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 AnalíticaUniversitat Jaume I

Spain&

CMDCM, Sao CarlosBrazil

Sao Carlos, Octubro 2011

- High-pressure phase transitions in crystalline systems

Applications in front-line research

- 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.

Adsorption processes on metal oxide surfaces.

Electronic and optical properties of piezoelectric and catalytic materials.

Cooperation

CTC Experimentalwork

Characterization of chemical species of difficult experimental detection

Prediction

Interpretation

High Pressure High Pressure EffectsEffects

Chemical Chemical ReactivityReactivity

Diffusion ProcessesDiffusion Processes

crystalline structurescrystalline structures-CompressibilityCompressibility(polyhedra, bonds)(polyhedra, bonds)- polymorphism- polymorphism

- reaction pathsreaction paths- activation barriersactivation barriers

Atoms (C, Li) in metals Atoms (C, Li) in metals and metal oxidesand metal oxides

- stationary pointsstationary points- reaction pathsreaction paths- crossing pointscrossing points

PESs of differentPESs of differentspin multiplicitiesspin multiplicities

• 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.

• Methodology: Density Functional Theory (DFT) Periodic Models Programs: CRYSTAL, VASP

• Characterization of phase transition mechanisms

Pressure effect

• MgAl2O4

METHODOLOGY

CRYSTAL ProgramDFT (B3LYP)8-511G*- Mg, Al8-411G* -O

iif

p

ppVNV

POLYHEDRA ANALYSIS

Optimización de la geometría

Curva ET-V

código GIBBS: Ecuación de Estado

V0, B0 , B0’

V

P-V

1 B

T

Pressure effect Physical Review B 66, 224114 (2002)

L. Gracia, A. Beltrán, J. Andrés, R. Franco and J. M. Recio

Occuped octahedra AlOAlO66 Occuped tetraheda MgOMgO

44

Unfilled octahedra OO66 Unfilled tetrahedra (O(O

44))11 y (O(O

44))22

MgO+Al2O3

P(GPa)

6050

G (

kJ/

mol

)

cubica

tipo-ferrita tipo-titanita

100

150

50

0

-50

0 40302010

MgO y -Al2O3

titanita ferrita

cúbica

ESTABILIDAD GLOBAL

distancia Mg2+-O2-

empaquetamiento

MgO y -Al2O3

IC (Mg2+) 4 6 8

ortorrómbicascúbica

COMPRESIBILIDADES LINEALES Al-O/Mg-O

• CdGa2Se4, CdCr2Se4

Cúbic Fd3m Cd2+ tetrahedraCr3+ octahedraTetragonal I4

POLYHEDRA ANALYSIS

CdCr2Se4CdGa2Se4B0 (GPa)

Exp

Teor

10148

92 (no magnetic)4480 (ferromagnetic)

Journal of Physics: Condensed Matter 16, 53-63 (2004).

A. Waskowska. L. Gerward, J. Staun Olsen, M. Feliz, R. Llusar, L. Gracia, M. Marqués and J. M. Recio

• Polymorphs of CO2

CO2-I Pa3 CO2-III Cmca

Programa VASPPAW (LDA) Análisis topológico (AIM)

METHODOLOGY

ESTRUCTURES

J. Physics: Condensed Matter 16, s1263 (2004)

L. Gracia, M. Marqués, A. Beltrán, A. Martín Pendás, and J. M. Recio

P212121I42dP42/mnmCO2-V CO2-V CO2-V

V0 (Å3)

B0 (GPa)

dC-O (Å)

36.87 36.97 37.05 22.95 22.28 17.44

16.6 15.0 16.9 133.6 142.7 327.2

1.168(2) 1.168(2) 1.265(2) 1.385(4) 1.385(4) 1.577(4)

1.679(2)

Pa3 Cmca(1) Cmca(2) P212121 I42d P42/mnm

Molecular to polymeric phase transition: CO2

Punto crítico firma sentido químico

máximo -3 nucleosPunto de silla -1 enlaces

- / 2

(r) = 0

TEORÍA DE ATOMOS EN MOLECULAS (AIM)

carácter y fuerza del enlace

polar C=O conCO2-I y CO2-III (1) / 2 > 0

covalente C-O conCO2-V / 2 <0

Isocontornos de la laplaciana de CO2-III (2):Configuration T

J. Phys. Chem. B 110, 23417 (2006)TiO2 polymorphs

(Å3)

