# Where can I find/generate force-field parameters for common inorganic anions in water?

I have to do simulations of some inorganic anions, specifically $$\ce{PO4^3-}$$ (ortho-phosphate), $$\ce{CO3^2-}$$ (carbonate), $$\ce{SO4^2-}$$ (sulfate), in an aqueous enviornment. However, I am having a lot of difficulties in getting hold of parameters for such ions. I am looking for mainly OPLS-AA parameters. (but I am willing to use other force-fields if I have to)

The official site for OPLS-AA parameters is the LigParGen server, however, it fails with any ionic species that I put in. The github issue-tracker for LigParGen seems to have been abandoned.

There are some papers which seem to have developed parameters for phosphate or other ions, but they all developed the parameters for solid state calculations (e.g. on apatite etc.). So, I am not sure if those parameters are transferable to liquid phase aqueous simulations.

There are also some parameters for ionic liquids, but the same problem of transferability is present.

I could find carbonate parameters in CgenFF, but it does not mention whether it is usable in water (or which model of water was used to parameterize it). The other two ions are not in CgenFF however.

My questions are—Are there any parameters for those ions to be used for aqueous simulations? Alternatively, is there any software/server which can generate the parameters for it?

Any parameters are better than no parameters. Part of using a FF is checking that results make sense, so if you can find something in this bare market for anions, try it. Proof will be in the pudding.

LigParGen can only generate ions between -2 and +2 charge, so $$\ce{PO4^3-}$$ is out. When I tried with $$\ce{SO4^2-}$$, it did not work. $$\ce{H2SO4}$$ also did not work. I then tried $$\ce{H3PO4}$$ (via SMILES) and it(LigParGen) did not work. I then tried $$\ce{H3PO4}$$ via pdb file, it worked. I tried $$\ce{CO3^2-}$$, it did not work, but $$\ce{H2CO3}$$ did work. I have attached the $$\ce{H3PO4}$$ and $$\ce{H2CO3}$$ pdbs so you can remake them if you wish, but also attach the GROMACS topology files (actually I have pasted them at the bottom... I don't know how to attach them...).

I did a quick and dirty geometry optimization in Avogadro using GAFF, so, we know that GAFF at least can do the anions(Avogadro says the molecular formula includes the hydrogens, so I am not sure if it is really doing the anion? I removed hydrogens anyways. Atomic properties does not list hydrogens...), so I would suggest looking into GAFF along with OPLS/AA.

My suggestion is to try using GAFF to get the bond/angle parameters (maybe GAFF[Antechamber] will even do the charges too, but I wouldn't want to use them). I would suggest generating MBIS partial charges. If GAFF will do the anions, then use the LJ parameters it generates. If it does not, generate the neutral molecules, for instance, $$\ce{H3PO4}$$ and $$\ce{H2SO4}$$ and "borrow" the LJ parameters as well as bond/angle parameters. You can tweak the bond/angle parameters using QM if you wish. Then get partial charges...I would use a partitioning method over a random number generator like RESP, but regardless, you can generate the partial charges using QM programs. Gaussian will do ESP/Hirshfeld/CM5 and many others. HORTON will do MBIS for you.

It is hopefully worth making the forcefield in this somewhat Frankenstein manner if you can't find one. The anions are small so you should be able to "tweak" parameters to make it work for the property you are interested in. Only trial and error will tell :S

$$\ce{H3PO4}$$ PDB file

COMPND    UNNAMED
AUTHOR    GENERATED BY OPEN BABEL 2.3.90
HETATM    1  P   UNL     1      -1.464   0.745  -2.751  1.00  0.00           P
HETATM    2  O   UNL     1      -2.421   1.312  -3.725  1.00  0.00           O
HETATM    3  O   UNL     1      -1.527  -0.862  -2.535  1.00  0.00           O
HETATM    4  H   UNL     1      -0.784  -1.161  -1.978  1.00  0.00           H
HETATM    5  O   UNL     1      -1.530   1.339  -1.276  1.00  0.00           O
HETATM    6  O   UNL     1       0.076   0.988  -3.056  1.00  0.00           O
HETATM    7  H   UNL     1      -2.453   1.221  -1.091  1.00  0.00           H
HETATM    8  H   UNL     1       0.145   0.489  -3.857  1.00  0.00           H
CONECT    1    2    3    5    6
CONECT    2    1
CONECT    3    1    4
CONECT    4    3
CONECT    5    1    7
CONECT    6    1    8
CONECT    7    5
CONECT    8    6
MASTER        0    0    0    0    0    0    0    0    8    0    8    0
END


