Tetrel Bonds with π-Electrons Acting as Lewis Bases—Theoretical Results and Experimental Evidences

MP2/aug-cc-pVTZ calculations were carried out for the ZFH3-B complexes (Z = C, Si, Ge, Sn and Pb; B = C2H2, C2H4, C6H6 and C5H5-; relativistic effects were taken into account for Ge, Sn and Pb elements). These calculations are supported by other approaches; the decomposition of the energy of interaction, Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) method. The results show that tetrel bonds with π-electrons as Lewis bases are classified as Z···C links between single centers (C is an atom of the π-electron system) or as Z···π interactions where F‒Z bond is directed to the mid-point (or nearly so) of the CC bond of the Lewis base. The analogous systems with Z···C/π interactions were found in the Cambridge Structural Database (CSD). It was found that the strength of interaction increases with the increase of the atomic number of the tetrel element and that for heavier tetrel elements the ZFH3 tetrahedral structure is more deformed towards the structure with the planar ZH3 fragment. The results of calculations show that the tetrel bond is sometimes accompanied by the Z-H···C hydrogen bond or even sometimes the ZFH3-B complexes are linked only by the hydrogen bond interaction.


Introduction
The tetrel bond is a Lewis acid-Lewis base interaction that may play an important role in some chemical and biological processes [1]; for example, it may be considered as a preliminary stage of the S N 2 reaction [2].This interaction was classified as the σ-hole bond by Politzer and coworkers since it may be defined as an interaction between the 14th Group element acting as the Lewis acid centre through its σ-hole and a region that is rich of the electron density by a lone electron pair, π-electron system etc.[3,4].The σ-hole is usually located in this case in the elongation of the covalent bond to the tetrel centre and it is often characterized by the positive electrostatic potential (EP) [3,4].It seems that first time the tetrel bond was analyzed in terms of the σ-hole concept in the SiF 4 complexes with amines [5].In spite of the fact that the term "tetrel bond" appeared recently [6] and also this interaction was classified as the σ-hole bond in the last decade [3][4][5] it was analyzed in earlier studies.For example, the SiF 4 •••NH 3 and SiF 4 •••(NH 3 ) 2 complexes were analyzed theoretically since ab initio MO calculations were performed with the use of STO-3G and STO-6G basis sets [7], another study that is more complex concerns a large sample of complexes of silicon derivatives with electron-rich groups [8].Both latter studies were performed before the proposition of the σ-hole concept [9,10] and the introduction of the tetrel bond term [6].
One can mention other studies on tetrel bonds as for example that one where this interaction was analyzed as a preliminary stage of the S N 2 reaction [11], the theoretical analysis of structural and energetic properties of acetonitrile complexes with the 14 Group tetrahalides [12]; a study on the Lewis acid carbon center, the corresponding interaction was labeled as the carbon bond and it was compared with the hydrogen bond [13]; it is worth mentioning that the carbon bond is a sub-class of the tetrel bond interactions [2,11].The tetrel-hydride interaction is another sub-class of tetrel bonds where the negatively charged H-atom plays the role of Lewis base center [14].
There are other, more recent studies on this kind of interaction; only few are mentioned here; the analysis of factors which influence the strength of tetrel bonds [15], the analysis of mechanisms of S N 2 reactions, among them at the C centre [16], the role of tetrel bonds in the crystal structures' stabilization [17], the theoretical analysis of the H-Si•••N and F-Si•••N linear or nearly so arrangements [18], comparison of neutral and charge assisted tetrel bonds [19], the geometry deformations of monomers linked by tetrel bond [20] or the balance between the attractive forces of tetrel interactions and the steric repulsions in crystal structures [21].
One may cite numerous other examples since the number of studies on this kind of interaction has increased rapidly.However, it seems that there are no systematic and extensive studies on the tetrel bonds with π-electrons playing a role of Lewis bases or at most they are very rare and they are not a main goal of investigations.For example, very recently, various σ-hole bonds were analyzed with the use of few theoretical approaches: halogen, chalcogen, pnicogen and tetrel bonds were compared [22]; three different types of Lewis bases were considered there, neutral species (NH 3 ), anion (Cl − ) and the π-electron system (C 2 H 2 ).Hence two tetrel bonded complexes with acetylene molecule playing a role of the Lewis base were analyzed there among various other complexes.These are the SiFH 3 [22].
The other issue that is not analyzed so frequently concerns the tetrel bond interactions with the heavier tetrel elements, such analyses are rather rare and mainly concern germanium species.There are more experimental studies on tetrel bonds with heavier tetrel elements playing a role of the Lewis acid centers, however only sometimes such experimental analyses are supported by theoretical results [23].
One of examples where heavier tetrel elements were considered in tetrel bonds is a study on the SnF 4 and PbF 4 complexes with NH 3 and HCN that play a role of Lewis bases through the nitrogen centre [24].A theoretical study analogous to the latter one was performed on the lighter tetrel species since the complexes of CF 4 , SiF 4 and GeF 4 Lewis acid units with NH 3 and AsH 3 Lewis bases were analyzed [25].
Returning to the π-electron species-numerous theoretical and experimental studies on interactions where such systems play a role of Lewis bases may be mentioned.These are mainly those studies that concern hydrogen bonded systems [26].However other Lewis acid-Lewis base interactions with π-electron donors were analyzed very often [27][28][29][30].One can even mention the triel bonds between the boron or aluminium Lewis acid center and acetylene or ethylene [31,32] or the recent study where the multivalent halogen centers act as the Lewis acids [33].
The aim of this study is an analysis of the tetrel bonds in complexes of ZFH 3 species, where Z labels the following centers; C, Si, Ge, Sn and Pb, thus light and heavy tetrels are taken into account; the acetylene, ethylene, benzene and cyclopentadienyl anion were chosen as the π-electron moieties acting as the Lewis bases.Different theoretical techniques are applied here to deepen the understanding of the nature of these tetrel bond interactions; i.e., the Quantum Theory of Atoms in Molecules (QTAIM) [34], Natural Bond Orbital (NBO) approach [35], the decomposition of the energy of interaction [36,37] as well as the analysis of the electrostatic potential (EP) distribution [38].The short descriptions of the theoretical approaches applied here are included in the section that concerns the computational details.

Energetic and Geometric Parameters
Figure 1 presents examples of complexes analyzed here.All kinds of Lewis bases that are considered are shown in selected examples of the figure.The molecular graphs are presented since they reflect geometry of species analyzed.However these graphs are discussed further here in the section on QTAIM results.

