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Resolve "Implement BR3P86"

Susi Lehtola requested to merge 371-implement-br3p86 into master

Closes #371 (closed)

Reproduction of data from Tables 1 and 2 with ERKALE, with the TZ2P basis set from CADPAC (https://github.com/MolSSI-BSE/basis_set_exchange/pull/245) and a (100,590) quadrature grid.

molecule R (Å) difference Eat (kcal/mol) difference
H2 0.740 -0.001 113.0 5.9
LiH 1.598 0.000 59.4 1.9
CH 1.123 0.000 86.0 3.8
NH 1.038 -0.000 87.2 4.5
OH 0.971 0.000 109.6 5.1
HF 0.919 -0.000 143.4 5.5
Li2 2.746 -0.001 21.8 0.5
LiF 1.576 -0.000 138.9 1.4
CN 1.158 0.000 177.6 2.5
CO 1.123 0.000 258.2 3.0
N2 1.089 0.000 221.4 3.6
NO 1.142 -0.001 149.7 2.8
O2 1.198 -0.001 123.5 2.6
F2 1.390 0.001 36.6 1.6
HCl 1.281 0.002 109.2 4.3
Si2 2.160 -0.109 70.4 -3.3
P2 1.889 -0.001 105.3 1.2
S2 1.906 -0.001 101.6 1.1
Cl2 2.017 0.002 56.5 0.7
SiO 1.509 0.000 187.5 1.7
CS 1.534 -0.001 166.4 1.8
SO 1.488 -0.001 124.7 1.6
ClO 1.582 0.004 64.1 1.2
ClF 1.640 0.001 61.0 1.1

The agreement is satisfactory except for Si2, and probably can be explained by non-converged data given that the paper doesn't specify the grid they used. The 1996 paper by Neumann et al that describes the implementation of meta-GGAs states

In our calculations involving first-row atoms, we used 46 radial points, 302 Lebedev angular points and a TZ2P basis set to be confident of our predictions and accuracy.

but this is likely far from sufficient for a Laplacian dependent functional.

Edited by Susi Lehtola

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