Transcript Free radicals

Synthesis: the different approaches
Usually, magnetic molecular compounds are classified in 3 main categories:
Purely organic
approach
All the spin carriers
are purely organic
molecules
Free radicals:
often nitroxides
O+
N
O
N
N
R
.
N
O
R
.
Inorganic
approach
Mixed
approach
The spin carriers are
usually transition
metal ions bridged by
organic molecules
Transition metal ions
bridged by organic
molecules that also
carry a spin
The magnetization distribution
4 Question ?
What are the microscopic mechanisms at the origin of the different magnetic
behaviors in these molecules ?
4 Main problem: complexity of these systems !
The limits of many models used for “classical” compounds are reached, and
reliable theoretical frameworks have still to be built up
4 A crucial piece of information: the magnetization distribution
Where are localized unpaired electrons in the molecules (magnetic orbitals) ?
C
H
N
• TPV free radical : one unpaired electron
Where ?
In the SOMO, wich is built from
individual atomic orbitals
Neutron
-> the magnetic moments are strongly
Diffraction !
delocalized over the molecules
Shape of the SOMO ?
Neutron diffraction
Neutron: two main interactions in condensed matter
• Nuclear interaction: with the nuclei of atoms
--> crystallography
some advantages compared to x-ray :
• low temperatures routinely
• precise localisation of H atoms
• Magnetic interaction : between the magnetic moment of the neutron
and the magnetic field H created by unpaired electrons
--> most widespread use of neutron diffraction:
magnetic structure determination, i.e. determination of the direction
and the amplitudes of magnetic moments in the ordered state.
Neutron diffraction
Magnetic structure determination: in this kind of studies, it is assumed
• the magnetic moment on each atom is a vector
• the magnetization distribution around each atom comes from atomic
calculations for free ions
-> ‘form factors ’ tabulated in the International Tables of crystallography
What is the form factor of such a molecule ?
To go beyond this approximation -> to investigate these distributions on a subatomic scale:
Polarised neutron diffraction
Classical polarised beam technique
Classical polarized beam technique
Polarized incident
neutrons
Scattered
+
Sample
Polarizing
monochromator
+ spin flipper
Detector
Cryomagnet/Vertical Field
Intensity of a mixed reflection with both
nuclear and magnetic signals
*
I(Q)  FN (Q)  FN
(Q)  Nuclear
M(Q)  M* (Q )  Magnetic
FN (Q )  M* (Q)  FN* (Q )  M(Q ) P0
Interference
neutrons
4 Q=
scattering vector
4 P0 = polarisation of the incident
neutron beam
4 FN = nuclear structure factor
Fourier component of the nuclear
density
4 M = magnetic interaction vector
proportional to the Fourier component
of the magnetization distribution
Increased Sensitivity
4
Suppose
M = 0.1 x FN
4
Unpolarized beam:
(10%)
I = FN2 + (0.1 x FN)2 = 1.01 FN2
4
(1% effect on the intensity)
Polarized beam:
I+ = FN2 + (0.1 x FN)2 + 2 FN x (0.1 x FN) = 1.21 FN2
(20% effect)
I- = FN2 + (0.1 x FN)2 - 2 FN x (0.1 x FN) = 0.81 FN2
(20% effect)
Limitations
• Interference:
-> the magnetic and nuclear signal should appear at the same positions
in reciprocal space
-> the magnetic cell and the nuclear cell should have the same
periodicity
-> Limitations:
in the different classes of compounds that could be studied by this technique
• Paramagnets under an applied field (to induce a long range
magnetization)
• Saturated ferromagnets (single domain)
• Ferrimagnets
• Some antiferromagnets (a few particular cases, with several Bravais
sublattices and in-phase nuclear and magnetic structure factors )
Experimental conditions
4
Experiments performed on a single crystal, usually in the paramagnetic state
4 In an applied magnetic field to induce a long range order of the magnetization