SnFH3-C2H2
SnFH3-C2H4 The molecular graphs of the selected complexes analyzed here; big circles-attractors, small green circles-BCPs, the nonnuclear attractor (NNA) is located (small red circle) between two BCPs of the CC bond in a case of the SnFH3-C2H2 complex.
The energetic parameters of analyzed complexes, among them, the binding and interaction energies corrected for BSSE, Ebin and Eint, respectively, are included in    The energetic parameters of analyzed complexes, among them, the binding and interaction energies corrected for BSSE, E bin and E int , respectively, are included in Table 1.One can see much stronger interactions, i.e., greater -E int and -E bin values, for complexes with the cyclopentadienyl anion, than for complexes with the other Lewis base units.This may be explained since the complexes of C 5 H 5 − anion that are linked through the tetrel bonds are assisted by negative charge; the latter anion is much stronger base than the remaining species chosen here.The following tendencies are also observed here, and it does not depend on the choice of -E int or -E bin value for the discussion; the strength of interaction for the same Lewis base increases in the following order of the tetrel center C < Si < Ge < Sn ∼ = Pb.It was observed earlier for tetrel bond interactions [3,4] and it was explained by the increase of the electrostatic part of the energy of interaction since the electrostatic potential (EP) at the tetrel σ-hole increases with the increase of the atomic number [3,4].The calculations performed here show the EP of tetrel σ-hole of the ZFH 3 species equal to 0.033; 0.062; 0.068; 0.081; 0.080 au for C, Si, Ge, Sn and Pb centers, respectively (0.001 au electron density surfaces were chosen).The EP values for tin and lead centers are almost equal one to each other.This is why for complexes analyzed here similar Lewis acid properties are observed for these centers; however the strongest interaction is observed for the SnFH 3 -C 5 H 5 − complex if the interaction energy is considered while if the binding energy is taken into account thus it is the PbFH 3 -C 5 H 5 − complex.The BSSE corrections are greater for stronger interactions, especially large values are observed for interactions in cyclopentadienyl complexes.The deformation energy, E def , is a parameter that is related to geometrical changes of the interacting systems.For example, in a case of the strong A-H•••B hydrogen bonds, the complexation often leads to the meaningful elongation of the A-H proton donating bond that results in the greater E def values [39].Steric effects are very important for tetrel bonded species [11,21] since the tetrel center, often characterized by the sp 3 hybridization and surrounded by four substituents (like for the systems considered here) is hardly available for the Lewis base (nucleophilic attack).Thus the tetrel-base link should cause greater deformations connected with the increase of the availability of the tetrel center.In other words the ZFH 3 tetrahedral system should be closer to the trigonal bipyramid in the ZFH 3-B complex with the ZH 3 part being closer to planarity.For complexes of acetylene, ethylene and benzene E def does not exceed 0.3 kcal/mol indicating negligible changes of geometry resulting from complexation.However for the C 5 H 5 − complexes, if one excludes the CFH 3 -C 5 H 5 − complex with this energy amounting only 0.3 kcal/mol, E def is close to 10 kcal/mol or even exceeds this value.This is in agreement with changes of geometry; one can see (Figure 1) the ZH 3 part close to planarity and the F-Z•••C arrangement close to linearity for two complexes presented; SnFH 3 -C 5 H 5 − and PbFH 3 -C 5 H 5 − .
The above-presented EP values at the Z-tetrel centre concern the σ-hole that occurs in the extension of F-Z bonds.For the ZFH 3 species analyzed here, similarly as for other sp 3 hybridized tetrel centers four σ-holes located in extensions of covalent bonds to Z-center occur.However the electronegative F-substituent enhances F-Z σ-hole [3,4] that results in greater positive EP values than those of other H-Z σ-holes.For example, for the SnFH 3 molecule the EP value at the F-Sn σ-hole is equal to +0.081 au while this value for the H-Sn σ-hole amounts +0.048 au.For the clarity of the results' presentation only interactions of the F-Z σ-hole are considered here; it means that the F-Z σ-hole is directed to the π-electron system in the configurations analyzed.
Table 1 presents the Lewis acid-Lewis base distances, for each of complexes the shortest Z•••C contact was chosen.One can see that these distances are usually greater than 3 Å, only for the C 5 H 5 − complexes where stronger interactions are observed such distances amount ~2.5 Å (except of the CFH 3 -C 5 H 5 − complex where this distance is equal to ~3.2 Å).It was pointed out in numerous studies that the distance between interacting units is roughly related to the strength of interaction, this was observed for the hydrogen bonded complexes [40] but it seems that such dependence occurs also for other types of interactions [2].It is often stated in various studies that the sum of van der Waals radii of two atoms being in contact roughly indicates at which distance a significant so-called noncovalent interaction begins [41].Table 1 presents how the Z•••C distances are related to the corresponding sum of Z and C van der Waals radii.These distances are greater than the corresponding sum for carbon complexes (Z = C) and for the SiFH 3 -C 2 H 2 complex while for the remaining ones these distances are lower than the van der Waals sum; the following van der Waals radii were applied here, H-1.Waals radii.If one considers only the Z•••C distances as a measure of the strength of interaction thus the interactions in the CFH 3 complexes are very weak and one may contest even their stabilizing nature.Table 2 presents geometrical parameters related to the changes resulting from complexation; one of them is a percentage elongation of the Z-F bond related to the corresponding isolated ZFH 3 species that is not involved in the tetrel bond.One can see that these elongations correspond to the deformation energies, the greatest values are observed for the cyclopentadienyl complexes.For the species analyzed here three F-Z-H angles in the Lewis acid unit are very close one to each other; however for each complex considered its average value is considered in the further discussions; the latter angle is defined in Figure 2.For the isolated ZFH 3 species this tetrahedral angle, labeled as α iso , amounts from 101.4 • for PbFH 3 to 108.8 • for CFH 3 .It decreases in the complex to α comp (up to 90 • corresponding to the planar ZH 3 system in the trigonal bipyramid structure).The angle decrease values, [(α iso − α comp )/α iso ] × 100%, are presented in Table 2.They correspond to the deformation energies discussed earlier here as well as to the elongations of the Z-F bonds since the greatest decreases are observed for the strongest interactions.The Z-F bond elongations result from the π CC → σ ZF * and σ CH → σ ZF * overlaps;   Table 2.The characteristics of complexes analyzed; ZF% and Angle% are the percentage increase of the Z-F distance and the percentage decrease of the F-Z-H angle, respectively; ENBO 1 and ENBO 2 are the NBO energies defined in the text (in kcal/mol); El-trans (au) is the electron charge transfer from the Lewis base to the Lewis acid while Z-charge is the charge of the Z-center in the complex considered (both charges in au calculated within NBO approach).Table 2 shows the electron charge transfer values from the Lewis base to the Lewis acid unit, these transfers are especially great for the ZFH3-C5H5 − complexes, except of the CFH3-C5H5 − one.Such electron charge redistributions resulting from complexation are usually great for those complexes where the geometry deformations are important [2]; this is observed also here.The charge of the Zcentral tetrel atom is shown in Table 2; one can see that this charge decreases (is "more negative") in complexes in comparison with the corresponding isolated ZFH3 species.This is in opposite to the A-H•••B hydrogen bonded systems where the complexation usually results in the increase of the positive charge of the central H-atom [35].Table 2 shows the electron charge transfer values from the Lewis base to the Lewis acid unit, these transfers are especially great for the ZFH 3 -C 5 H 5 − complexes, except of the CFH 3 -C 5 H 5 − one.

