3.1 Molecular electrostatic potentials
Molecular electrostatic potential (MEP) is a fundamentally important physical characteristic that very useful for understanding and predicting noncovalent interactions. Figure 1 shows the contour maps of MEPs for triplet biphenyclobin (DPC3) and LA (LA = AlF3, SiF4, PF5, SF2, ClF). The most positive electrostatic potentials (VS,max) and most negative electrostatic potentials (VS,min) on the 0.001 au contour of the molecular electron density are collected in Table 1. As shown in Fig. 1a, the contour map for DPC3 presents a few blue regions with negative MEPs. The positions of VS,min are located above and below the benzene ring, represented by blue dots, with the values of -13.7 and − 12.2 kcal/mol, respectively. From the contour map of MEP for AlF3 (Fig. 1b), aluminum atom acts as the Lewis acid center since it is characterized by the depletion of electron charge (π-hole) [7, 14]. This red region corresponds to the vacant p orbital perpendicular to the plane of AlF3 molecular framework, with a VS,max value of 104.7 kcal/mol. In the case of ClF, SF2, SiF4 and PF5, there are one or more σ-holes (red regions) with positive MEPs along the extension of the corresponding Cl-F, S-F, Si-F and P-F bond. The VS,max values were found to become increasingly more positive following the order AlF3 > SiF4 > ClF > SF2 > PF5.
Table 1
Most positive and negative MEPs of the monomers (VS,max, VS,min in kcal/mol)
Molecule
|
VS,min
|
VS,max
|
DPC3
|
-13.7/-12.2
|
-
|
AlF3
|
-
|
104.7
|
SiF4
|
-
|
47.4
|
PF5
|
-
|
39.9
|
SF2
|
-
|
41.4
|
ClF
|
-
|
44.6
|
3.2 Geometry, binding energy and NBO analysis
Based on the analysis of MEPs, the intermolecular interaction could form between the σ-hole or π-hole regions of LA (LA = AlF3, SiF4, PF5, SF2, ClF) and the negative electrostatic potential region of DPC3. Figure 2 shows the stable geometries of DPC3···LA (LA = AlF3, SiF4, PF5, SF2, ClF) complexes. It can be seen that the most stable interaction between DPC3 and LA (LA = AlF3, SiF4, PF5, SF2, ClF) occurs on the benzene ring of DPC3. The binding energy, binding distance and the main parameters of NBO analysis for the complexes are given in Table 2. The binding energy (ΔE) ranges from − 15.8 kJ/mol for pnicogen-bonded complex DPC3···PF5 to -65.7 kJ/mol for triel-bonded complexes DPC3···AlF3. The strength of intermolecular interaction become stronger along the sequence LA = PF5 < SiF4 < SF2 < ClF < AlF3. Binding distance (d) in the Table 2 refers to the distance between the atom of Group 13 to 17 in the LA (LA = AlF3, SiF4, PF5, SF2, ClF) and the nearest carbon atom of benzene ring in DPC3, which can be seen that the shorter the binding distance, the stronger the interaction. By comparing the data in Table 1 and Table 2, it is found that the binding energy between molecules is not well correlated with the VS,max values of Lewis acids, which may be due to the steric hindrance effect of SiF4 and PF5.
Table 2
Binding energy, binding distance, and main parameters of NBO and MFDD analyses for the complexes DPC3···LA (LA = AlF3, SiF4 PF5, SF2, ClF) (energy in kJ/mol, distance in Å, charge in e)
Complex
|
ΔE
|
d
|
Donor NBO
|
Acceptor NBO
|
E(2)
|
QCT
|
Δne
|
DPC3···AlF3
|
-65.7
|
2.368
|
BD(C-C)
|
LV(Al)
|
12.43
|
0.1078
|
0.1897
|
|
|
|
3C(C-C-C)
|
LV(Al)
|
17.95
|
|
|
DPC3···SiF4
|
-19.7
|
3.669
|
LP(F)
|
BD*(C-H)
|
0.88
|
-0.0045
|
0.0266
|
DPC3···PF5
|
-15.8
|
3.669
|
LP(F)
|
BD*(C-H)
|
0.84
|
-0.0027
|
0.0280
|
DPC3···SF2
|
-20.5
|
3.183
|
BD(C-C)
|
BD*(S-F)
|
4.43
|
0.0212
|
0.0378
|
DPC3···ClF
|
-30.1
|
2.651
|
BD(C-C)
|
BD*(Cl-F)
|
113.55
|
0.1690
|
0.0554
|
For a better understanding of orbital interaction and charge transfer between specific orbitals of each monomer, NBO analysis was performed at the B3LYP-D3/6-311 + + G** level. The lump sum of the charge transferred between the molecules is reported as QCT in the last column of Table 2. The values of QCT for the complexes DPC3···LA (LA = AlF3, SiF4, PF5, SF2, ClF) are 0.1078e, -0.0045e, -0.0027e, 0.0212e and 0.1690e, respectively. The positive CT quantities indicate that charge is transferred from DPC3 to AlF3, SF2 or ClF, as would be expected for triel bond, chalcogen bond and halogen bond. For the complexes formed by SiF4 and PF5, the