3.1 Interaction Energies of the σ-type,π-type and parallel halogen bond complexes
Figure 2 illustrates the geometry optimizations structures for the minimum energy of σ-type,π-type and parallel halogen bond complexes of the pyrazine and XF (X=F,Cl,Br and I ) .For all types of halogen atom X=F, Cl, Br and I, σ-type and π-type halogen-bonded minimum was located. However parallel halogen-bonded minima were only found for X = Cl, Br or I. The interaction energies of these parallel halogen bond༌σ-type and π-type halogen bond complexes are shown in Table 1.
Table 1
ΔE, BSSE and with BSSE correction (ΔECP) in kcal/mol.Vs.max in kcal/mol related with the X of XF and Vs,min on the XF surface
σ-type halogen bond complexes
|
MP2/aug-cc-pVTZ
|
CCSD(T)/aug-cc-pVTZ
|
|
ΔE
|
BSSE
|
ΔEcp
|
ΔE
|
BSSE
|
ΔEcp
|
Vs,max
|
C4H4N2-F2(I)
|
-2.31
|
0.63
|
-1.68
|
-2.22
|
0.51
|
-1.71
|
8.4
|
C4H4N2-ClF (I)
|
-14.14
|
1.52
|
-12.62
|
-13.78
|
1.21
|
-12.57
|
39.4
|
C4H4N2-BrF(I)
|
-22.68
|
5.16
|
-17.53
|
-21.57
|
4.73
|
-16.84
|
40.8
|
C4H4N2-IF(I)
|
-24.24
|
4.99
|
-19.25
|
-23.68
|
4.21
|
-19.47
|
46.4
|
π-type halogen bond complexes
|
ΔE
|
BSSE
|
ΔEcp
|
ΔE
|
BSSE
|
ΔEcp
|
Vs,min
|
C4H4N2-F2 (II)
|
-1.90
|
0.74
|
-1.16
|
-1.73
|
0.62
|
-1.11
|
-2.1
|
C4H4N2-ClF(II)
|
-4.22
|
0.97
|
-3.25
|
-3.94
|
0.76
|
-3.18
|
-8.6
|
C4H4N2-BrF(II)
|
-8.32
|
3.86
|
-4.46
|
-7.86
|
3.51
|
-4.35
|
-17.7
|
C4H4N2-IF(II)
|
-9.34
|
4.17
|
-5.17
|
-8.94
|
3.56
|
-5.38
|
-22.3
|
Parallel halogen
Bondcomplexes
|
ΔE
|
BSSE
|
ΔEcp
|
ΔE
|
BSSE
|
ΔEcp
|
Vs,min
|
C4H4N2-ClF(Ш)
|
-3.21
|
0.94
|
-2.27
|
-2.94
|
0.78
|
-2.16
|
-8.6
|
C4H4N2-BrF(Ш)
|
-5.36
|
2.78
|
-2.58
|
-5.12
|
2.45
|
-2.67
|
-17.7
|
C4H4N2-IF(Ш)
|
-5.96
|
2.83
|
-3.13
|
-5.68
|
2.42
|
-3.26
|
-22.3
|
As shown in the Table 1, the difference of interaction energies corrected for BSSE attained by MP2 and CCSD(T) level has been small. That suggests that MP2/aug-cc-pVTZ provided reliable calculation results for the σ-type, π-type and parallel halogen bond of these investigated dimers. The binding energies of these σ-type, π-type and parallel halogen bond all gradually increased orderly from from X=F to X =I of XF. For σ-type halogen bonded dimers, this order is close accociation with the maximum positive electrostatic potentials (Vs,max) of the σ-hole related with the X of XF, corresponding coefficients is 0.9717. Relative to the corresponding π-type and parallel halogen bond, this order is close accociation the maximum negative electrostiatic potential (Vs,min) on the XF surface, corresponding coefficients is 0.9776 and 0.9403, as shown in Figure 3.
A diagrams of the ΔECP energies of these σ-type, π-type and parallel halogen-bonded minimum structure in Figure 4 reveal that the π-type halogen bonding interactions are weaker than the corresponding σ-type halogen bonding interactions, and parallel halogen-bond interactions are weaker than the corresponding π-type halogen bonding interactions in C4H4N2-XF complexes.
