User Specified non-bonded potentials in gromacs

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1 Use Specified non-bonded potentials in gomacs Apil 8, Intoduction On fist appeaances gomacs, unlike MD codes like LAMMPS o DL POLY, appeas to have vey little flexibility with egads to the fom of the intemolecula inteactions as one must eithe choose a Lennad Jones 12-6 potential o a Buckingham inteaction in the [ defaults ] section of the topology file, which will subsequently be used thoughout. Thee is, o so it would seem, no option to define a wacky non-bonded inteaction o to have cetain pais of atom inteacting though a buckingham tem, while the emaining atoms inteact though Lennad-Jones. Thankfully howeve both these options exist although the documentation on how pecisely this should be done is split up in the manual. In the following theefoe we will bing all this infomation togethe into a single document. Fistly though a wod of caution. Obviously Buckingham and Lennad Jones inteactions ae vey standad desciptions fo the non-bonded tems in atoms. Hence, unless you have a specific eason to believe that you special functional fom is equied it is often best to stay with these tied and tusted functions. In addition, although a mixtue of Buckingham and Lennad-Jones tems povides a pefectly easonable desciption of the essential physics, you ente a wold whee thee ae no longe any convenient mixing ules fo the inte atomic foces. As a diect consequence thee ae going to be many moe tems that must be fitted in the potential. In shot don t do the following unless you ae confident that you have a sensible potential and a easonable way fo obtaining the coss tems. 1

2 These caveats aside a few wods on non-bonded potentials so as to define some tems. The inte molecula inteactions between atoms can be split into thee pats the electostatic inteaction, the dispesion inteaction and the shot ange epulsion. With this in mind we can wite the two body potential as: V () = q iq j 4πɛ 0 f() + Cg() + Ah() (1) whee the fist second and thid tems ae fom the electostatics, the dispesion and the shot ange epulsion espectively. The f(), g() and h() ae then use defined functions, while A, C and the chages ae the paametes of these functions. Fo the Lennad-Jones inteaction these functions ae: f() = 1 g() = 1 6 g() = 1 12 (2) while fo Buckingham f() and g() ae the same but h() = Ae B, whee B is an additional paamete. Gomacs, unless explicitly told othewise (see section 3), will use the same f(), g() and h() fo all the inte atomic inteactions in the system. One then specifies the paametes (A, C and B) in the topology file and by changing these paametes you can eflect the diffeences in the inteactions between diffeent atomic types. The fom of the inteaction is specified in the [ defaults ] section of the topoology file as follows: [ defaults ] ; nbfunc comb-ule gen-pais fudgelj fudgeqq 1 1 yes Hee only the fist two paametes in this line need concen us. By specifying 1 fo the fist we tell gomacs that we ae using Lennad-Jones inteactions athe than Buckingham tems (2=Buckingham). As a consequence gomacs assumes that two paametes ae equied fo each of the non-bonded inteactions (A and C in equation 1) 1. The second tem tells gomacs what mixing ules should be used and by extension how the paametes in the file should be intepeted. A 1 indicates that gomacs will intepet the paametes in C 1 Obviously if we eplace the 1 hee by a 2 gomacs will expect us to povide A, B and 2

3 the topology file as C and A diectly. 2 and 3 mean that we ae poviding the paametes fo ou Lennad Jones inteactions in epsilon-sigma fom: V () = 4ɛ [ (σ )12 ( σ ) 6 ] We thus poviding the ɛ and σ in the topology file fom which gomacs will calculate A and C using: A = 4ɛσ 12 C = 4ɛσ 6 (4) If you specify you own potentials these paametes must be both set equal to 1. 2 Changing the fom of the global inteaction We now descibe how to use tables to change the functions f(), g() and h() that gomacs uses to calculate inte-atomic inteactions. Fist we will examine how to change the global f(), g() and h() and show an example in which all the atoms inteact though a 9-6 inteaction fo which f(), g() and h() ae equal to: (3) f() = 1 g() = 1 6 g() = 1 9 (5) The mdp file in this file we must tell gomacs that it must ead in a table to get f(), g() and h(). This is a matte of simply including the following commands: vdw-type = use coulombtype = use What is moe the second of these is only equied if we wish to change f(). In the example we ae discussing we don t so we only need the fist command 2 The xvg/table file having told gomacs that it must ead in a table containing f(), g() and h() we must now povide the table. This file 2 We must still specify one of the othe options fo coulombtype - these othe options ae beyond the scope of this document howeve. 3

