Molecular Orbital Concepts Research Articles

Hans Bock (1928–2008)

In spite of all attempts to quantify and objectify it, science has always been first and foremost a deeply subjective endeavor. The scientific community would be unthinkable without distinguished and influential personalities. Never is this more apparent than in times of loss of such individuals, such as on January 21 with the passing of Hans Bock. Having grown up in the Allgäu region of Southern Germany, Hans Bock began his studies in chemistry in 1949 at the Ludwig-Maximilians-Universität Munich in an academically very stimulating environment. After his doctoral thesis with Egon Wiberg in 1958 and the ensuing habilitation on inorganic azo compounds, Hans Bock opted for an unusual, challenging period abroad by joining Edgar Heilbronner at the ETH Zürich in developing a practically oriented approach to the then relatively unfamiliar Hückel molecular orbital concept. The resulting, still recommendable book on “The HMO Model and its Application”1 has turned out to be enormously successful, not least because of its user-friendly approach attributable mainly to Hans Bock, which made the book popular even among ordinary chemists. At the same time, however, Hans Bock had begun to publish ground-breaking experimental results with his first outstanding co-workers, for example, introducing with H. tom Dieck the 1,4-diazabutadiene ligands which later found such wide application. The ultimate test for Hans Bock as a university professor came with the move to the chair of Inorganic Chemistry at the Johann-Wolfgang-Goethe-Universität Frankfurt am Main in the ominous year 1968. With his drive and “biblical firmness” (in his own words), but with a certain Bavarian charm, he made an impression on even the revolutionary students of that time. With his arrival and his adamant principle to hire only the best, the chemistry department at Frankfurt experienced an era of excellent science. The successive occupation of the “other” inorganic chair by H. W. Roesky, W. A. Herrmann, D. Fenske, R. Schlögl, F. Schüth, and M. Wagner during his watch has demonstrated Hans Bock's keen sense and affinity for scientific quality. In the same way, he has not only attracted excellent local students in great number, but also cultivated top-level international relations with the best scientists abroad, thus attracting many excellent foreign co-workers, Humboldt fellows, and guest professors, and he was honored over time with several prizes and awards. Similarly, Hans Bock has received much recognition from within Germany, for example through memberships in several renowned academies or as external scientific member of the Max Planck Society. Literally “obvious” was Hans Bock's talent for visualization. His lectures and the meticulously prepared scientific presentations were legend and will remain unforgettable. Although Hans Bock remained faithful to the chemistry of the main group elements (N, B, Si, P, S), his name is less connected with certain elements or to a group of compounds, but rather to a modern, meanwhile commonly adopted comprehensive approach to scientific questions with the latest available experimental and theoretical methods. Thus, his legacy and influence may not only be measurable in a quantitative way, such as through citation frequency, although Hans Bock could hardly be topped with more than 500 publications, many of them in Angewandte Chemie. Characteristic of his quite unique scientific approach was the continuous adoption of new research areas, starting from synthesis, via theoretical methods, physical techniques (UV/Vis, PE, and ESR spectroscopy), to crystal structure problems. Gas-phase reactivity of small molecules, organoelement chemistry in solution, and molecular structure analysis in the solid state all belonged to Hans Bock's research repertoire. Equipped with a healthy sceptical attitude towards things he considered too arty, Hans Bock's world nonetheless reached far beyond chemistry. As a connoisseur of excellent wines, ecclesiastical architecture, and as an enthusiast of alpine regions, he had cultivated many interests beyond the chemical profession. Although a baroque Bavarian attitude was his trademark, he drew strength for his intense professional activity from his home in Königstein in the Taunus mountains, supported by his cherished wife Luise, two sons, three daughters, and their families. The loss can only be alleviated by the certainty that he will never be forgotten by all who knew him.

