^{1,a)}and Rafael Ramírez

^{1}

### Abstract

Structural and thermodynamic properties of high-density amorphous (HDA) ice have been studied by path-integral molecular dynamics simulations in the isothermal-isobaric ensemble. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Quantum nuclear motion is found to affect several observable properties of the amorphous solid. At low temperature (*T* = 50 K) the molar volume of HDA ice is found to increase by 6%, and the intramolecular O–H distance rises by 1.4% due to quantum motion. Peaks in the radial distribution function of HDA ice are broadened with respect to their classical expectancy. The bulk modulus,*B*, is found to rise linearly with the pressure, with a slope ∂*B*/∂*P* = 7.1. Our results are compared with those derived earlier from classical and path-integral simulations of HDA ice. We discuss similarities and discrepancies with those earlier simulations.

This work was supported by Ministerio de Ciencia e Innovación (Spain) through Grant No. FIS2009-12721-C04-04 and by Comunidad Autónoma de Madrid through Program MODELICO-CM/S2009ESP-1691.

I. INTRODUCTION

II. COMPUTATIONAL METHOD

III. PREPARATION OF AMORPHOUSICE

IV. PROPERTIES OF HIGH-DENSITY AMORPHOUSICE

A. Volume

B. Interatomic distances

C. Kinetic energy

D. Bulk modulus

V. COMPARISON WITH EARLIER WORK

VI. SUMMARY

### Key Topics

- Ice
- 155.0
- Amorphous solids
- 32.0
- Atmospheric pressure
- 26.0
- Atmospheric temperature
- 18.0
- Elastic moduli
- 17.0

## Figures

Molar volume of ice as a function of pressure, as derived from PIMD simulations at *T* = 75 K. Open circles represent results derived from simulations starting from ice Ih. Solid circles are data points obtained from simulations starting from amorphous ice. Error bars are in the order of the symbol size. The dashed line is a guide to the eye. An open triangle at *P* = 0 indicates the volume measured by Mishima *et al.* ^{5} The solid line was calculated from the pressure-density data displayed in the review by Loerting and Giovambattista,^{14} adapted from Ref. 67.

Molar volume of ice as a function of pressure, as derived from PIMD simulations at *T* = 75 K. Open circles represent results derived from simulations starting from ice Ih. Solid circles are data points obtained from simulations starting from amorphous ice. Error bars are in the order of the symbol size. The dashed line is a guide to the eye. An open triangle at *P* = 0 indicates the volume measured by Mishima *et al.* ^{5} The solid line was calculated from the pressure-density data displayed in the review by Loerting and Giovambattista,^{14} adapted from Ref. 67.

Oxygen-oxygen radial distribution function of ice Ih (dashed line) and HDA ice (solid line) at *T* = 100 K and *P* = 1 atm, as derived from PIMD simulations.

Oxygen-oxygen radial distribution function of ice Ih (dashed line) and HDA ice (solid line) at *T* = 100 K and *P* = 1 atm, as derived from PIMD simulations.

Temperature dependence of the molar volume of ice at atmospheric pressure as derived from PIMD simulations: Ih (circles) and HDA ice (squares). Results of classical simulations for HDA ice are displayed as triangles. A solid line represents data obtained from classical molecular dynamics simulations by Tse *et al.* ^{13} For ice Ih the error bars are smaller than the symbol size. Lines are guides to the eye.

Temperature dependence of the molar volume of ice at atmospheric pressure as derived from PIMD simulations: Ih (circles) and HDA ice (squares). Results of classical simulations for HDA ice are displayed as triangles. A solid line represents data obtained from classical molecular dynamics simulations by Tse *et al.* ^{13} For ice Ih the error bars are smaller than the symbol size. Lines are guides to the eye.

Mean intramolecular O–H distance as a function of pressure for amorphous ice at 75 K, as derived from PIMD (squares) and classical (circles) simulations. Error bars are in the order of the symbol size. Lines are guides to the eye.

Mean intramolecular O–H distance as a function of pressure for amorphous ice at 75 K, as derived from PIMD (squares) and classical (circles) simulations. Error bars are in the order of the symbol size. Lines are guides to the eye.

