Drs. T. S. van Erp

Address:

Department of Chemical Engineering
University of Amsterdam
Nieuwe Achtergracht  166
1018 WV Amsterdam
tel: 0031 20 5256917
email: tsvanerp@science.uva.nl





Curriculum Vitae



Publication list:


T.S. van Erp, A. Fasolino, O. Radulescu and T. Janssen, Phys. Rev. B 60 , 6522-6528 (1999)
"Pinning and phonon localization in Frenkel-Kontorova models on quasiperiodic substrates" link .

Titus S. van Erp, Evert Jan Meijer, Chem. Phys. Lett. 333 , 290-296 (2001)
"Hydration of methanol in water. A DFT-based molecular dynamics study" link

T.S. van Erp, A. Fasolino and T. Janssen, Ferroelectrics 250 , 421-424 (2001)
"Structural Transitions and Phonon Localization in Frenkel Kontorova Models with Quasi-Periodic Potentials" postscript or pdf-file

T.S. van Erp and A. Fasolino, Europhysics Letters 59 , 330-336 (2002)
"Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems", link

Jan-Willem Handgraaf, Titus S. van Erp, and Evert Jan Meijer, Chem. Phys. Lett. 367 , 617-624 (2003)
"Ab Initio molecular dynamics study of liquid methanol", link

Titus S. van Erp, Daniele Moroni and Peter G. Bolhuis,
J. Chem. Phys. 118 , 7762-7774 (2003)
"A Novel Path Sampling Method for the Calculation of Rate Constants", link

Titus S. van Erp, and Evert Jan Meijer,
"Ab Initio Molecular Dynamics Study of Aqueous Solvation of Ethanol and Ethylene", link

Titus S. van Erp, and Evert Jan Meijer,
"Conversion of ethylene to ethanol in acid aqueous solution", in progress



Research Projects


Frenkel-Kontorova Models

Solvation of alcohols in water

Chemical reactions of alcohols in water

New method for rate constant calculation:Transition Interface Sampling




Hallucinary Number Theory ?!?! 		******************

MOVIES (animated gifs) of simulations:


1) solvated methanol molecule in water (6Mb)
2) succesfull reaction between water and ethene forming ethanol (1.7 Mb)
3) constrained (forced) reaction from ethanol to water and etheen, showing electron density and energy barrier. (0.3 Mb)
4) Same as 3) but with H3O+ as catalyst via the E1 mechanism (0.5 Mb)
5) Same as 3) but with H3O+ as catalyst via the E2 mechanism (1.0 Mb)



The Frenkel-Kontorova Model
on Quasiperiodic Substrate Potentials

The Frenkel-Kontorova model is the prototype of model to describe incommensurate structures. Related physical quantities are for instance the friction between two surfaces, charge-density waves and Josephson-junctions. One of the predicted theoretical phenomena is the so called superlubricity regime, what means that friction can completely vanish under certain conditions.
The FK model can easily be imagined as an infinite long chain of particles, connected with springs, superpositioned on a periodic potential, representing two one-dimensional surfaces, the upper flexible and the lower rigid.
Aubry showed that as long the attracting force between the surfaces (or equivalent the amplitude of the periodic potential) is below a certain critical value, there is no energy needed to let the upper chain slide over the barriers of the lower surface.
In Nijmegen we look at an extension of this model, in which the periodic potential is replaced by a quasi-periodic one. We discovered that this model possesses instead of one a much larger number of critical phase transitions. Together with Ovidiu Radulescu we published are results in: Phys. Rev. B 60 , 9 (1999) .
You can also download my thesis: script.ps.gz (gzipped postscript format) or script.pdf (PDF-format)


Further Research on the FK Model on QPSP

A way to describe the Aubry-transition is by means of the dynamical systems for which a transition to chaos occurs at the same critical value (We found later some evidents which contradicts this hypothesis, see below!). We looked at the extended dynamical systems derived from the equations for equilibrium in the FKM on QPSP. Lyapunov exponents and fractal dimensions show that two types of transitions can occur in these systems. Only one corresponds directly the a phase transition in the extended FK chain. Our results are published in Ferroelectrics .
For my poster of the conference APERIODIC July 2000 Nijmegen you can look to this PDF-file.
(Use the ZOOM-IN option on your acrobat-reader!)
Kc: transition to global chaos in the Standard Map = Kc: analyticity breaking Frenkel Kontorova ????

Our surprising answer: NO !
=> Violation of Greene's Hypothesis (1979)

The total force on a particle is determined by its position in the potential and by the distance of the nearest neighbours. In equilibrium the total force of each particle is zero. This implies that if the positions of two neighbouring particles are known, by iteration, the positions of all the other particles can be derived. The equations for this are equivalent to the standard map. This standard map has a critical value Kc at which global chaos occurs. This value is generally assumed to be the same value at which the Aubry-transition occurs in the FKM. Indeed numerical calculations with finite commensurate approximants show a critical value of ~ 0.97 close to the value of the standard map, which has been evaluated with high precision to be: 0.971635406. However we found an alternative way to calculate Kc in the FKM, not based on finite approximants, but based on Fourier and Taylor expansions of increasing order. Our value is Kc=0.97978, see figure below.

So our answer to the question is: No. Difference is small, but significant. The assumption that both values should be the same is based on Greene's hypothesis, first postulated in 1979. However despite of enormeous effort since then to prove this assumption, a rigourous proof has never been established. Our numerical calculations suggest that a proof will never be established, simply because the hypothesis is wrong! A paper of our findings is publised in Europhysics Letters.

