23

Additional to Alone Programmer's answer. The Lennard-Jones Potential (LJ 12-6) is the standard, but is not unique, in some cases the factor of 6 is changed to 8 to simulate better the hydrogen bonds. Also, there is the Buckingham potential, where the repulsion part ($r^{12}$ term) is modified to the exponential term. But the attractive long-range term ($r^{...


20

You are looking for Lennard-Jones potential. Basically, the interatomic interaction is modeled by this formula: $$U(r) = 4 \epsilon \Bigg [ \Big ( \frac{\sigma}{r} \Big )^{12} - \Big ( \frac{\sigma}{r} \Big )^{6} \Bigg ]$$ Particularly the term $r^{-6}$ in the above formula describes long-range attraction force based on van der Waals theory. Update: I'll ...


19

First I will try to directly answer this question: In terms of energy, how are van der Waals forces modelled (are there formulas that govern these)? The most common way to model the potential energy between two ground state (S-state) atoms that are far apart, is by the London dispersion formula: $$V(r) = -\frac{C_6}{r^6}$$ where $C_6$ depends on the ...


16

You can calculate U in an ab initio way via linear response theory, for instance. See an example here. However, there is no guarantee that a linear response U value is empirically ideal. That is part of the reason why, in practice, many people invoke some empirical U term and hope that it holds reasonably well for their system (especially compared to U = 0 ...


16

This is a bit late, but I would say the short answer to your direct question is: technically no, there is no "standard" reliable way, since there are several approaches to determining U self-consistently from first principles. By self-consistently I mean a first-principles U is calculated, which when applied changes the electronic structure, so a new U is ...


14

The answer is based on Chapter 1 - The DFT+U: Approaches, Accuracy, and Applications from the book Density Functional Calculations: Recent Progresses of Theory and Application For practical implementation of DFT+U, the strength of the on-site interactions is described by a couple of parameters: the on-site Coulomb term U and the site exchange term J. These ...


14

The quadratic potential is the simplest possible model for a bond. You can derive it by considering the Taylor expansion of the potential around the natural bond length $V(r - r_0) = V(r_0) + \frac{d V(r_0)}{d r} (r - r_0) + \frac{1}{2} \frac{d^2 V}{dr^2} (r - r_0)^2$ The constant term can be set to 0 since it does not contribute to the force and just sets ...


13

The short answer is that, while hydrogen bonds do have some covalent character, you can mimic that covalent character by increasing the electrostatic term. For example you can specify point charges to the oxygen and hydrogen atoms that are larger than they would otherwise be, and the overestimated electrostatic attraction will compensate for the neglect of ...


13

I would like to start off by saying this is first and foremost a thermodynamic problem. Secondly, and as a result of thermodynamics, refer to Gibbs Phase Rule which says \begin{equation} F = C - P + 2 \end{equation} Where F = degrees of freedom, C = number of components, and P = number of phases. You seem to be after a pure liquid so $C=1$, and, you are ...


11

Very short answer: No, classical molecular dynamics cannot break bonds. The potential you showed is the most common form of bond, the harmonic potential a.k.a. Hookes law. If you have ever broken a bond in QM (calculated a dissociation curve), you know it is a bit tricky, you need to use "unrestricted" settings, meaning, that a given pair of electrons does ...


10

I have looked for a similar set of benchmarks and haven't found one, unfortunately. Hopefully the data referred to in the comments comes through! In the meantime, I have an MIT-licensed implementation of the Wolf-like alternative to Ewald that @PhilHasnip linked to. Here is the repository. Forces and stresses are available. You could try benchmarking against ...


9

The current biomolecular force fields that I'm familiar with don't include any special energy terms for hydrogen bonds. Typically, hydrogen atoms that are capable of hydrogen bonding have very small Lennard-Jones radii and significant positive charges, which allow for very strong electrostatic interactions. For example, in the CHARMM force field, the alcohol ...


9

2007 (Becke & Johnson): XDM XDM stands for "exchange-hole dipole moment" which is a model introduced by Becke and Johnson in 2007 for calculating dispersion constants. The formulas are as follows: $$\begin{align} \!\!\!\!\!\!\!\!C_6 &= \frac{\alpha_i\alpha_j}{\mathcal{M}_i\alpha_j + \mathcal{M}_j\alpha_i} \mathcal{M}_i\mathcal{M}_j ...


9

They are included in long range type functionals. Here are some references: S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem. 27 (2006) 1787. M. Dion, H. Rydberg, E. Schroder, D. Langreth, B. Lundqvist, Van der Waals density functional for general geometries, Phys. Rev. Lett. 92 (2004) ...


8

Changing the force field parameters is not a good/recommended approach. This is due to the high number of parameters you have to know. Many of them, you cannot obtain from experimental data. Instead, you will need high precision methods like Density Functional Theory, Hartree-Fock, pos Hartree-Fock or semi-empirical methods to calculate them for two, three ...


7

Since you are referring to "the Morse potential", I assume you mean to use it for modeling van der Waals interactions? If not, please ignore this answer and consider updating your question to include what kind of potential you are modeling using the Morse potential. If so, here is my answer: There is a rule of thumb based on experience and a lot of ...


7

If you call wfn.compute_hessian(), Psi4 tries to compute the nuclear Hessian which is indeed not implemented for most methods. Calling np.gradient is not advisable, as it merely computes finite-difference approximations of derivatives instead of the true derivative. This is especially going to be a problem for cube files, since the resolution is poor from ...


7

Not a full answer of an alternative program, but just collecting the conclusions from the comments along with some additional suggestions. It appears that compute_gradient and compute_hessian aren't implemented yet for wavefunction objects in Psi4. Even still, what you are interested in is the density and its gradient/hessian rather than those of the ...


6

I think the effect of larger cutoffs will not affect your simulation. Shorter cutoffs will be more problematic and can see artifacts than the larger cutoffs. Even if you have larger cutoffs, the interaction strength will be very very weak as you go outward and eventually die. This will just increase your computational cost (neighbour list calculation) and ...


6

To the best of my knowledge, there is no universal or even near-universal heuristic for what the time constant should be. The only rule of thumb I have encountered is that the time constant should be around 10x-1000x larger than the timestep of the simulation. Beyond that point, I would treat the damping constant as a hyperparameter, do a sensitivity ...


5

2009 (Tkatchenko−Scheffler) TS The Tkatchenko−Scheffler model for van der Waals interactions (vdW) defines the $C_6^{AB}$ parameters in an ab-initio fashion. In TS model the vdW energy $E_{vdw}$ is defined as, \begin{equation} E_{\text{vdW}} = -\frac{1}{2}\sum_{A,B}f_{\text{damp}}\left(R_{AB},R^{0}_{A},R^{0}_{B}\right)C_{6}^{AB}R^{-6}_{AB} \tag{1} \end{...


4

You can do something with Lennard-Jones potentials instead of harmonic ones. I know this has been done for Coarse-Grained MD simulations using Go-Martini models as in https://pubs.acs.org/doi/abs/10.1021/acs.jctc.6b00986 Now this needs more testing, I have done some force-probe simulations with it but nothing too serious.


4

Following Tyberius's suggestion, I now turn my comment into an answer. As always, the most reliable way of estimating the effect of the dispersion correction is to actually do two simulations, one with the correction and one without it. But since a liquid simulation is expensive, it's better to test the effect of the correction on a simpler system that is ...


3

In short, the polarization catastrophe is the fact that the classical description of polarization applied to point dipoles contains a singularity which occurs at a distance which should regularly be sampled in the course of ordinary classical dynamics. More specifically, the polarization catastrophe is the failure that happens when one tries to describe the ...


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