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Chapter 1. Introduction, perspectives, and aims

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1 Chapter 1. Introduction, perspectives, and aims
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)

2 . 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)

3 Chapter 6. Calculation of physical and chemical properties of nanomaterials
Lourdes Gracia y Juan Andrés Departamento de Química-Física y Analítica Universitat Jaume I Spain & CMDCM, Sao Carlos Brazil Sao Carlos, Novembro 2010

4 Applications in front-line research
- High-pressure phase transitions in crystalline systems - Li Diffusion in Crystalline Systems - Two State Reactivity and heterogeneous catalysis

5 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.

6 Experimental CTC work Cooperation Prediction Interpretation
Characterization of chemical species of difficult experimental detection

7 High Pressure Effects Chemical Reactivity Diffusion Processes
crystalline structures Compressibility (polyhedra, bonds) - polymorphism stationary points reaction paths crossing points PESs of different spin multiplicities Diffusion Processes reaction paths activation barriers Atoms (C, Li) in metals and metal oxides

8 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 - Theoric vibrational spectra (Raman , IR), vibrational modes asignation, w, dw/dP. Characterization of phase transition mechanisms

9 Optimización de la geometría
L. Gracia, A. Beltrán, J. Andrés, R. Franco and J. M. Recio Pressure effect Physical Review B 66, (2002) MgAl2O4 Optimización de la geometría Curva ET-V METHODOLOGY CRYSTAL Program DFT (B3LYP) 8-511G*- Mg, Al 8-411G* -O código GIBBS: Ecuación de Estado V0, B0 , B0’ POLYHEDRA ANALYSIS

10 Occuped octahedra AlO6 Occuped tetraheda MgO4 Unfilled octahedra O6 Unfilled tetrahedra (O4)1 y (O4)2

11 COMPRESIBILIDADES LINEALES Al-O/Mg-O
ESTABILIDAD GLOBAL MgO+a-Al2O3 P(GPa) 60 50 G (kJ/mol) cubica tipo-ferrita tipo-titanita 100 150 -50 40 30 20 10 MgO y -Al2O3 cúbica titanita ferrita  distancia Mg2+-O2-  empaquetamiento MgO y -Al2O3 IC (Mg2+) ortorrómbicas cúbica COMPRESIBILIDADES LINEALES Al-O/Mg-O

12 CdGa2Se4, CdCr2Se4 POLYHEDRA ANALYSIS B0 (GPa) Exp Teor 101 48
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, (2004). CdGa2Se4, CdCr2Se4 POLYHEDRA ANALYSIS Cd2+ tetrahedra Cr3+ octahedra Cúbic Fd3m Tetragonal I4 CdCr2Se4 CdGa2Se4 B0 (GPa) Exp Teor 101 48 92 (no magnetic) 44 80 (ferromagnetic)

13 Polymorphs of CO2 METHODOLOGY Programa VASP PAW (LDA)
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

14 Molecular to polymeric phase transition: CO2
CO2-V CO2-V P212121 CO2-V P42/mnm I42d V0 (Å3) B0 (GPa) dC-O (Å) 1.168(2) (2) (2) (4) (4) (4) 1.679(2) Pa3 Cmca(1) Cmca(2) P I42d P42/mnm Molecular to polymeric phase transition: CO2

15 TEORÍA DE ATOMOS EN MOLECULAS (AIM)
Punto crítico firma sentido químico máximo nucleos Punto de silla enlaces (r) = 0 -  / 2 carácter y fuerza del enlace polar C=O con CO2-I y CO2-III (1)  / 2 > 0 covalente C-O con CO2-V  / 2 <0 Isocontornos de la laplaciana de CO2-III (2): Configuration T

16 TiO2 polymorphs anatase → brookite at 3.8 GPa
A. Beltrán, L. Gracia and J. Andrés TiO2 polymorphs J. Phys. Chem. B 110, (2006) anatase → brookite at 3.8 GPa rutile → brookite at 6.2 GPa.

