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The molecular orbital (MO) concept is a useful tool, which relates the molecular ground-state energy with the energies (and occupations) of the individual orbitals. However, analysis of the excited states from linear response computations is performed in terms of the initial state MOs or some other forms of orbitals, e.g., natural or natural transition orbitals. Because these orbitals lack the respective energies, they do not allow developing a consistent orbital picture of the excited states. Herein, we argue that Dyson’s orbitals enable description of the response states compatible with the concepts of molecular orbital theory. The Dyson orbitals and their energies obtained by mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) for the response ground state are remarkably similar to the canonical MOs obtained by the usual DFT calculation. For excited states, the Dyson orbitals provide a chemically sensible picture of the electronic transitions, thus bridging the chasm between orbital theory and response computations.

BaBiO3(BBO) is known to be a valence-skipping perovskite, which avoids the metallic state through charge disproportionation (CD), the mechanism of which is still unresolved. A novel mechanism for CD is presented here in the covalent limit using a molecular orbital (MO) picture under two scenarios: (case i) Bi 6sp-O 2p and (case ii) Bi 6p-O 2p hybridizations that favor 5+ and 3+ states, respectively. The proposed model is further validated by using a combinatorial approach of X-ray spectroscopic experiments and first-principle calculations. The bulk X-ray photoemission spectrum reveals that, at room temperature, the CD is dynamic in nature, whereas, at 200 K, it approaches a quasi-static limit. Under compressive strain, the octahedral breathing mode is damped and drives the system to a quasi-static limit even at room temperature, giving rise to asymmetric CD.

In the limit of dilute alloying-the so-called "single-atom alloy" (SAA) regime-certain bimetallic systems exhibit weak mixing between constituent metal wave functions, resulting in sharp, single-atom-like electronic states localized on the dilute component of the alloy. This work shows that when these sharp states are appropriately positioned relative to given molecular orbitals, selective hybridization is enhanced, in accordance with intuitive principles of molecular orbital theory. We demonstrate the phenomenon for activation pathways of crotonaldehyde, a model α,β-unsaturated aldehyde relevant to a wide range of chemical manufacturing. This analysis suggests new possible strategies for selectivity control in heterogeneous catalysis.

The observation and characterization of the anions: Th2O-, Th2Au-, and Th2AuO1,2- is reported. These species were studied through a synergetic combination of anion photoelectron spectroscopy and ab initio correlated molecular orbital theory calculations at the CCSD(T) level with large correlation-consistent basis sets. To better understand the energetics and bonding in these anions and their corresponding neutrals, a range of smaller diatomic to tetratomic species were studied computationally. Correlated molecular orbital theory calculations at the CCSD(T) level showed that in most of these cases, there are close-lying anions and neutral clusters with different geometries and spin states and are consistent with the experimentally observed spectra. Thus, comparison of experimentally determined and computationally predicted vertical detachment energies and electron affinities for different optimized geometries and spin states shows excellent agreement to within 0.1 eV. The structures for both the neutrals and anions have a significant ionic component to the bonding because of the large electron affinity of the Au atom and modest ionization potentials for Th2, Th2O, and Th2O2. The analysis of the bonding for the Th-Th bonds from the molecular orbitals is consistent with this ionic model. The results show that there is a wide variation in the bond distance from 2.7 to 3.5 A for the Th-Th bonds all of which are less than twice the atomic radius of Th of 3.6 A. The bond distances encompass bond orders from 4 to 0. There can be different bond orders for the same bond distance depending on the nature of the ionic bonding suggesting that one may not be able to correlate the bond order with the bond distance in these types of clusters. In addition, the presence of an Au atom may provide a unique probe of the bonding in such clusters because of its ability to accept an electron from clusters with modest ionization potentials.

The electronic structure of benzene is a battleground for competing viewpoints of electronic structure, with valence bond theory localising electrons within superimposed resonance structures, and molecular orbital theory describing delocalised electrons. But, the interpretation of electronic structure in terms of orbitals ignores that the wavefunction is anti-symmetric upon interchange of like-spins. Furthermore, molecular orbitals do not provide an intuitive description of electron correlation. Here we show that the 126-dimensional electronic wavefunction of benzene can be partitioned into tiles related by permutation of like-spins. Employing correlated wavefunctions, these tiles are projected onto the three dimensions of each electron to reveal the superposition of Kekulé structures. But, opposing spins favour the occupancy of alternate Kekulé structures. This result succinctly describes the principal effect of electron correlation in benzene and underlines that electrons will not be spatially paired when it is energetically advantageous to avoid one another., The electronic structure of benzene has been a test bed for competing theories along the years. Here the authors show via quantum chemistry calculations that the wavefunction of benzene can be partitioned into tiles which show that the two electron spins exhibit staggered Kekulé structures.

