3.1 Interaction Energies of the three types complexes
The geometry optimizations structures for the minimum energy of typeⅠ, type Ⅱ and type Ⅲ complexes of the three heterocyclic compounds (C4H4O, C5H5N and C4H4N2) and AtX (X = F, Cl and Br) is shown in Fig. 2, Fig. 3 and Fig. 4. The interaction energies of three types complexes are given in Table 1. Figure 5 also shows the interaction energies (ΔECP) of these type I, typeⅡand type Ⅲ minimum structure.
Table 1
ΔE, BSSE and with BSSE correction (ΔECP) in kcal/mol.
Type I complexes | ΔE | BSSE | ΔEcp |
C4H4O-AtF(I) | -13 .25 | 4.08 | −9.17 |
C4H4N2-AtF(I) | −27.39 | 6.19 | −21.20 |
C5H5N-AtF(I) | −30.35 | 6.43 | −23.92 |
C4H4O-AtCl(I) | −10.94 | 3.90 | −7.04 |
C4H4N2-AtCl(I) | −22.99 | 6.20 | −16.78 |
C5H5N-AtCl(I) | −25.98 | 6.52 | −19.46 |
C4H4O-AtBr(I) | −10.34 | 4.09 | −6.25 |
C4H4N2-AtBr(I) | −21.64 | 7.01 | −14.63 |
C5H5N-AtBr(I) | −24.78 | 7.39 | −17.39 |
Type II complexes | ΔE | BSSE | ΔEcp |
C4H4O-AtF (II) | −17.72 | 5.48 | −12.24 |
C4H4N2-AtF(II) | −11.96 | 5.52 | −6.44 |
C5H5N-AtF(II) | −14.85 | 5.87 | −8.98 |
C4H4O-AtCl(II) | −15.49 | 5.68 | −9.81 |
C4H4N2-AtCl(II) | −10.61 | 5.35 | −5.26 |
C5H5N-AtCl(II) | −13.04 | 5.67 | −7.37 |
C4H4O-AtBr(II) | −14.15 | 6.33 | −7.82 |
C4H4N2-AtBr(II) | −9.91 | 5.62 | −4.29 |
C5H5N-AtBr(II) | −11.83 | 6.37 | −5.46 |
Type Ш complexes | ΔE | BSSE | ΔEcp |
C4H4O-AtF (Ш) | −6.66 | 3.47 | −3.19 |
C4H4N2-AtF(Ш) | −7.16 | 3.72 | −3.44 |
C5H5N-AtF(Ш) | −7.58 | 3.75 | −3.84 |
C4H4O-AtCl(Ш) | −6.82 | 3.44 | −3.38 |
C4H4N2-AtCl(Ш) | −7.41 | 3.64 | −3.76 |
C5H5N-AtCl(Ш) | −8.08 | 3.74 | −4.35 |
C4H4O-AtBr(Ш) | −6.93 | 3.36 | −3.56 |
C4H4N2-AtBr(Ш) | −7.99 | 4.03 | −3.96 |
C5H5N-AtBr(Ш) | −10.01 | 4.82 | −5.19 |
From Fig. 5 we can see that the interaction energy decreases according to the sequence type I > type II > type Ш in C4H4N-AtX and C4H4N2-AtX complexes.
The interaction energy decreases according to the sequence type II > type I > type Ш in the C4H4O-AtX complexes.
The results in Table 1 and Fig. 5 reveal that the interaction energies (ΔECP) of typeⅠand type Ⅱ complexes all gradually decreased orderly from X = F to X = Br of AtX. For typeⅠand typeⅡdimers, this order is closely linked to the mximum positive electrostatic potentials (Vs,max) of the σ-hole related with the X of AtX, For type I complexes, corresponding coefficients are 0.9685, 0.9919 and 0.9888. For type II dimers, corresponding coefficients are 0.9885, 0.9919 and 0.9342. Relative to the corresponding type Ⅲ complexes, this order is closely linked to the maximum negative electrostiatic potential (Vs,min) on the AtX surface as shown in Fig. 6.
For the same AtX, the interaction energy of type I and type Ш complexes decreases according to the sequence C4H4N-AtX > C4H4N2-AtX > C4H4O-AtX while the interaction energy of type II complexes decreases according to the sequence C4H4O-AtX(II) > C4H4N-AtX(II) > C4H4N2-AtX(II) (See Fig. 7). For the same heterocyclic compounds, the interaction energy of type I and typeⅡcomplexes decreases according to the sequence AtF > AtCl > AtBr. While the interaction energy of type Ш complexes increases according to the sequence AtF < AtCl < AtBr. For type I and type Ш complexes, the interaction energy is related to he maximum negative electrostiatic potential (Vs,min) on the C4H4O, C4H4N2 and C5H5N surface with the same AtX. For typeⅡ Complexes, the interaction energy is related to the mximum positive electrostatic potentials (Vs,max) on the C4H4O, C4H4N2 and C5H5N surface (See Fig. 7).
