ES-GMTKN55: a cross-functional electronic-structure dataset for main-group chemistry (GMTKN55 x 16 methods)

Converged Kohn-Sham (and Hartree-Fock) orbitals, Fock matrices, energy components, cross-functional energies and one-electron properties for the 2,484 species entries of the GMTKN55 database, computed with 16 methods (HF, SVWN, PBE, revPBE, BLYP, TPSS, SCAN, r2SCAN, M06-L, PBE0, revPBE0, B3LYP, TPSS0, SCAN0, r2SCAN0, M06) in the def2-QZVPPD basis with PySCF 2.14.0 / libxc 7.0.0. 39,744 records; 635,904 cross-functional energies. All quantities are in atomic units (Hartree, bohr, e). See the data descriptor for methods and validation.

Files

file	content
data/<method>.h5 (16 files)	one HDF5 file per method; /<subset>/<species>/ holds one record (layout below)
index.csv	one row per record (39,744) with every scalar quantity of the HDF5 files (energies, components, cross-functional energies, dipole, flags)
reactions.csv	the 1,505 GMTKN55 reactions: subset, reaction number, species, stoichiometry, reference value (kcal/mol, original GMTKN55 values)
subsets.csv	the 55 subsets: category, number of species entries and reactions, mean absolute reference value
code/	PySCF drivers (drivers/), reconvergence of the 26 difficult records (reconvergence/), post-processing, verification and build scripts, and the reader module esdb.py

HDF5 layout (data/<method>.h5)

Root attributes: pyscf_version, libxc_version, basis, auxiliary_basis, grid, scf, linear_dependency, method, xc (libxc string), rung, cross_energy_methods, units, source, generated.

Group /<subset>/<species>/ (record) with attributes nao, nmo, nelec, nelec_alpha, nelec_beta, charge, spin (2S), natm, open_shell, S2 (<S^2>), level_shift (SCF needed the level-shift fallback), special (reconverged with a deviation from the default protocol) and special_flag (the deviation, as text), scf_time_s, prop_origin_bohr.

dataset	shape	content
mol	string	serialized PySCF molecule (pyscf.gto.Mole.loads): geometry, charge, spin, basis, ECP
scf/mo_coeff	(nao, nmo) *	molecular-orbital coefficients in the AO basis (nmo <= nao after canonical orthogonalisation)
scf/mo_energy, scf/mo_occ	(nmo,) *	orbital energies and occupations
scf/e_tot	()	self-consistent total energy
fock	(nao, nao) *	Fock matrix built from the converged density, AO basis
energy/nuc, energy/1e, energy/coul, energy/xc	()	nuclear repulsion; Tr[D h] (ECP included); 1/2 Tr[D J] with density-fitted J; E_xc = e_tot - (nuc + 1e + coul), i.e. DFT exchange-correlation plus exact exchange for HF and hybrids
cross_energy/E	(16,)	total energy of each of the 16 methods evaluated non-self-consistently on this record's density, in the order hf, svwn, pbe, revpbe, blyp, tpss, scan, r2scan, m06l, pbe0, revpbe0, b3lyp, tpss0, scan0, r2scan0, m06 (also in attribute methods); the entry of the record's own method equals scf/e_tot
cross_energy/hartree	()	the same with no exchange-correlation (nuc + 1e + coul)
prop/dipole	(3,)	dipole moment about the centre of nuclear charge
prop/quadrupole	(3, 3)	traceless quadrupole tensor (PySCF definition) about the same origin
prop/mulliken, prop/meta_lowdin	(natm,)	atomic charges from Mulliken and meta-Loewdin (ANO pre-orthogonalisation) population analysis
prop/mulliken_spin, prop/meta_lowdin_spin	(natm,)	atomic spin densities (N_alpha - N_beta); open-shell records only

* open-shell records (UKS) carry a leading spin dimension of 2, e.g. scf/mo_coeff is (2, nao, nmo).

Reading the data

import esdb                                   # code/esdb.py; needs h5py, numpy, pyscf
db  = esdb.open('data/pbe.h5')
rec = esdb.record(db, 'S22', '01')
mol, mf = esdb.to_pyscf(rec, 'pbe')           # RKS/UKS object with density fitting, grid level 4 and the stored orbitals
dm  = mf.make_rdm1()
esdb.energy(mf, 'scan')                       # E_SCAN[rho_PBE] == rec['cross_energy']['scan']

Plain h5py works as well; index.csv is the fastest way to select records by subset, charge, spin, size or flag.

Provenance and caveats

• Use PySCF 2.14.0 (libxc 7.0.0) to reproduce the stored energies exactly; other versions read the files but may give slightly different energies.
• Geometries, charges, multiplicities and reactions are taken unchanged from the original GMTKN55 web distribution of the Grimme group (Bonn). Reference values are the original (2017) values; WATER27 references were later revised by the GMTKN55 maintainers (v2 branch of github.com/grimme-lab/GMTKN55) and those are not used here.
• The SCF protocol is the same for every record (conv_tol 1e-8 Eh, ADIIS, grid level 4, density fitting). 151 records needed a level shift (level_shift), 26 were reconverged with a documented deviation (special, special_flag; details in code/reconvergence/). Four M06-L records (ALKBDE10/na, G21IP/na, MB16-43/06, MB16-43/16) carry relaxed convergence thresholds and should be used with care.
• The stored Fock matrix is built from the final density, whereas scf/mo_energy comes from the last SCF iteration, so F C = S C eps holds for the occupied orbitals to the SCF gradient tolerance (<= 5e-4) but not for virtual orbitals of functionals whose potential is ill-conditioned at low density (SCAN-type and M06-type functionals on small ions and atoms).
• For the 151 records with level_shift = True the stored virtual-orbital energies include the level shift of 0.5 Eh (1.5 Eh for MB16-43/06, see its special_flag); occupied-orbital energies, orbital coefficients and the Fock matrix are unaffected. Unshifted virtual energies are obtained by subtracting the shift or by diagonalizing the stored Fock matrix.
• Non-self-consistent energies use the same density fitting and grid as the self-consistent ones.

Citation

GMTKN55: Goerigk, L. et al. Phys. Chem. Chem. Phys. 19, 32184 (2017).