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 ...


13

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 ...


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 ...


12

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 ...


10

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

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 ...


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 ...


8

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) ...


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 ...


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

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 ...


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.


3

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 ...


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