charge transfer is very small and negative, reflecting the fact that little net charge is apparently transferred from SiF4/PF5 to DPC3; this may be the cause of steric crowding in tetrel bond and pnicogen bond. The tetravalent/pentavalent character of Si/P atom leaves only limited room for an incoming nucleophile to approach and engage in a noncovalent bond with a tetrel/phosphorus atom [47]. The charge transfer occurs mainly from the F lone pairs in SiF4/PF5 to the C-H antibonding orbital in the DPC3, with small second order perturbation energy (E(2)) 0.88 kJ/mol and 0.84 kJ/mol, respectively. From Table 2, the strongest orbital interaction is happened in the halogen-bonded complex DPC3···ClF. The E(2) value between the C-C bonding orbital (BD(C-C)) and antibonding Cl-F orbital (BD*(Cl-F)) was calculated to be 113.6 kJ/mol. In the triel-bonded complex DPC3···AlF3, the main electron transfer is from the C-C bond orbital (BD(C-C)) and 3-center bonding orbital (3C(C-C-C)) in the DPC3 to the lone vacancy of aluminum atom (LV(Al)) in the AlF3. For chalcogen-bonded complex DPC3···SF2, charge transfer occurs from the C-C bonding orbital in the DPC3 to the S-F antibonding orbital in the SF2 (BD(C-C) → BD*(S-F)), E(2) and CT were calculated to be 4.43 kJ/mol and 0.0212e .
3.3 Noncovalent interaction index
To verify the intermolecular interaction between DPC3 and LA (LA = AlF3, SiF4, PF5, SF2, ClF), the complexes were analyzed by noncovalent interaction index (NCI). This method, proposed by Yang's research group [48, 49], can not only describe the properties of the interacting molecules, but also show the characteristic information of the interaction through graphics. Based on the analysis of the electron density (ρ) and its reduced density gradient function (RDG), this approach combines with the electron density and sign(λ2) to analyze the type and strength of interactions between molecules, where sign(λ2) is the sign of the second eigenvalue of its Hessian. In the isosurface of the reduced density gradient function, blue represents strong attractive interaction, green represents weak interaction, and red indicates strong nonbonded overlap, such as steric effect in a ring or cage. Figure 3 shows the plots of the reduced density gradient versus the electron density multiplied by sign(λ2) (above) and gradient isosurfaces generated for s = 0.05 au (below). In the DPC3 complexes, several low-density isosurfaces (green regions) lie in the interacting portions between DPC3 and LA (LA = AlF3, SiF4, PF5, SF2, ClF), where noncovalent attractions are expected. There is another area of the low-density, low-gradient nonbonded overlap (red region) located at the center of each benzene ring, where steric repulsion in the benzene ring. For the triel-bonded complex, the blue isosurface lies between the π-hole of AlF3 and benzene ring of DPC3, reveals stronger interaction than in the other complexes. The locations of ρ(r) peaks for the complexes DPC3···LA (LA = AlF3, SiF4, PF5, SF2, ClF) are consistent with the interaction strengths.
3.4 QTAIM analysis
Based on the quantum theory of atoms in molecules (QTAIM) [50, 51], the molecular structures, the characters of chemical bonds and chemical reactions are closely related to the electron density distribution functions. The strength and properties of a chemical bond can be determined through the relative parameters of the electron density and the energy density at the critical points in molecules [52–54]. The common studied topological properties at the bond critical points (BCPs) are electron density (ρb), its Laplacian (∇2ρb), the local potential energy density (Vb), local kinetic energy density (Gb), and total energy density (Hb = Vb + Gb). According to criteria [55, 56], a positive ∇2ρb reflects an excess of kinetic energy in bonds and a relative depletion of electronic charge along a bond path. A positive Hb corresponds to a purely closed-shell interaction, whereas a negative Hb value corresponds to bonds with any degree of covalent character. If -Gb/Vb is greater than 1, then the interaction is noncovalent. If the ratio is between 0.5 and 1, the interaction is partly covalent in nature, and when this ratio is less than 0.5, the interaction is a shared covalent one.
