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General chemistry students need to understand the concept of intermolecular forces and use them to predict the properties of materials. To do this, they must create symbolic representations of mole...

Valence bond (VB) theory, as a helpful complement to the more popular molecular orbital theory, is a fundamental electronic-structure theory that aims at interpreting molecular structure and chemical reactions in a lucid way. Both theoretical and experimental chemists have shown great interest in VB theory because of its capability of providing intuitive insight into the nature of chemical bonding and the mechanism of chemical reaction in a clear and comprehensible language rooted in Lewis structure. Therefore, there is a great call for the renaissance of VB theory. Nevertheless, this is possible only after a series of methods and algorithms were developed and efficiently implemented in user-friendly programs so as to serve computational chemists for general applications. In the past three decades, we have devoted a great amount of scientific enthusiasm toward this goal. In this Account, we will concisely summarize and briefly but insightfully discuss recent developments in ab initio VB theory, especially the N-body reduced density matrices (RDM)-based approach and its applications in diabatic electronic-structure computations, which is very useful for the vivid interpretation of many fundamental chemical processes such as electron and energy transfers. Furthermore, because of the fundamentally important role that the diabatic state plays in electron and energy transfers, which are two frontier research topics in both molecular and biochemical sciences, there are a broad range of applications that VB theory can handle.We start by briefly reviewing the general feature of ab initio VB wave functions. In particular, we focus on the multistructural ab initio VB theory that uses strictly localized orbitals, including the fundamental VB self-consistent field (VBSCF) and two post-SCF methods, VBCI and VBPT2, that use the VBSCF wave function as reference. We then allot a section to describing the recent developments of the RDM-based VB approach in the second quantization language. In this section, the enhanced Wick theorem is first outlined, followed by a brief discussion of its applications in evaluating VBSCF energy gradients and a Hessian with respect to the orbital expansion coefficients, together with a short review of the implementation of an automatic formula and code generator (AFCG) designed for many-body methods with nonorthogonal orbitals. Then, we introduce the application of the RDM-based approach in implementing the post-SCF method that addresses dynamic electronic correlation via perturbation theory, viz., the icVBPT2 method that adopts an internal contraction technique naturally. We finish this section by incorporating VB theory with the concept of seniority number, in which the tensor analysis technique is carefully exploited with the RDM-based approach, resulting in significant improvements in both the number of the active electrons/orbitals and in the speedup of the computational efficiency, thus pushing VB theory to its new limit. With these achievements available, we present the applications of VB theory in diabatic electronic-structure computations by using the intuitive insight rendered by VB theory. Therefore, we believe that there is a bright future in VB theory with true opportunities and new challenges coexisting both for theoretical developments and computational applications.

Despite tremendous efforts by instructors and textbook authors, students find it difficult to develop useful chemical intuitions about preferred structures, structural trends, and properties of even the most common d-block element organometallic species, that is d6, d8, and d10 systems. A full molecular orbital analysis of a transition metal species is not always feasible or desirable, and crystal field theory, while generally useful, is often too simplistic and limited. It would be helpful to give students of organometallic chemistry an additional toolkit that helps them to understand d-block compounds, in particular highly covalent ones. It is well known in the research literature in organometallic chemistry that hybridization arguments involving s and d orbitals (such as sd and sd2 hybridization for d8 and d6 systems, respectively) provides useful insight. However, this knowledge is much underused in undergraduate teaching and not taught in undergraduate textbooks. The purpose of this article is to make descriptions of bonding that are based on s,d-hybridized orbitals more accessible in a way that is directly useful for undergraduate teaching. Geometries of unusual low-coordinate structures can be successfully predicted. An in-depth physical explanation for the trans-influence, the weakening of a bond due to a strong bond trans to it, is provided. A clear explanation is given for why the cis isomer normally more stable than the trans isomer in square-planar d8 complexes of the type MR2L2 (R = alkyl/aryl, L = relatively weakly bonded neutral ligand). Similarly, the relative stability of fac versus mer isomers in octahedral d6 complexes of the type MR3L3 is explained. Relevant to catalysis, the method explains why strongly donating ligands do not always facilitate oxidative addition and why 12-electron and 14-electron Pd(0) species are thermodynamically much more accessible than one might expect. The method capitalizes on 1st year knowledge such as the ability to write Lewis structures and to use hybridization arguments. It also ties into the upper-year experience, including graduate school, where covalent d-block complexes may be encountered in research and where the hybridization schemes described here naturally emerge from using the NBO formalism. It is discussed where the method might fit into the inorganic curriculum.

