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Spin-crossover molecules: puzzling systems for electronic structure methods
Andrea Droghetti School of Physics and CRANN, Trinity College Dublin
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Introduction
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Can we read a molecule spin?
Can we access electronic (and vibranic) states?
Can we write and read information in the spin state of a molecule?
Introduction
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Electronic structure of the molecule
Electronic structure of the device (equlibrium properties)
Transport properties of the device (out-of-equilibrium properties)
Introduction
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Electronic structure of the molecule
Electronic structure of the device (equlibrium properties)
Transport properties of the device (out-of-equilibrium properties)
DFT DMC
DFT beyond-DFT
DFT Beyond-DFT (?)(TDDFT, MDPT ?)
CASSCF
Introduction
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Electronic structure of the molecule
Electronic structure of the device (equlibrium properties)
Transport properties of the device (out-of-equilibrium properties)
DFT DMC
DFT beyond-DFT
DFTBeyond-DFT (?)(TDDFT, MDPT ?)
CASSCF
1- Accurate results (?)
Introduction
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Electronic structure of the molecule
Electronic structure of the device (equlibrium properties)
Transport properties of the device (out-of-equilibrium properties)
DFT DMC
DFT beyond-DFT
DFTBeyond-DFT (?)(TDDFT, MDPT ?)
CASSCF
Introduction
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DFT for infinite systems
.
HM
H RH L
H LM HMR
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DFT for infinite systems
.
HM
+ΣRΣL+
www.smeagol.tcd.ie
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DFT for infinite systems
.
HM
+ΣRΣL+
www.smeagol.tcd.ie
.
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The Theoretical Method
.
HM
+ΣRΣL+
.
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The Theoretical Method
.
HM
+ΣRΣL+
.
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The Theoretical Method
.
H 'M=H 0+V ee
+ΣRΣL+
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Continuous-time quantum Monte Carlo
(interaction/hybridization expansion)
Dyson eq.
Smeagol
if scf .true.
Else (analytic continuation)
Spectral function
Unitary trasf. for removing orbital
overlap
Double-counting correction
A. Droghetti & I. Rungger
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The Theoretical Method
.
H 'M=H 0+V ee
DMC two-particle density matrix = model two-particle density matrix
(Lucas Wagner)
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Electronic structure of the molecule
Electronic structure of the device (equlibrium properties)
Transport properties of the device (out-of-equilibrium properties)
DFT DMC
DFT beyond-DFT
DFT Beyond-DFT (?)(TDDFT, MDPT ?)
CASSCF
1- Accurate results (?)2- Allow to extract “first-principles” model Hamiltonians
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Spin-Crossover molecules
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Spin-crossover molecules
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
∆
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Spin-crossover molecules
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
∆
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Spin-crossover molecules
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
∆
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Spin-crossover molecules
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
eg
eg*
eg
t2g
Fe
Ligands
∆
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Spin-crossover molecules
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
eg
eg*
eg
t2g
Fe
Ligands
∆
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Magnetic molecules
G=GHS−GLS= E−T S
