Tag: theory and experiment

Localized vibrational modes of GeV-centers in diamond: Photoluminescence and first-principles phonon study

Authors: Kirill N. Boldyrev, Vadim S. Sedov, Danny E.P. Vanpoucke, Victor G. Ralchenko, & Boris N. Mavrin
Journal: Diam. Relat. Mater 126, 109049 (2022)
doi: 10.1016/j.diamond.2022.109049
IF(2020): 3.315
export: bibtex
pdf: <DRM>


GeV split vacancy defect in diamond and the phonon modes near the ZPL.
Graphical Abstract: GeV split vacancy defect in diamond and the phonon modes near the ZPL.


The vibrational behaviour of the germanium-vacancy (GeV) in diamond is studied through its photoluminescence spectrum and first-principles modeled partial phonon density of states. The former is measured in a region below 600 cm−1. The latter is calculated for the GeV center in its neutral, charged, and excited state. The photoluminescence spectrum presents a previously unobserved feature at 248 cm−1 in addition to the well-known peak at 365 cm−1. In our calculations, two localized modes, associated with the GeV center and six nearest carbon atoms (GeC6 cluster) are identified. These correspond to one vibration of the Ge ion along with the [111] orientation of the crystal and one perpendicular to this direction. We propose these modes to be assigned to the two features observed in the photoluminescence spectrum. The dependence of the energies of the localized modes on the GeV-center and their manifestation in experimental optical spectra is discussed.

On the influence of water on THz vibrational spectral features of molecular crystals

Authors: Sergey Mitryukovskiy, Danny E. P. Vanpoucke, Yue Bai, Théo Hannotte, Mélanie Lavancier, Djamila Hourlier, Goedele Roos and Romain Peretti
Journal: Physical Chemistry Chemical Physics 24, 6107-6125 (2022)
doi: 10.1039/D1CP03261E
IF(2020): 3.676
export: bibtex
pdf: <PCCP>


Graphical Abstract: Comparison of the measured THz spectrum of 3 phases of Lactose-Monohydrate to the calculated spectra for several Lactose configurations with varying water content.


The nanoscale structure of molecular assemblies plays a major role in many (µ)-biological mechanisms. Molecular crystals are one of the most simple of these assemblies and are widely used in a variety of applications from pharmaceuticals and agrochemicals, to nutraceuticals and cosmetics. The collective vibrations in such molecular crystals can be probed using terahertz spectroscopy, providing unique characteristic spectral fingerprints. However, the association of the spectral features to the crystal conformation, crystal phase and its environment is a difficult task. We present a combined computational-experimental study on the incorporation of water in lactose molecular crystals, and show how simulations can be used to associate spectral features in the THz region to crystal conformations and phases. Using periodic DFT simulations of lactose molecular crystals, the role of water in the observed lactose THz spectrum is clarified, presenting both direct and indirect contributions. A specific experimental setup is built to allow the controlled heating and corresponding dehydration of the sample, providing the monitoring of the crystal phase transformation dynamics. Besides the observation that lactose phases and phase transformation appear to be more complex than previously thought – including several crystal forms in a single phase and a non-negligible water content in the so-called anhydrous phase – we draw two main conclusions from this study. Firstly, THz modes are spread over more than one molecule and require periodic computation rather than a gas-phase one. Secondly, hydration water does not only play a perturbative role but also participates in the facilitation of the THz vibrations.

The 0.5THz finger-print mode of alpha-Lactose Monohydrate.

The 0.5 THz finger-print mode of alpha-lactose monohydrate.

