*library_books*

## Similar protocols

## Protocol publication

[…] All PBE calculations
(within the KS scheme) and PBE0 and RSH calculations (within the GKS
scheme) presented in this article were obtained within the QChem and **NWChem** codes,
using cc-PVTZ basis functions. All geometries
were optimized using the PBE functional. As the above-described tuning
scheme is based on components taken from well-established density
functionals (cf. eq ) and range-separation
is available in many different electronic structure codes, optimal
tuning of γ via eq is straightforward
to perform. Moreover, the tuning strategy is computationally efficient,
as it relies on a series of standard total-energy DFT calculations.
We note, however, that when charging the gas-phase molecule as part
of the above-explained tuning procedure, the configuration of the
cation and/or anion must be identified carefully, as it may affect
the results of the calculation.We illustrate the possible complications associated with different
ion configurations by considering pyridine—one of the molecules
of Figure , which is discussed extensively
in the results section. When tuning γ using the above-described
approach, it is important to ensure that the character of the HOMO
(related to the left-hand term in eq ) corresponds
to the “hole density,” defined as the charge-density
difference of the neutral and charged states (and, consequently, related
to the right-hand term in eq ). For pyridine,
the self-consistent solution of the GKS equation with the RSH functional
was found to lead to two different doublet configurations of the cation,
depending on the initial guess used in the procedure. These two configurations
correspond to two qualitatively different hole densities (see Figure , left part). As shown in the right part of Figure , the reason for the different hole densities is
that the two cation configurations possess two different LUMO orbitals;
i.e., the two cationic ground states represent two different ionization
processes. The main difference is that the electron “loss”
is, in one case, from a π orbital and, in the other case, from
a σ orbital. These two cationic configurations are energetically
close, which is consistent with the observation that the HOMO and
the HOMO–1 of pyridine are very close in energy (vide
infra). Importantly, however, only the “hole density”
depicted in Figure b—which is associated
with the configuration lower in energy, i.e., the true ground state
predicted for the cation—corresponds to the HOMO of pyridine
(see Figure c). Therefore, one has to ensure
that the cationic state shown in Figure b
is indeed the one entering the tuning procedure, in order to retain
consistency for the orbital energies and total energies required in
eq .For our analysis of the OT-RSH results, we also performed
comparative
GW calculations, as well as self-interaction-corrected calculations
and KS-PBE0 calculations (the latter are defined and explained below).
Our GW calculations are based on a standard G0W0 scheme, where quasi-particle energies
are computed via a first-order correction to DFT eigenvalues, with
no self-consistent update of the starting wave functions. The starting
quasi-particle wave function for the G0W0 corrections
was obtained from the PBE functional. The static dielectric function is computed within the random-phase
approximation and extended to finite frequency via the generalized
plasmon-pole (GPP) model of Hybertsen and Louie.Our G0W0 calculations were
performed using
the BerkeleyGW package, which employs
a plane-wave basis set to compute the dielectric function and self-energy,
using a PBE starting point. DFT-PBE calculations were performed within
the **Quantum** Espresso package, which is
compatible with BerkeleyGW. The nuclei and core electrons were described
by Troullier–Martins relativistic norm-conserving pseudopotentials, which are part of the Quantum Espresso pseudopotential
library. Here, one, four, five, and six electrons were explicitly
considered as valence electrons for H, C, N, and S, respectively,
with cutoff radii (in Bohr) of 1.3, 0.5, 1.0, and 1.7, respectively.
We used a plane-wave basis cutoff of 80 Ry for benzene and 120 Ry
for pyridine, pyrimidine, and 3N-thiol. These values lead to a total
DFT energy converged to <1 meV/atom. To avoid spurious interactions
with periodic images, we used a supercell with lattice vectors twice
the size necessary to contain 99% of the charge density and, when
computing the GW self-energy, the Coulomb interaction was truncated
at distances larger than half of the unit cell size. The supercell
dimensions, in atomic units, were 35 × 39 × 24; 30 ×
20 × 32, 19 × 30 × 30; and 64 × 26 × 15.5
for benzene, pyridine, pyrimidine, and 3N-thiol, respectively.Our static dielectric function and self-energy were constructed
from 4914, 5515, 5071, and 3598 unoccupied states, respectively, for
benzene, pyridine, pyrimidine, and 3N-thiol. For the former three
prototypical small molecules, this energy range corresponds to 90
eV above the vacuum energy, while for 3N-thiol, it corresponds to
50 eV above the vacuum energy. Fewer states were included for 3N-thiol
due to the greater computational expense associated with this rather
large system. A static remainder approach was applied to the self-energy
to approximately complete the unoccupied subspace. The plane-wave cutoff for the dielectric function was 30
Ry for pyridine and pyrimidine and 24 Ry for 3N-thiol and benzene.
We find that these parameters converge the HOMO energies of the prototypical
small molecules to less than 0.1 eV. On the basis of the convergence
behavior of these molecules and the residual differences that we find
for GW and OT-RSH HOMO energies (vide infra), we extrapolate the errors
associated with eigenvalues of the 3N-thiol calculation to be less
than 0.2 eV.All SIC calculations were based on the seminal
SIC concept of Perdew
and Zunger. However, we constructed a
spatially local, multiplicative exchange-correlation potential identical
for all orbitals in the system, which ensures that the SIC remains
within the KS realm., This is based on the generalized
optimized effective potential (OEP) equation, which extends the original
OEP equation to the case of unitarily variant functionals. It is solved
using the generalized Krieger–Li–Iafrate (KLI) approximation., Unlike the KLI approximation to the standard OEP equation, which
can introduce significant deviations for the SIC, the generalized KLI approximation used here has been shown
to be an excellent approximation to the generalized OEP. The additional
degree of freedom arising from the variance inherent to our procedure
can be used to construct a set of orbitals that minimize the total
SIC energy of the system, where we applied a complex-valued energy
minimizing unitary orbital transformation. For additional insights, we also used the PBE0 functional in conjunction
with a local multiplicative potential, constructed—in contrast
to traditional GKS schemes—via the KLI approximation for the exact exchange part of the functional. We
refer to these calculations as PBE0KS.All SIC and
PBE0KS calculations were performed with
the Bayreuth version of the PARSEC real-space
code, where we employed a grid-spacing
of 0.2 Bohr and Troullier–Martins norm-conserving pseudopotentials.Finally, for a meaningful comparison between
the results of different
functionals and/or computational approaches, we tested explicitly
that eigenvalues obtained from different codes and basis-set expansions
(Gaussian, planewave, real-space) do not differ by more than 0.1 eV
for the same underlying functional. Furthermore, we verified by visual
inspection, that eigenvalues calculated from
different methods correspond to the same molecular orbitals. […]

## Pipeline specifications

Software tools | NWChem, Quantum ESPRESSO |
---|---|

Application | Mathematical modeling |

Chemicals | Benzene |