Transcript 2 - Quantum Chemistry Group

Ab initio simulation of magnetic and optical
properties of impurities and structural
instabilities of solids (I)
M. Moreno
Dpto. Ciencias de la Tierra y Física de la Materia
Condensada
UNIVERSIDAD DE CANTABRIA
SANTANDER (SPAIN)
TCCM School on Theoretical Solid State Chemistry. ZCAM May 2013
Importance of calculations in the study of solids (pure and doped)
Goals of calculations
• Reproduce experimental data
but especially
Total energy (eV)
• Understand the microscopic origin of properties
-159.8
(x2-y2)1
(3z2-r2)1
-159.9
EJT
-160
-160.1
B
-21.6 pm 0
30.3
pm
Qq
It is nice to know that computer understands the
problem but I would like to understand it too
(E.Wigner)
EXPERIMENTAL DATA
CALCULATIONS
THEORETICAL BACKGROUND
H=E 
Understanding: Is there enough experimental information?
Some relevant data are often not accessible
• Electronic density for different orbitals
• Small changes in electronic density pressure or distortions
• Equilibrium geometry  excited states
• Equilibrium geometry ground state of impurities in solids
•Interpretation of available experimental data requires calculations
•It avoids speculations!
Outline I
1. Introduction. Motivation: Role of impurities in crystalline solids
2. Impurities in insulators. Localization
3. What are the calculations useful for?
 Microscopic origin of phenomena
 Relation with phenomena of pure solids
4. Substitutional Transition Metal Impurities in insulators
 Description of states
 Study of Model Systems Geometry and optical properties
*keeping(I) and changing(II) the host lattice structure
5. The colour of gemstones containing Cr3+
1. Introduction
Impurities in crystalline materials
In crystalline compounds there are always point defects
• Foreign atoms  Impurities
• Intrinsic defects like vacancies
1. Introduction
PURE
DOPED
• Crystals are often grown at high temperatures
• Equilibrium Minimize G=U-TS+PV
• Doped phase  Entropy increase Free energy reduction
• Upon cooling impurities are trapped in a crystal
Properties may depend on the sample!
1. Introduction
RESISTIVITY OF TWO DIFFERENT SAMPLES OF POTASSIUM
V

I
(arbitrary
units)
5
I
4
3
II
2
1
0
10
20
T (K)
Mc Donald et al, Proc Roy.Soc A 202, 103(1950)
• Clear differences at low temperatures
• Due to the presence of impurities and other defects
• For increasing the current impurities are unwanted
1. Introduction
Are impurities always undesirable?
p-n junction needs doped silicon !
Si
B
P
Conduction band
_
+
_
+
_
+

Valence band
1. Introduction
Impurities in insulators
New properties  Applications  Devices
 Lasers
Al2O3: Ti3+, Ruby
 Scintillators
NaI: Tl+, LiBaF3:Ce3+
 Storage phosphors
BaFCl: Eu2+
 Radiation Dosimeters
Al2O3: C4+
 Gemstones
Emerald (Be3Al2Si6O18: Cr3+)
1. Introduction
Ionic conductivity of NaCl doped with small quantities of CdCl2

(arbitrary
units)
24
20
16
12
8
4
0
15
30
45
60
105 Mole Fraction
Ionic conductivity increases by the presence of small amounts of Cd2+ impurities!
2. Impurities in insulators. Localization
What are we going to deal with
• Systems Transition metal impurities in insulators ( Gap> 4eV)
•Main Goal: Understand the microscopic origin of new properties
•Tools  Theoretical calculations and analysis of data.
2. Impurities in insulators. Localization
Microscopic insight for doped lattices
 More difficult than for pure compounds
 Translational symmetry broken
 However many insulators are made of ions
Active electrons from the impurity are localised
Transition Metal Complex MX6
z
5
4
x
3
2
1
6
Solid State Physics problem  Study of a trapped molecule
y
2. Impurities in insulators. Localization
KZnF3: Mn2+
J.Chem.Phys 47,
692(1986)
MnF64- complex
MnF2
Stout J.Chem.Phys 31,
709(1959)
• Broad bands
• Bandwidths up to 0.5eV!
