Transient bonds and chemical reactivity of molecules

Electron delocalization between the reagent and reactant molecules is the principal driving force of chemical reactions. It brings about the formation of new bonds and the cleavage of old bonds. By taking the aromatic substitution reaction as an example, we have shown the orbitals participating in electron delocalization. The interacting orbitals obtained are localized around the reaction sites, showing the chemical bonds that should be generated and broken transiently along the reaction path. By projecting a reference orbital function that has been chosen to specify the bond being formed on to the MOs of the reactant molecules, the reactive orbitals that are very similar to the interacting orbital have been obtained. The local potential of the reaction site for electron donation estimated for substituted benzene molecules by using these projected orbitals shows a fair correlation with the experimental scale of the electron-donating and -withdrawing strength of substituent groups. The reactivity is shown to be governed by local electronegativity and local chemical hardness and also by the localizability of interaction on the reaction site. © 1996 John Wiley & Sons, Inc.     

Computational developments in generalized valence bond calculations

In this article a procedure for generating starting orbitals for generalized valence bond (GVB) calculations is presented. This is achieved by selecting orbitals which correspond to specific bonds or electron pairs. These orbitals can be identified from the localized molecular orbitals, for both occupied and virtual orbitals, which are obtained through a unitary transformation of the Hartree-Fock canonical molecular orbitals using the Boys's localization method. A scheme has also been implemented which achieves optimum convergence of the pairwise orbital optimization. An object-oriented GVB program is developed which automatically generates reliable initial GVB orbitals, leading to proper and fast convergence. © 1996 by John Wiley & Sons, Inc.     

Charge fluctuations and correlation strength in chemical bonds: First-row homonuclear diatomic molecules

We investigate, by means of ab initio calculations, the strength of electron correlations within covalent bonds: the first-row homonuclear diatomics serve as test cases. As an appropriate measure of the correlation strength, we introduce the reduction of the mean-square deviations of the electronic charges in localized orbitals forming a bond. A recently developed population analysis in terms of local operators derived from localized molecular orbitals is thereby used. The correlation-strength parameter depends only weakly on dynamical correlations as test calculations demonstrate. Therefore, the full-valence complete active space self-consistent field (CASSCF) approximation is applied in order to study the changes in the correlation strength with changing bond length for different types of bonds. A number of simple rules emerge from this discussion. In addition, we show that charge fluctuations are not only a reliable measure of intrabond correlation effects, but also can be used to monitor intraatomic quasi-degeneracy effects as well as the interdependence within multiple bonds. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 157–173, 1998     

用分子片轨道逐步剔除法研究电子离域

估计分子中不同类型的电子离域作用（如p-π → d-π和p-π → σ~*）的相 对强弱对理解分子中化学键的本质有关键的作用。剔除某一分子片轨道（d-π或σ ~*）后分子体系能量的改变可用来计算电子离域到该轨道的离域能。由于轨道之间 的相互作用,使离域能的计算与轨道剔除的次序有关。为克服这种不确定性,可以 逐步轮流增加某一对特定轨道（d-π和σ~*）的库仑积分,以使这对轨道在分子波 函数中的比重逐步减少,即将这对轨道轮流逐步剔除。这样可将轨道间的相互影响 减小以至消除,从而得到各轨道的精确的离域能。以H_3PO中P-O键为例说明了轨道 逐步剔除方法的应用。     

On quadratic bond-order decomposition within molecular orbital space

A simple method of analysing and localization of canonical molecular orbitals for particular chemical bond using the MO-resolved bond-order decomposition scheme is presented. An alternative definition of classical bond order orbitals is provided and links to communication theory of the chemical bond are outlined and briefly discussed. The introduced procedure of decomposition of quadratic bond orders allows one to analyse two- as well as three- center chemical bonds within the framework of the same theory.     

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.     

