**From:** Otello Maria Roscioni (*otellomaria.roscioni_at_unibo.it*)

**Date:** Mon Oct 26 2015 - 12:29:02 CDT

**Next message:**Jessen Lucas: "Re: replica exchange module"**Previous message:**Kostas Malavazos: "Lennard-Jones and Electrostatic Forces and Energies"**In reply to:**Zhe Wu: "Re: Dielectric constant of water from MSM and PME simulations"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Dear Zhe, dear Axel,

it is very stimulating to receive such a detailed feedback on our

simulations and to discuss them with you.

First of all, I thank Axel for sharing his extensive benchmark of water

properties. Probably the different dielectric constants of bulk water

are a convergence issue. We will extend the production time by 60 ns for

both PME and MSM simulations, which hopefully should yield consistent

results.

Regarding the simulation of a thin-film of water, we wanted first to

exclude that we were doing no obvious mistakes with the simulation

set-up, since it was the first time we used the MSM method. If this is

not the case, we will proceed as follows.

As Zhu suggested, we will simulate a slab of water with MSM plus 3D

boundary conditions. For the sake of simplicity, we will consider from

now on a free-standing film of TIP3P-EW water with two harmonic

potential walls at around 2 nm from the water-vacuum interfaces.

We will also simulate the same system with the PME and MSM-2D methods.

For what concerns the calculation of the dielectric constant, it could

well be that the classic formula for tin-foil boundary conditions does

not hold in the MSM-2D scenario. In this case, I hope the simulations of

the free-standing films with the PME, MSM-2D and MSM-3D methods to

provide some hints.

Meanwhile, we can implement the calculation of the dielectric constant

using the formula 26.3.3D from Prof. Neumann paper for the case where

eps_RF = eps.

Talk back to you soon.

Best wishes,

Otello

On 23/10/15 17:46, Zhe Wu wrote:

*> Hi Mattia,
*

*>
*

*> Just want to put a different issue in a separate email.
*

*>
*

*> Since the eps_RF = infinite may not hold in a 2D system, one could
*

*> calculate dielectric constant in a more straight forward way: calculate
*

*> a PMF, the long-ranged part, of two charged particles in your 2D water
*

*> system. Please find details for such a calculation in my previous paper,
*

*> page 10528 (last paragraph).
*

*> http://pubs.acs.org/doi/abs/10.1021/jp1019763
*

*>
*

*> But I do encourage you to take a look at the dipole fluctuation formula
*

*> for dielectric constant calculation or even derive it. I am not sure
*

*> whether it is difficult to derive but it is not on the top of my head at
*

*> the moment. I somewhat recall that Charles Brooks might have derived the
*

*> formula in his 2D-PME papers.
*

*>
*

*> Please keep us updated. It is a very interesting project and I am very
*

*> eager to learn more!
*

*>
*

*> Best,
*

*> Zhe
*

*>
*

*> Zhe Wu
*

*> Klaus Schulten's Group,
*

*> Postdoc Fellow in NSF's Center for the Physics of Living Cells,
*

*> University of Illinois Urbana-Champaign
*

*> Beckman Institute, RM 3125,
*

*> 405 N. Mathews Ave. Urbana, IL 61820
*

*> Office: 217-224-3160
*

*> http://www.ks.uiuc.edu/~zhewu/
*

*>
*

*>> On Oct 23, 2015, at 10:31 AM, Zhe Wu <zephyrbless_at_gmail.com
*

*>> <mailto:zephyrbless_at_gmail.com>> wrote:
*

*>>
*

*>> Hi Mattia and Axel,
*

*>>
*

*>> Thanks for the following up. Thanks Axel for the help! I went through
*

*>> your slides and I really appreciate the very systematic benchmark.
*

*>> Nice work.
*

*>>
*

*>> Letâ~@~Ys first focus on Mattiaâ~@~Ys first calculation with fully periodic
*