In this paper, we develop a general but very simple mathematical foundation for the predefined coefficient graphical method of Huckel molecular orbital theory (HMO). We first present the general solution for the recurrence relation of the coefficients of Huckel molecular orbitals (MOs). Subsequently, for all the three unbranched hydrocarbons, i.e., open-chain, cyclic Huckel and Mobius polyenes, different boundary conditions are explored for obtaining the MOs and their energy levels. The analytic continuation of the recurrence relation, in which one extends the domain from integral to real, allows us to analyze the symmetric properties of Huckel MOs in an elegant fashion without even knowing the actual expressions. In fact, we can use the symmetric properties to derive the Huckel MOs of the unbranched hydrocarbons and some branched hydrocarbons such as naphthalene. Consequently, this work also provides a pedagogical alternative to present the HMO model for students in an advanced physical chemistry course. Finally, the graphical approach could be a good mnemonic device for students’ comprehension of the HMO theory.

Introductory chemistry textbooks often present valence bond (VB) theory as useful, but incorrect and inferior to molecular orbital (MO) theory, citing the electronic structure of O2 and electron de...

One challenge in chemistry is the plethora of often disparate models for rationalizing the electronic structure of molecules. Chemical concepts abound, but their connections are often frail. This work describes a quantum-mechanical framework that enables a combination of ideas from three approaches common for the analysis of chemical bonds: energy decomposition analysis (EDA), quantum chemical topology, and molecular orbital (MO) theory. The glue to our theory is the electron energy density, interpretable as one part electrons and one part electronegativity. We present a three-dimensional analysis of the electron energy density and use it to redefine what constitutes an atom in a molecule. Definitions of atomic partial charge and electronegativity follow in a way that connects these concepts to the total energy of a molecule. The formation of polar bonds is predicted to cause inversion of electronegativity, and a new perspective of bonding in diborane and guanine−cytosine base-pairing is presented. The electronegativity of atoms inside molecules is shown to be predictive of pKa.

The influence of Linus Pauling on the understanding of chemical bonding is critically examined. Pauling deserves credit for presenting a connection between the quantum theoretical description of chemical bonding and Gilbert Lewis’s classical bonding model of localized electron pair bonds for a wide range of chemistry. Using the concept of resonance that he introduced, he was able to present a consistent description of chemical bonding for molecules, metals, and ionic crystals which was used by many chemists and subsequently found its way into chemistry textbooks. However, his one-sided restriction to the valence bond method and his rejection of the molecular orbital approach hindered further development of chemical bonding theory for a while and his close association of the heuristic Lewis binding model with the quantum chemical VB approach led to misleading ideas until today.

Since a transition metal methyl complex corresponds to a compound in which one hydrogen atom of methane is replaced by a transition metal (M), the M–C linkage is considered to be a σ-bond and covalent. To understand the properties and reactivity of organometallic complexes, it is important to understand the character of M–C σ-bonds in transition metal alkyl complexes. The polarization of the bond and the effect of other C substituents on the strength of M–C bonds are explained. Taking a metal–carbonyl (CO) bond and a metal–olefin bond as examples, the σ-donation of electrons from a ligand to a metal and the π-back donation from a metal to a ligand are described. In addition, the Dewar–Chatt–Duncanson model is also explained. It is necessary to understand the application of molecular orbital theory to transition metal complexes. Although crystal field theory explains in a clear and simple way how the transition metal d orbital energies split when ligands approach the metal to form a complex, and this is sufficient for understanding Werner type complexes, it is insufficient for understanding organometallic complexes. Ligand field theory therefore emerged, combining molecular orbital and crystal field theory concepts, while remaining relatively simple. Applying this theory, it is apparent why organometallic complexes follow the 18-electron rule. In this chapter, crystal field theory, and its successor, ligand field theory, are described.

