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Transcript of t 2g states Crystal Field Effects e g states Crystal Field Effects in CTM als3ti4.rcn als4ti4a.rcg...
![Page 1: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/1.jpg)
t2g states
Crystal Field Effects
eg states
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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
![Page 3: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/3.jpg)
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 1P 6 S 0P 5 D 1Ti4+ 2p06 3d00 1 0.0000 0.0000 0.0000 0.0000 0.0000HR99999999Ti4+ 2p05 3d01 6 464.8110 3.7762 0.0322 6.3023 4.6284HR99999999 2.6334Ti4+ 2p06 3d00 Ti4+ 2p05 3d01 -0.26267( 2P//R1// 3D) 1.000HR 38-100 -99999999. -1
Change the first line in als4ti4a.rcf
Crystal Field Effects in CTM
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als4ti4a.racY % 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- 1.000RUN
Always the same rac-file in Oh symmetry
Crystal Field Effects in CTM
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0 7 = 2.13 eV
Crystal Field Effects in CTM
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als4ti4a.oraTRANSFORMED 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
![Page 7: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/7.jpg)
SO3 Oh (Butler) Oh (Mulliken)
S 0 0 A1
P 1 1 T1
D 2 2 + ^1 E+T2
F 3 ^0+ 1 +^1 A2+T1+T2
G 4 0 + 1 + 2 + ^1 A1+E+T1+T2
Crystal Field EffectsCrystal Field Effects
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TiIV ion in TiO2: 3d0-configuration: 1S, j=02p13d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4p-transition: 1P j=+1,0,-1
Write out all term symbols:1P1 1D2 1F3
3P0 3P1 3P2
3D1 3D2 3D3
3F2 3F3 3F4
1 3 4 3 1
2p XAS of TiO2 (atomic multiplets)
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J in SO3 Deg. Branchings in Oh Deg.
0 1 A1 A1 2
1 3 3T1 A2 3
2 4 4E, 4T2 T1 7
3 3 3A2, 3T1,3T2 T2 8
4 1 A1, E, T1, T2 E 5
12 25
Crystal Field Effect on XAS
<1S0|dipole|1P1> goes to <A1|T1|T1>
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Effect of 10Dq on XAS:3d0
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Effect of 10Dq on XAS:3d0
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 t2g and eg states)
![Page 12: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/12.jpg)
Comparison with Experiment
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Comparison with Experiment
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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 1P 6 S 0P 5 D 1Ti4+ 2p06 3d00 1 0.0000 0.0000 0.0000 0.0000 0.0000HR99999999Ti4+ 2p05 3d01 6 464.8110 3.7762 0.0322 6.3023 4.6284HR99999999 2.6334Ti4+ 2p06 3d00 Ti4+ 2p05 3d01 -0.26267( 2P//R1// 3D) 1.000HR 38-100 -99999999. -1
0 80998080 8065.47800 0000000 0 40994040 8065.47800 0000000
Crystal Field Effects in CTM
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Turning multiplet effects off
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J in SO3 Deg. Branchings in Oh Deg.
0 1 A1 A1 2
1 3 3T1 A2 3
2 4 4E, 4T2 T1 7
3 3 3A2, 3T1,3T2 T2 8
4 1 A1, E, T1, T2 E 5
12 25
Crystal Field Effect on XAS
<1S0|dipole|1P1> goes to <A1|T1|T1>
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in Oh Deg. in D4h Deg.
A1 2 A1 A1 2+5 7
A2 3 B1 A2 7 7T1 7 E+A2 B1 3+5 8
T2 8 E+B2 B2 8 8
E 5 A1+B1 E 7+8 15
25 45
Lower symmetry
<A1|T1|T1> goes to <A1|E+A2| E+A2 >
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Lower symmetry and angular dep.
Hasselstrom et al.Hasselstrom et al.PRB 62, 11192 (2000)PRB 62, 11192 (2000)
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Partly filled 3d-shells
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Crystal Field Effects: Tanabe-Sugano
![Page 21: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/21.jpg)
A1 -0.801748 0.603819 0.943165 5.315486T1 -1.472040 -0.734825 0.914685 1.097910E -1.492799 -0.730041 -0.515086 0.855732 1.906725T2 -2.572434 -1.420765 -0.629293 0.391811 0.886141 1.968931A2 -1.400139
Generating TSD from the program
als5ni2.ora file gives ground state energies
Order states by energy: complicated due to LS3d
A1 -0.801748 0.603819 0.943165 5.315486T1 -1.472040 -0.734825 0.914685 1.097910E -1.492799 -0.730041 -0.515086 0.855732 1.906725T2 -2.572434 -1.420765 -0.629293 0.391811 0.886141 1.968931A2 -1.400139 3A2 3T2 3T1 1E 1T2
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Ni2+ 2p06 3d08 4 0.0000 12.2341 7.5981 0.0832 0.0000HR99999999Ni2+ 2p06 3d08 4 0.0000 12.2341 7.5981 0.0002 0.0000HR99999999
Generating TSD from the program
Als5ni2z.rcg file switches off LS3d
3T2 = T1T2 = A2 + E + T1 + T2
A1 -0.687617 0.599870 0.883427 5.306541T1 -1.441638 -0.687618 0.883427 1.093059E -1.441639 -0.687617 -0.630865 0.883427 1.901225T2 -2.558384 -1.441639 -0.687618 0.422527 0.883427 1.964579A2 -1.441639 3A2 3T2 3T1 1E 1A1 3T1 1T1 1A1 1T2 1E 1T2
![Page 23: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/23.jpg)
Crystal Field Effects
![Page 24: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/24.jpg)
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
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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
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als5ni2.plo
Reduce Slater integrals to 50%
postscript als5ni2t2.psenergy_range 850 880frame_title Ni 2pXASlorentzian 0.2 999. range 0 860lorentzian 0.4 999. range 860 999gaussian 0.25frame_title GROUND STATE ALLold_racah als5ni2.oraframe_title T2 to T1spectrum fstate 1-frame_title T2 to Espectrum fstate 2-frame_title T2 to T2spectrum fstate ^1-frame_title T2 to A2spectrum fstate ^0-end
Plotting the result
![Page 27: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/27.jpg)
Plotting the result
T2
A2T1
E
Lowest energy of 4 different symmetries
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Plotting the result
No LS
AtomLS
Atom no LS
Effect of spin-orbit coupling and crystal field
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3d spin-orbit coupling
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3d spin-orbit coupling
![Page 31: 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.](https://reader035.fdocuments.us/reader035/viewer/2022062309/5697c0211a28abf838cd2895/html5/thumbnails/31.jpg)
Effect of 10Dq on XAS:3dN
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High-spin or Low-spin
10Dq > 3J(d4 and d5)
10Dq > 2J(d6 and d7)
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Conf. Ground State SO3
HS Ground State in Oh
LS Ground State in Oh
3d0 1S01A1 -
3d1 2D3/22T2 -
3d2 3F23T1 -
3d3 4F3/24A2 -
3d4 5D05E 3T1
3d5 6S5/26A1
2T2
3d6 5D25T2
1A1
3d7 4F9/24T1
2E
3d8 3F43A2 -
3d9 2D5/22E -
High-spin or Low-spin
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3d5 high-spin: Fe2O3
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3d5 low-spin: FeIII(tacn)2
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1. Copy als3ti4.rcn to exti4.rcn2. Copy als1ni2.plo to exti4.plo3. Copy als1ni2.rac to exti4.rac4. 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 values8. Copy exti4.rcn to exco3.rcn and modify the file from
Ti4+ to Co3+.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 Co3+