Quantum modelling of structural and electronic properties of solids


In the proposed project we aim at modelling structural and electronic properties of selected solids where quantum effects play substantial role.
1. Employing Path Integral MC simulations we will investigate the influence of quantum effects on graphene structure, focusing on the intrinsic ripples at low temperatures.
2. We will study structure and properties of amorphous nitrogen at high pressure and investigate the possible existence of structural transformations in amorphous phase (polyamorphism).

condensed matter physics
Vedecká časť: 

In the first aim we will focus on the influence of quantum effects on carbon atoms on
structure and properties of graphene. According to the Mermin-Wagner theorem long-wavelength fluctuations disrupt long-range order in 2D crystal. Similarly 2D membranes in harmonic approximation tend to crumple. It was shown that taking into account the anharmonic coupling between stretching and bending modes the 2D structure is stabilized but strong transverse height fluctuations persist. For large samples their amplitude may substantially exceed interatomic distances and the membrane develops intrinsic ripples. This interesting phenomenon was theoretically studied in Ref. [G1, G2] by means of classical MC simulations where graphene was modeled with a classical potential.  In these simulations, however, quantum fluctuations (kinetic energy) of carbon atoms were completely neglected. Since the carbon atom mass is not too large (12u) and the covalent bonds are strong, one can expect that quantum effects will be quantitatively significant even at room temperature. They will become even more important at lower temperatures where the amplitude of thermal fluctuations becomes smaller than that of quantum zero-point motion. To our knowledge to date there is no numerical study of the size and influence of quantum effects on structure and properties of graphene in the literature.

We plan to employ the Path Integral Monte Carlo (PIMC) method which is based on numerical simulation of the path integral and allows to calculate (in principle exactly) the average values of observable quantities in quantum system at finite temperature. Our project aims at detailed investigation of the influence of quantum effects on structural and mechanical properties of graphene in temperature range 50 – 300 K. Because of the paradigmatic importance of the system from theoretical and practical point of view we believe that an accurate quantitative determination of the influence of quantum effects is highly important. In particular we want to focus on ripples and height fluctuations of the membrane as well as radial and angular distribution functions, elastic properties and thermal expansion. The principal investigator has experience with application of the PIMC method to solids [G3].

In the second aim we plan to study the structure of amorphous nitrogen at high pressure. Among the most important characteristics of amorphous phases are short- and middle-range order. These properties of amorphous nitrogen are not known neither from experiments nor from numerical simulations. We will also focus on investigating the possible presence of structural transformations in the amorphous regime (polyamorphism). Amorphous or crystalline polymeric nitrogen (p-N) may be obtained by synthesis at high pressure, where single bonds created on compression have a potential to produce a vast amount of energy at the backward decompression and formation of molecular N2 phase (up to 3 eV per molecule [N1]). From the chemical point of view this is caused by a large difference between energies of single and triple nitrogen bonds. Polymeric nitrogen is thus considered as a potential high energy-density material and a source of energy in form of batteries, alternative rocket fuel or industrial explosives. Polymeric nitrogen was first obtained in a form of amorphous semiconducting solid - the μ-phase at pressures over 140 GPa and room temperature [N2]. On the other hand, crystalline form known as cg-N (cubic gauche-N), which was predicted based on ab initio simulations [N3], was first observed at 110 GPa and high temperature of 2000 K [N4]. The need for high temperature is caused by large energy barriers between molecular and polymeric forms. Amorphous μ-phase of p-N was surprisingly shown to be metastable at atmospheric pressure and low temperature of 100 K [N5]. To date, however, it is not clear whether this is a genuine amorphous form (on microscopic scale) or a system of nanocrystalline clusters with different size. The only observation is the average coordination, which is 2.5 [N2] indicating presence of mixed nitrogen coordinations. Details of the local structure of amorphous p-N are, however, unknown. The expected contribution of this work is the investigation and determination of properties of amorphous p-N, such as structure (short- and middle-range order - coordinations, angular distributions, structure factor etc.) and dynamics. To date there is no experimental or theoretical study published on this topic. Another possible new result would be uncovering eventual structural transformations occurring in the amorphous regime. We plan to solve the problem by ab initio molecular dynamics (MD) simulations which (unlike classical MD) are able to capture changes in the character of chemical bonds (polymerization) and implicitly account also for finite temperature effects. In order to adequately describe the amorphous structure it is necessary to simulate fairly large systems consisting of hundreds of atoms which in case of ab initio MD requires substantial computer resources.


[G1] A. Fasolino, J. H. Los & M. I. Katsnelson, Nature Materials 6, 858 - 861 (2007)
[G2] J. H. Los, M. I. Katsnelson, O. V. Yazyev, K. V. Zakharchenko, and A. Fasolino, Phys. Rev. B 80, 121405R (2009)
[G3] R. Martoňák, W. Paul, and K. Binder, Phys. Rev. E 57, 2425 (1998)

[N1] Uddin et al., Mol. Phys., 104, 745–749 (2006)
[N2] Goncharov et al., Phys. Rev. Lett., 85, 1262 (2000)
[N3] Mailhiot et al., Phys. Rev. B, 46, 14419-14435 (1992)
[N4] Eremets et al., Nat. Mat., 3, 558-563 (2004)
[N5] Eremets et al., Nature, 411, 170-174 (2001)

Socioekonomický a technologický dopad: 

Both aims represent fundamental research and therefore socioeconomic and technological impact can be expected on longer time scale.

Technická časť: 

For the PIMC simulations of graphene we have our own Fortran90 code which is parallelized using openMP.  The code scales efficiently up to 8 cores and we plan to run several independent MC runs on the same node simultaneously.

We plan to simulate the system with N=108864 atoms at temperatures T=300, 200, 100 and 50 K. For each temperature we plan to use 2 values of the Trotter number M corresponding to MT=2400 and 4800, respectively. Assuming 10^6 MC steps for equilibration and 5x10^6 MC steps for production runs we arrive at an estimate of at least 480000 CPU hours. Taking into account that some additional calculations for even larger systems might be necessary in some cases we estimate the upper bound to 640000 core-hours for PIMC graphene simulations.

For ab initio MD simulations on nitrogen we plan to employ the VASP code which for systems consisting of several hundred atoms is well known to efficiently scale up to 128 cores. We have experience with simulations of polymerizations of crystalline nitrogen. Based on these simulations we estimate the CPU time requirements for generating MD trajectories corresponding to the accumulated time of about 500 ps for system consisting of 192 atoms to 120000 core-hours.

Prepojenie s grantovými úlohami: 
VEGA 1/0904/15 Quantum modeling of structural and electronic properties of solids
4 864.00