In this work, two exercises are described that are designed to teach students about the evolution and behavior of the electronic bands of graphene and bilayer graphene. These exercises involve performing extended Huckel molecular orbital theory calculations on polyacenes and polycyclic aromatic hydrocarbons. In the first exercise, students investigate how the molecular orbitals of polyacenes converge into bands as polyacene size increases. Further, students learn that long-range interactions cause frontier-orbital crossing as the size of the polyacene increases. In the second exercise, the concepts of band structures, band crossing, and k-space are explored using the results of frontier orbital calculations on π-stacked dimers of polycyclic aromatic hydrocarbons, which represent molecular analogues of layered 2D materials. The results of these calculations show how the geometry and layer–layer offset of the dimer system can affect its electronic structure, and the results can be extrapolated to provide a framework for understanding why subtle changes in the relative orientations of the layers in bilayer graphene can produce qualitative changes in the electronic properties. These calculations are easily implemented with Python or with widely available algebraic manipulation software such as Maple or Mathematica. These exercises are accessible to students who have experience with extended Huckel molecular orbital theory and are suitable for inclusion in the physical chemistry curriculum at the upper-level undergraduate or introductory graduate level.

We discuss the concept of cation affinities (CA) and provide an overview of topical trends throughout the periodic table, inferred from state-of-the-art relativistic quantum-chemical computations. The CA of a base B (−) for a cation Y + is the energy or enthalpy required to dissociate the complex BY (+) into molecular fragments B (−) and Y + . Probably the best-known CA is the proton affinity (PA) of Lewis bases. We extend this concept here to include methyl cation (MCA) and other alkyl cation affinities (ACA) as well as alkali metal cation affinities (AMCA). The Lewis bases covered herein are the anionic and neutral element hydrides B − = XH n−1 − and B = XH n , respectively, as well as methyl-substituted variants thereof. The element “X” in our model Lewis bases covers the maingroup elements of groups 14–18 in rows 1–6 of the periodic table. Emerging trends are analyzed and explained in terms of quantitative molecular orbital (MO) theory as contained in Kohn–Sham density functional theory (KS-DFT). Making the often implicitly used idea of a CA explicit serves a more rational design of compounds with a particular affinity for, or reactivity toward, other species throughout the molecular sciences, from inorganic via organic to biological chemistry.

A fundamental and ubiquitous phenomenon in chemistry is the contraction of both C−H and C−C bonds as the carbon atoms involved vary, in s–p hybridization, along sp3 to sp2 to sp. Our quantum chemical bonding analyses based on Kohn–Sham molecular orbital theory show that the generally accepted rationale behind this trend is incorrect. Inspection of the molecular orbitals and their corresponding orbital overlaps reveals that the above‐mentioned shortening in C−H and C−C bonds is not determined by an increasing amount of s‐character at the carbon atom in these bonds. Instead, we establish that this structural trend is caused by a diminishing steric (Pauli) repulsion between substituents around the pertinent carbon atom, as the coordination number decreases along sp3 to sp2 to sp., A paradigm shift! Our quantum chemical analyses reveal that, for example, C−H bonds along ethane, ethylene, and acetylene, do not contract due to the changing s–p hybridization of the pertinent carbon atom from sp3 to sp2 to sp but, instead, because the steric congestion around this carbon atom decreases as the coordination number goes from 4 to 3 to 2.

This essay describes the successive births of valence bond (VB) theory during 1916–1931. The alternative molecular orbital (MO) theory was born in the late 1920s. The presence of two seemingly different descriptions of molecules by the two theories led to struggles between the main proponents, Linus Pauling and Robert Mulliken, and their supporters. Until the 1950s, VB theory was dominant, and then it was eclipsed by MO theory. The struggles will be discussed, as well as the new dawn of VB theory, and its future.

The binding of a positron to fluorobenzene molecules was theoretically demonstrated at Hartree-Fock level of multi-component molecular orbital theory. We confirmed that (i) 1,2-difluorobenzene, 1,2,3-trifluorobenzene, 1,2,3,4-tetrafluorobenzene molecules have bound states for a positron, and (ii) their positron affinity (PA) and two photon pair-annihilation rate (Γ2) are strongly correlated with their dipole moment. Analyzing the Γ2 values for each electronic molecular orbital in all the fluorobenzene molecules, we found that the electronic valence orbitals, consisting of 2p atomic orbitals of fluorine atoms, have the dominant contribution to the total Γ2 value.