17 Brookite Surfaces stabilities (010) < (110) < (100)
Ti5c [100] [010] [001] stabilities (010) < (110) < (100) the electronic structure: - direct band gap in all of them - minimum gap energy: (110) (010) Ti4c [010] [100] [001] (110) Ti5c [110] [001]

18 A. Beltrán, L. Gracia and J. Andrés
SnO2 polymorphs Journal of Physical Chemistry B 111, (2007). Highest bulk moduli values of 293 (pyrite) and 322 GPa (fluorite) phases

19 SnO2 polymorphs 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.

20 TiSiO4 a) CrVO4,-type b) zircon c) scheelite
B3LYP calculations (CRYSTAL06 program) 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%. Phys. Rev. B 80, (2009) L. Gracia, A. Beltrán and D. Errandonea

21 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

22 D. Errandonea, R. S. Kumar, L. Gracia, A. Beltrán, S. N. Achary, and A
D. Errandonea, R. S. Kumar, L. Gracia, A. Beltrán, S. N. Achary, and A. K. Tyagi Physical Review B 80, (2009) ThGeO4 fergusonite scheelite zircon PBE calculations (VASP program) 22

23 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 GPa Decompression fergusonite – scheelite: no histeresis zircon-scheelita: not reversible.

24 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)

25 CaSO4 Monazite Anhydrite a b c Scheelite Barite 1.955 1.958

26 H-P curve E-V curve Monazita Anhidrita Barita Scheelita AgMnO4 Structure anhydrite monazite barite scheelite AgMnO4 B0 (B0‘) 67.7 (5.61) 146.2 (4.28) 64.8 (6.94) 84.1 (5.86) 144.9 (4.19) B0 ‡ 73.3 160.9 77.1 102.6 152.2 Exp B0 (B0') ≈45 (-) 149.4 (4.25) Exp B0 ‡ - 151.2 (±21.4) anhydrite → monazite at Pt  5 GPa , reduction of volum -2% at 5GPa monazite → barite (and/or scheelite) at 8 GPa

27 SiO2 polymorphs -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, (2009).

28 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)

29 Experimental Study DAC  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

30 Diffusion Procesess Impurities in metals Alteration Structure
VASP Program Plane waves / GGA METHODOLOGY Structure Cleveage of adsorbates Catalysis Alteration Impurities in metals

31 DE(relative,eV): 0.00 > 0.41 > 0.52
Stability of C in Pd(111) - subsurface interstices tet1 tet2 oct2 Oct > Tet1 > Tet2 DE(relative,eV): 0.00 > 0.41 > 0.52 oct1 Unit cell R30º L. Gracia, M. Calatayud, J. Andrés, C. Minot and M. Salmeron Physical Review B 71, (-4) (2005).

32 Horizontal Diffusion tet1 oct1 tet2 oct2 DE (eV) ts2 ts1 tet2 tet1 oct
0.34 0.32 y 0.36 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 1.90 -0.53 -0.15 0.41 0.52 0.86 0.74 0.0 DE (eV) -0.92 2.4 -0.74 -0.35 2.0 tet1 tet2 oct2 9 10 11 oct1 7

33 To bulk Diffusion DE (eV) z ts1 ts2 1.93 1.80 tet1 1.14 tet2 0.63 0.27
oct1 0.8 0.6 y 0.4 1 1.5 2 2.5 3 3.5 ts1 ts2 DE (eV) 1.93 1.80 tet1 tet2 0.0 0.63 1.14 0.27 oct2 z 7

34 Maximum energy barrier
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 Cell 2x2 Pm3m Maximum energy barrier Minimum energy path distortion d(O1-O2) 2.65 Å without Li Å d(Li-O)= d(Li-W)=2.09 Å 4 O, 2 W

35 Energy barrier variation with x
(●) experimental data of DJ. (○) theoretical calculations relation with c=1.55 (simulation) and 1.25 (experiment). Rect lines Process more favorable for low doped systems

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

37 Intercalation and diffusion of Li: Li1+xTi2O4 (spinel )
M. Anicete-Santos, L. Gracia, A. Beltrán and J. Andrés Phys Rev. B 77, (2008)

