From: JC Gumbart (gumbart_at_ks.uiuc.edu)
Date: Sat Sep 13 2014 - 18:38:44 CDT
Hi Sebastian!
This is a very complex issue in general. Your interpretation of the original Hummer formula is incorrect. I quote from the paper preceding Eq. 11:
> This results in an expression for the energy difference ∆u between two configurations with different charge states q0 and q1 of an ion at position r,
Note that it references the charge state OF THE ION, not of the box as a whole. The correction comes from accounting for the interaction of the ion with its own images as well as with the neutralizing plasma (I’ve seen it called “gellium”). This gellium effectively enforces a neutrality condition, meaning that even if you *think* you set your system to be non-neutral, it is in fact always neutral. Gellium is uniform and contributes nothing to the forces, but it does shift the reference electric potential.
Here are a couple papers that might help clarify things (or confuse you more ;)
http://pubs.acs.org/doi/abs/10.1021/jp970882x
http://pubs.acs.org/doi/abs/10.1021/ct500195p
JC
On Sep 12, 2014, at 2:21 PM, Sebastian Stolzenberg <ss629_at_cornell.edu> wrote:
> Dear All,
>
> I think I found a possible answer to my question, but would highly appreciate
>
> , if somebody could explain this to me:
>
> For practicality, I re-did the computations just for the annihiliation of Na (i.e. without an extra water appearing):
>
>
> Na2_to_vac dG_FEP correction corr. dG_FEP whatif
> boxsize_67__q0=0_q1=-1 82.2 -7.0 75.2 89.2
> boxsize_67_q0=1_q1=0 82.5 7.0 89.5 89.5
> boxsize_128_q0=0_q1=-1 85.8 -3.7 82.1 89.5
> Boxsize_128_q0=1_q1=0 85.8 3.7 89.5 89.5
> all values are in kcal/mol.
>
> In the "whatif" column in
> boxsize_67__q0=0_q1=-1
> and
> boxsize_67__q0=0_q1=-1,
> I simply *added* instead of subtracted the corrections, and ended up with the same free energy values for different FEP experiments and different box sizes.
>
> Thank you, Best,
> Sebastian
>
>
> On 07.09.2014 17:23, Sebastian Stolzenberg wrote:
>> Dear All,
>>
>> let me give you some free energy difference values (in kcal/mol) for the email below:
>>
>> FEP experiment 1 (L=67A):
>> 75.96 (reverse run gives -75.50)
>> cr=-7.03
>>
>> FEP experiment 2 (L=67A):
>> 76.03 (reverse run gives -75.88)
>> cr=7.03
>>
>> I also did the same FEP runs just for the annihilation of Na2 (i.e. without an H2O appearing) and get the same odd result.
>>
>> Can anybody tell me what I am conceptionally missing here?
>>
>> Much appreciation,
>> Sebastian
>>
>>
>> Am 02.09.14 um 22:12 schrieb Sebastian Stolzenberg:
>>> Dear All,
>>>
>>> I stumbled over the following consistency check to see, whether I fully understand the size-dependent charge correction derived in
>>> Hummer, G.; Pratt, L. R.; Garcia, A. E. J. Phys. Chem. 1996, 100, 1206–1215,
>>> for FEP/TI with Ewald summation;
>>> this correction I denote here as cr=0.5*ξ*(q12-q02), where q0 and q1 are the total charges of the simulated system in the reference and target state, respectively, ξ=−2.837/L, and L is the length of the cubic simulation box.
>>>
>>> Given:
>>> - cubic water box with length L=67A (or 128A) with 0.15mM NaCl, neutral net charge
>>> - standard CHARMM36 ff, NPT, PME, NAMD 2.9
>>>
>>> FEP experiment 1:
>>> annihilate an Na ion, and let appear a water molecule
>>> (the Na and OH2 atoms are harmonically restrained to the same {x y z} position)
>>> => q0=0, q1=-1
>>> => cr<0
>>>
>>> FEP experiment 2:
>>> prior to FEP, delete a CL ion in the box, then
>>> annihilate an Na ion, and let appear a water molecule
>>> (the Na and OH2 atoms are harmonically restrained to the same {x y z} position
>>> => q0=+1, q1=0
>>> => cr>0
>>>
>>> I understand that the corrected free energy difference DG_cr is obtained from the computed DG (e.g. via NAMD FEP) via:
>>> DG_cr=DG+cr
>>> I am confused because in my FEP simulations, DG is nearly identical for both FEP experiments stated above (to the second digit). Therefore, I would receive different values of DG_cr for the same alchemical transformation (Na to water).
>>>
>>> Is there something I missed along the lines?
>>>
>>> With Thanks and Best Regards,
>>> Sebastian
>>>
>>
>
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