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List of Methods used and some cases developed by CECAM-IE scientists

  1. GW-BSE
  2. CI
  3. DFT-Hartree Fock
  4. TDFT
  5. CI
  6. Semi-Empirical
  7. Non-adiabatic quantum dynamics
  8. Rare-events methods and biased sampling
  9. Mesoscale Modelling
  10. Particle in Cell Simulations (astrophysics/plasma-physics)
  11. Particle Based Methods in Data-Analytics/Big-data

A story of scales and particles

A great variety of methods are used by the laboratories and groups associated with CECAM-IE, which collectively can be termed as particle based simulation.But what is a particle, much like beauty depends on the beholder.

At one extreme, individual electrons and nuclei may be simulated, typically at a quantum mechanical level.  The numerical methods and algorithms used in such contexts are termed “ab-initio”, i.e. first principles. They include  very sophisticated techniques known such as GW and BSE based on second quantization, Hartree Fock, Density Functional Theory (time dependent and stationary) , various forms of Configuration Interaction, and several Semi-Empirical Methods.  All of these methods invoke the  Born-Oppenheimer approximation, and in this sense are adiabatic approximations.  The adiabatic approximation is sometimes poor , this can happen  when quantum energy surfaces come very close.  In such cases non-adiabatic methods are required, which are also capable of taking into account de-coherence effects, which can be important for phenomena as apparently different as photo-synthesis and the much sought quantum computer.

Yet fortunately many phenomena can be well described by simple empirical or semi-empirical forcefields, where the atoms and molecules move according to Newtons law, which are then solved step step computationally.  In some instances however, the quantum nature of some of the particles involved cannot be neglected. Dealing with such a hydra led to the award of the  2013 Nobel prize in chemistry to this area, molecular simulation.

And yet even though we may know how to simulate a system, the large times during which nothing much happens, punctuated by rare but dramatic and extremely important events is often a problem for particle bases simulation. How to handle this problem is the focus of rare-event methods which employ typically biased sampling methods.

But the notion of  a particle can be useful at longer spatial and time scales lying one or two orders of magnitude above  the  molecular level, this is known  as mesoscale.

And what does this say about the price of onions you might ask. The earthly applications range from nanotechnology and semiconductors, to molecular medicine, medical devises  and  geology, not to mention food.

And if you  dare to  look up towards the the sky you may be surprised to hear that even there, the notion of particle is useful,  not only the subject of planets, put also plasma of charges particles in space. But then strangely we discover that such methods are used also on the lab-bench just above your feet.

All of these methods are used by groups and laboratories associated with CECAM-IE – indeed some of our number also are pushing these methods to the frontier of what is known and beyond, deriving and conniving new methods and faster algorithms to reveal what nature is doing, some of the time.