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

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.

Superposition of waves or densities: Which is the nature of chemical resonance?

Resonance is a fundamental and widely used concept in chemistry, but there exist two distinct theories of chemical resonance, based on quite different and incompatible premises: the wave-function-based resonance theory (WFRT), assuming the superposition of wave functions, versus the density-matrix-based resonance theory (DMRT), which interprets the resonance phenomenon as the superposition of density matrices. The latter theory, best known to the chemistry community as the natural resonance theory (NRT), has received much more popularity than the WFRT. In this contribution, the DMRT is shown to be inherently inadequate: (i) the exact density matrix expansion is mathematically impossible unless unphysical negative weights are introduced; (ii) any approximate density matrix representing the resonance hybrid lacks the idempotent property. Therefore, the validity of the NRT ansatz should be seriously questioned. The WFRT seems the only reasonable explanation of resonance so far, and has been shown to provide valuable insights into diverse chemical problems.

A reliable and efficient resonance theory based on analysis of DFT wave functions

Due to methodological difficulties and limitations of applicability, a quantitative bonding analysis based on the theory of resonance is presently not as convenient and popular as that based on the molecular orbital (MO) methods. Here, we propose an efficient quantitative resonance theory by expanding the DFT wave function in terms of a complete set of Lewis structures. By rigorously separating the resonance subsystem represented by a set of localized MOs, this approach is able to treat large molecules, nonplanar π-conjugate systems, and bonding systems mixing both σ and π electrons. Assessment in 2c-2e systems suggests a new projection-weighted symmetric orthogonalization method to evaluate the weights of resonance contributors, which overcomes the drawbacks of other weighting schemes. Applications to benzene, naphthalene and chlorobenzene show that the present method is insensitive to the basis set employed in the DFT calculations, and to the choices of the independent Lewis set determined by Rumer's rule. Advanced applications to diverse chemical problems provide unique and valuable insights into the understanding of hydrogen bonding, the π substituent effect on benzene, and the mechanism of Diels-Alder reactions.

NBO 7.0: New vistas in localized and delocalized chemical bonding theory

We briefly outline some leading features of the newest version, NBO 7.0, of the natural bond orbital (NBO) wavefunction analysis program. Major extensions include: (1) a new NPEPA module implementing Karafiloglou's "polyelectron population analysis" in the NBO framework; (2) new RDM2 program infrastructure for describing electron correlation effects based on full evaluation of the second-order reduced density matrix; (3) improved convex-solver implementation of natural resonance theory (NRT), allowing a greatly expanded range of applications and associated "resonance NBO" (RNBO) visualization of chemical reactivity; (4) a variety of other improvements in well-established NBO algorithms. We also provide brief introduction to the new NBOPro@Jmol utility program, a plugin to the Jmol chemical structure viewer that serves as a convenient tool to provide on-demand NBO descriptors or orbital visualizations for a broad variety of chemical inquiries in research or classroom applications. © 2019 Wiley Periodicals, Inc.

Study of Electron Delocalization in 1,2-, 1,3-, and 1,4-Azaborines Based on the Canonical Molecular Orbital Contributions to the Induced Magnetic Field and Polyelectron Population Analysis

The electron delocalization in 1,2-azaborine, 1,3-azaborine, and 1,4-azaborine is studied using canonical molecular orbital contributions to the induced magnetic field (CMO-IMF) method and polyelectron population analysis (PEPA). Contour maps of the out-of-plane component of the induced magnetic field (Bz(ind)) of the π system show that the three azaborines, in contrast with borazine, sustain much of benzene's π-aromatic character. Among them, 1,3-azaborine exhibits the strongest π delocalization, while 1,4-azaborine is the weakest. Contour maps of Bz(ind) for individual π orbitals reveal that the differentiation of the magnetic response among the three isomers originates from the π-HOMO orbitals, whose magnetic response is governed by rotational allowed transitions to unoccupied orbitals. The low symmetry of azaborines enables a paratropic response from HOMO to unoccupied orbitals excitations, with their magnitude depending on the shape of interacting orbitals. 1,3-Azaborine presents negligible paratropic contributions to Bz(ind) from HOMO to unoccupied orbitals transitions, where 1,2- and 1,4-azaborine present substantial paratropic contributions, which lead to reduced diatropic response. Natural bond orbital (NBO) analysis employing PEPA shows that only the 1,3-azaborine contains π-electron fully delocalized resonance structures.

