An analysis of valence electronic structure from a viewpoint of resonance theory: Tautomerization of formamide and diazadiboretidine

Abstract

The resonance theory is still very useful in understanding the valence electron structure.However, such a viewpoint is not usually obtained by general-purpose quantum chemical calculations, instead requires rather special treatment such as valence bond methods. In this study, we propose a method based on second quantization to analyze the results obtained by general-purpose quantum chemical calculations from the local point of view of electronic structure and analyze diazadiboretidine and the tautomerization of formamide. This method requires only the "PS"-matrix, consisting of the density matrix (P-matrix) and overlap matrix, and can be computed with a comparable load to that of Mulliken population analysis. A key feature of the method is that, unlike other methods proposed so far, it makes direct use of the results of general-purpose quantum chemical calculations.

Solvation in nitration of benzene and the valence electronic structure of the Wheland intermediate

“…We are interested in the four-electron π-valence electronic structure of the σ-complex. We outline the analysis method of valence electronic structures 31 for discussion in Section 3.4. This analysis is basically based on the mapping of molecular orbital (MO) type wave functions into resonance structures or VB type functions.…”

“…Since ASOs are distributed on atomic sites, the weight of an ASO-determinant is identified as the weight of the corresponding “resonance structure”. Here, the analysis method developed by us 31 is used to evaluate w i . For a single determinant case, the weight w of any ASO-determinant of the type of | χ α a χ α b χ β c χ β d | where χ σ μ is the ASO ( σ and μ are the spin and spacial labels, respectively) can be represented with the σ -spin density matrix P σ and overlap matrix S of the atomic orbital basis set as w (| χ α a χ α b χ β c χ β d |) = {( P α S ) aa ( P α S ) bb − ( P α S ) ab ( P α S ) ba } × {( P β S ) cc ( P β S ) dd − ( P β S ) cd ( P β S ) dc }.…”

“…The present method has been used successfully to analyse the wave functions of various molecules, and the results showed good agreement with ab initio VB results. 31…”

“…Ab initio valence bond (VB) methods are powerful tools to tackle this issue, and an interesting explanation of substitution effects on electrophilic aromatic substitutions was discussed. 29 We applied the recently proposed scheme of analysis, 31 briefly described in the next section, to reveal the valence π-electronic structure of the σ-complexes. Additionally, how solvation affects the electronic state is one of the issues, providing a way of qualitative understanding of the σ-complex.…”

Extraction of local spin-coupled states by second quantized operators

“…Notably, the present representation is closely related to the standard "Mulliken-type" partitioning, 8 utilized for the Mulliken population, 29 Mayer bond order, 28,30 and the recently reported quantity referred to as the "weight of resonance structure." 31 All of them can be formulated in the same second quantized formalism, and the correspondence between these quantities can be discussed on equal footing.…”