Reply to “Comment on the Paper ‘On the Limits of Highest-Occupied Molecular Orbital Driven Reactions: The Frontier Effective-for-Reaction Molecular Orbital Concept'”

ADVERTISEMENT RETURN TO ISSUEPREVCommentReply to “Comment on the Paper ‘On the Limits of Highest-Occupied Molecular Orbital Driven Reactions: The Frontier Effective-for-Reaction Molecular Orbital Concept'”Rodrigo R. da Silva, Teodorico C. Ramalho, Joana M. Santos, and J. Daniel Figueroa-VillarView Author Information Departamento de Química, Instituto Militar de Engenharia, Praça General Tibúrcio, 80, 22290-070, Rio de Janeiro-RJ, Brazil, Departamento de Química Geral e Inorgânica, Instituto de Química, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, 20550-013 Rio de Janeiro-RJ, Brazil, and Departamento de Química, Universidade Federal de Lavras, Campus Universitário, CP 3037, 37200-000 Lavras-MG, Brazil Cite this: J. Phys. Chem. A 2006, 110, 36, 10653–10654Publication Date (Web):August 12, 2006Publication History Received2 June 2006Published online12 August 2006Published inissue 1 September 2006https://doi.org/10.1021/jp068065xCopyright © 2006 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views278Altmetric-Citations10LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (13 KB) Get e-AlertsSUBJECTS:Acidity,Electrical energy,Molecular orbitals,Organic acids,Reactivity Get e-Alerts

COMPOUNDING QUANTA: PROBING THE FRONTIERS OF STUDENT UNDERSTANDING OF MOLECULAR ORBITALS

College level students are expected to be able to make sense of, and explain, aspects of chemical bonding and structure in terms of molecular orbital concepts. The present paper derives from in-depth research into the thinking of a small sample of college chemistry students. This study in one UK college revealed the ways in which students found the orbital concept problematic. A previous paper (“Conceptualizing quanta: illuminating the ground state of student understanding of atomic orbitals”) reports how these students struggled to make sense of atomic structure in orbital terms. The present paper considers the students’ understanding of the molecular orbital concept. It is suggested that when learners are introduced to ideas about molecular orbitals before they have mastered ideas about atomic systems, then their learning difficulties may be ‘compounded’ in the more complex context. For example, it was found that students often identified the orbitals involved in two-centre bonds as atomic orbitals. Representations of delocalised bonds invoked various alternative interpretations: but were seldom conceptualised as implying poly-centred molecular orbitals. These findings suggest that students are not given sufficient time to construct acceptable models of atoms and molecules as ‘quanticles’. [Chem. Educ. Res. Pract. Eur.: 2002, 3, 159-173]

Covalently bound molecular structures in the α + 16O system

Using the concept of covalent molecular orbitals for neutrons and the known properties of the local α + 16O potential the formation of asymmetric molecular structures in neon isotopes is discussed. Experimental evidence for parity doublets in 21Ne is reviewed and a corresponding band structure for the states in 21Ne at moderate excitation energy of E x = 0-8 MeV is proposed. The structure of some bands can be interpreted as consisting of an instrinsic asymmetric ( 4He + 16O) structure bound by a covalent neutron in σ and π orbitals. An extension of the observed structures to symmetric molecular structures in isotopes of Mg and heavier nuclei is suggested. In particular shape isomers in isotopes of magnesium, namely (He)2O molecules, can be predicted and an extended Ikeda diagram is proposed.

Augmented Lagrangian method for order-N electronic structure

Molecular electronic ground-state theories, whether ab initio, or semiempirical are most often formulated as a variational principle, where the electronic ground-state energy, considered a linear or nonlinear functional of a reduced density matrix, obtains a constrained minimum. In this communication, we present a Lagrangian analysis of the self-consistent-field electronic structure problem, which does not resort to the concept of orthogonal molecular orbitals. We also develop a method of constrained minimization efficiently applicable to nonlinear energy functional minimization, as well as to linear models such as tight-binding. The method is able to treat large molecules with an effort that scales linearly with the system size. It has built-in robustness and leads directly to the desired minimal solution. Performance is demonstrated on linear alkane and polyene chains.

