Download I believe the chemical bond is not so simple as people seem to think

Birth of a bond
Lecture 2
I believe the chemical bond is not so simple as people
seem to think - R. S. Mulliken
concentration (though not of ion activity), since this assumption is made
in the calculation from the freezing points, but not in that from the electromotive forces.
Happy Centenary!
Bos’roN, MASS.
[CONTRIBUTION
FROM THE CHEMICAL
LABOR~TORY
OF THE UNIVERSITY
OF CAGIFORNIA.
I
TRE ATOM APQD THE MOLECULE.
BY GILBSRT N. LBWIS.
Received January 26, 1916.
In a paper entitled “Valence and Tautomerism”l I took occasion
THISJOURXAL,35,1448 (1913);see also the important article of Bray and Branch,
IEd., 35,
14-40 (19x3).
To localize or not to localize ‘tis the question
•
Lewis dots,Valence bond
(Heitler-London,
Pauling,..)
•
Molecular Orbitals
(Hund, Mulliken,..)
•
Concept of a bond - a
dream or reality?
Seeing is believing!?
Others are more ambivalent. ‘At present I don’t see a clear way
to make a new definition of the chemical bond that is at the
same time practical and all-encompassing,’ says Alvarez.
’Probably we need to develop new ways of looking at
interatomic interactions, or maybe the improvement of
visualisation techniques at the atomic scale will provide
relevant information to help us develop a new systematic
scheme.’ But he agrees that the Lewis model still ‘works well
enough for the largest part of the "real" chemistry, and is a
good starting point for the analysis of anomalous cases’. In
other words, ‘classifying bonds into "covalent" and "noncovalent" is still something we can teach in high school and
early courses at college, since this provides a useful first
approximation’. Just don’t believe everything you learn there.
Philip Ball, What is a bond? chemistry world 2014
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ntal
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ould
urier
ame
elds,
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rent
ep in
ame.
the
the
l be
N2 .
ts as
rom
muhigh
that
rate
ion
n is
cket
at angle
v through
the two-A complete inversion of a general orbital requires knowledge of
aArgon
projection
v is equal
in aitscut
response
to strong
laser fields,
is veryPsimilar
to N2to
dimensional
Fourier
of the object.
This is the basis the
of relative phase and amplitude of each harmonic for two orthohaving
nearly the
same transform
ionization Fpotential
and intensity-depen6
computed
tomography
the inverse
transform.
. This on
is confirmed
byRadon
the dependence
of Our
dent
ionization
probabilitybased
29
dipole
is the Fourier
transform
projection
of the
atoms, and
for wavefunction,
different
the
instantaneous
ionization
ratesof afor
and so canofbeNinverted.
orientations
2 (ref. 30). That means that the first, critical, step in
the We
three-step
harmonic generation
process
is the same.recondescribehigh
the mathematical
details of
the tomographic
Because
theinlaser
field dominates
motion
the
struction
the Methods
section.wave
This packet
procedure
can in
reconstruct
direction
the laser
field,
the secondsuch
step, which
pg and puthe
, using
orbital of
shapes
with
symmetries
as jg, determines
be 08
chirp
of the re-colliding
packets
seen
by and
Ar or
2, will from
harmonics
17–51 of anwave
800-nm
laser
field
25Nangles
the
Thus, a[k(q)]
willneeded
be the same.
to same.
1808 (fewer
angles are
for symmetric molecules).
The
continuum
wave
packet
will
also
be
similar
1,2
1,3
1 for Ar and N2.
A complete
inversion
of a general
requires
knowledge
of, H. Pépin3, J. C. Kieffer3, P. B. Corkum1 & D. M. Villeneuve1
J. Itatani
, J. Levesque
, D.orbital
Zeidler
, Hiromichi
Niikura1,4
The
which
the electron
tunnels
thenarrow
relativesaddle
phasepoint
and through
amplitude
of each
harmonic
for acts
twoasortho-
article
Tomographic imaging of molecular
orbitals
1
a spatial filter
that removes
structure
the orbital
from Ontario K1A 0R6, Canada
National
Research much
Councilofofthe
Canada,
100 of
Sussex
Drive, Ottawa,
2
the continuum
waveofpacket.
