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Vème Journée de Simulations Numériques en Chimie de Paris-Saclay
Theoretical treatment of magnetic anisotropyin transition metal complexes
Benjamin Cahier, Nathalie Guihéry, Talal Mallah
24 - 11 - 2017
Molecular magnetism and Single-Molecule Magnets (SMM)
Magnetic properties Electronic spin
Molecular magnetism and Single-Molecule Magnets (SMM)
Mononuclear complexes
Magnetic properties Electronic spin
Molecular magnetism and Single-Molecule Magnets (SMM)
Clusters
Mononuclear complexes
Magnetic properties Electronic spin
Molecular magnetism and Single-Molecule Magnets (SMM)
Clusters
Mononuclear complexes
Defects in periodic lattice
Magnetic properties Electronic spin
[Mn12(O)12(Ac)16(H2O)4]
Hysteresis loop : bistability
Hysteresis loop of the magnetization at low T
Single Molecule Magnet (SMM) behavior
2.2 K
2.8 K
Sessoli et al., Nature 365, 141 (1993)
Potential applications :
• Classical data storage
• Quantum computation
Why such magnetic properties?
4 Mn4+ : d3, S=3/2
8 Mn3+ : d4, S=2
Mn4+ : d3
Mn3+ : d4
S = 2
S = 3/2
Strong echange interaction
Ground State : S = 10
Explain the magnetization but not the hysteresis loop
Mn4+- Mn4+ : Ferromagnetic interaction
Mn3+- Mn3+ : Ferromagnetic interaction
Mn4+- Mn3+ : Antiferromagnetic interaction
-10 -8 -6 -4 -2 0 2 4 6 8 10
MS
∆E = 42 cm-1
������ � ��� � �
��= -0.42 cm-1
The spin-orbit coupling break the degeneracy of the 2S+1 = 21 Ms levels
Magnetic properties are fully explained by the ZFS
The Mn12 Zero-Field Splitting (ZFS)
Magnetic anisotropy in transition metal complexes
[Co(Me6tren)Cl]+
3d orbitals
e
e
a1
S = 3/2
z
+3/2
+1/2
-1/2
-3/2
4 Ms levels : 4 possible orientations for
the magnetic moment
+3/2 +1/2 -1/2 -3/2
+3/2
+1/2 -1/2
-3/2
Ruamps, R. et al., Chemical Science 2014, 5 (9), 3418-3424
ΔE = 2D =
-16.2 cm-1
ZFS calculation
Two-step method :
1. Electronic structure
2. Spin-Orbit coupling
Need a precise treatment of :
• Electronic correlation
• Spin-orbit coupling
ZFS calculation
Two-step method :
1. Electronic structure
2. Spin-Orbit coupling
Virtual
orbitals
……
Electronic correlation
• Static correlation :
CASSCF method
• Dynamical correlation :
CASPT2 (perturbation)
DDCI (variation)
Active Space
3d orbitals
Inactive
orbitals
Need a precise treatment of :
• Electronic correlation
• Spin-orbit coupling
1
0
1000
2000
3000
4000
5000
6000
7000
E (
cm-1
)
A��
E�
A� �
A� �
d7 : 10 quadruplet and 40 doublet states
…
����
0
1000
2000
3000
4000
5000
6000
7000
E (
cm-1
)
D = -8,9 cm-1A�
�
E�
A� �
A� �
d7 : 10 quadruplet and 40 doublet states
…
�������� +
Spin-Orbit Couping
SOC matrix interaction is
diagonalized in the d-d states basis
Split all Ms degeneracy
Accurate reproduction of
experiments
2
Dcalc. = -8.9 cm-1
DEPR = -8.12 cm-1
Dcalc. = 51.4 cm-1
Which factors are important to rationalize the ZFS in TM complexes?
Why are these complexes different?
What are the similarity between them?