*>> boundary condition. I think the eps_RF = infinite should hold for MSM
*

*>> with FULLY periodic boundary (3D-MSM). So for Mattiaâ~@~Ys first
*

*>> simulation, the 3D-MSM result should agree with the PME one.
*

*>>
*

*>> The dielectric constant in our JCTC paper was calculated for TIP3P
*

*>> water in CHARMM. There is no question that the dielectric constant of
*

*>> TIP3P-CHARMM is different from the one of TIP3P-EW. In the original
*

*>> TIP3P-EW paper, the different results were shown.
*

*>>
*

*>> As Axel suggests, the different results with Mattiaâ~@~Ys TIP3P-EW
*

*>> simulations could be just a convergence issue. The reported value of
*

*>> 89 should be converged with the simulation time reported.
*

*>>
*

*>> Regarding to Mattiaâ~@~Ys second simulation with 2D periodic boundary, I
*

*>> am not sure whether the assumption of eps_RF = infinite still holds. I
*

*>> think Axel could be right and that could be the reason why the
*

*>> dielectric constant calculated with 2D-MSM is so large. Could Mattia
*

*>> try to perform a new MSM simulation with FULLY periodic boundary
*

*>> condition just like the PME one and see what is going on?
*

*>>
*

*>> My comments regarding water structure is related to the calculated 258
*

*>> dielectric constant. I think with 258 dielectric constant, a water
*

*>> molecule could only sense the waters very nearby and thus the water
*

*>> structure could be perturbed. It is effectively the same as performing
*

*>> a water simulation with parameter of eps = 3 instead of eps = 1.
*

*>> Mattiaâ~@~Ys g(r) shows a good water structure, which means the water
*

*>> dielectric constant should not that large. The large value could be a
*

*>> result of the dielectric constant calculation only.
*

*>>
*

*>> Best,
*

*>> Zhe
*

*>>
*

*>>
*

*>> Zhe Wu
*

*>> Klaus Schulten's Group,
*

*>> Postdoc Fellow in NSF's Center for the Physics of Living Cells,
*

*>> University of Illinois Urbana-Champaign
*

*>> Beckman Institute, RM 3125,
*

*>> 405 N. Mathews Ave. Urbana, IL 61820
*

*>> Office: 217-224-3160
*

*>> http://www.ks.uiuc.edu/~zhewu/
*

*>>
*

*>>> On Oct 23, 2015, at 9:47 AM, Axel Kohlmeyer <akohlmey_at_gmail.com
*

*>>> <mailto:akohlmey_at_gmail.com>> wrote:
*

*>>>
*

*>>>
*

*>>>
*

*>>> On Fri, Oct 23, 2015 at 9:57 AM, Mattia Felice Palermo
*

*>>> <mattiafelice.palerm2_at_unibo.it
*

*>>> <mailto:mattiafelice.palerm2_at_unibo.it>> wrote:
*

*>>>
*

*>>> Dear Zhe,
*

*>>>
*

*>>> thank you very much for your accurate answer.
*

*>>>
*

*>>> > Could you specify how you calculate the dielectric constant?
*

*>>>
*

*>>> It has been computed with a inhouse program using the classical
*

*>>> expression for the dielectric constant from the average dipole moment
*

*>>> <M^2> as in your JCTC paper.
*

*>>>
*

*>>> > The dielectric constant of TIP3P-EW water is 89 (D. J. Price, C. L.
*

*>>> > Brooks, J. Chem. Phys. 2004, 121, 10096), while you are getting
*

*>>> 96.8
*

*>>> > with PME and 83.3 with MSM. You can find the way we calculated the
*

*>>> > dielectric constant on page 773 of our JCTC paper.
*

*>>>
*

*>>> We suspect that the higher value found in our simulation with PME
*

*>>> might
*

*>>> be related to the size of the sample (N=1000 in the TIP3P-EW original
*

*>>> paper against N=11000 in our simulations). However the value is
*

*>>> not far
*

*>>> from the literature value of 89 (TIP3P-EW, model B) and from the
*

*>>> value of 104 reported in your JCTC paper. We also checked other
*

*>>> properties e.g. the oxygen-oxygen radial distribution function and
*

*>>> the average module of the molecular dipole moment, and they are in
*

*>>> agreement with the expected results for the model.
*

*>>>
*

*>>>
*

*>>> â~@~Kdear mattia,
*

*>>>
*

*>>> some comments on this subject. it has been a long time, since i
*

*>>> worked on dielectric properties of water as a graduate student and
*

*>>> later got a chance to do some follow-up work in my spare time.
*

*>>> for your reference, please have a look at pages 18-21 of
*

*>>> http://klein-group.icms.temple.edu/akohlmey/files/talk-trieste2004-water.pdf
*