Deep Eutectic Solvents as Non-flammable Electrolytes for Durable Sodium-ion Batteries

Authors: Dries De Sloovere, Danny E. P. Vanpoucke, Andreas Paulus, Bjorn Joos, Lavinia Calvi, Thomas Vranken, Gunter Reekmans, Peter Adriaensens, Nicolas Eshraghi, Abdelfattah Mahmoud, Frédéric Boschini, Mohammadhosein Safari, Marlies K. Van Bael, An Hardy
Journal: Advanced Energy and Sustainability Research 3(3), 2100159 (2022)
doi: 10.1002/aesr.202100159
IF(2022): ??
export: bibtex
pdf: <AdvEnSusRes> (OA)


Graphical Abstract: Understanding the electronic structure of Na-TFSI interacting with NMA.


Sodium-ion batteries are alternatives for lithium-ion batteries in applications where cost-effectiveness is of primary concern, such as stationary energy storage. The stability of sodium-ion batteries is limited by the current generation of electrolytes, particularly at higher temperatures. Therefore, the search for an electrolyte which is stable at these temperatures is of utmost importance. Here, we introduce such an electrolyte using non-flammable deep eutectic solvents, consisting of sodium bis(trifluoromethane)sulfonimide (NaTFSI) dissolved in N-methyl acetamide (NMA). Increasing the NaTFSI concentration replaces NMA-NMA hydrogen bonds with strong ionic interactions between NMA, Na+, and TFSI. These interactions lower NMA’s HOMO energy level compared to that of TFSI, leading to an increased anodic stability (up to ~4.65 V vs Na+/Na). (Na3V2(PO4)2F3/CNT)/(Na2+xTi4O9/C) full cells show 74.8% capacity retention after 1000 cycles at 1 C and 55 °C, and 97.0% capacity retention after 250 cycles at 0.2 C and 55 °C. This is considerably higher than for (Na3V2(PO4)2F3/CNT)/(Na2+xTi4O9/C) full cells containing a conventional electrolyte. According to the electrochemical impedance analysis, the improved electrochemical stability is linked to the formation of more robust surface films at the electrode/electrolyte interface. The improved durability and safety highlight that deep eutectic solvents can be viable electrolyte alternatives for sodium-ion batteries.

Impact of methane concentration on surface morphology and boron incorporation of heavily boron-doped single crystal diamond layers

Authors:  Rozita Rouzbahani, Shannon S.Nicley, Danny E.P.Vanpoucke, Fernando Lloret, Paulius Pobedinskas, Daniel Araujo, Ken Haenen
Journal: Carbon 172, 463-473 (2021)
doi: 10.1016/j.carbon.2020.10.061
IF(2019): 8.821
export: bibtex
pdf: <Carbon>


Graphical Abstract B doped diamond
Graphical Abstract: Artist impression of B incorporation during CVD growth of diamond.


The methane concentration dependence of the plasma gas phase on surface morphology and boron incorporation in single crystal, boron-doped diamond deposition is experimentally and computationally investigated. Starting at 1%, an increase of the methane concentration results in an observable increase of the B-doping level up to 1.7×1021 cm−3, while the hole Hall carrier mobility decreases to 0.7±0.2 cm2 V−1 s−1. For B-doped SCD films grown at 1%, 2%, and 3% [CH4]/[H2], the electrical conductivity and mobility show no temperature-dependent behavior due to the metallic-like conduction mechanism occurring beyond the Mott transition. First principles calculations are used to investigate the origin of the increased boron incorporation. While the increased formation of growth centers directly related to the methane concentration does not significantly change the adsorption energy of boron at nearby sites, they dramatically increase the formation of missing H defects acting as preferential boron incorporation sites, indirectly increasing the boron incorporation. This not only indicates that the optimized methane concentration possesses a large potential for controlling the boron concentration levels in the diamond, but also enables optimization of the growth morphology. The calculations provide a route to understand impurity incorporation in diamond on a general level, of great importance for color center formation.