can be
seen Ottawa,
in numerical
University
Ottawa,This
150 Louis
Pasteur,
OntariosimuK1N 6N5, Canada
31 3
measuring
the
ellipticity
dependence
of
the
high
lations . By
INRS- Energie et Materiaux, 1650 boulevard Lionel-Boulet, CP 1020, Varennes, Québec J3X 1S2, Canada
24
4
by and
N2 and
argon,Agency,
we confirmed
thatKawaguchi Saitama, 332-0012, Japan
harmonic signal
PRESTO,produced
Japan Science
Technology
4-1-8 Honcho
the lateral spread of the wave packets is similar. The ionization rate
30,32
, but is readily measured from the ion
of N2 is angle-dependent
....................................................................................................................................................................................................................
yield, and varies only by 25% for N2 (ref. 33). This variation is
almost cancelled by the angular dependence of the wave-packet
Single-electron wavefunctions, or orbitals, are the mathematical constructs used to describe the multi-electron wavefunctio
molecules. Because the highest-lying orbitals are responsible for chemical properties, they are of particular interest. To obs
these orbitals change as bonds are formed and broken is to observe the essence of chemistry. Yet single orbitals are difficu
observe experimentally, and until now, this has been impossible on the timescale of chemical reactions. Here we demonstrate
the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmo
generated from intense femtosecond laser pulses focused on aligned molecules. Applying this approach to a series of molec
alignments, we accomplish a tomographic reconstruction of the highest occupied molecular orbital of N2. The method also all
us to follow the attosecond dynamics of an electron wave packet.
The electrons that make up molecules are organized by energy in alignment19,20. It results in field-free alignment of linear molec
orbitals1,2. Although total electron density in molecules is routinely well after the aligning pulse has terminated. A 60-fs laser p
measured by X-ray diffraction or electron scattering, only two produces a rotational wave packet in N2. This wave packet peri
methods are able to ‘see’ the highest occupied molecular orbitals cally rephases, giving periods when the molecular axes are aligne
(HOMOs) — electron momentum spectroscopy and scanning tun- space. The probe pulse coincides with the first half-revival at 4
an (e,4 2e)
nelling microscopy. Electron momentum spectroscopy3 isFigure
(ref.
20).
The degree
angular alignment
Molecular
orbital
wavefunction
of N2. of
a, Reconstructed
wavefunctionisofgood
the enough to s
scattering technique that can determine the radially HOMO
averaged
the harmonic
58 rotation
of N2. The difference
reconstructionin
is from
a tomographicspectra
inversion for
of thea high
harmonic of the alignm
thewere
outermost
electrons.
Scanning
direction.
spectra taken at 19
projection angles. Both positive and negative values are present, so
Figure 3 Highdensity
harmonic of
spectra
recorded forvalence
N2 molecules
aligned at 19
different tunnelling
4
gives
thepolarization
electronaxisdensity,
distorted
microscopy
this isstates.
a wavefunction, not the square of the wavefunction, up to an arbitrary phase. b, The
angles between
0 and 908 relative
to the
of the laser.
For clarity,by
onlysurface
5–11
of the
some of the angles
have been
The highemission
harmonic spectrum
from argon is shape
jg orbital from an ab initio calculation. The colour scales are the same
allows
theN2 2pHigh
We show
thatplotted
highabove.
harmonic
from molecules
harmonic generation from molecules
also shown; argon
is used as the reference
atom. Clearly
spectra depend
on both theorbital
for both
three-dimensional
shape
of thethe highest
electronic
toimages.
