I think as always with MD and MC it depends on the simulated system and the specific problem one is interested in. I'd assume that the possible appearance of quantum effects does not affect macroscopic systems unless the system is in a Bose-Einstein condensate state, which is definitely not the case at T = 93 K. Since MD simulations usually are performed on systems on the macroscopic or mesoscopic scale, quantum effects on the electron scale don't factor in anyway. AFAIK, there have been papers in which low-temperature MD simulations have been performed.

For my PhD I worked together with a lab in Aarhus (DK) and did the MD simulations of Coulomb Crystals with a Paul trap. The temperature is of order mK and we got pretty good match with the lab results.

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Dear All

I want to simulate the solution of some small biomolecules in liquid methane at 93K. what do you think about that? Do the quantum effects appear in interamolecular and intermolecular interactions? Do you see any paper in this subject?

I would be tempt to say that the limitations of your MD at low temperature are those of your force field.  I'm afraid I don't understand what you mean by quantum effects. Quantum nature is always there because the force between nuclei is dictated by quantum mechanics rules. A force field aims to parametrize those forces. If you mean quantum effects in the movement of the atoms, then I would say that is very unlikely and if they exist they will be there at 0K and 300 K. 

Yes quantum effects will come into play at low enough temperature. Even old simulation books like Allen and Tildesley touch on addressing this problem.

It depends on the mass of your molecules/atoms as well as the temp. The more mass the more classical. If you wanted to simulate liquid Helium then there would be significant quantum effects at the atomic level.

Have a look in the first page of Simple Liquids by Hansen and McDonald, it tells you how to calculate the thermal de Broglie wavelength and how to get an indication of how classical your system is.

You will probably be ok, but you should check it out anyway.

We should distinguish two different effects: 1) is the quantum nature of nuclei. If this effect is important it means the Born-Oppenheimer approximation is valid. This effect is rarely an issue in a molecule that has not degenerate ground state and that is not made only of light atoms. This first effect does not depend on T.  2) second effect is due to the necessity of include "quantum statistical mechanics" (QMS) in the description of dynamical properties or ensemble averages. This last effect, as Stephen says, does depend on the temperature. The lowest T the larger the  thermal de Broglie wavelength (TBL) and more likely that you need to use QMS. Think on a simple molecules at 0K. Classical MD (classical mechanics!)  predicts that the molecule has not zero point vibrational motion. However, it seems tat the TBL of a biomolecule in a solvent at 90K is so small that you will be fine with classical MD. 90K is low temperature for us humans but is not low T foe many quantum effects. 

I would completely agree with previous answer that 93K is quite "warm" temperature for classical MD simulation, however different force fields have different limits of applicability. Also, necessity of considering TBL depends on what kind of properties you are about to study.

Dear All

Thanks very much for your kindly answers. Does anyone know which force field was parameterized at low temperatures like 90K? Which force field is suitable for simulation of a biomolecule residue in liquid methane?

Dear Dr. Alizadeh

As I said in my previous post, I want to simulate the small biomolecules (for example RNA oligomer) in liquid methane. I want to simulate the configuration, solvation, hydrogen bond length and ... of these molecules.

It depends on the mass of the atoms and the temperature. at 93 K, you have to calculate the thermal wavelength: h^2 /2 m l^2 = k_B T gives you the thermal wavelength l for a given mass m.

If the thermal wavelength is much smaller than the typical atomic displacement (say 1 ang) then you can use classical MD, otherwise quantum effects are important, and MD results are not so reliable.

 For a proton for example MD would not be reliable. For carbon, where the mass is 12, you get l=0.9 ang, which is at the limit of validity. So even for carbon MD would not be so reliable. Heavier elements would probably be OK.

I am afraid that there is no bio-molecular force field for such temperatures.  Bio-molecular force fields were designed for normal conditions and they are so-called "effective force field" and, accordingly, are tied to a specific temperature. The only thing that I know for a wide range temperatures is a TraPPE. However TraPPE does not support proteins.

However, this does not mean that simulation is not possible. Try and check.

Dear Mohammad Khodadadi-moghaddam,

At low temperatures the quantum nature of nuclei does begin to affect the behaviour of chemicals and materials significantly. As others have said, the definition of what we mean by "low temperature" varies according to the mass of the nuclei involved. For systems involving hydrogen even 300 K can sometimes be regarded as "low", as evidenced by some of the peculiar properties of liquid water! Experimentally, the simplest way to see whether quantum nuclear effects are significant is to repeat an experiment with deuterated chemical constituents -- if you get the same result, quantum effects are not significant.

Concerning your simulation more specifically, at 93 K quantum nuclear effects could well be important even for first-row elements. For example in SrTiO3 the quantum nature of oxygen changes the phase transition temperature for the antiferroelectric distortion from around 130 K to 105 K (see, e.g. Zhong and Vanderbilt, Phys. Rev. Lett. 74  2587 (1995)). 