Intuitive local picture for spin polarization of chemical bonds

The spin polarization of chemical bonds near radical centers is investigated by an analytical spin unrestricted Hartree–Fock model with numerical examples. The centroid analysis of localized molecular orbitals is also introduced to obtain an intuitive local picture for the spin polarization. The alternation of spin alignments in molecules are discussed with orbital symmetries and Hund's rule through chemical bonds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theory of electron localization and its application to blue-shifting hydrogen bonds

We propose a theory of electron localization or stabilization by electron localization through the interactions between occupied (i) and vacant (j*) orbitals under certain conditions, which have been believed so far to cause only electron delocalization. Electrons localize when the electrons redistributed by the interaction are more stable in the i-th occupied orbital than in the overlap region: h(ij*) > s(ij*)h(ii) for s(ij*) > 0. Electron delocalization occurs when h(ij*) < s(ij*)h(ii) for s(ij*) > 0. The h(ij*) and s(ij*)h(ii) terms represent the energy of the electrons in the overlap region and the energy of the redistributed electrons in the occupied orbital, respectively. The theory of electron localization is substantiated by the correlation of the C-H bond lengths of fluorinated methanes H(4-n)CF(n) (n = 1, 2, 3) to the electron population of the σ(CH) bonding orbital, and successfully applied to understanding blue-shifting hydrogen bonds in F(3)CH···X (X = CO, N(2), OC, Ne, OC(CH(3))(2)) and designing some proton donors, HCO(2)CH(3) and hypervalent molecules HPF(4) and HSF(5), for blue-shifting hydrogen bonds.     

Electron pairing and chemical bonds. Electron fluctuation and pair localization in ELF domains

This article reports the numerical comparison of the quantities characterizing the extent of electron fluctuation and pair localization in the domains determined by the direct minimization of electron fluctuation with the domains resulting from the partitioning of the molecules based on the topological analysis of the so-called electron localization function (ELF). Such a comparison demonstrates that the ELF partitioning can be regarded as a feasible alternative to computationally much more demanding direct optimization of minimum fluctuation domains. This opened the possibility of the systematic scrutiny of the electron pair model of the chemical bond, and as it was demonstrated, the previous pessimistic claims about the applicability of this model are not completely justified.     

Quasimolecules in Compressed Lithium

Under high pressure, some materials form electrides, with valence electrons separated from all atoms and occupying interstitial regions. This is often accompanied by semiconducting or insulating behavior. The interstitial quasiatoms (ISQ) that characterize some high pressure electrides have been postulated to show some of the chemical features of atoms, including the potential of forming covalent bonds. It is argued that in the observed high‐pressure semiconducting Li phase (oC40, Aba2), an example of such quasimolecules is realized. The theoretical evaluation of electron density, electron localization function, Wannier orbitals, and bond indices forms the evidence for covalently bonded ISQ pairs in this material. The quasimolecule concept thus provides a simple chemical perspective on the unusual insulating behavior of such materials, complementing the physical picture previously presented where the global crystal symmetry of the system plays the major role.     

An orbital localization criterion based on the topological analysis of the electron localization function

This work proposes a new molecular orbital localization procedure. The approach is based on the decomposition of the overlap matrix in accordance with the partitioning of the three‐dimensional physical space into basins with clear chemical meaning arising from the topological analysis of the electron localization function. The procedure is computationally inexpensive, provides a straightforward interpretation of the resulting orbitals in terms of their localization indices and basin occupancies, and preserves the σ/π‐separability in planar N‐electron systems. The localization algorithm is tested on selected molecular systems. © 2012 Wiley Periodicals, Inc.     

Fully optimized implementation of the cluster-in-molecule local correlation approach for electron correlation calculations of large systems

A fully optimized implementation of the cluster-in-molecule (CIM) local correlation method for faster and more accurate electron correlation calculations of large systems is reported. The speedup comes from the new procedure of constructing virtual localized molecular orbitals of clusters. In the new procedure, Boughton–Pulay projection method is employed instead of a much more expensive Boys localization procedure. In addition, basis set superposition error correction for binding energy calculations and parallelized electron correlation calculations of clusters are now implemented. Benchmark calculations and illustrative applications at the Møller–Plesset perturbation theory, coupled cluster singles and doubles (CCSD), and CCSD with perturbative triples correction levels show that this newly optimized CIM approach is a reliable theoretical tool for electron correlation calculations of various large chemical systems. © 2018 Wiley Periodicals, Inc.     

