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Representations are ubiquitous in chemistry. They are part of the chemistry language instructors use to communicate chemistry phenomenon to students. Literature calls in support of learning with multiple representations, but there is a pre-requisite for students to learn from a single representation. In this exploratory study, 1086 students in second semester general chemistry were randomly assigned to one of four representations showing bonding of sulfur dioxide: chemical formula, Lewis dot structure, an image of a ball and stick model, or an image of a space filling model. Students were asked to predict chemical properties of sulfur dioxide: relative bond length, molecular polarity, and the strongest intermolecular force with a water molecule. Using the lens of Multimedia Learning Theory on Learning with Text and Visual Representations, analyses of students’ prediction of chemical properties and the features cited when making predictions was conducted. Effect sizes were used to describe variations among representations in terms of how students predicted bond length, polarity and intermolecular forces. Meaningful differences were found across representations in students’ ability to correctly predict relative bond length and molecular polarity. These explorations generated the following hypotheses: (1) chemical formula leads students to depend on chemical conventions, (2) Lewis dot structure hinders predicting polarity when it shows an inaccurate shape, and (3) visual representations of ball and stick and space filling cue students to rely on visual estimations more than the other representations. Upon further testing, these hypotheses can inform instructors how to introduce representations and in the decision-making process of which representations to use to convey or assess a specific chemical property.

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.

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|2. Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

Understanding the mechanism of catalytic reactions is crucial for the future development of catalysts. In this computational study, dispersion-corrected Density Functional Theory (DFT) theory was used to calculate the various mechanistic pathways for ammonia and hydrazine synthesis on η-Mn3N2-(100) surfaces. A simple Lewis structure representation algorithm was used in order to locate various possible NxHy intermediates. Hydrogenation of dinitrogen results in significant activation of the inert triple bond and these intermediates have a significant role in the ammonia and hydrazine synthesis reaction on manganese nitrides via a Langmuir-Hinschelwood mechanism. It is anticipated that these findings are significant in developing new catalysts for hydrazine synthesis using η-Mn3N2 (100) catalysts.

International audience; A first step towards the construction of a quantum force field for electron pairs in direct space is taken. Making use of topological tools (Interacting Quantum Atoms and the Electron Localization Function), we have analyzed the dependency of electron pairs electrostatic, kinetic and exchange-correlation energies upon bond stretching. Simple correlations were found, and can be explained with elementary models such as the homogeneous electron gas. The resulting energy model is applicable to various bonding regimes: from homopolar to highly polarized and even to non-conventional bonds. Overall, this is a fresh approach for developing real space-based force fields including an exchange-correlation term. It provides the relative weight of each of the contributions, showing that, in common Lewis structures, the exchange correlation contribution between electron pairs is negligible. However, our results reveal that classical approximations progressively fail for delocalized electrons, including lone pairs. This theoretical framework justifies the success of the classic Bond Charge Model (BCM) approach in solid state systems and sets the basis of its limits. Finally, this approach opens the door towards the development of quantitative rigorous energy models based on the ELF topology.

A partitioning of the wavefunction into tiles allows electronic excitations to be viewed as electron vibrations., Since the conception of the electron pair bond, Lewis structures have been used to illustrate the electronic structure of a molecule in its ground state. But, for excited states, most descriptions rely on the concept of molecular orbitals. In this work we demonstrate a simple and intuitive description of electronic resonances in terms of localized electron vibrations. By partitioning the 3N-dimensional space of a many-electron wavefunction into hyper-regions related by permutation symmetry, chemical structures naturally result which correspond closely to Lewis structures, with identifiable single and double bonds, and lone pairs. Here we demonstrate how this picture of electronic structure develops upon the admixture of electronic wavefunctions, in the spirit of coherent electronic transitions. We show that π–π* transitions correspond to double-bonding electrons oscillating along the bond axis, and n–π* transitions reveal lone-pairs vibrating out of plane. In butadiene and hexatriene, the double-bond oscillations combine with in- and out-of-phase combinations, revealing the correspondence between electronic transitions and molecular normal mode vibrations. This analysis allows electronic excitations to be described by building upon ground state electronic structures, without the need for molecular orbitals.

