Investigation of the Substituent Effects on π -Type Pnicogen Bond Interaction

Intermolecular interactions between PH 2 Cl and Ar–R (R = H, OH, NH 2 , CH 3 , Br, Cl, F, CN, NO 2 ) were calculated by using MP2/aug-cc-pVDZ quantum chemical method. It has been shown from our calculations that the aromatic rings with electron-withdrawing groups represent much weaker binding affinities than those with electron-donating groups. The charge-transfer interaction between PH 2 Cl and Ar–R plays an important role in the formation of pnicogen bond complexes, as revealed by NBO analysis. Nevertheless, AIM analysis shows that the nature of the interactions between PH 2 Cl and Ar–R is electrostatic, and the interaction energies of the complexes are correlated positively with the electron densities in the bond critical points (BCPs). RDG/ELF graphical analyses were performed to visualize the positions and strengths of the pnicogen bonding, as well as the spatial change of the electron localization upon the formation of complexes. The π -type halogen bond was also calculated, and it has been revealed that the π -type pnicogen bond systems are more stable than the halogen bond ones.

. Comparing the ΔEint with CP E int  , the differences between them are 2.7 to 3.5 kcal· mol −1 , so BSSE correction is necessary for the π-type pnicogen bond systems. Complex 1 is the one formed by PH2Cl and the non-substituted benzene, whose corrected interaction energy is -3.81 kcal· mol −1 . The corrected interaction energies of complexes 2 and 3 are -7.56 and -9.65 kcal· mol −1 , respectively, which are much larger than that of complex 1. As the substituted groups -OH and -NH2 are electron donor ones, the electron density of π-electron system in the benzene ring is increased, which then leads to a stronger interaction between PH2Cl and π-electron, greater interaction energy of the complex and a more stable complex. Similarly, the electron donating capacity of the group -CH3 is weaker than the above two, so the interaction energy of complex 4 is smaller than that of 2 and 3. The corrected interaction energies of complexes 7～9 are -3.55, -3.44, and -3.45 kcal· mol −1 , respectively, which are smaller than the interaction energy of complex 1, i.e. complexes 7～9 are less stable than 1. This is because the electron-withdrawing groups, -F, -CN and -NO2, reduce the π-electron density in the benzene ring, and result in the weakening of the interaction between P and π-electron. It is worth noting that the substituting groups -Br and -Cl in complexes 5 and 6 are electron-withdrawing groups, but their interaction energies are a little larger than that of complex 1. The reason may be the weak hydrogen bond interaction between the hydrogen atom in PH2Cl and halogen atom of the substituting group. It can be clearly seen in the geometrical structure of chinaXiv:201711.00130v1 The halogen bond is the interaction between the electron donor and the halogen atom in the halogenous molecule. It was found earlier than the pnicogen bond, and the research on halogen bonds is more mature than the pnicogen bond. In our current research system, when the π-type pnicogen bond interaction can be generated between the PH2Cl molecule and the aromatic compound, a π-type halogen bond complex can be generated between π electron of the aromatic ring and atom Cl in the PH2Cl molecule. As a comparison, the molecular structures of nine typical halogen bond complexes are optimized at the MP2/aug-cc-pVDZ level, and then their corrected interaction energies ( ) of the corresponding halogen bond system, it has been found that the π-type pnicogen bond system is more stable than the π-type halogen bond system. It is caused by the unbalanced distribution of positive electrostatic potential in the PH2Cl. The structures of two representative halogen bond complexes are shown in Fig. 3, where the positive electrostatic potential at the top of atom P is larger than that at the top of atom Cl in the same aromatic π electron donor.  Table 2 shows the donor-acceptor orbital, the second-order perturbation stabilization energy (ΔE 2 ), and the charge transfer quantum (QCT) of 9 π-type pnicogen bond complexes at the level MP2/aug-cc-pVTZ. The second-order perturbation stabilization energy (ΔE 2 ) can be obtained from the following equation:

2 NBO analysis
where i q is the donor orbital occupancy, i  and j  are the diagonal elements (orbital energies), and F is the NBO Fock matrix element. It has been shown from the donor-acceptor orbital for complexes 1～9 in Table 2 that the pnicogen bonding interaction is mainly the interaction between the C-C π bonding orbital and the σ anti-bonding orbital of P-Cl in the monomer PH2Cl. The three complexes 3, 5 and 6 are further involved with the hydrogen bond interaction in addition to the pnicogen bond interaction. The second-order perturbation stabilization energy values indicate that the pnicogen bond interaction, followed by the hydrogen bond interaction, plays a key role in the complex stability. The existence of the supportive hydrogen bond interaction is the fact that complexes 5 and 6 have higher interaction energies than complex 1 in the above analysis, and why the angle α is smaller in complex 3.
According to the data in Table 2, the correlation between the second-order perturbation stabilization energy of the C-C π bonding orbital and the σ anti-bonding orbital of P-Cl and the corrected interaction energy are mapped in Fig. 4(a), and the following relational expression is obtained after fitting: The curve in Fig. 4(a) shows there is a bi-variable function relation between the second-order perturbation stabilization energy (ΔE 2 ) of the C-C π bonding orbital and the σ anti-bonding orbital of P-Cl and the corrected interaction energy ( Interaction energy (kcal/mol) Second-order perturbation stabilization energy (kcal/mol) (a)