be c, Cuts along the internuclear axis for the reconstructed (dashed) and
High harmonics are produced by ionizing atoms or molecules
VOLUME 85, NUMBER 11
PHYSICAL REVIEW LETTERS
11 SEPTEMBER 2000
Determination of the Bond Length and Binding Energy of the Helium Dimer by Diffraction
from a Transmission Grating
R. E. Grisenti, W. Schöllkopf, and J. P. Toennies
Max-Planck-Institut f ür Strömungsforschung, Bunsenstraße 10, 37073 Göttingen, Germany
G. C. Hegerfeldt, T. Köhler, and M. Stoll
Institut f ür Theoretische Physik, Universität Göttingen, Bunsenstraße 9, 37073 Göttingen, Germany
(Received 5 June 2000)
A molecular beam consisting of small helium clusters is diffracted from a 100 nm period transmission
grating. The relative dimer intensities have been measured out to the 7th order and are used to determine
the reduction of the effective slit width resulting from the finite size of the dimer. From a theoretical
analysis of the data which also takes into account the van der Waals interaction with the grating bars,
the bond length (mean internuclear distance) and the binding energy are found to be !r" ! 52 6 4 Å
and jEb j ! 1.1 1 0.3# 2 0.2 mK.
PACS numbers: 33.15. – e, 03.75.Be, 21.45. + v, 36.40.Mr
Virtually allMeasuring
our current knowledge ofathe structure of
Focus:
molecules is based on either NMR, microwave, infrared,
visible, or Raman spectroscopy—or on x-ray and electron
Fragile
Molecule
scattering. Since
these techniques all in one way or another
disturb the system, they are not suitable for very weakly
September
2000• Phys.
Focus
6, 9
bound 6,systems
withRev.
large
scattering
lengths. Such apparA team
of physicists
has precisely
length and
ently
exotic systems
have measured
recently the
attracted
considerable
strength
of the exceedingly
delicate
formed between
attention
in connection
withbond
Bose-Einstein
condensation
two of
helium
atoms.
ultralow temperature gases [1].
© 2000 Boson
Photodisc, Inc.
An outstanding example of a fragile
molecule
4
Butterfly
of molecules.
catching
measuring the
is the
helium Like
dimer
Hea2 .butterfly,
Its existence
was for a long
delicate molecule formed by two helium atoms requires a light touch.
time disputed because of its extremely small binding enThe helium dimer is the largest two-atom molecule and has the
27
ergy
which
is
now
thought
to
be
about
1
mK
($10
eV).
weakest chemical bond known.
Presently, theory predicts the He-He potential to support
only a single s wave bound state [2]. While a first indica-
of the dimers at the edges of the holes in a quantum mechanical theory [10]. This theory predicts that transmission
experiments provide an upper limit on !r" only.
The present experiments overcome these difficulties
by measuring only the coherently scattered dimers which
make up the intensity in the small angle low order peaks
in the diffraction from a transmission grating. From the
data, !r" is determined by a quantum mechanical theory
which includes the surface potential of the grating bars
and breakup effects. Then from !r" the binding energy is
determined to be jEb j ! 1.1 1 0.3# 2 0.2 mK, which is
the most precise determination to date.
The cluster beam diffraction apparatus is the same as
recently described in Ref. [11]. The cryogenic 4 He source
pressures P0 and temperatures T0 were varied between
HF exchange, are the procedures that are presently used to obtain approximate
wave functions for the prediction of expectation values for an atom, molecule, or
crystal.Invited
The eminently
useful and predictive models that come from MO theory, the
Review
crystal field=ligand field descriptions of electronic structures of metal complexes
and H€
uThe
ckel’s 4n
þ 2 rule of aromaticity,
for example,
exemplify the proper use of
Quantum
Mechanical
Basis
MO theory – the prediction of a molecule’s electronic structure by the successive
of Conceptual
Chemistry
occupation
of the orbitals. Orbital
ordering forms the basis for the application of
the ‘second-order Jahn-Teller’ symmetry rule [8] that underlies Fukui’s frontier
orbital theory [9].
Richard F. W. Bader!
Department of Chemistry, McMaster University, Hamilton ON, L8S 4M1 Canada
Impact of Quantum Mechanics on Conceptual Chemistry
Received this
November
30, 2004;
accepted December
6, 2004
Unfortunately
linking
of quantum
mechanics
with experiment did not extend
Published online May 4, 2005 # Springer-Verlag 2005
to the basic
concepts essential to the molecular structure hypothesis – of atoms
with characteristic and additive properties and of the bonding underlying molecular
Summary.
experimentalist
approaching literature
theory for anstatements
understandingtoofthe
conceptual
chemistry
structure.