An electron counting technique that easily provides Lewis structures from real space analyses of general wavefunctions is proposed. We base our approach on reformulating the adaptive natural density partitioning (AdNDP) algorithm proposed by Zubarev and Boldyrev (Phys. Chem. Chem. Phys., 2008, 10, 5207) in position space through the use of domain-averaged cumulant densities, which take into account many-electron correlations. Averages are performed over the basins provided by the quantum theory of atoms in molecules. The decomposition gives rise to a set of n-center, two-electron orbitals which describe the dominant Lewis structures of a molecular system, and is available both for single- and multi-determinant wavefunctions. As shown through several examples, chemically intuitive Lewis descriptions are now available from fully orbital invariant position space descriptors. In this sense, real space methods are now in a position to compete with natural bond order (NBO) orbital procedures without the many biases of the latter.

The papers mentioned in the title of the present comment article contain some calculations/results that are in disagreement with some basic concepts of chemistry. The calculations include (i) the calculation of an energy difference, more than 1000 J mol−1, between one pair of enantiomers, (ii) the calculation of an energy difference between the Lewis structures (resonance forms), and (iii) the calculation of bond orders in different pathways of resonance process.

Organic chemistry is possibly the most visual science of all chemistry disciplines. The process of scientific inquiry in organic chemistry relies on external representations, such as Lewis structures, mechanisms, and electron arrows. Information about chemical properties or driving forces of mechanistic steps is not available through direct perception, and thus looking beyond the respresentation is challenging for learners. In this study, we investigated the categorization behavior of undergraduate students enrolled in an organic chemistry course when engaged in various categorization tasks involving electrophilic addition reactions to alkenes. The critical attribute a student chose to make a category out of a set of reactions was classified as perceptual or relational and gave insights into how students process and store information about reactions at an early level of expertise. Our results support the notion that students are prone to the surface level of representations and make sense of reactions depicted in a very minimalistic fashion. Implications for approaching this phenomenon in teaching are discussed.

The properties and reactivities of transition metal complexes are rooted in the stereoelectronic properties of their ligands. While the bulk of a ligand can be easily evaluated and compared by the drawing of its Lewis structure, prediction on the electronic contributions is often less straightforward. Thus, several electronic parameters have been developed for the experimental evaluation of ligands throughout the years. This article accounts for the most recent one developed by the Huynh group, which employs 13C NMR spectroscopy to determine ligand donor strengths using N-heterocyclic carbene complexes. This parameter not only proves to be safer, more convenient and accurate in comparison to existing methodologies, but it also provides, in certain cases, more intuitive and reliable results. Furthermore, it is currently the only one that allows the direct comparison of various Werner-type and organometallic ligands on a unified scale.

In this work we report on the progress that has been made towards gaining an understanding of the molecular mechanism of 1,3-dipolar cycloadditions using the bonding evolution theory (BET). A detailed analysis of the flow of electron density along the reaction pathway of the formal 1,3-dipolar cycloaddition reaction between cyclic nitrones (pyrroline-1-oxide and 2,3,4,5-tetrahydropyridine-1-oxide) and ethyl acrylate, as a case study, allowed the nature of the molecular mechanisms to be characterized. The present study provides a deep insight into the reaction mechanism, based on the electron density rearrangements given by the structural stability domains, and their connection with the bond breaking/forming processes along the reaction pathway. The electron pushing formalism is a powerful tool to describe chemical reactivity. Here, we show how the Lewis structures can be recovered and how curly arrows describe electron density transfers in chemical reaction mechanisms based on the BET results. The reaction mechanism is described by four consecutive events taking place as the reaction progresses: (1) the population of the initial N–C double bond is transferred to the N and C atoms; (2) the population of the initial double C–C bond is transferred to the C atoms. Along the ortho pathway the next steps are: (3) the C–C bond-forming process, and (4) the O–C bond-forming process. The order of (3) and (4) is inverted in the meta channel. Based on the sequence of the structural stability domains along the intrinsic reaction coordinate, a new synchronicity index is proposed, allowing us to classify and quantify the (a)synchronicity of the 1,3-DC reactions and, therefore, the nature of the reaction mechanism.

