List of tables
III. Results and Discussion
3) Nature of X-π interaction in large π system
In our research models of CX4/X2-Bz, the σ-hole of molecules should be located in the tips of the X2 and CX4 molecules, but the concept of σ-hole doesn’t be easily touched to our thought unless we confirm it instinctively. But fortunately, we can be sure whether molecules have σ-hole or don’t have it, with the aid of the quantum calculation. Figure 3.3.1 shows the EPM of represented three diatomic halogen molecules, F2, Cl2, and Br2. EPM is a useful trick for confirming the presence of the σ-hole in the tip of bond axis because it can visually show the distribution of the electrons density and it can distinguish the relevant strength of electrostatic potentials by ranging the color such as red or blue. For example, when they are electronically positive, neutral, and negative, they represent them as the blue color, green color, and red color, respectively. That is, the blue section of the molecules is the relatively electronically positive region than other points.
In case of Cl2 and Br2, the blue colored holes are observed in their tip of bond axis while the F2 doesn’t show any distinct regions of the colors. That is, the Cl2 and Br2 have σ-hole and the size of it is bigger in case Br2 than Cl2 while F2 has it slightly.
Figure 3.3.1 EPM of diatomic halogen molecules, F2, Cl2, and Br2 on the 0.004 electrons/bohr3 surfaces at the PBE0-D3/aVTZ level of theory.
Therefore, The EPM of halogen molecules can confirm not only the presence of σ-hole but also the change of relative strength by the kind of X. The strength of the halogen bonding is increasing the order of the F, Cl, Br, and I, where the species of I can be strongest halogen bonding. In this respect to the strength of halogen bonding, it is quite understandable that the σ-holes of Br2/CBr4 are bigger
than theirs of Cl2/CCl4. Actually, The Br atom is less electronegative and has a more diffuse valence charge distribution than Cl, and then it provides a more pronounced σ-hole that leads to stronger halogen bonding in the case of Br.
Likewise, the other EPM of molecules consistently showed the trend of distribution of electrons. In case of the benzene, the delocalized π electrons are conjugated to the carbon atoms and the six hydrogens are attached to the side of benzene rings. From the basic concept of chemistry, the ring center should be more negative than ring side in this case. The Figure 3.3.2 shows the EPM of the benzene ring consistent with our expectation. The ring center shows red color and ring side shows the blue color because of the π electrons and the hydrogen atom, respectively.
Figure 3.3.2 EPM of aromatic benzene ring on the 0.004 electrons/bohr3 surfaces at the PBE0- D3/aVTZ level of theory (Top and Side view).
On the other hands, the X2/CX4 contains the halogen atoms which can be halogen bonding.
Because the halogen bonding comes from the electronically positive σ-hole, the relatively deficient orbital occupancy of the corresponding p orbital, the X2 and CX4 molecules show the electronically positive region in tips of their bond axis. Figure 3.3.3 shows the EPM of Cl2 and Br2 with the clear
viewing of the σ-holes on the tips of the bond axis. As we discussed before, the Br2 has the bigger σ- holes than Cl2 has due to the difference of the electronegativity.
Figure 3.3.3 EPM of X2 (X= Cl and Br) molecules on the 0.004 electrons/bohr3 surfaces at the PBE0- D3/aVTZ level of theory (Top and Side view).
In case of CX4, the CCl4 and CBr4 also show the four σ-holes on the tips of the C-X bond axis as shown in the Figure 3.3.4.
Figure 3.3.4 EPM of CX4 (X= Cl and Br) molecules on the 0.004 electrons/bohr3 surfaces at the PBE0- D3/aVTZ level of theory (Transparent and Solid format).
The lowest conformers of X2-Bz can be explained from the interaction of the σ-hole with the π electrons of the benzene ring as shown in the Figure 3.3.5
Figure 3.3.5 EPM of Cl2-Bz conformers (S1, S2, and S3) on the 0.004 electrons/bohr3 surfaces at the PBE0-D3/aVTZ level of theory.