3.2 NBO population analysis.
We used Natural bond orbital ( NBO) to analysis the studied σ-type, π-type and parallel halogen-bonded complexes. The value of ΔQ (charge transferred from donor to the acceptor) and ΔE2 (the second-order perturbation energy ) is shown in Table 2. For the σ-type halogen-bonded complexes, the charge transfer from the lone electron pair of the N atom of pyrazine was directed mainly at the X-F antibonding orbitals of the XF. For the π-type halogen-bonded complexes, the charge transfer from the bonding orbitals for the C4-C5 in the C4H4N2 is mainly refers to the C-N antibonding orbitals of the XF. In regard to parallel halogen-bonded complexes, the charge transfer from the lone electron pair of the F and X atom of XF was directed mainly at the C-N antibonding orbitals of in the C4H4N2.
Table 2
The NBO analysis of C4H4N2-XF complexes (ΔQ in au, ΔE2 in kcal/mol )
σ-type halogen bond complexes
|
Donor NBOs
|
Acceptor NBOs
|
ΔE2
|
ΔQ
|
ΔEcp
|
C4H4N2-F2(I)
|
LP N
|
BD* F - F
|
4.92
|
0.014
|
-1.68
|
C4H4N2-ClF (I)
|
LP N
|
BD* Cl- F
|
83.78
|
0.154
|
-12.62
|
C4H4N2-BrF(I)
|
LP N
|
BD* Br-F
|
98.30
|
0.148
|
-17.53
|
C4H4N2-IF(I)
|
LP N
|
BD* I-F
|
104.89
|
0.108
|
-19.25
|
π-type halogen bond complexes
|
Donor NBOs
|
Acceptor NBOs
|
ΔE2
|
ΔQ
|
ΔEcp
|
C4H4N2-F2 (II)
|
BD C4-C5
|
BD* F- F
|
2.83
|
0.004
|
-1.16
|
C4H4N2-ClF(II)
|
BDC4-C5
|
BD*Cl- F
|
10.02
|
0.022
|
-3.25
|
C4H4N2-BrF(II)
|
BD C4-C5
|
BD*Br- F
|
21.35
|
0.044
|
-4.46
|
C4H4N2-IF(II)
|
BD C4-C5
|
BD* I- F
|
38.63
|
0.050
|
-5.17
|
parallel halogen bond complexes
|
Donor NBOs
|
Acceptor NBOs
|
ΔE2
|
ΔQ
|
ΔEcp
|
C4H4N2-ClF(Ш)
|
LP Cl
LP Cl
LP F
LP F
|
BD*N3 - C4
BD* C5 - N6
BD*N3 - C4
BD* C 5 - N6
|
0.16
0.16
0.22
0.22
(sum 0.76)
|
0.004
|
-2.27
|
C4H4N2-BrF(Ш)
|
LP Br
LP Br
LP F
LP F
|
BD*N3 - C4
BD* C5 - N6
BD*N3 - C4
BD* C 5 - N6
|
0.21
0.21
0.28
0.28
(sum 0.98)
|
0.003
|
-2.58
|
C4H4N2-IF(Ш)
|
LP I
LP I
LP F
LP F
|
BD*N3 - C4
BD* C5 - N6
BD*N3 - C4
BD* C5 - N6
|
0.24
0.24
0.36
0.36
(sum 1.20)
|
0.002
|
-3.13
|
From the amount of ΔE2, ΔQ and the binding energies ΔECP, we discovered that the ΔE2 are concerned with the binding energies (ΔECP ) of σ-type, π-type and parallel halogen bond complexes (See Figure 5), corresponding coefficients 0.9562, 0.9144 and 0.9873, respectively.
As can been in the Table 3, ΔQ has no relevance to the ΔECP for σ-type and parallel halogen bond complexes. And for the π-type halogen bond complexes, ΔQ has relevance to the ΔECP, corresponding coefficients is 0.9867 (See Figure 6).
Table 3
A (Electron affinity) and I (Ionisation energy) of the different monomers. Global softness ( S) values, fI+ and fc− (local Fukui functions) in au and local softness (sI+ or sc+) values in au eV−1 on the X of XF.
