7 research outputs found
Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies
The
direct random phase approximation (dRPA) is a promising way
to obtain improvements upon the standard semilocal density functional
results in many aspects of computational chemistry. In this paper,
we address the slow convergence of the calculated dRPA correlation
energy with the increase of the quality and size of the popular Gaussian-type
Dunningâs correlation consistent aug-cc-pV<i>X</i>Z split valence atomic basis set family. The cardinal number <i>X</i> controls the size of the basis set, and we use <i>X</i> = 3â6 in this study. It is known that even the
very expensive <i>X</i> = 6 basis sets lead to large errors
for the dRPA correlation energy, and thus complete basis set extrapolation
is necessary. We study the basis set convergence of the dRPA correlation
energies on a set of 65 hydrocarbon isomers from CH<sub>4</sub> to
C<sub>6</sub>H<sub>6</sub>. We calculate the iterative density fitted
dRPA correlation energies using an efficient algorithm based on the
CC-like form of the equations using the self-consistent HF orbitals.
We test the popular inverse cubic, the optimized exponential, and
inverse power formulas for complete basis set extrapolation. We have
found that the optimized inverse power based extrapolation delivers
the best energies. Further analysis showed that the optimal exponent
depends on the molecular structure, and the most efficient two-point
energy extrapolations that use <i>X</i> = 3 and 4 can be
improved considerably by considering the atomic composition and hybridization
states of the atoms in the molecules. Our results also show that the
optimized exponents that yield accurate <i>X</i> = 3 and
4 extrapolated dRPA energies for atoms or small molecules might be
inaccurate for larger molecules
Simple Modifications of the SCAN Meta-Generalized Gradient Approximation Functional
We analyzed various
possibilities to improve upon the SCAN meta-generalized
gradient approximation density functional obeying all known properties
of the exact functional that can be satisfied at this level of approximation.
We examined the necessity of locally satisfying a strongly tightened
lower bound for the exchange energy density in single-orbital regions,
the nature of the error cancellation between the exchange and correlation
parts in two-electron regions, and the effect of the fourth-order
term in the gradient expansion of the correlation energy density.
We have concluded that the functional can be modified to separately
reproduce the exchange and correlation energies of the helium atom
by locally releasing the strongly tightened lower bound for the exchange
energy density in single-orbital regions, but this leads to an unbalanced
improvement in the single-orbital electron densities. Therefore, we
decided to keep the <i>F</i><sub>X</sub> ⤠1.174
exact condition for any single-orbital density, where <i>F</i><sub>X</sub> is the exchange enhancement factor. However, we observed
a general improvement in the single-orbital electron densities by
revising the correlation functional form to follow the second-order
gradient expansion in a wider range. Our new revSCAN functional provides
more-accurate atomization energies for the systems with multireference
character, compared to the SCAN functional. The nonlocal VV10 dispersion-corrected
revSCAN functional yields more-accurate noncovalent interaction energies
than the VV10-corrected SCAN functional. Furthermore, its global hybrid
version with 25% of exact exchange, called revSCAN0, generally performs
better than the similar SCAN0 for reaction barrier heights. Here,
we also analyzed the possibility of the construction of a local hybrid
from the SCAN exchange and a specific locally bounded nonconventional
exact exchange energy density. We predict compatibility problems since
this nonconventional exact exchange energy density does not really
obey the strongly tightened lower bound for the exchange energy density
in single-orbital regions
Accurate DielsâAlder Reaction Energies from Efficient Density Functional Calculations
We
assess the performance of the semilocal PBE functional; its global
hybrid variants; the highly parametrized empirical M06-2X and M08-SO;
the range separated rCAM-B3LYP and MCY3; the atom-pairwise or nonlocal
dispersion corrected semilocal PBE and TPSS; the dispersion corrected
range-separated ĎB97X-D; the dispersion corrected double hybrids
