Theoretical study on the noncovalent interactions involving triplet diphenylcarbene

The properties of some types of noncovalent interactions formed by triplet diphenylcarbene (DPC3) have been investigated by means of density functional theory (DFT) calculations and quantum theory of atoms in molecule (QTAIM) studies. The DPC3···LA (LA = AlF3, SiF4, PF5, SF2, ClF) complexes have been analyzed from their equilibrium geometries, binding energies, and properties of electron density. The triel bond in the DPC3···AlF3 complex exhibits a partially covalent nature, with the binding energy − 65.7 kJ/mol. The tetrel bond, pnicogen bond, chalcogen bond, and halogen bond in the DPC3···LA (LA = SiF4, PF5, SF2, ClF) complexes show the character of a weak closed-shell noncovalent interaction. Polarization plays an important role in the formation of the studied complexes. The strength of intermolecular interaction decreases in the order LA = AlF3 > ClF > SF2 > SiF4 > PF5. The electron spin density transfers from the radical DPC3 to ClF and SF2 in the formation of halogen bond and chalcogen bond, but for the DPC3···AlF3/SiF4/PF5 complexes, the transfer of electron spin density is minimal.


Introduction
The study of noncovalent interactions has been a hot topic in supramolecular chemistry, molecular recognition, and materials science [1]. The strength of noncovalent bonds is smaller than that of general chemical bonds about 1~2 orders of magnitude, but in the system containing large numbers of molecules, the noncovalent interactions accumulate and influence the structure, function, and physical and chemical properties of the system. Of the various noncovalent bonds, hydrogen bond and halogen bond are arguably the most important and prevalent [2][3][4][5]. Hydrogen bond is typically expressed as the positioning of two molecules such that the H atom of one molecule, R−H, acts as a bridge to another molecule R−H···D. The anisotropic charge distribution around atom of groups 12-18 allows them to act in a similar capacity. The concepts of σ-holes or πholes that have been pointed out by Politzer and Clark et al. [6][7][8][9][10][11][12] reflect the fact that covalently bonded atom tends to have anisotropic electronic densities, with regions of higher and lower density. An σ-hole or π-hole is a region of lower electronic density along the extension of a covalently bonded atom, or perpendicular to a planar portion of a molecule. This region gives rise to positive electrostatic potential and can be used as a Lewis acid to interact attractively with the rich electronic center (lone pairs, π electrons, anions, etc.) of a Lewis base. One or more σ-holes or π-holes have been found for all of the main-group elements in the Periodic Table and have been classified into a wide variety of noncovalent interactions: alkaline earth bonds for group 12, triel bonds for group 13, tetrel bonds for group 14, pnicogen bonds for group 15, chalcogen bonds for group 16, halogen bonds for group 17, and aerogen bonds for group 18 [4,5,[13][14][15][16][17][18][19][20][21][22]. Recently, noncovalent interactions involving σ-hole or σ-lump on a coinage metal have been reported [23][24][25].
As an organic reactive intermediate containing two unbonding valence electrons on a divalent carbon atom, Chunhong Zhao and Hui Lin contributed equally to this work.
carbene can activate small molecules under mild conditions, catalyze organic reactions, and act as ligands in transition metal catalysis [26]. Depending on whether two electrons in carbon atom of carbene are located in a same or a different orbital, they give place to a singlet or a triplet configuration, respectively. Because of its lone pairs, singlet carbene can be acted as electron-pair donor in the intermolecular interaction. Del Bene and Alkorta et al. [27][28][29][30] studied a series of carbenes and silyenes as hydrogen and pnicogen bond acceptors; they also shown that nitrogen heterocyclic carbenes (NHCs) might prefer noncovalent or covalent bonding to trap CO 2 and CS 2 . Some carbene lithium bonding, triel bonding, tetrel bonding, and pnicogen bonding interactions were predicted and characterized by theoretical calculations [31][32][33][34][35]. Sander et al. [36][37][38] investigated the interactions between diphenylcarbene (DPC) and H 2 O, CH 3 OH, or CF 3 I using matrix isolation spectroscopy (IR, UV-vis, and EPR) in combination with theoretical calculations. They showed that the spin ground state of DPC switches from triplet to singlet upon formation of the strongly hydrogen-bonded and halogenbonded complexes. Lu et al. [39] further discussed the influence of the formation of halogen bond on the spin state of DPC and the decisive factors in spin slip via density functional theory (DFT) calculations.
In view of the fact that diphenylcarbene is a prototypical transient carbene with a triplet ground state and has been subject to a large number of mechanistic studies using timeresolved or low-temperature spectroscopy, the bimolecular complexes between triplet diphenylcarbene (DPC 3 ) and a series of Lewis acids LA (LA = AlF 3 SiF 4 , PF 5 , SF 2 , ClF) from group 13-17 atoms were constructed in this work, in order to give insight into these kinds of noncovalent interactions. The main purposes of this paper are (1) to study the stability and strength of the complexes containing triplet DPC 3 , (2) to investigate the character of these σ/π-hole interactions, and (3) to analyze the influence of noncovalent interaction on the distribution of electron density and electron spin density.