Mono- and bis-decylated lumazines have been synthesized and characterized. Namely, mono-decyl chain [1-decylpteridine-2,4(1,3H)-dione] 6a and bis-decyl chain [1,3-didecylpteridine-2,4(1,3H)-dione] 7a conjugates were synthesized by nucleophilic substitution (SN 2) reactions of lumazine with 1-iododecane in N,N-dimethylformamide (DMF) solvent. Decyl chain coupling occurred at the N1 site and then the N3 site in a sequential manner, without DMF condensation. Molecular orbital (MO) calculations show a p-orbital at N1 but not N3 , which along with a nucleophilicity parameter (N) analysis predict alkylation at N1 in lumazine. Only after the alkylation at N1 in 6a, does a p-orbital on N3 emerge thereby reacting with a second equivalent of 1-iododecane to reach the dialkylated product 7a. Data from NMR (1 H, 13 C, HSQC, HMBC), HPLC, TLC, UV-vis, fluorescence and density functional theory (DFT) provide evidence for the existence of mono-decyl chain 6a and bis-decyl chain 7a. These results differ to pterin O-alkylations (kinetic control), where N-alkylation of lumazine is preferred and then to dialkylation (thermodynamic control), with an avoidance of DMF solvent condensation. These findings add to the list of alkylation strategies for increasing sensitizer lipophilicity for use in photodynamic therapy., Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

Chemical bond plays a central role in the description of the physicochemical properties of molecules and solids and it is essential to several fields in science and engineering, governing the material’s mechanical, electrical, catalytic and optoelectronic properties, among others. Due to this indisputable importance, a proper description of chemical bond is needed, commonly obtained through solving the Schrödinger equation of the system with either molecular orbital theory (molecules) or band theory (solids). However, connecting these seemingly different concepts is not a straightforward task for students and there is a gap in the available textbooks concerning this subject. This work presents a chemical content to be added in the physical chemistry undergraduate courses, in which the framework of molecular orbitals was used to qualitatively explain the standard state of the chemical elements and some properties of the resulting material, such as gas or crystalline solids. Here in Part 1, we were able to show the transition from Van der Waals clusters to metal in alkali and alkaline earth systems. In Part 2 and 3 of this three-part work, the present framework is applied to main group elements and transition metals. The original content discussed here can be adapted and incorporated in undergraduate and graduate physical chemistry and/or materials science textbooks and also serves as a conceptual guide to subsequent disciplines such as quantum chemistry, quantum mechanics and solid-state physics.

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.

What electrons are doing in molecules (at fixed positions of the nuclei) is described by their wave function – a solution to the Schrodinger equation. This equation however cannot be solved analytically. To obtain an approximate wave function the variational method is most useful. In this chapter a special kind of the variational method is presented, which restricts the form of the trial function to a single Slater determinant composed of molecular orbitals. In this way the variational method returns the best possible single Slater determinant. Each molecular orbital represents a kind of a single-electron wave function – a “home” for two electrons of opposite spin. We will now learn how to get the optimum molecular orbitals (Hartree–Fock method). Not only does this orbital picture give reasonable results, at the same time it also provides a kind of universal language of theoretical chemistry.

Principles are presented for the design of functional near-infrared (NIR) organic dye molecules composed of simple donor (D), spacer (π), and acceptor (A) building blocks in a D-π-A fashion. Quantitative Kohn-Sham molecular orbital analysis enables accurate fine-tuning of the electronic properties of the π-conjugated aromatic cores by effecting their size, including silaaromatics, adding donor and acceptor substituents, and manipulating the D-π-A torsional angle. The trends in HOMO-LUMO gaps of the model dyes correlate with the excitation energies computed with time-dependent density functional theory at CAMY-B3LYP. Design principles could be developed from these analyses, which led to a proof-of-concept linear D-π-A with a strong excited-state intramolecular charge transfer and a NIR absorption at 879 nm. © 2018 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Large-scale molecular orbital balloon models have been designed and developed for implementation in the general, organic, or physical chemistry classroom. The purposes of the models are to help students visualize and understand concepts of pi-bonding, conjugation, aromaticity, and cycloaddition reactions or symmetry-controlled reactions. Second-semester organic chemistry students have welcomed the models with positive responses, claiming that the 3D models bring 2D textbook and lecture images to life. The balloon models may be constructed and presented by the instructor during a formal lecture, or they may be constructed by students during problem-solving workshops. Short video tutorials have been created to demonstrate the construction of these inexpensive classroom manipulatives.

Electron pairs through the looking glass might well discover that they can show two faces, one delocalized or the other localized, and that both are perfectly correct. Going back and forth between these two representations, according to which one is the most relevant and insightful for the case at hand, is easy and essential to get a complete understanding of electronic structure.

