Supplementary Information for Quantum Simulation of Thermally-Driven Phase Transition

Supplementary Information for “Quantum simulation of thermally-driven phase transition and oxygen K-edge x-ray absorption of high-pressure ice”

Dongdong Kang1, Jiayu Dai1,*, Huayang Sun1, Yong Hou1 & Jianmin Yuan1,2,*

1Department of Physics, National University of Defense Technology, Changsha 410073, Hunan, People's Republic of China, 2State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, Hunan, People's Republic of China

Correspondence and requests for materials should be addressed to J. D. () or J. Y. ()

This supplementary file includes three figures. Figure S1 presents the average proton distribution function as a function of the proton position relative to the bond midpoint and the corresponding oxygen-oxygen separation in ab initio molecular dynamics (MD) and ab initio path-integral molecular dynamics (PIMD) simulations at 107.9 GPa. Figure S2 presents comparisons of the calculated x-ray absorption near-edge spectra (XANES) of ice between MD and PIMD simulations. In this figure, the pressure is from 34.5 GPa, 61.2 GPa to 107.9 GPa and the temperature is increased from 100 K, 200 K to 300 K. Figure S3 presents comparisons of the calculated XANES spectra of ice X obtained with 16 water molecules and 64 water molecules at 107.9 GPa and 100 K. The result indicates that we could obtain reliable XANES using the relatively small cell here.

FIG. S1. The average proton distribution function as a function of the proton position relative to the bond midpoint and the corresponding oxygen-oxygen separation in MD (left panels) and PIMD (right panels) simulations at 107.9 GPa. The corresponding temperature is 100 K, 200 K and 300 K from top to bottom.

FIG. S2. Comparisons of the calculated XANES spectra of ice between MD and PIMD simulations. The pressure is from 34.5 GPa (top), 61.2 GPa (middle) to 107.9 GPa (bottom) and the temperature is increased from 100 K (left), 200 K (middle) to 300 K (right).

FIG. S3. Comparisons of XANES spectra of ice X obtained with 16 water molecules (solid line) and 64 water molecules (dashed line). The temperature is 100 K and the pressure is 107.9 GPa. We note that the pre-edge in large cell simulation is almost same as the result with the small cell. The peak of main edge with large cell is higher than that with small cell, however, the position of peak do not shift. The post-edge in big-cell calculation is slightly different from the small-cell result. The difference between small-cell and big-cell calculations cannot influence the discussion about the nuclear quantum effects on XANES. It should be noted that although the small supercell with 16 H2O molecules will introduce the hole-hole interactions compared with the large supercell with 64 H2O molecules, the influence on K-edge and the peak shift can be neglected.