On the Quantum Chemical Nature of Lead(II)"Lone Pair"

We discuss the quantum chemical nature of the Lead(II) valence basins, sometime called the Lead"lone pair". Using various chemical interpretation tools such as the molecular orbital analysis, Natural Bond Orbitals (NBO), Natural Population Analysis (NPA) and Electron Localization Function (ELF) topological analysis, we study a variety of Lead(II) complexes. A careful analysis of the results show that the optimal structures of the lead complexes are only govern by the 6s and 6p subshells whereas no involvement of the 5d orbitals is found. Similarly, we do not find any significant contribution of the 6d. Therefore, the Pb(II) complexation with its ligand can be explained through the interaction of the 6s2 electrons and the accepting 6p orbitals. We detail the potential structural and dynamical consequences of such electronic structure organization of the Pb (II) valence domain.


I Introduction
Since the Antiquity, Lead has been considered as a metal of prime interest. However, we now know more about its toxicity but many industrial applications still use it and environmental impacts are large. 1 For this reason, beyond the constant interest for a deeper understanding of the synthetic chemistry and associated properties of Pb(II) compounds, a strong motivation exists towards designing molecules capable to selectively chelate Pb(II) towards applications in Medicine 2,3 or in Environment. 4 If many efforts were dedicated towards the analysis of solid-state properties of lead-containing materials 5,6 , the fine comprehension of the Pb(II) coordination at a molecular level remains less documented 7,8,9,10 and theoretical computations have been shown to be important. Indeed, since the first calculation by Shimoni-Livni 11 which highlighted the possibility of holodirected and hemidirected geometries for complexes where Pb(II) is coordinated to four ligands, the origin of the lacuna in low coordinated lead complex has been discussed. Its origin has been linked to the orbitals involved in the complexation.
The highest occupied orbital is the full 6s and the lowest unoccupied the empty 6p. The s nature of the HOMO orbital theoretically does not allow any directionality of the electronic pair, so the origin of the lacuna is still under discussion. The first hypothesis was that the s electronic pair was polarized by the 6p orbital that would enable to create a hybrid "sp" lone pair. However, the nature of the orbital and the Natural bond orbital (NBO) analysis show that the p character of the electronic pair is very weak, being about only 5%. 11,12 Understanding this bonding pattern is very important as the tendency of the Lead(II) cation to exhibit a lacuna in its coordination sphere seems strongly linked to the cation's toxicity (i.e. the wellknown Lead poisoning). We have shown in a previous work 13 that what we called the "Lead lone pair" was at the origin of perturbation of proteins through its ability to restructure the metallic coordination sphere.
In a previous paper dedicated to series of Lead ligands, we have studied by mean of the Electron Localization Function (ELF) topological analysis the evolution of the volume and the density of Lead(II) valence basin. 14 We obtained a population larger than two showing that charge transfer could play a role in the emergence of a directional valence basin.
However, all calculations were performed using large core pseudopotentials in which the 5d electrons were merged in the core so that only the 6s electrons remain. Therefore, we were not able to investigate the possible role of these low lying 5d orbitals. In this contribution we propose to come back to the subject using all the available analytic tools to investigate the nature of the Lead(II) cation valence basin cation in order to determine the orbital involved within it. Then, we will extend our study to the flexibility of the hemidirected structures of lead complexes.

