79 research outputs found
Density Functional Theory and the Basis Set Truncation Problem with Correlation Consistent Basis Sets: Elephant in the Room or Mouse in the Closet?
Two
recent papers in this journal called into question the suitability
of the correlation consistent basis sets for density functional theory
(DFT) calculations, because the sets were designed for correlated
methods such as configuration interaction, perturbation theory, and
coupled cluster theory. These papers focused on the ability of the
correlation consistent and other basis sets to reproduce total energies,
atomization energies, and dipole moments obtained from âquasi-exactâ
multiwavelet results. Undesirably large errors were observed for the
correlation consistent basis sets. One of the papers argued that basis
sets specifically optimized for DFT methods were âessentialâ
for obtaining high accuracy. In this work we re-examined the performance
of the correlation consistent basis sets by resolving problems with
the previous calculations and by making more appropriate basis set
choices for the alkali and alkaline-earth metals and second-row elements.
When this is done, the statistical errors with respect to the benchmark
values and with respect to DFT optimized basis sets are greatly reduced,
especially in light of the relatively large intrinsic error of the
underlying DFT method. When judged with respect to high-quality Feller-Peterson-Dixon
coupled cluster theory atomization energies, the PBE0 DFT method used
in the previous studies exhibits a mean absolute deviation more than
a factor of 50 larger than the quintuple zeta basis set truncation
error
Low-Lying Electronic States of Ir<sub><i>n</i></sub> Clusters with <i>n</i> = 2â8 Predicted at the DFT, CASSCF, and CCSD(T) Levels
Low-lying structures of the small
iridum clusters Ir<sub><i>n</i></sub> (<i>n</i> = 2â8) were optimized
using DFT methods. Ir<sub>2</sub> and Ir<sub>3</sub> were also optimized
using the CASSCF method. MRCI-SD (for Ir<sub>2</sub>) energies and
CCSDÂ(T) (for Ir<sub>2</sub> and Ir<sub>3</sub>) energies of the leading
configurations from the CASSCF calculations were done to predict the
low-lying states. The normalized atomization energies (â¨AEâŠ)
for Ir<sub><i>n</i></sub> (<i>n</i> = 2â8)
were calculated at the CCSDÂ(T) level up to the complete basis set
(CBS) limit in some cases using the B3LYP optimized geometries. The
ground state for Ir<sub>2</sub> is predicted to be <sup>5</sup>Î<sub>g</sub>, and the ground state of Ir<sub>3</sub> is linear <sup>2</sup>Î<sub>g</sub>, with the <i>D</i><sub>3<i>h</i></sub> <sup>4</sup>Aâł<sub>1</sub> state âź10 kcal/mol
higher in energy at the CASSCF level without coreâvalence corrections
and âź15 kcal/mol higher at the CCSDÂ(T)/CBS level with spinâorbit
and coreâvalence corrections. Inclusion of the spin orbit corrections
in the normalized bond dissociation energies â¨AE⊠for
Ir<sub><i>n</i></sub> is critical and will decrease the
â¨AE⊠by âź15 kcal/mol for <i>n</i> âĽ
4. The â¨AE⊠for Ir<sub><i>n</i></sub> increases
as <i>n</i> increases in general, and the â¨AEâŠ
is far from convergence to the bulk value at <i>n</i> =
8. The average coordination number (CN) and average bond length for
the low energy Ir<sub><i>n</i></sub> clusters are far from
being converged to the bulk values by <i>n</i> = 8
Machine-Learning Approach for the Development of StructureâEnergy Relationships of ZnO Nanoparticles
The structureâenergy
relationships for the zinc oxide morphologies
were investigated using a newly developed fragment-based energy decomposition
approach. In this approach, the local chemical compositions of a material
are abstracted as fragment types that serve as the materialâs
genes with respect to its thermodynamic properties. A machine learning-based
fragment recognition scheme was developed to learn about the fragment-related
knowledge from a relatively small training set consisting of computationally
viable ultrasmall nanoparticles. The knowledge gained including the
fragment geometries and fragment energy parameters can be used for
the classification and energy expression of the test sets consisting
of different polymorphs and morphologies of that material at various
scales. The stabilities of ZnO nanoparticles with different morphologies
were expressed explicitly as functions of the particle size. The size-related