Electron affinities of double bond π* orbitals determined by means of electron transmission spectroscopy

The electron transmission spectra of small molecules containing C=C, C=N, C=O, C=S and N=N double bonds are reported. The electron affinities of these functional groups, associated with electron capture into their empty π^* orbitals, are discussed in terms of heteroatom electronegativities, geometrical variations and localization properties of the π^* orbitals. The largest electron acceptor properties were observed in the thioketone derivative, which generates a stable π anion state. The ionization energy values relating to the heteroatom lone pair and the filled π orbitals are also reported.     

A study of the molecular orbital localization into an extended Hartree—Fock approach: Application to the BeH2 ground state

In this article, we present a study of the localization and properties of the molecular orbitals (MOs) of polyatomic systems by using a comprehensive version of the G1 model. In this version, the wave function is written as a DODS product of univocally determined spin orbitals (MOs), “projected” on the singlet ground state. A procedure for determining the MOs is given and applied to the BeH₂ ground state. Equivalent split shell and localized MOs are found. The Be orbitals are seen to exhibit sp hybridization and the localized valence MOs are found to produce − 13.7 kcal/mol localization energy. Multistructural calculations are carried out and show that the present approach is able to describe localized and well-oriented bonds whenever the molecule under study presents only a single well-defined nonresonant chemical structure. © 1996 John Wiley & Sons, Inc.     

Electron localization functions and local measures of the covariance

The electron localization measure proposed by Becke and Edgecombe is shown to be related to the covariance of the electron pair distribution. Just as with the electron localization function, the local covariance does not seem to be, in and of itself, a useful quantity for elucidating shell structure. A function of the local covariance, however, is useful for this purpose. A different function, based on the hyperbolic tangent, is proposed to elucidate the shell structure encapsulated by the local covariance; this function also seems to work better for the electron localization measure of Becke and Edgecombe. In addition, we propose a different measure for the electron localization that incorporates both the electron localization measure of Becke and Edgecombe and the Laplacian of the electron density; preliminary indications are that this measure is especially good at elucidating the shell structure in valence regions. Methods for evaluating electron localization functions directly from the electron density, without recourse to the Kohn-Sham orbitals, are discussed.     

Atoms and bonds in molecules and chemical explanations

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability domain) provide consistent definitions which accommodate chemistry and quantum mechanics.     

Charge distribution in homonuclear bonds: A semiempirical modeling

Atoms characterized by nonequivalent electronegativities form chemical bonds by exchanging electrical charge. The fraction of charge exchanged is dictated by the electronegativity differences among the system atoms. In the electronegativity equalization method, the charge distribution is estimated by forcing the system to relax to a common chemical potential, which corresponds to its configuration of energy minimum. By definition, this method cannot be applied to homonuclear bonds. A model is proposed to estimate the charge shared in molecular orbitals of homonuclear molecules. The model expands upon the electronegativity equalization method by adding formalism to describe the spin coupling characteristic of homonuclear bonds. Results are in excellent agreement with other quantum mechanical estimations of the charge distributions. © 2013 Wiley Periodicals, Inc.     

The concept of the chemical bond

The concept of the chemical bond is very old. Many interpretations have been proposed. Nevertheless, the problem is far from being solved. At the present time, the chemist has the choice between two models: the Lewis model (electron pairs) and the quantum model. In spite of a current opinion, both models are not logically equivalent. The localization of molecular orbitals is only a mathematical operation which does not involve any physic localization of the electrons. The loge theory is not more satisfying owing to the fact that loges with minimal fluctuation do not exist in all molecules. The theory of orbital domains seems to bring a solution. Nevertheless, its interpretation can be obtained only outside the strict framework of quantum mechanics.     

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998