Orbitals in chemistry: a modern guide for students

1. Energy, probability and electrons 2. An introduction to the dynamics of microsystems 3. One electron atoms: atomic orbitals 4. The one electron molecule H2+: molecular orbitals 5. Many electron atoms and the orbital concept 6. Orbitals in diatomic molecules 7. Orbitals in polyatomic molecules 8. Molecular orbitals and electron pair bonding 9. p Molecular orbitals: conjugation and resonance 10. Patterns in localised chemical bonds 11. The concept of molecular orbitals in other systems 12. Orbitals in action.

Spectroscopic Evidence in Support of the Molecular Orbital Confinement Concept: Case of Anthracene Incorporated in Zeolites

Spectroscopic Evidence in Support of the Molecular Orbital Confinement Concept: Case of Anthracene Incorporated in Zeolites

Syntheses and Structure of Hexacoordinated Selenium (λ6-Selane) and Tellurium (λ6-Tellane) Compounds

The first isolation of bis(2,2′-biphenylylene)dichloro- and difluoro-perchalcogenuranes, [12–Se–6(C4F2)] (λ6-selane); [12–Te–6(C4X2), X = Cl, F] (λ6-tellane) and the corresponding tellurane Te-oxide dimer [12–Te–6(C4O2)]2, and their crystal and molecular structures are described. Furthermore, on the basis of the difference between the 3c-4e bonds of the dodecet species and that of the decet species a new molecular orbital concept has been proposed on the 3c-4e bond of perchalcogenurane species [12–M–6, M = chalcogen atoms].

Generalized Molecular Orbital Theory II

The generalized molecular orbital (GMO) concept is extended to a higher order method, which begins with a pair-excited multiconfiguration self-consistent field (PEMCSCF) for the orbital optimization and is followed by a multireference configuration interaction calculation. Here, this method is referred to as GMO2. The method has the advantage of being variational, of handling large numbers of active electrons, and of only needing the user to specify the number of active electrons and orbitals without specifying a dominant MO or VB configuration. In this paper, we briefly review the PEMCSCF theory, describe in more detail a new and more efficient optimization procedure, and propose determining the energy with configuration interaction (CI) at the single, double, triple, and quadruple-excitation levels (SDTQ) as a replacement for the full CI, which is needed in a complete active space (CAS) method. Several examples of the application of the method are investigated: methane, tetrahydrogen, benzene, dinitrog...

Calculation of the solvent reorganization free energy in the dielectric cavity model

The solvent reorganization free energy, E s, is an important characteristics that affects the activation energy and spectral properties of different charge transfer processes in polar media. Calculation of E s implies two steps. The first step is evaluation of the charge redistribution upon transition. The second step is calculation of E s for a given charge redistribution. We developed a formalism that allows one to compute the charge redistribution from data of quantum chemical calculations, based on schemes which incorporate equilibrium solvent effects. The concept of transition molecular orbitals (MO) is used which assumes the electronic transition to be a transition of an electron between two transition MO: the highest occupied and the lowest unoccupied MO of the solute. For an electron transfer between different species the transition MO are the highest occupied MO of the donor and the lowest unoccupied MO of the acceptor. The difference between the electronic densities of the two transition MOs gives the charge redistribution. The changes of the other MOs upon transition are described as polarization of an effective electronic continuum of the cavity. The model of a cavity in dielectric continuum is used to describe a solute or a donor-acceptor complex in its reactive configuration. Our description of the solute charge redistribution allows the introduction of a ‘fixed charge density’ formulation for E s in the second step. As an example, application of our formalism to the photoinduced transition between the ground and the lowest excited states of an acridine dye is given. We estimated how strong the influence of the solute wave function's modulation through non-equilibrium environmental polarization is and studied the effect of the coupling between solute polar inertial modes and environmental polarization on the reorganization energy. We found that neglecting any of these effects can results in seriously overestimating the value of the reorganization energy.