UV-Curable Biobased Polyacrylates Based on a Multifunctional 2 Monomer Derived from Furfural

Authors: Jules Stouten, Danny E. P. Vanpoucke, Guy Van Assche, and Katrien V. Bernaerts
Journal: Macromolecules 53(4), 1388-1404 (2020)
doi: 10.1021/acs.macromol.9b02659
IF(2019): 5.918
export: bibtex
pdf: <Macromolecules> (Open Access)



Grapgical abstract ACS Macromolecules 2020
Graphical Abstract: The formation of biobased polyacrylates.


The controlled polymerization of a new biobased monomer, 4-oxocyclopent-2-en-1-yl acrylate (4CPA), was
established via reversible addition−fragmentation chain transfer (RAFT) (co)polymerization to yield polymers bearing pendent cyclopentenone units. 4CPA contains two reactive functionalities, namely, a vinyl group and an internal double bond, and is an unsymmetrical monomer. Therefore, competition between the internal double bond and the vinyl group eventually leads to gel formation. With RAFT polymerization, when aiming for a degree of polymerization (DP) of 100, maximum 4CPA conversions of the vinyl group between 19.0 and 45.2% were obtained without gel formation or extensive broadening of the dispersity. When the same conditions were applied in the copolymerization of 4CPA with lauryl acrylate (LA), methyl acrylate (MA), and isobornyl acrylate, 4CPA conversions of the vinyl group between 63 and 95% were reached. The additional functionality of 4CPA in copolymers was demonstrated by model studies with 4-oxocyclopent-2-en-1-yl acetate (1), which readily dimerized under UV light via [2 + 2] photocyclodimerization. First-principles quantum mechanical simulations supported the experimental observations made in NMR. Based on the calculated energetics and chemical shifts, a mixture of head-to-head and head-to-tail dimers of (1) were identified. Using the dimerization mechanism, solvent-cast LA and MA copolymers containing 30 mol % 4CPA were cross-linked under UV light to obtain thin films. The cross-linked films were characterized by dynamic scanning calorimetry, dynamic mechanical analysis, IR, and swelling experiments. This is the first case where 4CPA is described as a monomer for functional biobased polymers that can undergo additional UV curing via photodimerization.

Influence of diamond crystal orientation on the interaction with biological matter

Authors: Viraj Damle, Kaiqi Wu, Oreste De Luca, Natalia Ortí-Casañ, Neda Norouzi, Aryan Morita, Joop de Vries, Hans Kaper, Inge Zuhorn, Ulrich Eisel, Danny E.P. Vanpoucke, Petra Rudolf, and Romana Schirhagl,
Journal: Carbon 162, 1-12 (2020)
doi: 10.1016/j.carbon.2020.01.115
IF(2019): 8.821
export: bibtex
pdf: <Carbon> (Open Access)


Graphical Abstract Carbon paper with Romana
Graphical Abstract: The preferential adsorption of biological matter on oriented diamond surfaces.


Diamond has been a popular material for a variety of biological applications due to its favorable chemical, optical, mechanical and biocompatible properties. While the lattice orientation of crystalline material is known to alter the interaction between solids and biological materials, the effect of diamond’s crystal orientation on biological applications is completely unknown. Here, we experimentally evaluate the influence of the crystal orientation by investigating the interaction between the <100>, <110> and <111> surfaces of the single crystal diamond with biomolecules, cell culture medium, mammalian cells and bacteria. We show that the crystal orientation significantly alters these biological interactions. Most surprising is the two orders of magnitude difference in the number of bacteria adhering on <111> surface compared to <100> surface when both the surfaces were maintained under the same condition. We also observe differences in how small biomolecules attach to the surfaces. Neurons or HeLa cells on the other hand do not have clear preferences for either of the surfaces. To explain the observed differences, we theoretically estimated the surface charge for these three low index diamond surfaces and followed by the surface composition analysis using x-ray photoelectron spectroscopy (XPS). We conclude that the differences in negative surface charge, atomic composition and functional groups of the different surface orientations lead to significant variations in how the single crystal diamond surface interacts with the studied biological entities.

