What‘s the difference between quantum methods and molecular dynamics method?

- Quantum methods (mostly ab-initio calculations) incorporate nuclear and/or electronic (but not only!) interactions between particles; simulations are based on the Schroedinger equation, including (and within) different approximations (e.g. Born-Oppenheimer) mostly using of the action principle of its classical equivalent (classical mechanics), i.e. path integral (or resembling partition function).

- Molecular dynamics methods are used to solve Newtonian equations of motion.

Since both the quantum methods and molecular dynamics methods can be adopted to model the fracture progress of materials, what's the difference between them besides the scale limitation of the former methods?

- Differences become essential namely from the scale limitation; i.e. it depends only on the volume (size), shape (boundary conditions) of corresponding simulation boxes (3-d structures, 2-d grids, 1-d chains or 0-d points).

All depends on the problems you must solve. For example for some phase transitions (e.g. magnetic) it is necessary to treat the system quantum mechanically (magnetism is quantum phenomenon and consequently it should be described by the rules of Quantum mechanics only!). For other transitions is needed to threat them classically (for example some temperature and/or pressure phase transitions in materials).

I hope you will read one (not so) new, (but) interesting and more clarified (open sourced) paper (for me; without more mathematical equations) about this question to make all the things simplified - https://www.google.bg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwjS1c7hmqzXAhVFY1AKHW1UC2YQFggwMAE&url=https%3A%2F%2Farxiv.org%2Fpdf%2F1405.2831&usg=AOvVaw1G73hCJqejKspafzRK82mz

Enjoy it &

Regards.

The basic idea has underlain the description of fracture until now, but not been made explicit. Although quantum mechanics describes matter at the atomic scale, quantum effects are much more pronounced on the dynamics of electrons than on the dynamics of nuclei. The basic reason for this is that nuclei are thousands of times more massive than electrons, and as a consequence a classical description of nuclear motion can be employed. Quantum mechanics provides (in principle) a way to calculate what the forces on each atom will be, but once the forces as a function of atomic positions are known, the response of the nuclei can be computed as if they are purely classical particles.

cited from 2015 Particle methods in the study of fracture

MD employs classical Newtonian mechanics to describe the motions of atoms and molecules. Classical MD on its own cannot be used to model chemical reactions. QM methods more accurately describe the behavior of the electrons in atoms and molecules and can model chemistry -- the making and breaking of chemical bonds.

In quantum methods quantum physics is used for the calculations, but in forcefield methods (MD) classical physics (newton's second law equation) is used.

What‘s the difference between quantum methods and molecular dynamics method?

- Quantum methods (mostly ab-initio calculations) incorporate nuclear and/or electronic (but not only!) interactions between particles; simulations are based on the Schroedinger equation, including (and within) different approximations (e.g. Born-Oppenheimer) mostly using of the action principle of its classical equivalent (classical mechanics), i.e. path integral (or resembling partition function).

- Molecular dynamics methods are used to solve Newtonian equations of motion.

Since both the quantum methods and molecular dynamics methods can be adopted to model the fracture progress of materials, what's the difference between them besides the scale limitation of the former methods?

- Differences become essential namely from the scale limitation; i.e. it depends only on the volume (size), shape (boundary conditions) of corresponding simulation boxes (3-d structures, 2-d grids, 1-d chains or 0-d points).

All depends on the problems you must solve. For example for some phase transitions (e.g. magnetic) it is necessary to treat the system quantum mechanically (magnetism is quantum phenomenon and consequently it should be described by the rules of Quantum mechanics only!). For other transitions is needed to threat them classically (for example some temperature and/or pressure phase transitions in materials).

I hope you will read one (not so) new, (but) interesting and more clarified (open sourced) paper (for me; without more mathematical equations) about this question to make all the things simplified - https://www.google.bg/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwjS1c7hmqzXAhVFY1AKHW1UC2YQFggwMAE&url=https%3A%2F%2Farxiv.org%2Fpdf%2F1405.2831&usg=AOvVaw1G73hCJqejKspafzRK82mz

Enjoy it &

Regards.