The molecular graphs and the topological properties of electron density at the BCPs of the complexes are showed in Fig. 4 and Table 3. For DPC3···AlF3 complex, there exists a BCP between the π-hole of AlF3 and C atom of DPC3, and a pair of bond paths connect the BCP and the interacting Al and C atom. The values of ρb and ∇2ρb at the C···Al BCP were calculated to be 0.0296 au and 0.0710 au. Positive ∇2ρb value, negative Hb value, and -Gb/V value of about 0.8 indicate that this triel bond is of moderate strength with a partially covalent nature. For complex DPC3···SiF4 and DPC3···PF5, there exist several C···F BCPs and one H···F BCP between DPC3 and SiF4/PF5 molecules, the ρb values are less than 0.0090 au. From Fig. 4d and 4e, the C···S or C···Cl BCP in the DPC3···SF2 and DPC3···ClF complexes account for the chalcogen bond or pnicogen bond between DPC3 and σ-hole of SF2/ClF. The ρb and ∇2ρb values of the complexes DPC3···LA (LA = SiF4, PF5, SF2, ClF) are in the range of 0.0044 ~ 0.0296 au and 0.0155 ~ 0.0621 au. ∇2ρb > 0,Hb > 0༌and -Gb/Vb > 1 were calculated, showing the characters of a weak closed-shell noncovalent interaction.
Table 3
Topological properties of electron density at the bond critical points for the complexes DPC3···LA (LA = AlF3, SiF4 PF5, SF2, ClF) (in au)
Complex
|
BCP
|
ρb
|
∇2ρb
|
Gb
|
Vb
|
Hb
|
-Gb/Vb
|
DPC3···AlF3
|
C···Al
|
0.0296
|
0.0710
|
0.0230
|
-0.0283
|
-0.0053
|
0.8132
|
|
H···H
|
0.0063
|
0.0247
|
0.0048
|
-0.0035
|
0.0013
|
1.3788
|
|
H···F
|
0.0094
|
0.0332
|
0.0072
|
-0.0062
|
0.0011
|
1.1734
|
DPC3···SiF4
|
C···F
|
0.0052
|
0.0194
|
0.0040
|
-0.0031
|
0.0009
|
1.2868
|
|
C···F
|
0.0052
|
0.0195
|
0.0040
|
-0.0030
|
0.0009
|
1.3056
|
|
C···F
|
0.0044
|
0.0155
|
0.0031
|
-0.0024
|
0.0008
|
1.3178
|
|
H···F
|
0.0081
|
0.0306
|
0.0066
|
-0.0056
|
0.0010
|
1.1853
|
DPC3···PF5
|
H···F
|
0.0090
|
0.0338
|
0.0073
|
-0.0061
|
0.0012
|
1.1907
|
|
C···F
|
0.0061
|
0.0251
|
0.0052
|
-0.0041
|
0.0010
|
1.2623
|
|
C···F
|
0.0066
|
0.0244
|
0.0051
|
-0.0042
|
0.0010
|
1.2352
|
DPC3···SF2
|
C···S
|
0.0102
|
0.0292
|
0.0062
|
-0.0051
|
0.0011
|
1.2219
|
|
H···F
|
0.0080
|
0.0303
|
0.0065
|
-0.0055
|
0.0010
|
1.1841
|
DPC3···ClF
|
C···Cl
|
0.0258
|
0.0621
|
0.1512
|
-0.0149
|
0.0003
|
1.0219
|
3.5 Density difference of molecular formation analysis
The density difference during the formation of super molecules (A···B) can be described as ρd(r) = ρcomplex(r) – (ρmolA(r) + ρmolB(r)). According to Politzer et al. [57], polarization is a real physical phenomenon, corresponding to the electron density shifts from one molecule to the electric field of another, could be observed physically from the electronic density. Density difference of molecular formation (MFDD) analysis has often been used to study the formation of molecules and weak interactions [58–60]. Figure 5 present plots of computed density difference of the complexes, the shift of charge density during the forming of DPC3···LA (LA = AlF3, SiF4, PF5, SF2, ClF) complexes are clearly shown. The electronic fields of the π electrons in DPC3 and σ/π-hole in LA cause charge redistributions of each segment. From Fig. 5a and 5e, one can see a few negative regions (blue regions) outside the carbon atoms and Al/Cl atom, which means that a decrease in electron density when DPC3 and LA interact to form the complexes. An increased region in electron density (white region) between the carbon atoms and Al/Cl atom could be found during the formation of the triel bond and halogen bond. From AlF3, ClF to SF2, SiF4 and PF5, the degree of charge density in the intermolecular region becomes more and more slight. We chose this increased region as a cube to integrate the total charge of the density difference, the positive integral charge (Δne) were obtained and shown in the last column of Table 2. Linear correlation was found between the integral charges and the binding energies, with the correlation coefficients 0.982 (Fig. 6). The stronger DPC3···LA interaction increases the electric field in the intermolecular region, resulting in a larger increase in electron density between molecules. These results indicate that polarization effect plays an important role when DPC3 interact with Lewis acids.