Links:
Standard Map and also nice to see is this Java Applet
Java Applet on a dynamical Frenkel-Kontorova chain.




Ab Initio Molecular Dynamics Calculation: Chemical Reactions in Water

Ab Initio means that we start from the fundamental laws of quantum-mechanics. This is in contrary to the normal MD simulations, where they use empirical or semi-empirical pair-potentials, like Lennard-Jones. First fitting your parameters to experimental data and then show that your calculations do indeed give the same results as obtained from the experiments, is in our opinion cheating. We do not cheat !!... , maybe perhaps only a little bit. Besides this ethical part of not cheating, there is also a pragmatic part. If you want to study chemical reactions any method based on effective pair-potentials or what so ever will fail. During the process of a chemical reaction the electronic structure changes and therefore has to be calculated explicitly.
The difficulty is time. Even on the fastest super-computer quantum-chemical calculations take a very long time or, as we say it, are very expensive. Quantum MD actually means that we have to do these expensive calculations each time step, so about a few thousand times. Doing this in a naive straight forward way would take years, decades, ages !
In 1985 two Italians Car and Parrinello invented some very smart algorithm, which enables us to obtain at each time step a very good approximate for the electronic ground state, without doing the time-consuming calculation over and over again. The Car-parrinello method makes it possible to do calculations at small systems (100-200 atoms) within reasonable time (weeks-months).


The solvation of methanol in water
As our goal is to study reaction with alcohols in water, we performed a simulation to see whether the method describes the solvation of alcohol in water correctly. Although for pure physical interest this kind of simulation is actually not one which you would like to do with CPMD (=Car-Parrinello Molecular Dynamics) as normal MD is much faster and can handle much larger systems, the solvation effects of alcohols in water were never simulated in Ab Initio way before and it was therefore a sensible test to look at this first. Radial distribution functions, vibrational frequencies were analyzed and compared with experiments for two systems containing one methanol and respectively 31 and 63 water molecules. Conclusion were that radial distribution functions were in good agreement with experiment. The small system shows some deviation from the large one, but the results are still in reasonableagreement that we believe that systems of that size give high qulaitative results. Spectra show some discrepancy with experiment, a known feature of our density functional (Blyp). On qualitative basis the results show strongly the red-shifting of the OH stretch of the methanol, when hydrated in water. Our results are published in: chem. phys. letters

At the right you see a snapshot of our simulation. The box contains 31 waters and one methanol molecule, we used periodic boundary conditions. The methanol molecule is represented by balls and sticks, the waters only by sticks for visuality.
Atom colours: oxygen= red, carbon=grey and hydrogen=white. The hydrogen bonds are represented by the dashed yellow lines. To see more snapshots click here or even better for the 150-pictures movie click here .




REACTIONS WITH ALCOHOLS

In our next project we will look to the hydration of ethene into ethanol:

C2H4 + H2O <=> C2H5OH

This process is used on large scale in industry for the production of ethanol. On a smaller scale also the inverse reaction, dehydration of ethanol for the production of ethene, is used in developing countries, who don't have acces to large petroleum resources, but where fermentation alcohol is largely available.
The reaction proces is usually not direct as stated above but happens in general under influence of a catalist to lower the energy barrier between the reactant and the product state.
We will investigate this reaction in aqueous solutin with sulfuric acid (H2SO4) as catalyst. Although the present of the acid lowers the barrier a lot, the chance that we will see a spontaneous reaction is low. As a typical simulation time of 10 ps cost a few weeks calculating on a parallel computer. Therefore we have to force the reaction to happen by applying a constrained. In this way we are able to find reaction barriers, free energy diferences and reaction rates.

There are three possible reaction paths:


[A] Direct reaction without catalyst. (The dehydration of ethanol is forced by constrains here)

The reaction barrier for this mechanism is very high ~70 Kcal/mol.
For a hydration of ethene simulation click HERE to see a movie of a simulation, where we fired a water molecule with a speed of 5500 m/s towards the etheen molecule. This enormous speed is neccessary to lift the water molecule over the barrier. The temperatuur of the ethanol in the final state is about 1000 K.

The prence of H3O+ can lower the barrier (~40 Kcal/mol) in two ways.
[B] E1-mechanism
[C] E2-mechanism

E1 mechanism is known to the favoured for reaction with branched alcohols, while for linear alcohols like ethanol the E2 mechanism is favoured.






TRANSITION INTERFACE SAMPLING

This is a new develloped method I'm very proud of. Studying the Transition Path Sampling Method of David Chandler and collaborators I got the idea to use paths with variable length. To achieve this I thought of new state definitions: Overall states that exists next to the stable state defintions. This turned out to give an new elegant expression for the rate constant and the possibility for a new efficient algorithm to calculate this. Together with Daniele Moroni and Peter Bolhuis we worked this out and tested the method on a simple diatomic bistable molecule immersed in a fluid of purely repulsive particles. It shows that the new method is a factor two till five faster than the original Transition Path Sampling . In case of more complex systems the efficiency can be probably easily more than a factor ten better. I hope this new method will be used by many research groups in the future. This article is now submitted and the preprint can be found here.


Illustration of a calculated path and the interfaces from the new article.








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Last updated: 29-10-2002