II Computational details
A first set of calculations have been performed using the TURBOMOLE package 15 at MP2 the level of theory using a def2-TZVP basis set 16 (with associated small core pseudopotential for Pb and I atoms) in gas phase. The quantum chemical results have been analyzed by means of Natural Population Analyses (NPA) and Natural Bonding Orbital (NBO) analyses. 17 To   perform the topological analyses, we extracted the TURBOMOLE optimized geometries and   computed the wavefunction with GAUSSIAN09 version D01 package 18 within the B3LYP 19 formalism with the same basis set.
On the basis of this wavefunction, ELF (Electron Localization Function) calculations and the topological analysis of the ELF functions, together with specific integrations, have been performed using the TopMod package. 20,21,22,23,24,25,26,27 We here just recall that within the framework of the topological analysis of the ELF function, space is partitioned into basins, each of them having a chemical meaning. Such basins are classified as: i) core basins surrounding nuclei, ii) valence basins characterized by their synaptic order. 21 Further details can be found in the above-mentioned references.
It has been shown possible to extend the ELF approach to pseudopotential approaches. 28 Using small-core pseudopotentials provides the so-called semi-external cores and allows to determine the synapticity of well-defined valence basins. 29 Using large-core pseudopotentials preserves the number and the properties of valence basins. Only small core pseudo potential have been used. In the present contribution, we will focus on V(Pb), the valence monosynaptic basin associated to the valence electrons of Pb(II). For a given complex [Pb(II)Ln] q , we will use the following notations: V(Pb) is the ELF basin defined previously, N(Pb) and ω(Pb) are respectively the population and the volume associated to this basin. A last parameter is the distance d(Pb) between the ELF attractor of lead valence basin V(Pb) and the lead cation itself We want to point out, that for ligands in the first coordination sphere, there are very few observed differences for the bond lengths between the different methods. In practice, the values are closed to those already published as illustrated by the Table S1 ESI.

III Results and discussion
We performed full geometry optimization on several Lead complexes. First is the [Pb(CO)n] 2+ series, which is easy to analyze thanks to ligand rigidity. Second come complexes with various organic or inorganic ligands. All these complexes are a small sample of the potentially existing Lead complexes however they have all been studied and represent a variety of coordination modes and conformations. On all these complexes, we have studied the involvement of Lead orbitals in the coordination and on the complex topology.
Pb(II) electronic configuration is [Xe] 4f 14 5d 10 6s 2 6p 0 . The 4f shells are very deep, their absolute energies being about -3600 kcal/mol (4f7/2) and -3720 kcal/mol (4f5/2) 32 . From a chemical point of view, they are considered as inert and are included in the core potential. The 5d orbitals present a much higher energetic: -650 kcal/mol (5d5/2) and -714 kcal/mol (5d3/2). However, they remain low in energy, back-donation or electron promotion from these orbitals was checked: they are directional and can mix efficiently with the ligand p orbitals as frequently observed in transition metal complexes. 33 The population of full 5d orbitals or empty 6d orbital was checked through NBO analysis (from the MP2 calculations) for the whole series of complexes studied. The 5d orbitals are weakly depopulated and this depopulation seems to be independent from the ligand: there are 9.87 electrons in these The occupation of these orbitals almost does not differ from that of the isolated Pb 2+ cation and is furthermore almost ligand independent. As a conclusion, these orbitals are not involved in the bonding and will not be discussed any further. The true valence orbitals are therefore the full 6s1/2 (-355 kcal/mol) and the empty 6p orbitals: -138 kcal/mol (6p3/2) and -172 kcal/mol (6p1/2) that will be the focus of our study.
These two sets of orbitals are the most important as the 6p will accept electrons from donating ligands and the full 6s orbital thanks to its diffuseness will prevent a too short approach of the ligand. Their role has been discussed 11 and it has been shown that in the presence of a ligand field the external valence shell of the cation distorted to allow a close contact with the ligands. Therefore at this point the questions of the precise nature of the Lead(II) valence basin and of the concrete structural and dynamical consequences of its existence remain to be addressed.