Can Europium Atoms form Luminescent Centres in Diamond: A combined Theoretical-Experimental Study

Authors: Danny E. P. Vanpoucke, Shannon S. Nicley, Jorne Raymakers, Wouter Maes, and Ken Haenen
Journal: Diam. Relat. Mater 94, 233-241 (2019)
doi: 10.1016/j.diamond.2019.02.024
IF(2019): 2.650
export: bibtex
pdf: <DiamRelatMater>


Spin polarization around the various Eu-defect models in diamond. Blue and red represent the up and down spin channels respectively
Graphical Abstract: Spin polarization around the various Eu-defect models in diamond. Blue and red represent the up and down spin channels respectively.


The incorporation of Eu into the diamond lattice is investigated in a combined theoretical-experimental study. The large size of the Eu ion induces a strain on the host lattice, which is minimal for the Eu-vacancy complex. The oxidation state of Eu is calculated to be 3+ for all defect models considered. In contrast, the total charge of the defect-complexes is shown to be negative: -1.5 to -2.3 electron. Hybrid-functional electronic-band-structures show the luminescence of the Eu defect to be strongly dependent on the local defect geometry. The 4-coordinated Eu substitutional dopant is the most promising candidate to present the typical Eu3+ luminescence, while the 6-coordinated Eu-vacancy complex is expected not to present any luminescent behaviour. Preliminary experimental results on the treatment of diamond films with Eu-containing precursor indicate the possible incorporation of Eu into diamond films treated by drop-casting. Changes in the PL spectrum, with the main luminescent peak shifting from approximately 614 nm to 611 nm after the growth plasma exposure, and the appearance of a shoulder peak at 625 nm indicate the potential incorporation. Drop-casting treatment with an electronegative polymer material was shown not to be necessary to observe the Eu signature following the plasma exposure, and increased the background

Synthesis, characterization and thermodynamic stability of nanostructured ε-iron carbonitride powder prepared by a solid-state mechanochemical route

Authors: Seyyed Amin Rounaghi, Danny E. P. Vanpoucke, Elaheh Esmaeili, Sergio Scudino, and Jürgen Eckert
Journal: J. Alloys Compd. 778, 327-336 (2019)
doi: 10.1016/j.jallcom.2018.11.007
IF(2019): 4.650
export: bibtex
pdf: <JAlloysCompd>


Nanostructured epsilon iron carbonitride (ε-Fe3CxN1-x, x ∼ 0.05) powder with high purity (>97 wt%) was synthesized through a simple mechanochemical reaction between metallic iron and melamine. Various characterization techniques were employed to investigate the chemical and physical characteristics of the milling intermediates and the final products. The thermodynamic stability of the different phases in the Fe-C-N ternary system, including nitrogen and carbon doped structures were studied through density functional theory (DFT) calculations. A Boltzmann-distribution model was developed to qualitatively assess the stability and the proportion of the different milling products vs. milling energy. The theoretical and experimental results revealed that the milling products mainly comprise the ε-Fe3CxN1-xphase with a mean crystallite size of around 15 nm and a trace of amorphous carbonmaterial. The thermal stability and magnetic properties of the milling products were thoroughly investigated. The synthesized ε-Fe3CxN1-x exhibited thermal stabilities up to 473 K and 673 K in air and argon atmospheres, respectively, and soft magnetic properties with a saturation magnetization of around 125 emu/g.

Daylight saving and solar time

For many people around the world, last weekend was highlighted by a half-yearly recurring ritual: switching to/from daylight saving time. In Belgium, this goes hand-in-hand with another half-yearly ritual; The discussion about the possible benefits of abolishing of daylight saving time. Throughout the last century, daylight saving time has been introduced on several occasions. The most recent introduction in Belgium and the Netherlands was in 1977. At that time it was intended as a measure for conserving energy, due to the oil-crises of the 70’s. (In Belgium, this makes it painfully modern due to the current state of our energy supplies: the impending doom of energy shortages and the accompanying disconnection plans which will put entire regions without power in case of shortages.)