Studies of the electron density in the highest occupied molecular orbitals of PH3, PF3 and P(CH3)3 by electron momentum spectroscopy and Hartree-Fock, MRSD-CI and DFT calculations

The spherically averaged momentum profiles for the highest occupied molecular orbitals of PF3 and P(CH3)3 have been obtained by electron momentum spectroscopy. The measurements provide a stringent test of basis set effects and the quality of ab-initio methods in the description of these larger molecular systems. As in previous work on the methyl-substituted amines, intuitive arguments fail to predict the correct amount of s- and p-type contributions to the momentum profile while delocalized molecular orbital concepts provide a more adequate description of the HOMOs. The experimental momentum profiles have been compared with theoretical momentum profiles calculated at the level of the target Hartree-Fock approximation with a range of basis sets. New Hartree-Fock calculations are also presented for the HOMO of PH3 and compared to previously published experimental and theoretical momentum profiles. The experimental momentum profiles have further been compared to calculations at the level of the target Kohn-Sham approximation using density functional theory with the local density approximation and also with gradient corrected (non-local) exchange correlation potentials. In addition, total energies and dipole moments have been calculated for all three molecules by the various theoretical methods and compared to experimental values. Calculated ‘density difference maps’ show the regions where the HOMO momentum and position electron densities of PF3 and P(CH3)3 change relative to the corresponding HOMO density of PH3. The results suggest that methyl groups have an electron-attracting effect (relative to H) on the HOMO charge density in trimethyl phosphines. These conclusions are supported by a consideration of dipole moments and the 31P NMR chemical shifts for PH3, PF3 and P(CH3)3.

Ab initio molecular orbital calculations on the electronic structure of phosphate glasses. Binary alkali metaphosphate glasses

Ab initio molecular orbital calculations have been made for binary alkali metaphosphate glasses using H 2P 2O 7R 2 (R = Li, Na, K, Rb) as molecular models. The calculations have demonstrated that lithium and sodium ions interact equally with two terminal oxygens in each PO 2O − 2/2 tetrahedron, while potassium and rubidium ions interact favorably with one of the two terminal oxygens. The result indicates that the local environments of Na and Li are substantially different from those of K and Rb. The spectroscopic data observed for binary alkali metaphosphate glasses are also interpreted in terms of the molecular orbital concept.

Kinetic energy dependence of the reactions of Ru+, Rh+, Pd+, and Ag+ with O2

Reactions of Ru+, Rh+, Pd+, and Ag+ with molecular oxygen are studied as a function of kinetic energy by using guided ion beam mass spectrometry. By using a flow tube ion source, it has been possible to create Ru+, Rh+, Pd+, and Ag+ ions in their electronic ground state terms and primarily in the lowest spin–orbit levels. All reactions are observed to be endothermic. The reactivity of ground state Ag+ is found to be particularly inefficient and is believed to occur through an impulsive pairwise mechanism. Excited states of Ag+ are observed to react efficiently at thermal energies. Analyses of the endothermic reaction cross sections yield 0 K bond dissociation energies of D0(Ru+–O)=3.81±0.05 eV, D0(Rh+–O)=3.02±0.06 eV, D0(Pd+–O)=1.46±0.11 eV, and a speculative value of D0(Ag+–O)=1.23±0.05 eV. The reactivity differences among all four metal systems and the electronic states of Ag+ are explained by using simple molecular orbital concepts.

Cu K-edge x-ray-absorption spectroscopic study on the octahedrally coordinated trivalent copper in the perovskite-related compounds La2Li0.5Cu0.5O4 and LaCuO3.