It is well known that closo-borane dianions BnHn2− are stable aromatic cages and possess n + 1 valence electron pairs, in accordance with Wade's rules. However, the electronic structures of closo-BnHn2− cannot be explained by a Lewis structure because of their electron-deficient character, while recent theoretical and experimental studies reveal that multicenter bonding is a key part in their electronic structures. In this work, flexible multicenter bonding of BnHn2− (n = 2–17) is studied using the adaptive natural density partitioning (AdNDP) method in order to get insight into their stability and aromaticity. The large HOMO–LUMO gaps and negative NICS values indicate their close-shell electronic structure. Further chemical bonding analysis shows that all 2n + 2 delocalized valence electrons in closo-BnHn2− are involved in various delocalized σ and π multicenter bonding systems on their cage surface, well matched with different symmetric configurations. There are five types of multicenter bonds, including an open 3c–2e BBB bond, closed 3c–2e BBB bond, 4c–2e bond, 8c–2e bond and a fully delocalized bond, which are delocalized on a B3 broken-line, B3 triangle, B4 rhombus, B8 double-ring and the whole surface of the boron cage, respectively. Our work reveals the flexibility of multicenter bonding in diversified closo-BnHn2− clusters, giving new insights into the bonding nature of BnHn2−.

Consideration is given to (electronically) hypervalent increased-valence structures, which possess 2c–1e bonds, fractional 2c–2e bonds, and usually normal 2c–2e bonds., Consideration is given to (electronically) hypervalent increased-valence structures, which possess 2c–1e bonds, fractional 2c–2e bonds, and usually normal 2c–2e bonds. For singlet-spin electron-rich systems, increased-valence structures, with Heitler–London 2c–2e bond wavefunctions, are equivalent to resonance between non-hypervalent Kekulé and Dewar (or singlet diradical) type Lewis structures. Dewar structures are not considered in the Chem. Sci. 2015, 6, 6614 Edge article on hypervalency. Using one-electron delocalizations from lone-pair atomic orbitals into separate bonding molecular orbitals, increased-valence structures for PCl5, O3, SO42–, NO3–, N2O4 and SN2 reactions are derived from the Edge-article's Kekulé-type Lewis structures, and compared with the Edge article's hypervalent structures with 2c–2e bonds. It is also shown that Durrant's method to determine the γ parameter for XAY-type systems that possess a symmetrical 3c–4e bonding unit is related to the A-atom charge density.

The ability to use a chemical structure to predict and explain phenomenon is essential to a robust understanding of chemistry; however, previous research has shown that students find it difficult to make the connection between structure and properties. In this study we examine how student recognition of the connections between structure and properties evolves during the first two years of college chemistry courses. In addition, we investigate how an alternative general chemistry curriculum (Chemistry, Life, the Universe and Everything (CLUE)) impacts students' understanding during these first two-years. Using discrete-time survival analysis to analyze student responses to the Implicit Information from Lewis Structures Instrument (IILSI), we found that it takes multiple semesters for students enrolled in a traditional curriculum to recognize that chemical structures can be used as models to predict chemical and physical properties. Students in the CLUE curriculum, however, tend to make this connection earlier than a matched cohort of students from a traditional curriculum, and this advantage is maintained throughout the two semesters of organic chemistry. In general, the control group takes an additional year of organic chemistry to reach the same level as the CLUE students after a year of general chemistry.

