Transcript Diapositive 1

Chapter 1. Introduction, perspectives, and aims. On the science
of simulation and modelling. Modelling at bulk, meso, and nano
scale. (2 hours).
Chapter 2. Experimental Techniques in Nanotechnology. Theory
and Experiment: “Two faces of the same coin” (2 hours).
Chapter 3. Introduction to Methods of the Classic and Quantum
Mechanics.
Force
Fields,
Semiempirical,
Plane-Wave
pseudpotential calculations. (2 hours)
Chapter 4. Introduction to Methods and Techniques of Quantum
Chemistry, Ab initio methods, and Methods based on Density
Functional Theory (DFT). (4 hours)
Chapter 5. Visualization codes, algorithms and programs.
GAUSSIAN; CRYSTAL, and VASP. (6 hours)
.
Chapter 6. Calculation of physical and chemical properties of
nanomaterials. (2 hours).
Chapter 7. Calculation of optical properties. Photoluminescence.
(3 hours).
Chapter
8.
Modelization
of
the
growth
mechanism
of
nanomaterials. Surface Energy and Wullf architecture (3 hours)
Chapter
9. Heterostructures Modeling. Simple and complex
metal oxides. (2 hours)
Chapter 10. Modelization of chemical reaction at surfaces.
Heterogeneous catalysis. Towards an undertanding of the
Nanocatalysis. (4 hours)
Chapter 6. Calculation of physical and
chemical properties of nanomaterials
Juan Andrés
Departamento de Química-Física y Analítica
Universitat Jaume I
Spain
&
CMDCM, Sao Carlos
Brazil
Sao Carlos, Octubro 2011
Applications in front-line research
- High-pressure phase
crystalline systems
transitions
in
- Li Diffusion in Crystalline Systems
- Two State Reactivity and heterogeneous
catalysis
Computational and Theoretical Chemistry (CTC)
Solid State Chemistry
 Structrural properties of ceramic materials.
Substitution and doping processes.
 Electronic and optical properties of piezoelectric
and catalytic materials.
 Adsorption processes on metal oxide surfaces.
Cooperation
CTC
Experimental
work
 Prediction
 Interpretation
 Characterization of chemical species of
difficult experimental detection
High Pressure
Effects
crystalline structures
-Compressibility
(polyhedra, bonds)
- polymorphism
Chemical
Reactivity
Diffusion Processes
Atoms (C, Li) in metals
and metal oxides
- reaction paths
- activation barriers
PESs of different
spin multiplicities
- stationary points
- reaction paths
- crossing points
Pressure effect
• Methodology:
Density Functional Theory (DFT)
Periodic Models
Programs: CRYSTAL, VASP
• Properties :
- Geometry optimization, macroscopic parameters:
equations of state, B0 , e , n
- Electronic properties: r , DOS, band structure, dEg/dP
- Theoretical vibrational spectra (Raman , IR), vibrational modes
asignation, w, dw/dP.
• Characterization of phase transition mechanisms
L. Gracia, A. Beltrán, J. Andrés, R. Franco and J. M. Recio
Pressure effect
Physical Review B 66, 224114 (2002)
• MgAl2O4
METHODOLOGY
CRYSTAL Program
DFT (B3LYP)
8-511G*- Mg, Al
8-411G* -O
Optimización de la geometría
Curva ET-V
código GIBBS:
Ecuación de Estado
POLYHEDRA ANALYSIS
V0, B0 , B0’
V   N pV p
p
   f i i
B
 P 
 -V 

 V  T
1
Occuped octahedra AlO6
Unfilled octahedra O6
Occuped tetraheda MgO4
Unfilled tetrahedra (O4)1 y (O4)2
ESTABILIDAD GLOBAL
150
cúbica
100
titanita
50
G (kJ/mol)
MgO y a-Al2O3
MgO+a-Al2O3
ferrita
tipo-titanita
tipo-ferrita
0
cubica
-50
0
10
20
30
40
50
 distancia Mg2+-O2-
60
P(GPa)
 empaquetamiento
COMPRESIBILIDADES LINEALES Al-O/Mg-O
IC (Mg2+)
cúbica
MgO y a-Al2O3
4
6
ortorrómbicas
8
A. Waskowska. L. Gerward, J. Staun Olsen, M. Feliz, R. Llusar, L. Gracia, M. Marqués and J. M. Recio
Journal of Physics: Condensed Matter 16, 53-63 (2004).
