Insight into the nature of the noncovalent interactions of furan, pyridine, and pyrazine with AtX

The σ-hole, counterintuitive σ-hole, and lone pair-π interaction complexes formed between three heterocyclic compounds (C4H4O, C5H5N, and C4H4N2) and AtX (X = F, Cl, and Br) have been investigated with the MP2/aug-cc-pVTZ. The intensity of three noncovalent interactions formed by different heterocyclic compounds was compared, and the properties of these three noncovalent interactions were discussed. SAPT analysis shows that the electrostatic energy is dominant to the stronger interactions in the σ-hole and counterintuitive σ-hole complexes, while the dispersion energy is the main force responsible for the weaker interactions in the lone pair-π complexes. NBO analysis has also been employed. All the structures were optimized at the MP2/aug-cc-pVTZ (aug-cc-pVTZ-pp for Br to account for relativistic effects) level using the Gaussian 03W package (Gaussian, Inc., Wallingford, CT, USA). The basis bet superposition error (BSSE) is corrected using counterpoise method proposed by Boys and Bernardi. The NBO population analysis was carried out. The molecular electrostatic surface potentials of monomers were calculated by WFA-SAS program package. The interaction energies of the three types complexes were decomposed by using the symmetric adaptive perturbation theory SAPT of the open source ab initio electronic structure software package psi 4.0.0-beta5.


Introduction
Noncovalent interactions play important roles in materials science, catalysis, and biochemistry [1][2][3][4][5]. The σ-hole and counterintuitive σ-hole noncovalent interactions have been widely studied [6][7][8][9][10][11][12][13][14][15][16]. Lone pair-π interaction between an electron-poor π ring and a neutral electron-rich molecule is another important noncovalent interaction [17,18]. Electrostatic potential is a very general and useful tool to investigating the interaction properties of noncovalent interactions [19][20][21]. Figure 1 shows the electrostatic surface potentials of three heterocyclic compounds (furan, pyridine, and pyrazine) and halogenated astatine molecule AtX (X = F, Cl, and Br). Furan (C 4 H 4 O) is a kind of oxygencontaining five membered heterocyclic compound with wide application. Pyridine (C 5 H 5 N) is a six membered heterocyclic compound containing one nitrogen heteroatom while pyrazine (C 4 H 4 N 2 ) is a six-membered heterocyclic compound containing two nitrogen heteroatoms at positions 1 and 4.They are important organic chemical raw materials and can synthesize many important fine chemical products. It can be seen from Fig. 1 that the blue region of oxygen or nitrogen atom represents the most negative electrostatic surface potential, and on the lower and upper surfaces of heterocyclic ring associated with π-holes have positive electrostatic potentials. For the halogenated astatine molecule AtX (X = F, Cl, and Br), at the tip of the At atom, the red region with σ-hole is the positive potential region. The attractive Coulombic interactions between these positive potentials (σ-holes and π-holes) with negative sites such as lone pairs and electrons is promoted [22,23].
The σ-hole, counterintuitive σ-hole, and lone pair-π interaction complexes have been discovered if three heterocyclic compounds (furan, pyridine, and pyrazine) interacts with AtX (X = F, Cl, and Br).The σ-hole interaction complex is between the negative site on one of the oxygen or nitrogen of the heterocyclic compounds and the positive site on the At of AtX. The counterintuitive σ-hole interaction complexes are driven by polarization between a portion of the heterocyclic ring and the positive site on the At of AtX. The lone pair-π interaction is a noncovalent interaction between the lateral regions of the electron-rich molecule AtX and the position of the electron-poor π ring in heterocyclic compounds.
In this work, we have calculated the three types of noncovalent interactions between three heterocyclic compounds (C 4 H 4 O, C 5 H 5 N, and C 4 H 4 N 2 ) and AtX (X = F, Cl, and Br). The purpose of this study is to compare the strength of the three types of noncovalent interactions formed by different heterocyclic compounds and to explore the nature of the three types of noncovalent interactions.

