Predicting physical properties of crystalline solids

Transcription

1 redicting physical properties of crystalline solids CSC Spring School in Computational Chemistry Antti Karttunen Department of Chemistry Aalto University

2 Ab initio materials modelling Methods based on quantum mechanics Two major branches of methods Ab initio molecular orbital theory (MO) Density functional theory (DFT) No system-dependent parametrization required Only the universal physical constants and the unit cell coordinates of the system are required to predict the properties of the system Choosing the right level of theory for a chemical problem is a demanding task With the help of powerful computational resources, modern materials modelling techniques can be used to Assist in the interpretation and explanation of experimental results redict the existence and properties of new materials and molecules The predictive power of the modern materials modelling techniques enables computational materials design Most effective in close collaboration with experimental work 2

3 Level of theory The level of theory determines the reliability of the results: 1. How the electron-electron interactions are described (= method ) 2. How a single electron is described (= one electron basis set ) The computational resource requirements depend on The level of theory The size of the model system (number of atoms) The type of the model system (molecular or periodic in 1D/2D/3D) Here the focus is on calculations based on Density Functional Theory (DFT) Currently the most practical computational approach for solids Typically atoms in the unit cell e - e - Nucleus 3

4 Models: Three states of matter Gas Solid Liquid Going from left to right: Accurate, non-parametrized molecular and materials modelling research generally becomes more difficult Reliable interpretation of the experiments also often becomes somewhat more difficult Direct comparison between quantum chemical calculations and experiment becomes more difficult The main challenge for liquid systems: finite temperature (T > 0) 4

5 Solid state models Bulk (3D), surfaces (2D), polymers (1D) eriodic models are defined using a unit cell (lattice vectors + atomic positions) Amorphous solids are much more challenging and comparable to liquids in difficulty! Diamond (3D) Graphene (2D) Graphite (3D) Carbon nanotube (1D) Carbon fullerene (0D) 5

6 How to find structural data? ICSD (Inorganic Crystal Structure Database) Crystal structures of inorganic compounds Currently over structures ( ), over added every year Available at (if your university has a license) CSD (Cambridge Structural Database) Crystal structure data for organic and organometallic compounds Over structures in the 2015 release (> new structures / year) Mostly molecular crystals Available at (if your university has a license) Search the literature, the papers often include Unit cell parameters Atomic positions Or build it from scratch! 6

7 Builders / Visualization Accelrys Materials Studio (available via VESTA ( Mainly for visualization: VMD / Jmol 7

8 Introduction to CRYSTAL A general-purpose program for studying crystalline solids Development began already in the late 1970s, first public release in 1988 Symmetry handling was implemented extremely well very early to speed up the calculations Both ab initio wavefunction and DFT methods implemented First program to enable hybrid DFT calculations on solids (1998) Based on local Gaussian-type basis sets Electron-correlated ab initio calculations on solids are also possible: CRYSCOR Local-M2, feasible for systems with 100+ atoms in the unit cell

9 Models in CRYSTAL eriodic 3D/2D/1D/0D systems with full symmetry treatment 3D crystalline solids (230 space groups) 2D films and surfaces (80 layer groups) 1D polymers and nanotubes (75 rod groups + helical symmetries) 0D molecules (32 crystallographic point groups) Geometry manipulation and transformation with automatic symmetry handling 3D to n3d - supercell creation 3D to 2D - slab parallel to a selected crystalline face (hkl) 3D to 0D - cluster from a perfect crystal (H-saturated) 3D to 0D - extraction of molecules from a molecular crystal 2D to 1D - building nanotubes from a single-layer slab model 2D to 0D - building fullerene-like structures from a single-layer slab model 3D to 1D, 0D - building nanorods and nanoparticles from a perfect crystal 2D to 0D - construction of Wulff's polyhedron from surface energies Insertion, displacement, substitution, deletion of atoms

10 GTOs and lane waves Local Gaussian-type orbitals (GTO) eriodic (augmented) plane-waves Traditional choice in quantum chemistry articularly suitable for molecular calculations Relative performance: 0D > 1D > 2D > 3D Good for wavefunction methods and hybrid DFT Typical programs: CRYSTAL, Gaussian Traditional choice in material physics articularly suitable for 3D periodic calculations Relative performance: 3D > 2D > 1D > 0D Less suitable for wavefunction methods Typical programs: VAS, Quantum Espresso, ABINIT 10