• CdGa2Se4, CdCr2Se4
POLYHEDRA ANALYSIS
Cúbic Fd3m
Tetragonal I4
B0 (GPa) CdGa2Se4
Exp
48
Teor
44
CdCr2Se4
101
92 (no magnetic)
80 (ferromagnetic)
Cd2+ tetrahedra
Cr3+ octahedra
L. Gracia, M. Marqués, A. Beltrán, A. Martín Pendás, and J. M. Recio
J. Physics: Condensed Matter 16, s1263 (2004)
• Polymorphs of CO2
METHODOLOGY
Programa VASP
PAW (LDA)
Análisis topológico (AIM)
ESTRUCTURES
CO2-I Pa3
CO2-III Cmca
CO2-V P212121
CO2-V I42d
Pa3
Cmca(1)
Cmca(2)
P212121
CO2-V P42/mnm
I42d
36.97
37.05
22.95
22.28
V0 (Å3) 36.87
B0 (GPa) 16.6
15.0
16.9
133.6
142.7
dC-O (Å) 1.168(2) 1.168(2) 1.265(2) 1.385(4) 1.385(4)
P42/mnm
17.44
327.2
1.577(4)
1.679(2)
Molecular to polymeric phase transition: CO2
TEORÍA DE ATOMOS EN MOLECULAS (AIM)
Punto crítico
firma
máximo
Punto de silla
-3
-1
-  / 2 
nucleos
enlaces
(r) = 0
carácter y fuerza del enlace
CO2-I y CO2-III (1)
CO2-V
sentido químico
 / 2 > 0
polar C=O con
 / 2 <0
covalente C-O con
Isocontornos de la laplaciana de CO2-III (2):
Configuration T
A. Beltrán, L. Gracia and J. Andrés
TiO2 polymorphs
c
J. Phys. Chem. B 110, 23417 (2006)
c
c
b
b
a
a
a
b
-999.935
20
G relative to rutile (Hartree)
15
-999.94
E(Hartree)
-999.945
-999.95
10
5
0
anatase → brookite at 3.8 GPa
rutile → brookite at 6.2 GPa.
-5
-10
0
2
4
-999.955
6
8
P(GPa)
10
12
14
-999.96
Rutile
-999.965
Brookite
Anatase
-999.97
26
28
30
32
34
V (Å3)
36
38
40
Brookite Surfaces
(100)
Ti5c
[100]
[010]
stabilities
(010) < (110) < (100)
[001]
(010)
the electronic structure:
- direct band gap in all of
them
- minimum gap energy:
(110)
Ti4c
[010]
[100]
[001]
(110)
Ti5c
[110]
[110]
[001]
SnO2 polymorphs
A. Beltrán, L. Gracia and J. Andrés
Journal of Physical Chemistry B 111, 6479-6485 (2007).
Highest bulk moduli values of 293 (pyrite) and 322 GPa (fluorite) phases
a)
P42 /mnm
- 35.45
SnO2 polymorphs
- 35.46
The phase transition sequence is
consistent with an increase of
coordination number of the tin ions,
from 6 in the first three phases to
6+2 in the pyrite phase, 7 in the
ZrO2-type orthorhombic phase I, 8
in fluorite phase and 9 in cotunnite
orthorhombic phase II.
Pnam
- 35.48
- 35.49
Fm3m
- 35.50
Pbca
- 35.51
Pa3
Pbcn Pnnm
- 35.52
P42 /mnm
- 35.53
26
28
30
32
34
36
V (Å3)
b)
60
40
Enthalpy variation
E (Hartree)
- 35.47
20
0
0
5
10
15
20
-20
-40
P (GPa)
25
30
35
40
c
TiSiO4
b)
a)
b
c)
a
a) CrVO4,-type
b) zircon
c) scheelite
B3LYP calculations (CRYSTAL06 program)
-1439.74
H (KJ/mol)
-1439.75
E (Hartree)
enthalpy vs presión curve
(CrVO4-type as reference)
20
-1439.76
10
0
-10
-1439.77
-20
-1439.78
0
1
2
3
4
5
P (GPa)
-1439.79
Vt = [V2(Pt)-V1(Pt)] / V1(Pt)
- 0.8 GPa → volume change of 11.8%.
- 3.8 GPa → volume reduction of 8.5%.