such as PWPB95-D3; the direct random phase approximation, dRPA, with
HartreeâFock, PerdewâBurkeâErnzerhof, and PerdewâBurkeâErnzerhof
hybrid reference orbitals and the RPAX2 method based on a PerdewâBurkeâErnzerhof
exchange reference orbitals for the DielsâAlder, DARC; and
self-interaction error sensitive, SIE11, reaction energy test sets
with large, augmented correlation consistent valence basis sets. The
dRPA energies for the DARC test set are extrapolated to the complete
basis set limit. CCSDÂ(T)/CBS energies were used as a reference. The
standard global hybrid functionals show general improvements over
the typical endothermic energy error of semilocal functionals, but
despite the increased accuracy the precision of the methods increases
only slightly, and thus all reaction energies are simply shifted into
the exothermic direction. Dispersion corrections give mixed results
for the DARC test set. VydrovâVan Voorhis 10 correction to
the reaction energies gives superior quality results compared to the
too-small D3 correction. Functionals parametrized for energies of
noncovalent interactions like M08-SO give reasonable results without
any dispersion correction. The dRPA method that seamlessly and theoretically
correctly includes noncovalent interaction energies gives excellent
results with properly chosen reference orbitals. As the results for
the SIE11 test set and H<sub>2</sub><sup>+</sup> dissociation show
that the dRPA methods suffer from delocalization error, good reaction
energies for the DARC test set from a given method do not prove that
the method is free from delocalization error. The RPAX2 method shows
good performance for the DARC, the SIE11 test sets, and for the H<sub>2</sub><sup>+</sup> and H<sub>2</sub> potential energy curves showing
no one-electron self-interaction error and reduced static correlation
errors at the same time. We also suggest simplified DARC6 and SIE9
test sets for future benchmarking
A meta-GGA Made Free of the Order of Limits Anomaly
We have improved the revised TaoâPerdewâStaroverovâScuseria
(revTPSS) meta-generalized gradient approximation (GGA) in order to
remove the order of limits anomaly in its exchange energy. The revTPSS
meta-GGA recovers the second-order gradient expansion for a wide range
of densities and therefore provides excellent atomization energies
and lattice constants. For other properties of materials, however,
even the revTPSS does not give the desired accuracy. The revTPSS does
not perform as well as expected for the energy differences between
different geometries for the same molecular formula and for the related
nonbarrier height chemical reaction energies. The same order of limits
problem might lead to inaccurate energy differences between different
crystal structures and to inaccurate cohesive energies of insulating
solids. Here we show a possible way to remove the order of limits
anomaly with a weighted difference of the revTPSS exchange between
the slowly varying and iso-orbitals (one- or two-electron) limits.
We show that the new regularized (regTPSS) gives atomization energies
comparable to revTPSS and preserves the accurate lattice constants
as well. For other properties, the regTPSS gives at least the same
performance as the revTPSS or TPSS meta-GGAs
Construction and Application of a New Dual-Hybrid Random Phase Approximation
The
direct random phase approximation (dRPA) combined with KohnâSham
reference orbitals is among the most promising tools in computational
chemistry and applicable in many areas of chemistry and physics. The
reason for this is that it scales as <i>N</i><sup>4</sup> with the system size, which is a considerable advantage over the
accurate ab initio wave function methods like standard coupled-cluster.
dRPA also yields a considerably more accurate description of thermodynamic
and electronic properties than standard density-functional theory
methods. It is also able to describe strong static electron correlation
effects even in large systems with a small or vanishing band gap missed
by common single-reference methods. However, dRPA has several flaws
due to its self-correlation error. In order to obtain accurate and
precise reaction energies, barriers and noncovalent intra- and intermolecular
interactions, we construct a new dual-hybrid dRPA (hybridization of
exact and semilocal exchange in both the energy and the orbitals)
and test the performance of this new functional on isogyric, isodesmic,
hypohomodesmotic, homodesmotic, and hyperhomodesmotic reaction classes.
