The pipe dream of any theoretician is to model any material and predict its properties from the laws of quantum mechanics. The difficulty here comes from the high computational cost of applying these laws, particularly when modelling systems larger than hundreds of atoms at a finite temperature.

Our method to perform ab initio thermodynamics is to use machine learning methods to learn the atomic interactions from quantum mechanics, and thus avoiding otherwise prohibitively expensive calculations that explicitly consider electrons. In this study of water[1], not only are we able to reproduce closely the experimental values of many of the properties of water, but we can also rationalize phenomena including the density anomaly of water, the floating of ice, the difference between the melting point of heavy and normal water, and the six-fold symmetry of snowflakes, by identifying their physical origin.

In [2], we computed the phase diagram of water at three hybrid DFT levels of approximation, accounting for thermal and nuclear fluctuations as well as proton disorder. The computed phase diagrams are in qualitative agreement with experiment.

[1] Bingqing Cheng*, Edgar A Engel, Jörg Behler, Christoph Dellago, Michele Ceriotti. (2019) ab initio thermodynamics of liquid and solid water. Proceedings of the National Academy of Sciences, 116 (4), 1110-1115.

(see Research highlight in Nature Review Materials )

[2] Aleks Reinhardt*, Bingqing Cheng*. (2021) Quantum-mechanical exploration of the phase diagram of water. Nature communications 12.1: 1-7.

Deep inside giant planets, the pressure exceeds millions of standard atmospheres, under which hydrogen undergoes a phase transition: the covalent bonds inside hydrogen molecules break, and the gas becomes a metal. The existence of metallic hydrogen was theorized a century ago, but it is controversial how this process occurs.

We computed the phase diagram of dense hydrogen employed machine learning to mimic the interactions between hydrogen atoms, in order to overcome limitations of direct quantum mechanical calculations [1]. We found evidence for a continuous molecular to atomic transition in the dense hydrogen fluid, instead of a first-order one. The transition is smooth because the associated critical point is hidden under the melting line of hydrogen. Furthermore, this hidden critical point also induces other unusual phenomena, including density and heat capacity maxima.

In a seperate study [2], we computed the phase diagram of superionic water inside ice giants such as Uranus and Neptune. Our phase boundaries help resolve the fractions of insulating ice, different superionic phases and liquid water inside the ice giants.

[1] Bingqing Cheng*, Guglielmo Mazzola, Chris J. Pickard, Michele Ceriotti. (2020) Evidence for supercritical behaviour of high-pressure liquid hydrogen. Nature, 585, 217–220

(see the Cambridge Research and The Economist features)

[2] Bingqing Cheng*, Mandy Bethkenhagen, Chris J. Pickard, Sebastien Hamel. (2021) Phase behaviours of superionic water at planetary conditions. Nature Physics,17, 1228-1232.

Nowadays, a typical dataset in computational physics, chemistry and materials science contains thousands to millions of atomic structures, along with a diverse range of properties. It is thus be desirable to have a data-driven and automated framework for visualizing and analyzing such structural datasets.

In [1], we describe how to construct a low-dimensional representation of the datasets of materials and molecules. To largely automate the process, we have developed user-friendly software packages: ASAP [2] is a Python-based command-line tool that enables automatic analysis and mapping. [3] shows an example on how we apply the framework to crystal structure predictions. In [4], we revealed that the local environments characterizing the different ice phases are all present in the liquid water, which implies that water models created to describe the liquid can be transferred to study the ices.

[1] Bingqing Cheng*, et al. (2020) Mapping Materials and Molecules. Accounts of Chemical Research, 12697-12705.

[2] https://github.com/BingqingCheng/ASAP

[3] Aleks Reinhardt, Chris J. Pickard, Bingqing Cheng*. (2020) Predicting the phase diagram of titanium dioxide with random search and pattern recognition. Physical Chemistry Chemical Physics, 22: 12697–12705.

