Spin-crossover molecules: puzzling systems for electronic structure methods. Andrea Droghetti School of Physics and CRANN, Trinity College Dublin

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Spin-crossover molecules: puzzling systems for electronic structure methods Andrea Droghetti School of Physics and CRANN, Trinity College Dublin

Introduction

Introduction 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 Electronic structure of the molecule Electronic structure of the device (equlibrium properties) Transport properties of the device (out-of-equilibrium properties)

Introduction Electronic structure of the molecule DFT DMC CASSCF Electronic structure of the device (equlibrium properties) DFT beyond-dft Transport properties of the device (out-of-equilibrium properties) DFT Beyond-DFT (?) (TDDFT, MDPT?)

Introduction Electronic structure of the molecule DFT DMC CASSCF 1- Accurate results (?) Electronic structure of the device (equlibrium properties) DFT beyond-dft Transport properties of the device (out-of-equilibrium properties) DFT Beyond-DFT (?) (TDDFT, MDPT?)

Introduction Electronic structure of the molecule DFT DMC CASSCF Electronic structure of the device (equlibrium properties) DFT beyond-dft Transport properties of the device (out-of-equilibrium properties) DFT Beyond-DFT (?) (TDDFT, MDPT?)

DFT for infinite systems HM H LM H MR. HL HR

DFT for infinite systems HM ΣL+ +ΣR. www.smeagol.tcd.ie

DFT for infinite systems HM +ΣR ΣL+. www.smeagol.tcd.ie

The Theoretical Method HM +ΣR ΣL+.

The Theoretical Method HM +ΣR ΣL+.

The Theoretical Method H ' M =H 0 +V ee ΣL+ +ΣR.

Smeagol Unitary trasf. for removing orbital overlap Continuous-time quantum Monte Carlo Double-counting correction (interaction/hybridization expansion) Dyson eq. if scf.true. Else (analytic continuation) A. Droghetti & I. Rungger Spectral function

The Theoretical Method H ' M =H 0 +V ee. DMC two-particle density matrix = model two-particle density matrix (Lucas Wagner)

Electronic structure of the molecule DFT DMC CASSCF 1- Accurate results (?) - Allow to extract first-principles model Hamiltonians Electronic structure of the device (equlibrium properties) DFT beyond-dft Transport properties of the device (out-of-equilibrium properties) DFT Beyond-DFT (?) (TDDFT, MDPT?)

Spin-Crossover molecules

Spin-crossover molecules eg dx -y dz tg dxy dxz dyz

Spin-crossover molecules eg dx -y dz tg dxy dxz dyz

Spin-crossover molecules eg dx -y dz tg dxy dxz dyz

Spin-crossover molecules dx -y eg eg* dz tg dxy dxz dyz tg Fe eg eg Ligands

Spin-crossover molecules dx -y dz eg eg* tg dxy dxz dyz tg Fe eg eg Ligands

Magnetic molecules G=G HS G LS = E T S E 0 T C= S 0 E S

Transport through SCMs F. Prinz et al., Adv. Mat., 3, 1545 (011) N. Baadji & S. Sanvito, Phys. Rev. Lett. 108, 1701 (01) M.S. Alam et al., Angew. Chem. Int. Ed., 49, 1159 (010)

Model systems [Fe(HO)6]+ [Fe(NH3)6]+ [Fe(NCH)6]+ lower crystal field [Fe(CO)6]+ higher crystal field Spectrochemical series

Model systems [Fe(HO)6]+ [Fe(NH3)6]+ [Fe(NCH)6]+ lower crystal field [Fe(CO)6]+ higher crystal field Expected ground state: S= Δ E adia <0 S= Δ E adia <0 S= Δ E adia <0 S=0 Δ E adia >0

[Fe(HO)6]+ [Fe(NH3)6]+ ΔEadia (ev) LDA -0.49 GGA -1.04 B3LYP -1.37 PBE0-1.74 HH -.6 DMC -.54(1) ΔEadia (ev) LDA 0.96 GGA 0.08 B3LYP -0.59 PBE0-0.88 HH -1.68 DMC -1.59(1) E adia 0 E HS E LS [Fe(NCH)6]+ ΔEadia (ev) [Fe(CO)6]+ ΔEadia (ev) LDA 5.18 LDA.37 GGA 3.4 GGA 1.04 B3LYP 1.7 B3LYP -0.0 PBE0 1.3 PBE0-0.44 HH 0.4 HH -1.49 DMC -1.37(3) DMC 0.37(3) Caculations with CASINO Dirac-Fock Trail-Needs PP (small core for Fe) Slater-Jastrow (LDA orbitals) A. Droghetti & S. Sanvito and in collaboration with D. Alfe' (UCL)

Spin Crossover [FeL](BF4) (L=,6-dypirazol-1-yl-4-hydroxymethylpyridine) V.A. Money et al., Dalton Trans. 10, 1516 (004) adia ΔE ΔEadia (ev) (ev) GGA 1.4 LDA -0.49 B3LYP GGA 0.01-1.04 PBE0 B3LYP -0.3-1.36 HH -1.33 PB0-1.74 DMC -1.1(4) DFT A. Droghetti, D. Alfe' and S. Sanvito, J. Chem. Phys. 137, 14303 (01) A. Droghetti, D. Alfe' and S. Sanvito, Phys. Rev. B 87, 05114 (013)

Spin Crossover adia ΔE ΔEadia (ev) (ev) GGA 0.44 LDA -0.49 B3LYP GGA -0.33-1.04 PBE0 B3LYP -0.54-1.36 DMC -0.69(8) DFT CASPT 0.10 DMC with QWALK, (new) Burkatzki-Filippi-Dong PP Slater-Jastrow Calculations performed by A. Droghetti and M. Fumanal (Barcelona) Thanks to Lucas Wagner for the code and technical support

Spin Crossover [Fe(NCH)6]+ CAS(10,1) 4d-Fe dx -y eg dz eg* tg dxy dxz dyz tg Fe eg eg Ligands

Spin Crossover [Fe(NCH)6]+ dx -y tg eg dz eg* tg dxy eg CAS(10,1) 4d-Fe eg* dxz dyz tg Fe eg

Spin Crossover [Fe(NCH)6]+ dx -y tg eg dz eg* HF tg dxy eg CAS(10,1) 4d-Fe eg* dxz dyz tg Fe eg ΔEadia -3.8 ev CASSCF -1.96 ev CASPT -0.33 ev

Spin Crossover [Fe(NCH)6]+ ΔEadia HF -3.8 ev B3LYP -0.9 ev PBE 0.76 ev CASSCF -1.96 ev CASPT -0.33 ev ΔEadia DMC (HF) -1.16(5) ev DMC -1.05(5) ev (B3LYP) DMC -0.87(4) ev (PBE) DMC (Slater-Jastrow)

Spin Crossover [Fe(NCH)6]+ Energy (a.u) CSF1-0.698(1) CSF7-0.700(1) CSF13-0.706(1) CSF1-0.700(1)

Spin Crossover Energy (a.u) CSF1-0.645(1) CSF7-0.648(1) CSF13-0.647(1) CSF3-0.649(1)

Conclusions DFT, DMC and CASPT return different results (different order of magnitude!!) CASPT 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?

The algorithm Acknowledgements - 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!

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