Complex ZF% Angle% ENBO
Such electron charge redistributions resulting from complexation are usually great for those complexes where the geometry deformations are important [2]; this is observed also here.The charge of the Z-central tetrel atom is shown in Table 2; one can see that this charge decreases (is "more negative") in complexes in comparison with the corresponding isolated ZFH 3 species.This is in opposite to the A-H•••B hydrogen bonded systems where the complexation usually results in the increase of the positive charge of the central H-atom [35].

Nature of Interactions-Decomposition of Interaction Energy
Table 3 presents terms of the energy of interaction resulting from the Ziegler and Rauk decomposition scheme [36,37] (see the Computational Details section).
Table 3.The terms of the energy of interaction (kcal/mol); Pauli repulsion, ∆E Pauli , electrostatic, ∆E elstat , orbital, ∆E orb , dispersion, ∆E disp , and the total interaction energy, ∆E int .One can see that only for the CFH 3 complexes with acetylene, ethylene and benzene the dispersion term, ∆E disp , is the most important attractive one.This is typical for weak van der Waals interactions where attractive interaction energy terms related to charge distributions and to electron charge shifts, ∆E elstat and ∆E orb , are less important [2].For the above-mentioned three complexes, −∆E int does not exceed 3 kcal/mol, and in two cases it is close to 1 kcal/mol.The electron charge shifts for these complexes (Table 2) do not exceed 4 millielectrons!The latter is connected with the practically unchanged carbon charge in the CFH 3 unit in those complexes in comparison with the isolated CFH 3 molecule.For the remaining complexes electrostatic interaction energy is the most important attractive term, only in a case of the SiFH 3 -C 6 H 6 and GeFH 3 -C 6 H 6 complexes the dispersive term is slightly "less negative" than the electrostatic one.If one excludes the above-mentioned three CFH 3 complexes, thus for majority of remaining complexes the orbital interaction, ∆E orb , is the next most important attractive term, after electrostatic interaction.
It was discussed in recent studies on hydrogen bonds and on other σ-hole bonds that these interactions are accompanied by effects that are a response for the Pauli repulsion [2,44].The latter was also discussed for halogen bonds where multivalent halogen center plays a role of the Lewis acid while the π-electrons are the Lewis base [33].For such interactions correlations were found between the repulsion interaction energy and different terms of the attractive interaction.It was found in earlier studies than the orbital interaction energy (if one refers to the decomposition scheme applied here) well correlates with the repulsion term, correlations for other interaction energy terms are not so good.However, in general, the sum of all attractive terms correlates with the Pauli repulsion term [2,33,44].Figure 3 presents such a correlation for the complexes analyzed here.Thus the attractive interaction which is related to various effects related to complexation, among them to the electron charge redistribution, is a response for the Pauli repulsion.The orbital interaction reflecting electron shifts corresponds to energy terms which are named in the other way in other decomposition schemes; most often they are labeled as the delocalization interaction energy, induction, charge transfer, polarization and others [2]. Figure 4 shows, for the complexes analyzed here, the correlation between the orbital energy, ΔEorb, and the electron charge shift resulting from complexation.

Quantum Theory of Atoms in Molecules Parameters
Table 4 presents characteristics of the bond critical point (BCP) of the bond path that connects the Lewis acid and Lewis base units of the complex.It is a link between the tetrel center (tetrel attractor) or the hydrogen center (hydrogen attractor) and the critical point of the Lewis base species.This critical point may correspond to the carbon atom attractor, to the bond critical point (BCP) of the CC bond or to the non-nuclear attractor (NNA) located on the CC bond path.Hence one can see that there are various topologies of complexes analyzed here.The orbital interaction reflecting electron shifts corresponds to energy terms which are named in the other way in other decomposition schemes; most often they are labeled as the delocalization interaction energy, induction, charge transfer, polarization and others [2]. Figure 4 shows, for the complexes analyzed here, the correlation between the orbital energy, ∆E orb , and the electron charge shift resulting from complexation.The orbital interaction reflecting electron shifts corresponds to energy terms which are named in the other way in other decomposition schemes; most often they are labeled as the delocalization interaction energy, induction, charge transfer, polarization and others [2]. Figure 4 shows, for the complexes analyzed here, the correlation between the orbital energy, ΔEorb, and the electron charge shift resulting from complexation.

Quantum Theory of Atoms in Molecules Parameters
Table 4 presents characteristics of the bond critical point (BCP) of the bond path that connects the Lewis acid and Lewis base units of the complex.It is a link between the tetrel center (tetrel attractor) or the hydrogen center (hydrogen attractor) and the critical point of the Lewis base species.This critical point may correspond to the carbon atom attractor, to the bond critical point (BCP) of the CC bond or to the non-nuclear attractor (NNA) located on the CC bond path.Hence one can see that there are various topologies of complexes analyzed here.