[4] Bartomeu Monserrat, Jan Gerit Brandenburg, Edgar A Engel, Bingqing Cheng*. (2020) Liquid water contains the building blocks of diverse ice phases. Nature Communications 11.1: 1-8.

(see Chemistry Community blog post)

The thermal conductivity of a fluid measures how well it conducts heat. Understanding the heat transport process is not only fundamentally important, but also has technological implications in material manufacturing, thermoelectric conversion, energy saving, heat dissipation, and many more.

In [1], we proposed a method to compute the thermal conductivity of a bulk fluid unambiguously, just using equilibrium molecular dynamics trajectories. This method thus bypasses the conceptual and practial difficulties of using the conventional Green-Kubo method. No heat flux, no energy, no force, no Green-Kubo, no temperature gradient, no problem!

[1] Bingqing Cheng*, Daan Frenkel (2020) Computing the Heat Conductivity of Fluids from Density Fluctuations. Physical Review Letters, 125, 130602 (Editor's suggestion)

It is well-known that electrons have to be described quantum-mechanically. On the other hand, since atomic nuclei are much heavier, they are often treated as classical particles in atomistic simulations. However, for light elements such as hydrogen and lithium the classical approximation can break down , and nuclear quantum effects (NQEs) can play a crucial role in numerous phenomena such as the isotope effect, hydrogen transfer rates, and the heat capacity of solids.

We consider NQEs using a path-integral formalism, which exploits an isomorphism between a quantum-mechanical nucleus and a ring-polymer. We have studied NQEs related problems including isotope fractionations [1], kinetic energies of water [2], and hydrogen embrittlement[3].

[1] Bingqing Cheng, Michele Ceriotti. (2014) Direct path integral estimators for isotope fractionation ratios. The Journal of Chemical Physics, 141(24): 244112.

[2] Bingqing Cheng, Jörg Behler, Michele Ceriotti. (2016) Nuclear Quantum Effects in Water at the Triple Point: Using Theory as a Link Between Experiments. Journal of Physical Chemistry Letters, 7(12): 2210-2215.

[3] Bingqing Cheng, Anthony T Paxton, Michele Ceriotti. (2018) Hydrogen diffusion and trapping in a-iron: the role of quantum and anharmonic fluctuations. Physical Review Letters, 120(22): 225901.

When a nucleus grows inside a bulk phase, free energy is gained by the interior, while the interface incurs a penalty. The competition between the two contributions results in a free energy barrier, which the system must overcome for the nucleus to grow to a critical size ultimately leading to an avalanche of structural transitions.

Atomistic modeling is a powerful tool for capturing the dynamical processes and investigating the underlying mechanism of nucleation, but it is difficult to link between the atomistic picture with macroscopic nucleation theories.

Inspired by the Gibbs dividing surface proposed by one of the founding fathers of statistical mechanics, we formulated a thermodynamic framework that reconciles the atomisic picture with macroscopic theories of nucleation [1-2]. Crucially, by defining the interface between the two phases in a rigorous and self-consistent manner, we are able to extract accurately the free energy associated with the nucleus and the interface, enabling stringent validation and extension of macroscopic nucleation theories [3-5].

[1] Bingqing Cheng, Gareth A Tribello, Michele Ceriotti. (2015) Solid-liquid interfacial free energy out of equilibrium. Physical Review B, 92(18): 180102.

[2] Bingqing Cheng*, Michele Ceriotti. (2017) Bridging the gap between atomistic and macroscopic models of homogeneous nucleation. The Journal of Chemical Physics, 146(3): 034106.

[3] Bingqing Cheng*, Gareth A Tribello, Michele Ceriotti. (2017) The Gibbs free energy of homogeneous nucleation: from atomistic nuclei to the planar limit. The Journal of Chemical Physics, 147(10): 104707.

[4] Bingqing Cheng*, Michele Ceriotti. (2018) Computing the Tolman length for solid-liquid interfaces. The Journal of Chemical Physics, 148(23): 231102.