3.6 Electron spin density analysis
For open shell system, total electron density is the sum of α and β electron densities, i.e., ρ(total) = ρ(α) + ρ(β). The difference between ρ(α) and ρ(β), Δρ = ρ(α) - ρ(β), represents the electron spin density of the system. The value Δρ is equal to 0 and 2 in the LA and triplet DPC3 molecules. Figure 7 show the maps of electron spin density of DPC3 and its complexes DPC3···ClF and DPC3···SF2, the Δρ values of C atoms in DPC3 are marked out. Green regions represent positive and blue regions represent negative Δρ values. To illustrate the electron spin density transfer during bond formation, Table 4 lists the electron spin density changes of C atoms and LA in the formation of the complexes.
Table 4
Changes of electron spin density for carbon atoms and LA in the complexes (in au)
Complex
|
DPC3···AlF3
|
DPC3···SiF4
|
DPC3···PF5
|
DPC3···SF2
|
DPC3···ClF
|
ΔΔρ(C1)
|
0.0028
|
0.0087
|
0.0087
|
-0.0004
|
-0.0550
|
ΔΔρ(C2)
|
0.0077
|
0.0003
|
0.0016
|
-0.0001
|
0.0052
|
ΔΔρ(C3)
|
-0.0095
|
0.0032
|
0.0003
|
-0.0008
|
-0.0100
|
ΔΔρ(C4)
|
-0.0130
|
0.0010
|
-0.0017
|
-0.0015
|
-0.0097
|
ΔΔρ(C5)
|
0.0047
|
-0.0007
|
0.0004
|
0.0004
|
0.0036
|
ΔΔρ(C7)
|
0.0051
|
-0.0007
|
0.0004
|
0.0003
|
0.0035
|
ΔΔρ(C9)
|
-0.0128
|
0.0024
|
-0.0009
|
-0.0019
|
-0.0101
|
ΔΔρ(C13)
|
0.0160
|
0.0061
|
0.0051
|
0.0076
|
0.0089
|
ΔΔρ(C14)
|
-0.0021
|
-0.0138
|
-0.0097
|
-0.0126
|
-0.0516
|
ΔΔρ(C15)
|
-0.0235
|
-0.0070
|
-0.0052
|
-0.0083
|
-0.0029
|
ΔΔρ(C16)
|
0.0094
|
0.0050
|
0.0039
|
0.0068
|
0.0219
|
ΔΔρ(C18)
|
0.0203
|
0.0043
|
0.0041
|
0.0058
|
0.0087
|
ΔΔρ(C20)
|
-00056
|
-0.0103
|
-0.0077
|
-0.0107
|
-0.0126
|
ΔΔρ(LA)
|
-0.0004
|
0.0009
|
0.0002
|
0.0143
|
0.0980
|
The calculated results show that the electron spin density is primarily concentrated on the divalent C1 atom of DPC3, the Δρ value of C1 is 1.4038e in the monomer. In the process of formation of the complexes, there is a rearrangement of electron spin density. For the complexes DPC3···LA (LA = AlF3, SiF4, PF5), the sum of spin electron densities in LA is less than 0.0009. These values are too small to be significant, indicating that spin density rearranges within the DPC3 radicals, and the transfer of spin electron density from the electron donor to acceptor can be ignored. In DPC3···AlF3 complex, the change of spin electron density occurs mainly in C15 and C18 atoms of DPC3. In DPC3···SiF4/PF5 complexes, the change of spin electron density occurs mainly in C1, C14 and C20 atoms. In the process of chalcogen bond formation, the electron spin densities of the C14 and C20 atoms decrease and those of the S and F atoms increase; the sum of spin electron densities in SF2 is 0.0143. For the halogen-bonded complex DPC3…ClF, the changes of electron spin density in C1 and C14 atoms are − 0.0550 and − 0.0516, meanwhile, the sum of electron spin density in ClF is 0.0980. The increased values of SF2/ClF indicate that a quantity of electron spin density transfer from DPC3 to SF2/ClF.
Therefore, in the process of the formation of DPC3···LA (LA = AlF3, SiF4, PF5) complexes, the transfers of the electron spin density from DPC3 to LA is minimal, but it rearranges within the radical itself. For the chalcogen-bonded and halogen-bonded complex, certain electron spin density transfer from the radical to Lewis acid.