Molecular dynamics refers to calculations in which one tries to obtain a statistical description of a system by using the ansatz that a sufficiently long time average will be equivalent to the ensemble average. An alternative approach would be to utilize Monte Carlo methods to build the ensemble average directly. Choosing between them is something of a matter of taste, although dynamics calculations have the appeal that you can watch things evolve. This may prejudice you to this approach if you want to see a fracture evolve in time.

The interactions between atoms in either approach are best described by a quantum Hamiltonian, albeit even the best quantum calculations are not capable of chemical precision. Unfortunately, such calculations scale like N^8, where N is the number of electrons, for the best calculations and like N^3 or so for DFT calculations that are not as precise but not terrible.

To study something like a fracture, you probably need thousands, if not millions, of atoms in your model. Such a model size is well beyond the capability of any computer on the horizon. An alternative is to develop an empirical interaction potential, what is known as a force field, that can be rapidly computed. This will typically include some bonding terms to enforce the static structures of your system, along with van der Waals and Coulombic potentials as part of the non-bonded, long-range interactions.

Such an approach provides the ability to treat very large systems, at the expense of having to find some way to calibrate your calculations against experiment.

The molecular mechanics formulation is a vast simplification and only an approximation. You have to work diligently to demonstrate that it is not simply nonsense computed (relatively) easily. At the heart of the mechanical fracture is the rupture of chemical bonds. You will need to verify through quantum calculations on small systems that your molecular mechanics parameters describe that process in a satisfactory manner. At that point, you may have some confidence that whatever you have inferred from the large calculations have some basis in fact.

I'm not sure what your ultimate objective is. All ab initio codes use atomic units, whereas most force fields do not. If all you want to do is study electrostatic interactions, then you may just need to perform the relevant unit conversions to compare the two. Recognize, though, that the force fields are obtained through a parameterization process that may not include the geometries that you are studying. Their "accuracy" can be dubious.

If what you are trying to accomplish is to study the relative binding affinity of different substrates, then you can actually obtain sensible answers through a free energy calculation using force fields. The PIEDA calculation may serve as a rough approximation for the quantum free energy difference.

It is easy to do calculations but one doesn't need a hammer to tighten a bolt. A wrench would be more appropriate. So, what do you really intend to accomplish?

Mark

Feng:

To construct a force field parameterization of the quantum calculations, you have to start with very simple constituents, constrained to interact in specific geometries. From what I observe from the file you supplied, the quantum optimization generated nonsense. You began with a peptide chain but the QM optimization pulled the chain into a pretzel. This is not uncommon with QM calculations. Unless you add constraints, the quantum calculations, which take place in a vacuum, will lead to unnatural conformations that do not occur when the molecules are solvated.

In the development of CHARMM force fields, with which I am most familiar, the two interacting small molecules would be individually optimized (not with PIEDA or FMO). These optimized structures would be allowed to interact along a single degree of freedom (distance or angle) and the structures themselves would not be allowed to change. These sorts of calculations are quite tedious. Because you are using small molecules, there is no need for FMO.

So, are you thinking of developing a coarse-grained type of model or one with all atoms present? When you say aggregation, are you just looking at how things clump together or are you thinking of forming peptide bonds? What experimental results are you seeking to describe? Answering these questions will guide your next steps.

Mark

Dear Mark A Cunningham,

Thank you very much! Yes, my first optimized stucture is optimized in gas phase. In the second structure geometry optimization calculation, I used the PCM solvent model, but I didn't add the cavitation energy, dispersion, repulsion energy calculation during geometry optmization. So I'm doing the geometry optimization for this peptide with the cavitation energy, dispersion, repulsion energy calculation again. Then I think this result maybe is reasonable.

