Kristof Bal

FWO Fellow


I'm active in several research areas. Here you can find an overview of my main topics of interest, as well as some links to additional information, presentations, and software.

Collective Variable-Driven Hyperdynamics


The collective variable-driven hyperdynamics (CVHD) method is an accelerated molecular dynamics technique based on both hyperdynamics and metadynamics. In hyperdynamics, a bias is added to the potential energy of the system to destabilize minima and consequently accelerate transitions to other minima (such as chemical reactions, conformational changes, diffusion events, etc.). Finding a suitable form of such a bias potential is, however, a far from trivial task and most hyperdynamics implementations are very system-specific.

To create a more general hyperdynamics implementation, CVHD borrows two concepts from metadynamics:

  1. The bias potential is only a function of a single collective variable (CV) that describes the complete to-be-biased dynamics. This way, the bias potential itself is not directly dependent on the system itself but, rather, a simplified representation of how far the system is from undergoing a transition.
  2. The value and shape of the bias potential does not have to be predefined. During the wait for each process, the bias potential is slowly "grown" via a metadynamics procedure, which means that the strength of the bias potential is made to match the current demands of the system, and no specific knowledge is needed a priori about activation energies of the various process the system might encounter. As such, the CVHD bias is self-learning.

In essence, CVHD is a sequence of metadynamics simulations, each in a subsequent state of the system, as depicted below.



The CVHD method has already been succesfully applied to a wide variety of problems, namely:

  • Diffusion on the Cu(001) surface at temperatures as low as 150 K and reaching time scales of up to 500 s, which is about 109 faster than MD.
  • Catalysis. Decomposition of a CH4 molecule on Ni(111) at 800 K, tracking the full dehydrogenation pathway until C(ad) + 4H(ad). This process requires vastly different bias potentials due to the huge time scale difference between the different elemental steps: only about 50 ps is needed to break a C-H bond in adsorbed CH2, but dissociating adsorbed CH takes up to 1 ms. The self-learning bias of CVHD makes handling this problem trivial. We also investigated CO2 decomposition on supported single atom catalysts.
  • Pyrolysis and combustion of n-dodecane, using the ReaxFF potential. The chemistry under realistic engine conditions takes place at millisecond-to-second time scales, and can only be captured by MD when using artifically raised temperatures, whereas self-learning CVHD can access all timescales relevant to the process on-the-fly.
  • Graphite etching. In a collaboration with researchers from the Dutch Institute for Fundamental Energy Research (DIFFER), the interaction of graphite with a hydrogen plasma was investigated. The time scale limitation of MD simulations has meant that previous MD studies of hydrogen atom etching of materials had to impose artificially high fluxes in order to observe any relevant mechanisms. By applying CVHD in between individual hydrogen impacts, we could tune the inter-impact time and, hence, the overall ion flux—the longest inter-impact times (>1 µs) corresponded to the conditions on experimentally feasible set-ups.


Plasma catalysis

Recently, plasma catalysis is gaining interest as an alternative to traditional thermo-catalytic techniques. Due to the non-equilibrium physical state of the plasma, with much energy stored in a limited number of degrees of freedom, specific chemical processes can be selectively stimulated or inhibited, and the location of the chemical equilibrium can be shifted. Various physical effects at the plasma–catalyst interface—such as vibrationally excited molecules, excess charges, and electric fields—are nonexistent under purely thermal conditions, and can dramatically change the chemistry at the catalyst surface. However, very little is known about this new frontier in surface science due to lack of dedicated experiments or detailed models.

I work on several topics related to the chemistry induced by out-of-equilibrium plasma effects, theoretically as well as experimentally (although really just as the resident theory person).

Gas adsorption or storage on charged materials

A solid in contact with plasma accumulates a negative surface charge due to influx of free electrons. Excess surface electrons can reach densities in the order of 1017 m-2, and remain trapped for long times up to days. Large electric fields are also found in common plasma-catalytic setups, which can polarize the surface.