Quantum Theory of Atoms in Molecules Parameters
Table 4 presents characteristics of the bond critical point (BCP) of the bond path that connects the Lewis acid and Lewis base units of the complex.It is a link between the tetrel center (tetrel attractor) or the hydrogen center (hydrogen attractor) and the critical point of the Lewis base species.This critical point may correspond to the carbon atom attractor, to the bond critical point (BCP) of the CC bond or to the non-nuclear attractor (NNA) located on the CC bond path.Hence one can see that there are various topologies of complexes analyzed here.The above-mentioned bond path may concern the tetrel bond if the Z-center of the Lewis acid unit is linked with the Lewis base critical point or it may concern the hydrogen bond if the H-atom attractor of the Lewis acid is linked with the Lewis base critical point.One may expect the (Z)H•••C bond paths show some "artificial interactions", especially since the meaning of the bond path and its usefulness to analyze interactions is often a subject of controversies [45] and disputes [46,47].The presented here preliminary results on tetrel bonds where π-electrons play a role of Lewis bases need additional extended studies.However few arguments that the accompanying (Z)H•••C bond paths observed for some benzene and cyclopentadienyl complexes may correspond to weak hydrogen bonds are listed here.The electron densities at the (Z)H•••C bond critical points (BCPs) are not meaningless and they are comparable sometimes with such values for the Z•••C BCPs; see the GeFH 3 -C 6 H 6 complex for example (Table 4).The PbFH 3 -C 5 H 5 − complex is an example where the greatest electron density at the Particularly the following cases of bond paths are observed for complexes analyzed here.For the CFH 3 -C 2 H 2 and CFH 3 -C 2 H 4 complexes the irregular and nonlinear carbon-carbon bond paths are observed that may result from weak interactions (Figure 5); formally according to the QTAIM approach, they may be attributed to the tetrel bonds.For the CFH 3 -C 6 H 6 (Figure 1) and CFH In a case of the SiFH3-C5H5 − complex the clear almost linear Si•••C bond path corresponding to the strong tetrel bond is observed, similarly as for the other ZFH3-C5H5 − complexes for Z = Ge, Sn and Pb.In a case of the PbFH3-C5H5 − complex the additional H•••C bond path corresponding to the Pb-H•••C hydrogen bond is observed (Figure 1).For the ZFH3-C6H6 complexes (Z = Ge, Sn, Pb) the tetrel and hydrogen bonds are observed with the corresponding bond paths, the SnFH3-C6H6 complex representing such a situation is presented in Figure 1.Similarly the SnFH3-C2H2, SnFH3-C2H4 complexes in Figure 1 reflect the same situation in analogues tin and lead complexes; in the case of acetylene Lewis base the Z•••NNA bond path is observed while in the case of ethylene Lewis base this is the Z•••BCP bond path.
The characteristics of bond critical points presented in Table 4 reflect the strength of interaction.It was discussed in various studies that these characteristics may be often treated as measures of the strength of interaction [49]; especially for homogeneous samples of complexes.Numerous relationships were found between characteristics of the H•••B BCP and the strength of interaction for the A-H•••B hydrogen bonds.For complexes analyzed here greater values of the electron density at the bond critical point, ρBCP's, are observed for the C5H5 − complexes.The Laplacian of the electron density at BCP, ∇ 2 ρBCP, is positive for all complexes analyzed which may show these are not covalent interactions; the HBCP values are positive and close to zero for all complexes of acetylene, ethylene and benzene as well as for the CFH3-C5H5 − complex.For the remaining complexes of the C5H5 − anion the negative HBCP values are observed that may indicate these are partly covalent in nature interactions.
One may ask what is the difference between the Z•••π and Z•••C tetrel bonds that are presented here.These "two kinds" of connections correspond to the types of bond paths.For the majority of acetylene and ethylene complexes former connections are observed while for the benzene and cyclopentadienyl complexes the latter ones.The Z•••π bond path is a link between Z-attractor that corresponds to the nucleus and BCP or NNA located at the CC bond of acetylene or ethylene (see Figure 1).The Z•••C bond path is a link between Z and C attractors corresponding to nuclei.This difference occurs within the Quantum Theory of Atoms in Molecules (QTAIM) scheme but it seems it is not observed in other approaches; for example in both cases the same orbital-orbital overlaps occur that correspond to the Z•••π interactions; i.e., πCC → σZF * ones.All other accompanying overlaps specified earlier here are the same in both cases of contacts.The similar situations were observed earlier for the hydrogen bonded complexes with the π-electron systems playing a role of Lewis bases [50].The characteristics of bond critical points presented in Table 4 reflect the strength of interaction.It was discussed in various studies that these characteristics may be often treated as measures of the strength of interaction [49]; especially for homogeneous samples of complexes.Numerous relationships were found between characteristics of the H•••B BCP and the strength of interaction for the A-H•••B hydrogen bonds.For complexes analyzed here greater values of the electron density at the bond critical point, ρ BCP 's, are observed for the C 5 H 5 − complexes.The Laplacian of the electron density at BCP, ∇ 2 ρ BCP , is positive for all complexes analyzed which may show these are not covalent interactions; the H BCP values are positive and close to zero for all complexes of acetylene, ethylene and benzene as well as for the CFH 3 -C 5 H 5 − complex.For the remaining complexes of the C 5 H 5 − anion the negative H BCP values are observed that may indicate these are partly covalent in nature interactions.
One may ask what is the difference between the Z•••π and Z•••C tetrel bonds that are presented here.These "two kinds" of connections correspond to the types of bond paths.For the majority of acetylene and ethylene complexes former connections are observed while for the benzene and cyclopentadienyl complexes the latter ones.The Z•••π bond path is a link between Z-attractor that corresponds to the nucleus and BCP or NNA located at the CC bond of acetylene or ethylene (see Figure 1).The Z•••C bond path is a link between Z and C attractors corresponding to nuclei.This difference occurs within the Quantum Theory of Atoms in Molecules (QTAIM) scheme but it seems it is not observed in other approaches; for example in both cases the same orbital-orbital overlaps occur that correspond to the Z•••π interactions; i.e., π CC → σ ZF * ones.All other accompanying overlaps specified earlier here are the same in both cases of contacts.The similar situations were observed earlier for the hydrogen bonded complexes with the π-electron systems playing a role of Lewis bases [50].

Computational Details
The calculations were performed with the Gaussian16 set of codes [51] using the second-order Møller-Plesset perturbation theory method (MP2) [52], and the aug-cc-pVTZ basis set [53].
The relativistic effects for the heavier Ge, Sn and Pb atoms were taken into account.The calculations for these elements were done with quasi-relativistic small-core effective core potentials: ECP10MDF, ECP28MDF and ECP60MDF, for Ge, Sn and Pb, respectively [54].For the latter elements the basis sets corresponding to aug-cc-pVTZ were applied, i.e., ECP10MDF_AVTZ, ECP28MDF_AVTZ and ECP60MDF_AVTZ, respectively [55].Frequency calculations were performed for the complexes analyzed and their monomers to confirm that the optimized structures correspond to energetic minima.The binding energy, E bin , was calculated as difference between the energy of the complex and the sum of energies of monomers optimized separately while the interaction energy, E int , is a difference between the energy of the complex and the sum of energies of monomers which geometries come from the geometry of the complex considered [56].The binding and interaction energies are negative but their difference-the deformation energy, E def = E bin − E int , is positive and it is connected with the change of geometries of monomers resulting from the complexation [39].The Counterpoise (CP) correction was applied to calculate the basis set superposition error BSSE [57]; hence the E bin and E int values corrected for BSSE are analyzed in this study.
The Quantum Theory of 'Atoms in Molecules' (QTAIM) was also applied to characterize critical points (BCPs) in terms of the electron density (ρ BCP ), its Laplacian (∇2 ρ BCP ) and the total electron energy density at BCP (H BCP ) which is the sum of the potential electron energy density (V BCP ) and the kinetic electron energy density (G BCP ) [34].The AIMAll program was used to carry out the QTAIM calculations [58].
The Natural Bond Orbital (NBO) method [35] was applied to calculate atomic charges, the electron charge shifts from the Lewis bases to the Lewis acids as well as the orbital-orbital interactions.The n B → σ AH * orbital-orbital interaction is characteristic for the A-H•••B hydrogen bond; n B labels