Computational methods
All calculations were performed with Gaussian 09 program package [40]. The geometries of the monomers and complexes were fully optimized using the B3LYP functional with D3 empirical dispersion correction and 6-311++G** basis set. Harmonic frequencies were calculated to confirm the equilibrium geometries to be true minima and yielded zero-point energy. The keyword Counterpoise was used for the calculation of corrected binding energies, excluding the inherent basis set superposition error (BSSE) [41]. The binding energies of the bimolecular complexes were computed as the difference between the energy of the complex and the sum of energies of corresponding isolated monomers, in which the geometries of monomers were optimized solely. The electrostatic potentials were calculated on the 0.001 a.u. (electrons/Bohr 3 ) contour of the electron density of the molecule with the WFA surface analysis suite [42]. To have a more detailed and in-depth understanding of the interactions, topological properties of the electron density at the bond critical points were computed by the AIMAll program [43]. Noncovalent interaction index (NCI) and electron spin density analysis were carried out using Multiwfn software [44], and the related plots were graphed using the VMD program [45].

Molecular electrostatic potentials
Molecular electrostatic potential (MEP) is a fundamentally important physical characteristic that is very useful for understanding and predicting noncovalent interactions. Figure 1 shows the contour maps of MEPs for triplet biphenyclobin (DPC 3 ) and LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , ClF). The most positive electrostatic potentials (V S,max ) and most negative electrostatic potentials (V S,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 DPC 3 presents a few blue regions with negative MEPs. The positions of V S,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 AlF 3 (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 AlF 3 molecular framework, with a V S,max value of 104.7 kcal/mol. In the case of ClF, SF 2 , SiF 4 , and PF 5 , 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 V S,max values were found to become less positive following the order AlF 3 > SiF 4 > ClF > SF 2 > PF 5.

Geometry and binding energy
Based on the analysis of MEPs, the intermolecular interaction could form between the σ-hole or π-hole regions of LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , ClF) and the negative electrostatic potential region of DPC 3 . Figure 2 shows the stable geometries of DPC 3 ···LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , ClF) complexes. It can be seen that the most stable interaction between DPC 3 and LA (LA= AlF 3 , SiF 4 , PF 5 , SF 2 , ClF) occurs on the benzene ring of DPC 3 . The binding energy and binding distance for the complexes are given in Table 2. The binding energy (ΔE) ranges from − 15.8 kJ/mol for pnicogen-bonded complex DPC 3 ···PF 5 to − 65.7 kJ/mol for triel-bonded complexes DPC 3 ···AlF 3 . The strength of intermolecular interaction become stronger along the sequence LA = PF 5 < SiF 4 < SF 2 < ClF < AlF 3 . Binding distance (d) in Table 2 refers to the distance between the atom of groups 13 to 17 in the LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , ClF) and the nearest carbon atom of benzene ring in DPC 3 , which can be seen that the shorter the binding distance, the stronger the interaction. By comparing the data in Tables 1 and 2, it is found that the binding energy between molecules is not well correlated with the V S,max values of Lewis acids, which may be due to the steric hindrance effect of SiF 4 and PF 5 . 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 [46,47].

Noncovalent interaction index
To verify the intermolecular interaction between DPC 3 and LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , 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 (λ 2 ) to analyze the type and strength of interactions between molecules, where sign (λ 2 ) 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 (λ 2 ) (above) and gradient isosurfaces generated for s = 0.05 au (below). In the DPC 3 complexes, several low-density isosurfaces (green regions) lie in the interacting portions between DPC 3 and LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , ClF), where noncovalent attractions are expected. There is another area of the low-density, lowgradient nonbonded overlap (red region) located at the center of each benzene ring, where steric repulsion in the benzene