Computational details
All the structures of the isolated monomers and dimers were optimized at the MP2/aug-cc-pVTZ (aug-cc-pVTZ-pp for Br to account for relativistic effects) level [24,25] using the Gaussian 03 program [26]. In addition, the vibration frequency was calculated at the same lever to confirm that the equilibrium geometry corresponding to the minimum energy point. The basis bet superposition error (BSSE) is corrected using counterpoise method proposed by Boys and Bernardi when calculating the supramolecular interaction energy [27]. To understand the three types of noncovalent interactions, the NBO population analysis [28] was carried out at the same level.
The molecular electrostatic surface potentials of monomers at the 0.001 au were calculated by WFA-SAS program package [29]. In addition, the interaction energies of the three types of complexes were decomposed by using the symmetric adaptive perturbation theory SAPT [30,31] of the open source ab initio electronic structure software package psi 4.0.0-beta5 [32].

Interaction energies of the three types of complexes
The geometry optimizations structures for the minimum energy of the three types of complexes of the three heterocyclic compounds (C 4 H 4 O, C 5 H 5 N, and C 4 H 4 N 2 ) and AtX (X = F, Cl, and Br) is shown in Figs. 2, 3, and 4. For the σ-hole interaction complexes, the heterocyclic compounds and AtX are almost in the same plane, and the X-At•••O (or N) angle is almost 180°. For the counterintuitive σ-hole and the lone pair-π interaction complexes, the At atom of AtX points to the point O (the middle of the C-C bond of heterocyclic compounds). The X-At•••O angle is almost 180° in the counterintuitive σ-hole, while the X-At•••O angle is almost 90° in the lone pair-π interaction complexes. The counterintuitive σ-hole interaction is along the extension of the At-X bond while the lone pair-π interaction is not along the extension of the At-X bond, but with the lateral side of the At in AtX.
The interaction energies of the three types of complexes are given in Table 1. Figure 5 also shows the interaction energies (ΔE CP ) of the three types of minimum structure. We can see from Fig. 5 that the interaction energy decreases in the order of the σ-hole interaction > the counterintuitive σ-hole interaction > the lone pair-π interaction in C 5 H 5 N-AtX and C 4 H 4 N 2 -AtX complexes. The interaction energy decreases in the order of the counterintuitive σ-hole interaction > the σ-hole interaction > the lone pair-π interaction in the C 4 H 4 O-AtX complexes.
The results in Table 1 and Fig. 5 reveal that the interaction energies (ΔE CP ) of the σ-hole and counterintuitive σ-hole complexes all gradually decreased orderly from X = F to X = Br of AtX. For the σ-hole and counterintuitive σ-hole complexes, this order is closely linked to the maximum positive electrostatic potentials (V s,max ) of the σ-hole related with the X of AtX. For the σ-hole complexes, the corresponding coefficients are 0.9685, 0.9919, and 0.9888. For the counterintuitive σ-hole complexes, the corresponding coefficients are 0.9885, 0.9919, and 0.9342. Relative to the corresponding lone pair-π interaction complexes, this order is closely linked to the maximum negative electrostatic potential (V s,min ) on the AtX surface as shown in Fig. 6.
For the same AtX, the interaction energy of the σ-hole and counterintuitive σ-hole complexes decreases according to the sequence C 5 H 5 N-AtX > C 4 H 4 N 2 -AtX > C 4 H 4 O-AtX while the interaction energy of the counterintuitive σ-hole complexes decreases according to the sequence C 4 H 4 O-AtX > C 5 H 5 N-AtX > C 4 H 4 N 2 -AtX (see Fig. 7). For the same heterocyclic compounds, the interaction energy of the σ-hole and counterintuitive σ-hole complexes decreases according to the sequence AtF > AtCl > AtBr. While the interaction energy of the lone pair-π interaction complexes increases according to the sequence AtF < AtCl < AtBr. For the σ-hole and the lone pair-π interaction complexes, the interaction energy is related to the maximum negative electrostatic potential (V s,min ) on the C 4 H 4 O, C 4 H 4 N 2 , and C 5 H 5 N surface with the same AtX. For the counterintuitive σ-hole complexes, the interaction energy is related to the maximum positive electrostatic potentials (V s,max ) on the C 4 H 4 O, C 4 H 4 N 2 , and C 5 H 5 N surface (see Fig. 7).