Computational Details
The calculations were performed with the Gaussian16 set of codes [51] using the second-order Møller-Plesset perturbation theory method (MP2) [52], and the aug-cc-pVTZ basis set [53].The relativistic effects for the heavier Ge, Sn and Pb atoms were taken into account.The calculations for these elements were done with quasi-relativistic small-core effective core potentials: ECP10MDF, ECP28MDF and ECP60MDF, for Ge, Sn and Pb, respectively [54].For the latter elements the basis sets corresponding to aug-cc-pVTZ were applied, i.e., ECP10MDF_AVTZ, ECP28MDF_AVTZ and ECP60MDF_AVTZ, respectively [55].Frequency calculations were performed for the complexes analyzed and their monomers to confirm that the optimized structures correspond to energetic minima.The binding energy, Ebin, was calculated as difference between the energy of the complex and the sum of energies of monomers optimized separately while the interaction energy, Eint, is a difference between the energy of the complex and the sum of energies of monomers which geometries come from the geometry of the complex considered [56].The binding and interaction energies are negative but their difference-the deformation energy, Edef = Ebin − Eint, is positive and it is connected with the change of geometries of monomers resulting from the complexation [39].The Counterpoise (CP) correction was applied to calculate the basis set superposition error BSSE [57]; hence the Ebin and Eint values corrected for BSSE are analyzed in this study.
The Quantum Theory of 'Atoms in Molecules' (QTAIM) was also applied to characterize critical points (BCPs) in terms of the electron density (ρBCP), its Laplacian (∇ 2 ρBCP) and the total electron energy density at BCP (HBCP) which is the sum of the potential electron energy density (VBCP) and the kinetic electron energy density (GBCP) [34].The AIMAll program was used to carry out the QTAIM calculations [58].
The Natural Bond Orbital (NBO) method [35] was applied to calculate atomic charges, the electron charge shifts from the Lewis bases to the Lewis acids as well as the orbital-orbital interactions.The nB → σAH * orbital-orbital interaction is characteristic for the A-H•••B hydrogen bond; nB labels the lone electron pair of the B Lewis base center and σAH * is the antibonding orbital of the A-H Lewis acid bond [35].In a case of the hydrogen bonds where π-electrons and σ-electrons play a role of the Lewis bases, A-H•••π and A-H•••σ systems, the πB → σAH * and σB → σAH * overlaps, respectively, are the most important orbital-orbital interactions [59].The similar situation occurs for the tetrel bonds analyzed here, they may be classified as the Z•••π or Z•••C interactions (Z labels the tetrel centre).The πCC → σZF * and πCC → σZH * overlaps are observed here as the most important interactions; besides the σCH → σZF * and σCH → σZH * overlaps are also detected but they are characterized by lower energies than the former interactions.For example, the πCC → σZF * interaction is calculated as the second-order perturbation theory energy (Equation (1)): ⟨πCC|F|σZF * ⟩ designates the Fock matrix element and (ε(σZF * ) − ε (πCC)) is the orbital energy difference.
The similar equations (to Equation ( 1)) for the remaining above-mentioned orbital-orbital interactions may be given.
The energy decomposition analysis (EDA) [36,37] was carried out with the BP86 functional [60,61] in conjunction with the Grimme dispersion corrections (BP86-D3) [62] using uncontracted Slater-type orbitals (STOs) as basis functions for all elements with triple-ζ quality (ADF-basis set TZP).The energy decomposition analysis (EDA) was performed with the use of the ADF2013.01 program [63] for all complexes analyzed here and characterized by geometries resulting from the MP2/aug-cc-pVTZ optimizations.The EDA method follows the energy partition of Morokuma [36,37].The interaction energy, ΔEint, between two fragments (A and B) in the A-B link, in the particular electronic reference state and in the frozen geometry of AB is considered in this approach.The ΔEint interaction energy is divided into three components and the additional dispersion term, ΔEdisp (Equation ( 2)):