Cations CpOq+ (p ≤ 7 with q = 1,2) and CpO3+ (p = 4-7) and corresponding neutrals are modeled by B3LYP/jun-cc-pVTZ to rationalize previous mass spectrometric observations of ion reactions with neutral C3O2. Modeling yields optimized potential energies, geometries, Mulliken spin populations, electric dipole moments, electron configurations, and thermochemical parameters. Lewis diagrams are derived. Mono- and dioxide cations typically have unbranched carbon chains, but trioxides are branched. The ions are most stable as spin doublets, but low-lying quartets are found for monoxides with even p. For trioxide ions, the quartets for p = 5,7 are lower-lying than for p = 4,6. For neutral mono- and dioxides resulting from possible electron transfer to the ions, triplets are more stable than singlets for even p. Neutral trioxides are most stable as triplets except C5O3 with a singlet slightly more stable. Singlet C4O3 and C6O3 are unstable with respect to CO loss. Charge transfer is likely only for CpO+ (p = 1-3) and CpO3+ (p = 4, 6). Monocarbon insertion by C3O2 is understood as two sequential CO losses without a hypothetical C6O4+• intermediate and is thermochemically favorable for all ions considered.

Lewis structures are a very important, foundational concept in chemistry. Students usually acquire this knowledge in General Chemistry and need to review it in preparation for Organic Chemistry. However, many students find the task of drawing Lewis structures to be challenging, and not all instructors can budget enough time in class to review this material when they start Organic Chemistry. To address this issue, we created a web application (web app; Lewis Structure Builder) that lets students review Lewis structures in their own time, allowing them to position individual atoms, build and break bonds, and get real-time feedback on the accuracy of their structures. The web app was designed to be intuitive, requiring very little training to use, and students could use desktops, laptops, or mobile devices to participate. In working through a sequence of target molecules to build, students had the freedom to try out different atomic structures to see what works and receive real-time feedback about their decisions. Upon successful completion of a molecule, students received visual and haptic feedback as a form of positive reinforcement. Afterward, students saw their solution next to the same molecule shown as an extended structure and as built using a model kit. A pilot study was conducted with 37 students who were enrolled in Organic Chemistry I. Participants were given an assessment to determine their level of proficiency in drawing Lewis structures, followed by an opportunity to use the web app and a post-test. After using the web app, 21% of the participants showed improved outcomes, and most students reported satisfaction with the user interface and perceived benefits from the experience.

The structure and stability of the compounds MRg+ and MRgF (Rg=Ar, Kr, and Xe; M=Co, Rh, and Ir) were investigated using the B3LYP, MP2, MP4(SDQ) and CCSD(T) methods. We reported the geometry, vibrational frequencies and thermodynamics properties of these compounds. A series of theoretical methods on the basis of wavefunction analysis, including natural bond orbitals, atoms in molecules, electron localization function, and energy decomposition analysis, were performed to explore bonding nature of the M−Rg and Rg−F bonds. These bonds are mainly noncovalent, the metal weakly interacts with Rg in MRg+, but their interaction is much stronger in MRgF. The neutral molecule MRgF can be well described by the Lewis structure [MRg]+F−.

A simple method to determine Lewis electron dot structures and formal charges without a need to sum all of the valence electrons, reorganize electron pairs, draw and pair up individual electrons, or remember a formal charge formula is described. The formal charge is determined by the group number (number of valence electrons) and the number of bonds, with the sum of formal charges then being equal to the total charge. This leads directly to a valid Lewis structure. The facility of the procedure allows the student to focus more on the chemical aspects of deciding which valid Lewis structure (or structures) is the correct or most important one.

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.

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 11B2 and 21A1 are the challenging ones. As the 11A2, 11B1, and 11B2 states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 21A1 states and the 11A1 ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 11B2 states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 21A1 ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 21A1 state of ozone and predicting some diradical character in the so-called "ionic" 11B2 states.

Conceptual understanding of the subject matter is crucial for teachers in conducting instruction. The covalent bond is one of the essential knowledge of chemistry. This knowledge underlies most of the chemistry body knowledge. The purpose of this study is to investigate the chemistry teachers' conceptual understanding of covalent bonds. This study applied a descriptive qualitative research design. The research subjects were eight chemistry teachers from different schools. Data collection was carried out using a diagnostic interview technique guided by the semi-structured interview protocol. Data analysis was performed using phenomenography techniques. The results show that 25.00% of the interviewees well understood the covalent bond concepts, 22.75% do not understand, and 52.25% have misconceptions. Chemistry teachers have misconceptions about the concepts of intents of atom forming bonds, coordination bonds, types of atoms that form covalent bonds, polar and nonpolar covalent bonds, the level of covalent bonds polarity, Lewis structure writing, and covalent bond length.

Chemical formulas are represented with the help of Lewis structures. To illustrate reaction mechanisms, these structures are provided with arrows and the new structural formula is recorded. This procedure presents blind pupils with several hurdles: - How do these structures come about? - How can students spontaneously create tactile formulas in class? - How can the movements shown by arrows be traced? For the representation of atomic symbols, for which the element symbols from the periodic table are normally used, magnets were developed that differ in shape, color, and size. Since only a handful of symbols occur regularly and in large numbers in school, only a few symbols have been permanently assigned, some are variable and can be used appropriately defined for the respective teaching situation. With this symbol set, it is possible to quickly and individually manufacture almost all molecules relevant in school. These magnets allow the independent determination of reaction mechanisms in the further course of the lesson. Due to the mobility of the elements on the magnetic base, electrons and atoms can be moved and thus result in a new bonding situation that is reinterpreted by the students. The advantage of this procedure is that the pupils do not just paint arrows, but consciously think about all processes and can also make mistakes. When analyzing intermediate products, you can determine that your actions were either not compliant or compliant but not effective. This enables individual active learning in the classroom.

