the spin-flip method, Hartree-Fock is used to describe the reference system, so there
is still some dependence on HF being able to determine the correct electronic
configuration.
Multireference methods such as the multiconfigurational self-consistent field
(MCSCF) [19] and complete active space perturbation theory, second order
(CASPT2) [20], among many others, are designed specifically to recover nondynamical correlation energy. However, there are drawbacks to these methods
[21, 22]. The scaling of these methods is such that it is generally limited to systems
of no more than sixteen active electrons within sixteen active orbitals [19]. Furthermore, the selection of an appropriate active space can be system dependent and
ensures that these methods are by no means “black box”. The HF wavefunction
generally serves as the reference wavefunction for these methods as well and can be
used to help determine the orbitals that should be included within the active space.
A wavefunction that has converged to the wrong state can lead to very slow convergence or to completely inappropriate orbitals included within the active space.
Another popular approach to incorporate some degree of electron correlation is
density functional theory (DFT). It has found use in the calculation of ground state
properties for organic and inorganic molecules [23]. DFT has the benefit of
including correlation within the calculation beyond the mean field correlation that is
included within Hartree-Fock, yet the computational cost is on par with a HartreeFock calculation. DFT generally achieves a reasonable balance between computational cost and accuracy [23]. However, as a single reference method, it may
suffer from some of the same limitations as Hartree-Fock theory.
The molecules included in this study were chosen for illustrative purposes only.
While the molecules all have been the focus of prior extensive theoretical and
experimental studies, our goal is not to provide a broad review of the literature, but
rather to illustrate some of the problems that can manifest when the optimized
orbital occupancy is not considered.
2 Computational Methods
The diatomic molecules chosen for this study were O 2 , F 2 , Cl 2 , Br 2 , LiF, NaCl,
CaO, MgO, ScO, FeO, TiO, YO, and ZrO. These molecules cover many parts of the
periodic table including main group diatomics with light and heavy atoms, diatomics containing s-block elements, and diatomics containing transition metals.
Additionally, both closed shell and open shell species are included. All molecules
studied were the neutral species. The experimental bond lengths were taken from
the NIST Chemistry WebBook (http://www.webbook.nist.gov) [24].
To gauge the possible multireference character of the molecules, T 1 and D 1
diagnostic values were calculated [25–27]. The T 1 and D 1 diagnostic values are
related to the magnitude of the oscillator strength of single excitations and thus
are frequently used to estimate the multireference character of a molecule. A T 1
value of 0.02 and a D 1 value of 0.05 are considered the multireference thresholds
The Importance of Orbital Analysis
7
is still some dependence on HF being able to determine the correct electronic
configuration.
Multireference methods such as the multiconfigurational self-consistent field
(MCSCF) [19] and complete active space perturbation theory, second order
(CASPT2) [20], among many others, are designed specifically to recover nondynamical correlation energy. However, there are drawbacks to these methods
[21, 22]. The scaling of these methods is such that it is generally limited to systems
of no more than sixteen active electrons within sixteen active orbitals [19]. Furthermore, the selection of an appropriate active space can be system dependent and
ensures that these methods are by no means “black box”. The HF wavefunction
generally serves as the reference wavefunction for these methods as well and can be
used to help determine the orbitals that should be included within the active space.
A wavefunction that has converged to the wrong state can lead to very slow convergence or to completely inappropriate orbitals included within the active space.
Another popular approach to incorporate some degree of electron correlation is
density functional theory (DFT). It has found use in the calculation of ground state
properties for organic and inorganic molecules [23]. DFT has the benefit of
including correlation within the calculation beyond the mean field correlation that is
included within Hartree-Fock, yet the computational cost is on par with a HartreeFock calculation. DFT generally achieves a reasonable balance between computational cost and accuracy [23]. However, as a single reference method, it may
suffer from some of the same limitations as Hartree-Fock theory.
The molecules included in this study were chosen for illustrative purposes only.
While the molecules all have been the focus of prior extensive theoretical and
experimental studies, our goal is not to provide a broad review of the literature, but
rather to illustrate some of the problems that can manifest when the optimized
orbital occupancy is not considered.
2 Computational Methods
The diatomic molecules chosen for this study were O 2 , F 2 , Cl 2 , Br 2 , LiF, NaCl,
CaO, MgO, ScO, FeO, TiO, YO, and ZrO. These molecules cover many parts of the
periodic table including main group diatomics with light and heavy atoms, diatomics containing s-block elements, and diatomics containing transition metals.
Additionally, both closed shell and open shell species are included. All molecules
studied were the neutral species. The experimental bond lengths were taken from
the NIST Chemistry WebBook (http://www.webbook.nist.gov) [24].
To gauge the possible multireference character of the molecules, T 1 and D 1
diagnostic values were calculated [25–27]. The T 1 and D 1 diagnostic values are
related to the magnitude of the oscillator strength of single excitations and thus
are frequently used to estimate the multireference character of a molecule. A T 1
value of 0.02 and a D 1 value of 0.05 are considered the multireference thresholds
The Importance of Orbital Analysis
7