4 must contain the values of f(), g(), h() and thei deivatives at a seies of values of. Gomacs will then use the cubic splines pocedue descibed in section 6.7 of the manual to calculate the values of the functions fo any value of that occus duing the simulation. This file must be geneated by the use. Each line consists of the values of the vaious functions fo a paticula and consists of seven columns containing, f(), f (), g(), g (), h() and h () 3. You table must contain must go fom = 0 to = c + 1, whee c is the lagest cutoff distance specified in the mdp file. In addition, it is ecommended that the spacing between the adjacent s in you table should equal nm o nm fo the single and double pecision vesions of gomacs espectively. Some example tables can be found in shae/gomacs/top. Fo ou 9-6 inteaction example ou table could be geneated using the following shot fotan code: pogam gen table implicit none eal, paamete :: del=0.002, cut=1.0 eal :: intege :: nbins, j nbins=int( (cut+1)/del ) + 1 do j=0,nbins =del*j 10 wite(6,*), 1/, 1/(*), 1/(**6), 6/(**7), 1/(**9), 9/(**10) end do end pogam Cae must be taken fo = 0 as the code above would obviously poduce infinity o not a numbe fo this case. To esolve this include an if condition that outputs a value of zeo fo f(), f (), g(), g (), h() and h () fo vey small. This will have no effect on the dynamics as no atoms will eve be this close. Finally, note that we have povided meaningful data fo f() and f () despite the fact that we ae not using coulombtype=use. This is equied as gomacs will complain othewise. 3 Accoding to the manual the spline pocedue is diffeent in gomacs 3 and so you table must contain, f(), f (), g(), g (), h() and h () 4

5 The topology file the only emaining job equied is to povide the A and C paametes fo you potential. These must must be placed in the topology file. Fist, howeve ensue that you have set both nbfunc and comb-ule equal to one as descibed in the intoduction. The paametes fo inteactions between atoms of the same type ae then set in the [ atomtypes ] section, which comes immediately afte the defaults section: [ atomtypes ] ; name bond type mass chage ptype C A Na Na A 1.0e e-06 Cl Cl A 2.0e e-06 As fo the coss tems, unless you have specific eason to believe that gomacs will mix the tems coectly using mixing ule 1, you must povide these explicitly in the [ nonbond paams ] section immediately afte the [ atomtypes ] section as follows: [ nonbond paams ] ; i j func C A Na Cl E E-06 Please note that the paametes given above ae complete guff and should not be used in any simulation of sodium chloide. Running a calculation To un the above you then geneate the binay input file using gompp in the nomal way and then un mdun with the -table flag as below: gompp -f md.mdp - p topol.top -c conf.go mdun -table table.xvg When executed gomacs will look in the active diectoy and in shae/gomacs/top fo the xvg file specified afte the table flag. N.B. If thee ae 1-4 pai inteactions in you molecule you must also sepaately specify which table is to be used to calculate them by using the -tablep extension. The fudgelj facto specified in the [ defaults ] section of you topology file is still taken into account in the calculation of these tems. As such unless the fom of the f(), g() and h() functions is diffeent fo the pai inteactions you may un using the following: gompp -f md.mdp - p topol.top -c conf.go mdun -table table.xvg -tablep table.xvg 5

6 3 Specifying the fom fo a paticula inteaction In the pevious section we have seen how to change globally the f(), g() and h() functions. Howeve, what if one simply wants to have a paticula pai of atom types inteacting with diffeent f(), g() and h() functions. Fo example imagine we have sodium chloide in which the Na Na and Cl Cl inteactions ae given by buckingham tems while the Na Cl inteaction has a Lennad Jones fom. Gomacs is able to use tables to esolve this poblem as well. The mdp file Much like in the pevious section we must fist tell gomacs that it will be using a use-defined, tabulated potential using the following flags: vdw-type = use coulombtype = use In addition though we ae also equied to define which f(), g() and h() functions ae to be used fo the vaious inteactions. This is done using the following lines: enegygps = Na Cl enegygp table = Na Na Cl Cl The fist of these tells gomacs that it must deal with the enegies of all the atoms in the enegy goups Na and Cl sepaately - we will etun to this momentaily. The second line meanwhile tells gomacs that it must ead in specific table files in ode to get the f(), g() and h() functions fo the Na Na and Cl Cl inteactions. The emaining inteactions ( the Na Cl in this case ) should be then be calculated using the default table file. If this default table file is called table.xvg then the table containing the Na Na inteactions will be called table Na Na.xvg while the table containing the Cl Cl inteactions will be called table Cl Cl.xvg. The table files Fo ou sodium chloide example gomacs now expects to find thee table files when it is un; namely, table.xvg, table Na Na.xvg and table Cl Cl.xvg. These table files ae set up in the exactly same manne descibed in section 2. It is impotant to note howeve that when a combination of Lennad Jones and Buckingham tems is equied tabulated potentials 6