2. Impurities in insulators. Localization
Electron Paramagnetic Resonance
• Spectroscopy in the electronic ground state if S0
• Transitions among Zeeman sublevels when H0 
• Microwave absorption
• Direct observation of hyperfine interactions with close nuclei
M=+1/2
S=1/2
M=-1/2
H=0
H0
2. Impurities in insulators. Localization
Evidence of Localization
square-planar complex NiF43-
CaF2:Ni+ EPR spectrum
Studzinski et al. J.Phys C 17,5411 (1984)
Ni+: 3d9 ion
Bo || <100> T = 20 K
5 superhyperfine lines
F
Ni+
 I(F) =1/2  Total spin I=4(1/2)=2  2I+1=5 lines
 No interaction with further fluorine ions detected! 
2. Impurities in insulators. Localization
The concept of complex (A. Werner 1893)
z
A Solid State Physics problem
5
3
4
What are the properties of a molecule?
2
1
x
y
6
The colour of a transition group complex is dependent to
any large extent only on the ligands directly attached to the
central ion while solvents or the formation of solid salts
with different anions have only a very minute influence
C.K Jørgensen
Absorption Spectra and Chemical Bonding in Complexes (1962)
2. Impurities in insulators. Localization
Pictorial description
R
• Active electrons are confined in the complex
• Close ions to ligands lying outside the complex Chemical pressureR
• Few atoms clusters (100) reproduce the properties due to the
impurity.
3. What are the calculations useful for?
Substitutional Impurities
• Isotropic relaxation  Geometry is kept
• Example  KMgF :Mn
3
2+
• What is the metal-ligand distance, R?
• What is the origin of the colour?
• Can we understand the effects due to pressure?
J.Phys.: Condens. Matter 18 R315-R360(2006)
3. What are the calculations useful for?
Ruby under pressure
S. Duclos et al.
PRB 41, 5372(1990)
•The two broad absorption bands are very sensitive to pressure
•The sharp emission line is little affected by pressure
Why?
3. What are the calculations useful for?
Electronic structure  Equilibrium geometry
Structural Instabilities. Static Jahn-Teller effect
z
5
3
4
2
1
x
y
6
• d9 ions ( Cu2+, Ag2+) in cubic sites
• Local symmetry becomes tetragonal
• What is the magnitude of the distortion?
• Is the octahedron elongated or compressed? Why?
J.Phys.: Condens. Matter 18 R315-R360(2006)
3. What are the calculations useful for?
Structural Instabilities. Off-centre motion
SrCl2 :Mn2+(d 5) on-centre
SrCl2:Fe+ (d7) off-centre
• What is the origin of the distortion?
• What is the distance corresponding to the off centre displacement?
• Why it does not happen for a Mn2+ impurity?
3. What are the calculations useful for?
Structural Instabilities
BaF2:Mn2+
a2u mode
• Cube surrounding Mn2+ is distortedTd symmetry!
• But no distortion when BaF2 is changed by CaF2 or SrF2
• What is the origin if there is not a Jahn-Teller effect?
• Why at T>50K the system appears as cubic? Phase transition?
3. What are the calculations useful for?
More examples
Req
Cu2+
Rax
H
N
z
CuCl4(NH3)22- in NH4Cl Tetragonal
Cl-
CuCl4(H2O)22- in NH4Cl
Req
Cu2+
O
Rax
H
z
•The four equatorial Cl- are not equivalent !
• Orthorhombic symmetry when axial
NH3  H2O?
What is found in pure compounds containing CuCl4X22- units (X = NH3, H2O)?
• In CuCl2(NH3)2 the CuCl4(NH3)22- units have tetragonal symmetry
• In Rb2CuCl4(H2O)2 the CuCl4(H2O)22- units have orthorhombic symmetry
3. What are the calculations useful for?
Impurities in insulators  pure ionic materials
• Optical spectrum of KZnF3: Mn2+ and MnF2 are very similar
• The same situation holds comparing Al2O3: Cr3+ ( ruby) with Cr2O3
• Ferroelectricity in BaTiO3 involves an off centre motion!
