Toward Accurate Theoretical Thermochemistry of First Row Transition Metal Complexes Page: 873
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The Journal of Physical Chemistry A
Table 1. Different Variants of the ccCA-TM Algorithma
cc-CA-TMgeometry optimization
ZPE
HF/CBS
MP2/CBS
correlation corrections
core-valence correctionsB3LYP/cc-pVTZ
experimental values for atoms
B3LYP/cc-pVTZ
harmonic frequencies scaled by 0.989
for molecules
HF/aug-cc-pVTZ-DK
HF/aug-cc-pVQZ-DK
E(n) = E(HF/CBS) + A exp(-1.63n)
MP2/aug-cc-pVDZ-DK
MP2/aug-cc-pVTZ-DK
MP2/aug-cc-pVQZ-DK
"P": eq3b
"S3": eq4b
"S4": eqSb
"PS3": 1/2 ("P" + "S3")b
"S3h": eq6
"S4h": eq 7
CCSD(T)/cc-pVTZ-DK - MP2/cc-pVTZ-DK
CCSD(T,FC1)/aug-cc-pCVDZ
- CCSD(T)/aug-cc-pCVDZspin-orbit corrections experimental values for atoms when applicable
FOCI Stuttgart ECP for molecules
when applicable
a Both ROHF and UHF references can be considered for open-shell
molecules. b lmax = n for "TQ' or (n + 1) for "QS".
To reduce the computational cost, the aug-cc-pCVDZ-DK basis
set is used instead of aug-cc-pCVTZ-DK.
AE(CV) = E[CCSD(T, FC1)/aug -cc-pCVDZ-DK]
- E[CCSD(T)/aug-cc-pCVDZ-DK] (9)
The notation "FC1" indicates that the inner shell closest to the
valence shell is included as active, which means, in addition to
valence electrons, is electrons are correlated for Li-Ne, 2s2p
electrons correlated for Na-Ar, 3s3p electrons correlated for
K-Zn including 3d transition metals, and 3s3p3d electrons
correlated for Ga-Kr. The aug-cc-pCVDZ-DK basis sets are
generated by adding the core/valence basis set functions to aug-
cc-pVDZ-DK without further optimization. All ccCA-TM var-
iants and their corresponding notations are detailed in Table 1.
The spin-orbit coupling corrections6s were calculated for
molecules when applicable and tractable. Spin-orbit interac-
tions were approximately considered as the energy difference
between the lowest L-S state and the state averaged, where the
energies of each L-S state were obtained by diagonalizing the
effective spin-orbit Hamiltonian on the basis of contracted
CASSCF wave functions.
In this study, all CASSCF computations are performed with
the cc-pVTZ-DK basis set, and T1/D1 diagnostics and spin
contamination are extracted from CCSD/cc-pVTZ-DK calcula-
tions on the basis of HF or ROHF canonical orbitals. All
computations were performed using MOLPRO 2006.166 except
for UHF ccCA-TM energies, which were obtained in Gaussian
03.67 In Gaussian 03 DKH calculations, the nuclei are simulated
as point charges so that the scalar relativistic energies for closed-
shell systems are equivalent to those computed in MOLPRO.68When the experimental enthalpies of formation from various
sources are in disagreement, the experimental value with the least
experimental uncertainty is usually selected for the molecules.
Values from recent literature are adopted when the experimental
uncertainties are comparable to earlier data. We note that
occasionally experimental data reported with a large uncer-
tainty are found in better agreement with theoretical prediction,
for example, the standard enthalpy of Cr03 as discussed in ref 8.
No attempts were generally made to select the experimental data
in better agreement with theoretical predictions. Decisions made
on the adopted experimental value of specific cases (and the rare
exceptions) are explicitly detailed below, and a full listing of all
experimental values located in the literature is provided in Tables
S3 and S4 of the Supporting Information.
RESULTS AND DISCUSSION
A. Effects of CBS Extrapolation Schemes. The Peterson
extrapolation (eq 3) and its averaged PS3 extrapolation with S3
(eq 4) for correlation energies have been used previously in the
CCSD(T) CBS69'70 and main group ccCA studies.48 Although it
is inconclusive that one extrapolation is generally superior to
others for the CCSD(T) CBS limits, it is beneficial to assess the
effectiveness of the possible schemes (Table 1). Consistent with
our earlier observations,7' utilization of the ROHF reference
wave function for open-shell molecules gives substantially better
results than a UHF reference wave function by minimizing the
effect of spin contamination. Only ROHF-ccCA-TM results are
discussed below. For the ccCA-TM/11 set, the differences
among different extrapolations are less than 0.2 kcal mol-1,
except for S3(Q5), which has a MAD of 4.72 kcal mol-, 0.37
kcal mol-1 greater than the ROHF-ccCA-TM-P MAD of 4.35
kcal moll (Figure 1). For subsets of different experimental
uncertainty ranges, the S3(Q5) MAD is 0.4-1.1 kcal mol-
larger than the best CBS extrapolation scheme. The S4(TQ) and
PS3(TQ) schemes remain close to ccCA-TM-P with a differ-
ence of less than 0.05 kcal mo' in MAD for all subsets as well as
the overall set, and thus can be considered equivalent alterna-
tives. As the size of set increases, the CBS extrapolations choice
has less impact on the accuracy on average. Different patterns are
found in mean signed deviation (MSD) of various extrapolation
schemes. While the P, S4(TQ) variants have negative MSDs for
all subsets, S3(TQ), PS3(TQ), S4h, S4(Q5), and PS3(Q5)
show a change from positive MSD to negative MSD as the subset
size increases, and S3(Q5) and S3h have positive MSDs for all
subsets. Similar to the findings for CCSD(T) CBS energies,69,70
historically preferred extrapolations do not show statistically
significant differences. In the following, only the ROHF-ccCA-
TM results with the mixed Gaussian/inverse exponential form
("P", eq 3) are discussed. "ROHF" is omitted unless specified
otherwise.
B. 3d Transition Metal-Containing Species and Metal
Dimers. The ccCA-TM algorithm has been applied to calculate
the standard AHfs for the ccCA-TM/11all set of 225 transition
metal species, about 4 times larger than the set in our previous
study." Although numerous theoretical studies have been per-
formed on some of the species in our test set, and the thermo-
dynamic properties and electronic structure of their ground state
have been well-established (for examples, see a comprehensive
review of the electronic structure of diatomic 3d block molecules
by Harrison72), there are also quite a few species for which littleinformation exists on the equilibrium geometry, spin multiplicity,
dx.doi.org/1O.1021/jp205710e IJ. Phys. Chem. A 2012, 116, 870-885
873
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Jiang, Wanyi; DeYonker, Nathan J. & Wilson, Angela K. Toward Accurate Theoretical Thermochemistry of First Row Transition Metal Complexes, article, November 22, 2011; Washington, DC. (https://digital.library.unt.edu/ark:/67531/metadc991034/m1/4/: accessed July 15, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.