In the Cl2-Bz conformers, σ-hole of S1 conformer located perpendicular to the cloud of π electrons and others don’t directly connect to the cloud of π electrons. The perpendicular position of the σ-hole can be stronger halogen bonding from an additional electrostatic interaction. Therefore, the interaction of the S1 conformer is larger than the S2 and S3 conformers because the binding energy of S1 conformer is contributed from the electrostatic and dispersion. While the S2 and S3 conformers, the dispersion energy becomes more important than electrostatic interaction, and consequently the halogen bonding weakens by losing the optimally oriented conformation.
Figure 3.3.6 EPM of CCl4-Bz conformers (S1 and S2) on the 0.004 electrons/bohr3 surfaces at the PBE0-D3/aVDZ level of theory.
Figure 3.3.6 shows the interaction of CCl4-Bz complex with EPM. The S1 conformer located in the cloud of π electrons and S2 conformer located the side of the benzene ring. The two conformers are highly contributed from the dispersion interaction, but the S1 has weak halogen bonding from tilted σ-hole and π electrons. Since the σ-hole doesn’t have a perpendicular position to the benzene ring, the electrostatic interaction is not distinct in CX4-Bz-S1 conformer. However, the S1 has additional electrostatic interaction and larger dispersion interaction than S2 conformer, the binding energy of the S1 is larger than S2 conformer.
Likewise, the EPM of molecules can confirm the presence of σ-hole and it can give the reasonable binding trends of the X2/CX4-Bz models.
Figure 3.3.7 RMSD in kJ/mol of various DFT methods with respect to CCSD(T)/CBS for the cases of S1 conformers.
In the previous section III-2: Benchmark study for X-π interaction, we carried out a lot of DFT calculations to search the reasonable methods for our systems. Figure 3.3.7 shows the summary of our previous results. We compared the RMSD values of S1 conformer for X2/CX4-Bz with respect to the CCSD(T)/CBS. Because the S1 conformer of X2/CX4 well represented the X-π interaction the smaller derivation means good agreement methods. Finally, we can conclude that the PBE0-D3/TS functional is proper to calculate the X-π interaction.
In this section, we carried out the previous calculation(X2/CX4-Bz) to Cor and Gr cases by using the PBE0 functional with different basis set and dispersion correlation method to know the relation between binding energy and the number of the aromatic ring. The table 3.3.1 shows the binding energies (kJ/mol) of X2-Cor and CX4-Cor. The S1 and S2 conformer of Cl2/Br2-Cor have 15.7/20.3 kJ/mol and 16.7/20.7 kJ/mol, respectively, at the PBE0-D3/CBS level. These S1 and S2 conformers show a similar binding trend in both cases Cl2, and Br2. However, in case of S3 conformer, the binding energies are smaller than other conformers due to the lack of dispersion interaction. For other basis set and dispersion corrected method, the binding energies show good agreement to the PBE0-D3/CBS.
They show consistent binding trend according to the same PBE0 methods.
The relation of the dispersion contribution and binding energies well shows in the CX4-Cor case. The S1, S2 and S3 conformer of CCl4/CBr4-Cor have 26.8/33.2, 23.3/28.2, and 11.0/11.9 kJ/mol respectively, at the PBE0-D3/CBS level. In the S1 conformer CX4-Cor, the CX4 located in the ring
center with strong dispersion interaction of three halogen molecules and Cor. However, in the S2 and S3 conformer, the CX4 moved to the edge side of Cor and the CX4 of S3 conformer located on the ring side. Therefore, the contribution of dispersion interaction of CX4 and Cor in S1-S3 conformers should decrease when the CX4 move to the ring side, so the S1 conformer has largest binding energies and the S3 conformer has smallest binding energies.