IndeedAnone
can find numerous
contrary:
‘that that
can concepts
be related toof
measurable
properties,
focuses
the electron density
One finds to
in the
while the
atoms and
structure
areonundeniably
usefuldistribution.
if not essential
topology
the not
electron
density the from
definition
of an atom,
of the bonding
atoms,
and of the
chemistry,
theyofare
recoverable
quantum
mechanics’
andbetween
the link
between
boundary condition for the extension of quantum mechanics to an open system – to an atom in a
experiment
and conceptual theory was not established. Such statements come at the
molecule. This paper describes this approach, as it evolved from the failure of existing models to a
end of study
arbitrary
or failed attempts to define the elements of conceptual chemistry
of molecular charge distributions and of how these studies resulted in the extension of quantum
using either
valence
bondsystem
or molecular
orbital
theory and are frequently expressed
mechanics
to an open
using the action
principle.
in terms of the ‘atomic orbital’ basis functions used in their expansion. This is
Keywords. Electron density; Atoms; Molecular structure.
an acknowledged
failure of the orbital approach. Libit and Hoffmann [10], for
example, after stressing the logic of substituent effects that made possible the
great strides
in synthetic and mechanistic organic and inorganic chemistry state:
Introduction
‘‘Nothing like this logic comes out of molecular orbital calculations. Every molecule is Conceptual
treated as aChemistry
whole and no set of transferable properties associated with a
functional
groupis emerges.’’
Notexperiment,
only are the
properties
of functional
groups
Science
observation,
and
theory. This
is the path
that known
led to the
experimentally
to beofcharacteristic,
the properties
can in
somea molecule
instancesisappear
to
development
the molecular structure
hypothesis
– that
a collection
exhibitofperfect
transferability
[11],
giving rise
to by
thea network
existenceof of
experimental
atoms with
characteristic
properties
linked
bonds
that impart a
mad
me
n
gy
ed
he
al
h
rH
sad
id
as
r,
o
).
raht
y
Real-Space Identification of
Intermolecular Bonding with Atomic
Force Microscopy
Jun Zhang,1* Pengcheng Chen,1* Bingkai Yuan,1 Wei Ji,2† Zhihai Cheng,1† Xiaohui Qiu1†
We report a real-space visualization of the formation of hydrogen bonding in 8-hydroxyquinoline
(8-hq) molecular assemblies on a Cu(111) substrate, using noncontact atomic force microscopy
(NC-AFM). The atomically resolved molecular structures enable a precise determination of the
characteristics of hydrogen bonding networks, including the bonding sites, orientations, and
lengths. The observation of bond contrast was interpreted by ab initio density functional
calculations, which indicated the electron density contribution from the hybridized electronic
state of the hydrogen bond. Intermolecular coordination between the dehydrogenated 8-hq and
Cu adatoms was also revealed by the submolecular resolution AFM characterization. The direct
identification of local bonding configurations by NC-AFM would facilitate detailed investigations
of intermolecular interactions in complex molecules with multiple active sites.
Controversial?
I
ntermolecular bonding has been experimentally characterized mainly through crystallography via x-ray and electron diffractions, as
well as through infrared, Raman, nuclear magnetic resonance, and near-edge extended absorption fine-structure spectroscopy (1, 2). At the
single-molecule level, state-of-the-art scanning
tunneling microscopy (STM) is a technique widely used to elucidate the molecular structure and
chemical specificity of surface-immobilized spe-
high-resolution AFM images, and the local bonding configuration was determined with the atomic
precision. We also observe the coordination complex composed of dehydrogenated 8-hq and Cu
adatoms. The observations were validated with ab
initio density functional theory (DFT) calculations.
The 8-hq molecules deposited on Cu(111)
at LHe temperature appeared as individual molecules or randomly assembled aggregates (fig. S1)
(13). For the single 8-hq molecules, DFT calcu-
image (Fig.
the heterocy
primarily se
near the Fer
with a COmolecular s
range Pauli
calculated e
itatively rep
quency shif
AFM senso
components
electrostatic
negative Df
attractive v
uted to the
without ato
range Pauli
atomic cont
spect to the
was decreas
proportion
enhanced co
a quantitativ
mechanism
tween the A
ture of a mo
case, the he
group of 8-h
idine ring in
which may