-1439.0
scheelite
-1439.81
zircon
CrVO4
-1439.82
45
50
55
V (Å3)
60
65
70
L. Gracia, A. Beltrán and D. Errandonea
Phys. Rev. B 80, 094105 (2009)
In scheelite the low frequency mode with g < 0 , T(Bg), suggest the possibility of a
transition to the post-scheelite structure, fergusonite or wolframite
D. Errandonea, R. S. Kumar, L. Gracia, A. Beltrán, S. N. Achary, and A. K. Tyagi
Physical Review B 80, 094101 (2009)
ThGeO4
Volume (Å3)
-184
250
275
300
325
350
375
400
-185
-186
Energy (eV)
-187
-188
-189
-190
-191
-192
-193
fergusonite
scheelite
zircon
-194
PBE calculations (VASP program)
Computations:
Zircon as the most stable to 2 GPa
Scheelite
P > 2 GPa
Fergusonite (post-scheelite) at 31 Gpa
XRD:
Zircon
 Scheelite  Fergusonite
11 GPa
26GPa
Decompression
fergusonite – scheelite: no histeresis
zircon-scheelita: not reversible.
Bastide diagram for ABX4 structures
Dashed lines: evolution of the ionic radii ratio with pressure
D. Errandonea, F.J. Manjón , Progress in Materials Science, 53, 711 (2008)
CaSO4
Monazite
Anhydrite
c
a
b
Scheelite
Barite
1.955
1.958
H-P curve
E-V curve
60
50
-2753.07
40
-2753.09
30
H (kJ/mol)
E ( hartree)
-2753.05
-2753.11
-2753.13
20
10
0
AgMnO4
-2753.15
Scheelita
-10
Barita
Monazita
Anhidrita
-2753.17
-2753.19
55
60
65
70
75
80
85
-20
-30
90
0
1
2
3
V (Å3)
4
5
6
7
8
9 10 11 12 13 14 15
P (GPa)
Structure
anhydrite
monazite
barite
scheelite
AgMnO4
B0 (B0‘)
B0 ‡
67.7 (5.61)
73.3
146.2 (4.28)
160.9
64.8 (6.94)
77.1
84.1 (5.86)
102.6
144.9 (4.19)
152.2
≈45 (-)
-
149.4 (4.25)
151.2 (±21.4)
Exp B0 (B0')
Exp B0 ‡
anhydrite → monazite at Pt  5 GPa , reduction of volum -2% at 5GPa
monazite → barite (and/or scheelite) at 8 GPa
SiO2 polymorphs
a-cristobalite is 0.1 eV more stable than stishovite at P=0
transition as low as 0.5 GPa with a large volume collapse
a-cristobalite
stihovite
L. Gracia, J. Contreras-García, A. Beltrán and J. M. Recio High Press Res 29, 93-96 (2009).
SiO2 polymorphs
The atomic displacements connecting both polymorphs can be described under a
martensitic approach (collective and concerted movements of all the atoms) in
terms of a transition path of P41212 symmetry. The transition path is traced up
using a normalized coordinate: x, that evolves continuously from 0 (a-cristobalite,
c) to 1 (stishovite, s)
c c
  - 
a
a
   c  
c c
  - 
 a c  a  s
Experimental Study
DAC 
Diamond Anvil Cell
Sincrotrones
Electrones acelerados a una energía de 7 mil
millones de electron-volts (7 GeV).
Radiación sincrotrón: radiación
electromagnética producida por partículas
cargadas que se mueven a alta velocidad
(una fracción apreciable de la velocidad de
la luz) en un campo magnético.
ALBA
Nuevos Beamlines dedicados a altas presiones
(APS/ESRF/SPring8/Diamond/Soleil/ALBA)
Ionización del
aire producida
por un haz de
rayos X en un
sincrotrón
 Diffusion Procesess
METHODOLOGY
VASP Program
Plane waves / GGA
Impurities in metals
Alteration
 Structure
 Cleveage of adsorbates
 Catalysis
• Stability of C in Pd(111)
- subsurface interstices
tet1
oct1
tet1
Unit cell
2

3x2 3 R30º
tet2
oct2
Oct > Tet1 > Tet2
E(relative,eV): 0.00 > 0.41 > 0.52
L. Gracia, M. Calatayud, J. Andrés, C. Minot and M. Salmeron
Physical Review B 71, 033407-1(-4) (2005).