7 must be used fo all the non-bonded inteactions even fo the Lennad Jones. In ou sodium chloide example the following thee tables ae equied: f() g() h() table.xvg Fo Na Cl table Na Na.xvg e B NaNa Fo Na Na table Cl Cl.xvg e B ClCl Fo Cl Cl In addition, because, when tables ae used gomacs always assumes the non-bonded inteaction to be given by equation 1, sepaate tables ae equied fo each of the buckingham tems as it is only in the table file that the diffeent values fo the B paametes ae taken into account. The index/ndx file The final job, pio to unning gomacs, is to define the Na and Cl enegy goups. These goups ae defined in index file. Fo the following.go file: Some sodium chloide 8 1SOD Na SOD Na SOD Na SOD Na CHL Cl CHL Cl CHL Cl CHL Cl The index file should ead: [ Na ] [ Cl ] as the fist fou atoms in the configuation ae sodium while the emainde ae chloine. Running The topology file is set up in the manne descibed in the pevious section and the calculation is un by executing: gompp -f md.mdp - p topol.top -c conf.go -n index.ndx mdun -table table.xvg with all the table files in the diectoy whee mdun is unning. 7

8 4 Dealing with molecules The pevious sections have shown how poweful gomacs can be in handling inte atomic foces. If you system is molecula all of the above can be used as typically intemolecula inteactions ae calculated as a sum of inteactions between the vaious atoms that make up the molecules. Thee is howeve one impotant caveat egading how the molecules must be defined in the topology file, which we will illustate though the following example. Conside the the following extact fom a topology file which defines a TIP3P wate molecule: [ atoms ] ; at type es n es name at name cg n chage mass 1 OW 1 SOL OW HW 1 SOL HW HW 1 SOL HW Now imagine we set up ou calculation so that the OW OW f(), g() and h() ae diffeent fom the OW HW and HW HW f(), g() and h(). To do this we would put the following in the mdp file: vdw-type = use enegygps = OW enegygp table = OW OW and would set up the tables and index file in the manne descibed in the pevious section. This setup would give a eo when un though gommpp howeve. The eason fo this is elated to the way that gomacs deals with the calculation of neighbo lists and cutoffs. This is done though so called chage goups and the essential poblem is that an enegy goups must contain all contain eithe all o none of the atoms in any given change goup. Howeve, the chage goups ae defined in the topology file in the column headed cg n so by simply changing ou molecule definition to: [ atoms ] ; at type es n es name at name cg n chage mass 1 OW 1 SOL OW HW 1 SOL HW HW 1 SOL HW

9 we can bypass this poblem and do the calculation in the manne equied. Cae must be taken when this pocedue is caied out especially when one is using a cutoff o on the electostatic inteactions fo the easons descibed in section of the manual. Howeve, this should not be a poblem if you ae using pme o ewald electostatics. Thee is an additional poblem if you ae using constaints as you can now no longe use settles to constain the wate molecule and must define the constaints and use LINCS instead. In addition splitting the chage goups in this way means you can only use shake to enfoce the constaints if you un without domain decomposition. 9

(a, b) x y r. For this problem, is a point in the - coordinate plane and is a positive number.

(a, b) x y r. For this problem, is a point in the - coordinate plane and is a positive number. Illustative G-C Simila cicles Alignments to Content Standads: G-C.A. Task (a, b) x y Fo this poblem, is a point in the - coodinate plane and is a positive numbe. a. Using a tanslation and a dilation, show