Computational Details
The calculations were performed with the Gaussian16 set of codes [51] using the second-order Møller-Plesset perturbation theory method (MP2) [52], and the aug-cc-pVTZ basis set [53].The relativistic effects for the heavier Ge, Sn and Pb atoms were taken into account.The calculations for these elements were done with quasi-relativistic small-core effective core potentials: ECP10MDF, ECP28MDF and ECP60MDF, for Ge, Sn and Pb, respectively [54].For the latter elements the basis sets corresponding to aug-cc-pVTZ were applied, i.e., ECP10MDF_AVTZ, ECP28MDF_AVTZ and ECP60MDF_AVTZ, respectively [55].Frequency calculations were performed for the complexes analyzed and their monomers to confirm that the optimized structures correspond to energetic minima.The binding energy, Ebin, was calculated as difference between the energy of the complex and the sum of energies of monomers optimized separately while the interaction energy, Eint, is a difference between the energy of the complex and the sum of energies of monomers which geometries come from the geometry of the complex considered [56].The binding and interaction energies are negative but their difference-the deformation energy, Edef = Ebin − Eint, is positive and it is connected with the change of geometries of monomers resulting from the complexation [39].The Counterpoise (CP) correction was applied to calculate the basis set superposition error BSSE [57]; hence the Ebin and Eint values corrected for BSSE are analyzed in this study.
The Quantum Theory of 'Atoms in Molecules' (QTAIM) was also applied to characterize critical points (BCPs) in terms of the electron density (ρBCP), its Laplacian (∇ 2 ρBCP) and the total electron energy density at BCP (HBCP) which is the sum of the potential electron energy density (VBCP) and the kinetic electron energy density (GBCP) [34].The AIMAll program was used to carry out the QTAIM calculations [58].
The Natural Bond Orbital (NBO) method [35] was applied to calculate atomic charges, the electron charge shifts from the Lewis bases to the Lewis acids as well as the orbital-orbital interactions.The nB → σAH * orbital-orbital interaction is characteristic for the A-H•••B hydrogen bond; nB labels the lone electron pair of the B Lewis base center and σAH * is the antibonding orbital of the A-H Lewis acid bond [35].In a case of the hydrogen bonds where π-electrons and σ-electrons play a role of the Lewis bases, A-H•••π and A-H•••σ systems, the πB → σAH * and σB → σAH * overlaps, respectively, are the most important orbital-orbital interactions [59].The similar situation occurs for the tetrel bonds analyzed here, they may be classified as the Z•••π or Z•••C interactions (Z labels the tetrel centre).The πCC → σZF * and πCC → σZH * overlaps are observed here as the most important interactions; besides the σCH → σZF * and σCH → σZH * overlaps are also detected but they are characterized by lower energies than the former interactions.For example, the πCC → σZF * interaction is calculated as the second-order perturbation theory energy (Equation (1)): ⟨πCC|F|σZF * ⟩ designates the Fock matrix element and (ε(σZF * ) − ε (πCC)) is the orbital energy difference.
The similar equations (to Equation ( 1)) for the remaining above-mentioned orbital-orbital interactions may be given.
The energy decomposition analysis (EDA) [36,37] was carried out with the BP86 functional [60,61] in conjunction with the Grimme dispersion corrections (BP86-D3) [62] using uncontracted Slater-type orbitals (STOs) as basis functions for all elements with triple-ζ quality (ADF-basis set TZP).The energy decomposition analysis (EDA) was performed with the use of the ADF2013.01 program [63] for all complexes analyzed here and characterized by geometries resulting from the MP2/aug-cc-pVTZ optimizations.The EDA method follows the energy partition of Morokuma [36,37].The interaction energy, ΔEint, between two fragments (A and B) in the A-B link, in the particular electronic reference state and in the frozen geometry of AB is considered in this approach.The ΔEint interaction energy is divided into three components and the additional dispersion term, ΔEdisp (Equation ( 2)): rformed with the Gaussian16 set of codes [51] using the second-order heory method (MP2) [52], and the aug-cc-pVTZ basis set [53].The ier Ge, Sn and Pb atoms were taken into account.The calculations for th quasi-relativistic small-core effective core potentials: ECP10MDF, for Ge, Sn and Pb, respectively [54].For the latter elements the basis pVTZ were applied, i.e., ECP10MDF_AVTZ, ECP28MDF_AVTZ and ely [55].Frequency calculations were performed for the complexes s to confirm that the optimized structures correspond to energetic Ebin, was calculated as difference between the energy of the complex onomers optimized separately while the interaction energy, Eint, is a of the complex and the sum of energies of monomers which geometries e complex considered [56].The binding and interaction energies are the deformation energy, Edef = Ebin − Eint, is positive and it is connected of monomers resulting from the complexation [39].The Counterpoise calculate the basis set superposition error BSSE [57]; hence the Ebin and are analyzed in this study.Atoms in Molecules' (QTAIM) was also applied to characterize critical ectron density (ρBCP), its Laplacian (∇ 2 ρBCP) and the total electron energy the sum of the potential electron energy density (VBCP) and the kinetic P) [34].The AIMAll program was used to carry out the QTAIM al (NBO) method [35] was applied to calculate atomic charges, the the Lewis bases to the Lewis acids as well as the orbital-orbital ital-orbital interaction is characteristic for the A-H overlaps are observed here as the most important → σZF * and σCH → σZH * overlaps are also detected but they are es than the former interactions.For example, the πCC → σZF * interaction er perturbation theory energy (Equation (1)): k matrix element and (ε(σZF * ) − ε (πCC)) is the orbital energy difference.tion (1)) for the remaining above-mentioned orbital-orbital interactions on analysis (EDA) [36,37] was carried out with the BP86 functional e Grimme dispersion corrections (BP86-D3) [62] using uncontracted basis functions for all elements with triple-ζ quality (ADF-basis set tion analysis (EDA) was performed with the use of the ADF2013.01 s analyzed here and characterized by geometries resulting from the ons.The EDA method follows the energy partition of Morokuma y, ΔEint, between two fragments (A and B) in the A-B link, in the state and in the frozen geometry of AB is considered in this approach.s divided into three components and the additional dispersion term, performed with the Gaussian16 set of codes [51] using the second-order theory method (MP2) [52], and the aug-cc-pVTZ basis set [53].The avier Ge, Sn and Pb atoms were taken into account.The calculations for with quasi-relativistic small-core effective core potentials: ECP10MDF, F, for Ge, Sn and Pb, respectively [54].For the latter elements the basis cc-pVTZ were applied, i.e., ECP10MDF_AVTZ, ECP28MDF_AVTZ and tively [55].Frequency calculations were performed for the complexes ers to confirm that the optimized structures correspond to energetic y, Ebin, was calculated as difference between the energy of the complex monomers optimized separately while the interaction energy, Eint, is a gy of the complex and the sum of energies of monomers which geometries f the complex considered [56].The binding and interaction energies are e-the deformation energy, Edef = Ebin − Eint, is positive and it is connected ies of monomers resulting from the complexation [39].The Counterpoise to calculate the basis set superposition error BSSE [57]; hence the Ebin and E are analyzed in this study.of 'Atoms in Molecules' (QTAIM) was also applied to characterize critical e electron density (ρBCP), its Laplacian (∇ 2 ρBCP) and the total electron energy is the sum of the potential electron energy density (VBCP) and the kinetic BCP) [34].The AIMAll program was used to carry out the QTAIM bital (NBO) method [35] was applied to calculate atomic charges, the the Lewis bases to the Lewis acids as well as the orbital-orbital orbital-orbital interaction is characteristic for the A-H overlaps are observed here as the most important CH → σZF * and σCH → σZH * overlaps are also detected but they are gies than the former interactions.For example, the πCC → σZF * interaction order perturbation theory energy (Equation (1)): ock matrix element and (ε(σZF * ) − ε (πCC)) is the orbital energy difference.uation (1)) for the remaining above-mentioned orbital-orbital interactions ition analysis (EDA) [36,37] was carried out with the BP86 functional the Grimme dispersion corrections (BP86-D3) [62] using uncontracted as basis functions for all elements with triple-ζ quality (ADF-basis set osition analysis (EDA) was performed with the use of the ADF2013.01 exes analyzed here and characterized by geometries resulting from the ations.The EDA method follows the energy partition of Morokuma ergy, ΔEint, between two fragments (A and B) in the A-B link, in the ce state and in the frozen geometry of AB is considered in this approach.y is divided into three components and the additional dispersion term, designates the Fock matrix element and (ε(σ ZF * ) − ε (π CC )) is the orbital energy difference.The similar equations (to Equation (1)) for the remaining above-mentioned orbital-orbital interactions may be given.
The energy decomposition analysis (EDA) [36,37] was carried out with the BP86 functional [60,61] in conjunction with the Grimme dispersion corrections (BP86-D3) [62] using uncontracted Slater-type orbitals (STOs) as basis functions for all elements with triple-ζ quality (ADF-basis set TZP).The energy decomposition analysis (EDA) was performed with the use of the ADF2013.01 program [63] for all complexes analyzed here and characterized by geometries resulting from the MP2/aug-cc-pVTZ optimizations.The EDA method follows the energy partition of Morokuma [36,37].The interaction energy, ∆E int , between two fragments (A and B) in the A-B link, in the particular electronic reference state and in the frozen geometry of AB is considered in this approach.The ∆E int interaction energy is divided into three components and the additional dispersion term, ∆E disp (Equation (2)): The ∆E elstat term corresponds to the electrostatic interaction between the unperturbed charge distributions of atoms and is usually attractive.The Pauli repulsion, ∆E Pauli , is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wavefunction which properly obeys the Pauli principle through explicit antisymmetrization and renormalization of the product wavefunction; it comprises the destabilizing interactions between electrons of the same spin on either fragment.The orbital interaction, ∆E orb , accounts for charge transfer and polarization effects.
Figure 6 presents the correlation between the interaction energy calculated within the MP2/aug-cc-pVTZ approach (Table 1), thus at the level corresponding to the systems' optimizations, and ∆E int DFT energy calculated with the use of ADF codes.The excellent correlation observed here partly justifies the use of DFT calculations for the previously optimized MP2 geometries.
The ΔEelstat term corresponds to the electrostatic interaction between the unperturbed charge distributions of atoms and is usually attractive.The Pauli repulsion, ΔEPauli, is the energy change associated with the transformation from the superposition of the unperturbed electron densities of the isolated fragments to the wavefunction which properly obeys the Pauli principle through explicit antisymmetrization and renormalization of the product wavefunction; it comprises the destabilizing interactions between electrons of the same spin on either fragment.The orbital interaction, ΔEorb, accounts for charge transfer and polarization effects.
Figure 6 presents the correlation between the interaction energy calculated within the MP2/augcc-pVTZ approach (Table 1), thus at the level corresponding to the systems' optimizations, and ΔEint DFT energy calculated with the use of ADF codes.The excellent correlation observed here partly justifies the use of DFT calculations for the previously optimized MP2 geometries.