Visuo-semiotic models, such as Lewis structures and ball & stick models, are widely used to enhance students’ learning. However, there is limited research about the impact of these models on specific visuo-semiotic reasoning skills. In the current research, we aimed to determine the extent to which physical molecular models could enhance specific visuo-semiotic reasoning skills among students. The research question that we explored was, “what is the impact of physical molecular models on Grade 11 students’ visuo-semiotic reasoning skills related to Lewis structures and ball & stick models of ammonia?” In this mixed-methods research, we collected data from purposively selected Grade 11 chemistry students aged between 15 and 18 from an under-resourced school in South Africa. Through a quasi-experimental design, participants in the experimental group (n = 101) used physical molecular models to learn about Lewis structure and ball & stick models of ammonia while participants in the control group (n = 100) did not. We subsequently tested students' visuo-semiotic reasoning skills. Results show that using physical molecular models significantly improved students' visuo-semiotic reasoning skills and reduced associated learning difficulties. We, therefore, recommend that these models should be used as an instructional tool to enhance learning. Keywords: ball & stick models, Lewis structures, physical models, visuo-semiotic reasoning.

Lewis structure is a sub-material that exists in chemical bonding material that is not mastered by students, so a diagnostic test is needed to reveal the difficulties experienced by students. This study aims to describe the difficulties of class X high school students in Palangka Raya City in understanding the concept of Lewis structure which is traced using two tier multiple choice instruments. The subjects of this study were students of class X from Public Senior High School 1 Palangka Raya, Public Senior High School 3 Palangka Raya and Public Senior High School 4 Palangka Raya with the total number of research subjects being 346 students. This research was conducted in the 2018/2019 academic year. Student difficulties were captured using the Lewis Structure Concept Understanding Test (TPKSL) in the form of reasoned multiple choice questions (Two Tier Multiple Choice) and interviews to confirm the difficulties experienced by students. The results showed that the difficulty of students in state high schools in the city of Palangka Raya in understanding the concept of Lewis structure with the smallest to the largest percentage of difficulties was to determine the electron configuration by 65.59%, determine the valence electron by 67.33%, determine the Lewis symbol by 67.33 %, and determine Lewis's structure 69.37%.

The prototype Diels-Alder (DA) reaction between butadiene and ethene (system 1) and the DA reaction involving 1-methoxy-butadiene and cyano-ethylene (system 2) are investigated with an explicit-time-dependent Density Functional Theory approach. Bond orders and atomic net charges obtained in the dynamics at the transition state geometry and along the reaction coordinate toward reactants are used to provide a picture of the process in terms of VB/Lewis resonance structures that contribute to a resonance hybrid. The entire dynamics can be divided into different domains (reactant-like, product-like, and transition state domains) where different Lewis resonance structures contribute with different weights. The relative importance of these three domains varies along the reaction coordinate. In addition to the usual reactant-like and product-like covalent Lewis structures, ionic Lewis structures have non-negligible weights. In system 2, the electron-donor OCH3 on the diene and the electron-acceptor CN on the dienophile make more important the contributions of ionic Lewis structures that stabilize the transition state and determine the decrease of the reaction barrier with respect to system 1.

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.

Latimer and Rodebush (J Am Chem Soc 42: 1419-1433, 1920) discussed the ways a Lewis dot structure could be drawn for liquid water and proposed that the H held between two octets constitutes a bond in 1920. When it was realized that the other molecule of life, DNA, owes its double helix structure to specific hydrogen bonds between A-T (two) and C-G (three) base pairs, the interest in hydrogen bonding grew dramatically. While hydrogen bonding could be readily seen in water and DNA, it was not so easy to understand leading to continuous debates about what it means. This article gives a personal perspective of the evolution of hydrogen bonding since the Latimer and Rodebush paper to the recent IUPAC definition of hydrogen bond, published in 2011 and now. Is there a third C-H center dot center dot center dot O hydrogen bond in the A-T base pair?

Dative Bond (IUPAC): "The coordination bond formed upon interaction between molecular species, one of which serves as a donor and the other as an acceptor of the electron pair to be shared in the complex formed… The distinctive feature of dative bonds is that their minimum-energy rupture in the gas phase or in inert solvent follows the heterolytic bond cleavage path." This definition encompasses an immense number of molecules such as Lewis adducts, transition-metal complexes, supposedly hypervalent or hypovalent systems, and many molecules with multifaceted Lewis structures. Still, there is a large reticence to include dative bonds in the regular depiction of molecules, and even a larger unawareness of the dative bond arrow in many chemical circles. Herein we will discuss in simple chemical terms the past, present and future of such bonds. In addition, we will try to provide cleaner options to represent intricate molecules without sacrificing physical accuracy.