3.2 NBO population analysis
Natural bond orbital ( NBO) were used to analysis the studied the three types
complexes. The value the second-order perturbation energy (ΔE2) and of charge transferred from donor to the acceptor (ΔQ) are shown in Table 2. With regard to typeⅠcomplexes, the charge transfer from the lone electron pair of the N or O atom of the heterocyclic compounds (C4H4O, C4H4N and C4H4N2) was directed mainly at the At-X antibonding orbitals of the At-X. With regard to the typeⅡdimers, the charge transfer from the bonding orbitals for the C-C in the heterocyclic compounds (C4H4O, C4H4N and C4H4N2) is mainly refers to the At-X antibonding orbitals of the At-X and the charge transfer from the lone electron pair of the At atom of the At-X was directed at the C4-C5 or C5-C6 antibonding orbitals of in the heterocyclic compounds. With regard to type Ⅲ complexes, the charge transfer from the lone electron pair of the At and X atom of AtX was directed at antibonding orbitals of in the heterocyclic compounds (the molecule with a positive π-hole) and the charge transfer from the bonding orbitals for the C-C in the heterocyclic compounds is refers to the At-X antibonding orbitals of the At-X.
Table 2
The NBO analysis of the three types complexes (ΔE2 in kcal/mol, ΔQ in au ).
Type I complexes | Donor NBOs | Acceptor NBOs | ΔE2 | ΔQ | ΔEcp |
C4H4O-AtF(I) | LP O | BD* At - F | 19.93 | 0.036 | −9.17 |
C4H4N2-AtF(I) | LP N | BD* At- F | 70.18 | 0.098 | −21.20 |
C5H5N-AtF(I) | LP N | BD* At-F | 77.54 | 0.115 | −23.92 |
C4H4O-AtCl(I) | LP O | BD* At-Cl | 16.27 | 0.031 | −7.04 |
C4H4N2-AtCl(I) | LP N | BD* At-Cl | 63.37 | 0.102 | −16.78 |
C5H5N-AtCl(I) | LP N | BD* At-Cl | 60.41 | 0.121 | −19.46 |
C4H4O-AtBr(I) | LP O | BD* At-Br | 14.26 | 0.027 | −6.25 |
C4H4N2-AtBr(I) | LP N | BD* At-Br | 50.09 | 0.098 | −14.63 |
C5H5N-AtBr(I) | LP N | BD* At-Br | 56.83 | 0.117 | −17.39 |
Type II complexes | Donor NBOs | Acceptor NBOs | ΔE2 | ΔQ | ΔEcp |
C4H4O-AtF (II) | BD C5-C6 LP At | BD* At- F BD*C5- C6 | 56.34 10.21 (sum 66.55) | 0.094 | −12.24 |
C4H4N2-AtF(II) | BD C4-C5 LP At | BD*At- F BD* C4- C5 | 43.78 7.25 (sum 51.03) | 0.046 | −6.44 |
C5H5N-AtF(II) | BD C5-C6 LP At | BD* At- F BD* C5- C6 | 44.70 6.98 (sum 51.68) | 0.047 | −8.98 |
C4H4O-AtCl(II) | BD C5-C6 LP At | BD* At-Cl BD* C5- C6 | 36.74 9.21 (sum 46.95) | 0.104 | −9.81 |
C4H4N2-AtCl(II) | BD C4 - C5 LP At | BD* At-Cl BD*C4- C5 | 20.16 5.16 (sum 25.32) | 0.047 | −5.26 |
C5H5N-AtCl(II) | BD C4 - C5 LP At | BD* At-Cl BD*C4- C5 | 21.02 4.59 (sum 25.61) | 0.051 | −7.37 |