4 One measures the ratio R (“flipping ratio”) between the scattered intensities
for P0 and -P0
4 From the measurement of R and the knowledge of FN(Q), one deduces the
magnetic structure factors FM(Q) of the different Bragg reflections Q with both
sign and amplitude (centric cases)
+ Fourier components of the magnetization distribution
4 They contain information on :
+
all the atoms carrying magnetization
+
all the shells involved
+
spin + orbital contributions (if present) M(r) = Ms(r) + M(r)
Data treatment
• The experiment gives the magnetic structure factors FM(Q) of the different
Bragg reflections Q with both sign and amplitude (centric cases)
•The FM(Q)’s are the Fourier components of the magnetization distribution M(r)
• To retrieve the magnetization distribution in real space, an inverse Fourier
problem should be solved
Several methods:
+ Direct (model free)
methods
• use nothing but the
experimental data
• necessary step before any
attempt to refine a model
+ Raw Fourier transform
+ Maximum of Entropy analysis
+ Model refinements
• they require the system to
be well enough understood for
a model to be proposed
+ Multipolar expansion
+ Wave function analysis
Magnetic Molecular Clusters
Molecules formed by a large number of strongly interacting metal ions
+ Used as models of nanometric-size single-domain magnetic particles
+ They offer the opportunity to study the magnetism at a mesoscopic scale
using macroscopic samples (without broad distributions in size and shape)
+ Clusters with high spins in the ground state and large Ising-type anisotropy
have attracted a lot of interest in recent years.
• Superparamagnetic behaviour
• Slow relaxation of the magnetization
• Quantum tunneling of the magnetization
+ Large interest to study the exact nature of the ground state of these
clusters (coupling scheme) to explain the observed properties.
The Fe8 Cluster
Magnetization distribution map (MAXENT)
Cluster formed of 8 Fe3+
ions (s = 5/2)
Competing antiferromagnetic
interactions -> S = 10
J. Am. Chem. Soc. 121 (1999) 5342
The 8 iron atoms are splitted in two sets:
• 6 iron atoms with moments parallel
to the applied field
• 2 iron atoms with moments antiparallel
to the applied field
The Mn10 Cluster
Magnetization distribution map (MAXENT)
• Cluster formed of 6 Mn2+
ions (Mn1 and Mn2, S=5/2)
and 4 Mn3+ ions (Mn3, S=2)
Antiferromagnetic
interactions -> S = 12
Physica B 241-243 (1998) 600
• Magnetization only at the Mn sites
(nothing on the ligands)
• Mn1 opposed to both Mn2 and Mn3
• Spherical shape on Mn1 and Mn2
(S=5/2)
• Elongated on Mn3 (S=2)
The free radical TPV
C
N
H
• Stable free radical
• Spin 1/2
• Zig-zag chains in the
crystal
• Antiferromagnetic
ordering TN = 1.8 K
• delocalization on the phenyls
• sign alternation on the phenyls
• negative density on the C
• inequivalent nitrogen atoms:
N1, N5 : 0.54(1) mB
N2, N4 : 0.15(1) mB
Isolated Free Radicals
• Spin delocalisation
the magnetism of a free radical is attributed to an unpaired electron in the
SOMO, built from individual atomic orbitals.The magnetic moments are no
longer well localized around one atom, but delocalized over the molecules
• Spin polarisation
Concern the sign of the magnetization distribution.
In a neutron experiment, the external applied field aligns the spin density
Negative spin density ?
Trivial case: several spin carriers, with an antiferromagnetic coupling ->
regions of positive and negative spin densities
Free radicals: more subtle because only one unpaired electron
-> Intramolecular exchange interaction (positive spins attracted by the
positive spin on the SOMO, leaving the negative spins on the nodes of the
SOMO.
• Shape of the distribution: 2p character, bonding, antibonding …
Interacting Radicals
What are the modifications on the magnetization distribution due to the
magnetic interactions in the crystal ?