Oxidation number (ON) is taught as an electron-counting concept for redox reactions in chemistry curriculum. The molecular formula method, the Lewis formula method, and the structural formula method have all been used to determine ON. However, the task of assigning ON still poses problems for some teachers and students. This paper explores a new method, the fragmentation method, which is a visual approach for counting the individual ON of any atom according to its structural formula. The critical step is to break the carbon-heteroatom bond into organic fragments and inorganic fragments. The individual ON of carbon atoms and heteroatoms can be determined by the bond cleavages in the organic and biological compounds. The mean ON of carbons can be calculated by the arithmetic mean of all individual ON of carbons in a molecule or molecular ion. The step-by-step operating procedures and examples are provided. When comparing corresponding molecules in organic conversions, the change of individual ON of atoms can be used as a tool for determining the number of transferred electrons. Furthermore, a reaction site can be identified by their changes of individual ON, chemical composition, and bond order in metabolic redox reactions.

Understanding chemical models can be challenging for many university students studying chemistry. This study analysed students’ understanding of molecular structures using the Lewis structure as a model, and examined what hinders their understanding. We conducted pre- and post-tests to analyse students’ conceptions and changes in them. The measures contained multiple-choice questions and drawing tasks testing their understanding of concepts, such as polarity, geometry, charge or formal charge and expanded octet. The pre-test revealed a lack of knowledge and several misconceptions in students’ prior knowledge. For example, the concept of polarity was well-known, but the combination of polarity and geometry appeared to be difficult. For some students, the representation of molecules was intuitive and lacking a systematic approach. Certain students used mnemonics and draw ball-and-stick models connected to surficial representations. After the chemistry courses, the conceptions and drawings had generally changed, and the level of the students’ knowledge increased markedly. Although, fewer ball-and-stick models were drawn in the post-test, some students still used them. The main result was that students who drew ball-and-stick models in the pre-test were less capable of drawing the correct Lewis structures with electrons in the post-test. In addition, heuristics seem to hinder learning and some concepts, such as resonance, remained difficult. This is probably due to the fact that understanding molecular structures requires systemic understanding, where several matters must be understood at the same time. Our study highlights that the understanding of molecular structures requires conceptual change related to several sub-concepts.

Many compounds can be represented well in terms of the two-center–two-electron (2c–2e) bond model. However, it is well-known that this approach has limitations; for example, certain compounds require the use of three-center–two-electron (3c–2e) bonds to provide an adequate description of the bonding. Although a classic example of a compound that features a 3c–2e bond is provided by diborane, B2H6, 3c–2e interactions also feature prominently in transition metal chemistry, as exemplified by bridging hydride compounds, agostic compounds, dihydrogen complexes, and hydrocarbon and silane σ-complexes. In addition to being able to identify the different types of bonds (2c–2e and 3c–2e) present in a molecule, it is essential to be able to utilize these models to evaluate the chemical reasonableness of a molecule by applying the octet and 18-electron rules; however, to do so requires determination of the electron counts of atoms in molecules. Although this is easily achieved for molecules that possess only 2c–2e bonds, the situation is more complex for those that possess 3c–2e bonds. Therefore, this article describes a convenient approach for representing 3c–2e interactions in a manner that facilitates the electron counting procedure for such compounds. In particular, specific attention is devoted to the use of the half-arrow formalism to represent 3c–2e interactions in compounds with bridging hydrogen atoms.

Using computational approaches, we qualitatively and quantitatively assess the bonding components of a series of experimentally characterized Au(I) diarylallenylidene complexes (N.Kim, R.A.Widenhoefer, Angew. Chem. Int. Ed. 2018, 57, 4722-4726). Our results clearly demonstrate that Au(I) engages only weakly in pi-backbonding, which is, however, a tunable bonding component. Computationally identified trends in bonding are clearly correlated with the substitution patterns of the aryl substituents in the Au(I) diarylallenylidene complexes and good agreement is found with the previously reported experimental data, such as IR spectra, C-13 NMR chemical shifts and rates of decomposition together with their corresponding barrier heights, further substantiating the computational findings. The description of the bonding patterns in these complexes allow predictions of their spectroscopic features, their reactivity and stability.

Noninnocent ligands do not allow an unambiguous definition of the oxidation state of a coordinated atom. When coordinated, the ligands also cannot be adequately represented by a classic Lewis structure. A noninnocent system thus harbors oxidizing (holes) or reducing equivalents (electrons) that are delocalized over both the ligand and the coordinated atom. To a certain degree, that is true of all complexes, but the phenomenon is arguably most conspicuous in complexes involving ligands with extended π-systems. The electronic structures of such systems have often been mischaracterized, thereby muddying the chemical literature to the detriment of students and newcomers to the field. In recent years, we have investigated the electronic structures of several metallocorrole families, several of which have turned out to be noninnocent. Our goal here, however, is not to present a systematic account of the different classes of metallocorroles, but rather to focus on seven major tools (in a nod to A. G. Cairns-Smith's

This article contrasts the normal method for drawing Lewis structures with a two-step systematic approach. The latter approach uses a known molecular connectivity and a knowledge of the number of valence electrons that each atom possesses to visualize bonds that are formed by pairing electrons, one from each atom. This process is repeated until at least one of the non-hydrogen atoms in each bond has an octet. Donor bonds are added when atoms with six and eight electrons are adjacent. In forming donor bonds charges are added to the atoms involved to maintain electron accounting and there is no need to use a formula to calculate formal charges. The general importance of adhering to the octet rule for p-block compounds is stressed and the difference between covalent and donor bonds and the use of the recent IUPAC definition of oxidation state which is based on Lewis structures is included in the discussion. When students are able to draw Lewis structures they can be given access to PC software, available on an academic free basis, which will draw rotatable Lewis structures in 3D for p-block compounds. The software allows the user to move electron pairs in a bow and arrow fashion within the structures and atoms are highlighted when the octet is exceeded.

