GROMACS version: any
GROMACS modification: No
Hi,
I’m a postdoc. Improper dihedral angles – hereafter referred to as “improper dihedrals” – have always been difficult for me to understand. They are, and continue to be, my Achilles heel. Could you please help me?
Dihedral angles (“dihedrals”) are, in general, angles between two planes. For proper dihedrals, the atoms involved are connected by bonds in order. If we have a proper dihedral defined by atoms i, j, k, and l bonded in series, then the proper dihedral is i-j-k-l. The proper dihedral is the angle between the plane i-j-k and the plane j-k-l, and the torsion is about bond j-k.
On the other hand, for IMproper dihedrals, the atoms involved do not follow bond order. Yet, the improper dihedral is still an angle between two planes: namely, plane (i,j,k) and plane (j,k,l); that’s how the Gromacs manual defines improper dihedrals. Here’s a snapshot from the Gromacs manual:
https://i.imgur.com/k2JMgHM.jpg
In Gromacs, the improper dihedral angle, Greek letter xi, is defined as the angle between planes (i,j,k) and (j,k,l). Gromacs’s default type of improper dihedral is the harmonic type with the form given in Eq. 5.175 in the image at this link:
https://i.imgur.com/G8NVHWp.jpg
Gromacs also includes a periodic improper dihedral type, a Fourier form (Eq. 5.180), shown in the image at this link:
https://i.imgur.com/B0VF674.jpg
If you’d like to see the complete discussion in the Gromacs manual, it’s available around pages 372-376 at the following link:
https://manual.gromacs.org/current/manual-2022.4.pdf
Now, I’d like to specify improper dihedrals in Gromacs for alkylimidazolium cations according to the force field developed by Canongia Lopes and Padua et al. For reference, the citation and link to that paper is as follows:
Canongia Lopes, J.; Deschamps, J.; Padua, Agilio A. H. J. Phys. Chem. B 2004, 108, 2038-2047.
links: https://doi.org/10.1021/jp0362133 or https://pubs.acs.org/doi/abs/10.1021/jp0362133
Note there is a correction to this paper with citation as follows. But the correction only affects a few of the numbers, and does not affect any of the qualitative forms.
Canongia Lopes, J.; Deschamps, J.; Padua, Agilio A. H. J. Phys. Chem. B 2004, 108, 11250.
links: https://doi.org/10.1021/jp0476996 or https://pubs.acs.org/doi/10.1021/jp0476996
I’m looking at the dihedrals section of Table 3 on page 2041. (Again, some of the actual numbers are corrected in the correction, but none of the qualitative forms is affected.) I have posted a screenshot of that part of Table 3 at the following link (yellow highlighting and annotations are mine):
https://i.imgur.com/wvWlPbB.jpg
That table lists a number of dihedral types for alkylimidazolium cations in Canongia Lopes & Padua’s force field for those cations. (Their force field is based on the OPLS force field of Jorgensen et al.) However, just two of those dihedral types are improper dihedral types: the last two: X-NA-X-X and X-C_{W/R}-X-X, as indicated by the superscript italicized “c”. The potential energy coefficients listed there (V1, V2, and V3) correspond to the Fourier-type dihedral form used in the OPLS force field.
Meanwhile, the entries in that table with headings C1, C2, C4, C6, C12, and C18 refer to the number of occurrences of each term in an alkylmethylimidazolium cation with that number of carbon atoms in the longer side chain. For example, C2 refers to the cation 1-ethyl-3-methylimidazolium (EMI+), whose structure I have posted in the image here:
https://i.imgur.com/cnZth1J.jpg
Table 3 ( https://i.imgur.com/wvWlPbB.jpg ) lists the number of occurrences of the improper dihedrals for the EMI+ cation (column C2). Specifically, there are 4 occurrences of X-NA-X-X and 6 occurrences of X-C_{W/R}-X-X in EMI+. Could you please help me to understand where these occurrences are and how I can correctly specify them? Here are some specific questions:
(1) Does “number of occurrences” in Table 3 ( https://i.imgur.com/wvWlPbB.jpg ) refer to the number of dihedral TYPES or the total number of DIHEDRALS? I was thinking it was the latter, but I’m not certain.
(2) The symmetries of the potential energy forms for X-NA-X-X and X-C_{W/R}-X-X are the same, but their barrier heights are different (V2 = 8.37 vs. 9.2 kJ/mol). Since atom type NA is directly adjacent to both atom types CR and CW, it seems to me that there could be overlap (“intersection”) between the two types of improper dihedrals, X-NA-X-X and X-C_{W/R}-X-X. An improper dihedral X-NA-CW-X, for example, has both NA and CW in the “2” position, if one defines the “2” position as one away from the “end” of the quadruplet. How do I deal with this? Do I include BOTH the X-NA-X-X and X-C_{W/R}-X-X potentials, or just one?
(3) What specifically are the occurrences of X-NA-X-X and X-C_{W/R}-X-X? In the image at the link below, I have enumerated two sets of quadruplets, red and blue, with the red being X-NA-X-X improper dihedrals and the blue being X-C_{W/R}-X-X improper dihedrals:
https://i.imgur.com/Ubqz0Nn.jpg
I have identified 8 “red” and 8 “blue,” and each “blue” seems to be a duplicate of a “red.”
In the analysis for (3), however, I have neglected the hydrogens HA bonded to each of CR, CW, and CW.
(4) As a final attempt, I have considered the hydrogens. In the image at the following link, it now seems I can come up with four X-NA-X-X improper dihedrals and five (not six) X-C_{W/R}-X-X improper dihedrals:
https://i.imgur.com/PqDggrw.jpg
Are those correct? Have I missed any? What is the sixth X-C_{W/R}-X-X improper dihedral? Again, Gromacs improper dihedrals are specified i-j-k-l, where (i,j,k) and (j,k,l) are the two planes.
Thanks so much for your time, and for any guidance you can provide,
Andrew DeYoung, PhD
Department of Chemistry
Carnegie Mellon University