38 Chemical Reactivity METHODOLOGY d q Program GAUSSIAN DFT (B3LYP)
TS’ R TS P PC Program GAUSSIAN DFT (B3LYP) 6-311G(2d,p) Vibrational Analysis IRC METHODOLOGY IRCs by Yoshizawa et al. IRC minimum TS closer Single-point energy calculation with the other spin electronic state geometries MECP by Harvey et al. Ei y d q Ei Gradients Parallel to SEPs ortogonal to CP

39 Spin inversion processes crossing points
V(OH)2+ + C3H4 VO+ + CO(CH3)2 / CHOC2H5 C3H6 + VO2+ VO+ + CHOCH3 C2H4 V(OH)2+ + C2H4 VO+ + H2O + C2H4 C2H6 NbO3- + H2O + O2 NbO5- + H2O MO(H2O) M(OH)2+ M=(V, Nb, Ta) Reaction mechanisms Spin inversion processes crossing points Topological analysis of electron density

40 VO2+ + C2H4 VO+ + CHOCH3 Mecanismo 1 Mecanismo 2
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 D G (kcal/mol) -80 -60 -40 -20 20 40 s-TS2/3 s-TS1/2 s-3 s-2 s-VO 2 + + s-C H 4 t-VO + s-CHOCH 3 s-1 s-4 s-TS1/4 s-TS4/5 s-5 s-TS5/3 t-TS4/5 t-5 t-TS5/3 t-3 t-TS2/3 t-2 Mecanismo 1 CP2 CP1 Mecanismo 2

41 VO+ + H2O + C2H4 VO2+ + C2H6 V(OH)2+ + C2H4
. Gracia, J. Andrés, J. R. Sambrano, V. S. Safont, and A. Beltrán VO2+ + C2H6 VO+ + H2O + C2H4 V(OH)2+ + C2H4 Organometallics 23, 730 (2004) 50 D G (kcal/mol) t-VO2+ + s-C2H6 s-TS5 s-VO+ + s-H2O + s-C2H4 30 t-TS1/2 t-TS5 t-VO++ s-H2O + s-C2H4 10 t-1 s-VO2+ s-C2H6 7.3 s-TS1/2 s-5 t-TS2/3 s-TS3/4 s-V(OH)2+ + s-C2H4 s-6 -10 s-TS2/3 t-TS3/4 t-6 s-1 t-2 t-5 CP -30 t-V(OH)2+ + s-C2H4 s-2 s-4 -50 t-4 s-3 + t-3 -70

42 V(OH)2+ + C3H4 VO2+ + C3H6 VO+ + CO(CH3)2 CHOC2H5
L. Gracia, J. R. Sambrano, J. Andrés and A. Beltrán VO2+ + C3H6 V(OH)2+ + C3H4 VO+ + CO(CH3)2 CHOC2H5 Organometallics 25, 1643 (2006) s-propene + S-VO2+ t-1 s-TS1Al s-1Al s-3 s-2 s-1 t-1Al t-2/3 t-TS1P t-TS1Ac 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+ DG (kcal/mol) -70 -60 -50 -40 -30 -20 -10 10 20 CP

43 NbO3- (1A1)+ H2O + O2 (3Sg) NbO5- (1A’)+ H2O
t-NbO2(OH)2- G (kcal/mol) t-NbO3- + H2O t-TS1 41.5 -59.0 43.9 35.7 D t-NbO3(H2O)- t-NbO4(OH)2--A -22.4 -12.0 -23.1 -1.9 -4.0 t-NbO5 (H2O)- s-NbO5- 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 20 40 60 -3.7 s-NbO3- s-NbO2(OH)2- s-TS1 s-NbO3(H2O)- t-TS2 t-NbO4(OH)2--B t-TS3 CP2 CP1 R. Sambrano, L. Gracia, J. Andrés, S. Berski and A. Beltrán J. Phys. Chem. A 108, (2004)

44 Oxidation of Methanol to Formaldehyde on a Hydrated Vanadia Cluster
five-fold V 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, (2010).

45 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 Actividad investigadora: Resultados Modelo Hidratado tetrahedral V

46 The vanadia/titania catalysts
Int1 TS on V=O on V-O-Ti 4.9 14.9 -7.5 Int4 on V=O 29.3 17.2 Int1 on V-O-Ti TS Int4 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

47 Comparison between both B3LYP/6-311G(2d,p) energy profiles
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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