Probing the electron density transfers during a chemical reaction can provide important insights, making possible to understand and control chemical reactions. This aim has required extensions of the relationships between the traditional chemical concepts and the quantum mechanical ones. The present work examines the detailed chemical insights that have been generated through 100 years of work worldwide on G. N. Lewis's ground breaking paper on The Atom and the Molecule (Lewis, G. N. The Atom and the Molecule, J. Am. Chem. Soc. 1916, 38, 762–785), with a focus on how the determination of reaction mechanisms can be reached applying the bonding evolution theory (BET), emphasizing how curly arrows meet electron density transfers in chemical reaction mechanisms and how the Lewis structure can be recovered. BET that combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) provides a powerful tool providing insight into molecular mechanisms of chemical rearrangements. In agreement with physical laws and quantum theoretical insights, BET can be considered as an appropriate tool to tackle chemical reactivity with a wide range of possible applications. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds for a given reaction mechanism, providing detailed physical grounds for this type of representation. The ideas underlying the valence-shell-electron pair-repulsion (VSEPR) model applied to non-equilibrium geometries provide simple chemical explanations of density transfers. For a given geometry around a central atom, the arrangement of the electronic domain may comply or not with the VSEPR rules according with the valence shell population of the considered atom. A deformation yields arrangements which are either VSEPR defective (at least a domain is missing to match the VSEPR arrangement corresponding to the geometry of the ligands), VSEPR compliant or pseudo VSEPR when the position of bonding and non-bonding domains are interchanged. VSEPR defective arrangements increase the electrophilic character of the site whereas the VSEPR compliant arrangements anticipate the formation of a new covalent bond. The frequencies of the normal modes which account for the reaction coordinate provide additional information on the succession of the density transfers. This simple model is shown to yield results in very good agreement with those obtained by BET. We wish to thank Professors R. J. Gillespie, Henry H. Rzepa and Patrick Chaquin and L. R. Domingo for stimulating discussions and the referees for their very constructive comments

A thermally robust triple-decker complex [bis(η5-pentamethylcyclopentadienyltitanium)-μ-(η4:η4-1,2,4,5-tetrakis(trimethylsilyl)cyclohexa-1-4-diene-3,6-diyl)] (3) was obtained in 4% yield by thermolysing Cp*TiMe3 in the presence bis(trimethylsilyl)acetylene (BTMSA). The solid-state structure of centrosymmetric 3 features rather long all C–C bonds in the nearly planar bridging ligand (1.4720(14)–1.4896(15) A) and a short distance of its least-square plane to the titanium atoms (1.7381(5) A). Computational results revealed the bonding of the central ligand to be accomplished through back-bonding of its two CC bonds and through the simultaneous generation of two σ-Ti–C(H) bonds. Based on CASSCF and CASPT2 results, the molecule acquires several electronic configurations simultaneously, which hinders its representation by one single Lewis structure. Apart from being coordinated to the central ligand, the metal atoms are involved in a direct Ti–Ti bonding by the formation of one σ- and two δ-bonds between them. The bond order of this Ti–Ti overlap shows only a slight decrease upon electronic excitation. The presence of ionic contribution to the bonding of the central ligand is manifested by the charge −1.4e summed on the carbon atoms of the bridging ring. Based on computational results, the spin multiplicity of the ground state is singlet, while the first low lying excitation state is triplet. This is in agreement with the absence of EPR signal in either toluene solution and glass, and with slight downfield shifts of broadened 1H NMR signals of SiMe3 and Cp* methyl groups observed with increasing temperature.

An embedding method for a one-electron reduced density matrix (1-RDM) is proposed. It is based on partitioning of 1-RDM into domains and describing each domain in the effective potential of the other ones. To assure N-representability of the total 1-RDM N-representability and strong-orthogonality conditions are imposed on the domains. The total energy is given as a sum of single-domain energies and domain-domain electron interaction contributions. Higher than two-body inter-domain interaction terms are neglected. The two-body correlation terms are approximated by deriving inter-domain correlation from couplings of density fluctuations of two domains at a time. Unlike in most density embedding methods kinetic energy is treated exactly and it is not required that densities pertaining to the domains are only weakly overlapping. We propose to treat each domain by a corrected perfect-pairing functional. On a few examples it is shown that the embedding reduced density matrix functional method (ERDMF) yields excellent results for molecules that are well described by a single Lewis structure even if strong static intra-domain or dynamic inter-domain correlation effects must be accounted for.