NBO population analysis
Natural bond orbital (NBO) was used to analyze the studied three types of complexes. The value the second-order perturbation energy (ΔE 2 ) and of charge transfer from donor to the acceptor (ΔQ) are shown in Table 2. With regard to the σ-hole complexes, the charge transfer from the lone electron pair of the N or O atom of the heterocyclic compounds (C 4 H 4 O, C 5 H 5 N, and C 4 H 4 N 2 ) is mainly directed to the At-X antibonding orbitals of the At-X. With regard to the counterintuitive σ-hole complexes, the charge transfer from the Fig. 3 The geometry optimization structures for the minimum energy of the three types of complexes of the C 4 H 4 N 2 and AtX bonding orbitals for the C-C in the heterocyclic compounds (C 4 H 4 O, C 5 H 5 N, and C 4 H 4 N 2 ) is mainly directed to the At-X antibonding orbitals of the At-X. With regard to the lone pair-π interaction complexes, the charge transfer from the lone electron pair of the At and X atom of AtX is mainly directed to the antibonding orbitals of in the heterocyclic compounds (the molecule with a positive π-hole).
According to the value of ΔQ, ΔE 2 and the interaction energies ΔE CP , we found out that the ΔE 2 is related to the interaction energies (ΔE CP ) of the σ-hole and counterintuitive σ-hole complexes (see Fig. 8). As shown in Table 2, ΔQ has no direct connection to the ΔE CP for the three types of complexes.

Energy decomposition by SAPT
Energy decomposition of the investigated three types of noncovalent interactions has been carried out, and the related results are given in Table 3. Compared with MP2 method, the energy difference of SAPT method is very small. The interactive energy (E int ) of the three types of complexes are separated into four terms: dispersion energy (E disp ), induction energy (E ind ), exchange energy (E exch ), and electrostatic energy (E elst ).
As shown in Table 3, the electrostatic energy (E elst ) is predominantly of the attraction for the σ-hole complexes, and the E elst contribution is about 49.61 to 52.70%. For the counterintuitive σ-hole complexes, the electrostatic term is dominant although the dispersion and induction terms are also important in the total attractive interaction. For the lone pair-π interaction complexes, the contribution of dispersion term (E disp ) is slightly greater than that of the electrostatic term (E elst ) while the contribution of induction term (E ind ) is very small. Thus, the physical origin of the interaction between the heterocyclic compounds (C 4 H 4 O, C 5 H 5 N, and C 4 H 4 N 2 ) and AtX depends on the interaction type. In summary, the electrostatic energy has a Fig. 4 The geometry optimization structures for the minimum energy of the three types of complexes of the C 5 H 5 N and AtX main contribution to the stronger interactions in the σ-hole and counterintuitive σ-hole complexes, while the dispersion energy is the main force responsible for the weaker interactions in the lone pair-π interaction complexes.

Conclusions
In the current work, the three types of complexes between the three heterocyclic compounds (C 4 H 4 O, C 5 H 5 N, and C 4 H 4 N 2 ) and AtX (X = F, Cl, and Br) have been studied at the MP2/aug-cc-pVTZ level. For the C 5 H 5 N-AtX and C 4 H 4 N 2 -AtX complexes, the calculated interaction energy decreases according to the sequence σ-hole interaction > the counterintuitive σ-hole interaction > the lone pair-π interaction. For the C 4 H 4 O-AtX complexes, the interaction energy decreases according to the sequence the counterintuitive σ-hole interaction > the σ-hole interaction > the lone pair-π interaction. For the same AtX, the interaction energy of the σ-hole and the lone pair-π interaction complexes decreases according to the sequence C 5 H 5 N > C 4 H 4 N 2 > C 4 H 4 O. while for the counterintuitive σ-hole complexes, the interaction energy decreases according to the sequence C 4 H 4 O > C 5 H 5 N > C 4 H 4 N 2 . It can be see that the ΔE 2 is related to the interaction energies (ΔE CP ) for the σ-hole and counterintuitive σ-hole complexes. The SAPT results indicate that the electrostatic energy is the main contribution to the stronger interactions while the dispersion energy is the main force responsible for the weaker interactions.      . 8 Correlation between the second-order perturbation energy and interaction energies in the σ-hole and counterintuitive σ-hole complexes