The synaptic order a key concept  to understand multicenter bonding synaptic
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The synaptic order a key concept to understand multicenter bonding synaptic

The synaptic order a key concept to understand multicenter bonding synaptic

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    The synaptic order a key concept  to understand multicenter bonding synaptic The synaptic order a key concept to understand multicenter bonding synaptic Presentation Transcript

    • The synaptic order: a key concept to understand multicenter bonding Bernard Silvi Laboratoire de Chimie Théorique Université Pierre et Marie Curie 4, place Jussieu 75252 -Paris
    • Multicenter bond
      • An apparently odd concept for the chemist
        • bonds are represented by lines between symbols
        • Not accounted for by the valence concept
        • bonds are characterized by:
          • bond lengths
          • bond energies
      • Energy decomposition
        • atom-atom pair potential
        • Axilrod-Teller term is very weak
      • Not in Lewis’s theory
        • original cubic atoms
      • Not in Pauling’s textbook but in Coulson’s
    • Origins of the concept
      • The diborane problem
      or classical Hydrogen bridges (Dilthey 1921) in contradiction with boron valence and electron count
      • Answer given by spectroscopy
        • high barrier to internal rotation (Stitt 1940)
        • infrared spectrum (Price 1947)
      • Electronic structure proposals
        • K shell binding (Hellriegel 1930)
        • resonance structures (Nekrassov 1940, Syrkin and Dyatkina 1941, Seel 1945)
      • The protonated double bond (Pitzer 1945)
      • MO representation (Longuet-Higgins 1949)
    • Generalisation: 3c-2e bond
      • In B 2 H 6
    • Generalisation: 3c-2e bond
      • B-B-B bonds
    • Generalisation: 3c-4e bonds
      • F-Xe-F
    • Strengths and weaknesses
      • Acknowledged model in boron chemistry
        • Lipscomb’s works
        • predictive tool
      • Interpretation of the numerical procedure
        • chemical meaning given to the wave function
        • depends of the expansion basis
        • non invariance of the MO’s
    • Bonds and related concepts
      • Bonds are not quantum mechanical observables
      • They belong to an other (chemical) level of understanding
      • Definitions often lack precision
      • Is a three-center bond a bond?
    • Chemical concepts related to bonding
      • Describe molecules and solids in terms of bonds, lone pairs, etc...
        • Bonds are links between atoms
          • According to Lewis a bond is made of an electron pair
          • The octet rule should be satisfied
          • According to chemistry bonds are classified as:
            • Covalent, polar, dative, metallic, ionic
          • The VSEPR model enables to predict molecular geometry
        • These concepts ratonalize the stoichiometry and the molecular structure
        • The approach of Chemistry has been and still is very successful
    • Il me faut cependant avouer que la chimie proprement dite ne m’a jamais beaucoup intéressé. Pourquoi ? Peut être parce que des notions telles que celles de valence, de liaison chimique etc., m’ont toujours semblé peu claires du point de vue conceptuel. René Thom Paraboles et catastrophes However I have to confess that I have never been very interested in Chemistry Why? Maybe because notions such as those of valence, chemical bond, etc., seem to me unclear from a conceptual point of view
    • What should be a theory of the chemical bond
      • Investigate the local properties of matter with a well suited mathematical theory
        • mathematics reveal relationships and behaviours which are the consequence of the intelligibility of the Nature
        • mapping chemical concepts with mathematical objects should improve their definitions and enable to introduce new concepts
        • isomorphism provides the mathematical model
    • The starting point
      • Statistical interpretation of Quantum Mechanics
        • epistemologically valid
        • provides a bridge between microscopic and classical worlds
        • position space representation
        • pioneered by Daudel with the Loge theory
          • hampered by numerical complexity
          • what to do after?
    • Topological theories of bonding
      • Purpose: provide rigorous qualitative information:
        • mathematical model of Lewis’s theory
        • Non ambiguous definitions of bonds
      • Mathematical background: dynamical system theory
      • Achievements: AIM (R. Bader)
      • Gradient dynamical system bound on  3
        • vector field X =  V ( r )
        • V( r ) potential function defined and differenciable for all r
        • the analogy with a velocity field X =d r /dt enables to build trajectories
        • moreover V( r ) depends upon a set of parameters {  i } called the control space, i.e.: V( r ;{  i })
      Some definitions
      • Critical points
        • index: number of positive eigenvalues of the second derivative matrix (hessian)
        • hyperbolic critical point: all eigenvalues are non zero
        • stable manifold
          • basin: stable manifold of critical point of index 0
          • separatrix: stable manifold of a critical point of index >0
        • Poincaré-Hopf relation
        • structural stability:
          • condition: all the critical points are hyperbolic
      More definitions....
    • A meteorological example: V( r {  i })=-P Basin 2 Basin 1
    • Domains
      • Definition
      • That’s all with maths
      a b
    • Atoms In Molecules theory
      • Bond path
        • unstable manifold of an index 1 critical point
        • bond critical point
        • only 2 centre bonds are possible
    • Back to bonding theory
      • Lewis theory is based on the electron pair concept, therefore the potential function should be related to pair densities and to probe the efficiency of the Pauli principle