A method based on a real space partitioning to measure the importance of Lewis structures is proposed in this work. A matrix containing diverse QTAIM atomic and diatomic properties endowed with significance within a Lewis structure framework is expanded in terms of what we call Lewis-structure matrices. Each of these matrices flawlessly describes an individual resonance structure and its associated linear expansion coefficient (Q-ALE coefficient) indicates the importance or convenience of the given Lewis structure. These coefficients were inspected looking at their evolution in a series of usual chemical issues. Among all the results, we find of interest that σ resonance structures in systems with π electrons are more important than normally expected, which justifies why the qualitative predictions arising from the application of the resonance model and the quantitative results based on QTAIM properties are sometimes discrepant. Likewise, we observe that the variation of the dielectric constant of the medium affects the π resonance to a greater extent than it does the σ one. Other interesting results in this manuscript are connected to homolytic dissociation of diatomic molecules, periodic trends in hydrogen compounds, and polarization of aromatic systems as a consequence of their interaction with electric fields and with diverse ions.

The concept of covalent bonding is characterized by an interconnected knowledge framework based on Lewis and quantum models of atoms and molecules. Several research studies have shown that students at all levels of chemistry learning find the quantum model to be one of the most difficult subjects to understand. We have tried in this paper to analyze the extent to which Algerian students, at the end of their training, have integrated the covalent bonding theories based on the quantum model of atom theory and are able to interpret Lewis structures using the quantum model. The analysis of the responses to a written questionnaire showed that this integration was not achieved by our students and that they are not able to correctly describe covalent bonds in a Lewis structure using the concepts of the quantum model. They have a “quantum box” conception of atomic or hybrid orbitals. This conception acts as a “pedagogical learning impediment” to the integration of the geometrical representations of atomic and hybrid orbitals, the conditions of their overlapping to give bonds and consequently the description of covalent bonds using the quantum model. So, the students use an alternative conceptual framework based on the use of Lewis model paired valence electrons to form covalent bonds that we have named the: “electrons pair framework”. Furthermore, the students restricted the denomination of a covalent bond to the sharing of one electron (either s or p but not spn) from each atom to give one “electron pair σ”, and thought that σ bonds are only formed in single bonds.

Lewis structures are a simplified two dimensional “cartoon” of molecular structure that allow a knowledgeable user to predict the types of properties a particular substance may exhibit. However, prior research shows that many students fail to recognize these structure-property connections and are unable to decode the information contained in the structures, thus resulting in students' inability to use Lewis structures for their intended purposes. We have developed a survey instrument using responses from student interviews and open-ended questions from a previous research study to determine students' beliefs about the information that can be obtained from Lewis structures. The survey was found to be reliable and valid through multiple administrations to a total of 3203 students, including first- and second-semester general chemistry and organic chemistry students, junior/senior level undergraduate chemistry students, and graduate level chemistry students. We propose that this survey can be a useful informational tool for instructors for a wide range of courses where students' understanding of structure-function relationships is important.

Topological analysis of the Electron Localization Function (ELF) within the framework of Quantum Chemical Topology (QCT) has been applied to study the nature of the boron–nitrogen bonds. A series of 10 compounds have been chosen, with the B–N bond length ranging between 1.698 A (B–N) and 1.258 A (BN). According to the Lewis formula three types of bonds have been recognized. These are: the single B–N bond with a basin population of 1.91 ÷ 2.09e, the double BN bond with a population of 3.78 ÷ 4.28e, and the triple BN bond with a basin population of 5.72 ÷ 5.74e. In the case of partial double bonds (BN), where formally two or more resonance hybrids have to be considered, our calculations strongly support the concept of double boron–nitrogen bonding (BN).