phase transitions among various morphologies including wurtzite prisms,
wurtzite octahedrons, body-centered tetragonal particles, sodalite-like
particles, single-layered cages, multilayered cages, and nonpolar
hexagonal prisms were predicted. The multilayered cages with nonpolar
surfaces exhibit superior stability among the low-energy morphologies,
but wurtzite nanoparticles are more favorable under practical synthesis
and growth conditions under the control of the kinetics. The growth
mechanism for ZnO clusters, ultrasmall nanoparticles, nanocrystals,
and bulk-sized particles is proposed based on the synergy between
the size-related phase transitions and external factors that affect
the surface energies of the particles. Our interpretation of the Wulff
theorem at a fragment-sized resolution provides new chemical insight
for understanding the structural phase transition and particle growth
for ZnO at various scales
Computational Study of H<sub>2</sub> and O<sub>2</sub> Production from Water Splitting by Small (MO<sub>2</sub>)<sub><i>n</i></sub> Clusters (M = Ti, Zr, Hf)
Coupled
cluster [CCSDÂ(T)] theory and density functional theory
(DFT) have been used to study the production of H<sub>2</sub> and
O<sub>2</sub> from hydrolysis products generated from H<sub>2</sub>O addition to (MO<sub>2</sub>)<sub><i>n</i></sub> (M =
Ti, Zr, Hf, <i>n</i> = 1â3) clusters on both the
lowest singlet and triplet potential energy surfaces (PESs). H<sub>2</sub> production occurs via the formation of an MâH containing
intermediate followed by HâH recombination and H<sub>2</sub> desorption from M<sub><i>n</i></sub>O<sub>2<i>n</i></sub>(OH)<sub>2</sub> and M<sub><i>n</i></sub>O<sub>2<i>n</i>+2</sub>. The hydrogen transfer reactions to form the MâH
bond are the rate determining steps and can be considered to be proton
coupled, electron transfer (PCET) reactions with one or two electrons
being transferred. Oxygen is produced by breaking two weak MâO
bonds in an atomic oxygen saturated metal oxide from an M<sub><i>n</i></sub>O<sub>2<i>n</i></sub>â˘O<sub>2</sub> intermediate. On the triplet PES, the activation energies for the
first and second H transfer to the metal are calculated to be âź10
to 50 kcal/mol and âź75 to 90 kcal/mol depending on the size
of the clusters and the metal. The barriers on the singlet surface
for the first and the second H transfer are predicted to be 110 to
140 kcal/mol, in general larger than the HâO bond dissociation
energy. The activation barriers for the step of HâH recombination
are 15 to 50 kcal/mol, and the H<sub>2</sub> desorption energies are
less than 10 kcal/mol on the singlet and triplet PESs. The oxygen
desorption energies follow the order Ti < Zr < Hf for the triplets
and Ti < Zr â Hf for the singlets. The oxygen desorption
energy is approximately independent of the size of the cluster for
the same metal. The water splitting reactions prefer to take place
on the triplet surface. A low excess potential energy is needed to
generate 2H<sub>2</sub> and O<sub>2</sub> from 2H<sub>2</sub>O after
the endothermicity of the reaction is overcome on the triplet PES
Computational Study of Ethanol Conversion on Al<sub>8</sub>O<sub>12</sub> as a Model for ÎłâAl<sub>2</sub>O<sub>3</sub>
Correlated molecular orbital theory
at the coupled cluster CCSDÂ(T)
level with density functional theory geometries is used to study ethanol
dehydration, dehydrogenation, and condensation reactions on an the
Al<sub>8</sub>O<sub>12</sub> cluster which is a model for Îł<b>-</b>Al<sub>2</sub>O<sub>3</sub>. The Al in the active site on
the cluster is a strong Lewis acid. The reactions begin with formation
of a very stable Lewis acidâbase ethanolâcluster adduct.
Dehydration proceeds by β-H transfer to a bicoordinate oxygen
leading to the direct formation of ethylene and two OH groups following
an E2 mechanism. Dehydrogenation proceeds directly by Îą-H transfer
to the active metal center and a proton transfer to a bicoordinate
bridge O to form acetaldehyde plus a metal hydride and a hydroxyl,
again an E2 mechanism. After addition of a second ethanol, diethyl
ether is generated by an Îą-C transfer from the first to the
second ethanol, an acid-driven S<sub>N</sub>2 mechanism. Condensation
and dehydration with two alcohols have comparable energy barriers.