By means of molecular orbital theory and the analysis of charge transfer and electrostatic forces, we discuss the features of non-covalent hole interactions of the halogen, chalcogen and pnictogen bond families. The use of MOs allows us to explain and predict the location of holes, and to design novel interactions such as systems with σ and π holes on the same or opposite sides. In view of the orbital origin of the hole interactions, we suggest that many chalcogen and pnictogen bonds are largely based on π holes and not on the commonly accepted σ holes. In addition, a new type of hole interaction based on δ holes is found on the sextuply bonded dimolybdenum.

The “Yet Another extended Huckel Molecular Orbital Package” (YAeHMOP) has been merged with theAvogadro open-source molecular editor and visualizer. It is now possible to perform YAeHMOP calculations directly from the Avogadro graphical user interface for materials that are periodic in one, two, or three dimensions, and to visualize band structures, total and projected density of states, and crystal orbital overlap/Hamilton populations (COOPs/COHPs). Calculations on graphite, silicon, sodium, and a one-dimensional hydrogen chain are provided to illustrate the functionality. Similar exercises have been carried out in an upper-level undergraduate quantum theory course.

The present study proposes a methodology that advances the selection of initial orbitals for subsequent use in correlation calculations. The initial orbital sets used herein are split-localized orbitals that span a full-valence orbital space and were developed in a previous study ( J. Chem. Phys. 2013 , 139 , 234107 ) in order to reveal the bonding patterns of molecules in a specific, quantitative manner. On the basis of the quantitative chemical features of these localized orbitals, this new method systematically extracts orbital sets and assigns excitation levels that systematically recover strong correlation with smaller numbers of configurations than can be achieved with traditional as well as nontraditional correlation methods. Moreover, this method not only provides organized initial orbitals for correlation calculations but also results in compact configuration interaction expansions via the use of the split-localized orbitals.

We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multi-configuration and multireference (MR) electronic structure calculations. Concretely, the technique constructs active molecular orbitals capable of describing all relevant electronic configurations emerging from a targeted set of atomic valence orbitals (e.g., the metal d orbitals in a coordination complex). This is achieved via a linear transformation of the occupied and unoccupied orbital spaces from an easily obtainable single-reference wavefunction (such as from a Hartree-Fock or Kohn-Sham calculations) based on projectors to targeted atomic valence orbitals. We discuss the premises, theory, and implementation of the idea, and several of its variations are tested. To investigate the performance and accuracy, we calculate the excitation energies for various transition metal complexes in typical application scenarios. Additionally, we follow the homolytic bond breaking process of a Fenton reaction along its reaction coordinate. While the described AVAS technique is not an universal solution to the active space problem, its premises are fulfilled in many application scenarios of transition metal chemistry and bond dissociation processes. In these cases the technique makes MR calculations easier to execute, easier to reproduce by any user, and simplifies the determination of the appropriate size of the active space required for accurate results., Comment: 51 pages

In a recent work, we performed free-energy analyses for hydration of benzene by conducting QM/MM-ER simulations, where the total solvation free energy was decomposed into contributions and . is the...

The low-energy structures of AlnCm (n = 4, 6; m = 1–4) are determined by using the genetic algorithm combined with density functional theory and the QCISD models. The electronic structures and bonding features are analyzed through the density of states (DOS), valence molecular orbitals (MOs), and electron localization function (ELF). The results show that the carbon atoms tend to aggregate and sit at the center of the clusters. The C–C bond lengths in most cases agree with the double C═C bond. Because of the large difference between the electronegativities of carbon and aluminum atoms, almost all of the 3p electrons of Al transfer to C atoms. The 3s orbitals of Al and the 2s2p orbitals of C form bonding and antibonding orbitals; the bonding orbitals correspond to the covalent C–Al bonds, and the antibonding orbitals form lone pair electrons on the outer side of Al atoms. The lone pair electrons form large local dipole moments and enhance the electrostatic interactions between C and Al atoms. Planar geomet...