E0 S0
TC= E S
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Transport through SCMs
N. Baadji & S. Sanvito, Phys. Rev. Lett. 108, 217201 (2012)
F. Prinz et al., Adv. Mat., 23, 1545 (2011)
M.S. Alam et al., Angew. Chem. Int. Ed., 49, 1159 (2010)
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Model systems
[Fe(H2O)
6]2+ [Fe(NH
3)
6]2+ [Fe(CO)
6]2+[Fe(NCH)
6]2+
lower crystal field higher crystal field
Spectrochemical series
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Model systems
[Fe(H2O)
6]2+ [Fe(NH
3)
6]2+ [Fe(CO)
6]2+[Fe(NCH)
6]2+
lower crystal field higher crystal field
S=2
Expected ground state:
S=2 S=2 S=0
Δ Eadia<0 Δ Eadia<0 Δ Eadia<0 Δ Eadia>0
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[Fe(H2O)
6]2+ [Fe(NH
3)
6]2+
Eadia0 EHSELS
[Fe(CO)6]2+[Fe(NCH)
6]2+
ΔEadia (eV)
LDA 0.96GGA 0.08B3LYP -0.59PBE0 -0.88HH -1.68DMC -1.59(1)
ΔEadia (eV)
LDA 2.37GGA 1.04B3LYP -0.20PBE0 -0.44HH -1.49DMC -1.37(3)
ΔEadia (eV)
LDA -0.49GGA -1.04B3LYP -1.37PBE0 -1.74HH -2.26DMC -2.54(1)
ΔEadia (eV)
LDA 5.18
GGA 3.42
B3LYP 1.27
PBE0 1.32
HH 0.24
DMC 0.37(3)
Caculations with CASINODirac-Fock Trail-Needs PP (small core for Fe)Slater-Jastrow (LDA orbitals)
A. Droghetti & S. Sanvito and in collaboration with D. Alfe' (UCL)
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Spin Crossover
[FeL2](BF
4)
2
(L=2,6-dypirazol-1-yl-4-hydroxymethylpyridine)
V.A. Money et al., Dalton Trans. 10, 1516 (2004)
DFT ΔEadia (eV)
LDA -0.49
GGA -1.04
B3LYP -1.36
PB0 -1.74
ΔEadia (eV)
GGA 1.24
B3LYP 0.01
PBE0 -0.23
HH -1.33
DMC -1.21(4)
A. Droghetti, D. Alfe' and S. Sanvito, J. Chem. Phys. 137, 124303 (2012)
A. Droghetti, D. Alfe' and S. Sanvito, Phys. Rev. B 87, 205114 (2013)
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Spin Crossover
DFT ΔEadia (eV)
LDA -0.49
GGA -1.04
B3LYP -1.36
ΔEadia (eV)
GGA 0.44
B3LYP -0.33
PBE0 -0.54
DMC -0.69(8)CASPT2 0.10
DMC with QWALK,(new) Burkatzki-Filippi-Dong PPSlater-Jastrow
Calculations performed by A. Droghetti and M. Fumanal (Barcelona)Thanks to Lucas Wagner for the code and technical support
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Spin Crossover
[Fe(NCH)6]2+
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
eg
eg*
eg
t2g
Fe
Ligands
4d-Fe CAS(10,12)
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Spin Crossover
[Fe(NCH)6]2+
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
eg*
eg
t2g
Fe
4d-Fe CAS(10,12)
t2g
eg
eg*
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Spin Crossover
[Fe(NCH)6]2+
dxy
dxz
dyz
dz2d
x2-y2
eg
t2g
eg*
eg
t2g
Fe
4d-Fe CAS(10,12)
t2g
eg
eg*
HF -3.82 eV
CASSCF -1.96 eVCASPT2 -0.33 eV
ΔEadia
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Spin Crossover
[Fe(NCH)6]2+
HF -3.82 eV
ΔEadia DMC(HF)
-1.16(5) eV
DMC (B3LYP)
-1.05(5) eV
DMC(PBE)
-0.87(4) eV
ΔEadia
DMC (Slater-Jastrow)B3LYP -0.29 eV
PBE 0.76 eV
CASSCF -1.96 eV
CASPT2 -0.33 eV
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Spin Crossover
[Fe(NCH)6]2+
CSF1 -220.698(1)
CSF7 -220.700(1)
CSF13 -220.706(1)
CSF21 -220.700(1)
Energy (a.u)
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Spin Crossover
CSF1 -220.645(1)
CSF7 -220.648(1)
CSF13 -220.647(1)
CSF23 -220.649(1)
Energy (a.u)
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Conclusions
● DFT, DMC and CASPT return different results (different order of magnitude!!)
● CASPT2 – chemsists say that we should trust it as reference
● DMC...trial wave-function seems not to matter much
● Pseudo-potential...hard to say...but can a “bad pseudo-potential” be responsible for an systematic error of about more than 0.5 eV on an energy difference?
● What else?
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The algorithmAcknowledgements
- European Union for funding (ACMOL projects)
- Irish Centre For High-End Computing (ICHEC) and Trinity Centre for High Performing Computing (TCHPC) for computational resources
- Alin Elena (ICHEC) for technical support
Thank you!