• Perovskites like KMF3 (M:Mg,Zn,Ni) are cubic but KMnF3 is
tetragonal
3. What are the calculations useful for?
Structural Instabilities in pure solids
KMgF3  Cubic Perovskite
KMnF3  Tetragonal Perovskite
P.Garcia –Fernandez et al. J.Phys.Chem letters 1, 647 (2010)
4. Substitutional Transition Metal Impurities
Description
Free TM ions  Cr3+( 3d3) ; Mn2+( 3d5) ; Ni2+( 3d8) ; Cu2+( 3d9)
Fivefold degeneracy partially removed even in cubic symmetry
Octahedral Complex
z
eg (x2-y2; 3z2-r2)
5
10Dq
d
t2g (xy;xz,yz)
3
4
x
2
1
6
y
4. Substitutional Transition Metal Impurities
• Direct evidence of the cubic field splitting, 10Dq
• Absorption in the red region of Cu(H2O)62+ complexes blue colour
10Dq
Cu2+( 3d9)
eg (x2-y2; 3z2-r2)
10Dq
d
t2g (xy;xz,yz)
Units: 103 cm-1
Holmes et al. JCP 26,1686(1957)
What is the origin of the strong absorption for > 30.000cm-1?
4. Substitutional Transition Metal Impurities
Ground and excited states of octahedral Cr3+( 3d3) impurities
3z2-r2
x2-y2
10Dq
10Dq
10Dq
10Dq
xy
4A
3
2 (t2g )
2E (t 3)
2g
2E 4A
4T (t 2
2 2g
eg1)
xy
4T (t 2
1 2g
eg1)
2
Duclos et al. PRB 41, 5372(1990)
•2E 4A2 depends on <xz(1),yz(2) e2/r12 xz(2),yz(1)>
•4A2 4T2 is equal to 10Dq
•4A2 4T1 depends on 10Dq and on interelectronic repulsion
4. Substitutional Transition Metal Impurities
The Rough Crystal Field Model
Main Assumptions
 Ligands are taken only as point charges
 Properties depend on the d-electrons of the impurity
 d-electrons feel the electrostatic potential, VCF, coming from ligands
 In octahedral complexes VCF exhibits cubic symmetry
6e2 Z L 35Z L e2  4
3 4
4
4
VCF (r) 

 x  y  z  r   ..
5
R
4R 
5 
10Dq =5 ZLe2<r4>/3R5
4. Substitutional Transition Metal Impurities
Appraisal of 10Dq =5 ZLe2<r4>/3R5 from Crystal Field (CF) model
• <r4>3d = 4.26 au for Cr3+
• R = 2.39 Å for CrCl63• 10Dq (CF) = 830 cm-1
• 10Dq (Exper.) = 12800 cm-1
• CF gives 10Dq one order of magnitude smaller than the
experimental value
• 10Dq mainly reflects the chemical bonding inside a complex
z
5
4
x
3
1
6
2
y
4. Substitutional Transition Metal Impurities
Electronic levels for an isolated octahedral fluorine complex
eg()3z2-r2; x2-y2
10Dq
t2g()xy; xz; yz
3d (Cr3+)
t1g()
t1u(;)
z
t2u()
t2g()
5
4
x
3
1
6
2
y
2p (F)
t1u(;)
eg()
ag()
2s (F)
•Unpaired electrons in antibonding t2g() and eg() levels
• Allowed t1u(; )  eg() jumps: ChargeTransfer transitions
4. Substitutional Transition Metal Impurities
The Cu(H2O)62+ complex
10Dq
Units: 103 cm-1
What is the origin of the strong absorption for > 30.000cm-1 ?
• Due to allowed charge transfer transitions
•They cannot be understood within the crystal field model
•They reflect the chemical bonding in the complex
4. Substitutional Transition Metal Impurities
Model systems (I)
Impurities in cubic lattices with the same structure
• What is the metal–ligand distance for the ground state?
•How varies 10Dq and the optical spectra?
