My question is regarding Molecular Dynamics forcefield parameters (FF-params). To the best of my knowledge, FF-params are determined as a first guess from potential energy scans using ab-inito / density functional approaches and, in some cases, slightly adapted to fit experimental quantities. However, these experimental quantities are usually strongly temperature dependent, e.g. diffusion coefficients, dielectric constants, dipole moments, separation free energies, equilibrium constants etc. How reliable is then a hypothetical MD-simulation at another temperature (e.g. 350 K) in relation to a classical parameterisation at (let's say) room temperature (RT) ? Is it actually true to say that the observables obtained in MD behave linear with an increase in temperature with RT ff-params, or are there systematic deviations? I might assume that there are deviations. How would that affect replica exchange Molecular Dynamics simulations, where the same parameter set is used for the full temperature range? Thanks in advance.
In principle not, but in practice yes. As you heat up the system, the interactions between atoms change due to a different electronic distribution. This is particularly true in metals and less so in semiconductors and insulators. So in the latter case, you should not expect much change in the force field, especially if the temperature scale is much smaller than the band gap.
To leading order, as you said, one can assume the change to be linear in T. But keep in mind this change is usually small. To get this linear correction, you would need to do ab initio MDs at a given T, and redo the fitting to get the new force field parameters, and assume (and later verify) the change is linear in T to get the linear coefficients.
Classical force fields are not very accurate to begin with. So this small change in them is not going to affect your results in a considerable way. I would not worry much about their temperature dependence and blame the latter if the MD results do not agree with experimental ones, because this is usually not the leading source of errors.
Dear Emanuel,
Molecular dynamics method uses molecular mechanics laws. DFT, ab initio and semi-empirical methods are not part of the molecular dynamics.
The following text describes the disadvantages of using molecular dynamics:
Limitations of the method are related not only to the parameter sets used, but also to the underlying molecular mechanics force fields themselves. A single run of an MD simulation optimizes the potential energy, rather than the free energy of the protein, meaning that all entropic contributions to thermodynamic stability of protein structure are neglected. The neglected contributions include the conformational entropy of the polypeptide chain (which is the main factor that destabilizes protein structure) and hydrophobic interactions that are known as main driving force of protein folding.[11] Another important factor are intramolecular hydrogen bonds,[12] which are not explicitly included in modern force fields, but described as Coulomb interactions of atomic point charges. This is a crude approximation because hydrogen bonds have a partially quantum mechanical nature. Furthermore, electrostatic interactions are usually calculated using the dielectric constant of vacuum, although the surrounding aqueous solution has a much higher dielectric constant. Using the macroscopic dielectric constant at short interatomic distances is questionable. Finally, van der Waals interactions in MD are usually described by Lennard-Jones potentials based on the Fritz London theory that is only applicable in vacuum. However, all types of van der Waals forces are ultimately of electrostatic origin and therefore depend on dielectric properties of the environment.[13] The direct measurement of attraction forces between different materials (as Hamaker constant) shows that "the interaction between hydrocarbons across water is about 10% of that across vacuum".[13] The environment-dependence of van der Waals forces is neglected in standard simulations, but can be included by developing polarizable force fields.
Hoping this will be helpful,
Rafik
Hi Emanuel,
apart from what Rafik already wrote: my group has developed several tools for FF optimization and especially for the non-bonded interactions, we run test simulations with 3-7 different temperatures to check wheater the T-dependence is ok or not. Feel free to browse through our publications w.r.t. this...
Dirk
The MD temperature is defined via the velocity of the atoms and the coefficient of expansion of the crystal lattice, obtained in equilibrium. Change the other parameters is implicit.
Dears Drs
It is NOT nice that you down-vote my answer because you are not convinced. My answer was taken from peer-reviewed articles.
I need an explanation.
Rafik
I have up-voted You, Rafik.
My answer is that force constants are evidently temperature dependent.
Hi,
I'd like to address the final part of your question regarding temperature REMD. While it is true that one might not expect a given MD force field (FF) parameter set to perform well over a large temperature range, if you are only interested at properties at say 300 K it doesn't necessarily matter in REMD that your parameters perform well at 350 K, only that sampling is enhanced at that temperature. The reason is that the exchange criterion will eventually drive each temperature in the REMD simulation to its correct Boltzmann-weighted ensemble given enough sampling (according to your FF parameters of course). This is the concept behind Hamiltonian replica exchange (the general case of T-REMD): you only need one "target" replica; your other replicas only need to enhance sampling and be able to exchange with other replicas.
However, if you are interested in the other temperatures (to e.g. create a melting curve), then your only recourse unfortunately is to verify that your FF parameters are giving good results for the properties that you want at the other temperatures by comparison to experiment. Sometimes MD parameters give OK results at different temperatures, but sometimes not. As an example, one of the first projects I worked on I saw cold denaturation of the trpzip2 peptide in MD simulations that was definitely not observed experimentally...
Hope this helps,
-Dan
Melting point of the classical TIP3P water model is 146K. That for me is the stand-out fact in relation to this question.
To answer your question about REMD, this is not a problem at all for as long as you take the view the higher temperature simulations are there to help exploration of the 300K replica. If you are looking at thermophile proteins or something like that, where 350K is a meaningful temperature that you are directly interested in, then I would say go ahead but with caution. Be aware that chemistry might happen at high temperatures, pKas will shift etc, but take comfort that the entropy-dominated unfolded state is probably not that sensitive to details of the forcefield anyway.
Put it simply, there are two main strategies to develop force fields for molecular simulations based on: (1) the physics behind the intermolecular forces and (2) ad hoc simple models which are capable of reproducing a number of (thermo)dynamic properties of interest fairly good. The parameters of the first model potential are strictly temperature independent by construction since they are refined so as to reproduce first principles (ab initio) calculations (at T=0 K). To compare with experiment, a number of well defined procedures have been developed to take temperature effects into account. Since the parameters of the second model are tuned to reproduce some thermodynamic and/or structural properties of a system usually at non-zero temperature(s), they are unavoidably temperature dependent.
Some examples of the first approach are:
Millot, C. et al. J. Phys. Chem. A 1998, 102, 754-770
Torheyden, M. and Jansen, G. Mol. Phys. 2006, 104, 2101-2138
Jankowski, P. et al. J. Phys. Chem. A 2015, 119, 2940-2964
Cencek W. et al. J. Phys. Chem. A 2013, 117, 7542–7552
Some recent examples of the second strategy are:
Stoebener, K. et al. Fluid Phase Equilib. 2014, 373, 100-108
Kraemer, A. et al. Comp. Phys. Commun. 2014, 185, 3228-3239
(the last work is from the group of Dirk Reith)
In principle not, but in practice yes. As you heat up the system, the interactions between atoms change due to a different electronic distribution. This is particularly true in metals and less so in semiconductors and insulators. So in the latter case, you should not expect much change in the force field, especially if the temperature scale is much smaller than the band gap.
To leading order, as you said, one can assume the change to be linear in T. But keep in mind this change is usually small. To get this linear correction, you would need to do ab initio MDs at a given T, and redo the fitting to get the new force field parameters, and assume (and later verify) the change is linear in T to get the linear coefficients.
Classical force fields are not very accurate to begin with. So this small change in them is not going to affect your results in a considerable way. I would not worry much about their temperature dependence and blame the latter if the MD results do not agree with experimental ones, because this is usually not the leading source of errors.
From quantum mechanical point of view, temperature can be considered as an excitation of energetic states of atoms. In this assumption, electron orbitals is affected by temperature and, since pair potentials represent the orbitals interaction, they must depend on temperature.
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