1. Quantum Monte Carlo Simulation of Vibrational Frequency Shifts in Pure and Doped Solid para-Hydrogen Lecheng Wang, Robert J. Le Roy and Pierre- Nicholas Roy Chemistry Department, University of Waterloo Waterloo, Ontario, Canada Page1

2. Open Questions for Pure Solid pH 2 H. P. Gush and co-workers, Can. J. Phys 176, 38 (1960), Isaas F. Silverra, Rev. Mod. Phys. 393, 52(1980) T. Oka, Annu. Rev. Phys. Chem. 299, 44(1993) G. Tejeda and co-workers, Phys. Rev. Lett. 223401, 92(2004) Theoretical insights of vibrational frequency shift of pH 2 in solid pH 2 are still unclear. observed in pH 2 clusters and solid Page2 schematic diagram of

3. H. Li and co-workers, J. Chem. Phys. 139, 164315 (2013) M. E. Fajardo, J. Phys. Chem. A 117, 13504 (2013) Open Questions for CO Doped Solid pH 2 Theoretical investigation of of CO in doped solid pH2 is still left undetermined. of CO in pH 2 clusters of CO isotopes in pH 2 solid: fcc structure: -2.961 cm -1 hcp structure: -2.974 cm -1 Page3 fcc crystalhcp crystal A B A C A B B A A

4. Part I - Pure Solid pH 2 -Methodologies Algorithms:  Path Integral Monte-Carlo (PIMC)  Periodic Boundary Conditions  First order perturbation theory Simulate at temperature: T = 4.2 K Isaas F. Silverra, Rev. Mod. Phys. 393, 52, (1980) N. Blinov and co-workers, J. Phys. Chem. A, 120, 5916, (2004) M. Boninsegni and co-workers, Phys. Rev. Lett. 96, 070601, (2006) R. J. Hinde, J. Chem. Phys., 128, 154308, (2008) H. Li and co-workers, J. Chem. Phys.,130, 144305, (2009) N. Faruk and co-workers, (under revision) pH 2 ‐ pH 2 potential: recently obtained 1D potential averaged from Hinde’s 6D H 2 ‐ H 2 potential. Page4

5. Part I - Pure Solid pH 2 -Methodologies Fittings of numbers of beads P: N. Blinov and co-workers, J. Phys. Chem. A, 120, 5916, (2004) M. Boninsegni and co-workers, Phys. Rev. Lett. 96, 070601, (2006) Our choice: P = 64 compared with: extrapolated values ( ) Energy discrepancy: 6.4% discrepancy: 1.5% Extrapolation of E obtained with 144 atoms in hcp cell Page5

6. Part I - Pure Solid pH 2 - Structures R: distance between nearest neighbors in solid. In periodic boundary conditions: R is determined by the size of the cell. Isaas F. Silverra, Rev. Mod. Phys. 393, 52(1980) E varies as a function of R (144 pH 2 in hcp cell) Observed R of hcp pH 2 solid: 3.789 Å Calculated R of both hcp and fcc pH 2 solid: 3.780 Å Page6

7. Part I - Pure Solid pH 2 - N: Number of atoms inside one cell in periodic boundary conditions. H. P. Gush and co-workers, Can. J. Phys 176, 38 (1960), varies linearly with 1/N: PIMC (left) and classical MC (right)(fcc) First-order perturbation theory Page7

8. Part I - Pure Solid pH 2 - and Densities H. P. Gush and co-workers, Can. J. Phys 176, 38 (1960) Isaas F. Silverra, Rev. Mod. Phys. 393, 52(1980) Energy (left) and (right) varies as a function of density (hcp) Observed densities for 0 pressure hcp crystal: 0.026 Å -3 Observed for 0 pressure hcp crystal: -11.38 cm -1 Calculated with 144 atoms in the cell Page8