AnataseBrookite

Rutile

G r

elat

ive

toru

tile

(Har

tree

)

-999.97

-999.965

-999.96

-999.955

-999.95

-999.945

-999.94

-999.935

26 28 30 32 34 36 38 40

E(H

artr

ee)

V

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14P(GPa)

(Å3)

AnataseBrookite

Rutile

G r

elat

ive

toru

tile

(Har

tree

)

-999.97

-999.965

-999.96

-999.955

-999.95

-999.945

-999.94

-999.935

26 28 30 32 34 36 38 40

E(H

artr

ee)

V

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14P(GPa)

ab

c

ab

c

b

c

a b

c

a ab

c

ab

c

anatase → brookite at 3.8 GParutile → brookite at 6.2 GPa.

A. Beltrán, L. Gracia and J. Andrés

Brookite Surfaces

stabilities (010) < (110) < (100)

the electronic structure: - direct band gap in all of

them- minimum gap energy:

(110)

(100)

Ti5c

Ti4c

Ti5c

[100][010]

[001]

[010][100]

[001]

[110][110]

[001]

(010)

(110)

Journal of Physical Chemistry B 111, 6479-6485 (2007). SnO2 polymorphs

Highest bulk moduli values of 293 (pyrite) and 322 GPa (fluorite) phases

A. Beltrán, L. Gracia and J. Andrés

SnO2 polymorphs

-35.53

-35.52

-35.51

-35.50

-35.49

-35.48

-35.47

-35.46

-35.45

26 28 30 32 34 36

V (Å3)

E (

Har

tree

)

PnnmPbcnPa3

Pnam

Pbca

Fm3m

P42/mnmP4

P42/mnmP4-35.53

-35.52

-35.51

-35.50

-35.49

-35.48

-35.47

-35.46

-35.45

26 28 30 32 34 36

V (Å3)

E (

Har

tree

)

PnnmPbcnPa3

Pnam

Pbca

Fm3m

P42/mnmP4

P42/mnmP4

P (GPa)

Ent

halp

yva

riatio

n

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40

P (GPa)

Ent

halp

yva

riatio

n

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40

a)

b)

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.

a) b) c)

ab

c

ab

c

a) CrVO4,-type b) zircon c) scheelite

TiSiO4

B3LYP calculations (CRYSTAL06 program)

Phys. Rev. B 80, 094105 (2009)

L. Gracia, A. Beltrán and D. Errandonea 45 50 55 60 65 70

V (Å3)

zircon

scheelite

CrVO4

-1439.82

-1439.81

-1439.0

-1439.79

-1439.78

-1439.77

-1439.76

-1439.75

-1439.74

E (

Har

tree

)

45 50 55 60 65 70

V (Å3)

zircon

scheelite

CrVO4

-1439.82

-1439.81

-1439.0

-1439.79

-1439.78

-1439.77

-1439.76

-1439.75

-1439.74

E (

Har

tree

)

H (

KJ/

mol

)

P (GPa)

-20

-10

0

10

20

0 1 2 3 4 5

H (

KJ/

mol

)

P (GPa)

-20

-10

0

10

20

0 1 2 3 4 5

enthalpy vs presión curve(CrVO4-type as reference)

Vt = [V2(Pt)-V1(Pt)] / V1(Pt) - 0.8 GPa → volume change of 11.8%. - 3.8 GPa → volume reduction of 8.5%.

In scheelite the low frequency mode with < 0 , T(Bg), suggest the possibility of a transition to the post-scheelite structure, fergusonite or wolframite

ThGeO4

zircon

scheelite

fergusonite

PBE calculations (VASP program)

Physical Review B 80, 094101 (2009)

D. Errandonea, R. S. Kumar, L. Gracia, A. Beltrán, S. N. Achary, and A. K. Tyagi

Computations: Zircon as the most stable to 2 GPa Scheelite P > 2 GPaFergusonite (post-scheelite) at 31 Gpa

XRD:Zircon Scheelite Fergusonite 11 GPa 26GPa

Decompressionfergusonite – scheelite: no histeresis zircon-scheelita: not reversible.