11 Comparison of CRYSTAL and VAS CRYSTAL: BE0/SV; VAS: HSE/AW ( BE0/AW) 1 Lattice constant a Bulk modulus B 0 CRYSTAL (Å) VAS (Å) Exp. (Å) C (-0.1%) (-0.5%) Si (+0.5%) (+0.1%) Ge (+1.0%) (+0.4%) Sn (+1.1%) (+1.1%) CRYSTAL (Ga) VAS (Ga) Exp. (Ga) C 470 (+6.0%) 467 (+5.4%) 442 Si 102 ( %) 99 ( %) Ge 71.8 ( %) 71 ( %) Sn N/A 1 Hummer K.; Harl, J.; Kresse, G. hys. Rev B 2009, 80,

12 hysical properties in CRYSTAL14 1 R. Dovesi, et al. Int. J. Quant. Chem. 2014, 114,

13 Molecular orbitals in a benzene molecule (HOMOs) Orbital/band energies For solids, we take periodicity into account by plotting E(k), where k is a wave vector Energy bands in bulk silicon (band-projected electron density, isovalue 0.02 a.u.) 13

14 Band structure and band gap Empty bands Occupied bands NaCl: insulator, large energy gap between occupied and nonoccupied bands Silicon: semiconductor, energy gap between occupied and nonoccupied bands Copper: metal, partially filled bands 14

15 IR and Raman spectra Both IR and Raman intensities are available Together with an analysis of the normal modes (e.g. Jmol), allows for very detailed interpretation Experimental and predicted Raman spectrum of Ba(BrF 4 ) 2 Ivlev, S.; Sobolev, V.; Hoelzel, M.; Karttunen, A. J., Müller, T.; Gerin, I.; Ostvald, R.; Kraus, F. Eur. J. Inorg. Chem., 2014, 6261.

16 Elastic properties (1) Bulk modulus: The resistance to uniform compression 500 Bulk modulus (Ga) α (dia) I II III IV V VI VII VIII H II-4H I-100 II-100 IV-100 Carbon Silicon Germanium Tin Karttunen, A. J.; Härkönen V. J.; Linnolahti, M.; akkanen, T. A. J. hys. Chem. C 2011, 115,

17 Elastic properties (2) Young s modulus: A measure of the stiffness of a material A F L L 17

18 Thermal expansion Quasiharmonic approximation (utilize frequency / volume dependence) Calculations carried out with Quantum Espresso Härkönen, V. J.; Karttunen, A. J. hys. Rev. B 2014, 89,

19 Thermal conductivity Second and third-order force constants determined with Quantum Espresso Boltzmann Transport Equation solved iteratively with ShengBTE 1. Giannozzi et al. J. hys. 2009, 21, W. Li, J. Carrete, N. A. Katcho, N. Mingo, Comp. hys. Commun. 2014, 185,

20 ZnO lattice thermal conductivity (κ l ) κ l (W/(m K) κ (exp. film - Tynell) κ (exp. Bulk - Slack) κ_xx (DFT-BE) κ_zz (DFT-BE) T (K) 1 T. Tynell et al., J. Mater. Chem. A 2014, 2, 12150; 2 G. A. Slack, hys. Rev. B 1972, 6, A. J. Karttunen, T. Tynell, M. Karppinen, manuscript 20

21 Thermoelectricity 21

22 Thermoelectricity (2) Band structure from CRYSTAL Band structure dependent thermoelectric quantities from Boltzmann transport equation (BoltzTra, Comput. hys. Commun. 2006, 175, 67) I 12 [As 12 Ge 56 ] Karttunen, A. J.; Fässler, T. F. ChemhysChem 2013, 14,

23 How to start? A CRYSTAL14 evaluation copy is available free of charge for Linux & Windows operating systems. All functionalities of the full version are active, the number of atoms in the primitive cell is just restricted to CASTE + Materials Studio (via CSC) Quantum Espresso (large user base, active development) GAW (available at CSC) C2K (available at CSC, great for ab initio molecular dynamics) Gaussian09 Robust, but very slow if you try to run it with the defaults. lease read at least 23