OPLS/AA FF for $$\ce{H3PO4}$$

;
; GENERATED BY LigParGen Server
; Jorgensen Lab @ Yale University
;
[ atomtypes ]
opls_806  H806     1.0080     0.000    A    0.00000E+00   0.00000E+00
opls_801  O801    15.9990     0.000    A    2.96000E-01   8.78640E-01
opls_800  P800    30.9738     0.000    A    3.74000E-01   8.36800E-01
opls_807  H807     1.0080     0.000    A    0.00000E+00   0.00000E+00
opls_805  O805    15.9990     0.000    A    3.12000E-01   7.11280E-01
opls_802  O802    15.9990     0.000    A    3.12000E-01   7.11280E-01
opls_804  O804    15.9990     0.000    A    3.12000E-01   7.11280E-01
opls_803  H803     1.0080     0.000    A    0.00000E+00   0.00000E+00
[ moleculetype ]
; Name               nrexcl
UNL                   3
[ atoms ]
;   nr       type  resnr residue  atom   cgnr     charge       mass
1   opls_800      1    UNL   P00      1     2.8980    30.9738
2   opls_801      1    UNL   O01      1    -1.2051    15.9990
3   opls_802      1    UNL   O02      1    -1.0619    15.9990
4   opls_803      1    UNL   H03      1     0.4728     1.0080
5   opls_804      1    UNL   O04      1    -1.0008    15.9990
6   opls_805      1    UNL   O05      1    -0.9984    15.9990
7   opls_806      1    UNL   H06      1     0.4508     1.0080
8   opls_807      1    UNL   H07      1     0.4445     1.0080
[ bonds ]
2     1     1      0.1480 439320.000
3     1     1      0.1610 192464.000
4     3     1      0.0945 462750.400
5     1     1      0.1610 192464.000
6     1     1      0.1610 192464.000
7     5     1      0.0945 462750.400
8     6     1      0.0945 462750.400

[ angles ]
;  ai    aj    ak funct            c0            c1            c2            c3
2     1     3     1    108.230    836.800
1     3     4     1    108.500    460.240
2     1     5     1    108.230    836.800
2     1     6     1    108.230    836.800
1     5     7     1    108.500    460.240
1     6     8     1    108.500    460.240
3     1     5     1    102.600    376.560
5     1     6     1    102.600    376.560
3     1     6     1    102.600    376.560

[ dihedrals ]
; IMPROPER DIHEDRAL ANGLES
;  ai    aj    ak    al funct            c0            c1            c2            c3            c4            c5

[ dihedrals ]
; PROPER DIHEDRAL ANGLES
;  ai    aj    ak    al funct            c0            c1            c2            c3            c4            c5
4    3    1    2        3       0.000   0.000   0.000  -0.000  -0.000   0.000
7    5    1    2        3       0.000   0.000   0.000  -0.000  -0.000   0.000
8    6    1    2        3       0.000   0.000   0.000  -0.000  -0.000   0.000
7    5    1    3        3       0.000   0.000   0.000  -0.000  -0.000   0.000
8    6    1    5        3       0.000   0.000   0.000  -0.000  -0.000   0.000
8    6    1    3        3       0.000   0.000   0.000  -0.000  -0.000   0.000
7    5    1    6        3       0.000   0.000   0.000  -0.000  -0.000   0.000
5    1    3    4        3       0.000   0.000   0.000  -0.000  -0.000   0.000
6    1    3    4        3       0.000   0.000   0.000  -0.000  -0.000   0.000

