t 2g states Crystal Field Effects e g states

Crystal Field Effects in CTM als3ti4.rcn als4ti4a.rcg als3ti4.rcf als4ti4a.m14 rcn2 als3ti4 rcg2 als4ti4a MODIFY als3ti4.plo plo2 als3ti4 als3ti4.ps als4ti4a.rac rac2 als4ti4a als4ti4a.ora

als4ti4a.rcg SHELL SPIN INTER SHELL SPIN INTER P 6 S 0 P 5 D 1 Ti4+ 2p06 3d HR Ti4+ 2p05 3d HR Ti4+ 2p06 3d00 Ti4+ 2p05 3d ( 2P//R1// 3D) 1.000HR Change the first line in als4ti4a.rcf Crystal Field Effects in CTM

als4ti4a.rac Y % vertical 1 1 butler O3 to Oh endchain actor 0+ HAMILTONIAN ground PRINTEIG OPER HAMILTONIAN BRANCH 0+ > OPER SHELL2 BRANCH 4+ > actor 0+ HAMILTONIAN excite PRINTEIG OPER HAMILTONIAN BRANCH 0+ > OPER SHELL2 BRANCH 4+ > actor 1- plane transi PRINTTRANS oper MULTIPOLE branch 1- > RUN Always the same rac-file in Oh symmetry Crystal Field Effects in CTM

07 = 2.13 eV Crystal Field Effects in CTM

als4ti4a.ora TRANSFORMED MATRIX for TRIAD 2 ( ) (1*7) DIM :1:3:3 ACTOR PLANE ---- MATRIX ---- PRINTTRANS BRA/KET : : TRANSFORMATION FINISHED 7 lines with energy and intensity Crystal Field Effects in CTM

SO 3 O h (Butler)O h (Mulliken) S00A1A1 P11T1T1 D22 + ^1E+T 2 F3 ^0+ 1 +^1A 2 +T 1 +T 2 G ^1A 1 +E+T 1 +T 2 Crystal Field Effects

Ti IV ion in TiO 2 : 3d 0 -configuration: 1 S, j=0 2p 1 3d 9 -configuration: 2 P  2 D = 1,3 PDF j’=0,1,2,3,4 p-transition: 1 P  j=+1,0,-1 Write out all term symbols: 1 P 1 1 D 2 1 F 3 3 P 0 3 P 1 3 P 2 3 D 1 3 D 2 3 D 3 3 F 2 3 F 3 3 F p XAS of TiO 2 (atomic multiplets)

J in SO 3 Deg.Branchings  in O h Deg. 01A1A1 A1A T13T1 A2A  E, 4  T 2 T1T  A 2, 3  T 1, 3  T 2 T2T2 8 41A 1, E, T 1, T 2 E5  Crystal Field Effect on XAS goes to

Effect of 10Dq on XAS:3d 0

EXERCISE: 1.Try to reproduce this figure by calculating the crystal field multiplet spectrum of Ti4+ as a function of the crystal field strength. The parameter to change is the value of the line " BRANCH 4+ > ". 2.Set the crystal field values to negative numbers (this inverts the ordering of t 2g and e g states)

Comparison with Experiment

als4ti4a.rcg SHELL SPIN INTER P 6 S 0 P 5 D 1 Ti4+ 2p06 3d HR Ti4+ 2p05 3d HR Ti4+ 2p06 3d00 Ti4+ 2p05 3d ( 2P//R1// 3D) 1.000HR Crystal Field Effects in CTM

Turning multiplet effects off

J in SO 3 Deg.Branchings  in O h Deg. 01A1A1 A1A T13T1 A2A  E, 4  T 2 T1T  A 2, 3  T 1, 3  T 2 T2T2 8 41A 1, E, T 1, T 2 E5  Crystal Field Effect on XAS goes to

 in O h Deg.  in D 4h Deg. A1A1 2A1A1 A1A A2A2 3B1B1 A2A2 7 7 T1T1 7E+A 2 B1B T2T2 8E+B 2 B2B2 88 E5A 1 +B 1 E  Lower symmetry goes to

Lower symmetry and angular dep. Hasselstrom et al. PRB 62, (2000)

