Shruba Gangopadhyay 1,2 & Artëm E. Masunov 1,2,3 1 NanoScience Technology Center 2 Department of Chemistry 3 Department of Physics University of Central Florida Quantum Coherent Properties of Spins - III First Principle Simulations of Molecular Magnets: Hubbard-U is Necessary on Ligand Atoms for Predicting Magnetic Parameters
43
Embed
Shruba Gangopadhyay 1,2 & Artëm E. Masunov 1,2,3 1 NanoScience Technology Center
First Principle Simulations of Molecular Magnets : Hubbard-U is Necessary on Ligand Atoms for Predicting Magnetic Parameters. Shruba Gangopadhyay 1,2 & Artëm E. Masunov 1,2,3 1 NanoScience Technology Center 2 Department of Chemistry 3 Department of Physics University of Central Florida. - PowerPoint PPT Presentation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Shruba Gangopadhyay1,2 & Artëm E. Masunov1,2,3
1NanoScience Technology Center 2Department of Chemistry
3Department of PhysicsUniversity of Central Florida
Quantum Coherent Properties of Spins - III
First Principle Simulations of Molecular Magnets: Hubbard-U is Necessary on Ligand Atoms for Predicting Magnetic
Molecular Magnets – possible element in quantum computing
5Leuenberger & Loss Nature 410, 791 (2001)
Molecular Magnet is promising implementation of QubitUtilize the spin eigenstates as qubits Molecular Magnets have higher ground spin states
It can be in |0> and |1> state simultaneouslyAdvantages of Molecular MagnetsUniform nanoscale size ~1nmSolubility in organic solvents Readily alterable peripheral ligands helps to fine tune the propertyDevice can be controlled by directed assembly or self assembly
6
2-qubit system: Molecular Magnet [Mn12(Rdea)] contains two weakly coupled subsystems
M=Methyl diethanolamine M=allyl diethanolamine
Subsystem spin should not be identical
7
Ion substitution may be used to redesign MM
Cr8 Molecular Ring Cr7Ni Molecular Ring
[1] M. Affronte et al., Chemical Communications, 1789 (2007).[2] M. Affronte et al., Polyhedron 24, 2562 (2005).[3] G. A. Timco et al., Nature Nanotechnology 4, 173 (2009).[4] F. Troiani et al., Phys Rev Lett 94, 207208 (2005).
To redesign MM we need reliable method to predict magnetic properties
Ferromagnetic (F) – when the electrons have Parallel spin Antiferromagnetic (AF) – having Antiparallel spin
2J
)(E)(E
ZeemanAnisotropyHeisenbergMagnetic HHHH
8
Heisenberg-Dirac-Van Vleck Hamiltonian
J = exchange coupling constantSi= spin on magnetic center i
Electronic density n(r) determines all ground state properties of multi-electron system. Energy of the ground state is a functional of electronic density:
Density Functional Theory (DFT)prediction of J from first principles
Where are KS orbitals, is the system of N effective one-particle equations
Energy can be predicted for high and low spin states
10
Density Functional Theory (DFT) E=E[ρ]to simplify Kinetic part, total electron density is separated into KS orbitals, describing 1e each:
Electron interaction accounted for self-consistently via exchange-correlation potential
)()()'|'|
)'(( 221 rrVdr
rrrV iiixcext
2
1
|)(|)( rr i
N
ii
Hybrid DFT and DFT+U can be used for prediction of J
Pure DFT is not accurate enough due to self interaction error Broken Symmetry DFT (BSDFT) – Hybrid DFT (The most used method so far)
Unrestricted HF or DFT Low spin –Open shell
(spin up) β (spin down) are allowed to localized on different atomic centers
Representation of J in Broken symmetry terms is now E(HS) - E(BS) = 2JS1S2 Another alternative for Molecular Magnet DFT+U
11
12
DFT+U may reduce self-interaction error
The +U correction is the one needed to recover the exact behavior of theenergy. What is the physical meaning of U?
From self-consistent ground state (screened response)
From fixed-potential diagonalization(Kohn-Sham response)
U “on-site” electron-electron repulsion
We used DFT+U implemented in Quantum Espresso
Both metal and ligand need Hubbard term U
Idea: Empirically Adjust U parameter on both Metal and the coordinated ligand
The oxide dianions (Oµ), and aliphatic N atoms pure σ-donors- have spin polarization opposite to that of the nearest Mn ion, in agreement with superexchange
The aromatic N atoms have nearly zero spin-polarization. O atoms of the acetate cations have the same spin polarization as the nearest Mn cations.
