Magnetic Properties: NMR, EPR, Susceptibility

Transcription

1 Magnetic Properties: NMR, EPR, Susceptibility Part 3: Selected 5f 2 systems Jochen Autschbach, University at Buffalo, jochena@buffalo.edu J. Autschbach Magnetic Properties 1

2 Acknowledgments: Funding: Current and former graduate students: Ben Pritchard: paramagnetic NMR, EPR studies, Molcas developments new group members: Robert Martin, Alex Marchenko, Tom Duignan: paramagnetic NMR, actinyl species in solution, misc. Support from: Center for Computational Research, SUNY Buffalo Current and former postdocs: Frederic Gendron: f -element studies Fredy Aquino, Prakash Verma: NWChem relativistic magnetic property modules Kamal Sharkas: Molcas developments Collaborators: Boris LeGuennic, Helene Bolvin: f -element projects N. Govind, W. A. de Jong, B. McNamara, H. Cho: NMR & other magnetic properties D. Peng, M Reiher: X2C implementation in NWChem S. Patchkovskii: paramagnetic NMR J. Autschbach Magnetic Properties 2

3 Plutonyl(VI) CAS-SO natural spin-z orbitals (m z ) for UO 2 +, NpO 2 2+, PuO 2 2+ (only the formally non-bonding 5f orbitals are shown) Free plutonyl(vi): close to SR limit. Orbitally degenerate spin triplet F. Gendron, B. Pritchard, H. Bolvin, JA, Inorg. Chem. 53 (2014), J. Autschbach Magnetic Properties 3

4 Plutonyl(VI) State ordering: CF vs. SO (CAS(2,4)PT2) 1 Γ g (δ 2 ) Relative Energy (cm -1 ) Π g (δ 1 φ 1 ) 1 Σ + g (δ 2,φ 2 ) 3 Π g (δ 1 φ 1 ) 3 Σ g (δ 2,φ 2 ) 3 H g (δ 1 φ 1 ) 2 g 6 g 1 g 0 + g 0 - g 5 g 100% 3 Π g 92% 3 H g + 8% 1 I g 70% 3 Σ g + 8% 3 Π g + 17% 1 Π g 61% 3 Π g + 8% 3 Σ g + 27% 1 Σ + g 100% 3 Π g 99% 3 H g 1 g 49% 3 Π g + 26% 3 Σ g + 23% 1 Π g g 54% 3 Σ g + 26% 3 Π g + 17% 1 Σ + g SC SO 1st order SO 4 g 2nd order 98% 3 H g + 2% 1 Γ g PuO 2 2+ J. Autschbach Magnetic Properties 4

5 Plutonyl(VI) PuO 2 2+ ground state derives from the SR 3 H 4g term of Pu 6+ SO interaction mixes SR 3 H 4g (m l1 = ±3, m l2 = ±2) with 1 Γ 4g (m l1 = ±2, m l2 = ±2). Nitrate, carbonate ligands: D 3h symmetry, splitting of 5f φ orbitals. Equatorial CF mixes 3 Π 2 (m l1 = 3, m l2 = ±2) into the wavefunction. Model space in terms ( of Slater determinants ) a, b ψa (1), ψ = 1/2 det b (1) with ψ ψ a (2), ψ b (2) a, ψ b being m l, m s orbitals: 3 H 4 = 3, 1 2, 2, Γ 4 = 2, 1 2, 2, Π 2 = 3, 1 2, 2, 1 2 J. Autschbach Magnetic Properties 5

6 Plutonyl(VI) PuO 2 2+ model Hamiltonian: H CF + H SO 3 H 4g 1 Γ 4g 3 H 4g E( 3 H) 5 2 ζ 3 2 ζ 1 3 Γ 4g 2 ζ E(1 Γ) Model wavefunction and g-factors: E( 3 H) = Λ + J(3, 2) K (3, 2) E( 1 Γ) = 2Λ + J(2, 2) Λ = splitting between δ and φ ζ = SO coupling constant J(m l1, m l2 ), K (m l1, m l2 ) = Coulomb, exchange integrals ψ = A 3 H 4g + B 1 Γ 4g g = ±(6A 2 + 8B 2 ) = A 3, 1 2, 2, B 2, 1 2, 2, 1 2 g = ±g PuO Λ Ζ J. Autschbach Magnetic Properties 6