C4H4O-AtBr(II) | BD C4-C5 LP At | BD* At-Br BD*C4- C5 | 35.47 8.03 (sum 43.50) | 0.099 | −7.82 |
C4H4N2-AtBr(II) | BD C4-C5 LP At | BD* At-Br BD*C4- C5 | 18.76 4.58 (sum 23.34) | 0.044 | −4.29 |
C5H5N-AtBr(II) | BD C4-C5 LP At | BD* At-Br BD*C4- C5 | 19.11 5.67 (sum 24.78) | 0.049 | −5.46 |
Type Ш complexes | Donor NBOs | Acceptor NBOs | ΔE2 | ΔQ | ΔEcp |
C4H4O-AtF (Ш) | BD C1 - C2 BD C3 - C4 LP F LP At LP At | BD*At- F BD*At-F BD* C1-C2 BD*C1-C2 BD* C1-O5 | 1.56 0.25 0.13 0.83 0.39 (sum 3.16) | 0.006 | −3.19 |
C4H4N2-AtF(Ш) | BD C5 - N6 BD N3-C4 BD C1 - C2 LP F LP F | BD*At- F BD*At- F BD*At- F BD* N3 - C4 BD* C5 - N6 | 0.53 0.52 0.30 0.46 0.46 (sum 2.27) | 0.001 | −3.44 |
C5H5N-AtF(Ш) | BD C3 - C4 LP At LP F | BD*At- F BD* C2 - N7 BD* C3 - C4 | 1.42 0.17 0.75 (sum 2.34) | 0.004 | −3.84 |
C4H4O-AtCl(Ш) | BD C2 - C3 BD C4 - C5 LP At LP At LP At LP Cl | BD* At- Cl BD* At- Cl BD* C2-C3 BD* C2-O6 BD* C5-O6 BD* C2-C3 | 0.32 0.58 0.40 0.32 0.26 0.22 (sum 2.14) | 0.001 | −3.38 |
C4H4N2-AtCl(Ш) | BD C2 - C3 LP At LP At LP Cl LP Cl | BD* At- Cl BD* N3-C4 BD* C5-N6 BD* N3-C4 BD* C5-N6 | 0.17 0.22 0.22 0.45 0.45 (sum 1.51) | 0.005 | −3.76 |
C5H5N-AtCl(Ш) | BD C4 - C5 BD C6 - N7 LP At LP Cl | BD* At- Cl BD* At- Cl BD* C6 - N7 BD* C4-C5 | 0.15 0.13 0.28 0.60 (sum 1.16) | 0.006 | −4.35 |
C4H4O-AtBr(Ш) | BD C4 - C5 LP At LP At LP At LP At LP Br | BD* At- Br BD* C2-C3 BD* C2-O6 BD* C4-C5 BD* C5-O6 BD* C2-C3 | 0.18 0.25 0.21 0.25 0.24 0.65 (sum 1.78) | 0.006 | −3.56 |
C4H4N2-AtBr(Ш) | BD C1 - C2 LP At LP At LP Br LP Br | BD* At- Br BD* N3-C4 BD* C5-N6 BD* N3-C4 BD* C5-N6 | 0.16 0.22 0.22 0.56 0.56 (sum 1.72) | 0.007 | −3.96 |
C5H5N-AtBr(Ш) | BD C2 - N7 LP At LP Br | BD* At-Br BD* C2-N7 BD* C3-C4 | 0.12 0.16 0.65 (sum 0.93) | 0.008 | −5.19 |
According to the value of ΔQ, ΔE2 and the interaction energies ΔECP, we found out that the ΔE2 are related to the interaction energies (ΔECP ) of typeⅠ and type Ⅱ complexes (See Fig. 8). As shown in the Table 2, ΔQ has no direct connection to the ΔECP for the three types complexes.
3.5 Energy disintegration by SAPT
Energy disintegration of the investigated three types noncovalent interactions has been carried out, and the results are shown in Table 3. Compared with MP2 method, the energy difference of SAPT method is very small. The interactive energy (Eint) of the three types complexes are separated into four aspects: dispersion energies (Edisp ), induced energies (Eind ), exchange energies (Eexch) and electrostatic interaction (Eelst ).
Table 3
Energy decomposition (kcal/mol) for the type I, type II and type Ш complexes obtained from SAPT.
