for main group and s-block containing molecules, while the more recently proposed
thresholds of T 1 greater than 0.05 and D 1 greater than 0.15 are used for transition
metal-containing compounds [28].
Calculations were performed using GAMESS [13]. Restricted Hartree-Fock
(RHF or ROHF) calculations were performed for all of the molecules. Unrestricted
HF (UHF) calculations also were performed for O 2 and FeO as UHF can describe
multireference character arising from bond breaking, albeit with the disadvantage of
producing wave functions that are not spin eigenfunctions. CR-CC(2,3) calculations
also were performed to examine the impact of the Hartree-Fock reference on a
correlated wave function method. The Sapporo-2012 triple-ζ all-electron basis sets
were used for all calculations [29]. The Sapporo-2012 basis sets were chosen
because they cover most of the periodic table and are generally more compact than
other correlation consistent basis sets. Potential energy curves (PECs) for each
diatomic were calculated from about 1.4 Å to about 3.5 Å in 0.1 Å increments, then
decreased to 0.01 Å and then 0.001 Å around the minimum of the curve, when
possible in order to determine the equilibrium bond length accurate to 10
−3
Å.
Restricted open-shell (RO) DFT also was used to calculate PECs for FeO using four
popular DFT functionals: B3LYP [30, 31], PBE0 [32, 33], M06 [34], and M11
[35]. All calculations were restricted to C 2v symmetry.
When single point energy calculations resulted in an excited state for FeO, the
full excited state potential energy curves were constructed using the Maximum
Overlap Method (MOM) of Gilbert, Besley, and Gill [2]. In this approach, excited
state solutions to the Hartree-Fock equations are determined by populating the
orbitals that overlap the most with the previously occupied orbitals in contrast to
occupation according to the aufbau principle, in which the lowest energy orbitals
are always populated first. Using this approach keeps the wave function from
collapsing to the lowest energy solution.
3 Results and Discussion
The calculated ground state of each molecule, the experimental bond lengths, and
the equilibrium bond lengths based on the computed potential energy curves at both
the HF and CR-CC(2,3) levels of theory are shown in Table 1. Bond lengths
computed using both the H core and Hückel guesses are reported, as well as the mean
signed deviation (MSD), mean absolute deviation (MAD), and root-mean-square
deviation (RMSD).
On average, HF underestimates the bond lengths by 0.014 and 0.020 Å, while
CR-CC(2,3) overestimates the bond lengths by 0.033 and 0.039 Å for the H core and
Hückel guesses, respectively, as accounting for electron correlation tends to make
the electron density more diffuse [36, 37]. Two notable exceptions from this trend
are NaCl and FeO. The HF calculated equilibrium bond length for NaCl is 0.027 Å
too long using either guess. In the case of FeO, the HF calculated bond length using
the H core guess is 0.054 Å too long, while the Hückel guess is unable to produce a
8
R. Weber et al.
thresholds of T 1 greater than 0.05 and D 1 greater than 0.15 are used for transition
metal-containing compounds [28].
Calculations were performed using GAMESS [13]. Restricted Hartree-Fock
(RHF or ROHF) calculations were performed for all of the molecules. Unrestricted
HF (UHF) calculations also were performed for O 2 and FeO as UHF can describe
multireference character arising from bond breaking, albeit with the disadvantage of
producing wave functions that are not spin eigenfunctions. CR-CC(2,3) calculations
also were performed to examine the impact of the Hartree-Fock reference on a
correlated wave function method. The Sapporo-2012 triple-ζ all-electron basis sets
were used for all calculations [29]. The Sapporo-2012 basis sets were chosen
because they cover most of the periodic table and are generally more compact than
other correlation consistent basis sets. Potential energy curves (PECs) for each
diatomic were calculated from about 1.4 Å to about 3.5 Å in 0.1 Å increments, then
decreased to 0.01 Å and then 0.001 Å around the minimum of the curve, when
possible in order to determine the equilibrium bond length accurate to 10
−3
Å.
Restricted open-shell (RO) DFT also was used to calculate PECs for FeO using four
popular DFT functionals: B3LYP [30, 31], PBE0 [32, 33], M06 [34], and M11
[35]. All calculations were restricted to C 2v symmetry.
When single point energy calculations resulted in an excited state for FeO, the
full excited state potential energy curves were constructed using the Maximum
Overlap Method (MOM) of Gilbert, Besley, and Gill [2]. In this approach, excited
state solutions to the Hartree-Fock equations are determined by populating the
orbitals that overlap the most with the previously occupied orbitals in contrast to
occupation according to the aufbau principle, in which the lowest energy orbitals
are always populated first. Using this approach keeps the wave function from
collapsing to the lowest energy solution.
3 Results and Discussion
The calculated ground state of each molecule, the experimental bond lengths, and
the equilibrium bond lengths based on the computed potential energy curves at both
the HF and CR-CC(2,3) levels of theory are shown in Table 1. Bond lengths
computed using both the H core and Hückel guesses are reported, as well as the mean
signed deviation (MSD), mean absolute deviation (MAD), and root-mean-square
deviation (RMSD).
On average, HF underestimates the bond lengths by 0.014 and 0.020 Å, while
CR-CC(2,3) overestimates the bond lengths by 0.033 and 0.039 Å for the H core and
Hückel guesses, respectively, as accounting for electron correlation tends to make
the electron density more diffuse [36, 37]. Two notable exceptions from this trend
are NaCl and FeO. The HF calculated equilibrium bond length for NaCl is 0.027 Å
too long using either guess. In the case of FeO, the HF calculated bond length using
the H core guess is 0.054 Å too long, while the Hückel guess is unable to produce a
8
R. Weber et al.