7 Plutonyl(VI) [PuO 2 (NO 3 ) 3 ] : equatorial ligands break degeneracy of 5f φ orbitals Model Hamiltonian (Λ was subtracted on the diagonal) H CF + H SO 3 H 4 1 Γ 4 3 Π 2 3 H 4 J(3, 2) K (3, 2) 5 2 ζ 3 1 Γ ζ 2 2 Γ 2 ζ Λ + J(2, 2) 0 3 Π Γ 0 J(3, 2) K (3, 2) ζ The new interaction is 3, ± 1 2 ĤCF 3, ± 1 2 = 1 2 Γ, mixing the PuO 22+ ground state with 3 Π 2 (m l1 = 3, m l2 = ±2). eq. CF reduces g : 7 6 Λ 5 ±g PuO 2 CO Λ 10 Λ Γ Ζ CAS(8,10)PT CAS(8,10)PT Expt Expt 5.92 Pu-O eq distance reduced by 0.05Å measured for related acetate complex J. Autschbach Magnetic Properties 7

8 Plutonyl(VI) Actinyl-tris-carbonate complexes (isostructural with nitrate) Environmentally important NMR data available Using Bertini / Bleaney equations for axial system: 3cos 2 Θ δ dip = 1 12πr χ 3 ax (3 S(S + 1) cos2 θ 1) ; χ ax = χ χ ; χ i = µ 0 µ 2 B g2 i 3kT assumption: small contact spin densities at carbons ( note: this assumes a point magnetic ion) g > g negative dipolar eq. 13 C shifts Π 4 Θ F. Gendron, B. Pritchard, H. Bolvin, JA, Inorg. Chem. 53 (2014), J. Autschbach Magnetic Properties 8

9 Plutonyl(VI) PuO22+ : gk g δ dip ( 13C) Experimental PNMR shift relative to carbonate: -376 ppm Compare non-coll. spin density of the [AnO2 (CO3 )3 ]4 species: NpVI : PuVI : g-factors agree reasonably well with experimental data for the analogous nitrate complex J. Autschbach Magnetic Properties 9

10 Electronic structure and magnetic properties of uranium(vi) complexes (C 5 Me 4 UNO (C 5 Me 4 UCl (C 5 H 5 ) 3 UCl (C 5 H 5 ) 3 UCH 3 For details see F. Gendron, B. LeGuennic, JA, Inorg. Chem. (2014), in press J. Autschbach Magnetic Properties 10

11 Scalar relativistic DFT orbital diagrams: Energy (ev) a2 (fφ) a1 (fσ) e (fδ) a1 (dz 2 ) e (fπ) a1 (fφ) a 2 (fφ) a1 (fσ) a 1 (d 2 z ) e (fπ) a1 (fφ) e (fδ) a 2 (fφ) a 1 (fσ) a1 (dz 2 ) e (fπ) e (fδ) a1 (fφ) a 1 (σ) π e (π) (C 5Me 4U σ (C 5Me 4UNO NO (C 5Me 4U (C 5Me 4UCl Cl (C 5H 5) 3U (C 5H 5) 3UCH 3 CH 3 (C 5 Me 4 UNO: Strong π bonding with NO ligand gives closed-shell GS (C 5 Me 4 UCl, (C 5 H 5 ) 3 UCl, (C 5 H 5 ) 3 UCH 3 : spin-triplet GS, low-energy excited states very different magnetic properties J. Autschbach Magnetic Properties 11

12 Temperature-independent paramagnetism (TIP) vs. Curie law (C/T ) van Vleck equation for one of the principal paramagnetic susceptibility components (nonrel. Zeeman operator) : χ u = 1 Q µ 0µ 2 B Q = λ,a λ e βe λ, β = 1 kt [ e βe λ β ψ λa L u + g e S u ψ λa 2 a,a + 2 λ λ a,a ψ L λa u + g e S u ψ 2 ] λ a E λ E λ 2-level model, non-degenerate GS, degenerate magnetic excited state: T 0: only GS populated, χ(t ) const. (TIP) from SOS part T very high: both states equally populated, SOS parts cancel, χ 1/T J. Autschbach Magnetic Properties 12

13 Plots of χt versus T (linear slope > 0 indicates TIP, vanishing slope means χ 1/T ): Calc. C5Me4H 3UCl 1.0 Expt. ΧMT cm 3 K mol ΧMT cm 3 K mol C5Me4H 3UCl 0.2 C5Me4H 3UNO 0.2 C5Me4H 3UNO T K T K (C 5 Me 4 UNO: singlet GS, excited states much higher, TIP up to room temperature (C 5 Me 4 UCl: singlet GS, excited states at low energy, TIP only below ca. 70 K J. Autschbach Magnetic Properties 13

14 3 H 6 1 G 1 G 4 1 G Energy 3 F 3 H 3 F 3 3 H 5 3 F 3 H Energies of the Spin-Free (SF) and Spin-Orbit (SO) states of a 5f 2 complex with the crystal-field (CF) treated a priori (left) and a posteriori (right) 3 F 2 3 H, L = 5, S = 1: 33 micro-states. 3 H 4 3 H J : 9 micro-states for J = 4, 11 for J = 5, 13 for J = 6, total 33. SF SF + CF SF + SO + CF SF + SO SF J. Autschbach Magnetic Properties 14