Fig. 4. Relationship between the second-order perturbation stabilization energy and interaction energy
The molecular interaction is always accompanied by charge transfer, whose quantities in complexes 1～9 are shown in Table 2

3 AIM analysis
To further analyze the nature of π-type pnicogen bond interaction, the AIM (Atom in Molecule) theory developed by Bader is used, as the theory is often used in researches on molecular weak interactions [32][33][34][35] . The typical pnicogen bond complex molecular diagram has been shown in Fig. 6, in which a critical point between the atom P and the aromatic ring is observed, and therefore the existence of π-type pnicogen bonds is proved. Table 3 shows the electron densities (ρb), Laplacian of electron densities ( 2 ρb), three eigenvalues (λ1, λ2, λ3) of Hessian matrix, kinetic energy densities (Gb), potential energy densities (Vb) and electronic energy density (Hb) of the 9 π-type pnicogen bond complexes at the bond critical point of pnicogen bond (BCP) at the MP2/aug-cc-pVDZ level.
According to the AIM theory, charges are dispersed and the bond ionicity is stronger at BCP when |λ1 + λ2| < λ3 and  2 ρb > 0, but charges are centralized and the bond covalence is stronger when |λ1 + λ2| > λ3 and  2 ρb < 0. The data in Table 3 suggest that, the Laplacian quanta ( 2 ρb) at BCP are larger than zero and |λ1 + λ2| < λ3, which means the ionicity of π-type pnicogen bond is stronger in complexes 1～9. The electronic energy density Hb (sum of the kinetic energy density Gb and the potential energy density Vb) is often deemed as a correct index for understanding the weak interaction [36,37] . The interaction is a static interaction when Hb > 0, and is a covalence interaction when Hb < 0. All Hb values in Table 3 are larger than zero, which means that the interactions of the 9 π-type pnicogen bond complexes belong to the static interaction, and it complies with the above conclusion that "charges are dispersed and the bond ionicity is stronger at BCP when |λ1 + λ2| < λ3 and  2 ρb > 0". The electron density (ρb) at BCP is correlated to the bond strength, as the bond strength is larger if the electron density is higher. The relationship of the electron density (ρb) at BCP and the corrected interaction energy of the complex is mapped (Fig.   7), and the correlation coefficient R is 0.915.

4 RDG/ELF analysis
Yang Weitao's subject team [38] has developed a visualized method for the weak interaction research, through which the calculated values of reduced density gradient (RDG) function and sign (λ2(r))ρ(r) of each point in the space are visualized in the RDG isosurface map. The gradient isosurfaces are colored according to the corresponding values of sign (λ2(r))ρ(r), which is found to be a good indicator of interaction strength. We used this method in analyzing the position and strength of the interaction between hydrogen bonds, halogen bonds and pnicogen bonds and the coordination bond, and the result was promising [39][40][41] . The electron localization function (ELF) is an important tool for electron structure researches, and it is often used to study chemical problems [42] such as the molecular interaction. These two analysis methods are applied to π-type pnicogen bond interaction in order to visualize the interaction change. Fig. 8 shows the isosurface map for complexes 1 and 2 obtained from the combination of RDG and ELF (Fig. 8a) and the electron localization isosurface map of PH2Cl (Fig. 8b). In the case, the spatial position of molecular interaction can be expected, and the interaction strength is also observed according to the color of RDG map, in which blue represents the strong interaction, green the weak interaction, and red the repulsion. Comparing the color-filled RDG isosurface maps for complex 1 and complex 2, we can find the blue zone of complex 2 is deeper than that of complex 1, which suggests complex 2 has stronger pnicogen bond interaction than 1. The white column and vacuum ring zones in Fig. 8a represent the localization spaces of the lone-pair electron, π electron and valence electron. The localization space (V(P)) of the lone-pair electron on the atom P is obviously weakened (Fig. 8b). The reason for such phenomenon is that the intermolecular distance is shortened by the weak interaction, and some repulsion is generated between π electron and the lone-pair electron on the atom P. Such weak interaction force shortening the intermolecular distance is mainly the static interaction. According to the AIM analysis, the pnicogen bond interaction is mainly the static acting force. In other words, what is weakening the lone-pair electron localization space on P atom is the pnicogen bond interaction to a certain extent. The geometrical structural optimization, energy calculation and topological and graphic analyses for the various pnicogen bond system of PH2Cl and Ar-R (R = H, OH, NH2, CH3, Br, Cl, F, CN, NO2) have been made at level MP2/aug-cc-pVDZ. The results showed that the complex pnicogen bond interaction is strengthened when the substituting group in the benzene ring is the electron donating group, and the complex pnicogen bond interaction is weakened when the substituting group is the electron withdrawing group. To compare the interaction energy of the π-type pnicogen bond system with the halogen bond system, the interaction energy of π-type halogen bond system is also calculated, and it is showed that the π-type pnicogen bond system is more stable. NBO theory is used to analyze the correlation between the second-order perturbation stabilization energy and the charge transfer quantum with the interaction energy, and the result shows that the charge transfer plays an important role in the stability of the pnicogen bond complex. AIM analysis has indicated that, the nature of pnicogen bond interaction is the electrostatic interaction, and the electron density at BCP is positively correlated to the interaction energy of the pnicogen bond complex. RDG analysis showed the position and strength of pnicogen bond interaction, and ELF analysis indicated the change of lone-pair electron localization space on P atom after the complex formation.