Novel DNA triangular pyrimidine derivatives are designed by metal decoration through replacement of H by Cu in the Watson–Crick hydrogen bond region. The DFT method is used to examine the coordination of triangle-arranged Cu with three pyrimidines in nonplanar three-bladed turbine geometries. The Cu···Cu cuprophilic bonds are ascribed to the partially occupied d orbitals without direct molecular orbital (MO) interactions. Four-center bonds depend on Cu–N/O bonds, which are contributed by p orbitals of N/O atoms along or perpendicular to the bond axis. The activity of frontier MOs is modulated, leading to the decrease of gaps, ionization potentials (IPs), and electron affinities (EAs) desired for the improvement of conductivity. The hole trapping ability is assured by virtue of the spin density distributed on Cu. On average, the single electron density is located on π orbitals of three aromatic base rings. There is paramagnetic electron delocalization on the inner d orbitals of triangle region. The analysis of electron localization function ELF-π and electrostatic potential maps reveals that the outer strong π–π stacking interaction together with the inner d orbital channel enable effective transduction of electrical signals along the Cu–DNA nanowires. The 3Cu-induced triangular pyrimidines have important potential applications as structural motifs of molecular electronic devices.

First-principles calculations predict that atomic iron (Fe) combines with fluorine (F) to produce stable molecular complexes having the form FeF n ( n = 1–6) and the species with n ≥ 3 exhibit superhalogen properties. Electron affinities of the complexes are found to increase successively upto 8.20 eV for FeF 6 . The unusual properties of these complexes are due to the involvement of inner shell 3d -electrons, which allow FeF n complexes to belong to the class of superhalogens and also due to the tendency of Fe to have valency that can exceed the value of 3. Quantum chemical calculations were carried out using an all-electron linear combination of atomic orbitals scheme within the density functional theory (DFT) framework utilizing the popular B3LYP (Becke, three-parameter, Lee–Yang–Parr) exchange correlation functional. Analysis of HOMO-LUMO gaps, molecular orbitals and binding energies of these complexes indicate that the FeF n complexes are stable. Population analysis of molecular orbitals was also carried out to determine the percentage (%) contribution of Fe and F atoms to the frontier orbitals (LUMO and HOMO). The orbital overlap population (OOP) diagrams provide information related to bonding and anti-bonding nature of overlap in the molecular orbitals. The principle of maximum hardness was applied to determine the relative stability of the complexes. Also, the stability and viability of novel salt series Li-(FeF n ) has been tested by analyzing the molecules Li-(FeF 4 ), Li-(FeF 5 ) and Li-(FeF 6 ) in detail.

In Hartree-Fock calculations for atoms and molecules, multicenter-expansion methods are commonly used, especially those based on linear combinations of atomic orbitals (LCAO) using Gaussian-type orbitals (GTOs) or Slater-type orbitals (STOs). Artificial nodes, which are not expected to exist in real wave functions, arise in many calculations. For the hydrogen molecular ion (H2+) there are no nodes in the exact solution of its ground state ((1σg) 2Σg). The occurrence of artificial nodes and the cause of the problem are investigated for this state. Calculations of LCAO with GTOs and of single-center expansion (SCE) with Laguerre-type orbitals (LTOs) have been performed as part of this study. It is found that an excess of diffuse basis functions is responsible for artificial nodes.

Once electron correlation is included in an effective one-particle operator, one has a correlated orbital theory (COT). One such theory is Kohn-Sham density functional theory (KS-DFT), but there are others. Such methods have the prospect to redefine traditional Molecular Orbital (MO) theory by building a quantitative component upon its conceptual framework. This paper asks the question what conditions should such a theory satisfy and can this be accomplished? One such condition for a COT is that the orbital eigenvalues should satisfy an ionization theorem that generalizes Koopmans’ approximation to the exact principal ionization potentials for every electron in a molecule. Guided by this principle, minimal parameterizations of KS-DFT are made that provide a good approximation to a quantitative MO theory .

Frontier orbital theory is demonstrated by investigating the appropriately divided parts of transition states, useful for understanding an essential aspect of transition-metal- and lanthanide-mediated reactions. Atomic orbitals are in phase with each other in the outer space of the antibonding orbitals of the bonds between transition-metal and main-group atoms.

The Td-symmetric [CsO4]+ ion, featuring Cs in an oxidation state of 9, is computed to be a minimum. Cs uses outer core 5s and 5p orbitals to bind the oxygen atoms. The valence Cs 6s orbital lies too high to be involved in bonding, and contributes to Rydberg levels only. From a molecular orbital perspective, the bonding scheme is reminiscent of XeO4: an octet of electrons to bind electronegative ligands, and no low-lying acceptor orbitals on the central atom. In this sense, Cs+ resembles hypervalent Xe.