≠
γ = 0° γ = 3° γ = 6° γ = 9° γ = 9° γ = 8,7°γ = 0°
D (cm-1) : 51,4 34,6 20,7 7,6 0,12 -12,8 -8,9
γ = 0° γ = 3° γ = 6° γ = 9° γ = 9° γ = 8,7°γ = 0°
D (cm-1) : 51,4 34,6 20,7 7,6 0,12 -12,8 -8,9
0
1000
2000
3000
4000
5000
6000
7000
E (
cm-1
)
A��
E�
A� �
A� �
A� ���
A� ���
A� ��
E� ��
26,2522,43
18,77
16,4213,68
15,25
44,90
-11,35-18,89
-21,87-28,19
-27,76
��� ���� �������
�1
2 + 1 (���
���� Γ�γ� Γ� Γ���Γ γ Γ ���� Γ��
Selection rules for spin-orbit coupling in molecules
• ΔS = 0, ±1
• ΔMS = 0, ±1
���� ≈ "#�. � + "#% . % + "#&. &
D < 0 D > 0
• Γ� ⊗Γ ( ⊗Γ) ∋ Γ�
Explain if and how excited states contributes to the ZFS
ZFS
co
ntr
ibu
tio
n (
cm-1
)
Electronic energy (cm-1)
0
10
20
30
40
50
60
0 20000 40000 60000
C3v symmetry : all the A1 and E states should be coupled to the GS (3/4 of all states)
CoII complexes : 2 or 3 highly excited doublets are coupled to the GS
The selection rules are incomplete!
", , ,, � ". - "�, �, ,�, �� � .1 /0 10�2//12 1"� � , " 1
" "# "� �
Selection rules
Δ" � 0,51
Δ � 0,51Δ, � Δ� � 0
For Co2+ ion :
6� ��� 6�
7� ��� 6�
8� ��� 6�
Selection rules for spin-orbit in the atom
✘
✔
✔
Influence of 2G on 4F
Influence of 4P on 4F
Electronic spectrum SO spectrum
The atomic nature of the metal still play a role in the magnetic properties of TM complexes
Effect of excited states on the 4F
SO spectrum
E (cm-1)
0
3629
3847
4083
4499
7627
7713
20291
20510
21827
4P
4F
4T1
4T1
4T2
4A2
4E
4A2
4E
4E4A1
4A2
4A2
9 3 → <= →>?@8� → <�
� → A�� � 0
8� → <�� → B� � 0,03
6� → <�� → A�
� = 0,2
6� → <�� → B� = 0,81
6� → <�� → B� = 28,79
6� → <�� → A�
� = −19,07
9 3 <= >?@
D = 18.4 cm-1
Other parameters?
Effect of the ligand?
[Co(Me6tren)F]+ [Co(Me6tren)Cl]+ [Co(Me6tren)Br]+ [Co(Me6tren)I]+
D = -17,7 cm-1 D = -8.1 cm-1D = -4.6 cm-1
D = ±2 cm-1
[Co(Me6tren)Cl]+[Fe(Me6tren)Cl]+ [Ni (Me6tren)Cl]+
Effect of the metal?
Conclusion
• Magnetic properties of TM complexes are really sensitive to geometry and symmetry
• Small energy difference are involved : need high precision calculations
• Ab initio calculation are expensive but provides useful informations
Perspective
• Bigger systems, polynuclear complexes
• Control of magnetic properties using external stimulus
• Interaction with surfaces/matrices/others molecules
• Relaxation process and spin dynamics
Thank you for your attention
D( B��� 6� ) = + 26.25 cm-1
D( A��� 7� ) = +13.02 cm-1
D( B��� 7� ) = - 3.03 cm-1
D( B��� 8� ) = +0.58 cm-1
CAS CAS+SDCAS+S DDCI2 DDCI3
1p 1h 1h-1p 2h 2p 1h-2p 2h-1p 2h-2p
Esp
ace
acti
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