Quantum Monte Carlo Study of the Equation of State and Vibrational Frequency Shifts of Solid para-hydrogen

Transcription

1 Quantum Monte Carlo Study of the Equation of State and Vibrational Frequency Shifts of Solid para-hydrogen Lecheng Wang, Robert J. Le Roy and Pierre-Nicholas Roy Chemistry Department, University of Waterloo Waterloo, Ontario, Canada Page 1

2 Open Questions for Pure Solid ph 2 An accurate and reliable model for solid ph 2 is highly desirable. A B C A of CO in ph 2 solid: fcc structure: cm -1 hcp structure: cm -1-1 hcp cm fcc fcc crystal hcp crystal A B A B A EOS obtained by different H 2 -H 2 PES F. Operetto et al., Phys. Rev. B 73, (2006) M. E. Fajardo, J. Phys. Chem. A 117, (2013) Page 2

3 Open Questions for Pure Solid ph 2 Theoretical insights regarding vibrational frequency shift ph 2 in solid ph 2 are still unclear. of schematic diagram of observed in ph 2 clusters and solid H. P. Gush et al., Can. J. Phys 176, 38 (1960), Isaas F. Silvera, Rev. Mod. Phys. 393, 52(1980) T. Oka, Annu. Rev. Phys. Chem. 299, 44(1993) G. Tejeda et al., Phys. Rev. Lett , 92(2004) Page 3

4 Part I Theory and Methods ph 2 ph 2 potential: recently obtained 1D potential averaging over Hinde s 6D H 2 H 2 potential. Methodology: Path Integral Monte-Carlo (PIMC) Periodic Boundary Conditions First order perturbation theory for vibrational shift v P(R) V H dr P( R) V ( R) 2 total H 2 is normalized to (N-1) V (R) is the difference potential: Simulate at temperature: T = 4.2 K V ( R) ( V ( R) V ( R )) I. F. Silvera, Rev. Mod. Phys. 393, 52, (1980), N. Blinov et al., J. Chem. Phys., 120, 5916, (2004) M. Boninsegni et al., Phys. Rev. Lett. 96, , (2006), R. J. Hinde, J. Chem. Phys., 128, , (2008) H. Li et al., J. Chem. Phys.,130, , (2009) N. Faruk et al., J. Chem. Phys., 141, , (2014) Page 4

5 Part I Theory and Methods EOS obtained by different 2 / N, E( ) E( 0) a Extrapolation of E( ) for ρ=0.0263å N. Blinov et al., J. Chem. Phys, 120, 5916, (2004) Page 5

6 Part I Theory and Methods EOS obtained by different N extrapolation of N Page 6

7 Part II.A Result and Discussion - Global EOS The global EOS is calculated by: fcc crystal 256 molecules arranged on 4X4X4 elementary cells extrapolation of 0 Both the extrapolation of N and the difference between fcc and hcp crystal are indistinguishable in this density interval. The EOS values are fitted to: ( E / N) ( ) a b c global EOS of solid ph 2 F. Operetto et al., Phys. Rev. B 73, (2006) Page 7

8 Part II.A Result and Discussion - Global EOS different global EOSs of solid ph 2 different PESs of solid ph 2 dimer F. Operetto et al., Phys. Rev. B 73, (2006) N. Faruk et al., J. Chem. Phys., 141, , (2014) Page 8

9 Part II.B Result and Discussion - EOS Near Equilibrium Density : equilibriu R 0 0 m density :distance between tw o nearest neighbors EOSs obtained with and without extrapolation 0 Å -3 R 0 Å N 256 N Exp (hcp) I. F. Silvera, Rev. Mod. Phys. 393, 52, (1980) Page 9

10 Part II.B Result and Discussion - EOS Near Equilibrium Density 0 :energy per particle at equilibriu m density 0 Å -3 Å R0 0 K EOSs of fcc and hcp structured solid ph 2 fcc hcp Exp (hcp) hcp is the preferred structure of solid ph 2 at 4.2K A. F. Schuch et al., Phys. Rev. 165, 1032 (1968) I. F. Silvera, Rev. Mod. Phys. 393, 52, (1980) F. Operetto et al., Phys. Rev. B 73, (2006) Page 10

11 Part II.B Result and Discussion - EOS Near Equilibrium Density different EOSs around 0 different PESs around R 0 F. Operetto et al., Phys. Rev. B 73, (2006) N. Faruk et al., J. Chem. Phys., 141, , (2014) Page 11

12 Part II.C Result and Discussion - Temperature Invariance of EOS The EOS at 2K is calculated by: fcc crystal 256 molecules arranged on 4X4X4 elementary cells extrapolation of 0 T 0 R0 0 Å -3 Å K EOSs of different T 4.2K K Page 12

13 Part II.D Result and Discussion - Vibrational Band Origin Shift The global curve is calculated by: v as a function of fcc crystal 256 molecules arranged on 4X4X4 elementary cells extrapolation of 0 The curve is obtained by fitting: v( ) a b c Page 13

14 Part II.D Result and Discussion - Vibrational Band Origin Shift v : v 0 value correspond ing to 0 v curves of fcc and hcp structured solid ph 2 v 0 cm -1 fcc(256) fcc( ) hcp( ) Exp T. Oka, Annu. Rev. Phys. Chem. 299, 44(1993) Page 14

15 Part II.D Result and Discussion - Vibrational Band Origin Shift v observed in ph 2 clusters and solid (R) of cluster and solid ph 2 2 N 1 dr4r ( R) 2 v dr4r ( R) V ( R), V ( R0 ) 0 T. Oka, Annu. Rev. Phys. Chem. 299, 44(1993) N. Faruk et al., J. Chem. Phys., 141, , (2014) Page 15

16 Part III Conclusion and Remarks Observed structures, densities and vibrational band origin shifts of both fcc and hcp ph 2 crystal have been satisfyingly reproduced. To precisely reproduce realistic solid ph 2, extrapolation of both the number of time slices and the number of particles is necessary. The EOS curve obtained depends strongly on the (ph 2 ) 2 PES used. The hcp is the preferred strcture of ph 2 at 4.2 K. The structure of solid ph 2 is invariant with temperature, while the total energy becomes more negative when temperature decreases. The larger number of nearby ph 2 molecules is the source of the large difference between the shift of solid ph 2 and the shift of cluster ph 2. Page 16

17 Acknowledgement Supervisors: Prof. Robert J. Le Roy Prof. Pierre-Nicholas Roy Prof. Marcel Nooijen Prof. Hui Li Dr. Tao Zeng Nabil Faruk Matthew Schmidt Thank You! Theoretical Chemistry Group, University of Waterloo $$: NSERC and CFI Canada Page 17