      • localization function  ( r ;  i )
      • ELF (Becke and Edgecombe 1990) has been elected by our community cf: Workshop “ Content and interpretation of ELF and related functions ” Dresden, june 2001
    • What is ELF ?
      • Taylor expansion of the spherically averaged conditional pair probability:
      • Physical scaling by the homogeneous electron gas
      • Cosmetic scaling to confine ELF in the 0-1 range
      • Can be determined from experimental densities
    • Analysis: classification of basins
      • Core and valence basins
      • Nomenclature
        • C(A) core
        • V(A, ..) valence
        • color code
      Graphical representation: isosurfaces of the function V(O) C(C) C(O) V(C, H) V(O, H) V(C, O)
    • Analysis of localization domains :
      • Bounded by the isosurface  (r)=f
        • reducible and irreducible domains
        • core-valence separation Localization domains  (r cv )
        • hierarchy of basins: bifurcation diagram
      parent domain cores valence S  lone pairs bond
    • Detailed diagram: Parent domain C(O ) valence C(S) V(S) Valence O V(S,O ) V 1 (O)+V 2 (O) V 1 (O) V 2 (0)
    • Hierarchy of localization domains: complex
      • Valence-valence separation  (r vv )
        • Ex: FH CO 2
      Parent domain HF CO2 valence C(F) C(O) valence C(O) , V(C,O) V(O)
    • Hierarchy of localization domains: ionic pair
      • Core-valence separation  (r cv )
        • Ex: LiF
      Parent domain C(Li) F C(F) V(F)
    • The two processes filled-filled: 2 chemical single chemical objects (or more) complex, ionic pair, physisorption hollowed-filled: 1 chemical single chemical object molecule, ion, chemisorption
    • The synaptic order
      • The synaptic order  of a valence basin or of a group of valence basins ( cwm) is the number of cores belonging to the same single chemical object with which it shares a boundary (separatrix)
        • proton counted 1
        • complementary of the valence concept
    • Synaptic order: CH 3 F mon osynaptic disynaptic Protonated disynaptic
    • Synaptic order and chemical reactions
      • Covalent bond breaking: C 2 H 6
    • Synaptic order and chemical reactions
      • Dative bond breaking: BH 3 NH 3
    • 3c-2e multicenter bond
      • Protonated bonds: B 2 H 6
      Protonated trisynaptic
    • 3c-2e multicenter bond
      • B-B-B bonds: B 4 H 4
    • 3c-2e multicenter bond
      • Agostic hydrogen: RuClCH 3 CH 2 (PH 3 )
    • 3c-2e multicenter bond
      • Agostic protonation
      0.223 0.235
    • 3c-2e bonds: high coordination of C
      • Pentacoordinated sp 3 : Al 2 H 4 (CH 3 ) 2
    • Planar tetracoordinated carbons R. Choukroun, B. Donnadieu, J-S. Zhao, P. Cassoux, C. Lepetit et B. Silvi , Organometallics , 19, 1901-1911 (2000)
    • Planar pentacoordinated carbon P. v. R. Schleyer, private communication
    • Planar hexacoordinated carbon P. v. R. Schleyer, private communication
    • Metallic bond
      • Metal cluster:Li 6
    • Metallic bond
      • Bcc structures
    • Metallic bond
      • Fcc structures
    • Metallic bond
      • Electron-phonon interaction?
    • 3c-4e multicenter bonds
      • Hypervalent molecules: XeF 2
    • Conclusions
      • The topological analysis of ELF provides
        • unambiguous position space definition of multicenter bonding
        • 3c-2e bonds are true multicenter bonds
        • 3c-4e bonds are not multicenter bonds
      • The synaptic order of a basin is a good descriptor
        • It is complementary of the valence concept
      • However, the choice of the localization function remains an open problem
    • Nevertheless… Many forms of localization functions have been tried, and will be tried in this world of sin and woe. No one pretends that ELF is perfect or all-wise. Indeed, it has been the worst form of localization function except all those others that have been tried from time to time. Many forms of government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed, it has been the worst form of government except all those others that have been tried from time to time. W. Churchill
    • Acknowledgements
      • Laboratoire de Chimie Théorique (Paris): H. Chevreau, F. Colonna, H. Demirdjian, I. Fourré, F. Fuster, H. Gérard, C. Giessner-Prettre, A. Hénoux, L. Joubert, X. Krokidis, S. Noury, J. Pilme, A. Savin, A. Sevin
      • Laboratoire de Spectrochimie Moléculaire (Paris): E. A. Alikhani
      • Departament de Ciències Experimentals (Castelló): J. Andrés, A. Beltrán, M. Calatayud, M. Feliz, R. Llusar
      • Université de Wroclaw: S. Berski, Z. Latajka
      • Centro per lo Studio delle Relazioni tra Struttura e Reattività Chimica CNR (Milan): C. Gatti
      • Laboratoire de Chimie de Coordination (Toulouse): C. Lepetit
      • Universitad de Oviedo: J. M. Recio, P. Mori Sanchez
      • University of Helsinki: J. Lundell, M. Sundberg
      • McMaster University: R. G. Gillespie
    • That's all folks
    • Is a 3-center bond a bond?
      • Rely on the definition of the bond
        • A bond is not an observable
        • It belongs to Chemistry
        • Lewis’s definition
        • Pauling’s definition
        • Daudel’s definition: a chemical bond can be considered to be a part of space in which the fluctuation of the number of electrons is small and the correlation between them is high
    • Nevertheless… Many forms of localization functions have been tried, and will be tried in this world of sin and woe. No one pretends that ELF is perfect or all-wise. Indeed, it has been the worst form of localization function except all those others that have been tried from time to time. Many forms of government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed, it has been the worst form of government except all those others that have been tried from time to time. W. Churchill
    • Integrated conditional probability (Dobson and Savin)
      • Six come three
      • Limit for q  0