A puzzle has been created that introduces bonding configurations and the structures of some common classes of organic compounds. Template pages with blank spaces that correspond to organic molecules are taped to the various walls of the classroom by the instructor. Students are each given a sticky note with an atom and bonds written on it which they must attach to the template pages in the correct configurations with their classmates. This seemingly simple task is actually very complex because (1) there are seven template molecules provided and students are not told what those molecules are, (2) students are not told which molecule their atom belongs to, (3) the puzzle pieces are square and thus offer no clues, and (4) there is only one correct solution for all of the pieces in the classroom. While students are focusing on the assigned task of building a molecule, they are simultaneously learning valid combinations of atoms and discussing them with their classmates. It is a fun way to either introduce or ...

The shared electron-pair bonding model was suggested by Gilbert Lewis more than 100 years ago. Emerging from the chemical experience of the time, Lewis structures described contemporary aspects of chemical reality in terms of empirically adapted models without any (then unknown) quantum physical underpinnings. This Perspective details the origins and historical development of the Lewis model, which we contrast with the physical understanding of chemical bonding in terms of contemporary quantum chemistry. Some intuitively plausible classical explanations of the past, not least of which are the sharing of electrons by two atoms and the subtypes of shared electron-pair bonding and dative bonding, turned out to be well founded. Some other chemical dogmata, including the concept that bonding occurs only between two nuclei and is caused by spin coupling or that bond energy is of purely electrostatic origin, are less well founded. We now know that covalent bonding is not driven by the formation of an electron pair but rather by the lowering of the kinetic energy density of the shared electrons in the bonding region, which is provided by the interference of the atomic wavefunctions. Lewis structures remain highly useful models for describing chemical bonding in molecular structures and chemical reactions, particularly when supported by quantum chemistry. The concepts behind the three most common quantum chemical approximations — the valence bond, molecular orbital and density functional theories — are described. These methods allow us to learn that bonding is an energetic phenomenon, from which descriptors such as bond length, bond dissociation energies and force constants are derivable. The energetic origins of bonding point to bond energy decomposition analysis as a natural tool for elucidating the actions of bonding electrons. Lewis’ shared electron-pair model was a stroke of genius, describing the structure and reactivity of molecules purely on the basis of his tremendous knowledge of empirical chemistry without any quantum chemistry. Unprecedented in simplicity, its success unfortunately concealed some misleading interpretations of the physical origin of chemical bonding.

Lewis structures are fundamental to learning chemistry, yet many students struggle to develop a complex understanding of its meaning and uses. Writing-to-Learn supports students in developing a deeper conceptual understanding of the topic, making it an ideal pedagogy to apply to student learning of Lewis structures. One difficulty often associated with classroom writing is the capacity of instructors to provide feedback to each student on their written work; however, this practical constraint can be mitigated through incorporating peer review. Peer review and revision are known to support conceptual learning and yet are underutilized in STEM (Science, Technology, Engineering, and Math) classrooms. Additionally, peer review is an authentic, common, and necessary practice in chemistry research, which warrants its incorporation early on in chemistry courses. A major concern regarding the use of peer review-based feedback is the ability of students to provide concept-based feedback that is both correct and de...

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.

We present, for the ground and first excited states of fulvene, the complete 3-D bond-path framework set B = {(p0,p1), (q0,q1), (r0,r1)} from the quantum theory of atoms in molecules (QTAIM) and B σH = {(pσH0,pσH1), (qσH0,qσH1), (r0,r1)} and B σ = {(pσ0,pσ1), (qσ0,qσ1), (r0,r1)} from the stress tensor within the QTAIM partitioning. We find that both the QTAIM bond-path framework sets B = {(p0,p1), (q0,q1), (r0,r1)} and the stress tensor B σ = {(pσ0,pσ1), (qσ0,qσ1), (r0,r1)} provide a quantitative 3-D rendering of the bonding that is consistent with understanding of the bonding provided by using Lewis structures.

Building chemical models from state-of-the-art electronic structure calculations is not an easy task, since the high-dimensional information contained in the wave function needs to be compressed and read in terms of the accepted chemical language. We have already shown ( Phys. Chem. Chem. Phys. 2018, 20, 21368) how to access Lewis structures from general wave functions in real space by reformulating the adaptive natural density partitioning (AdNDP) method proposed by Zubarev and Boldyrev ( Phys. Chem. Chem. Phys. 2008, 10, 5207). This provides intuitive Lewis descriptions from fully orbital invariant position space descriptors but depends on not immediately accessible higher order cumulant density matrices. By using an open quantum systems (OQS) perspective, we here show that the rigorously defined OQS fragment natural orbitals can be used to build a consistent real space adaptive natural density partitioning based only on spatial information and the system's one-particle density matrix. We show that this rs-AdNDP approach is a cheap, efficient, and robust technique that immerses electron counting arguments fully in the real space realm.