Horizontal Diffusion
-0.92
1.9
tet1
oct1
E (eV)
2.4
7
1.9
-0.74
ts2
1.9
-0.75
-0.17
oct2
-0.13
ts1
0.86
0.74
tet2
11
9
2.8
10
tet2 0.52
tet1 0.41
2.0
-0.53
2.0
-0.15
oct
1.90
0.0
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
oct
y
-0.35
To bulk Diffusion
oct1
E (eV)
7
ts1
ts2
1.93
tet1
1.80
tet1
1.14
tet2
0.63
0.63
0.27
0.0
oct2
oct1
0.4
0.6
y
0.8
1
1.5
tet2
2
2.5
3
z
3.5
oct2
L. Gracia, J. García Cañadas, G. García-Belmonte, A. Beltrán, J. Andrés and J. Bisquert
Electrochemical and Solid State Letters. 8, J21 (2005
• Li in WO3
W
O
Li
O1
c
a
Cell 2x2
Pm3m
d
e
b
O2
Minimum energy path
Maximum energy barrier
distortion d(O1-O2)
2.65 Å without Li - 4.25 Å
4 O, 2 W
d(Li-O)= d(Li-W)=2.09 Å
Energy barrier variation with x
(●) experimental data of DJ.
(○) theoretical calculations
Rect lines
relation E  ck BT lnx
with c=1.55 (simulation) and 1.25 (experiment).
Process more favorable
for low doped systems
Intercalation and diffusion of Li: Li1+xTi2O4 (spinel )
Li diffusion processes from tetrahedral 8a sites to ctahedral 16c sites are
thermodynamically favorable only in the compositions x > 0.250.
M. Anicete-Santos, L. Gracia, A. Beltrán and J. Andrés Phys Rev. B 77, 085112 (2008)
Intercalation and diffusion of Li: Li1+xTi2O4 (spinel )
M. Anicete-Santos, L. Gracia, A. Beltrán and J. Andrés Phys Rev. B 77, 085112 (2008)
 Chemical Reactivity
PC
R’
R
TS’
TS
TS
TS’
TS’
PC
P
PC
R’
R’
P’
TS
PC
P’
P
R
P
R
P’
METHODOLOGY
Program GAUSSIAN
DFT (B3LYP)
6-311G(2d,p)
• Vibrational Analysis
• IRC
• IRCs by Yoshizawa et al.
TS closer
IRC
minimum
geometries
• MECP by Harvey et al.
Ei y d Ei
Gradients
dq
Single-point energy calculation
with the other spin electronic state
ortogonal to CP
Parallel to SEPs
+
VO2+
+
C2H4
VO+ + CHOCH3
C2H6
VO+ + H2O + C2H4
V(OH)2+ + C2H4
V(OH)2+ + C3H4
VO+ + CO(CH3)2 /
CHOC2H5
+ C3H6
NbO3- + H2O + O2
MO(H2O)+
M(OH)2+
NbO5- + H2O
M=(V, Nb, Ta)
 Reaction mechanisms
 Spin inversion processes crossing points
 Topological analysis of electron density
L. Gracia, J. R. Sambrano, V. S. Safont, M. Calatayud, A, Beltrán and J. Andrés
J. Phys. Chem. A 107, 3107 (2003)
VO2+ + C2H4
VO+ + CHOCH3
 G (kcal/mol)
Mecanismo 1
Mecanismo 2
40
+
+
20
t-VO + s-CHOCH 3
t-VO + s-CHOCH 3
CP2
s-VO2 + + s-C2 H4
s-TS4/5
s-5
t-TS4/5
t-5
s-TS5/3
0
s-TS1/2
t-TS5/3
-20
CP1
s-TS2/3
s-3
t-2
s-TS1/4
-40
s-2
s-1
s-4
s-3
s-1
t-TS2/3
-60
t-3
t-3
‡
‡
-80
‡
‡
‡
VO+
VO2 + C2H6
+
50
+ H 2O +
. Gracia, J. Andrés, J. R. Sambrano, V. S. Safont, and A. Beltrán
C 2H 4
Organometallics 23, 730 (2004)
V(OH)2+ + C2H4
 G (kcal/mol)
s-TS5
t-VO2+ + s-C2H6
s-VO+ + s-H2O + s-C2H4
30
t-TS1/2
t-TS5
10
t-VO++ s-H2O + s-C2H4
t-1
7.3
s-VO2+ s-C2H6
s-TS1/2
s-5
t-TS2/3
s-V(OH)2+ + s-C2H4
s-TS3/4
s-6
-10
s-TS2/3
t-TS3/4
t-6
t-2
s-1
t-5
CP
-30
s-2
t-V(OH)2+ + s-C2H4
s-4
-50
s-3
t-4
‡
t-3
‡
-70
‡
‡
+