Bastide diagram for ABX4 structuresDashed lines: evolution of the ionic radii ratio with pressure

D. Errandonea, F.J. Manjón , Progress in Materials Science, 53, 711 (2008)

1.958

Anhydrite

1.955

Scheelite

Barite

ab

c

MonaziteCaSO4

E-V curve

MonazitaAnhidrita

BaritaScheelita

AgMnO4

StructureStructure anhydritanhydritee

monazitemonazite baritebarite scheelitescheelite AgMnOAgMnO44

BB00 (B (B00‘)‘) 67.7 (5.61)67.7 (5.61) 146.2 (4.28)146.2 (4.28) 64.8 (6.94)64.8 (6.94) 84.1 (5.86)84.1 (5.86) 144.9 (4.19)144.9 (4.19)BB00 ‡‡ 73.373.3 160.9160.9 77.177.1 102.6102.6 152.2152.2Exp BExp B00 (B(B00') ')

≈≈45 (-)45 (-) 149.4 (4.25)149.4 (4.25)

Exp BExp B00 ‡‡ -- 151.2 151.2 (±21.4)(±21.4)

H-P curve

anhydrite → monazite at Pt 5 GPa , reduction of volum -2% at 5GPa

monazite → barite (and/or scheelite) at 8 GPa

SiO2 polymorphs

stihovite

-cristobalite

-cristobalite is 0.1 eV more stable than stishovite at P=0

transition as low as 0.5 GPa with a large volume collapse

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 (-cristobalite, c) to 1 (stishovite, s)

sc

c

ac

ac

ac

ac

Experimental StudyDAC Diamond Anvil

Cell

Sincrotrones ALBA

Nuevos Beamlines dedicados a altas presiones (APS/ESRF/SPring8/Diamond/Soleil/ALBA)

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.

Ionización del aire producida por un haz de rayos X en un sincrotrón

Diffusion Procesess

Structure Cleveage of adsorbates Catalysis

Alteration

Impurities in metals

VASP ProgramPlane waves / GGA

METHODOLOGY

tet1

tet2

oct2tet1

Oct > Tet1 > Tet2Oct > Tet1 > Tet2 E(relative,eV):E(relative,eV): 0.000.00 >> 0.410.41 >>

0.520.52

oct1

• Stability of C in Pd(111)

Unit cell R30º

- subsurface interstices

L. Gracia, M. Calatayud, J. Andrés, C. Minot and M. Salmeron Physical Review B 71, 033407-1(-4) (2005).

oct

0.340.32 y0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50

tet1

tet2

ts1

ts2 -0.17

-0.13

1.9-0.75

2.8

oct

1.90

-0.53-0.15

0.41

0.52

0.86

0.74

0.0

E (eV)

-0.92

2.4

1.9

1.9

-0.74

-0.352.0

2.0

Horizontal Diffusion

tet1tet2

oct2

9

10

11

oct17

To bulk Diffusion

oct1

0.80.6

y

0.4

1 1.5 2 2.5 3 3.5

ts1ts2

E (eV)

1.93

1.80

tet1

tet2

0.0

0.63

1.14

0.27

oct2

z

0.63

tet1

tet2

oct2

oct17

• Li in WO3

WOLi

ab

cd

eO1

O2

WOLi

ab

cd

eO1

O2

Maximum energy barrier

Minimum energy pathdistortion d(O1-O2)

2.65 Å without Li - 4.25 Å

d(Li-O)= d(Li-W)=2.09 Å

4 O, 2 W

Cell 2x2Pm3m

Electrochemical and Solid State Letters. 8, J21 (2005)

L. Gracia, J. García Cañadas, G. García-Belmonte, A. Beltrán, J. Andrés and J. Bisquert

xTckE ln B

(●) experimental data of DJ.

(○) theoretical calculations

Energy barrier variation with x

Rect lines relation

with c=1.55 (simulation) and 1.25 (experiment).

Process more favorable for low doped systems

Intercalation and diffusion of Li: Li1+xTi2O4 (spinel )

Phys Rev. B 77, 085112 (2008) M. Anicete-Santos, L. Gracia, A. Beltrán and J. Andrés

Li diffusion processes from tetrahedral 8a sites to ctahedral 16c sites are thermodynamically favorable only in the compositions x > 0.250.