This chapter presents the results obtained when the level of student preparedness for 2nd year Inorganic chemistry module was investigated. This was done by using a diagnostic test based mainly on concepts that are pre-requisite or foundational knowledge (high school and 1st year chemistry syllabi) to the 2nd year Inorganic Chemistry course, CHE 2521. The diagnostic test covered the following concepts: hybridization, electronegativity, octet rule, bonding, periodic table, electronic configuration, Lewis structures and resonance. The study highlighted the presence of misconceptions and general lack of preparedness for the subsequent CHE 2521 module. The most important misconceptions suggested by students’ responses are described and discussed, and, where possible, suggestions on their sources are outlined.

Fermi--L\"owdin orbitals (FLO) are a special set of localized orbitals, which have become commonly used in combination with the Perdew--Zunger self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained for a set of occupied orbitals by specifying a classical position for each electron. These positions are known as Fermi-orbital descriptors (FODs), and they have a clear relation to chemical bonding. In this study, we show how FLOs and FODs can be used to initialize, interpret and justify SIC solutions in a common chemical picture, both within FLO-SIC and in traditional variational SIC, and to locate distinct local minima in either of these approaches. We demonstrate that FLOs based on Lewis' theory lead to symmetry breaking for benzene -- the electron density is found to break symmetry already at the symmetric molecular structure -- while ones from Linnett's double-quartet theory reproduce symmetric electron densities and molecular geometries. Introducing a benchmark set of 16 planar, cyclic molecules, we show that using Lewis' theory as the starting point can lead to artifactual dipole moments of up to 1 Debye, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking. The role of hovering FODs is also briefly discussed., Comment: 14 pages, 8 figures, includes the SI as an attachment Changes to v1: Added some more theory, adjusted Fig.1 for better readability

Chemists explaining a molecule’s stability and reactivity often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a ring delocalization in cyclic planar systems which abide certain number rules. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths. Most notably, the famous 4n + 2 Hückel rule is generalized and derived from nothing but the antisymmetry of fermionic wave functions., The concept of delocalization, resonance and aromaticity are commonly discussed within electronic structure frameworks relying on specific wave function expansions. Here the authors propose a redefinition of these concepts from first-principles by investigating saddle points of the all-electron probability density.

The way chemists represent chemical structures as two-dimensional sketches made up of atoms and bonds, simplifying the complex three-dimensional molecules comprising nuclei and electrons of the quantum mechanical description, is the everyday language of chemistry. This language uses models, particularly of bonding, that are not contained in the quantum mechanical description of chemical systems, but has been used to derive machine-readable formats for storing and manipulating chemical structures in digital computers. This language is fuzzy and varies from chemist to chemist but has been astonishingly successful and perhaps contributes with its fuzziness to the success of chemistry. It is this creative imagination of chemical structures that has been fundamental to the cognition of chemistry and has allowed thought experiments to take place. Within the everyday language, the model nature of these concepts is not always clear to practicing chemists, so that controversial discussions about the merits of alternative models often arise. However, the extensive use of artificial intelligence (AI) and machine learning (ML) in chemistry, with the aim of being able to make reliable predictions, will require that these models be extended to cover all relevant properties and characteristics of chemical systems. This, in turn, imposes conditions such as completeness, compactness, computational efficiency and non-redundancy on the extensions to the almost universal Lewis and VSEPR bonding models. Thus, AI and ML are likely to be important in rationalizing, extending and standardizing chemical bonding models. This will not affect the everyday language of chemistry but may help to understand the unique basis of chemical language.

Students in a second semester general chemistry course used quantum chemical calculations to investigate and reinforce general chemistry concepts. Students explored the isomers of hypochlorous acid, made predictions of miscibility via dipole moments calculated from ab-initio means, experimentally validated/disqualified their miscibility predictions, and used molecular models to visualize intermolecular attraction forces between various compounds. Student responses in pre-/post-exercise assessments show evidence of student learning. Responses in pre-/post-exercise surveys showed an increase in student understanding of basic concepts and of the importance of quantum mechanics in common general chemistry topics.