L. Gracia, J. R. Sambrano, J. Andrés and A. Beltrán
VO2+ + C3H6
V(OH)2+ + C3H4
Organometallics 25, 1643 (2006)
VO+ + CO(CH3)2
CHOC2H5
G (kcal/mol)
20
s-Propanal + s-VO+
s-TS1Ac
s-TS2Al
10
0
s-Acetona + s-VO+
s-propene
+
S-VO2+
s-TS1P
s-TS1Al
s-1
s-Aleno + s-V(OH)2+
t-TS2Al
t-TS1Ac
t-2/3
-10
t-1Al
-20
-30
-40
s-Propanal + t-VO+
CP
t-TS1P
s-Acetona + t-VO+
s-TS1Al
s-Aleno + t-V(OH)2+
t-1
s-2P
s-2
s-3
s-1Al
s-2Ac
t-2Al
-50
‡
t-2P
-60
s-2Al
-70
t-2Ac
‡
• NbO3- (1A1)+ H2O + O2 (3Sg)
NbO5- (1A’)+ H2O
 G (kcal/mol)
60
40
t-NbO3+
H2O
t-NbO3(H2O)-
t-TS1
43.9
41.5
35.7
20
0
t-NbO2(OH)2-
s-NbO3+
H2O
17.9
+O2
0.0
s-NbO3(H2
-20
-12.4
O)-
1.3
CP1
-1.9
t-TS3
-12.0
s-TS1
-19.2
-13.4
-22.4
t-NbO4(OH)2--A
+O2
26.0
CP2
-12.1
t-TS2
-2.3
-3.7
-4.0
t-NbO5 (H2O)-
-23.0
-23.1
t-NbO4(OH)2--B
-4.4
s-NbO5+
H2O
-40
+O2
-59.0
-60
‡
s-NbO2(OH)2-
‡
‡
-80
R. Sambrano, L. Gracia, J. Andrés, S. Berski and A. Beltrán J. Phys. Chem. A 108, 10850 (2004)
Oxidation of Methanol to Formaldehyde
on a Hydrated Vanadia Cluster
 E (kcal/mol)
60
T
CSS
OSS
LS
40
20
0
-20
22.5
35.3
52.9
MECP1
58.8
39.3
36.3
31.7
33.0
23.6
19.5
TS2
M3
35.1
8.1
0.0
-12.8
five-fold V
-40
M1
TS1
M2
M4 + H2O
M5 + H2O
+ CH2O
The main effect of hydration can be associated to the destabilization of the
methoxy-intermediates
P. González-Navarrete, L. Gracia, M. Calatayud and J. Andrés
J Comput Chem 31, 2493-2501(2010).
Two intermediates, a five-fold coordinate and a tetrahedral vanadium, have
been considered with C-H bond breaking barriers of 23.6 kcal/mol and 45.3
Actividad
investigadora:
Modelo
HidratadoResultados
kcal/mol
respectively.
The penta-coordinate species, although it is 11.5
kcal/mol less stable than the tetrahedral one, might be regarded as a
potential reactive intermediate
MECP2
T
67.9
tetrahedral V
60
CSS
OSS
LS
40
58.8
51.0
48.6
43.7
48.1
 E (kcal/mol)
35.1
45.3
20
7.04
0
16.6
0.0
-1.6
-9.6
-12.2
-20
-40
M6
TS3
M7
M8 + H2O
TS4 + H2O
M4 + H2O
M5 + H2O
+ CH2O
The vanadia/titania catalysts
TS
Int1
on V=O
35
29.3
30
25
on V-O-Ti
on V=O
17.2
20
14.9
15
TS
Int1
10
Int4
5
4.9
0
-5
on V-O-Ti
Int4
-7.5
-10
V-O-Ti site leads to lower barrier, more stable dissociation product
P. González-Navarrete, L. Gracia, M. Calatayud and J. Andrés J. Phys. Chem. C, Vol. 114, No. 13, 2010
Comparison between both B3LYP/6-311G(2d,p) energy profiles. Path1 and Path2.
a Broken-symmetry transition states and projected energies. bTriplet intermediates.
30,0
25,0
20,0
15,0
TS1a
25.1
TS2a
23.7
Int3b
19.5
Int3b
19.5
+ Methanol
18.2
Int2b
15.4
PATH2
Int2b
15.4
PATH1
E + ZPE (kcal/mol)
20.1
10,0
5,0
Int1
5.0
3.7
40.9
25.2
0,0
10.7
-5,0
-7.0
-7.0
-10,0
-15,0
-20,0
Int4
-17.2
Reactive complex
Int4
Int1
Read
Structural Stability of High-Pressure Polymorphs in In2O3 Nanocrystals: Evidence of StressInduced Transition?**
A. Gurlo, Angew. Chem. Int. Ed. 2010, 49, 2–5