Intercalation and diffusion of Li: Li1+xTi2O4 (spinel )

Phys Rev. B 77, 085112 (2008) M. Anicete-Santos, L. Gracia, A. Beltrán and J. Andrés

Chemical Reactivity

R’ P’

TS’

R

TS

P

PCPC

R

TS

P

R’

P’

TS’

PC

TS

TS’

R

R’

P

P’

PC

Program GAUSSIANDFT (B3LYP)6-311G(2d,p)

•Vibrational Analysis

•IRC

METHODOLOGY

• MECP by Harvey et al.

Ei y q

Ei GradientsParallel to SEPsortogonal to CP

• IRCs by Yoshizawa et al. IRC minimum TS closer

Single-point energy calculation with the other spin electronic state

geometries

V(OH)2+ + C3H4

VO+ + CO(CH3)2 / CHOC2H5

C3H6+

VO2+

VO+ + CHOCH3C2H4+

V(OH)2+ + C2H4

VO+ + H2O + C2H4C2H6+

NbO3- + H2O + O2

MO(H2O)+ M(OH)2+ M=(V, Nb, Ta)

Reaction mechanisms Spin inversion processes crossing points Topological analysis of electron density

NbO5- + H2O

VO2+ + C2H4 VO+ + CHOCH3

G (kcal/mol)

-80

-60

-40

-20

0

20

40

s-TS2/3

s-TS1/2

s-3 s-2

s-VO2+ + s-C2H4

t-VO+ + s-CHOCH3

s-1

s-4s-TS1/4

s-TS4/5 s-5 s-TS5/3

s-3s-1

t-TS4/5 t-5 t-TS5/3

t-3

t-TS2/3

t-3

t-2

‡ ‡ ‡ ‡‡

t-VO+ + s-CHOCH3

Mecanismo 1

CP2

CP1

Mecanismo 2

J. Phys. Chem. A 107, 3107 (2003)L. Gracia, J. R. Sambrano, V. S. Safont, M. Calatayud, A, Beltrán and J. Andrés

t-VO++ s-H2O + s-C2H4

s-VO+ + s-H2O + s-C2H4

-70

-50

-30

-10

10

30

50

s-1

t-1

s-TS1/2

s-TS2/3

t-TS2/3

t-TS1/2

s-3

s-2

t-2

t-4

t-TS3/4

s-TS3/4

t-3

s-4

s-5

s-6

t-6

t-TS5

s-TS5

t-5

G (kcal/mol)

7.3

t-VO2+ + s-C2H6

s-VO2+ s-C2H6

CP

‡

+

‡‡‡

VO2+ + C2H6

VO+ + H2O + C2H4

V(OH)2+ + C2H4

s-V(OH)2+ + s-C2H4

t-V(OH)2+ + s-C2H4

Organometallics 23, 730 (2004). Gracia, J. Andrés, J. R. Sambrano, V. S. Safont, and A. Beltrán

s-propene +

S-VO2+

t-1

s-TS1Al

s-1Als-3

s-2

s-1

t-1Al

t-2/3

t-TS1P

t-TS1Ac

s-TS1Al

s-TS1P

s-TS1Ac

t-2Ac

s-2Al

t-2P

t-2Al

s-2Ac

s-2P

s-TS2Al

t-TS2Al

s-Propanal + s-VO+

s-Acetona + s-VO+

s-Aleno + s-V(OH)2+

s-Propanal + t-VO+

s-Acetona + t-VO+

s-Aleno + t-V(OH)2+

G (kcal/mol)

-70

-60

-50

-40

-30

-20

-10

0

10

20

‡ ‡

CP

VO2+ + C3H6

V(OH)2+ + C3H4

VO+ + CO(CH3)2

CHOC2H5

Organometallics 25, 1643 (2006)