For the calculation method, how about the EFMO method? In the geometry optimization by using the FMO, it takes me about 15 day by using 1 node 20 core. So does the HF method is faster than FMO and EFMO? And for our system, yes, the monomer is very small, but in the later we also want to calculate the dimer or trimer. Does in this situation, is the HF available for the dimer or trimer also?

We want to produce a all atom force field which can welly reveal the aggregation of peptide and protein, and we do not consider the situation of peptide bond formation. We want to describe the aggregation process of protein or peptides.

Best wishes,

Feng

All of the common force fields have parameterizations for the amino acids. These are very well characterized over a wide variety of studies. So, you can already build your short peptide sequence, put several (2 or 20000) of them in a solvent box and let them go. They will (very slowly) explore conformational space. It will be challenging to accumulate enough conformational sampling to make any comparison to experimental measurements. The problem of conformational sampling for large objects: protein-protein and even protein-substrate is very much an open problem. It will be slightly better if you are looking at short peptide sequences but the conformational space of two of your peptides is quite large.

So, I don't understand why you are trying to compare quantum calculations to force field results. As I mentioned, the force fields are built from small groups, like the carboxyl from acetic acid. There are way too many degrees of freedom to start from something like an eight-amino acid peptide. Individual amino acids like glutamic acid and aspartic acid were built up self-consistently from those initial acetic acid studies. There are a number of choices built into the development of parameters for each of the different force fields that enforce the self-consistency. You have to use the same development methodology for whichever one you choose.

Undertaking parameter development is a very large task. There are thousands of man-hours involved in such a project. So, how do you propose to improve the existing force field representation? They certainly have limitations but most improvements, like polarization and the like, require vast complications for little rewards. My own prejudice would be to use hybrid methods and only deal with quantum in regions where polarization or bond formation is critical. The existing force fields work pretty well for basic, structural studies. In which case you don't need quantum at all.

As far as trying to compute a quantum result for your peptides, FMO is probably faster than DFT but I don't think that it is helping you with the problem that you want to solve.

Mark

Dear Mark A Cunningham,

Thank you for your kindness explain. In our this step, we just want to use the FMO or EFMO method to find out weak points in the all-atom force fields, and then guide the tuning of their parameters to obtain a better representation of protein-protein and protein-water interactions. In this step we will also do the EFMO-MD or FMO-MD simulation to help us to find the weak point, which will be compared with the MD simulation of force field. So we made the PIEDA analysis. But when I compare the interaction energy of each two residues between the force field and QM calculation I'm confusing on the energy results, because it is very different. As show in my plot the energy from the QM calculation is quietly large than the energy from the force field. The unit of QM calculation is Kcal/mol, but in the force field it is KJ/mol. So I'm confusing the difference in the energy between two method. The 6 slide is the energy decomposition analysis of force field for the gas peptide.

Best wishes,

Feng

The interactions of proteins and peptides are through the electrostatic and van der Waals forces in the force field representation. Glaring defects are the lack of polarization effects and the lack of coordination in the spherical vdW potentials that are employed in most standard force fields. That is, nothing in the force field enforces octahedral coordination, say, of metal ions. Improving this in a modified force field is challenging and tends to be very specific to particular geometries and moieties. There are some attempts to treat polarization effects but I personally found them very messy to employ and had dubious improvements.

That said, there is a factor of 4 between kCal./mol and kJ/mol and it is likely that you are looking at total energies from the MM calculations. I believe the PIEDA calculation is reporting the non-bonded interactions only but you should investigate this more thoroughly. You can generally extract the non-bonded components of the energy from the MM results; how to do so depends upon your simulation package. Comparing the non-bonded terms, I think is the closest that you will get to what you want to do but I think that you will have to be cautious about conformational differences between your two calculations. Perhaps you can calculate the MM results using the QM structures, so that you are comparing apples to apples and not to some other fruit.

Good luck,

Mark

Dear Mark A Cunningham,

Thanks for all of your detailed explanation!

Best wishes,

Feng