How does this affect the surface chemistry?

As it turns out, this effect has been theoretically studied in the context of gas capture and storage. Nanomaterials such as hexagonal boron nitride (h-BN) or 2D borophene typically do not bind molecules such as CO2 or H2, but they do if excess electrons or strong electric fields are present. Moreover, transition metal dichalogenides (such as MoS2 and the like) can undergo charge-induced phase transitions.

However, when trying to reproduce published results, I encountered quite a few inconsistencies in the literature. These could be traced back to an inconsiderate treatment of periodicity (you may recall that the energy of a charged infinite system diverges). As a first step towards more accurate models, I proposed an approach to eliminate these inconsistencies.

Correlation is charge-induced surface chemistry

In addition, by performing calculations on several different charged materials (all derived from h-BN through doping or defect engineering) and using different theoretical approximations, I uncovered some general principles.

  • Adsorption of CO2 on charged materials can be described by a universal response function. The amount of work required to charge the material is directly correlated to the adsorption strength of the chemisorbed molecule. The efficiency by which this energy is converted depends on the adsorption site.
  • Materials with defects or dopants are easier to charge. Consequently, the doped materials are stabilized by excess charge. This way, charging can be a tool to selectively synthesize certain doped materials.
  • The self-interaction error is a very prominent factor in theoretical calculations of adsorption thermochemistry on charged materials, as opposed to its minor impact on (neutral) traditional catalysis. Therefore, careful benchmarking with hybrid DFT functionals is a must in this field.

Surface chemistry under plasma-induced charging

While the charge response of simple 2D materials is interesting from a theoretical point of view, it is not quite clear how these insights translate to more realistic catalysts exposed to a plasma. To this end, I constructed DFT-based model systems that capture some key aspects of these systems. I developed a simple model of the charge distribution around the surface—the plasma sheath—and applied it to supported M/Al2O3 (M = Ti, Ni, Cu) single atom catalysts. 

Again considering CO2 activation as a probe reaction, i found that:

  • The presence of a negative surface charge dramatically improves the reductive power of the catalyst, strongly promoting the splitting of CO2 to CO and oxygen.
  • The relative activity of the investigated transition metals is also changed upon charging, making "weak" catalysts much stronger.

These results strongly point to plasma-induced surface charging of the catalyst as an important factor contributing to the plasma-catalyst synergistic effects frequently reported for plasma catalysis, and a powerful additional parameter to tune catalyst activity and selectivity.


Presentations and posters

I have presented my work a few times, some relevant materials are collected here.

Long time scale simulation methods

(Plasma) Catalysis

General presentations


Several of my simulation techniques have been implemented in leading software packages, commercial & open source.

force-bias Monte Carlo

If you're interested in trying fbMC yourself, the method is implemented in two major simulation packages: LAMMPS and ADF. A detailed manual for the LAMMPS implementation of fbMC is available on the LAMMPS website. Furthermore, LAMMPS is open source, so extension and modification of the code's capabilities is possible for those with more theoretical or technical interest. ADF also has documentation available.

Reference: K. M. Bal & E. C. Neyts, On the time scale associated with Monte Carlo simulations. J. Chem. Phys. 141, 204104 (2014). (PDF)

The CVHD method

The reference implementation of CVHD is currently available in a dedicated branch of my own fork of the PLUMED plugin.

PLUMED can be interfaced with all commonly used MD codes, making CVHD widely usable. You should definitely check out its excellent manual first to familiarize yourself with how it works. Then, you can turn to the manual of the CVHD functions and get crackin'. Of course, you can still drop me a note if you have a question.

My old COLVARS-based code is available here (updated 27 May 2016).

Moreover, CVHD has also been implemented in ADF.

Reference: K. M. Bal & E. C. Neyts, Merging Metadynamics into Hyperdynamics: Accelerated Molecular Simulations Reaching Time Scales from Microseconds to Seconds. J. Chem. Theory Comput. 11, 4545-4554 (2015). (PDF)