Partly filled 3d-shells

Crystal Field Effects: Tanabe-Sugano

A T E T A Generating TSD from the program als5ni2.ora file gives ground state energies Order states by energy: complicated due to LS 3d A T E T A A2 3T2 3T1 1E 1T2

Ni2+ 2p06 3d HR Ni2+ 2p06 3d HR Generating TSD from the program Als5ni2z.rcg file switches off LS 3d 3T2 = T1T2 = A2 + E + T1 + T2 A T E T A A2 3T2 3T1 1E 1A1 3T1 1T1 1A1 1T2 1E 1T2

Crystal Field Effects

Calculation of transition matrices Als5ni2.ora gives these matrices Reduce Slater integrals to 50% CALCULATIONS for ACTOR:PLANE TRANSI CALCULATING MATRIX for TRIAD 5 ( ) (4*7) MATRIX HAS 21 ZERO, 7 REAL and 0 COMPLEX ELEMENTS CALCULATING MATRIX for TRIAD 17 ( ) (4*2) MATRIX HAS 5 ZERO, 3 REAL and 0 COMPLEX ELEMENTS CALCULATING MATRIX for TRIAD 18 ( ) (4*7) MATRIX HAS 19 ZERO, 9 REAL and 0 COMPLEX ELEMENTS CALCULATING MATRIX for TRIAD 19 ( ) (4*5) MATRIX HAS 14 ZERO, 6 REAL and 0 COMPLEX ELEMENTS CALCULATING MATRIX for TRIAD 20 ( ^1- 0) (4*8) MATRIX HAS 21 ZERO, 11 REAL and 0 COMPLEX ELEMENTS

Als5ni2.ora gives these matrices Reduce Slater integrals to 50% TRANSFORMED MATRIX for TRIAD 42 ( ^ ) (6*7) DIM :3:3:3 ACTOR PLANE ---- MATRIX ---- PRINTTRANS BRA/KET : : : : : : : Calculation of transition matrices

als5ni2.plo Reduce Slater integrals to 50% postscript als5ni2t2.ps energy_range frame_title Ni 2pXAS lorentzian range lorentzian range gaussian 0.25 frame_title GROUND STATE ALL old_racah als5ni2.ora frame_title T2 to T1 spectrum fstate 1- frame_title T2 to E spectrum fstate 2- frame_title T2 to T2 spectrum fstate ^1- frame_title T2 to A2 spectrum fstate ^0- end Plotting the result

T2 A2T1 E Lowest energy of 4 different symmetries

Plotting the result No LS AtomLS Atom no LS Effect of spin-orbit coupling and crystal field

3d spin-orbit coupling

Effect of 10Dq on XAS:3d N

High-spin or Low-spin 10Dq > 3J (d 4 and d 5 ) 10Dq > 2J (d 6 and d 7 )

Conf. Ground State SO 3 HS Ground State in O h LS Ground State in O h 3d 01S01S0 1A11A1 - 3d 12 D 3/2 2T22T2 - 3d 23F23F2 3T13T1 - 3d 34 F 3/2 4A24A2 - 3d 45D05D0 5E5E 3T13T1 3d 56 S 5/2 6A16A1 2T22T2 3d 65D25D2 5T25T2 1A11A1 3d 74 F 9/2 4T14T1 2E2E 3d 83F43F4 3A23A2 - 3d 92 D 5/2 2E2E- High-spin or Low-spin

3d 5 high-spin: Fe 2 O 3

3d 5 low-spin: Fe III (tacn) 2

1.Copy als3ti4.rcn to exti4.rcn 2.Copy als1ni2.plo to exti4.plo 3.Copy als1ni2.rac to exti4.rac 4.Run RCN2 and modify the exti4.rcf file in order to do crystal field multiplet calculations. 5.Calculate a crystal field multiplet spectrum for a crystal field of 0.0 eV, 1.52 eV and 3.04 eV. 6.Modify the exti4.plo file to plot the 3 spectra. 7.Repeat the calculation for negative values 8.Copy exti4.rcn to exco3.rcn and modify the file from Ti 4+ to Co Calculate a crystal field multiplet spectrum for a crystal field of 0.0 eV, 1.52 eV and 3.04 eV. 10.What happens between 1.52 eV and 3.04 eV? Exercise: Crystal Field Effects on Co 3+