Lewis structures are important for learning chemistry as they serve as an essential link between the structure of chemical compounds and their function. Unfortunately, the creation of valid Lewis structures remains an elusive goal for many students. In recent years, several web-based programs have been created that allow students to receive immediate feedback on the structures that they draw; however, the interface in most of these programs is not naturalistic, and there is a significant learning curve for students. This article describes the development, features, and pilot testing of OrganicPad, an innovative and user-friendly program that has been designed to allow students to draw Lewis structures by using the natural user interface of a Tablet PC.

The Electron Localisation Function, ELF pictorially visualises chemists' intuitive ideas of single and multiple bonds as well as non-bonding electron pairs in molecules. The power of the representation of chemical bonds via ELF is that on the one hand covalent, polar, and ionic bonds are distinguishable, and that on the other hand ELF can be calculated for molecules and solids. This enables us to transfer the ideas of chemical bonding from molecular to intermetallic compounds. Localised two-electron-two-centre bonds and lone pairs are present in solid-state valence compounds (Zintl phases) as expected by the 8-N rule. In solids, lone pairs are generally more contracted than in molecules due to 'lone-pair repulsion'. In intermetallic compounds localised electrons predominantly occur in the form of lone pairs. Lattice vibrations influence the strength of lone pair interactions and non-bonded interactions lead to an exchange of delocalised and localised electrons. Such a mechanism of local electron pair formation gives rise to ideas of a chemical view of the phenomenon of superconductivity in intermetallic compounds.

A modification to Lewis's theory of valency is proposed to make it more consistent with the results of quantum-mechanical calculations on molecules containing polar covalent bonds (e.g., ClF) and hypervalent atoms (e.g., SF6). A distinction is drawn between the valence shell of an atom (VS) and the Lewis shell (LS). [Chem. Educ. Res. Pract. Eur.: 2001, 2, 67-72]

The experimental charge density of trimethylammonionitramidate, (CH3)3N+–N- –NO2, has been determined by high resolution X-ray diffraction. We find the distribution of charge to be more complex than the Lewis formula suggests. Despite the fact that the trimethylammonium fragment bears a full positive charge, the ’onium nitrogen is determined to have a substantial negative charge due to electron donation from the methyl groups by the alkyl inductive effect. The formally negative nitrogen atom of the N+–N- bond has its charge substantially reduced by the electron-withdrawing nitro group considerably stabilising the molecule. The topological properties of the -∇2ρ(r) distribution for this nitrogen atom suggest it to be sp2 hybridised.

Non-aqueous solutions of alkaline-earth metal perchlorates M(ClO4)2(M = Ba, Sr, Ca, Mg) have been investigated by IR and Raman spectroscopy. The association of M2+ and ClO4– into mononuclear species M(ClO4)x(x= 1 or 2) depends on the cation and on the solvent. In a given solvent the association extent decreases from Ba to Mg. In all cases it has been possible to find at least one associating solvent (ester, cyclic ether) where the association into M(ClO4)2 is complete. In the associated species the coordination of ClO4 can be monodentate (C3v) or bidentate (C2v). The monodentate coordination is the only mode in Mg(ClO4)2 while bidentate coordination is predominent with the other cations. In that case there is a minor proportion of monodentate ClO4 groups which decreases from Ca to Ba. The two kinds of coordination are distinguished by the shift Δν1 of ν1 relative to free ClO4– which is either positive (monodentate) or negative (bidentate). This criterion has been established by the investigation of the other vibrational modes of ClO4. Wavenumber shifts and splittings have been correlated to the cation polarizing power. Force constant variations calculated on BaClO4+ and LiClO4 are correctly interpreted by Lewis structures.