The basic idea behind daylight saving time is to align the daylight hours with our working hours. A vision quite different from that of for example ancient Rome, where the daily routine was adjusted to the time between sunrise and sunset. This period was by definition set to be 12 hours, making 1h in summer significantly longer than 1h in winter. As children of our time, with our modern vision on time, it is very hard to imagine living like this without being overwhelmed by images of of impending doom and absolute chaos. In this day and age, we want to know exactly, to the second, how much time we are spending on everything (which seems to be social media mostly 😉 ). But also for more important aspects of life, a more accurate picture of time is needed. Think for example of your GPS, which will put you of your mark by hundreds of meters if your uncertainty in time is a mere 0.000001 seconds. Also, police radar will not be able to measure the speed of your car with the same uncertainty on its timing.

Turing back to the Roman vision of time, have you ever wondered why “the day” is longer during summer than during winter? Or, if this difference is the same everywhere on earth? Or, if the variation in day length is the same during the entire year?

Our place on earth

To answer these questions, we need a good model of the world around us. And as is usual in science, the more accurate the model, the more detailed the answer.

Let us start very simple. We know the earth is spherical, and revolves around it’s axis in 24h. The side receiving sunlight we call day, while the shaded side is called night. If we assume the earth rotates at a constant speed, then any point on its surface will move around the earths rotational axis at a constant angular speed. This point will spend 50% of its time at the light side, and 50% at the dark side. Here we have also silently assumed, the rotational axis of the earth is “straight up” with regard to the sun.

In reality, this is actually not the case. The earths rotational axis is tilted by about 23° from an axis perpendicular to the orbital plane. If we now consider a fixed point on the earths surface, we’ll note that such a point at the equator still spends 50% of its time in the light, and 50% of its time in the dark. In contrast, a point on the northern hemisphere will spend less than 50% of its time on the daylight side, while a point on the southern hemisphere spends more than 50% of its time on the daylight side. You also note that the latitude plays an important role. The more you go north, the smaller the daylight section of the latitude circle becomes, until it vanishes at the polar circle. On the other hand, on the southern hemisphere, if you move below the polar circle, the point spend all its time at the daylight side. So if the earths axis was fixed with regard to the sun, as shown in the picture, we would have a region on earth living an eternal night (north pole) or day (south pole). Luckily this is not the case. If we look at the evolution of the earths axis, we see that it is “fixed with regard to the fixed stars”, but makes a full circle during one orbit around the sun.* When the earth axis points away from the sun, it is winter on the northern hemisphere, while during summer it points towards the sun. In between, during the equinox, the earth axis points parallel to the sun, and day and night have exactly the same length: 12h.

So, now that we know the length of our daytime varies with the latitude and the time of the year, we can move one step further.

How does the length of a day vary, during the year?

The length of the day varies over the year, with the longest and shortest days indicated by the summer and winter solstice. The periodic nature of this variation may give you the inclination to consider it as a sine wave, a sine-in-the-wild so to speak. Now let us compare a sine wave fitted to actual day-time data for Brussels. As you can see, the fit is performing quite well, but there is a clear discrepancy. So we can, and should do better than this.

Instead of looking at the length of each day, let us have a look at the difference in length between sequential days.** If we calculate this difference for the fitted sine wave, we again get a sine wave as we are taking a finite difference version of the derivative. In contrast, the actual data shows not a sine wave, but a broadened sine wave with flat maximum and minimum. You may think this is an error, or an artifact of our averaging, but in reality, this trend even depends on the latitude, becoming more extreme the closer you get to the poles.

This additional information, provides us with the extra hint that in addition to the axial tilt of the earth axis, we also need to consider the latitude of our position. What we need to calculate is the fraction of our latitude circle (e.g. for Brussels this is 50.85°) that is illuminated by the sun, each day of the year. With some perseverance and our high school trigonometric equations, we can derive an analytic solution, which can then be calculated by, for example, excel.