The electronic structure of LaYbO 3 was investigated by the full potential linearized augmented plane wave plus local orbital (FLAPW + lo) method with the modified Becke–Johnson potential combined with the local density approximation correlation plus onsite Coulomb interaction (MBJ–LDA + U ) for the sake of localized f electrons. This approach was suitable for evaluating electronic structure of LaYbO 3 system from view point of calculation cost and time. The band gap, the difference in energy between the valence band (VB) and conduction band (CB), was estimated to be 6.0 eV by the present method. The evaluated value was very close to the reported experimental value. In the VB, Yb 4 f orbitals and O 2 p orbitals were well hybridized each other to state predominantly. The lower potential region in CB was mainly composed of La 4 f orbitals, while the upper region in CB was mainly consisted of La 5 d orbitals.

X-ray photoelectron spectral analysis of dicaesiumtetrachlorodioxoplutonate (Cs2PuO2Cl4) single crystal was done in the binding energy range 0-~35 eV on the basis of binding energies and structure of the core electronic shells (~35 eV-1250 eV), as well as the relativistic discrete variation calculation results for the PuO2Cl4 (D4h). This cluster reflects Pu close environment in Cs2PuO2Cl4 containing the plutonyl group PuO2. The many-body effects due to the presence of cesium and chlorine were shown to contribute to the outer valence (0-~15 eV binding energy) spectral structure much less than to the inner valence (~15 eV- ~35 eV binding energy) one. The filled Pu 5f electronic states were theoretically calculated and experimentally con- firmed to present in the valence band of Cs2PuO2Cl4. It corroborates the suggestion on the direct participation of the Pu 5f electrons in the chemical bond. The Pu 6p atomic orbitals were shown to participate in formation of both the inner and the outer valence molecular orbitals (bands), while the filled Pu 6p and O 2s, Cl 3s electronic shells were found to take the largest part in formation of the inner valence molecular orbitals. The composition of molecular orbitals and the sequence order in the binding energy range 0-~35 eV in Cs2PuO2Cl4 were established. The quantitative scheme of molecular orbitals for Cs2PuO2Cl4 in the binding energy range 0-~15 eV was built on the basis of the experimental and theoretical data. It is fundamental for both understanding the chemical bond nature in Cs2PuO2Cl4 and the interpretation of other X-ray spectra of Cs2PuO2Cl4. The contributions to the chemical binding for the PuO2Cl4 cluster were evaluated to be: the contribution of the outer valence molecular orbitals -66 %, the contribution of the inner valence molecular orbitals -34 %.

This article dwells on the nature of “inverted bonds”, which make reference to the σ interaction between two s-p hybrids by their smaller lobes, and their presence in [1.1.1]propellane 1. Firstly we study H 3 C-C models of C-C bonds with frozen HCC angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane 1 and [1.1.1]bicyclopentane 2 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 state of 1 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 CC interaction in propellane. Within 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 ca. 50 kcal/mol. In bicyclopentane 2, despite a strong σ-type repulsion, a weak bonding (15-20 kcal/mol) exists between both central CC, 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 s-p hybrids by their smaller lobes, appears highly questionable.

Molecular orbital theory and its fragment orbital approach allow computational chemists to analyze complicated wavefunctions using familiar and highly intuitive concepts of chemical bonding. In this chapter, we discuss electronic structure descriptors such as atomic charges, molecular orbital compositions, 2- and multi-center bond orders as tools for the analysis of chemical bonding in organic and inorganic compounds. Further, we demonstrate the usage of an approach of building wavefunctions of multi-component systems from fragment wavefunctions in different problems of the molecular orbital analysis. This approach can be applied to answer questions ranging from evaluation of contributions to the total electronic interaction energy from individual pairs of orbital interactions to the valence description in redox noninnocent complexes. Calculation of these electronic structure descriptors is done using wavefunctions obtained from common quantum mechanical software packages, thus, greatly simplifying this analysis.

Iodine-doped graphene has recently attracted significant interest as a result of its enhanced conductivity and improved catalytic activity. Using density functional theory calculations, we obtain the formation energy, desorption rate, and electronic properties for graphene systems doped with polyiodide chains consisting of 1–6 iodine atoms in the low-concentration limit. We find that I3 and I5 act as p-type surface dopants that shift the Fermi level 0.46 and 0.57 eV below the Dirac point, respectively. For these two molecules, molecular orbital theory and analysis of the charge density show that doping transfers electronic charge to iodine π* molecular orbitals oriented perpendicular to the graphene sheet. For even-length polyiodides, we find that I6 and I4 decompose to I2, which readily desorbs at 300 K. Adsorption energy calculations further show that I3 acts as an effective catalyst for the oxygen reduction reaction on graphene by stabilizing the rate-limiting OOH intermediate.