Type I complexes | Eelst | Eind | Edisp | Eexch | Eint(SAPT) | ΔECP | %Eelst | %Eind | %Edisp |
C4H4O-AtF(I) | −15.20 | −7.92 | −7.52 | 21.76 | −8.89 | −9.17 | 49.61 | 25.85 | 24.54 |
C4H4N2-AtF(I) | −38.81 | −22.28 | −13.16 | 53.68 | −20.57 | −21.20 | 52.27 | 30.01 | 17.72 |
C5H5N-AtF(I) | −42.61 | −24.76 | −13.76 | 57.32 | −23.82 | −23.92 | 52.52 | 30.52 | 16.96 |
C4H4O-AtCl(I) | −13.08 | −6.03 | −6.94 | 19.47 | −6.58 | −7.04 | 50.21 | 23.15 | 26.64 |
C4H4N2-AtCl(I) | −37.35 | −20.48 | −13.04 | 54.44 | −16.42 | −16.78 | 52.70 | 28.90 | 18.40 |
C5H5N-AtCl(I) | −41.57 | −23.55 | −13.82 | 59.29 | −19.66 | −19.46 | 52.66 | 29.83 | 17.51 |
C4H4O-AtBr(I) | −12.01 | −5.32 | −6.67 | 18.09 | −5.92 | −6.25 | 50.04 | 22.17 | 27.79 |
C4H4N2-AtBr(I) | −35.85 | −19.34 | −12.85 | 53.61 | −14.43 | −14.63 | 52.69 | 28.42 | 18.89 |
C5H5N-AtBr(I) | −40.05 | −22.53 | −13.68 | 58.71 | −17.54 | −17.39 | 52.52 | 29.54 | 17.94 |
Type II complexes | Eelst | Eind | Edisp | Eexch | Eint(SAPT) | ΔECP | Eelst% | Eind% | Edisp% |
C4H4O-AtF (II) | −18.69 | −16.53 | −11.50 | 34.42 | −12.29 | −12.24 | 40.00 | 35.38 | 24.61 |
C4H4N2-AtF(II) | −9.11 | −10.72 | −10.75 | 24.40 | −6.19 | −6.44 | 29.79 | 35.06 | 35.15 |
C5H5N-AtF(II) | −13.14 | −12.07 | −11.41 | 28.03 | −8.60 | −8.98 | 35.88 | 32.96 | 31.16 |
C4H4O-AtCl(II) | −19.54 | −15.35 | −11.81 | 37.13 | −9.57 | −9.81 | 41.84 | 32.87 | 25.29 |
C4H4N2-AtCl(II) | −8.50 | −8.18 | −10.08 | 21.22 | −5.54 | −5.26 | 31.76 | 30.57 | 37.67 |
C5H5N-AtCl(II) | −11.93 | −9.40 | −10.67 | 25.25 | −6.75 | −7.37 | 37.28 | 29.38 | 33.34 |
C4H4O-AtBr(II) | −18.47 | −13.92 | −11.48 | 35.94 | −7.94 | −7.82 | 42.10 | 31.73 | 26.17 |
C4H4N2-AtBr(II) | −8.32 | −7.37 | −9.94 | 20.24 | −4.59 | −4.29 | 40.00 | 35.38 | 24.61 |
C5H5N-AtBr(II) | −11.36 | −8.44 | −10.41 | 24.96 | −5.26 | −5.46 | 29.79 | 35.06 | 35.15 |
Type Ш complexes | Eelst | Eind | Edisp | Eexch | Eint(SAPT) | ΔECP | Eelst% | Eind% | Edisp% |
C4H4O-AtF (Ш) | −5.79 | −1.30 | −6.03 | 9.83 | −3.29 | −3.19 | 44.13 | 9.91 | 45.96 |
C4H4N2-AtF(Ш) | −5.00 | −0.95 | −6.35 | 8.68 | −3.63 | −3.44 | 40.65 | 7.72 | 51.63 |
C5H5N-AtF(Ш) | −5.11 | −0.70 | −6.18 | 7.85 | −4.14 | −3.84 | 42.62 | 5.84 | 51.54 |
C4H4O-AtCl(Ш) | −5.88 | −1.39 | −6.13 | 9.93 | −3.47 | −3.38 | 43.88 | 10.37 | 45.75 |
C4H4N2-AtCl(Ш) | −4.93 | −0.61 | −6.85 | 8.70 | −3.69 | −3.76 | 39.79 | 4.92 | 55.29 |
C5H5N-AtCl(Ш) | −5.33 | −0.49 | −6.81 | 8.36 | −4.26 | −4.35 | 42.20 | 3.88 | 53.92 |
C4H4O-AtBr(Ш) | −4.63 | −0.53 | −6.29 | 8.03 | −3.43 | −3.56 | 40.44 | 4.63 | 54.93 |
C4H4N2-AtBr(Ш) | −4.94 | −0.65 | −7.41 | 9.20 | −3.81 | −3.96 | 38.00 | 5.00 | 57.00 |
C5H5N-AtBr(Ш) | −5.18 | −0.502 | −7.22 | 8.08 | −4.83 | −5.19 | 40.15 | 3.89 | 55.96 |
As Talbe 3 shows, the electrostatic interaction (Eelst ) are predominantly of the attraction for the intuitive σ-hole (typeⅠ) complexes and are about 49.61–52.70%. while in the type Ⅲ complexes are mainly electrostatic and dispersion energy, the induced energy (Eind ) is smaller compared with electrostatic and induction energy. With regard to the counterintuitive σ-hole (typeⅡ) complexes, the dispersion, induction and electrostatic term have been playing the same important role in the total attractive interaction.