There are basically three ways to include quantum effects in MD:

1. Relax the Born-Oppenheimer approximation

If we include a nuclear wavefunction in our simulations, then of course we can reproduce all the quantum effects. This is complex, complicated and computationally demanding so is rarely done except for simple systems or small numbers of light particles (e.g. positrons or muons). The most common approach here is the double-adiabatic approximation, where you have a wavefunction for the lightest nuclei (almost always hydrogen) and use Born-Oppenheimer for the other nuclei.

2. Path-integral MD (PIMD)

Using Feynman's path-integral formalism of quantum mechanics allows a mapping between the quantum system and a set of interacting classical systems (strictly, the quantum partition function). In practice this essentially requires running many parallel MD calculations ("beads") which are linked weakly to each other via harmonic potentials ("springs"). The computational cost is basically the cost for an ordinary MD calculation multiplied by the number of beads -- the number of beads required increases as lighter nuclei are studied and/or the temperature is lowered. 

PIMD has the advantage of including the quantum effects of *all* nuclei, and at considerably lower computational cost than a nuclear wavefunction method. However the usual PIMD schemes are technically only valid for bosons, so at high densities the results for hydrogen (a fermion) may be inaccurate.

For systems with hydrogen at around 100 K, you might need 20-30 beads. However the different beads only interact weakly, so on a parallel computer the computational effort scales almost perfectly as you distribute beads across cores so with enough computer power the "time-to-science" is the same as for classical MD. For an example, see M. J. Gillan and F. Christodoulos, Int. J. Mod. Phys. C 04, 287 (1993) or M.I.J. Probert and M.J. Glover, Hydrogen in Matter. ed. / GR Myneni; B Hjorvarsson. MELVILLE : AMER INST PHYSICS, 2006. p. 311. There are more sophisticated PIMD methods too, see e.g. the work of Michele Ceriotti and David Manolopoulos.

3. Effective forcefield MD

This method is really cheating, because it requires someone else to have done all the hard work! Nevertheless if you have good data for simulations using methods (1) or (2) you can often re-parametrise your MD forcefield to reproduce the correct ensemble properties. Of course the easiest is if someone else has already re-parametrised the forcefield too!

These methods are largely designed to reproduce the ensemble average properties of the system, which is usually what MD is used for. However if you want to reproduce actual trajectories, you need to investigate more sophisticated methods such as Centroid PIMD -- of course then you need to worry much more about your thermostats and barostats too.

Hope that helps,

Phil Hasnip

Dear Philip James Hasnip

Thanks very much for your detailed answer. Unfortunately I do not have a suitable computer hardware for massive computations.

So I have an idea: I want to use quantum mechanical method (for example DFT) for simulation of a small part of biomolecule (for example one base pair) with 10-20 methane molecule (a cluster of solute with 10-20 solvent molecules). I want to investigate the influence of methane molecules on hydrogen bond between bases and the geometry of these solvent molecules around the bases. 

What do you think about this idea? As an expert researcher, please let me know your opinion.

Also I would be highly appreciated if other researchers tell me their opinions.

Best Wishes

Dear Mohammad,

If you run ab initio MD using DFT on this system then it would still neglect the quantum *nuclear* effects, though of course the electrons' quantum nature would be accounted for (at the level of the DFT approximation of course). At low temperatures the quantum nuclear effects are important, so ab initio PIMD would be the obvious method, though of course it would take longer to compute than ordinary MD.

Although I said you might need 20-30 beads for 93 K this is, of course, a rough guess for good simulation accuracy. You could run an ab initio MD simulation followed by an ab initio PIMD simulation with, for example, 4 beads and compare your results: if they're essentially the same then you don't need to worry about quantum effects; if they're different then you do! A 4 bead PIMD calculation will only take 4 times longer to perform than an ordinary MD calculation on one compute core so the time isn't too prohibitive, and on a parallel machine it will be less than 4 times the cost because the parallel distribution for PIMD is more efficient than an ordinary MD calculation.

All the best,

Phil

If we go down from heaven to earth, we have to recognize that, for such problems, we have not a practical method to account for the quantum nature of the nuclei. The only thing that we can practically do is to use effective force fields. If there are none for a desired temperature then either developed it or to use what is for normal conditions.

To be closer to a particular issue. Bio-molecules at liquid methane are almost solid bodies, so no worries about the conformational behavior. Therefore, suitable any biomolecular field. Methane is not there. Therefore, it must be taken from another field that surely developed for the low temperature.

I would largely second Philip here.

 You have to distinguish between two problems:

For the systems that you want to study, you are essentially stuck with force fields.All of these are simple parametrizations, cannot be improved systematically, and may fail in unusual situations (bond distances far from equilibrium, for example).Using DFT may not really improve matters; especially the coupling between the classical (force-field) and the quantum (DFT) system can be tedious (or so I remember being told).

I would suggest to try out different reasonable force fields and see if the results are stable, and to watch out for unusual geometries (I could imagine that, say, proton transfer reactions may be difficult).

 Regarding the quantum nuclei, PIMD is probably a rather simple way to incorporate quantum effects (simple in terms of easy implementation, not in terms of underlying theory), but I have no first-hand experience here.