This observation contradicts simple superexchange picture and can be explained with dative mechanism.
The acetate has vacant π-orbital extended over 3 atoms, and can serve as π-acceptor for the d-electrons of the Mn cation. As a result, Anderson’s superexchange mechanism, developed for σ-bonding metal-ligand interactions, no longer holds.
Resulting from spin–orbit coupling, Produces a uniaxial anisotropy barrier Separating opposite projections of the spin along the axis
Relativistic Pseudopotential
Non-Collinear Magnetism
28
Prediction of Anisotropy for Ce based Complex
U(eV)J
(cm-1)Ce O N 0 0 0 -359.023 0.5 0.2 -12.574 0.5 0.2 -4.034 0.8 0.2 -3.86 U(eV)
D(cm-1)Ce O N
0 0 0 169.924 0.5 0.2 8.384 0.8 0.2 0.16
Jexpt=-0.75 cm-1, Dexpt= 0.21 cm-1
29
Summary
To predict correct J values we need to include U parameters on both metal and ligand
Geometry Optimization of ground state is extremely important for correct prediction of J values
Exclusion of U Parameters on ligand atoms leads incorrect ferromagnetic ground state
Anisoptropy prediction needs relativistic pseudopotential For Anisotropy we need good starting wave function for
ground spin state of the molecule
30
Prediction of Anisotropy for Mn12 based wheel Heisenberg Exchange constants
Ion substituted Mn12 wheel Mn12 cation/anion Mn12 wheel on the metal surface
Future Work
31
Acknowledgements
Prof. Michael Leuenberger Eliza Poalelungi Prof. George Christou Arpita Pal NERSC Supercomputing Facilities (m990) ACS Supercomputing Award for Teragrid
32
tunneling from macroscopic world
to quantumland through the
rabbit hole
Questions &
Suggestions
34
35
PseudopotentialPseudopotentials replace electronic degrees of freedom in the Hamiltonian of chemically inactive electron by an effective potential
A sphere of radius (rc) defines a boundary between the core and valence regions
For r ≥ rc the pseudopotential and wave function are required to be the same as for real potential.
Pseudopotential excludes (does not reproduce) core states – solutions are only valence states
Inside the sphere r ≤ rc , pseudopotential is such that wave functions are nodeless εi(at) = εi(PS)
For Iron1s2 2s2 2p6 3s2 3p6 3d6 4s2
Faliure of bs-dft
Bimetallic complexes with Acetate Bridging ligand
Complexes with Ferromagnetic Coupling Mix valence complexes
36
Different transition metals in molecular magnets
37
38
J for other transition metal complexes
J cm-1(FeIII-FeIII)Exp BSDFT DFT+U-121 -77 -141
J cm-1(FeIII-FeIII)Exp BSDFT DFT+U
-16 -10
39
J cm-1 (CrIII-CrIII)Exp BSDFT DFT+U
-15 -10
J cm-1(CrIII-MnIII)Exp BSDFT DFT+U
-17 -29
Application- biocatalysisPolyneuclear – Transition metal centers in the
enzymeImportant for biocatalysis -Understand the stability of
biradical at transition state
40S Sinnecker, F Neese, W Lubitz, J Biol Inorg Chem (2005) 10: 231–238
DFT+U in Quantum Espresso
The formulation developed by Liechtenstein, Anisimov and Zaanen, referred as basis set independent generalization
41
}]n[{E}]n[{E)]r(n[E)]r(n[E IDC
ImHubLDAULDA
n(r) is the electronic density
the atomic orbital occupations for the atom I experiencing the “Hubbard” term
The last term in the above equation is then subtracted in order to avoid double counting of the interactions contained both in EHub and, in some average way, in ELDA.
Imn
Future Plans
Compute J for heteroatom (Cr)
containing molecular magnetic
wheel42
Alternative Approach: DFT+U
The DFT+U method consists in a correction to the LDA (or GGA) energy functional to give a better description of electronic correlations. It is shaped on a Hubbard-like Hamiltonian including effective on-site interactions
It was introduced and developed by Anisimov and coworkers (1990-1995)
Advantages Over Hybrid DFT Computationally less expensive Possibility to treat large systems