localized on the Sc atom. Thus, the Sc atom had more potential to participate in the nucleophilic attack.

Electronic structure of the [TiPc] a (a = -1, 0, and +1) complexes
The optimized structures of the [TiPc] a (a = -1, 0, and +1) complexes are shown in Figure 2a. Although both the [TiPc] −1 and [TiPc] 0 complexes were completely planar, the [TiPc] +1 complex had a nonplanar structure, in which the Ti atom was about 0.814 Å out of the molecular plane. The calculated Ti-N bond distances were 2.012, 2.015, and 2.009 Å for the [TiPc] +1 , [TiPc] 0 , and [TiPc] −1 complexes, respectively. These results showed that the Ti-N bond lengths in the reduced and oxidized states were 0.006 and 0.003 Å less than in the neutral state, which showed that this bond was stronger than that of their neutral counterparts.
The NBO analysis revealed that there was no actual bond between the Ti and N atoms in any of the three considered TiPc complexes, which explained why the isolated TiPc complex was not observed experimentally. Accordingly, to stabilize the TiPc complexes, it is important to use a substrate. However, the oxo-TiPc adsorbed from the O-head on a substrate or the directly synthesized TiPc on a surface may be used as a bare TiPc complex in practical applications. The base on the NBO analysis (see Table 1) and the titanium atoms present positive charges, at values of 1.42, 1.37, and 1.15 e in the [TiPc] +1 , [TiPc] 0 , and [TiPc] −1 complexes, respectively, were due to the fact that a part of the induced charge remained close to the Ti atom after reducing the TiPc complex.
According to the spatial distribution of the FMOs of TiPc complexes (see Figure 2b), the LUMOs of [TiPc] −1 and [TiPc] 0 complexes were more localized on the Ti atom, which indicated that when these complexes were attacked by a nucleophilic compound, the electrons went to the d orbital of the Ti atom. This was further confirmed by the MEP plots, where the positive charges were distributed across the Ti atom and created an electric field on the surface of the [TiPc] −1 and [TiPc] 0 complexes (see Figure 2c). This may lead to the polarization of the incoming gas molecules during nucleophilic attacks.
The complexes, respectively. These results showed that the V-N bond lengths in the oxidized and neutral states were 0.010 and 0.013 Å higher than in the reduced state, which showed that this bond was weaker than that of their reduced counterparts.
The NBO population analysis (see Table 1 Based on the spatial distribution of the FMOs (see Figure 3b), it was observed that the LUMOs of the [VPc] 0 and [VPc] +1 complexes protruded more from the molecular plane, which indicated that the V atom of these complexes can be used as a target site under nucleophilic attacks. In the case of the [VPc] −1 complex, the HOMO was mainly localized on the V atom, which demonstrated that when an electron was extracted from this complex, the extracted electron was from the V atom. The negative electrostatic potential was mainly localized on the whole surface of the [VPc] −1 complex, which suggested that the [VPc] −1 complex may be inert under nucleophilic attacks (see Figure 3c). The [VPc] 0 , and [VPc] −1 complexes were 1.19, 2.34, and 2.17 eV, respectively. It was predicted that the [VPc] +1 complex may be more reactive than its counterparts towards gas adsorption.

