2. t 2g states Crystal Field Effects e g states

3. 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

4. als4ti4a.rcg 10 1 0 00 4 4 1 1 SHELL00000000 SPIN00000000 INTER8 10 1 0 14 2 4 1 1 SHELL03000000 SPIN03000000 INTER8 0 80998080 8065.47800 0000000 1 2 1 12 1 10 00 9 00000000 0 8065.4790.00 1 P 6 S 0 P 5 D 1 Ti4+ 2p06 3d00 1 0.0000 0.0000 0.0000 0.0000 0.0000HR99999999 Ti4+ 2p05 3d01 6 464.8110 3.7762 0.0322 6.3023 4.6284HR99999999 2.6334 Ti4+ 2p06 3d00 Ti4+ 2p05 3d01 -0.26267( 2P//R1// 3D) 1.000HR 38-100 -99999999. Change the first line in als4ti4a.rcf Crystal Field Effects in CTM

5. als4ti4a.rac Y % vertical 1 1 butler O3 to Oh endchain actor 0+ HAMILTONIAN ground PRINTEIG OPER HAMILTONIAN BRANCH 0+ > 0 0+ 1.0 OPER SHELL2 BRANCH 4+ > 0 0+ 7.00 actor 0+ HAMILTONIAN excite PRINTEIG OPER HAMILTONIAN BRANCH 0+ > 0 0+ 1.0 OPER SHELL2 BRANCH 4+ > 0 0+ 7.00 actor 1- plane transi PRINTTRANS oper MULTIPOLE branch 1- > 0 1- 1.000 RUN Always the same rac-file in Oh symmetry Crystal Field Effects in CTM

6. 07 = 2.13 eV Crystal Field Effects in CTM

7. als4ti4a.ora TRANSFORMED MATRIX for TRIAD 2 ( 0+ 1- 1- 0) (1*7) DIM :1:3:3 ACTOR PLANE ---- MATRIX ---- PRINTTRANS BRA/KET : 461.1850 461.9710 463.0501 463.5387 465.4900 468.5141 470.9370 -------------------------------------------------------------------------------- 0.00000: 0.009445 0.015776 0.137714 0.021110 0.505803 0.346162 0.963990 TRANSFORMATION FINISHED 7 lines with energy and intensity Crystal Field Effects in CTM

8. SO 3 O h (Butler)O h (Mulliken) S00A1A1 P11T1T1 D22 + ^1E+T 2 F3 ^0+ 1 +^1A 2 +T 1 +T 2 G40 + 1 + 2 + ^1A 1 +E+T 1 +T 2 Crystal Field Effects

9. 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 4 1 3 4 3 1 2p XAS of TiO 2 (atomic multiplets)

10. J in SO 3 Deg.Branchings  in O h Deg. 01A1A1 A1A1 2 13 3T13T1 A2A2 3 24 4  E, 4  T 2 T1T1 7 33 3  A 2, 3  T 1, 3  T 2 T2T2 8 41A 1, E, T 1, T 2 E5  12 25 Crystal Field Effect on XAS goes to

11. Effect of 10Dq on XAS:3d 0

12. 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+ > 0 0+ 0.00 ". 2.Set the crystal field values to negative numbers (this inverts the ordering of t 2g and e g states)

13. Comparison with Experiment

15. als4ti4a.rcg 10 1 0 14 2 4 1 1 SHELL03000000 SPIN03000000 INTER8 0 80998080 8065.47800 0000000 1 2 1 12 1 10 00 9 00000000 0 8065.4790.00 1 P 6 S 0 P 5 D 1 Ti4+ 2p06 3d00 1 0.0000 0.0000 0.0000 0.0000 0.0000HR99999999 Ti4+ 2p05 3d01 6 464.8110 3.7762 0.0322 6.3023 4.6284HR99999999 2.6334 Ti4+ 2p06 3d00 Ti4+ 2p05 3d01 -0.26267( 2P//R1// 3D) 1.000HR 38-100 -99999999. 0 80998080 8065.47800 0000000 0 40994040 8065.47800 0000000 Crystal Field Effects in CTM