The unsymmetrical coordination of gold(I) by 2,2'-bipyridine (bipy) in some planar, three-coordinate cations has been examined by crystallographic and computational studies. The salts [(Ph3P)Au(bipy)]XF6 (X = P, As, Sb) form an isomorphic series in which the differences in Au-N distances range from 0.241(2) to 0.146(2) A. A second polymorph of [(Ph3P)Au(bipy)]AsF6 has also been found. Both polymorphs exhibit similar structures. The salts [(Et3P)Au(bipy)]XF6 (X = P, As, Sb) form a second isostructural series. In this series the unsymmetrical coordination of the bipy ligand is maintained, but the gold ions are disordered over two unequally populated positions that produce very similar overall structures for the cations. Although many planar, three-coordinate gold(I) complexes are strongly luminescent, the salts [(R3P)Au(bipy)]XF6 (R = Ph or Et; X = P, As, Sb) are not luminescent as solids or in solution. Computational studies revealed that a fully symmetrical structure for [(Et3P)Au(bipy)]+ is 7 kJ/mol higher in energy than the observed unsymmetrical structure and is best described as a transition state between the two limiting unsymmetrical geometries. The Au-N bonding has been examined by natural resonance theory (NRT) calculations using the "12 electron rule". The dominant Lewis structure is one with five lone pairs on Au and one bond to the P atom, which results in a saturated (12 electron) gold center and thereby inhibits the formation of any classical, 2 e- bonds between the gold and either of the bipy nitrogen atoms. The nitrogen atoms may instead donate a lone pair into an empty Au-P antibonding orbital, resulting in a three-center, four-electron (3c/4e) P-Au-N bond. The binuclear complex, [μ2-bipy(AuPPh3)2](PF6)2, has also been prepared and shown to have an aurophillic interaction between the two gold ions, which are separated by 3.0747(3) A. Despite the aurophillic interaction, this binuclear complex is not luminescent.

International audience; This article dwells on the nature of “inverted bonds”, which refer to the σ interaction between two sp hybrids by their smaller lobes, and their presence in [1.1.1]propellane. Firstly, we study H3C−C models of C−C bonds with frozen H‐C‐C angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane and [1.1.1]bicyclopentane are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate bond energies. Triplet and cationic states of [1.1.1]propellane species are also considered to confirm the bonding/antibonding character of MOs in the parent molecule. These approaches show an essentially non‐bonding character of the σ central C−C interaction in propellane. Within the MO theory, this bonding is thus only due to π‐type MOs (also called “banana” MOs or “bridge” MOs) and its total energy is evaluated to approximately 50 kcal mol−1. In bicyclopentane, despite a strong σ‐type repulsion, a weak bonding (15–20 kcal mol−1) exists between both central C−C bonds, also due to π‐type interactions, though no bond is present in the Lewis structure. Overall, the so‐called “inverted” bond, as resulting from a σ overlap of the two sp hybrids by their smaller lobes, appears highly questionable.

It is shown how use of valence bond structures of the type for a 5-electron 3-centre bonding unit can help to provide compact valence bond representations of the electronic structures for NO2, N2O4, excited O3 and SO2, SO3, SO2Y2 (with Y = OH−, O− or F), ClO2, SO2−, S2O42−, [Cu(H2O)6]2+ and an N H N linkage. Without atomic valence shell expansions, many of these structures provide electronic interpretations for hypervalent 19th century type bond diagrams. As an example, it is shown that the 5-electron 3-centre valence bond structure for N2O4 (which is equivalent to resonance between 144 canonical Lewis structures) provides an electronic interpretation for Frankland’s 1866 bond diagram with pentavalent nitrogen atoms.

Phosphine‐stabilized germaborenes featuring an unprecedented Ge=B double bond with short B⋅⋅⋅Ge contacts of 1.886(2) (4) and 1.895(3) Å (5) were synthesized starting from an intramolecular germylene–phosphine Lewis pair (1). After oxidative addition of boron trihalides BX3 (X=Cl, Br), the addition products were reduced with magnesium and catalytic amounts of anthracene to give the borylene derivatives in yields of 78 % (4) and 57 % (5). These halide‐substituted germaborenes were characterized by single‐crystal structure analysis, and the electronic structures were studied by quantum‐chemical calculations. According to an NBO NRT analysis, the dominating Lewis structure contains a Ge=B double bond. The germaborenes undergo a reversible, photochemically initiated [2+2] cycloaddition with the phenyl moiety of a terphenyl substituent at room temperature, forming a complex heterocyclic structure with GeIV in a strongly distorted coordination environment., Germaborenes with the first authentic Ge=B double bond were synthesized. Upon photoactivation, germaborenes undergo a reversible [2+2] cycloaddition reaction with an arene moiety.

An explanation is presented for the unusual conformations of some molecules that contain the C═C-C═C core, namely, butadienes, biphenyls, and styrenes. Small substituents often induce a synclinal conformation, which brings the substituents into close proximity, and sometimes, there is no anticlinal minimum at all. This would not be predicted from steric repulsion arguments nor would it be expected that atoms that are nonbonded in a Lewis structure would approach closer than the sum of their van der Waals radii. Atomic energies calculated according to the quantum theory of atoms in molecules (QTAIM) do not show a consistent pattern for these structurally similar molecules, nor are intersubstituent bond paths consistently found, nor favorable diatomic interaction energies calculated using the interacting quantum atoms (IQA) scheme. Instead, the synclinal conformations are found to be driven by the attraction energy of the electron distribution of the carbon atoms and the nuclei of the molecule.