Table 3.3.1 Binding energies (kJ/mol) of Cl2/Br2-Cor and CCl4/CBr4-Cora
Cl2/Br2-Cor CCl4/CBr4-Cor
S1 S2 S3 S1 S2 S3
PBE0-D3/CBS 15.7/20.3 16.7/20.7 7.0/8.6 26.8/33.2 23.3/28.2 11.0/11.9 PBE0-D3/PW 16.0/20.8 16.9/20.6 7.4/8.6 27.5/33.5 22.9/27.4 10.9/12.9 PBE0-TS/PW 15.6/19.2 18.4/20.6 7.4/8.4 30.3/34.4 25.1/28.1 9.9/12.6 PBE0-TS/tier3 15.1/18.9 17.7/20.3 7.0/8.1 30.3/34.1 25.8/27.7 10.5/11.9 PBE0-TS/tier2 14.9/18.5 17.6/20.0 7.0/8.0 30.1/33.8 25.7/27.5 10.5/11.9
aThe geometries used with non-PW basis sets are based on aVDZ or light-tier2/tier3 basis set
For the cases of X2/CX4-Gr, the binding energies of X2-Gr and CX4-Grshows in the Table 3.3.2. The binding energies of S1 conformer of Cl2/Br2-Gr are 16.7/22.5 kJ/mol at the PBE0-D3/PW level and the binding energies of S2 conformer of Cl2/Br2-Gr are 19.8/25.3 kJ/mol. The X2 molecules more favor the S2 conformer than S1 conformer about ~3kJ/mol in both cases. Other PBE0 methods also show a similar trend. All case of X2-Gr shows the S2 conformer has larger binding energies than S1 conformer about ~3kJ/mol. Indeed, in the X2 cases, the X2 molecules experience the conformational change on the Gr sheet. The previous Bz and Cor model showed larger and similar binding energy of S1 conformer with respect to binding energies of S2 conformer but in X2-Gr, the S2 conformer has larger binding energies than S1 conformer. Because the diatomic halogen molecules(X2) is perpendicular to the Gr sheet in S1 conformer and parallel to the Gr sheet in S2 conformer, we can notice that the X2 molecules favor the stacked structure than stand-up structure.
The Figure 3.3.8 shows the EPM of various π systems, C6H6, C54H18, and C150H30. The C150H30
represent the larger conjugated π systems like graphene and the C6H6 represent previous our model. The EPM of Bz shows distinct π electrons cloud as a red-colored region but EPM of C150H30 doesn’t show any distinct electronically negative region. The aromatic system loses their electronically negative region when they are extended. Therefore, the infinitely extended π system should be electronically neutral. We already know that the graphene sheet is also electronically neutral like the extended π systems. Since the graphene sheet is electronically neutral, the diatomic halogen molecules can’t any significant halogen bonding in the graphene sheet. So, the stacked structure (S2) is favored in their binding than stand-up structure (S1) because the stacked structure has the advantage to obtain their
binding energy from the dispersion energy. The faced surface between X2 and Gr is larger in case S2 than S1. The S1 would be favored in small π system due to the halogen bonding but it doesn’t have the advantage in a largely extended system because they can’t be significant halogen bonding.
Figure 3.3.7 The electrostatic potential maps(EPM) of C6H6, C54H18, and C150H30 on the 0.004 electrons/bohr3 surfaces at the PBE0-D3/6-31G(d) level of theory.
In the case of CX4-Gr, the binding energies of CCl4/CBr4-Gr are 34.1/42.2 and 31.5/39.7 for S1 and S2 conformers. They are similar binding energies in both cases, and other methods. The atom- top position (S1) is favored than ring-center top position (S2) because of the position of conjugated π electrons in Gr sheet.
Overall, the binding energies are not proportional to the number of aromatic rings because the halogen bonding, kinds of electrostatic interaction, is weaker as the π system is extended. The binding energy of X2-π system increased by 1.5 times from benzene to graphene while the binding energy of CX4-π system increased by 3 times from benzene to graphene. Because the CX4 is more sensitive to the dispersion interaction, the binding energy of CX4 is more changed than the binding energy of X2.
Table 3.3.2 Binding energies (kJ/mol) of Cl2/Br2-Grand CCl4/CBr4-Gr.