16. Turning multiplet effects off

17. J in SO 3 Deg.Branchings  in O h Deg. 01A1A1 A1A1 2 13 3T13T1 A2A2 3 24 4  E, 4  T 2 T1T1 7 33 3  A 2, 3  T 1, 3  T 2 T2T2 8 41A 1, E, T 1, T 2 E5  12 25 Crystal Field Effect on XAS goes to

18.  in O h Deg.  in D 4h Deg. A1A1 2A1A1 A1A1 2+57 A2A2 3B1B1 A2A2 7 7 T1T1 7E+A 2 B1B1 3+58 T2T2 8E+B 2 B2B2 88 E5A 1 +B 1 E7+8 15  25 45 Lower symmetry goes to

19. Lower symmetry and angular dep. Hasselstrom et al. PRB 62, 11192 (2000)

20. Partly filled 3d-shells

21. Crystal Field Effects: Tanabe-Sugano

22. A1 -0.801748 0.603819 0.943165 5.315486 T1 -1.472040 -0.734825 0.914685 1.097910 E -1.492799 -0.730041 -0.515086 0.855732 1.906725 T2 -2.572434 -1.420765 -0.629293 0.391811 0.886141 1.968931 A2 -1.400139 Generating TSD from the program als5ni2.ora file gives ground state energies Order states by energy: complicated due to LS 3d A1 -0.801748 0.603819 0.943165 5.315486 T1 -1.472040 -0.734825 0.914685 1.097910 E -1.492799 -0.730041 -0.515086 0.855732 1.906725 T2 -2.572434 -1.420765 -0.629293 0.391811 0.886141 1.968931 A2 -1.400139 3A2 3T2 3T1 1E 1T2

23. Ni2+ 2p06 3d08 4 0.0000 12.2341 7.5981 0.0832 0.0000HR99999999 Ni2+ 2p06 3d08 4 0.0000 12.2341 7.5981 0.0002 0.0000HR99999999 Generating TSD from the program Als5ni2z.rcg file switches off LS 3d 3T2 = T1T2 = A2 + E + T1 + T2 A1 -0.687617 0.599870 0.883427 5.306541 T1 -1.441638 -0.687618 0.883427 1.093059 E -1.441639 -0.687617 -0.630865 0.883427 1.901225 T2 -2.558384 -1.441639 -0.687618 0.422527 0.883427 1.964579 A2 -1.441639 3A2 3T2 3T1 1E 1A1 3T1 1T1 1A1 1T2 1E 1T2

24. Crystal Field Effects

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

26. Als5ni2.ora gives these matrices Reduce Slater integrals to 50% TRANSFORMED MATRIX for TRIAD 42 ( ^1+ 1- 1- 0) (6*7) DIM :3:3:3 ACTOR PLANE ---- MATRIX ---- PRINTTRANS BRA/KET : 852.903 854.301 855.088 855.312 856.419 871.640 873.099 -------------------------------------------------------------------------------- -2.57243: 0.084753 0.000524 0.073496 0.054465 0.000005 0.139178 0.005166 -1.42076: 0.010636 0.028672 0.181098 0.000208 0.040343 0.069081 0.074203 -0.62929: 0.013535 0.044253 0.100561 0.027063 0.059448 0.003079 0.088162 0.39181: 0.001357 0.004753 0.002328 0.047212 0.190545 0.031137 0.078262 0.88614: 0.012572 0.029788 0.082503 0.002168 0.033906 0.000366 0.140053 1.96893: 0.000184 0.001708 0.001732 0.012048 0.088378 0.022026 0.069046 Calculation of transition matrices

27. als5ni2.plo Reduce Slater integrals to 50% postscript als5ni2t2.ps energy_range 850 880 frame_title Ni 2pXAS lorentzian 0.2 999. range 0 860 lorentzian 0.4 999. range 860 999 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

28. T2 A2T1 E Lowest energy of 4 different symmetries

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

30. 3d spin-orbit coupling

32. Effect of 10Dq on XAS:3d N

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

34. 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

35. 3d 5 high-spin: Fe 2 O 3

36. 3d 5 low-spin: Fe III (tacn) 2

37. 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 3+. 9.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+