1. VLab development team UNIVERSITY OF MINNESOTA Indiana University Florida State Louisiana State University Thermoelastic Properties within VLab

2. Method --- Density Functional Theory (Hohenberg and Kohn, 1964) --- LDA and GGA (Ceperley and Alder, 1985) (Perdue at al.,1996) --- Plane wave basis – pseudopotential (Troullier and Martins, 1991 von Bar and Car) --- Variable Cell Shape Molecular Dynamics (Wentzcovitch, 1991) --- Density Functional Perturbation Theory for phonons +QHA (Baroni et al., 1987) --- Quantum ESPRESSO package (DEMOCRITOS)

3. Thermodynamic Method VDoS and F(T,V) within the QHA N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS IMPORTANT: crystal structure and phonon frequencies depend on volume alone!!….

4. Typical Computational Experiment Damped dynamics (Wentzcovitch, 1991) P = 150 GPa (Wentzcovitch, Martins, and Price, PRL 1993)

5. Summation (integration) over the Brillouin Zone In general: 1)Compute and diagonalize the dynamical matrix at few ’s (CPU intensive procedure) 2)Extract “force constants” 3)Recompute dynamical matrices at several points using those force constants 4)Summation over tetrahedral volume elements is very accurate for DoSs Ex: square BZ is the “multiplicity” of a point determined by symmetry

6. Phonon dispersions in MgO Exp: Sangster et al. 1970 (Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000) - cubic 2 atoms/cell

7. Zero Point Motion Effect Volume (Å 3 ) F (Ry) MgO Static 300K Exp (Fei 1999) V (Å 3 ) 18.5 18.8 18.7 K (GPa) 169 159 160 K´ 4.18 4.30 4.15 K´´(GPa -1 ) -0.025 -0.030 ZP Karki, Wentzcovitch,de Gironcoli, Baroni, Science 1999

8. equilibrium structure  kl re-optimize Adiabatic thermoelastic constant tensor C ij S (T,P) 11x8x6=528 runs for MgO 11x6x16=1056 runs for MgSiO 3 -pv

9. cijcij (Wentzcovitch, Karki, Cococciono, de Gironcoli, Phys. Rev. Lett. 2004) 300 K 1000K 2000K 3000 K 4000 K ( Oganov et al,2001) C ij (P,T) MgSiO 3 -pv

10. Today Demo (real run) to fit the allocated time Regatta, Altix, and Macs at MSI Thermodynamic properties of MgO Parameter sampling 11 pressures, 4x4x4 q-grid (8 q in the IBZ) Plots of thermodynamic properties

11. MgSiO 3 -perovskite and MgO Exp.: [Ross & Hazen, 1989; Mao et al., 1991; Wang et al., 1994; Funamori et al., 1996; Chopelas, 1996; Gillet et al., 2000; Fiquet et al., 2000] 4.8 (256)