Generally, the long-range electronic communication between spatially orthogonal orbitals is inefficient and limited to field and inductive effects. In this work, we provide experimental evidence that such communication can be achieved via intramolecular electron transfer between two degenerate and mutually orthogonal frontier molecular orbitals (MOs) at the transition state. Interaction between orthogonal orbitals is amplified when the energy gap between these orbitals approaches zero, or at an "orbital crossing". The crossing between two empty or two fully occupied MOs, which do not lead to stabilization, can be "activated" when one of the empty MOs is populated (i.e., electron injection) or one of the filled MOs is depopulated (i.e., hole injection). In reductive cycloaromatization reactions, such crossings define transition states with energies defined by both the in-plane and out-of-plane π-systems. Herein, we provide experimental evidence for the utility of this concept using orbital crossings in reductive C1-C5 cycloaromatization reactions of enediynes. Communication with remote substituents via orbital crossings greatly enhances regioselectivity of the ring closure step in comparison to the analogous radical cyclizations. We also present photophysical data pertaining to the efficiency of electron injection into the benzannelated enediynes.

A new approach for formulating the self-interaction correction, referred to as the Fermi-Lowdin orbital-based self-interaction correction (FLO-SIC), is briefly reviewed and applied to the Fe(II)-po...

The atomic structure of the highest molecular orbitals (MO) of small tetra-heme cytochrome (STC) c 1M1P is studied in large-scale ab initio all-electrons Hartree–Fock calculations. It is shown that the highest MOs of STC are mainly formed by atomic orbitals of negatively charged amino acid atoms whose types and corresponding numbers are determined. The results obtained permit the conclusion that these amino acids can be considered as possible active centers in the electron transfer reaction between STC and an external electron acceptor.

The extent of ligand to metal donation bonding and mixing of 4f (and 5d) orbitals with ligand orbitals is studied by Kohn-Sham (KS) calculations for LaX3 (X = F, Cl, Br, I), GdX3, and LuX3 model complexes, CeCl6(2-), YbCp3, and selected lanthanide complexes with larger ligands. The KS delocalization error (DE) is quantified via the curvature of the energy for noninteger electron numbers. The extent of donation bonding and 4f-ligand mixing correlates well with the DE. For Lu complexes, the DE also correlates with the extent of mixing of ligand and 4f orbitals in the canonical molecular orbitals (MOs). However, the localized set of MOs and population analyses indicate that the closed 4f shell is localized. Attempts to create situations where mixing of 4f and ligand orbitals occurs due to a degeneracy of fragment orbitals were unsuccessful. For La(III) and, in particular, for Ce(IV), Hartree-Fock, KS, and coupled cluster singles and doubles calculations are in agreement in that excess 4f populations arise from ligand donation, along with donation into the 5d shell. Likewise, KS calculations for all systems with incompletely filled 4f shells, even those with "optimally tuned" functionals affording a small DE, produce varying degrees of excess 4f populations which may be only partially attributed to 5d polarization.

A localization method for molecular orbitals is presented which exploits the locality of the eigenfunctions associated with the largest eigenvalues of the matrix representation of spatially localized functions. Local molecular orbitals are obtained by a projection of the canonical orbitals onto the set of the eigenvectors which correspond to the largest eigenvalues of these matrices. Two different types of spatially localized functions were chosen in this work, a two-parameter smooth-step-type function and the weight functions determined by a Hirshfeld partitioning of the molecular volume. It is shown that the method can provide fairly local occupied molecular orbitals if the positions of the set of local functions are set to the molecular bond centers. The method can also yield reasonably well-localized virtual molecular orbitals, but here, a sensible choice of the positions of the functions are the atomic sites and the locality then depends more strongly on the shape of the set of local functions. The method is tested for a range of polypeptide molecules in two different conformations, namely, a helical and a β-sheet conformation. Futhermore, it is shown that an adequate locality of the occupied and virtual orbitals can also be obtained for highly delocalized systems.

Electron orbitals are ubiquitous in chemistry for the description of bonding and molecular properties. This article outlines a theoretical framework for the generation and application of orbitals for the analysis of the electronic structure, chemical bonding, and magnetic properties of metal complexes from relativistic quantum chemical wavefunction calculations. Examples from the author’s research of f-element complexes are used to illustrate these concepts, with emphasis on open-shell systems.