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][53][54]. The common studied topological properties at the bond critical points (BCPs) are electron density (ρ b ), its Laplacian (∇ 2 ρ b ), the local potential energy density (V b ), local kinetic energy density (G b ), and total energy density (H b = V b + G b ). According to the criteria [55,56], a positive ∇ 2 ρ b reflects an excess of kinetic energy in bonds and a relative depletion of electronic charge along a bond path. A positive H b corresponds to a purely closedshell interaction, whereas a negative H b value corresponds to bonds with any degree of covalent character. If − G b /V b 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 shown in Fig. 4 and Table 3. For DPC 3 ···AlF 3 complex, there exists a BCP between the π-hole of AlF 3 and C atom of DPC 3 , and a pair of bond paths connect the BCP and the interacting Al and C atom. The values of ρ b and ∇ 2 ρ b at the C···Al BCP were calculated to be 0.0296 au and 0.0710 au. Positive ∇ 2 ρ b value, negative H b value, and − G b /V value of about 0.8 indicate that this triel bond is of moderate strength with a partially covalent nature. For complex DPC 3 ···SiF 4 and DPC 3 ···PF 5 , there exist several C···F BCPs and one H···F BCP between DPC 3 and SiF 4 /PF 5 molecules, the ρ b values are less than 0.0090 au. From Fig. 4d, e, the C···S or C···Cl BCP in the DPC 3 ···SF 2 and DPC 3 ···ClF complexes account for the chalcogen bond or pnicogen bond between DPC 3 and σ-hole of SF 2 /ClF. The ρ b and ∇ 2 ρ b values of the complexes DPC 3 ···LA (LA = SiF 4 , PF 5 , SF 2 , ClF) are in the range of 0.0044~0.0296 au and 0.0155~0.0621 au. ∇ 2 ρ b > 0, H b > 0, and − G b /V b > 1 were calculated, showing the characters of a weak closed-shell noncovalent interaction.

Density difference of molecular formation analysis
The density difference during the formation of super molecules (A···B) can be described as ρ d (r) = ρ complex (r) − (ρ molA (r) + ρ molB (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 Fig. 2 Optimized geometries of the complexes: a DPC 3 ···AlF 3 ; b DPC 3 ···SiF 4 ; c DPC 3 ···PF 5 ; d DPC 3 ···SF 2 ; e DPC 3 ···ClF Fig. 3 Plots of the reduced density gradient versus the electron density multiplied by the sign of the second Hessian eigenvalue (above) and gradient isosurfaces generated for s = 0.05 a.u (below) for complexes: a DPC 3 ···AlF 3 , b DPC 3 ···SiF 4 , c DPC 3 ···PF 5 , d DPC 3 ···SF 2 , e DPC 3 ···ClF Table 3 Topological properties of electron density at the bond critical points for the complexes DPC 3 ···LA (LA = AlF 3 , SiF 4 PF 5 , SF 2 , ClF) (in au) molecules and weak interactions [58][59][60]. Figure 5 present plots of computed density difference of the complexes, the shift of charge density during the forming of DPC 3 ···LA (LA = AlF 3 , SiF 4 , PF 5 , SF 2 , ClF) complexes are clearly shown. The electronic fields of the π electrons in DPC 3 and σ/πhole in LA cause charge redistributions of each segment. From Fig. 5a, e, 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 DPC 3 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 AlF 3 , ClF to SF 2 , SiF 4 , and PF 5 , 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 charges (Δn e ) 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 DPC 3 ···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 DPC 3 interact with Lewis acids.

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 DPC 3 molecules. Figure 7 shows the maps of electron spin density of DPC 3 and its complexes DPC 3 ···ClF and DPC 3 ···SF 2 , the Δρ values of C atoms in DPC 3 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. The calculated results show that the electron spin density is primarily concentrated on the divalent C1 atom of DPC 3 ; 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 DPC 3 ···LA (LA = AlF 3 , SiF 4 , PF 5 ), 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 DPC 3 radicals, and the transfer of spin electron density from the electron donor to acceptor can be ignored. In DPC 3 ···AlF 3 complex, the change of spin electron density occurs mainly in C15 and C18 atoms of DPC 3 . In DPC 3 ···SiF 4 /PF 5 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 SF 2 is 0.0143. For the halogen-bonded complex DPC 3 … 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 SF 2 /ClF  Computed density difference plots for the complexes: a DPC 3 ···AlF 3 , b DPC 3 ···SiF 4 , c DPC 3 ···PF 5 , d DPC 3 ···SF 2 , e DPC 3 ···ClF spin density from DPC 3 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.

Conclusions
In this work, the intermolecular interactions between the triplet biphenylcarbene radical DPC 3 and a series of Lewis acids LA (LA = AlF 3 , SiF 4, PF 5 , SF 2 and ClF) have been investigated. The analyses of NCI, AIM, and MFDD generated the following conclusions: (1) The strength of intermolecular interaction between DPC 3 and a series of Lewis acids LA decreases gradually in the order of LA = AlF 3 > ClF > SF 2 > SiF 4 > PF 5   (2) The intermolecular interaction induces a build-up of electric charge between molecules. The integral value of the positive charge of density difference is consistent with the binding energy, and polarization effect plays an important role. (3) In the process of halogen bond and chalcogen bond formation, the electron spin density is transferred from DPC 3 to ClF and SF 2 , while during the interaction of DPC 3 with AlF 3 , SiF 4 , and PF 5 , the transfer of electron spin density between molecules is negligible, the electron spin density rearrange within the radical itself.
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