Example: Mn2+ in cubic fluoroperovskites
4. Substitutional Transition Metal Impurities
Model systems (I)
Determination of the Mn2+-F- distance, R
Whole series study through DFT calculations
R follows RH but R < RH
Host
lattice
KMgF3
KZnF3
RbCdF3
CsCaF3
RH(pm)
199
203
220
226
R (pm)
206
208
213
215
Ba2+
Li+
F-
K+
Mn2+-F- distance wants to be close to r(Mn2+) + r(F-) = 212 pm
Mg2+
4. Substitutional Transition Metal Impurities
Model systems (I)
Determination of the Mn2+-F- distance, R
Variation of
the Mn2+-F- distance in the series
RH  Distance in the pure lattice
R /RH = 0.30
J.Phys.: Condens.Matter 11, L525 (1999)
4. Substitutional Transition Metal Impurities
Model systems (I)
Analysis of optical spectra
Sharp line independent on 10Dq.
10Dq
KMgF3
It is at the same place along the series
10Dq variations along the series
only due to R changes!
RH=1.99Å
10Dq = KR-n
n = 4.7
CsCaF3
RH=2.26Å
J.Chem.Phys 47, 692 (1986)
4. Substitutional Transition Metal Impurities
Model systems (I)
Results from Theoretical calculations
R dependence of 10Dq
V. Luaña et al, J Chem.Phys 90, 6409(1989)
10Dq    KR-n
MnF64-in KZnF3
n=5.5
Reliable theoretical calculations reproduce the experimental behaviour
Calculated values of the exponent n  J.Phys.:Condens.Matter 4, 9481(1992)
4. Substitutional Transition Metal Impurities
Model systems (I)
Experimental Evidence of 10Dq  = KR-5  NiO under pressure
H.G.Drickamer, J.Chem.Phys 47,1880(1967)
The exponent cannot be understood through Crystal field Theory which gives
10Dq =5 ZLe2<r4>/3R5
4. Substitutional Transition Metal Impurities
Model systems (II)
Impurities in different host lattices
Impurities (Mn2+,Ni2+,Co2+) in the LiBaF3 inverted perovskite
LiBaF3
Mg2+
Li+
Ba2+
KMgF3
K+
F-
Fa
 In LiBaF3
Mn2+ enters Li+ site with remote charge compensation
Observed by Magnetic Resonance measurements
An octahedral MnF64- complex is also formed
Yosida et al, J.Phys.Soc.Japan 49, 127 (1980)
B. Henke et al, Phys. Stat. Solidi C 2, 380 (2005)
4. Substitutional Transition Metal Impurities
Model systems (II)
Excitation Spectra of KMgF3: Mn2+ and LiBaF3: Mn2+
2000 cm-1
1000 cm-1
10Dq
KMgF3: Mn2+
LiBaF3: Mn2+
400
500
600
 Remarkable differences!
 10Dq is 1000 cm-1 higher for LiBaF3: Mn2+
 Does it reflect a different Mn2+-F- distance?
 (nm)
4. Substitutional Transition Metal Impurities
Model systems (II)
Increase of the experimental 10Dq value from KMgF3:M2+ to LiBaF3:M2+
M
10Dq (cm-1)
LiBaF3:M2+
10Dq(cm-1)
KMgF3:M2+
Mn
9800
8400
Ni
8400
7800
Co
9360
8000
• Is it due to a different R value?
• Difficult to accept !
RH(Å)
LiBaF3
KMgF3
1.998
1.993
4. Substitutional Transition Metal Impurities
Model systems (II)
What at are the impurity-ligand distances for LiBaF3:M2+ from
calculations?
M
R(Å)
LiBaF3:M2+
R(Å)
KMgF3:M2+
Mn
2.06
2.06
Ni
2.04
2.02
Co
2.03
2.04
 R is essentially the same in both lattices
 What is the origin of the different 10Dq?
Phys.Rev B 75, 155101 (2007); 78, 075108 (2008)
Chem.Phys 362, 82 (2009)
4. Substitutional Transition Metal Impurities
Model systems (II)
10Dq values
 10Dq is bigger for MnF64- in LiBaF3 than in KMgF3
 However R is essentially the same for both systems
 LiBaF3 :Mn2+ does not fit into the pattern of normal perovskites
4. Substitutional Transition Metal Impurities
Model systems (II)
Effect of the rest of the lattice
•
•
•
Ions are charged
Long range Coulomb potential due to ions outside the complex
Do the electrons in the complex feel this internal electric field?