• hydrogen bonds
• through atoms of the substituents
• direct coordination with a metal center
The free radical tempone
O
Alkyl nitroxyde
4
4
4
4
Free radicals (zero charge and
one unpaired electron)
Stable
Can be handled under ordinary
conditions
Carry a spin 1/2 from the NO
group (1 unpaired electron)
N
C
H
O
N
R
Changing R
-> flexible chemical
structures
-> fine “tuning” of
magnetic
interactions
Tempone
4
4
Spin 1/2 molecule (from the NO group)
In the solid state it remains
paramagnetic down to very low
temperatures (0.05 K), with very small
interactions with neighboring molecules
Well isolated radical
+
The free radical tempone
O
N
C
4
4
4
H
Spin density mainly localised on the NO bond in a antibonding orbital
built from the 2pz of N and O
Roughly equal repartition N / O (0.40(2) / 0.36(2)mB) -> 53/47%
21% of the total spin delocalised on the molecule skeleton (dimethyl
groups)
The free radical tempol
O
O
N
C
Tempone
4
4
4
4
4
N
H
O
H
Tempol
2 very similar molecules : free radicals with a spin 1/2 from the NO group
But different chemical function : tempone -> keton / tempol -> alcohol
Tempone : well isolated molecules + Curie law
Tempol : hydrogen bonds in the solid between H from OH and O from NO
+ linear chains
Susceptibility -> maximum around 5 K then fall + antiferromagnetic interactions
The free radical tempol
O
N
Tempol
4
4
4
4
O
H
Spin density mainly localised on the NO bond in a antibonding orbital built from the
2pz of N and O (like in the case of tempone)
But : compared to the tempone, density on the O involved in the H bond depleted and
density on N reinforced (repartition N/O 61/39% compared to 53/47% )
Small negative density found on the H of the hydrogen bond
11% of the total spin delocalised on the molecule skeleton (dimethyl groups)
Phenyl Nitronyl Nitroxyde
Nitronyl nitroxides
4 Play a key role in molecular based magnetic
materials
4 Stable
4 Can be handled under ordinary conditions
4 Can be linked to two metallic ions by the 2
NO groups
+ linear chains
R
O
N
N
4 They carry a spin 1/2 from the 2 NO
groups (1 unpaired electron)
Phenyl derivative
4 Curie law down to very low temperatures
4 Very little interactions with neighboring molecules
+ Well isolated radical
The knowledge of the ground state of this isolated
radical necessary to understand the properties of the
interacting derivatives
.
O
H
C
O
N
Phenyl derivative
Phenyl Nitronyl Nitroxyde
Maximum of entropy projections of the magnetization distribution :
model free, no assumption on the shape
Projection along
the *
direction
Projection onto
the  plane
• Most of the spin density on the 2 NO groups
• Equivalence of the 2 NO groups
• Equivalence of N and O
•  shape of the magnetic molecular orbital
Phenyl Nitronyl Nitroxyde
O
N
R
N
O
4 1 unpaired electron in a * antibonding orbital
built from the 2pz of the two N and the two O
4 Magnetization equally shared between these
4 atoms
4 Fraction delocalized on the rest of the
molecule very small
4 Large negative contribution (1/3 of the
contributions on each N or O) on the sp2
bridging carbon
+ Spin polarization effect (intramolecular
J. Am. Chem. Soc. 116 (1994) 2019
exchange interaction, like the sign alternating
densities on the phenyl ring)
The free radical NitPy(C=C-H)
H
16
H16
N
O1-
C8
N2+
O2
N3
Ferromagnetic interactions
along the chains (J = 1.4 K)
The molecules are
organized in zig-zag
chains via an
hydrogen bond :
-CC-H16•••O 1N(2.14 Å -> weak H
bond)
The free radical NitPy(C=C-H)
Most of the
spin density on
the O-N-C-N-O
fragment
Negative
contribution on
C8
Significant
density on H16 :
0.045(10) mB
O2 0.258 (9) mB
N2
N3
0.188 (10) mB O1
H16
H16
C8
O1
N2
N3
O2
Active role played by the H bond in the propagation of
the exchange interaction along the chains
J. Am. Chem. Soc. 122 (2000) 1298