III.1 Structures and properties of lead complexes
Different sets of Pb(II) complexes were investigated to test the influence of several parameters on the geometries. First, we recall the results for the [Pb(CO)n] 2+ series (n=1 to 6) which topology will be explored further. Then we compare the structures of [Pb(X)3]complexes (X = HO -, CN -, HS -, H -, Cl -) to understand the influence of the anion on the structure. On the [Pb(CO)n] 2+ series, we retrieve the results previously published 34 : from n=1 to n=3, the Pb-C distances are insensitive to n (see Table 1). We observe a small depopulation of the 6s orbital (less than 0.1 electrons) and a steady increase of the 6p electron population.
However, it should be noticed that this 6s depopulation increases from n=1 to n=3 and is almost nil for higher coordination numbers. This could be linked to the presence of close carbonyl that destabilize the 6s orbital to ensure coordination. Starting from coordination number 4, the Pb-C distances are no longer identical. In [Pb(CO)4] 2+ complex, there are two short distances and two longer. The latter corresponding to the two CO being in trans position and the former to CO for which there are no ligand in trans position. As the lengthening of the Pb-C distances diminishes the interactions, the 6s population is allowed to increase whereas the 6p population exhibit a more modest increase as the long Pb-C distances disfavor the ligand donation. The general shape of the complexes is a butterfly for n=4, square based pyramid for n=5, the lead cation being outside the square plane and a perfect octahedron for n=6. Interestingly, even for n=2, the structure deviates from the ideal 90° for the C-Pb-C angle, the value is smaller, despite the ligand-ligand repulsion showing that it is not this interaction that governs the structure.

population (N(Pb) in electrons) of lead valence basin and distance (d(Pb) in Å) of the V(Pb) ELF attractor and cation.
The second series of complexes studied is [Pb(Cl)n] q with n = 1 to 4 ( Figure 1). All attempts to optimize higher coordinated structure led to ligand decoordination. The Pb-Cl distances are shorter than the Pb-C distances (see Table 2) and we can link this to the slightly larger 6s    [ Finally, we compare the structure of a series of Pb(L)3 complexes, either dicationic or monoanionic (Table 3).       Figure 3). This suggests that when searching a new ligand to extract lead from a media, not only the direct coordination sphere has to be considered but also a positive pole may play a role to complex this coordination sphere.

III.3 Topology and nature of interactions
In a previous work, we have shown that the presence of the lead valence controls the structure of lead complexes. Especially, this basin explains the deactivation of a zinc finger metalloenzyme 13 or the structure of various complexes. We were able to correlate its properties (volume and density) to the nature of the ligand and also to put in evidence some unsuspected effect on the ligand like with thiocyanate ligand 14 .
The ELF basins structures of Lead are strongly dependent on the cation coordination sphere.
As we use a pseudopotential for our calculations, the computed ELF basins only contain the 5s, 5p, 5d, 6s and 6p shells.  Upon ligand coordination, the valence basin is highly distorted. When a ligand binds to the cation, the basin population increases due to the 6p population. Furthermore, these orbitals being directional, they allow for the distortion of the basin, which is repelled to the opposite side of the ligand. In a multi-ligated complex, the valence basin tends to localize in the area of the weakest ligand field. This means that for low coordination (n = 1 to 3), the ligand field  11 , it seems that more the ligand is σ-donor, the higher the probability for the structure to be holodirected. It is the case for the halide (except fluoride) or for the hydride and H3C -. To our knowledge, for n = 5, the complex have only been observed in a hemidirected structure, forming an octahedron in which the valence basin localizes in the lacunary position. For n = 6, the complex is holodirected. Table 2  For these compounds there are three valence basins. The description of Pb2+ valence basins cannot be easily reduced to a hybridized sp 3 lone pair, it is much more versatile.