Cu K-edge x-ray-absorption spectra for the chemically well-defined ${\mathrm{Cu}}^{\mathrm{III}}$-containing oxides, ${\mathrm{La}}_{2}$${\mathrm{Li}}_{0.5}$${\mathrm{Cu}}_{0.5}$${\mathrm{O}}_{4}$ and ${\mathrm{LaCuO}}_{3}$, have been carefully studied in order to correlate the complex spectral features with the copper valence, the local symmetry, and the bonding nature. According to the extended x-ray-absorption fine structure spectra, it was found that the (Cu-O) bond distances for both compounds agree well with the x-ray crystallographic data, but in x-ray absorption near-edge structure (XANES) spectra, a clear higher-energy shift of the Cu K-edge position was observed for both trivalent copper oxides compared to divalent ones of ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4}$ and ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. When the site symmetry of trivalent copper is lowered from ${\mathit{O}}_{\mathit{h}}$ to ${\mathit{D}}_{4\mathit{h}}$ as in ${\mathrm{La}}_{2}$${\mathrm{Li}}_{0.5}$${\mathrm{Cu}}_{0.5}$${\mathrm{O}}_{4}$, the feature by the shakedown process was observed to be split to A and A', corresponding to transitions to the \ensuremath{\Vert}1${\mathit{s}}^{1}$3${\mathit{d}}^{\mathit{n}+1}$${\mathit{L}}^{\mathrm{\ensuremath{-}}1}$4${\mathit{p}}_{\mathrm{\ensuremath{\pi}}}^{1}$〉 final state and \ensuremath{\Vert}1${\mathit{s}}^{1}$3${\mathit{d}}^{\mathit{n}+1}$${\mathit{L}}^{\mathrm{\ensuremath{-}}1}$4${\mathit{p}}_{\mathrm{\ensuremath{\sigma}}}^{1}$〉 one, respectively. Therefore, it is proposed that Cu K-edge XANES spectral fine features below the main edge should be interpreted with the molecular-orbital concept, mainly depending upon the copper valence and the crystal-field effect by the local symmetry on the copper site. This work also reveals that a spectral separation (\ensuremath{\sim}2.7 eV) between ${\mathrm{Cu}}^{\mathrm{II}}$ and ${\mathrm{Cu}}^{\mathrm{III}}$ compounds is smaller than the theoretically expected one (\ensuremath{\sim}4 eV), and the XANES spectrum of metallic compound shows a tendency of a lower energy shift compared to that of insulating or semiconducting one. Thus these facts should be taken into account when determining the presence of trivalent copper from Cu K-edge XANES spectra of copper-based superconductors.

Ion-molecule reaction chemistry of Fe+ with NO: excited-versus ground-state reactions

Ion-molecule reactions of excited- and ground-state Fe[sup +] with NO are reported. The charge-exchange and clustering ion-molecule reactions of Fe[sup +] with Fe(CO)[sub 5] are used to study the reaction dynamics of metastable versus ground electronic state Fe[sup +] ions. The ground-state [sup 6]D(4s[sup 1]3d[sup 6]) Fe[sup +] ions are unreactive with NO. Conversely, the metastable electronic states react with NO to form charge-transfer product ions (NO[sup +]) and radiative association adduct ions [Fe[sup +](NO)] and by the collisional relaxation process. The collisional relaxation process gives rise to the ground-state [sup 6]D(4s[sup 1]3d[sup 6]) and excited-state [sup 6]S(4s[sup 2]3d[sup 5]) Fe[sup +] ions. The [sup 6]S(4s[sup 2]3d[sup 5]) Fe[sup +] ion is unreactive with NO and constitutes approximately 6% of the Fe[sup +] ion population. Molecular orbital concepts are used to explain the lack of reactivity for the [sup 6]S(4s[sup 2]3d[sup 5]) Fe[sup +] ions and also the collisional relaxation process by the high-lying 4s[sup 1]3d[sup 6] states to form the [sup 6]S(4s[sup 2]3d[sup 5]) Fe[sup +] ions. 31 refs., 5 figs.