Conclusions and Perspectives
The tetrel bonds in complexes where the π-electron system plays a role of the Lewis base were analyzed here.Practically for all complexes considered the NBO approach shows the existence of the πCC → σFZ * overlaps, however in a case of complexes of CFH3 with acetylene, ethylene and benzene the corresponding energies are negligible thus the existence of tetrel bonds is problematic.On the other hand for the remaining complexes the above-mentioned interactions are significant that may indicate the existence of the tetrel bonds.The QTAIM approach often shows the complicated topology, sometimes the additional bond paths corresponding to the hydrogen bonds are observed, or like for the CFH3-C5H5 − complex, only C-H•••C intermolecular link is observed that may indicate the existence of the hydrogen bond and not of the tetrel bond.However for the other cyclopentadienyl complexes the interactions are very strong and the Z•••C bond paths exist there.Hence there is no doubt that these complexes are linked by the tetrel bonds; all theoretical approaches applied in this study support the existence of such interactions in these complexes.
Only for some of acetylene and ethylene complexes one may observe the link between tetrel center and the site corresponding to π-electrons, NNA or BCP of the CC bond of the Lewis base unit (see the SnFH3-C2H2 and SnFH3-C2H4 complexes in Figure 1 as examples).In a case of the C6H6 and C5H5 -aromatic systems, the Z•••C bond path is observed that suggest the one-atom Lewis base center and not the π-electron system.It means that the existence of two types of tetrel bonds may be considered within the QTAIM approach, Z•••π and Z•••C.However other approaches applied here do not distinguish rather between these types.Such a situation was earlier observed for the hydrogen bonded complexes [50].

Conclusions and Perspectives
The tetrel bonds in complexes where the π-electron system plays a role of the Lewis base were analyzed here.Practically for all complexes considered the NBO approach shows the existence of the π CC → σ FZ * overlaps, however in a case of complexes of CFH 3 with acetylene, ethylene and benzene the corresponding energies are negligible thus the existence of tetrel bonds is problematic.On the other hand for the remaining complexes the above-mentioned interactions are significant that may indicate the existence of the tetrel bonds.The QTAIM approach often shows the complicated topology, sometimes the additional bond paths corresponding to the hydrogen bonds are observed, or like for the CFH 3 -C 5 H 5 − complex, only C-H•••C intermolecular link is observed that may indicate the existence of the hydrogen bond and not of the tetrel bond.However for the other cyclopentadienyl complexes the interactions are very strong and the Z•••C bond paths exist there.Hence there is no doubt that these complexes are linked by the tetrel bonds; all theoretical approaches applied in this study support the existence of such interactions in these complexes.
Only for some of acetylene and ethylene complexes one may observe the link between tetrel center and the site corresponding to π-electrons, NNA or BCP of the CC bond of the Lewis base unit (see the SnFH 3 -C 2 H 2 and SnFH 3 -C 2 H 4 complexes in Figure 1 as examples).In a case of the C 6 H 6 and C 5 H 5 -aromatic systems, the Z•••C bond path is observed that suggest the one-atom Lewis base center and not the π-electron system.It means that the existence of two types of tetrel bonds may be considered within the QTAIM approach, Z•••π and Z•••C.However other approaches applied here do not distinguish rather between these types.Such a situation was earlier observed for the hydrogen bonded complexes [50].
The question arises if the interactions analyzed theoretically here really exist.This is why the Cambridge Structural Database (CSD) [64] search was performed.The following search criteria were taken into account; non-disordered structures, R less than 10%, 3D coordinated determined, non polymeric structures, single crystal structures and no errors (CSD updates up to February of 2018 were taken into account).The additional condition was that the Z tetrel center (C, Si, Ge, Sn and Pb) has to form two intermolecular Z•••C contacts within corresponding sum of van der Waals radii.Two Z•••C contacts were required since one may expect that in a case of double and triple CC bonds, or if CC bond concerns delocalized aromatic system; at least two Z•••C distances within the van der Waals sum should be observed.218 systems of crystal structures fulfilling those requirements were found in CSD.However only in 10 cases the clear tetrel-CC bond contacts with the tetrahedral (sp 3 hybridized) tetrel center were observed which suggest the existence of the tetrel•••π-electrons interactions.Figure 7 shows an example where one can observe the F-Si•••CC contact (CC bond of the aromatic phenyl ring).This issue requires additional studies on the experimental crystal structures however.It seems that the search criteria could be also improved.More detailed study on experimental crystal structures' results is in the progress.
Molecules 2017, 22, x FOR PEER REVIEW 13 of 16 The question arises if the interactions analyzed theoretically here really exist.This is why the Cambridge Structural Database (CSD) [64] search was performed.The following search criteria were taken into account; non-disordered structures, R less than 10%, 3D coordinated determined, non polymeric structures, single crystal structures and no errors (CSD updates up to February of 2018 were taken into account).The additional condition was that the Z tetrel center (C, Si, Ge, Sn and Pb) has to form two intermolecular Z•••C contacts within corresponding sum of van der Waals radii.Two Z•••C contacts were required since one may expect that in a case of double and triple CC bonds, or if CC bond concerns delocalized aromatic system; at least two Z•••C distances within the van der Waals sum should be observed.218 systems of crystal structures fulfilling those requirements were found in CSD.However only in 10 cases the clear tetrel-CC bond contacts with the tetrahedral (sp 3 hybridized) tetrel center were observed which suggest the existence of the tetrel•••π-electrons interactions.Figure 7 shows an example where one can observe the F-Si•••CC contact (CC bond of the aromatic phenyl ring).This issue requires additional studies on the experimental crystal structures however.It seems that the search criteria could be also improved.More detailed study on experimental crystal structures' results is in the progress.Funding: Financial support comes from Eusko Jaurlaritza (GIC IT-588-13) and the Spanish Government MINECO/FEDER (CTQ2016-80955).Funding: Financial support comes from Eusko Jaurlaritza (GIC IT-588-13) and the Spanish Government MINECO/FEDER (CTQ2016-80955).