We also use a test set of 14 DielsâAlder reactions, six atomization
energies (AE6), 38 hydrocarbon atomization energies, and 100 reaction
barrier heights (DBH24, HT-BH38, and NHT-BH38). For noncovalent complexes,
we use the NCCE31 and S22 test sets. To test the intramolecular interactions,
we use a set of alkane, cysteine, phenylalanine-glycine-glycine tripeptide,
and monosaccharide conformers. We also discuss the delocalization
and static correlation errors. We show that a universally accurate
description of chemical properties can be provided by a large, 75%
exact exchange mixing both in the calculation of the reference orbitals
and the final energy
Construction of a Spin-Component Scaled Dual-Hybrid Random Phase Approximation
Recently, we have constructed a dual-hybrid
direct random phase
approximation method, called dRPA75, and demonstrated its good performance
on reaction energies, barrier heights, and noncovalent interactions
of main-group elements. However, this method has also shown significant
but quite systematic errors in the computed atomization energies.
In this paper, we suggest a constrained spin-component scaling formalism
for the dRPA75 method (SCS-dRPA75) in order to overcome the large
error in the computed atomization energies, preserving the good performance
of this method on spin-unpolarized systems at the same time. The SCS-dRPA75
method with the aug-cc-pVTZ basis set results in an average error
lower than 1.5 kcal mol<sup>â1</sup> for the entire <i>n</i>-homodesmotic hierarchy of hydrocarbon reactions (RC0âRC5
test sets). The overall performance of this method is better than
the related direct random phase approximation-based double-hybrid
PWRB95 method on open-shell systems of main-group elements (from the
GMTKN30 database) and comparable to the best <i>O</i>(<i>N</i><sup>4</sup>)-scaling opposite-spin second-order perturbation
theory-based double-hybrid methods like PWPB95-D3 and to the <i>O</i>(<i>N</i><sup>5</sup>)-scaling RPAX2@PBEx method,
which also includes exchange interactions. Furthermore, it gives well-balanced
performance on many types of barrier heights similarly to the best <i>O</i>(<i>N</i><sup>5</sup>)-scaling second-order perturbation
theory-based or spin-component scaled second-order perturbation theory-based
double-hybrid methods such as XYG3 or DSD-PBEhB95. Finally, we show
that the SCS-dRPA75 method has reduced self-interaction and delocalization
errors compared to the parent dRPA75 method and a slightly smaller
static correlation error than the related PWRB95 method
Accurate, Precise, and Efficient Theoretical Methods To Calculate AnionâĎ Interaction Energies in Model Structures
A correct
description of the anionâĎ interaction is essential for
the design of selective anion receptors and channels and important
for advances in the field of supramolecular chemistry. However, it
is challenging to do accurate, precise, and efficient calculations
of this interaction, which are lacking in the literature. In this
article, by testing sets of 20 binary anionâĎ complexes
of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene,
1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine
and 30 ternary ĎâanionâĎⲠsandwich
complexes composed from the same monomers, we suggest domain-based
local-pair natural orbital coupled cluster energies extrapolated to
the complete basis-set limit as reference values. We give a detailed
explanation of the origin of anionâĎ interactions, using
the permanent quadrupole moments, static dipole polarizabilities,
and electrostatic potential maps. We use symmetry-adapted perturbation
theory (SAPT) to calculate the components of the anionâĎ
interaction energies. We examine the performance of the direct random
phase approximation (dRPA), the second-order screened exchange (SOSEX),
local-pair natural-orbital (LPNO) coupled electron pair approximation
(CEPA), and several dispersion-corrected density functionals (including
generalized gradient approximation (GGA), meta-GGA, and double hybrid
density functional). The LPNO-CEPA/1 results show the best agreement
with the reference results. The dRPA method is only slightly less
accurate and precise than the LPNO-CEPA/1, but it is considerably
more efficient (6â17 times faster) for the binary complexes
studied in this paper. For 30 ternary ĎâanionâĎâ˛
sandwich complexes, we give dRPA interaction energies as reference
values. The double hybrid functionals are much more efficient but
less accurate and precise than dRPA. The dispersion-corrected double
hybrid PWPB95âD3Â(BJ) and B2PLYPâD3Â(BJ) functionals perform
better than the GGA and meta-GGA functionals for the present test
set