Some calculations

The figure above shows a 3D sketch of the situation on the left, and a 2D representation of the latitude circle on the right. α is related to the latitude, and β is the angle between the earth axis and the ‘shadow-plane’ (the plane between the day and night sides of earth). As such, β will be maximal during solstice (±23°26’12.6″) and exactly equal to zero at the equinox—when the earth axis lies entirely in the shadow-plane. This way, the length of the day is equal to the illuminated fraction of the latitude circle: 24h(360°-2γ). γ can be calculated as cos(γ)=adjacent side/hypotenuse in the right hand side part of the figure above. If we indicate the earth radius as R, then the hypotenuse is given by Rsin(α). The adjacent side, on the other hand, is found to be equal to R’sin(β), where R’=B/cos(β), and B is the perpendicular distance between the center of the earth and the plane of the latitude circle, or B=Rcos(α).

Combining all these results, we find that the number of daylight hours is:



How accurate is this model?

All our work is done, the actual calculation with numbers is a computer’s job, so we put excel to work. For Brussels we see that our model curve very nicely and smoothly follows the data (There is no fitting performed beyond setting the phase of the model curve to align with the data). We see that the broadening is perfectly shown, as well as the perfect estimate of the maximum and minimum variation in daytime (note that this is not a fitting parameter, in contrast to the fit with the sine wave). If you want to play with this model yourself, you can download the excel sheet here. While we are on it, I also drew some curves for different latitudes. Note that beyond the polar circles this model can not work, as we enter regions with periods of eternal day/night.


After all these calculations, be honest:

You are happy you only need to change the clock twice a year, don’t you. 🙂



* OK, in reality the earths axis isn’t really fixed, it shows a small periodic precession with a period of about 41000 years. For the sake of argument we will ignore this.

** Unfortunately, the data available for sunrises and sunsets has only an accuracy of 1 minute. By taking averages over a period of 7 years, we are able to reduce the noise from ±1 minute to a more reasonable value, allowing us to get a better picture of the general trend.

External links

Building bridges towards experiments.

Quantum Holy Grail: The Ground-State

Quantum mechanical calculations provide a powerful tool to investigate the world around us. Unfortunately it is also a computationally very expensive tool to use, which puts a boundary on what is possible in terms of computational materials research. For example, when investigating a solid at the quantum mechanical level, you are limited in the number of atoms that you can consider. Even with a powerful supercomputer at hand, a hundred to a thousand atoms are currently accessible for “routine” investigations. The computational cost also limits the number of configurations/combinations you can calculate.

However, in the end— and often with some blood sweat and tears—these calculations do provide you the ground-state structure and energy of your system. From this point forward you can continue characterizing its properties, life is beautiful and happy times are just beyond the horizon. At this horizon your experimental colleague awaits you. And he/she tells you:

Sorry, I don’t find that structure in my sample.

After recovering from the initial shock, you soon realize that in (materials science) experiments one seldom encounters a sample in “the ground-state”. Experiments are performed at temperatures above 0K and pressures above 0 Pa (even in vacuum :p ). Furthermore, synthesis methods often involve elevated temperatures, increased pressure, mechanical forces, chemical reactions,… which give rise to meta-stable configurations. In such an environment, your nicely deduced ground-state may be an exception to the rule. It is only one point within the phase-space of the possible.

So how can you deal with this? You somehow need to sample the phase-space available to the experiment.

Sampling Phase-Space for Ball-milling synthesis.

For a few years now, I have a very fruitful collaboration with Prof. Rounaghi. His interest goes toward the cheap fabrication of metal-nitrides. Our first collaboration focused on AlN, while later work included Ti, V and Cr-nitrides. Although this initial work had a strong focus on simple corroboration through the energies calculated at the quantum mechanical level, the collaboration also allowed me to look at my data in a different way. I wanted to “simulate” the reactions of ball-milling experiments more closely.