The addition of a second ethanol or a water molecule raises the energy
barriers. Condensation and dehydration are predicted to be more likely
than dehydrogenation. The computational results for the mechanism
and the energetics agree well with the available experimental data
Absolute Hydration Free Energy of Small Anions and the Aqueous p<i>K</i><sub>a</sub> of Simple Acids
Heats of formation and gas phase acidities for the simple
acids
and their deprotonated anions (Aâ = Fâ, Clâ, Brâ, Iâ, OHâ, SHâ, SeHâ, TeHâ, OClâ, OBrâ, and OIâ) were calculated using the FellerâPetersonâDixon
(FPD) method with large basis sets including DouglassâKroll
scalar relativistic corrections. Hydration of the neutral and anionic
species was predicted using the supermolecule-continuum approach,
resulting in absolute hydration free energies that, when combined
with calculated gas phase acidities, produce aqueous acidities and
pKa values for these simple acids that
are, in general, in excellent agreement with experimental literature
values. Absolute hydration free energy values converged quickly in
terms of the experimental values for neutral species, requiring only
four explicit H2O molecules. HI is anomalous in that it
fully dissociates ionically in a water tetramer and was treated without
explicit water molecules. The hydration energies of anionic species
converged more slowly and were modeled with up to 16 explicit H2O molecules. Calculated values for ÎHf and ÎGgas agree with
experimental values within ca. 1.2 kcal/mol, and
ÎGaq and ÎÎGhyd agree with experimental values within ca. 2 kcal/mol in most cases
Electronic Structures of Small (RuO<sub>2</sub>)<sub><i>n</i></sub> (<i>n</i> = 1â4) Nanoclusters and Their Anions and the Hydrolysis Reactions with Water
Group 8 (RuO<sub>2</sub>)<sub><i>n</i></sub> (<i>n</i> = 1â4)
nanoclusters, their anions, and the hydrolysis
reactions of the neutral clusters have been studied with the density
functional theory (DFT) as well as coupled cluster CCSDÂ(T) theory.
The ground state is predicted to be a singlet and a doublet for the
neutral RuO<sub>2</sub> clusters and anionic clusters, respectively.
The CCSDÂ(T) method is required to predict the correct ground state.
The calculated singletâtriplet gaps (<15 kcal/mol) and fluoride
affinities (<95 kcal/mol) are smaller than those of the group 4
(MO<sub>2</sub>)<sub><i>n</i></sub> and group 6 (MO<sub>3</sub>)<sub><i>n</i></sub> metal oxide clusters. The electron
affinities range from 2.2 to 3.4 eV, showing that the RuO<sub>2</sub> clusters are quite reducible. Clustering energies and heats of formation
are calculated. The water physisorption energies are predicted to
be â10 to â20 kcal/mol with the adsorption energy for
the singlet being generally more exothermic than that for the triplet.
The hydrolysis reactions are exothermic for the monomer and dimer
clusters and are slightly endothermic or neutral for the trimer and
tetramer. H<sub>2</sub>O is readily dissociated on the monomer and
dimer but not on the trimer and tetramer. The physisorption and chemisorption
energies are less exothermic, and the barriers for the hydrolysis
reactions are larger for RuO<sub>2</sub> nanoclusters than for the
corresponding group 4 ZrO<sub>2</sub> nanoclusters
Benchmark-Quality Atomization Energies for BeH and BeH<sub>2</sub>
The total atomization energies for
BeH and BeH<sub>2</sub> have
been calculated using the FellerâPetersonâDixon approach
to better than Âą1 kcal/mol. The calculations are based on CCSDÂ(T)
all-electron calculations extrapolated to the complete limit, and
CCSDT and CCSDTQ corrections are included. A scalar relativistic correction
and a diagonal BornâOppenheimer correction are included. Accurate
zero-point energies are used. The total atomization energies at 0
K are 47.7 kcal/mol for BeH and 140.0 kcal/mol for BeH<sub>2</sub> with error of at most Âą0.3 kcal/mol
1,2-Ethanediol and 1,3-Propanediol Conversions over (MO<sub>3</sub>)<sub>3</sub> (M = Mo, W) Nanoclusters: A Computational Study
The dehydration and dehydrogenation
reactions of one and two 1,2-ethanediol
and 1,3-propanediol molecules on (MO<sub>3</sub>)<sub>3</sub> (M =
Mo, W) nanoclusters have been studied computationally using density
functional and coupled cluster (CCSDÂ(T)) theory. The reactions are
initiated by the formation of a Lewis acidâbase complex with
an additional hydrogen bond. Dehydration is the dominant reaction
proceeding via a metal bisdiolate. Acetaldehyde, the major product
for 1,2-ethanediol, is produced by Îą-hydrogen transfer from
one CH<sub>2</sub> group to the other. For 1,3-propanediol, the CâC
bond breaking pathways to produce C<sub>2</sub>H<sub>4</sub> and HCHîťO
simultaneously and proton transfer to generate propylene oxide have
comparable barrier energies. The barrier to produce propanal from
the propylene oxide complex is less than that for epoxide release
from the cluster. On the Mo<sub>3</sub>O<sub>9</sub> cluster, a redox
reaction channel for 1,2-ethanediol to break the CâC bond to
form two formaldehyde molecules and then to produce C<sub>2</sub>H<sub>4</sub> is slightly more favorable than the formation of acetaldehyde.