L. Gracia, J. R. Sambrano, J. Andrés and A. Beltrán

t-NbO2(OH)2-

G (kcal/mol)

t-NbO3-

+ H2O

t-TS1

41.5

-59.0

43.9

35.7

t-NbO3(H2O)-

t-NbO4(OH)2--A

-22.4

-12.0

-23.1

-1.9-4.0

t-NbO5 (H2O)- s-NbO5

-

+ H2O

26.0

+O2

0.0

-12.4 -13.4

17.9

-19.2 -12.1 -23.0

1.3-2.3

-4.4

-80

-60

-40

-20

0

20

40

60

-3.7

s-NbO3-

+ H2O

s-NbO2(OH)2-

s-TS1 s-NbO3(H2O)-

t-TS2

t-NbO4(OH)2--B

t-TS3

+O2

‡

‡ ‡

+O2

•

CP1

CP2

NbO3- (1A1)+ H2O + O2 (3g) NbO5

- (1A’)+ H2O

J. Phys. Chem. A 108, 10850 (2004) R. Sambrano, L. Gracia, J. Andrés, S. Berski and A. Beltrán

E (

kca

l /mo

l)

E (

kca

l /mo

l)

-40

-20

0

20

40

60

-12.8

M1 M2

8.1

0.0

M5 + H2O+ CH2O

58.8

35.1

M4 + H2OTS1

22.5

TS2

39.3

33.0

M3

19.5

52.9MECP1

T

CSS

36.331.7

OSSLS

35.3

23.6

E (

kca

l /mo

l)

E (

kca

l /mo

l)

-40

-20

0

20

40

60

-12.8

M1 M2

8.1

0.0

M5 + H2O+ CH2O

58.8

35.1

M4 + H2OTS1

22.5

TS2

39.3

33.0

M3

19.5

52.9MECP1

T

CSS

36.331.7

OSSLS

35.3

23.6

Oxidation of Methanol to Formaldehydeon a Hydrated Vanadia Cluster

P. González-Navarrete, L. Gracia, M. Calatayud and J. AndrésJ Comput Chem 31, 2493-2501(2010).

The main effect of hydration can be associated to the destabilization of the methoxy-intermediates

five-fold V

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 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

-40

-20

0

20

40

60

TS3 M8 + H2O

-1.60.0

M5 + H2O+ CH2O

58.8

TS4 + H2O

7.04

51.0

-9.6

M6 M7

-12.2

67.9

48.1

35.1

M4 + H2O

MECP2

T

CSS

48.643.7

OSSLS

E (

kcal

/mo

l)

E (

kcal

/mo

l)

16.6

45.3

-40

-20

0

20

40

60

TS3 M8 + H2O

-1.60.0

M5 + H2O+ CH2O

58.8

TS4 + H2O

7.04

51.0

-9.6

M6 M7

-12.2

67.9

48.1

35.1

M4 + H2O

MECP2

T

CSS

48.643.7

OSSLS

E (

kcal

/mo

l)

E (

kcal

/mo

l)

16.6

45.3

Modelo HidratadoActividad investigadora: Resultados

tetrahedral V

-10

-5

0

5

10

15

20

25

30

35

on V-O-Ti

4.9

14.9

-7.5

Int4

on V-O-Ti

TS

on V=O

TS

V-O-Ti site leads to lower barrier, more stable dissociation product

Int1

Int4

on V=O

29.3

17.2

Int1

P. González-Navarrete, L. Gracia, M. Calatayud and J. Andrés J. Phys. Chem. C, Vol. 114, No. 13, 2010

The vanadia/titania catalystsThe vanadia/titania catalysts

-20,0

-15,0

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

25,0

30,0E

+Z

PE

(kca

l/mol

)

PATH1PATH2

+ Methanol

40.9

10.7

25.2

20.1

5.0

-7.0

18.2

15.4

25.1

19.5

-7.0

3.7

-17.2

23.7

15.4

19.5

Reactive complex

Int1

TS1a

Int2b

Int3b

Int2b

Int3b

Int1

Int4

Int4

TS2a

Comparison between both B3LYP/6-311G(2d,p) energy profiles. Path1 and Path2. a Broken-symmetry transition states and projected energies. bTriplet intermediates.

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Structural Stability of High-Pressure Polymorphs in In2O3 Nanocrystals: Evidence of Stress-Induced Transition?**

A. Gurlo, Angew. Chem. Int. Ed. 2010, 49, 2–5