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

t2g states

Crystal Field Effects

eg 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

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


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


0 7 = 2.13 eV


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


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

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)

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>

Effect of 10Dq on XAS:3d0

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)

Comparison with Experiment

Comparison with Experiment

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


Turning multiplet effects off

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>

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 >

Lower symmetry and angular dep.

Hasselstrom et al.Hasselstrom et al.PRB 62, 11192 (2000)PRB 62, 11192 (2000)

Partly filled 3d-shells

Crystal Field Effects: Tanabe-Sugano

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

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

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 ( 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

Als5ni2.ora gives these matrices


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

als5ni2.plo


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

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

3d spin-orbit coupling

Effect of 10Dq on XAS:3dN

High-spin or Low-spin

10Dq > 3J(d4 and d5)

10Dq > 2J(d6 and d7)

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

3d5 high-spin: Fe2O3

3d5 low-spin: FeIII(tacn)2

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+

Documents

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