15 Ab-initio calculations: A 2 3 A2 Relative Energy (cm -1 ) H 3 A2 3 A1 3 A1 1 A 2 1 A1 1 A2 1 A1 3 H5 3 F 2 3 H 3 A1 3 A 1 1 A2 1 A1 1 A 2 1 A1 3 H5 3 F 2 3 H 3 A 1 3 A A2 A 3 1 H 5 1 A2 1 A1 3 F 2 2 E A1 1 A1 1 A A2 1 A1 3 H4 1 A2 1 A 1 3 H 4 1 A 2 1 A1 3 H4 Free Ion SCF-SF SCF-SO Free Ion SCF-SF SCF-SO Free Ion SCF-SF SCF-SO (C5Me4H)3UCl (C5H5)3UCl (C5H5)3UCH3 (C 5 Me 4 UCl, (C 5 H 5 ) 3 UCl, (C 5 H 5 ) 3 UCH 3 : Ordering of the low-energy electronic states from CAS(2,7)SCF calculations. CASPT2 gave too much symmetry breaking J. Autschbach Magnetic Properties 15

16 NOs from scalar relativistic calculations: f A1 f E f E f E f A1 f E (C 5 H 5 ) 3 UCH 3 f E f E f E f E f A1 f A (C 5 H 5 ) 3 UCl (C 5 H 5 ) 3 UCH 3 : ground state, approximately f 1 φ f 1 δ corresponding to the M L = ±5 components of 3 H term, similar to PuO (C 5 Me 4 UCl: 3 A 1 ground state corresponding to the M L = 0 components of 3 H term, involving f δ and f π orbitals with canceling orbital angular momenta J. Autschbach Magnetic Properties 16

17 At the SO level the situation is more complicated. SO coupling mixes 3 H 4 and 1 G 4 terms, and the CF mixes the components of 3 H 4. A model wavefunction for the magnetic doublets is in terms of J, M J components a which leads to g-factors (g J = 4/5) ψ ± = a 4, ±4 + b 4, 2 + c 4, ±1 g = 2g J (4a 2 2b 2 + c 2 ) and g = 0 As was done for PuO 2 2+, one can fit a CF model to the CAS state energies and determine a, b, c. An assignment of the electronic states of the Cl and CH 3 complex is given on the next slide a considering the CF induced mixing of M J component under C 3v symmetry, B. R. Judd, Proc. Roy. Soc. A 232 (1955), 458. See also Amberger et al., Inorg. Chim. Acta 141 (1988), 313 J. Autschbach Magnetic Properties 17

18 State E Weight of 2S+1 L J g Eigenvectors in the J = 4, M J basis g (C 5 Me 4 UCl A H 4, G E H 4, G ± ± E H 4, G ± ± A H 4, G E H 4, G ± ± A H 4, G (C 5 H 5 ) 3 UCH 3 A H 4, G E H 4, G ± ± E H 4, G ± ± A H 4, G E H 4, G ± ± A H 4, G Deviations for g between the model and the CAS calculations mainly due to lack of considering 1 G 4 in the model J. Autschbach Magnetic Properties 18

19 (C 5 Me 4 UCl susceptibility ΧMT cm 3 K mol T K a c b exp d (a) sum over all calculated states, optimized structure (b) optimized structure, using only the states deriving from 3 H 4 (c) same as (b) but with experimental structure (d) experimental structure, using only the lowest A 1 and the lowest E state to calculate the susceptibility Deviations from experiment likely due to a combination of underestimating the energies of higher excited states and overestimating the Zeeman matrix elements between ground and higher excited states, leading to a too high TIP susceptibility. Experimental data from Evans et al., JACS 134 (2012), 1243 J. Autschbach Magnetic Properties 19

20 (C 5 Me 4 UNO: NOs indicate significant multi-configurational character π 1 π 2 π1 SF SO π2 f δ f δ SF SO Effective bond order: SF: 1.31 SO: 1.18 SO coupling mixes bonding f π with non-bonding f δ f σ f φ f φ SF SO J. Autschbach Magnetic Properties 20

21 (C 5 Me 4 UNO susceptibility ΧMT cm 3 K mol exp c T K a b (a) sum over all calculated states, experimental structure (b) experimental structure, using only the lowest A 1 and the two lowest E states to calculate the susceptibility (c) experimental structure, using only the lowest A 1 and the lowest E state to calculate the susceptibility. The magnetic coupling between the GS and the second excited E state is mainly responsible for the magnitude of the TIP susceptibility. Other sources of error similar to (C 5 Me 4 UCl. Experimental data from Evans et al., JACS 134 (2012), 1243 J. Autschbach Magnetic Properties 21