Formaldehyde adsorption on the metal phthalocyanine complexes ([MPc] a , M = Sc, Ti, and V; a = -1, 0, and +1)
Based on the results, the calculated C-H bond length and H-C-H bond angle of the free CH 2 O was 1.11 Å and 115.2°, which was in good agreement with the reported experimental data of 1.01 Å and 118°, respectively [41]. These results suggested that the theoretical method used in this study was accurate to describe the studied system. In order to obtain the stable structure of the CH 2 O adsorbed on the surface of the MPcs, several possible initial adsorption geometries were considered, including the hydrogen site, oxygen site, and CH 2 O surface perpendicular or parallel to the surface of the MPcs. However, the adsorption of the CH 2 O from the O-side led to a more stable structure that was in good accordance with other theoretical and experimental studies [42][43][44]. Figure 4 shows the calculation results, where it can be seen that the Sc-O bond lengths in the reduced and oxidized states were 0.002 and 0.241 Å less than that of the neutral state. It was obvious that the [ScPc] +1 complex had less tendency to adsorb the FA gas in comparison with the other studied Sc complexes. Moreover, the projection of the Sc atom from the plane of the [CH 2 O/ScPc] a complex was ~0.17 Å smaller than that of the bare clusters. This clearly demonstrated that the adsorption of CH 2 O molecule over the three considered forms of the [ScPc] a complexes helped to stabilize these complexes.
In the optimized structure of the [CH 2 O/TiPc] a complexes (Figure 4), the Ti-O bond distances were found as 1.934, 1.914, and 1.844 Å for the [TiPc] −1 , [TiPc] 0 , and [TiPc] +1 complexes, respectively. Therefore, it can be inferred that CH 2 O was strongly bonded to the Ti atom in the oxidized state when compared to its counterparts. Furthermore, the main change that happened during the CH 2 O adsorption over the [TiPc] −1 and [TiPc] 0 complexes was the projection of the Ti atom out of the molecular plane of these complexes (~0.15 Å). It is important to mention that other optimized structure parameters, such as the M-N and N-C bond lengths, did not change dramatically after CH 2 O adsorption over the studied complexes, due to the interaction of CH 2 O with only the metal ion of the MPcs. Moreover, the Pc molecules only had a role as host for the M atom and created an avenue for the charge transfer during adsorption.
The partial charges of the M atom on the CH 2 O/MPcs complexes derived from the NBO analysis are tabulated in Table  2, where it can be seen that the adsorption of CH 2 Table 2). These values showed that the CH 2 O molecule was strongly bonded to [ScPc] Table 2). In experimental studies, the variation in electrical conductivity after gas adsorption was measured as a sign of the sensitivity of an electronic sensor toward a specific molecule [45,46]. In theoretical studies, the change of E g was considered as a characteristic of the sensor to simulate electrical conductivity [47,48]. In this regard, the ScPc and TiPc complexes that showed a decrease in E g after CH 2 O adsorption could demonstrate high electrical conductivity. In other words, by tracing the electrical conductivity variation of the ScPc and TiPc complexes before and after CH 2 O adsorption, the presence of this molecule can be detected in the air (see Figure 5). Moreover, among the studied forms of the MPc complexes, it was determined that the [ScPc] +1 and [TiPc] 0 complexes can be a promising CH 2 O sensing material due to the significant decrease in E g after CH 2 O adsorption. This result was confirmed by the total density of the state plots (TDOS) of CH 2 O  adsorption over the MPc complex (see Figure 6), where the appearance of a new peak between the HOMO and LUMO after adsorption led to a decrease in the E g value of the [ScPc] +1 and [TiPc] 0 complexes. In addition to these results, Figure  4a indicated that, in the case of [ScPc] 0 , the newly formed Sc-O bond in comparison with other M-O bonds in the neutral form of MPcs was short (1.915 Å), but the E g value (see Table 2) after adsorption changed somewhat (~0.03 eV), due to significant structural distortion. Moreover, the adsorption of CH 2 O over the vanadium complexes did not alter the E g value, due to the distortion of the structure of the VPc complexes after CH 2 O adsorption. It is important to mention that, the calculations herein were 298.15 K and 1 atm. However, the calculation results at other temperatures, pressures, and FA concentrations might be different, which should be taken into consideration by experimental and theoretical researchers in future studies.

Conclusions
First-principle calculations were performed to study the adsorption and interaction of the CH 2 O molecule toward a variety of [MPc] a (M = Sc, Ti, and V; a = -1, 0, and +1) complexes. It was found that the adsorption of CH 2 O over the MPCs was able to significantly alter the electronic properties of the Sc and Ti complexes. The results of the present study revealed that the most pronounced effect on the electronic structure of the MPcs was observed with [ScPc] +1 , where the E g value of [ScPc] +1 showed a variation of about 48% after CH 2 O adsorption. It is expected that the present study will stimulate experimental efforts to confirm the results of this work as well as devise chemical modification strategies to design effective MPcs-based gas sensors by employing MPc (M = Sc, Ti, and V) complexes.