Ab initio and density functional calculations for five vertex cage compounds of the type P2(YB)2EH2, (E=C, Si, Ge, Sn, Y=H, H2N) using 6-311G++(d,p) and 3-21G++(d,p) basis sets, showed that they adopt a trigonal bipyramidal structure of C2v symmetry with the two phosphorus atoms occupying the apical position, the HB or NB groups residing in the trigonal basal plane. The theoretical results agree well with the experimental data for E=Si, Ge and Sn. For the carbon cage P2(HB)2CH2 this structure is a transition state and the minimum is a cage of Cs symmetry with a distorted B–B–C ring in the equatorial plane. Key structural parameters within the cages show a linear dependence on the covalent radii and the diffuseness of the orbitals of the heteroatom E. The results of the natural population analysis (NPA) and the values of nucleus independent chemical shifts (NICS) calculated reveal a bonding description very close to the idealized localized Lewis structure, in contrast to the parent P2(HB)3 cage. This is more pronounced in the case of the NH2 substituted cages.

The results of ab initio valence bond calculations for dinitrogen show that resonance between the valence bond structures [graphic omitted] and [graphic omitted] with electron-pair σ bonds and one-electron π bonds, generates a lower energy than does the triple-bond structure [graphic omitted]N ≡ N[graphic omitted] with Coulson–Fischer-type wavefunctions for the two π bonds. When the wavefunctions for these two sets of structures are expressed as linear combinations of wavefunctions for nine canonical Lewis structures, it is found that the triple-bond structure overestimates the importance of the highly polar canonical structures [graphic omitted] and [graphic omitted], and this is the origin of the higher energy for the triple-bond structure.

The results of some STO-6G valence-bond calculations, with single-zeta and double-zeta basis sets, are reported for the ground state of NO2. 18 Lewis structures that differ in the locations of the four π electrons and the odd electron are included in the main calculations, subsequent to the determination of the approximate structure of the σ-electron core via energy optimization with a smaller number of structures. Regardless of the nature of the orbital basis set in the 18 structure calculations, the spin-paired diradical structure A, [graphic omitted] as well as structures of types B and C, [graphic omitted] is calculated to be a primary contributor to the resonance scheme. Therefore, NO2 has considerable spin-paired diradical as well as free-radical character.The results of some single-zeta VB calculations are also reported for CO–2, and consideration is given to the increased-valence and non-paired spatial orbital representations for the π electrons of NO2. One formulation of the wavefunction for resonance between the increased-valence structures is equivalent to the best linear combination of the wavefunctions for the 18 Lewis structures.

The results of ab initio valence-bond calculations, with an STO-6G basis set, are reported for the ground state of ozone. Both Heitler–London and localized molecular-orbital procedures have been used to construct the wavefunctions for the σ-bonds. Hybridization of the orbitals on each atom has been determined by energy considerations.In accord with previous results, the primary Lewis structure is calculated to be the spin-paired diradical structure (6) with two σ-bonds, and a long, or formal, π-bond associated with the terminal atoms. However, the sum of weights for four Lewis structures (11)–(14), which arise from polarization of either σ-bond in (6), is calculated to exceed the weight for (6).Particular attention is given to the calculation of energies for “increased-valence” structures (1) and (2), which are constructed by spin-pairing the two unpaired electrons of ground-state O2 with those of a ground-state oxygen atom. If a two-centre molecular orbital is used to accommodate the two electrons of the O—O σ-bond in each of these structures, then resonance between these structures is equivalent to resonance between numerous Lewis structures including (6)+(11)–(14), when Heitler–London procedures are used to formulate the wavefunctions for all electron-pair bonds in the Lewis structures. The results of calculations which utilize this approach indicate that resonance between increased-valence structures provides the primary valence bond representation for the O3 ground state. Such structures are stabilized slightly by interaction with the Lewis structures that involve excited states for the O atom and the O2 molecule. The resulting energy for resonance between these four valence-bond structures lies at least 0.134 au below the STO-6G RHF-MO energy of –224.091 au.

When the diradical intermediates in 1,3-dipolar cycloadditions are written as Lewis structures with paired-electron bonds, the losses in bond energy which accompany their formation are much greater than the experimental activation energies. However, the use of Linnett structures for the 1,3-dipoles and diradicals produces good agreement between bond-energy losses and activation energies. Although the results do not uniquely confirm the diradical mechanism, they do show that it cannot be ruled out on the basis of energy arguments alone.