C8 -0.066 (11) mB
Depletion of
density on O1
(involved in H
bond) in favour
of O2
The paranitrophenyl nitronyl nitroxyde
Paranitrophenyl nitronyl nitroxide : first purely organic
ferromagnet Tc = 0.65 K
In the crystal, the
nitrogen atom of the
NO2 group at the
midpoint of two O of
the NO’s
The paranitrophenyl nitronyl nitroxyde
Positive spin density found on the nitrogen of the NO2
group, with a p shape and orthogonal to the  orbital of
the nitroxide
-> positive coupling according the Kahn & Briat model
-> Exchange interaction through this nitrogen atom
Copper Phenyl Nitronyl Nitroxide Complex
O
Cu
4
4
Equatorial coordination
This complex is built of 3 discrete entities formed by 1 Copper (s=1/2) ion and 2
nitroxides (s=1/2 each)
The Cu is in a square environment formed by 2 Cl atoms and 2 oxygens from the 2 Nit
+ the overlap between magnetic orbitals is large
+
4
N
a strong negative coupling is expected
Susceptibility measurements: Curie Law with S=1/2 for the molecule -> very strong
antiferromagnetic coupling between the 3 s=1/2 spins of each sub-unit
Copper Phenyl Nitronyl Nitroxide Complex
4 Magnetization density positive on the two
nitroxides and negative on the copper
(antiferromagnetic coupling)
N
O
O
4 Repartition 2/3 (Nit) - 1/3 Cu - 2/3 (Nit)
(expected for one of the two doublets
resulting from the coupling of 3 spins 1/2)
Cu
N
4 No magnetization density on theoxygens
bonded to Cu, while the spin populations on
the 2 N and on the other O are nearly equal
+
Spin distribution completely upset by the
strong antiferromagnetic interaction
J. Am. Chem. Soc. 115 (1993) 3610
Experiment vs ab-initio calculations
Polarized neutron experiment: roughly 2 weeks of beam time in a cryomagnet
+
It is necessary to know very well the low temperature crystal structure
--> another weak on a 4 circle
do we have to measure or calculations are reliable enough ?
Ab-initio Calculations
N
 1 2 N Z  n 1
ZLZM
M
H     
 
 
r
r
rLM
 1  2
M 1 M  m , 1 m
L,M 1
n
Kinetic
energy
4
4
nuclei
attraction
m 
electron
repulsion
LM
nuclei
repulsion
Problem !
Because of the electron-electron repulsion term, no analytical solution
+ approximations
Two main families of ab-initio calculations
• Methods based on the Hartree-Fock approximation
• Methods based on the local density approximation
Hartree-Fock approximation
• The molecular wave function is expressed as a Slater determinant of single particle
atomic wave functions
• The hamiltonian is replaced by a sum of single particle hamiltonians, including kinetic
energy, Coulomb attraction by the nuclei and the Coulomb repulsion by the other
electrons
+ this last term is calculated assuming that the other electrons are distributed over
their wave function -> self consistent calculations
4 Problem : exchange - correlation !
Electrons don’t stay unperturbed on their wave function when another electron is in the
neighborhood
-> exchange correlation hole
4 How to take it into account ?
• polarised basis sets (d and f orbitals for 2p electrons)
• perturbation theory -> admixing of excited states
according to the level of perturbation : MP2, MP3 (Moller-Plesset), or
full CI (configuration interaction) -> more and more time consuming
4 Restricted Hartree-Fock: each molecular orbital is doubly occupied (the dsp is > 0)
4 Unrestricted Hartree-Fock: the orbitals for spin up and spin down are different
(the dsp may be negative)
Local density approximation (LDA)
4 Hohenberg - Kohn theorem
• The energy of an ensemble of electrons is a functional of the charge density
and the ground state minimizes this functional
• This functional contains a kinematic term, a Coulomb term and an exchangecorrelation term
4 Problem
Nobody knows the analytical expression of the exchange-correlation term !