An efficient generalized polyelectron population analysis in orbital spaces: the hole-expansion methodology

We present relations leading to an efficient generalized population analysis in orbital spaces of usual delocalized molecular orbital wave functions. Besides the calculation of the diagonal elements of the reduced density matrices of any order, one can also calculate efficiently the probabilities (or, in general, the weights) of various occupation schemes of local electronic structures, by using generalized density operators referring to both electrons and electron holes. Within this population analysis, correlated molecular orbital wave functions can be used, and there are no restrictions to the number of the analyzed electrons and electron holes. It is based on the hole-expansion methodology, according to which a given electronic population is expanded in terms involving only electron holes, which as shown, can be calculated very efficiently; usual difficulties arising from the necessity to handle extremely large local determinantal basis sets are avoided, without introducing approximations. Although an emphasis is given for populations in the basis of orthogonal orbital spaces (providing probabilities), the case of nonorthogonal ones is also considered in order to show the connection of the generalized populations and the traditional weights obtained from valence-bond wave functions. Physically meaningful populations can be obtained by using natural orbitals, such as the natural atomic orbitals (NAOs) (orthogonal orbitals) or the pre-NAO's (nonorthogonal orbitals); numerical applications for pyrrole molecule are presented in the basis of these natural orbitals.

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

The strength and, mainly, the direction of a static electric field can be used to control delocalization effects occurring in a non-polar pi-system. The delocalization energy, the weights, and the probabilities of some local electronic structures, the behavior of electron pairs, and the electronic fluctuations are considered and examined in cis-butadiene, used as model system. The effects of the electric field are detected and evaluated in the basis of natural orbital spaces appropriate to investigate the behavior of one- and poly-electron distributions. The consequences of modifying the delocalization effects on structural changes are also investigated. Full geometry optimizations in both Hartree-Fock and MP2 levels show that the changes in bond lengths, guided by the changes of the behavior of the electronic assembly, can be controlled by means of the electric field.

A New Analysis of Molecular Orbital Wave Functions Based on Resonance Theory

A new method to evaluate the weights of resonance structures from molecular orbital wave function is proposed, which is based on the second quantization of singlet-coupling. The present method is useful to analyze molecules of which the electronic structures are well localizable. The evaluation is carried out through localization of molecular orbitals followed by algebraic calculation of density matrices. This method is applied to H(2)O, H(3)O(+), and BH(3). The calculated weights of covalent and ionic structures are in excellent agreement with those of the previous works and our chemical intuition.

The behavior of transition metal nitrido bonds towards protonation rationalized by means of localized bonding schemes and their weights

A new computational scheme is applied to rationalize the different protonation behaviors of the nitrido complexes [L'Mn(V)(N)(acac)](+), [LCr(V)(N)(acac)](+), and [LV(V)(N)(acac)](+). L and L' represent the macrocycles 1,4,7-triazacyclononane and its N-methylated derivative, respectively, and acac is the bidentate monoanion pentane-2,4-dionate. The bonds of the complexes are partitioned into bonds to be investigated and bonds of lesser interest. The investigated bonds are the transition metal nitrido bonds M(V)[triple chemical bond]N| (M = Mn, Cr, and V) and the bonds of lesser interest are located in the ligands. The ligand bonds are described by means of the strongly occupied natural bond orbitals. The electrons in the M(V)[triple chemical bond]N| nitrido bonds, however, are treated more accurately. A full configuration interaction procedure is applied in the space spanned by the strongly occupied natural bond orbitals and their corresponding antibonding orbitals. Localized bonding schemes and their weights are obtained for the d(pi)-p(pi) bonds of interest. This is achieved by representing the two-center natural bond orbitals for a d(pi)-p(pi) bond by the one-center natural hybrid orbitals localized at the bond atoms. The obtained bonding schemes are close to orthogonal valence bond structures. Their weights indicate that the nitrido nitrogen in [LV(V)(N)(acac)](+) is more easily protonated than the nitrido nitrogens in [L'Mn(V)(N)(acac)](+) and [LCr(V)(N)(acac)](+). This result is in good accord with experiment.