Investigating the possibility of simultaneously finding an electron-hole and an electron-pair in a molecule: Delocalization,competition of ionic vs. covalent character,and related effects in push–pull ethylenes

This work examines the possibility of finding an electron-hole and an electron-pair simultaneously in a π-system substituted by an electron-donating (NH₂) and/or electron-withdrawing (NO₂) group. The contributions of various ionic [(+), ( ↑ ↓ )] structures are calculated from ab initio SCF –CI wave functions, using a recently developed general multielectron population analysis. The molecules studied are two monosubstituted ethylenes, aminoethylene and nitroethylene, and a disubstituted ethylene, the 2-nitroethenamine (push–pull ethylene) in its two configurational forms. The influence of the NH₂ and/or NO₂ group in delocalization and ionic (vs. covalent) character of the C?C double bond are investigated, along with examining the experimental chemist formalism of electron-pair “displacements” in several resonance structures. Analysis of mutual dependence of an electron-hole and an electron-pair, at short and long distances, leads to the conclusion that a push–pull π-system can stimulate the simultaneous existence of an electronhole and an electron-pair even for nonvicinal positions. The relationship between the electronpair distributions and contributions of the corresponding structures are also examined; the effects of electronic correlation are analyzed as well. © 1992 John Wiley & Sons, Inc.     

Simultaneous presence of two charges or two spins in a linear polyene

Summary In this work we examine the ease of finding simultaneously two charges or two spins in various AO positions of a linear neutral polyene such as octatetraene. By applying the general multi-electron population analysis on a correlated wave function we calculate contributions from various ionic and covalent (in a probabilistic sense) resonance structures as well as electron-pair distributions with parallel and anti-parallel spins; the initial wave function used is a PPP + (quasi-total) CI wave function. Based on the second and fourth order anticommutation relations (and independently of the level of the MO wave function used) we show existing relationships between the quantities considered, as well as their constant behaviour. Covalent structures depend strongly on the parity and distance between the AO positions, while ionic ones arequasi-constant along the polyene. It is also shown that when the AO positions considered are non-vicinal, (+) and (–) charges appearmutually independent and the -electron conjugation has, rather surprisingly, no effect on them.     

Chemical structures from multi-electron density operators

A theory is presented, which allows the calculation of the contributions of chemical structures of a given molecular system. Starting from the case of an orthogonal AO basis set, we define as contribution of a chemical structure the expectation value of a multi-electron density operator; it gives the probability to find a few electrons in some target atomic spin orbitals (ASOs), while simultaneously the remaining electrons can reside anywhere else, except in some other ASOs, as this is imposed from the usual graph of a chemical structure. The anticommutation relations of these multi-electron density operators and some useful relations of their expectation values, are then established. The case of a non-orthogonal AO basis set is further considered by introducing occupation numbers coherent with the expectation values of the orthogonal case. As examples, we present some chemical structures for the ground electronic states of the benzene and the methane molecules.     

Unpaired electrons,spin polarization,and bond orders in radicals from the 2‐RDM in orbital spaces: Basic notions and testing calculations

Adopting the second‐order reduced density matrix level, the conventional α‐ and β‐spin populations in radicals are split into paired and unpaired or electropon (referring to the simultaneous occurrence of an electron and a hole of opposite spins in an orbital) populations. This analysis gives the possibility to distinguish the (un)favorable for chemical bonding electronic interactions by means of positive or negative Coulomb and/or Fermi correlations of two electropons. To overcome the conceptual difficulties originated from the subtle superposition of unpaired electrons due to spin density and those responsible for chemical bonding, we use the notion of properly unpaired electrons. The quantity describing this notion provides a global picture for the ability of electrons of a given orbital to form covalent bonds with the electrons of all remaining orbitals. More detailed information, concerning the behavior of electrons in two distinct target orbitals, is obtained by means of the two‐electropon correlations. As shown, the boundary values of the used quantities are physically meaningful, and the whole theory is tested from various points of view concerning: localized and delocalized radical centers, orthogonal and nonorthogonal orbitals, uncorrelated and correlated levels, Coulomb and Fermi correlations. We also check the electropon based analysis by investigating the spin polarization effects and bond orders in radicals. The tests are achieved for well‐known radicals, and to preserve the stability of the numerical results and the invariance of the obtained conceptual pictures, we used natural basis sets introduced within the natural bond orbital methodology. © 2014 Wiley Periodicals, Inc.     

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding,and coulomb and fermi correlations in closed shell systems

The usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.     

Extent of the sudden polarization effect for long polyenes: an analytical study

The sudden polarization effect is studied for a series of dodecahexenes, by means of minimal basis set ab initio calculations, followed by limited configuration interaction. In order to understand the somewhat surprising results, the CI process is modeled and an analytical formula for calculating the polarization is demonstrated Simple rules are then stated which govern the polarization within the restricted open shell + limited CI framework.     

Natural polyelectron population analysis

A method to perform a polyelectron population analysis of correlated molecular orbital wave functions on the basis of natural atomic orbitals (NAO s), as given by Weinhold, is presented. The method allows calculations of the probabilities of finding various types of electronic events occuring in some target AO positions, including the contributions of ionic and covalent resonance structures. This method is general and neither the theory nor the developed algorithm limit the number of electrons and holes that can be considered. Thus, the analyzed MO wave function can be a usual CI or a MCSCF one, and apart from Weinhold's NAO s. any other type of orthogonal AO s can be used as analyzers, provided that these AO s are linear combinations of the SCF-AO s. Numerical applications are given for ethylene, formaldehyde, butadiene, and acroleine, by adopting various AO basis-set levels (STO ?4G , 4–31G , and 6–31G ) and by analyzing correlated wave functions (CISD ). Improvements in the polyelectron populations when increasing the quality of AO basis sets and the corresponding valence NAO s are revealed by several examples. Furthermore, it is shown that the electroegativity of oxygen in acroleine only has an effect on contributions of ionic and covalent resonance structures, but not on delocalization of the double bonds. 1993 John Wiley & Sons, Inc.     

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.     

Origin of the conical intersection between the singlet ionic excited surfaces of twisted ethylene

The potential surfaces of the two valence ionic singlet excited states of twisted ethylene are known to exhibit a conical intersection for a twist angle of the double bond near 82°, and no pyramidalization of the CH₂ groups. The factors responsible for the stabilization of the symmetric excited state near 90° are shown to be ( )² and ( ^*)² double excitations. The analysis is performed in the Quasi Degenerate Perturbation Theory formalism. The analogy with the ¹ A _g ³ B _u ordering problem of the diradical ground and lower triplet states through a double spin polarization of the system is established.