4. Substitutional Transition Metal Impurities
Model systems (II)
Calculated rest of the lattice potential, VR, upon electronic
levels of MnF64-complex in a cubic perovskite
Energy of one electron → (-e) VR
VR is very flat
J.Phys.: Condens.Matter 18 R315-R360(2006)
4. Substitutional Transition Metal Impurities
Is it so for every crystalline lattice?
4. Substitutional Transition Metal Impurities
Model systems (II)
Internal electric field on ligands in LiBaF3
•Main effects along metal-ligand directions: Raises the eg() level
<100>
eg*
BaLiF3
KMgF3
Mn2+
eg*
(10Dq)v+ R
(10Dq)v
F
t2g*
 No electric field on the central ion  Oh symmetry
 But active electrons spread over the complex. VR not flat!
Additional extrinsic contribution to 10Dq from VR
t2g*
4. Substitutional Transition Metal Impurities
Model systems (II)
What do cluster calculations say?
R
10Dq = [10Dq(R)]v + R
Phys.Rev 78, 075108(2008)
There is a
shift
 [10Dq(R)]v  R4.6  In vacuo
 R Shift  Extrinsic contribution
 Microscopic origin?
4. Substitutional Transition Metal Impurities
Model systems (II)
Differences in 10Dq in normal and inverted perovskites
+2
KMgF3
+1
+1
LiBaF3
•First shell +1
•First shell  +2
•Second shell  +2
•Second shell +1
Positive charges
Cube  (10Dq)>0
Octahedron   (10Dq)<0
+2
Phys.Rev 75, 155101 (2007)
KMgF3: First shell contribution ( +1 ions) cancelled from that from
second shell (+2 ions)
 LiBaF3: Positive first shell contribution ( +1 ions) dominates
5. The colour of gemstones containing Cr3+
Huge amount of work carried out on Cr3+ based gemstones
Ruby
Al2O3:Cr3+
Emerald
Be3Si6Al2O18:Cr3+
d2
d1
d2
d3
Al
Os
Si
Ol
Ol
Als
C3 symmetry
Al
All
d3
Os
d4
Os
Ol
Be
Al
d1
O
D3 symmetry
•Both host lattices are ionic
•In both cases Cr3+ replaces Al3+ and a CrO69- complex is formed
5. The colour of gemstones containing Cr3+
Experimental data
Ruby
Emerald
Relative Shift
10Dq (eV)
2.24
2.00
-11%
2E 4A (eV)
2
1.79
1.82
1.7%
R. G. Burns, Mineralogical applications of crystal field theory (Cambridge Univ. Press, Cambridge, 1993))
(T1; T2)
10Dq
2E 4A
Ruby
2
S. Duclos et al. PRB 41, 5372(1990)
• Why 10Dq and the colour are so different?
5. The colour of gemstones containing Cr3+
For explaining the colour shift if has often been assumed
Active electrons are localized in the CrO69- complex
 But the average Cr3+-O2- distance is 6 pm smaller in ruby than in emerald
L. Orgel , Nature 179, 1348 (1957)
d2
d1
d2
d3
Al
Os
All
Al
d3
Ol
Ol
Als
Os
Si
Os
Ol
d4
Be
Al
O
d1
5. The colour of gemstones containing Cr3+
Experimental data for pure host lattices
System
Symmetry
RH
(pm)
Be3Si6Al2O18
D3
190.6
Al2O3
C3
191.3
E. Gaudry, Ph. D. Thesis, Université Paris 6 (2004)
• RH = average Al3+ -O2- distance ( in pm) for the host lattice
• Both are nearly identical
• Can it be true that R(emerald)-R(ruby) = 6 pm ??
