Three‐electron two‐center bonding in cycloimmonium ylides

Abstract

ABSTRACT:We explore the possibility that a 3-electron-2-center bonding exists in cycloimmonium ylides. To detect this bonding in a polyatomic system, 3-electron-1-hole density operators, characterizing a Pauling 3-electron bond, are used in the framework of second quantization formalism. The weights of 3-electron resonance structures are calculated and compared with the weights of 2-electron structures for the ylide bond of pyridinium dicyanomethylide; the correlations of (12) and (1) electronic events, involved in the 3-electron resonance structures, are also investigated. The calculations are performed in various approximation levels, and both orthogonal and nonorthogonal natural atomic orbitals are adopted. All calculations show that a 3-electron bond exists between N and C atoms of ylide bond, but this bonding is not extended in C atoms of the pyridinium group. The interactions of ␣,␤ electrons (at the configuration interaction [CI] level) increase the localization of electrons, the weights of 3-electron resonance structures, and thus the probability for 3-electron bonding.

Control of delocalization and structural changes by means of an electric field

“…The same process holds for both orthogonal and non-orthogonal NAOs, but in the present work we used orthogonal ones, because the comparison of results obtained by means of these two types of NAOs for p systems shows that both are totally equivalent, leading to the same conclusions. 20,21 In a totally different context, the equivalence of using orthogonal and nonorthogonal orbitals is explored within a CASVB (Complete Active Space VB) framework.…”

“…where W(D 1 ) is the weight of the spin-dependant local determinant D 1 ¼kj 2 j 3 j 4 j 4 ... s i s 1 ... k. Since the employment of orthogonal and non-orthogonal NAOs in p systems provides totally equivalent results, 20,21 for simplicity we used the orthogonal ones. The weight W(D 1 ) is calculated as the expectation value of the following density operator ða 1 a" 1 a…”

“…4-8 Such a type of investigations began by introducing the generalized Wiberg indices, 5a which are proportional to exchange correlations. In this context, the behavior of electron pairs can be examined by means of exchange correlations in natural orbital spaces, 8,10,20 which can be used for a quantitative estimation of the weakness or reinforcing of chemical bonds. In the present work we have considered the influence of the electric field in electron pairing by examining exchange correlations, which Figure 5.…”

“…Let O is the region defined by centers V and W; the fluctuations, in this region, L(O), symbolized also as L(V,W), provide a measure of the degree of the localization of electrons between two p centers V and W, and are calculated as follows 8,10,20 :…”

“…[4][5][6][7][8][9] The two-and poly-electron distributions as well as the corresponding local structures, describing various types of delocalization and correlation, [10][11][12][13] can be approached by means of the general methodology of poly-electron population analysis (PEPA). [14][15][16] The employed quantum chemical methods and the corresponding computer codes hold for any type of orbitals, but the development of the multi-determinantal molecular wave functions in the basis 17,18 of NBOs or natural atomic orbitals (NAOs) 19 offers the possibility to approach and describe electronic structures 11,12,20,21 inspired from valence bond (VB) 22,23 theory. In a totally different context, the localization (and, thus, the delocalization) in threedimensional spaces can be investigated by means of electron localization function, which is revealed to be a quite useful tool for analyzing chemical bonds in coordinate space.…”