[ pairs ]
2     4    1
4     5    1
2     7    1
4     6    1
3     7    1
2     8    1
3     8    1
6     7    1
5     8    1


$$\ce{H2CO3}$$ PDB file

COMPND    UNNAMED
AUTHOR    GENERATED BY OPEN BABEL 2.3.90
HETATM    1  C   UNL     1       0.943   0.994  -1.701  1.00  0.00           C
HETATM    2  O   UNL     1       1.658   0.127  -2.342  1.00  0.00           O
HETATM    3  O   UNL     1       1.315   2.096  -2.237  1.00  0.00           O
HETATM    4  H   UNL     1       1.969  -0.472  -1.669  1.00  0.00           H
HETATM    5  H   UNL     1       1.933   1.686  -2.870  1.00  0.00           H
HETATM    6  O   UNL     1       0.632   0.886  -0.535  1.00  0.00           O
CONECT    1    2    3    6
CONECT    2    1    4
CONECT    3    1    5
CONECT    4    2
CONECT    5    3
CONECT    6    1
MASTER        0    0    0    0    0    0    0    0    6    0    6    0
END


$$\ce{H2CO3}$$ Topology file

;
; GENERATED BY LigParGen Server
; Jorgensen Lab @ Yale University
;
[ atomtypes ]
opls_804  H804     1.0080     0.000    A    0.00000E+00   0.00000E+00
opls_801  O801    15.9990     0.000    A    3.12000E-01   7.11280E-01
opls_805  O805    15.9990     0.000    A    2.96000E-01   8.78640E-01
opls_802  O802    15.9990     0.000    A    3.12000E-01   7.11280E-01
opls_803  H803     1.0080     0.000    A    0.00000E+00   0.00000E+00
opls_800  C800    12.0110     0.000    A    3.55000E-01   2.92880E-01
[ moleculetype ]
; Name               nrexcl
UNL                   3
[ atoms ]
;   nr       type  resnr residue  atom   cgnr     charge       mass
1   opls_800      1    UNL   C00      1     0.6339    12.0110
2   opls_801      1    UNL   O01      1    -0.6044    15.9990
3   opls_802      1    UNL   O02      1    -0.4751    15.9990
4   opls_803      1    UNL   H03      1     0.4774     1.0080
5   opls_804      1    UNL   H04      1      0.475     1.0080
6   opls_805      1    UNL   O05      1    -0.5067    15.9990
[ bonds ]
2     1     1      0.1364 376560.000
3     1     1      0.1364 376560.000
4     2     1      0.0945 462750.400
5     3     1      0.0945 462750.400
6     1     1      0.1229 476976.000

[ angles ]
;  ai    aj    ak funct            c0            c1            c2            c3
2     1     3     1    118.180    584.923
1     2     4     1    113.000    292.880
1     3     5     1    113.000    292.880
2     1     6     1    121.000    669.440
3     1     6     1    121.000    669.440

[ dihedrals ]
; IMPROPER DIHEDRAL ANGLES
;  ai    aj    ak    al funct            c0            c1            c2            c3            c4            c5
6     1     2     3    4        180.000     43.932     2

[ dihedrals ]
; PROPER DIHEDRAL ANGLES
;  ai    aj    ak    al funct            c0            c1            c2            c3            c4            c5
4    2    1    3        3      23.012   0.000  -23.012  -0.000  -0.000   0.000
5    3    1    2        3      23.012   0.000  -23.012  -0.000  -0.000   0.000
6    1    2    4        3      23.012   0.000  -23.012  -0.000  -0.000   0.000
6    1    3    5        3      23.012   0.000  -23.012  -0.000  -0.000   0.000

[ pairs ]
3     4    1
2     5    1
4     6    1
5     6    1

• +1. Would you consider to use ChemJax for the chemical formulas like I just did (and the OP did in their question)? Jul 26 '21 at 2:50
• @B.Kelly, Thanks! I guess I was hoping for a cleaner solution, but if that's not possible I will have to take parameters from different force fields. Weirdly, the parameters for H3PO4 that you posted seems to have all dihedral parameters set to 0, those are probably missing from OPLS-AA. Jul 26 '21 at 2:59
• @NikeDattani sure, I can do that. Jul 26 '21 at 11:16
• @SRMaiti it is not unusual for dihedrals to be zero, many don't have parameters. In this case, when "borrowing" you wouldn't borrow those anyways :) I too hope there is a cleaner solution. I am pessimistic of anion forcefields though, even if there is one, it is probably rubbish. Jul 26 '21 at 11:16