9. Part I - Pure Solid pH 2 - Summaries H. P. Gush and co-workers, Can. J. Phys 176, 38 (1960) Isaas F. Silverra, Rev. Mod. Phys. 393, 52(1980) hcp experimental hcp calculated fcc calculated (Å) 3.789 3.780 with 144 atoms in cell 3.780 with 108 atoms in cell (cm -1 ) -11.38-11.21 by extrapolate -11.08 by extrapolate (Å -3 ) 0.026 0.0262 with 144 atoms in cell 0.0262 with 108 atoms in cell Page9 fcc cell hcp cell

10. Part II – CO Doped Solid pH 2 - Methodology H. Li, P.-N. Roy, and R. J. Le Roy, J. Chem. Phys. 133, 104305 (2010) H. Li and co-workers, J. Chem. Phys.,139, 164315, (2013) M. E. Fajardo, J. Phys. Chem. A 117, 13504 (2013) pH 2 ‐ pH 2 potential: same as the study of pure solid pH 2. pH 2 ‐ CO potential: obtained from Hui Li’s 4D H 2 ‐ CO potential using Adiabatic Hindered Rotor approximation. Algorithms:  Path Integral Monte-Carlo (PIMC)  First order perturbation theory Simulate at temperature: T = 2.4 K Number of beads in PIMC: Page10

11. Part II – CO Doped Solid pH 2 - Methodology jiggling lattices in a rigid frame P. Tao, thesis for master degree of science, University of Waterloo(2005) pH 2 : Green ones: hold fixed pH 2 : Blue ones: relaxing CO: located in the center, translating and rotating R all pH 2 with R < R relax is relaxing, and similar treatment when choosing the total number of pH 2 in the model. Page11 R relax

12. Part II – CO Doped Solid pH 2 - Structures Studies of substitution site: N remove =0: pure pH 2 N remove =1: single substitution N remove =1: double substitution Obtained by fcc structure N relax = 42 N fix = 822 Page12 Classical MC PIMC Single substitution is most stable.

13. Part II – CO Doped Solid pH 2 - Structures minimal energy structure of single substitution in solid fcc pH 2 icosahedral pH 2 cage in (pH 2 ) 12 ‐ CO cluster S. Baroni and S. Moroni, Chem. Phys. Chem. 6, 1884 (2005) Page13

14. Part II – CO Doped Solid pH 2 - convergence studies of the number of relaxing pH 2 (left) and the total number of pH 2 (right) in fcc pH 2 matrix using of CO N relax = 54, N total = 1260: good approximation for pH 2 matrix. N relax is corresponding to R relax = 7.56 Å ≈ R H2-H2 + R H2-CO Page14

15. Part II – CO Doped Solid pH 2 - cm -1 experimental-2.961-2.974-0.013 calculated-3.244(1)-3.251(1)-0.007(2) M. E. Fajardo, J. Phys. Chem. A 117, 13504 (2013) of CO in solid pH2 of different structure Page15

16. Part II – CO Doped Solid pH 2 - PIMC vs MC Page16 distribution of pH 2 around CO PIMC Classical MC Centre of mass of CO R θ pH2pH2 CO

17. Conclusion  Observed structures, densities and of both fcc and hcp pH 2 crystal have been satisfyingly reproduced.  Single substitution site is most stable for CO doped pH 2 matrix.  The obtained different values of in fcc and hcp pH 2 matrix, and the difference agree with observations very well.  Quantum mechanical treatment is critical to simulate pH 2 matrix. Page17

18. Future works  Scaling pH 2 ‐ pH 2 potential to provide a more realistic solvation environment for doped CO in pH 2 matrix.  Incorporating Worm Algorithm to handle the Bose Exchange, thus to predict the rotational dynamics of doped CO in pH 2 matrix.  Scaling pH 2 ‐ CO potential to different isotopes of CO to study isotope effect of. Page18

19. Page19 Acknowledgement Supervisors: Prof. Robert J. Le Roy Prof. Pierre-Nicholas Roy Prof. Marcel Nooijen Prof. Hui Li Dr. Tao Zeng Nabil Faruk Matthew Schmidt Theoretical Chemistry Group, University of Waterloo $$: NSERC and CFI Canada Thank You !