[5] Bingqing Cheng*, Michele Ceriotti, Gareth A Tribello (2020) Classical nucleation theory predicts the shape of the nucleus in homogeneous solidification. The Journal of chemical physics, 152(4), 044103.

Nucleation is ubiquitous, from the ice formation in clouds to the preparation of pharmaceutical compounds, from metal casting to the tempering of chocolates, and from the growth of beautiful nautilus shells to the assembly of microtubules in cells. Despite that classical nucleation theory provides a simple physical picture, we have not yet reached a quantitative understanding of how high the free energy barrier is or how fast the rate of nucleation is for specific systems.

One of the most common and technologically-relevant nucleation phenomena involves homogeneous ice nucleation from undercooled liquid water. In [1], we present a protocol for computing the homogeneous ice nucleation rate at a physically relevant undercooling, taking into account the diffuse nature of ice-water interfaces, stacking disorders in ice nuclei, and the addition rate of particles to the critical nucleus. We disentangled and investigated the relative importance of all the terms, including interfacial free energy, entropic contributions and kinetic prefactor, that contribute to the overall nucleation rate.

[1] Bingqing Cheng*, Christoph Dellago, Michele Ceriotti. (2018) Theoretical prediction of the homogeneous ice nucleation rate: disentangling thermodynamics and kinetics. Physical Chemistry Chemical Physics, 20 (45), 28732-28740.

The Gibbs free energy is the fundamental thermodynamic potential underlying the relative stability of different states of matter under constant-pressure conditions. However, computing this quantity from atomic-scale simulations is far from trivial, so often times harmonic free energies or potential energies of a system are used as a proxy, which we have shown can be rather inaccurate for certain systems at high temperatures [1].

One of our long-term research pursuits is developing and extending free energy methods, as well as applying them to a broad class of problems in materials science and chemistry.

[1] Bingqing Cheng*, Michele Ceriotti. (2018) Computing the absolute Gibbs free energy in atomistic simulations: applications to defects in solids. Physical Review B, 97(5): 054102.

Structural materials need to support their loading and themselves. Therefore, the knowledge of their strength and plastic response plays a crucial role in their development, selection, and utilization.

In [1-4], we study the atomistic mechanism of crystal plasticity of nano-sized metallic particles, Such nanoscopic mechanisms are becoming more and more relevant in an era when people make machines and structures smaller and smaller. In [5-7], we model plastic behavior of bulk materials, using a mesoscopic approach.

1. Bingqing Cheng*, Alfonso H W Ngan. (2013) Crystal plasticity of Cu nanocrystals during collision. Materials Science and Engineering, 585:326-334.

2. Bingqing Cheng, Alfonso H W Ngan. (2013) The sintering and densification behaviour of many copper nanoparticles: A molecular dynamics study. Computational Materials Science, 74:1-11.

3. Bingqing Cheng*, Alfonso H W Ngan. (2013) Thermally induced solid-solid structural transition of copper nanoparticles through direct geometrical conversion. The Journal of Chemical Physics, 138(16):164314.

4. Bingqing Cheng, Alfonso H W Ngan. (2013) The crystal structures of sintered copper nanoparticles: A molecular dynamics study. International Journal of Plasticity, 47: 65-78.

5. Peggy S S Leung, Hing Shun Leung, Bingqing Cheng, Alfonso H W Ngan. (2015) Size dependence of yield strength simulated by a dislocation-density function dynamics approach. Modelling and Simulation in Materials Science and Engineering, 23(3): 035001.

6. Bingqing Cheng, Hing Shun Leung, Alfonso H W Ngan. (2014) Strength of metals under vibrations - Dislocation-density-function dynamics simulations. Philosophical Magazine, 95(16-18):1-21.

7. Hing Shun Leung, Peggy S S Leung, Bingqing Cheng, Alfonso H W Ngan. (2014) A New Dislocation-density-function Dynamics Scheme for Computational Crystal Plasticity by Explicit Consideration of Dislocation Elastic Interactions. International Journal of Plasticity, 67: 1-25.