*>>>
*

*>>> â~@~Kthe following points matter for computing the static dielectric
*

*>>> constant from dipolar fluctuations (NOTE: not the average but the
*

*>>> fluctuations) :
*

*>>> - â~@~Kit is a *local* property. system size has very little to no
*

*>>> impact. when you sit down derive the expression of the fluctuation
*

*>>> formula, you will quickly see that the number of molecules will
*

*>>> cancel out.
*

*>>> - it is a *slowly* converging property. most published data is simply
*

*>>> not fully converged.
*

*>>> - it is of monumental importance to use the correct fluctuation
*

*>>> formula. most likely you have used the one for ewald summation with
*

*>>> conducting boundary condition. in that case what you are simulating
*

*>>> is effectively an infinitely large sphere assembled from rectangular
*

*>>> unit cells embedded in a conducting dielectric (epsilon = infinity).
*

*>>> i seriously doubt that this is applicable to MSM. it would be more
*

*>>> likely, that you need to derive the fluctuation formula for a
*

*>>> situation where epsilon is equal to the computed epsilon. but don't
*

*>>> take my word for it. these issues are extremely subtle and i had to
*

*>>> twist my brain quite hard for months to finally get a grip on it and
*

*>>> come up with consistent and convincing explanations for the
*

*>>> observations from my simulations.
*

*>>>
*

*>>> on the notion of g(r) being reproduced. that means *nothing*. you
*

*>>> need to get them right, too. but with the same g(r) you can have very
*

*>>> different total system dipole fluctuations. the conducting boundary
*

*>>> conditions of commonly used ewald summation (and equivalent) actually
*

*>>> enhances fluctuations. if you switch to a vacuum embedding (epsilon =
*

*>>> 0), then those total dipole fluctuations are strongly suppressed, yet
*

*>>> you can't tell a difference from the g(r), as the average structure
*

*>>> is practically unaffected (you are looking at the second moment,
*

*>>> after all, and the average cancels out).
*

*>>>
*

*>>>
*

*>>> > It is very surprising to see a dielectric constant of water to be
*

*>>> > 258. How is the water structure? With such a large dielectric
*

*>>> > constant, the water structure should be very unphysical.
*

*>>>
*

*>>> The first surprising fact is that the dielectric constant of bulk
*

*>>> water differs if the MD simulations is carried out with PME and MSM
*

*>>> methods. The dielectric constant of water with value 258 was obtained
*

*>>> for a thin film of water supported on silicon dioxide and using the
*

*>>> MSM method, while when using the PME method we obtain a
*

*>>> dielectric constant
*

*>>> of 91.5. Visual inspection of the samples through VMD did not
*

*>>> show any
*

*>>> unphysical structure of the water. We also computed the oxygen-oxygen
*

*>>> radial distribution g(r)_O-O for the films, which you can find
*

*>>> attached, and
*

*>>> it does not show any significant difference between the two
*

*>>> simulations.
*

*>>>
*

*>>>
*

*>>> based on my observations outlined above, â~@~Ki am not surprisedâ~@~K. and
*

*>>> more importantly, you cannot easily transfer the method to other
*

*>>> simulation environments. you will need to derive the proper
*

*>>> fluctuation formula for such a situation as well..
*

*>>>
*

*>>> axel.
*

*>>>
*

*>>>
*

*>>> > Also, could you give us a little bit more details about your VDW
*

*>>> > cutoff scheme? As reported in TIP3P-EWâ~@~Ys original paper, a model
*

*>>> > that incorporates a long-range correction for truncated VDW will
*

*>>> > give a dielectric constant of 76 instead of 89. Are you using the
*

*>>> > same cutoff scheme for both PME and MSM?
*

*>>>
*

*>>> Yes we used the same cutoff scheme for both simulations. More in
*

*>>> detail,
*

*>>> these are the settings for the MSM simulations:
*

*>>>
*

*>>> cutoff 12.0
*

*>>> switching on
*

*>>> switchdist 10.0
*

*>>> pairlistdist 14.0
*

*>>>
*

*>>> timestep 2.0
*

*>>> nonbondedFreq 1
*

*>>> fullElectFrequency 2
*

*>>> stepspercycle 10
*

*>>>
*

*>>> langevin on
*

*>>> langevinDamping 1
*

*>>> langevinTemp 298.15
*

*>>>
*

*>>> LangevinPiston on
*

*>>> LangevinPistonTarget 1.01325
*

*>>> LangevinPistonPeriod 250
*

*>>> LangevinPistonDecay 100
*

*>>> LangevinPistonTemp 298.15
*

*>>>
*

*>>> cellBasisVector1 63.340 0.0 0.0
*

*>>> cellBasisVector2 0.0 63.340 0.0
*

*>>> cellBasisVector3 0.0 0.0 63.340
*

*>>>
*

*>>> rigidBonds all
*

*>>>
*

*>>> MSM yes
*

*>>>
*

*>>> The same setting were used for the PME simulations, except of
*

*>>> course for
*

*>>> the calculation of electrostatics:
*

*>>>
*

*>>> PME yes
*

*>>> PMEGridSpacing 1.5
*

*>>>
*

*>>> Thank you very much for your help!
*

*>>>
*

*>>> P.s.: I changed the subject of this email to have all future
*

*>>> contributions sorted in the same thread. Sorry for the confusion!
*

*>>>
*

*>>> --
*

*>>> Mattia Felice Palermo - Ph.D.
*

*>>> UniversitÃ di Bologna
*

*>>> Dipartimento di Chimica Industriale "Toso Montanari"
*

*>>>
*

*>>>
*

*>>>
*

*>>> --
*

*>>> Dr. Axel Kohlmeyer akohlmey_at_gmail.com <mailto:akohlmey_at_gmail.com>
*

*>>> http://goo.gl/1wk0
*

*>>> College of Science & Technology, Temple University, Philadelphia PA, USA
*

*>>> International Centre for Theoretical Physics, Trieste. Italy.
*

*>>
*

*>
*

-- Otello M. Roscioni, PhD Dipartimento di Chimica Industriale "Toso Montanari" UniversitÃ di Bologna Viale Risorgimento 4 40136 Bologna, Italy

**Next message:**Jessen Lucas: "Re: replica exchange module"**Previous message:**Kostas Malavazos: "Lennard-Jones and Electrostatic Forces and Energies"**In reply to:**Zhe Wu: "Re: Dielectric constant of water from MSM and PME simulations"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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