For W<sup>VI</sup>, the energy barrier for the reduction pathway is
larger due to the lower reducibility of W<sub>3</sub>O<sub>9</sub>. Similar reduction on Mo<sup>VI</sup> for 1,3-propanediol to form
propene is not a favorable pathway compared with the other pathways
as additional CâH bond breaking is required in addition to
breaking a CâC bond. The dehydrogenation and dehydration activation
energies for the selected glycols are larger than the reactions of
ethanol and 1-propanol on the same clusters. The CCSDÂ(T) method is
required because density functional theory with the M06 and B3LYP
functionals does not predict quantitative energies on the potential
energy surface. The M06 functional performs better than does the B3LYP
functional
Role of Electronegative Substituents on the Bond Energies in the Grubbs Metathesis Catalysts for M = Fe, Ru, Os
Coupled
cluster theory [CCSDÂ(T)] with the aug-cc-pVDZ/aug-cc-pVDZ-PP
basis sets is used to predict the thermodynamic properties of models
of the Grubbs catalyst, H<sub>2</sub>ImMÂ(PH<sub>3</sub>)Â(CRRâ˛)
and H<sub>2</sub>ImMÂ(C<sub>2</sub>H<sub>4</sub>)Â(CRRâ˛) for
M = Fe, Ru, and Os and CRRⲠ= CH<sub>2</sub>, CHF, and CF<sub>2</sub>. The PH<sub>3</sub> and C<sub>2</sub>H<sub>4</sub>, imidazolinium
carbene (H<sub>2</sub>Im), and CRRⲠbond dissociation energies
(BDEs) are reported. Because of low metal-carbene BDEs, the M = Fe
complexes are unlikely to form, so they will not be good catalysts
for olefin metathesis. The metalâcarbene BDE is an important
component in metathesis catalyst design and correlates with the singletâtriplet
splitting in the carbene. The two metallacyclobutane intermediates
(cis and trans to the imidazolinium carbene) formed by reaction of the CRRâ˛îťCRRâ˛
with the 14-electron active species (H<sub>2</sub>ImMÂ(CRRâ˛))
(R and RⲠeither H or F) are investigated at the same level
of theory. The metallacycles cis to the nitrogen heterocyclic carbene
are lower in energy than the trans conformer with the exception of
four M = Fe metallacycles in the gas phase and in CH<sub>2</sub>Cl<sub>2</sub> solution at 298 K. The olefin Ď complex for the simplest
CH<sub>2</sub> ligand plus C<sub>2</sub>H<sub>4</sub> reactant combination
is more stable in the gas phase, but in CH<sub>2</sub>Cl<sub>2</sub> solution at 298 K, the cis metallacycles are more stable than the
Ď complexes or the trans metallacycles on the free energy scale
as a result of the large dipole moments in the cis metallacycles.
The results show that the best energy balance is achieved with M =
Ru, a CH<sub>2</sub> carbene substituent, and a C<sub>2</sub>H<sub>4</sub> reactant. The energetics for the Grubbs catalysts are shown
to differ from those of the Schrock catalysts
- âŚ