We are trying to benchmark/compare the energies computed with the same DFT functional but different grids. Is there a way to print as much information as possible concerning the grid used in such jobs?
If not, is there a way to deduce the number of points used for each atom in a molecule for a given grid, say SG-1?
This functionality used to exist but seems to have been removed. However, you can get the number of points from the original literature. For SG-1 it’s a bit tricky (requires you to compute the radial quadrature values), paper is here: https://doi.org//10.1016/0009-2614(93)80125-9. For SG-2 and SG-3, see Table 1 of this paper: https://doi.org/10.1002/jcc.24761.
Here is the SG-1 grid specification, in the same format as Table 1 of the SG-2/SG-3 paper cited above.
Elements H-He:
6^16 38^5 86^4 194^9 86^16 (N = 3752)
Elements Li-Ne:
6^14 38^7 86^3 194^9 86^17 (N = 3816)
Elements Na-Ar:
6^12 38^7 86^5 194^7 86^19 (N = 3760)
Remaining elements:
38^12 194^38 (N = 7828)
This was very useful, thank you. One last thing to complete the discussion.
How are the radial points (or shells) defined? Are they the same for each element or is there a dependence on the atomic radius?
For SG-1 I understand that there are 50 radial points but what is the mapping of these points from the closest to the furthest from the nucleus?
Radial shells are defined by some kind of a mapping between the interval [0,1], or sometimes [-1,1], onto the semi-infinite interval [0,infinity). Precise mapping function that is used varies depending on the grid. See my SG-2/SG-3 paper cited above for one example and references to others, e.g., one of the original ones is Murray, Handy, & Laming, Ref. 26
The idea is that if there are Nr radial points (e.g., Nr = 50 for SG-1, Nr = 75 for SG-2, Nr = 99 for SG-3), one obtains them by dividing [0,1] up onto Nr equal segments and mapping those out onto the semi-infinite interval. Practical upshot is that the radial shells get farther apart as one moves away from the nucleus, which is appropriate because the density is slowly-varying when it is far away from all nuclei.
The mapping can be atomic-number dependent, e.g., the alpha exponents in Table 1 of the SG-2/SG-3, which are different for different nuclei and are used in the mapping function of Eq. (6).
N.B., the radial mapping functions are not the same for different grids. In Q-Chem specifically, SG-1 uses and different radial mapping as compared to SG-2 and SG-3, and the unpruned Euler-Maclaurin-Lebedev (EML) grids use a different mapping altogether. This means, for example, that XC_GRID = 000075000302, which requests an unpruned (75,302) grid, uses different radial values as compared to SG-2, even though the latter is a pruned version of a (75,302) grid – but it’s a different radial quadrature scheme. This is done for a reason (discovery of new and better quadrature schemes over time) but is an occasional point of confusion.