ELF analysis

These features are reasonable. The shortening of bond distances is associated with increased valency. The non-VSEPR geometry is understandable in terms of MO and ELF analysis. The implication of the ligand is associated... 

This work has been accomplished in the framework of GDR "Dynamique Moleculaire Quantique Appliquee a la Catalyse" financial support of the French Ministry of Education. Technology and Research is gratefully acknowledged. We are grateful to Pr. B. Silvi for his help in the ELF analysis. We thank CNRS-IDRIS for computing facilities. 

In two recent works the phosphorus analogues of pyridones 109-111 (Scheme 58) have been studied computationally [317, 318], 110 is planar, while for 109 and 111 the planar structures are transition states with 11.0 and 19.8 kcal moH above the nonplanar minimum, respectively. The low barriers to inversion indicate that the planar structures have considerable aromaticity, which is shown by the NICS values exhibiting 67%, 51%, and 33% of the benzene value for 109,110, and 111, respectively [317], ELF analysis also indicates a certain aromaticity in these compounds [317], The bonding situation in 109 is similar to the cyclic phosphinocarbene isomer of phosphinine 112 [319] (Scheme 59), which was shown to be planar and aromatic. Stabilization of this carbene can be achieved by incorporating it to an anne-lated ring system 113, and also by the electron donor effect of an ylide formed with an additional o4,l5-P (114) [319],... 

Several alternatives to the Mulliken population have been presented that attempt to provide more rigorous estimates of the charges on atoms in molecules or clusters although not all have been applied in chemisorption and catalysis. We quote the Natural Bond Order analysis, and the elegant topological analysis of the electron density or of the electron localization function, ELF, introduced by Becke and Edgecombe. " ELF analysis has... 

ELF analysis has been probed to be a powerful scheme to elucidate between the pericyclic and pseudopericyclic character of bonding at concerted transition states. In this context, ELF methodology has been recently applied to get new insights concerning the nature of bonding at the transition states of the thermal electrocyclization of (Z)-l,2,4,6-heptatetraene (X=CH2) and its heterosubstituted analogues, (2Z)-2,4,5-hexatrienal (X=0) and (2Z)-2,4,5-hexatrien-l-imine (X=NH) (see Scheme 2).67... 

Scheme 4 [ls,3a]hydrogen, [la,3s]methyl and [la,3s]fluorine sigmatropic rearrangements in the allyl system. ELF analysis reveals a concerted interaction in the first case, a biradical interaction in the second one and a ion-pair interaction in the last one... 

We would also like to mention here that ELF analysis has been also found valuable into the detailed description of intramolecular proton-transfer reactions in some thiooxalic acid derivatives HY-C(=0)-C(S)-XH, (1) X=0,Y=0 (2) X=0, Y=S (3) X=S, Y=S, depicted in Scheme 6.85... 

In all these cases, ion-pair transition structures have been characterized, and the intimate nature of bonding has been discussed using the electron properties arising from ELF analysis. In particular, charge separations of 0.48e, 0.42e and 0.18e can be deduced from the basin structure and populations for the oxygen to oxygen, sulfur to oxygen and sulfur to sulfur proton-transfer transition states, respectively. 

Some general aspects related to the derivation, and interpretations of ELF analysis, as well as some representative applications have been briefly discussed. The ELF has emerged as a powerful tool to understand in a qualitative way the behaviour of the electrons in a nuclei system. It is possible to explain a great variety of bonding situations ranging from the most standard covalent bond to the metallic bond. The ELF is a well-defined function with a nice pragmatic characteristic. It does not depend neither on the method of calculation nor on the basis set used. Its application to understand new bond phenomenon is already well documented and it can be used safely. Its relationship with the Pauli exclusion principle has been carefully studied, and its consequence to understand the chemical concept of electron pair has also been discussed. A point to be further studied is its application to transition metal atoms with an open d-shell. The role of the nodes of the molecular orbitals and the meaning of ELF values below 0.5 should be clarified. 

In this section, ELF analysis for NII3R systems (with R = H, CH3,NH2,OH) and molecular complexes of N2II7 is presented. The color convention for all pictures is green for NH bonds, blue for lone pair electrons, and red for Rydberg electrons. Note that in some figures there are small red dots which correspond to core electrons. These features will be ignored in tables and in qualitative descriptions. 

Figure 6 ELF analysis along the reaction profile for internal conversion of NH4 DRA to H NH3 complex...

The strength of the intramolecular hydrogen bond can be estimated within the ELF analysis by the core valence bifurcation index AHB . This index is defined as the... 

Finally, some of the unexpected results revealed for iodophenols warn against the use of large core pseudopotentials in the ELF analysis. It is noteworthy that the analysis of the topology of the ELF enables us to predict favoured protonation sites with the help of a least topological change principle which will be discussed in a following section. 

In the present study, we consider the bond analysis in metal porphyrins. In the following discussion, the porphyrin will be often indicated as phy. We apply Electron Localization Function (ELF) analysis and Maximum Probability Domains (MPDs) analysis for understanding the eventual differences between transition metal and non-transition metals inserted into the porphyrin ring. As an example of nontransition metal, we consider Be, Mg, and Zn (a d metal, so d orbitals can be considered core-Uke). For transition metals, we consider Fe, Co, and Ni. Due to the difficulties in finding experimental examples of pure square planar coordination... 

Fig. 12 ELF profiles along the N-M-N segments. Left plot refers to Mg phy left), right plot refers to Ni phy. From left to right of each plot, the following ELF localization domains are distinguishable N core, N lone pair. Metal outer and inner core, N lone pair and N core. The ELF analysis provides the same picture for the non-transition and the transition metal compound...

The topological analysis of the density and of the ELF funetion provides new information to understand the nature of the Si-0 bond. On the one hand, the atomic population and the bond ellipticities tell us that the SiO bond is partly ionic and also that there is no evidence for a partial double bond character. This latter point is confirmed by the analysis of the ELF function since there is only one attractor between the oxygen and silicon cores and that its basin population is always less than or equal to 2 electrons. Moreover, it appears more important to consider the oxygen than the silicon to discuss the bonding in silica. The Si-0 bond is found to belong to the electron shared interaction by the ELF analysis. 

In his review on highly polar metal-metal bonds in early-late heterodi-metalhe eomplexes Gade expected the topological approach to find more widespread use in future studies of metal-metal bond polarity. A consistent picture of the nature of the Ti-Co bonds in dinuclear complexes was obtained by a combination of AIM and an ELF analysis. The covalent metal-metal bond order was less than 0.5, and high partial charges of > 0.5e emphasized the highly polar character of the Ti-Co bonds. 

Joubert et al presented a systematic study of the structural and bonding properties of selected lanthanide trihalide molecules, LnXa (Ln = La, Gd, Lu X = F, Cl). An ELF analysis revealed typical ionic bonding properties, emphasizing the increasing ionic character of the Ln-X bonds through the rare-earth series. Moreover the authors pointed out a strong distortion of the outer core shell of the metal. 

Fuster et performed a topological ELF analysis to investigate electrophilic aromatic substitution. In the case of /r-donor substituents the aromatic domain is first opened elose to the substituted C and then in the vicinity of the meta C, whereas for attractor substituents it is first opened in the ortho and para... 

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