Molecule
|
I(eV)
|
A(eV)
|
S(eV)
|
f X+
|
f x−
|
sx+
|
sx−
|
F2
|
0.055
|
-0.670
|
1.379
|
-0.500
|
-0.500
|
-0.690
|
-0.690
|
ClF
|
0.025
|
-0.500
|
1.905
|
-0.722
|
-0.794
|
-1.375
|
-1.513
|
BrF
|
0.006
|
-0.457
|
2.160
|
-0.752
|
-0.813
|
-1.624
|
-1.756
|
IF
|
-0.010
|
-0.406
|
2.525
|
-0.808
|
-0.890
|
-2.040
|
-2.247
|
3.3 Research on the conceptual DFT
In the current study, using these reactivity indices, we have studied the reactivity properties of the interacting molecules in σ-type,π-type and parallel halogen bond complexes by the conceptual density functional theory (conceptual DFT). The local softness s(r) is an important factor in quantifying soft-soft interactions (or orbital -controlled reactivity) [36]. It is calculated from s(r) = f (r) S, where f(r) is the Fukui function and S is the global softness of the system.The the global softness S can be approximated as 1/(I-A).I is the vertical ionization energies of the system and A is the electron affinity [37].
The pertinent calculated reactivity indices are shown in Table 3 for different lewis bases and acids considered in σ-type,π-type and parallel halogen bond complexes.For the lewis acids XF (X=F,Cl,Br and I) of the σ-type halogen-bonded complexes, it was revealed that the local softness s+ on the X of XF is linked to the binding energies (ΔECP ),corresponding coefficients is 0.9752. For the lewis bases XF (X=F,Cl,Br and I) of π-type and parallel halogen bond complexes, it was revealed that the local softness s− on X of XF is linked to the ΔECP, corresponding coefficients are 0.9875 and 0.9995 (see Figure 7).
3.4 Topological analysis
The topological analysis of the Laplacian function and its electron charge density is a powerful tool for studying the physical nature of halogen bonding [38, 39].Table 4 displays the topological parameters, including electron density (ρb) [40] at the σ-type,π-type and parallel halogen bond critical points, its Laplacian(∇2ρb ) and the electron energy density ( Hb ). The types of interaction can be classified according to the sign of Hb and ∇2ρb. The halogen bond is generated when the X of XF used as a Lewis acid for the formation of σ-type halogen bond complex. Hb is negative and ∇2ρb is positive, this corresponds to a partial colvalent interaction [41–43].Nevertheless, the π-type and parallel halogen bond arises when the X of XF acts as lewis bases, both Hb and ∇2ρb are positive, demonstrating a closed-shell molecular interactions [44].
Table 4
Density (ρb), Eigenvalues of the hessian Matrix (λ1, λ2 and λ3), laplacian of (∇2ρb) and ellipticity(ε) at bond critical points between halogen bond acceptors and halogen bond donors, all units are atomic units.
complexes
|
ρb
|
λ1
|
λ2
|
λ3
|
∇2ρb
|
ε
|
Hb
|
C4H4N2-F2(I)
|
0.0226
|
-0.0253
|
-0.0243
|
0.1774
|
0.1278
|
0.0412
|
-0.0017
|
C4H4N2-ClF (I)
|
0.0758
|
-0.0784
|
-0.0751
|
0.3124
|
0.1588
|
0.0439
|
-0.0214
|
C4H4N2-BrF(I)
|
0.0816
|
-0.0685
|
-0.0652
|
0.2812
|
0.1474
|
0.0506
|
-0.0228
|
C4H4N2-IF(I)
|
0.0878
|
-0.0512
|
-0.0485
|
0.2438
|
0.1440
|
0.0557
|
-0.0148
|
C4H4N2-F2 (II)
|
0.0117
|
-0.0106
|
-0.0040
|
0.0700
|
0.0554
|
1.6500
|
0.0029
|
C4H4N2-ClF(II)
|
0.0169
|
-0.0124
|
-0.0034
|
0.0732
|
0.0573
|
2.6471
|
0.0013
|
C4H4N2-BrF(II)
|
0.0231
|
-0.0164
|
-0.0043
|
0.0848
|
0.0641
|
2.8140
|
0.0001
|
C4H4N2-IF(II)
|
0.0241
|
-0.0139
|
-0.0034
|
0.0710
|
0.0538
|
3.0882
|
0.0004
|
C4H4N2-ClF(Ш)
|
0.0075
|
-0.0052
|
-0.0010
|
0.0353
|
0.0291
|
4.2001
|
0.0015
|
C4H4N2-BrF(Ш)
|
0.0083
|
-0.0055
|
-0.0011
|
0.0352
|
0.0285
|
4.0000
|
0.0013
|
C4H4N2-IF(Ш)
|
0.0086
|
-0.0050
|
-0.0012
|
0.0317
|
0.0255
|
3.1667
|
0.0011
|
On the base of QTAIM, ρb (the electron density) should be a reflection of the bond strength. Normally, the greater of the value of the electron density,the greater bond strength.In the Table 4, the value of ρb of the σ-type halogen bond complex is from 0.0226 to 0.0878.The amount of ρb of the π-type halogen-bonded complexes is from 0.0117 to 0.0241.The amount of the parallel halogen bond complexes is from 0.0075 to 0.0086.The intermolecular forces of σ-type halogen bond complexes are noticeably stronger than that of appropriate π-type or parallel halogen bond complexes. The higher electron densities ρb and the greater the interaction energy (ΔECP), the stronger the σ-type, π-type or parallel halogen bond. The ε (ellipticity ) can be defined as λ1/λ2-1 and measures the extent to which charge is preferentially accumulated [45].