Oxygen-hydrogen radial distribution function at 75 K and *P* = 1 atm, as derived from quantum PIMD simulations for H_{2}O (solid line) and D_{2}O (dashed line) amorphous ice, as well as from classical molecular dynamics simulations (dashed-dotted line). Inset: RDF in the region around 1 Å, showing the peak corresponding to intramolecular O–H bonds.

Oxygen-hydrogen radial distribution function at 75 K and *P* = 1 atm, as derived from quantum PIMD simulations for H_{2}O (solid line) and D_{2}O (dashed line) amorphous ice, as well as from classical molecular dynamics simulations (dashed-dotted line). Inset: RDF in the region around 1 Å, showing the peak corresponding to intramolecular O–H bonds.

Hydrogen-hydrogen radial distribution function for HDA ice at *P* = 1 atm. Solid and dashed lines show results obtained from PIMD and classical simulations, respectively, at *T* = 75 K. The dashed-dotted line was derived from neutron diffraction experiments at 80 K.^{78}

Hydrogen-hydrogen radial distribution function for HDA ice at *P* = 1 atm. Solid and dashed lines show results obtained from PIMD and classical simulations, respectively, at *T* = 75 K. The dashed-dotted line was derived from neutron diffraction experiments at 80 K.^{78}

Oxygen-oxygen radial distribution function for HDA ice at *P* = 1 atm. Solid and dashed lines represent results derived from PIMD and classical simulations, respectively, at *T* = 75 K. The dashed-dotted line was derived from neutron-scattering experiments at 80 K.^{45}

Oxygen-oxygen radial distribution function for HDA ice at *P* = 1 atm. Solid and dashed lines represent results derived from PIMD and classical simulations, respectively, at *T* = 75 K. The dashed-dotted line was derived from neutron-scattering experiments at 80 K.^{45}

Oxygen-oxygen radial distribution function for amorphous ice at *T* = 75 K and several pressures, as derived from PIMD simulations. Different lines represent results for *P* = 1 atm, and 1, 3, 6 GPa, as indicated in the labels.

Oxygen-oxygen radial distribution function for amorphous ice at *T* = 75 K and several pressures, as derived from PIMD simulations. Different lines represent results for *P* = 1 atm, and 1, 3, 6 GPa, as indicated in the labels.

Kinetic energy of hydrogen in ice Ih and amorphous ice as a function of pressure at two temperatures: 75 K (squares) and 250 K (circles). Open and solid symbols correspond to ice Ih and amorphous ice, respectively. Error bars for the crystalline phase are less than the symbol size. Lines are guides to the eye.

Kinetic energy of hydrogen in ice Ih and amorphous ice as a function of pressure at two temperatures: 75 K (squares) and 250 K (circles). Open and solid symbols correspond to ice Ih and amorphous ice, respectively. Error bars for the crystalline phase are less than the symbol size. Lines are guides to the eye.

Kinetic energy of oxygen in ice Ih and amorphous ice as a function of pressure at two temperatures: 75 K (squares) and 250 K (circles). Open and solid symbols correspond to ice Ih and amorphous ice, respectively. Error bars for the crystalline and amorphous solids are less than the symbol size. Lines are guides to the eye.

Kinetic energy of oxygen in ice Ih and amorphous ice as a function of pressure at two temperatures: 75 K (squares) and 250 K (circles). Open and solid symbols correspond to ice Ih and amorphous ice, respectively. Error bars for the crystalline and amorphous solids are less than the symbol size. Lines are guides to the eye.

Pressure dependence of the bulk modulus of amorphous ice at *T* = 75 K (solid circles) and 250 K (solid squares), as derived from PIMD simulations. Open circles correspond to ice Ih at 75 K. Error bars for the crystalline phase are in the order of the symbol size. Dashed lines are guides to the eye. The solid line was obtained by numerical differentiation from the pressure-density data displayed in the review by Loerting and Giovambattista,^{14} adapted from Ref. 67.

Pressure dependence of the bulk modulus of amorphous ice at *T* = 75 K (solid circles) and 250 K (solid squares), as derived from PIMD simulations. Open circles correspond to ice Ih at 75 K. Error bars for the crystalline phase are in the order of the symbol size. Dashed lines are guides to the eye. The solid line was obtained by numerical differentiation from the pressure-density data displayed in the review by Loerting and Giovambattista,^{14} adapted from Ref. 67.

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