4 Approximation
• The exchange-correlation term for an electron in a crystal is taken as the
one for an homogeneous interacting electron gas in a box !
• This approximation has been extended to magnetic systems by introducing a
functional for spin up electrons and one for spin down electrons (Local spin
density approximation, or LSD)
4 To go beyond: corrections of the exchange-correlation term : non local
potential, gradient methods ....
The free radical tempone
Experiment
Hartree-Fock
LSD
N/O repartition : 53/47%
N/O repartition : 44/56%
N/O repartition : 50/50%
Delocalization: calculated by both method much smaller than observed
experimentaly
LSD: stronger delocalization (carbons) than Hartree - Fock
Phenyl Nitronyl Nitroxyde
Experiment
6-311G** UHF
321-G UHF
O
O
O
N
0.2
O
N
0.4
0.4
N
O
O
N
N
0.2
N
0.1
0.2
0.0
0.0
0.0
-0.2
-0.2
C
C
C
321-G CI
321-G MP2
O
O
N
L o ca l S pin D en sity
0 .0 2
mB
Ѓ
O
N
N
0.3
3
O
N
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
C
-0.2
J. Am. Chem. Soc. 116 (1994) 2019
C
The free radical tempol
Experiment
Hartree-Fock
LSD
N/O repartition : 61/39%
N/O repartition : 52/48%
N/O repartition : 54/46%
Both calculation agree with a transfer from O to N compared to the tempone
Influence of the H bond stronger for Hartree-Fock
Population on H: calculated one order of magnitude too small compared to the experiment
NitPy(C=C-H): calculs
Depletion of
density on O1
(involved in H
bond) in favour
of O2
H16
C8
O1
N2
N3
Significant
density on H16 :
0.045(10) mB
O2
Atom
Exp(1mB)
LSD(1 Mol) LSD(crystal)
O1
N2
C8
N3
O2
H16
0.20(1)
0.24(1)
-0.07(1)
0.22(1)
0.28(1)
0.05(1)
0.270
0.212
-0.086
0.230
0.312
0.000
------------------------------------------------------------------------------------------------------------
0.239
0.188
-0.075
0.212
0.312
0.004
The paranitrophenyl nitronyl nitroxyde
Positive spin density found on the nitrogen of the NO2
group, with a p shape and orthogonal to the  orbital of
the nitroxide
-> positive coupling according the Kahn & Briat model
-> Exchange interaction through this nitrogen atom
Atom
Exp(1mB)
LSD(1 Mol)
LSD(crystal)
O1
N1
O2
N2
0.283(7)
0.257(7)
-0.002(5)
0.021(5)
0.291
0.193
-0.001
-0.001
0.274
0.198
-0.001
0.001
---------------------------------------------------------------------------------------------------------------------
Copper Phenyl Nitronyl Nitroxide Complex
Atom
Experiment
LSD
--------------------------------------Cu
-0.36(4)
-0.123
Cl
-0.02(5)
-0.035
--------------------------------------N1
0.32(4)
0.144
O1
-0.01(4)
0.082
--------------------------------------N2
0.35(4)
0.142
O2
0.33(4)
0.263
--------------------------------------C1
-0.19(4)
-0.042
C2
-0.06(4)
-0.004
C3
-0.04(4)
-0.005
LSD : 0.58 mB on Nit, -0.19 on Cu,
far from the 2/3 -1/3 2/3 observed
experimentaly
Conclusion
Ab-initio calculations :
You can’t always get what you want
.....
But if you try sometimes, you might find
You get what you need ...
(Sir Michael Philip Jagger & Keith Richards)
Experiments :
Still required !!