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<body class='hmmessage'><div style="text-align: left;">Hi,<br><br>A test case like with two atoms is an unrealistic system.<br>For two atoms one could use a cut-off of half the box length and accurate Ewald summation<br>and gets things right. But you get things right for a periodic replication of two atoms<br>which is never a realistic system.<br><br>For many realistic systems the LJ error might be more problematic than the Coulomb error.<br>All LJ forces beyond the cut-off are attractive and therefore you miss a large amount<br>of attractive energy in a condensed system.<br><br>The Coulomb forces on the other hand will have an inaccuracy on the order of 1 kJ/mol nm,<br>but these are local inaccuracies. The potential will not deviate systematically, but fluctuate<br>around the correct value when looking across the whole box volume. Moreover, the Coulomb<br>forces will have differing signs, meaning that for a condensed system there will be some<br>cancellation of errors.<br><br>What accuracy you need for the Coulomb forces can differ strongly depending on the system<br>and the questions you are asking. Point charges in bio-molecular force fields are just approximations<br>and the error of the approximation is much higher that the force error.<br>The real question to answer is if for the particular property you are interested in<br>a certain PME force error would give you a systematic deviation in that property.<br></div><br>Berk.<br><br><br><hr id="EC_stopSpelling">Date: Mon, 7 Jul 2008 23:25:37 -0400<br>From: nicklefan@gmail.com<br>To: gmx-users@gromacs.org<br>Subject: [gmx-users] Accuracy of force calculation and doubts on PME parameter choice<br><br><div>Dear all:</div>
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<div>In most studies, we focus on the accuracy of potential energy. How about the force? Consider two systems:</div>
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<div>1. Two LJ particles (sigma=0.33nm, epsilon=0.625kJ/mol): If the force is cutoff at 2.5*sigma, so the maximum error in force is at the cutoff length and equal to ~0.08 kJ/mol nm.</div>
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<div>2. Two point charges in a 3*3*3.3nm box (charge separation: 0.5 nm, q1=e, q2=-e): I tried the following calculations:</div>
<div>a. Ewald summation, rcutoff=1.0nm, ewald_tol=1e-5, FFT_spacing=0.1nm: This produces: f1=-f2=542.2 kJ/mol nm;</div>
<div>b. PME, rcutoff=1.0 nm, ewald_tol=1e-5; 4th order, FFT_spacing=0.1nm, this produces: f1=-f2=543.9 kJ/mol nm;</div>
<div>c. PME, rcutoff=1.0 nm, ewald_tol=1e-5; 4th order, FFT_spacing=0.11nm, this produces: f1=543.97 kJ/mol nm, f2=-544.96 kJ/mol nm;</div>
<div>d. PME, rcutoff=1.0 nm, ewald_tol=1e-5; 4th order, FFT_spacing=0.12nm, this produces: f1=543.43 kJ/mol nm, f2=-545.49 kJ/mol nm;</div>
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<div>Clearly, for LJ particles, the maximum accuracy is ~0.08kJ/mol nm - which sounds small. But for electrostatics, the error is quite large: if we take the Ewald results to be the exact solution, then for choice d (which seems to be a popular choice among gmx-users), the error amounts to be ~ 2.0 kJ/mol nm. Is this error acceptable?</div>
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<div>Thanks for your time.</div>
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<div>Nick</div>
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