The synaptic order: a key concept to The synaptic order: a key concept to understand multicenter bondingunderstand multicenter bonding
Bernard SilviLaboratoire de Chimie Théorique
Université Pierre et Marie Curie4, 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
B B B
H
B
H
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 B2H6
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 precisionIs a three-center bond a bond?
Chemical concepts related to bondingDescribe 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 ThomParaboles et catastrophes
However I have to confess that I have never been very interested in ChemistryWhy?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=dr/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....
)(1 MpI
p
A meteorological example: V(r{i})=-P
Basin 2Basin 2Basin 1Basin 1
Domains
Definition
That’s all with maths
a
b
Atoms In Molecules theoryBond 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
)())(())(( ),( v2 rrrrr DTTP WScondr '
23/5 )](/)([1
1)(
rcrDr
F
Analysis: classification of basins
Core and valence basins
Nomenclature C(A) core V(A, ..) valence color code
V(O)
C(C) C(O)V(C, H)
V(O, H)
V(C, O)
Graphical representation: isosurfaces of the function
Analysis of localization domains:Bounded by the isosurface (r)=f
reducible and irreducible domains core-valence separation Localization domains
(rcv) hierarchy of basins: bifurcation diagram
parent domain
cores valence
S
lone pairs bond
Parent domain
C(O) valence C(S)
V(S) Valence O
V(S,O) V1(O)+V2(O)
V1(O) V2(0)
Detailed diagram:
Hierarchy of localization domains:complex Valence-valence separation (rvv)
Ex: FH CO2
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 (rcv) 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 objectmolecule, 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: CH3F
monosynaptic
disynaptic
Protonated disynaptic
Synaptic order and chemical reactions
Covalent bond breaking: C2H6
Synaptic order and chemical reactions
Dative bond breaking: BH3NH3
3c-2e multicenter bond
Protonated bonds: B2H6
Protonated trisynaptic
3c-2e multicenter bond
B-B-B bonds: B4H4
3c-2e multicenter bond
Agostic hydrogen: RuClCH 3CH2(PH3)
3c-2e multicenter bond
Agostic protonation
0.223
0.235
3c-2e bonds: high coordination of C
Pentacoordinated sp3: Al2H4(CH3)2
Cl2Zr
CH
CH
VCl2
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
CC
C
C C
C
B
B
B
B
BB
P. v. R. Schleyer, private communication
Planar hexacoordinated carbon
P. v. R. Schleyer, private communication
B
B
B
B
B
B
C
Metallic bond
Metal cluster:Li6
Metallic bondBcc structures
Metallic bondFcc structures
Metallic bondElectron-phonon interaction?
3c-4e multicenter bonds
Hypervalent molecules: XeF2
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
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 q0
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