Reactions of alkaline earth ions with hydrogen, deuterium, and hydrogen deuteride

Guided ion beam mass spectrometry is used to study the kinetic energy dependence of the reactions of ground-state Mg^+ and Sr^+ with molecular hydrogen and its isotopomers. The results for reactions of Sr^+ are analogous to those previously observed for reactions of Ca^+ and Ba^+ with H_2, D_2, and HD. We observe qualitatively different cross sections for the reactions of Mg^+ with H_2, D_2, and HD, even though the monopositive ions in this group all have an ns valence electron configuration above completely filled core orbitals. The different pattern of reactivity can be explained with molecular orbital concepts, focusing on the interaction of the empty orbitals of the reactant ion with those of the hydrogen molecule. The threshold behavior of these reactions is analyzed to yield 0 K bond dissociation energies for SrH^+ of 2.17 ± 0.06 eV (50.0±f 1.3 kcal/mol) and an estimate for MgH^+ of 1.94 ± 0.06 eV (44.7 ± 1.5 kcal/mol).

Spin preferences of conjugated polyradicals: the disjoint NBMO analysis

The concept of disjoint nonbonding molecular orbitals (NBMOs) has been extended from its original application to biradicals to molecules with more than two NBMOs. It is shown how the disjointness of NBMOs in polyradicals can be related to their spin preferences. Ab initio molecular orbital calculations are reported which demonstrate the validity of the disjoint NBMO analysis

Ionization energies of the cations of metallocene (M(C 5H 5) +2), their half-sandwich complexes MC 5H +5 and the bare transition-metal ions M + (M = Fe, Co, Ni)

Charge stripping experiments indicate that in the reaction M + → M 2 + e − the doublycharged transition-metal ions M 2+ (M = Fe, Co, Ni) are formed in excited states. Introduction of one or two C 5H 5 ligands drastically reduces the Q min values of the reaction M(C 5H 5) + x → M(C 5H 5) 2+) x + e − (x = 1, 2) by at least 3.5 eV. The experimental findings support existing molecular orbital concepts of metallocene compounds.

Effect of kinetic and electronic energy on the reactions of Ti + with H 2, HD, and D 2

Reactions of atomic titanium ions with H 2, HD, and D 2 have been examined using guided ion beam tandem mass spectrometry. The a 4 F ground electronic state and the b 4 F first excited state of Ti + are very closely spaced, 0.11 eV, and this makes definitive determination of their relative reactivities difficult. Either both states react efficiently above their thermodynamic thresholds or the a 4 F state is fairly unreactive. In the reactions of these states with HD, formation of the metal hydride ion and the metal deuteride ion are nearly equal in the threshold region, which indicates a statistically behaved intermediate. Excited states of Ti + produced by electron impact also appear to react at their thermodynamic threshold with an efficiency about 4 times that of the 4 F states. With HD, these states react to form TiH + preferentially, indicating a direct reaction. These results complement those of other atomic transition metal ions and can be explained by using simple molecular orbital concepts. These data are analyzed to yield a 0 K bond dissociation energy for TiH + of 2.31 ± 0.11 eV (53.3 ± 2.5 kcal mol −1).

Methane activation by titanium(1+): electronic and translational energy dependence

The reaction of Ti/sup +/ with methane is studied as a function of translational energy in a guided ion beam tandem mass spectrometer. The effect of electronic excitation is also studied by varying the conditions for forming Ti/sup +/. The a/sup 2/F excited state is found to form the two main products, TiH/sup +/ and TiCH/sub 2//sup +/, substantially more efficiently than the a/sup 4/F ground and b/sup 4/F first excited states. The results indicate that reaction occurs primarily through a doublet H-Ti/sup +/-CH/sub 3/ intermediate. The reactivities of the different electronic states of Ti/sup +/ can be explained by using simple molecular orbital concepts and spin conversation. The thresholds for these reactions and for related reactions in other systems are interpreted to give D/sup 0/(Ti/sup +/-H) = 54.2 +/- 2.5, D/sup 0/(Ti/sup +/-CH/sub 3/) = 57.5 +/- 2.8, D/sup 0/(Ti/sup +/-CH/sub 2/) = 93.4 +/- 3.5, and D/sup 0/(Ti/sup +/-CH) = 121 +/- 4, all in kcal/mol.