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

f