Figure 1
Figure 1 presents examples of complexes analyzed here.All kinds of Lewis bases that are considered are shown in selected examples of the figure.The molecular graphs are presented since they reflect geometry of species analyzed.However these graphs are discussed further here in the section on QTAIM results.

Figure 1 .
Figure1.The molecular graphs of the selected complexes analyzed here; big circles-attractors, small green circles-BCPs, the nonnuclear attractor (NNA) is located (small red circle) between two BCPs of the CC bond in a case of the SnFH 3 -C 2 H 2 complex.

Figure 2 .
Figure 2. The definition of the angle expressing the change of the tetrahedral structure into the structure being closer to the trigonal bipyramid.

Figure 2 .
Figure 2. The definition of the angle expressing the change of the tetrahedral structure into the structure being closer to the trigonal bipyramid.

Figure 3 .
Figure3.The linear correlation between the repulsion interaction energy and the sum of attractive terms (both in kcal/mol) for the ZFH3-B complexes analyzed here.

Figure 4 .
Figure 4.The linear correlation between the orbital interaction energy, ΔEorb, and the electron charge shift from the Lewis base unit to the Lewis acid (au).

Figure 3 .
Figure3.The linear correlation between the repulsion interaction energy and the sum of attractive terms (both in kcal/mol) for the ZFH 3 -B complexes analyzed here.

Molecules 2017 , 16 Figure 3 .
Figure3.The linear correlation between the repulsion interaction energy and the sum of attractive terms (both in kcal/mol) for the ZFH3-B complexes analyzed here.

Figure 4 .
Figure 4.The linear correlation between the orbital interaction energy, ΔEorb, and the electron charge shift from the Lewis base unit to the Lewis acid (au).

Figure 4 .
Figure 4.The linear correlation between the orbital interaction energy, ∆E orb , and the electron charge shift from the Lewis base unit to the Lewis acid (au).
3 -C 5 H 5 − complexes the H•••C intermolecular bond paths are observed which may be attributed to the C-H•••C hydrogen bonds!For the SiFH 3 -C 2 H 2 , SiFH 3 -C 2 H 4 and CFH 3 -C 6 H 6 complexes the non-linear bond paths are detected, similarly as for the CFH 3 -C 2 H 2 and CFH 3 -C 2 H 4 complexes, which are attributed to the Si•••C or H•••C intermolecular links (Table 4).In a case of the SiFH 3 -C 5 H 5 − complex the clear almost linear Si•••C bond path corresponding to the strong tetrel bond is observed, similarly as for the other ZFH 3 -C 5 H 5 − complexes for Z = Ge, Sn and Pb.In a case of the PbFH 3 -C 5 H 5 − complex the additional H•••C bond path corresponding to the Pb-H•••C hydrogen bond is observed (Figure 1).For the ZFH 3 -C 6 H 6 complexes (Z = Ge, Sn, Pb) the tetrel and hydrogen bonds are observed with the corresponding bond paths, the SnFH 3 -C 6 H 6 complex representing such a situation is presented in Figure 1.Similarly the SnFH 3 -C 2 H 2 , SnFH 3 -C 2 H 4 complexes in Figure 1 reflect the same situation in analogues tin and lead complexes; in the case of acetylene Lewis base the Z•••NNA bond path is observed while in the case of ethylene Lewis base this is the Z•••BCP bond path.Molecules 2017, 22, x FOR PEER REVIEW 10 of 16

Figure 5 .
Figure 5.The molecular graphs of the CFH 3 -C 2 H 2 and CFH 3 -C 2 H 4 complexes; big circles-attractors, small green circles-BCPs, the nonnuclear attractor (NNA) is located (small red circle) between two BCPs in a case of the CFH 3 -C 2 H 2 complex.

π
CC |F|σ ZF * Molecules 2017, 22, x FOR PEER REVIEW 11 of 16 •••B hydrogen bond; of the B Lewis base center and σAH * is the antibonding orbital of the Acase of the hydrogen bonds where π-electrons and σ-electrons play a •••π and A-H•••σ systems, the πB → σAH * and σB → σAH * overlaps, ortant orbital-orbital interactions [59].The similar situation occurs for , they may be classified as the Z•••π or Z•••C interactions (Z labels the * and πCC → σZH * •••B hydrogen bond; air of the B Lewis base center and σAH * is the antibonding orbital of the Aa case of the hydrogen bonds where π-electrons and σ-electrons play a -H•••π and A-H•••σ systems, the πB → σAH * and σB → σAH * overlaps, portant orbital-orbital interactions [59].The similar situation occurs for ere, they may be classified as the Z•••π or Z•••C interactions (Z labels the ZF * and πCC → σZH *

Figure 6 .
Figure6.The linear correlation between the MP2 Eint interaction energy and the ΔEint energy calculated within the DFT approach; both energies in kcal/mol.

Figure 6 .
Figure6.The linear correlation between the MP2 E int interaction energy and the ∆E int energy calculated within the DFT approach; both energies in kcal/mol.

Table 1 .
TheIf the Lewis acid unit is the same thus the interaction strength increases in the following orderC 2 H 2 < C 2 H 4 < C 6 H 6 < C 5 H 5− .One can also see that the -E int or -E bin values do not exceed 6 kcal/mol for all complexes of acetylene, ethylene and benzene while they are much greater in a case of complexes with cyclopentadienyl, especially large values are observed for the above-mentioned tin and lead complexes.
energetic parameters of complexes analyzed (in kcal/mol); interaction energy, E int , binding energy, E bin , deformation energy, E def and BSSE correction.The distance between Lewis base and Lewis acid units is included-the shortest Z•••C distance was chosen, the values in parentheses show if this distance is greater than the corresponding sum of van der Waals radii (positive values) or if it is lower (negative ones), distances in Å.

Table 2 .
The characteristics of complexes analyzed; ZF% and Angle% are the percentage increase of the Z-F distance and the percentage decrease of the F-Z-H angle, respectively; E NBO 1 and E NBO 2 are the NBO energies defined in the text (in kcal/mol); El-trans (au) is the electron charge transfer from the Lewis base to the Lewis acid while Z-charge is the charge of the Z-center in the complex considered (both charges in au calculated within NBO approach).

Table 4 .
The QTAIM parameters (in au) of BCP of the Lewis acid-Lewis base bond path; electron density at BCP, ρ BCP , its laplacian, ∇ 2 ρ BCP , and the total electron energy density at BCP, H BCP .The bond path type is also indicated.
[48]CBCP is observed since it amounts 0.015 au; note that for the medium in strength hydrogen bond in the water dimer the electron density at the H•••O BCP is equal to 0.023 au (MP2/6-311++G(d,p) results[48]).Additionally the H•••C intermolecular contacts correspond to the attractive electrostatic interactions since the carbon centers of the C 6 H 6 and C 5 H 5 − moieties are characterized by the negative electrostatic potentials (EPs) while the H-centers of the ZFH 3 species by the positive EPs.