The ellipticity (ε) supplies a measure of the π properties of a bond. The larger the ellipticity ε, the more obvious π character the bond shows. It can be seen that the ε of the π-type and parallel halogen bond complexes are much larger than those of the σ-type halogen bond.
3.5 Energy partition by SAPT
Energy decomposition gives us to have a very useful understanding the nature of the studied three types halogen bond interactions [46, 47]. The interactive energy of the three types complexes can be divided into four items:exchange energy, induced energy dispersion energy and electrostatic energy. The results are listed in table 5.
Table 5. Energy decomposition (kcal·mol-1) for the σ-type, p-type and parallel halogen bond complexes of C4H4N2-XF gained from SAPT
σ-type halogen bond
complexes
|
Eelst
|
Eind
|
Edisp
|
Eexch
|
Eint(SAPT2)
|
ΔECP
|
%Eelst
|
%Eind
|
%Edisp
|
C4H4N2-F2(I)
|
-6.02
|
-3.53
|
-3.41
|
11.21
|
-1.75
|
-1.68
|
46.5
|
27.2
|
26.3
|
C4H4N2-ClF (I)
|
-45.18
|
-32.37
|
-13.31
|
78.21
|
-12.65
|
-12.62
|
49.7
|
35.6
|
14.6
|
C4H4N2-BrF(I)
|
-54.14
|
-31.26
|
-13.31
|
81.56
|
-17.14
|
-17.53
|
54.8
|
31.7
|
13.5
|
C4H4N2-IF(I)
|
-40.28
|
-25.66
|
-13.12
|
60.55
|
-18.51
|
-19.25
|
50.9
|
32.5
|
16.6
|
p-type halogen bond
complexes
|
Eelst
|
Eind
|
Edisp
|
Eexch
|
Eint(SAPT2)
|
ΔECP
|
Eelst%
|
Eind%
|
Edisp%
|
C4H4N2-F2 (II)
|
-1.87
|
-1.63
|
-3.33
|
5.84
|
-0.98
|
-1.16
|
27.4
|
23.9
|
48.8
|
C4H4N2-ClF(II)
|
-4.60
|
-4.92
|
-6.40
|
13.14
|
-2.78
|
-3.25
|
28.9
|
30.9
|
40.2
|
C4H4N2-BrF(II)
|
-9.09
|
-8.71
|
-8.02
|
21.49
|
-4.34
|
-4.46
|
35.2
|
33.7
|
31.1
|
C4H4N2-IF(II)
|
-7.30
|
-8.45
|
-8.87
|
19.76
|
-4.86
|
-5.17
|
29.7
|
34.3
|
36.0
|
parallel halogen bond complexes
|
Eelst
|
Eind
|
Edisp
|
Eexch
|
Eint(SAPT2)
|
ΔECP
|
Eelst%
|
Eind%
|
Edisp%
|
C4H4N2-ClF(Ш)
|
-2.51
|
-0.57
|
-5.06
|
6.05
|
-2.08
|
-2.27
|
30.8
|
7.0
|
62.2
|
C4H4N2-BrF(Ш)
|
-3.48
|
-0.70
|
-4.89
|
6.31
|
-2.76
|
-2.58
|
38.4
|
7.7
|
53.9
|
C4H4N2-IF(Ш)
|
-4.07
|
-0.84
|
-5.54
|
7.07
|
-3.38
|
-3.13
|
38.9
|
8.0
|
53.0
|
As described in talbe 5, the electrostatic energy are the major source of the attraction for the σ-type halogen bonding interactions while the parallel halogen-bond interactions are mainly dispersion energy in C4H4N2-XF complexes. For the π-type halogen bonding interactions in C4H4N2-XF(X=F and Cl) complexes, electrostatic energy are the major source of the attraction, while in C4H4N2-XF(X=Br and I) complexes the electrostatic, induction and dispersion term play equally important role in the total attractive interaction.