5. The colour of gemstones containing Cr3+
RH (Host) (Å)
MgO:Cr3+
Emerald
Ruby
2.11
1.906
1.913
Cr3+
Mg2+
10Dq (eV)
2E 4A
2 (eV)
2.00
1.78
2.00
1.82
2.24
1.79
O2-
• Is it true that 10 Dq only depends on the Cr3+ - O2- distance, R ?
• Is R different in ruby and emerald but the Al3+ - O2- distance is the same?
• Is R the same in MgO:Cr3+ and emerald although RH is very different?
5. The colour of gemstones containing Cr3+
Experimental and calculated Cr3+-O2- distances in ruby
Rs(Å)
Rl (Å)
R=(Rs+Rl)/2
EXAFS data (a)
1.92
2.01
1.97
Calculated ( b)
1.94
2.00
1.97
Calculated ( c)
1.92
1.99
1.96
a: Gaudry et al Phys. Rev. B 67, 094108 (2003) ;
b: Aramburu et al, Phys.Rev B 85, 245118 (2012)
c :S. Watanabe et al. Phys. Rev. B 79, 075109 (2009)
d1
d2
d3
Al
Os
All
Ol
Ol
Als
Os
Os
Ol
Al
5. The colour of gemstones containing Cr3+
Experimental and calculated Cr-X distances (in Å) for
emerald
EXAFS data (a)
Calculated (b)
Calculated (a)
1.970.005
1.968
1.99
Cr-Be
2.695
2.70
Cr-Si
3.306
3.31
Cr-O
a: Gaudry et al Phys. Rev. B 76, 094110 (2007) ;
b: Aramburu et al, Phys.Rev B 85, 245118 (2012)
d2
Al
d3
Si
d4
Be
O
d1
5. The colour of gemstones containing Cr3+
Additional Contribution to 10Dq from the internal field
ER(r)
Isolated complex
Addition of the internal field
eg*
eg*
(10Dq)v
t2g*
(10Dq)v+ R
t2g*
R Extrinsic contribution to 10Dq due to the internal field felt by the complex
5. The colour of gemstones containing Cr3+
eg
51.36
2.00 eV
t2g
49.36
-52.22
-52.48
-56.41
-56.36
-0.86
-5.36
1.95 eV
-7.31
2.26 eV
-3.12
Isolated CrO69-
+ ER ruby
+ ER emerald
• In ruby ER(r) produces a shift of  -52.2 eV on both eg and t2g levels
• However the decrease is a little higher (0.26 eV) for t2g than for eg
•This explains the red color of ruby
•By contrast ER(r) has no effect on emerald green
Aramburu et al, Phys.Rev B 85, 245118 (2012)
5. The colour of gemstones containing Cr3+
Electrostatic potential VR(r)ER(r)
MgO:Cr3+
-54
-54
-55
Cr3+
-eVR(r) (eV)
Mg2+
[111]
-56
-56
-57
[100]
-58
-58
-59
-60
-60
[110]
-61
-62
-62
O2-
-63
-64
-64
0
0
Cr3+-O2- distance =2.03 Å
eg
0.5
0.5
1
1.0
r (Å)
1.5
1.5
49.82
1.80 eV
• t2g decreases a bit more than eg  10Dq  !
t2g
48.02
-54.36
-54.57
• Mg2+ along <110> are the closest ions to the
complex
-4.54
2.01 eV
-6.55
{VR(r) - VR(0)} First order perturbation
Isolated CrO69-
+ (-e)VR(r)
2
2.0
3. The Isolated Complex is a True Molecule
Microscopic insight
eg*
R dependence of 10 Dq
(eg)
t2g*
(t2g)
d

Admixture of 3z2-r2; x2-y2 levels with 2p and 2s raises
Admixture of xy; xz; yz
10Dq


10 Dq   d   p   p2   p2 N 2   d   s  N 2 s2
p contribution
J.Phys.: Condens.Matter 18 R315-R360(2006)
s contribution
s
eg by (eg)
levels with 2p  raises t2g by (t2g)
=(eg )- (t2g )
p
p
3. The Isolated Complex is a True Molecule
Description of antibonding levels. Covalency
Admixture with 2p and 2s orbitals if ligands are F,O
2s
3d
2p

eg  N 3z 2  r 2   p  p  s  s
Octahedral complexes.