Figure 5 : Position of the V(Pb) attractors (top) and associated ELF isosurface (η η η η=0.59, bottom) of [Pb(OH2)3] 2+ (left) and [Pb(OH)3] -(right) complexes.
From Table 1 and Table 2, it is shown that this attractor goes further from the cation up to n=3 then its distances does not evolve any longer in the hemidirected structures. This is the effect of the Pb 2+ polarization due to the ligand field. This is confirmed by Table 3 This valence basin arising from the polarization of the Pb 2+ external electronic shell traduces an excess of electronic density trans to the more σ-donor ligand. In consequence, there will be a discrimination on the ligand which can bind on the cation: the less donating will be expelled from the coordination sphere when being in trans to a stronger donor group. This is illustrated by the [Pb(CO)3(CN)3]complex in which the neutral CO are unstable in the first coordination sphere. This valence basin will also have further consequence on the organization of the cation second coordination sphere. As already mentioned, this valence basin forms an electronic shield preventing further coordination on this position. However, we attempted to approach an HCl molecule on the cation either through the chlorine atom or through the hydrogen atoms. The structure with the hydrogen atom pointing toward the lead (Pb-H distance at 2.781Å) is more stable by 4.3 kcal/mol than the conformer (Pb-Cl distance at 3.941 Å). The NCI analysis performed on the optimized structures ( Figure 2) shows the presence of an attractive electrostatic force between the ELF valence basin of the cation and the hydrogen valence basin of the HCl. This traduces that the cation valence basin occupying the complex lacuna can be described as a negative pole which is able to interact with positively charged fragment mimicking a sort of hydrogen bond as suggested by Hancock. 36 Furthermore, it should be noticed that all the structures discussed until now have been

III.4 Interconversion barriers
The hemidirected character of the [Pb(L)3] q complexes (isostructural to NH3) implies the existence of two conformer separated by an interconversion barrier. For some complexes, we have computed the transition state between the two minima and determined this barrier. These calculations have been performed with GAUSSIAN. Surprisingly, the transition state for the interconversion of most complexes is not of D3h but adopt a T-shape ( Figure 7).
Consequently, the three Pb-L distances are not identical with one short and two long for the two ligands in trans position. Only the mono atomic ligand (H -, Fand Cl -) exhibits a D3h transition state.
The interconversion barrier is strongly dependent of the ligand ( Table 4 Table 2). The T-shape structure for the TS allows to weaken only two of the lead -ligand interactions. The geometry can also be as square planar complex in which one of the positions is occupied by the valence basin ( Figure 3).   To explore further the relationship between the interconversion barriers (Table 4)

IV Conclusion
In this contribution, we have studied the nature of the lead valence basins and especially what we call lone pair in previous studies. Through molecular orbital analysis, NBO and NPA analyses and study of molecular contribution to ELF basin, we have shown that the structures of the lead complexes were only govern by the 6s and 6p subshells. No involvement of the d orbitals has been observed: the depopulation of the 5d orbitals is small and does not seem to be ligand dependant according to NBO analysis and charge transfer to the empty 6d is negligible. The 5d subshell is too low in energy and too contracted to interact with the valence orbital of the ligands. Similarly, the 6d orbitals are too high in energy and does not contribute.
The complexation of Pb 2+ can be explained through interaction with the 6s 2 electrons and the accepting 6p orbitals.
The number of ELF attractors depends on the nature of the Pb 2+ ligands, the less donor ones (essentially the neutral ones as OH2) generate three attractors, whereas the stronger σ-donor generate only one attractor. It is thus difficult to reduce the presence of the valence basin to a hybridized sp 3 lone pair, due to the weak contribution of the p orbitals to this lone pair as already shown by Shimoni. 11 The existence of this valence basin has structural and dynamic consequences. Generated by the promotion of 6s electrons to the 6p orbitals and by the σ-donation from the ligand, its volume and population will increase with the strength of the Pb-L interaction.
Simultaneously, the distribution of the ligand will be governed by the trans effect. This means that if a strong σ-donor ligand binds to Pb 2+ , the position in trans (considering an octahedron) will be destabilized as we observed on our attempt to optimize the [Pb(CN)3(CO)3]complex.
Also, this imposes that a second σ-donor ligand will bind preferentially in cis position. This is due to the polarization of the valence basin of lead, which is repelled trans to the ligand and strongly weakens the electrophilicity of the cation in this position in the sense that locally the electronic density increases. In [Pb(L)3] q complexes, this can even lead to local nucleophilicity as illustrated by the preference for an interaction with the H atom of HCl of the [Pb(CN)3]complex. This opens the way for the design of new families of specific ligand for Pb 2+ having a positive pole in their structure.
Other consequences concern the dynamical effect of this lone pair. To our knowledge, no