MN15: A Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions

We report a global-hybrid approximation, MN15, to the exchange–correlation functional of Kohn–Sham theory with broadly accurate performance for both multi-reference and single-reference systems.


Table of contents
Density functionals tested in this paper and SI. S-3 Grids, basis sets, and geometries S-4 Table S1. 83 density functionals tested in the paper and SI with the percentage of nonlocal Hartree-Fock exchange, the year that the functional was published, and the original reference or references S- 5   Table S2. The mean unsigned errors on 27 databases of atomic and molecular energies as calculated by local spin density approximations (LSDAs) and generalized gradient approximations (GGAs) S-8 Table S3. The mean unsigned errors on 27 databases of atomic and molecular energies as calculated by GGAs, N12, GAM, and global hybrid GGAs S-9  Table S5. The mean unsigned errors on 27 databases of atomic and molecular energies as calculated by range-separated hybrid GGAs, N12-SX, meta-GGAs, and MN15-L S- 11   Table S6. The mean unsigned errors on 27 databases of atomic and molecular energies as calculated by hybrid meta-GGAs S- 12   Table S7. The mean unsigned errors on 27 databases of atomic and molecular energies as calculated by hybrid meta-GGAs, M11, MN12-SX, and MN15 S-13 Table S8. The mean unsigned errors intermolecular charge transfer database (CT7) calculated by 83 density functionals in the order of increasing MUE of CT7 database S-14 Table S9. The mean unsigned errors for molecular energy database and its subdatabases calculated by 83 density functionals in the same order as Table S1 S- 15   Table S10. The average and median mean unsigned errors for the molecular energy database and its subdatabases calculated by 83 density functionals S-17 Table S11. The mean unsigned errors for molecular energy databases and its subdatabases calculated by 83 density functionals in the order of increasing MUE of atomic and molecular database (AME471) S- 18   Table S12. The mean unsigned errors on three molecular databases calculated by 83 density functionals in the same order as Table S1 S-20 Table S13. The mean unsigned errors on three molecular databases calculated by 83 density functionals in the order of increasing MUE of molecular structure database (MS10) S-21 Table S14. Geometries, charge, and multiplicities of alkyl bond dissociation energies (ABDE13), six dimers at six intermonomer distances (S6x6), semiconductor band gaps (SBG31), and excitation energies of selected organic molecules (EE69) S-22 References S-65 S-3

S-4
For each of the functionals in the above list, Table S1 shows the percentage of nonlocal Hartree-Fock exchange, the year that the functional was published, and the original reference or references.
S-6 value is for small interelectronic distances, and the second value is for large interelectronic distances. Details of the functional form that joins these regions of interelectronic separation are given in the references.
S-8 b GVWN5 denotes the Gáspár approximation for exchange and the VWN5 fit to the correlation energy; GVWN3 denotes Gáspár approximation for exchange and the VWN fit to the correlation energy; this is an example of the local spin density approximation (LSDA), and it has the keyword SVWN5 and SVWN in the Gaussian 09 program. Note that Kohn-Sham exchange is the same as Gáspár exchange, but Slater exchange (not tested here) is greater by a factor of 1.5.
c PW91 formally satisfies the gradient expansion for exchange to second order but only at such small values of the gradient that for practical purposes it should be grouped with functionals that do not satisfy the gradient expansion to second order.
d RS denotes range-separated.
e MM denotes molecular mechanics (also called empirical dispersion correction), which in this case corresponds to atom-atom pairwise damped dispersion terms added post-SCF to the calculated energy.