Sometimes covalency measured by 
Fribourg-Freiburg June 2009
fs 
 N s 
3

2
; f
N  


p
3
2
Species
(nLp)- (nLs)
Species
(nLp)- (nLs)
Li
1.85
F
22.9
Be
2.75
F-
24.3
C
4.5
Cl
15.4
N
10.3
Cl-
15.9
O
16.7
Br
14.6
S
12.0
Br-
14.9
Units: eV
3. The Isolated Complex is a True Molecule
Results from Theoretical calculations
R dependence of (Np)2  f 2p covalency
FeF63-
a
a
• f nearly independent on R
• All methods are coincident
Phys. Rev B 61, 6525 (2000)
Fribourg-Freiburg June 2009
3. The Isolated Complex is a True Molecule
Results from Theoretical calculations
R dependence of (Ns)2 fs 2s covalency
FeF63Main Conclusions
• f>> fs
• But
fs = AR-n(s)
• n(s)  7
•Strong R dependence !
Phys. Rev B 61, 6525 (2000)
Fribourg-Freiburg June 2009
4. Covalency and 10Dq: dependence on the metal-ligand distance
Analysis of covalent contributions to 10Dq from ab initio
calculations
10 Dq  10 Dq  p  10 Dq  s
10Dq  p   d   p   3 f  4 f 
10Dq  s  3  d   s  f s
Complex
(10Dq)s (103 cm-1)
(10Dq)p (103 cm-1)
CrF63-
12.4
3.8
CrBr63-
8.9
3.8
CrI63-
6.2
2.3
• 10Dq is determined mainly by the residual 3d – nLs hybridization
• The reduction of Racah parameters is controlled by the global
covalency  Ne2; Nt2
J.Phys.Chem A 115, 1423 (2011)
(a)
(b)
Equidensity contours of the difference density function, , for
a CrF63+ complex when the metal-ligand distance is: a) 1.75
Å, and b) 2.15 Å
3. Results. Color Shift and Polarization
-e VR(r)
(eV)
-40
-45
Diagonal Als-Cr-All
-50
d1
d2
-55
d3
Al
Os
All
Ol
Ol
Als
Os
Os
Ol
-60
C3 Axis
-65
-70
-75
-80
Al
-85
-90
-2
Cr
Als
1.5
-
-1
-0.5
0
All
0.5
1
1.5
2
Å
•VR(r) is asymmetric when r >1Å
•It tends to decrease the energy of t2g levels increase of 10Dq
3. Results. Internal Fields in Emerald
d2
-45
-45
d3
-eVR(r) (eV)
-50
d4
-55
-55
Al
d1
-60
Si
-65
-65
d4
d2
-70
-75
-75
-2
-2
Be
-1.5
-1
-1
-0.5
00
0.5
11
1.5
d3
O
22
r (Å)
• Smaller variations of VR(r) in emerald
•For some directions VR(r) - VR(0) >0 while for others it is negative
•Is there some compensation?
•What happens if only the nearest Be2+ are taken into account?
d1
3. Results. Internal Fields in Emerald
System
Isolated CrO69- unit
CrO69- + 3 Be2+
CrO69- + 3 Be2+ + 6 Si4+
CrO69- + all lattice charges
10Dq(eV)
2.00
2.20
1.93
1.95
d2
Al
d3
•VR(r) - VR(0) is determined by the first shells
Si
• Second shell cancels the effects of the first one
d4
Be
O
d1
• Somewhat similar to perovskite
5. Model Systems (II): Mn2+ in LiBaF3
Host lattices data
RH=a/2
KMgF3
LiBaF3
1.987Å
1.998Å
Cluster Calculations on Doped lattices
KMgF3: Mn2+
LiBaF3 : Mn2+
R ( 21átoms)
2.06 Å
2.06 Å
R ( 57átoms)
2.05 Å
2.04 Å
Phys.Rev 78, 075108(2008)
1. Introduction
Impurities in crystalline materials
•In crystalline compounds there are always foreign atoms  Impurities