Due to the size-limitations of quantum mechanical calculations I played with the following idea:

  • Assume there exists a general master reaction which describes what happens during ball-milling.

X Al + Y Melamine → x1 Al + x2 Melamine + x3 AlN + …

where all the xi represent the fractions of the reaction products present.

  • With the boundary condition that the number of particles needs to be conserved, you end up with a large set of (x1,x2,x3,…) configurations which each have a certain energy. This energy is calculated using the quantum mechanical energies of each product. The configuration with the lowest energy is the ground state configuration. However, investigating the entire accessible phase-space showed that the energies of the other possible configurations are generally not that much higher.
  • What if we used the energy available due to ball-milling in the same fashion as we use kBT? And sample the phase-space using Boltzmann statistics.
  • The resulting Boltzmann distribution of the configurations available in the phase-space can then be used to calculate the mass/atomic fraction of each of the products and allow us to represent an experimental sample as a collection of small units with slightly different configurations, weighted according to their Boltzmann distribution.

This setup allowed me to see the evolution in end-products as function of the initial ratio in case of AlN, and in our current project to indicate the preferred Iron-nitride present.

Grid-sampling vs Monte-Carlo-sampling

Whereas the AlN system was relatively easy to investigate—the phase space was only 3 dimensional— the recent iron based system ended up being 4 dimensional when considering only host materials, and 10 dimensional when including defects. For a small 3-4D phase-space, it is possible to create an equally spaced grid and get converged results using a few million to a billion grid-points. For a 10D phase-space this is no longer possible. As you can no longer keep all data-points (easily) in storage during your calculation (imagine 1 Billion points, requiring you to store 11 double precision floats or about 82Gb) you need a method that does not rely on large arrays of data. For our Boltzmann statistics this gives us a bit of a pickle, as we need to have the global minimum of our phase space. A grid is too course to find it, while a simple Monte-Carlo just keeps hopping around.

Using Metropolis’s improvement of the Monte-Carlo approach was an interesting exercise, as it clearly shows the beauty and simplicity of the approach. This becomes even more awesome the moment you imagine the resources available in those days. I noted 82Gb being a lot, but I do have access to machines with those resources; its just not available on my laptop. In those days MANIAC supercomputers had less than 100 kilobyte of memory.

Although I theoretically no longer need the minimum energy configuration, having access to that information is rather useful. Therefore, I first search the phase-space for this minimum. This is rather tricky using Metropolis Monte Carlo (of course better techniques exist, but I wanted to be a bit lazy), and I found that in the limit of T→0 the algorithm will move toward the minimum. This, however, may require nearly 100 million steps of which >99.9% are rejected. As it only takes about 20 second on a modern laptop…this isn’t a big issue.

Finding a minimum using Metropolis Monte Carlo.

Finding a minimum using Metropolis Monte Carlo.

Next, a similar Metropolis Monte Carlo algorithm can be used to sample the entire phase space. Using 109 sample points was already sufficient to have a nicely converged sampling of the phase space for the problem at hand. Running the calculation for 20 different “ball-milling” energies took less than 2 hours, which is insignificant, when compared to the resources required to calculate the quantum mechanical ground state energies (several years). The figure below shows the distribution of the mass fraction of one of the reaction products as well as the distribution of the energies of the sampled configurations.

Metropolis Monte Carlo distribution of mass fraction and configuration energies for 3 sets of sample points.

Metropolis Monte Carlo distribution of mass fraction and configuration energies for 3 sets of sample points.

This clearly shows us how unique and small the quantum mechanical ground state configuration and its contribution is compared to the remainder of the phase space. So of course the ground state is not found in the experimental sample but that doesn’t mean the calculations are wrong either. Both are right, they just look at reality from a different perspective. The gap between the two can luckily be bridged, if one looks at both sides of the story.