There is a great variety of bond analysis tools that aim to extract information on the bonding situation from the molecular wavefunction. Because none of these can fully describe bonding in all of its complexity, it is necessary to regard a balanced selection of complementary analysis methods to obtain a reliable chemical conclusion. This is, however, not a feasible approach in most studies because it is a time-consuming procedure. Therefore, we provide the first comprehensive comparison of modern bonding analysis methods to reveal their informative value. The element-oxygen bond of neutral Hn XOH model compounds (X=Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl) is investigated with a selection of different bond analysis tools, which may be assigned into three different categories: i) real space bonding indicators (quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the Raub-Jansen index), ii) orbital-based descriptors (natural bond orbitals (NBO), natural resonance theory (NRT), and valence bond (VB) calculations), and iii) energy analysis methods (energy decomposition analysis (EDA) and the Q-analysis). Besides gaining a deep insight into the nature of the element-oxygen bond across the periodic table, this systematic investigation allows us to get an impression on how well these tools complement each other. Ionic, highly polarized, polarized covalent, and charge-shift bonds are discerned from each other.

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.

This study explores first-year university students’ reasoning as they learn to draw Lewis structures. We also present a theoretical account of the formal procedure commonly taught for drawing these structures. Students’ discussions during problem-solving activities were video recorded and detailed analyses of the discussions were made through the use of practical epistemology analysis (PEA). Our results show that the formal procedure was central for drawing Lewis structures, but its use varied depending on situational aspects. Commonly, the use of individual steps of the formal procedure was contingent on experiences of chemical structures, and other information such as the characteristics of the problem given. The analysis revealed a number of patterns in how students constructed, checked and modified the structure in relation to the formal procedure and the situational aspects. We suggest that explicitly teaching the formal procedure as a process of constructing, checking and modifying might be ...

The nature of the electronic-structure of polyenes, their delocalization features, and potential diradicaloid characters constitute a fundamental problem in chemistry. To address this problem, we used valence bond self-consistent field (VBSCF) calculations and modeling of polyenes, C2nH2n+2 (n = 2–10). The theoretical treatment shows that starting with n = 5, the polyene’s wave function is mainly a shifting 1,4-diradicaloid, a character that increases as the chain length increases, while the contribution of the fundamental Lewis structure with alternating double and single bonds (1) decays quite fast and becomes minor relative to the diradicaloid pack. We show how, nevertheless, it is this wave function that predicts that polyenes will still exhibit alternating short/long CC bonds like the fundamental structure 1. Furthermore, despite the decay of the VB contribution of 1, it remains the single structure with the largest weight among all the individual structures. The mixing of all the 1,4-diradicaloid st...

A stand-alone polymer unit, centered on a tie-dye activity, was used to introduce the concept of polymers and the process of polymerization to three different groups of beginning-level chemistry students. This polymer unit consists of three parts. First, each student used a molecular model kit to construct the monomer units, β-d-glucose. Students combined these monomer units to learn the polymerization process and visualize the formation of the cellulose polymer in conjunction with writing the balanced equation for the polymerization reaction. Second, students tie-dyed cotton t-shirts made of cellulose fibers using dyes purchased from local craft stores. Finally, a primary literature exercise engaged students in understanding the chemical reactions that bind the cellulose fibers to the dye molecules permanently, producing a colorfast tie-dyed t-shirt. This stand-alone polymer unit can be used in any beginning college or high school chemistry course to introduce students to polymer chemistry and the proces...

Quantum chemical calculations have been carried out to study the electronic structure of metalated ylides particularly in comparison to their neutral analogues, the bisylides. A series of compounds of the general composition Ph3P−C−L with L being either a neutral or an anionic ligand were analyzed and the impact of the nature of the substituent L and the total charge on the electronics and bonding situation was studied. The charge at the carbon atom as well as the dissociation energies, bond lengths, and Wiberg bond indices strongly depend on the nature of L. Here, not only the charge of the ligand but also the position of the charge within the ligand backbone plays an important role. Independent of the substitution pattern, the NBO analysis reveals the preference of unsymmetrical bonding situations (P=C−L or P−C=L) for almost all compounds. However, Lewis structures with two lone‐pair orbitals at the central carbon atom are equally valid for the description of the bonding situation. This is confirmed by the pronounced lone‐pair character of the frontier orbitals. Energy decomposition analysis mostly reveals the preference of several bonding situations, mostly with dative and ylidic electron‐sharing bonds (e.g., P→C−−L). In general, the anionic systems show a higher preference of the ylidic bonding situations compared to the neutral analogues. However, in most of the cases different resonance structures have to be considered for the description of the “real” bonding situation.

Mastering the ability to construct and manipulate Lewis structures is an important first step along the journey to reaching representational competence. Lewis structures serve as a convenient organizational scheme that can help students to scaffold their chemical knowledge and help them to apply it to predict a variety of physical and chemical properties. Our previous research documented the many problems that students encountered in developing these skills and suggested that cognitive load may play an important role in the successful construction of Lewis structures. This study sought to better understand the structural characteristics and complexities that contributed significantly to the cognitive load of chemistry students drawing Lewis structures and to determine how those load-inducing characteristics changed as students gained additional chemical expertise. The results of the inquiry show that the inclusion of nearly any structural characteristic induced a significant increase in cognitive load for...