Although the M06 functional was fairly broadly parameterized in the course of
its construction, problems still arise when calculating a potential energy curve for
FeO (Fig. 18). Using the H core initial guess, only the points between 1.7 and 2.0 Å
converged successfully. From this point, however, the optimized orbitals from a
converged point were used as the initial guess for the next point on the curve with
orbital rotations restricted. Similar to the MOM method, this does ensure that the
calculated curve is constrained to one electronic state. However, with the exception
of a converged point at 2.6 Å, the points for the remainder of the curve past 2.2 Å
do not converge. Using the Hückel initial guess results in only two points that
converged, at 1.8 and 2.0 Å. With the optimized orbitals from these two points,
points at 1.7 and 1.9 Å were converged. For the remainder of the curve, however,
even utilizing the optimized orbitals as an initial guess did not provide a good
enough starting guess for the calculations to converge.
The M11 functional performed by far the best of the tested functionals in calculating the potential energy curve for FeO (Fig. 19). Using the H core initial guess a
curve was produced that was mostly smooth around the minimum with the
exception of a point at 1.55 Å. The calculated electronic state is
5 A 1, a state that
results from a combination of an A 2 , A 1 , B 2 , and B 1 orbitals, all of which are iron
d orbitals. The H core initial guess was sufficient for the points to converge from 1.4
to 1.64 Å. At 1.65 Å, the optimized orbitals were used for the starting guess, but it
was not necessary to restrict orbital rotations to reach convergence until points in
the IID region of the curve (specifically, 2.2, 2.3, 2.5, 3.2, and 3.3 Å). The point at
2.5 Å is a
5 A 2 electronic state, from the occupation of a B 1 , B 2 , and two A 1 orbitals,
all of which are still iron d orbitals. At 2.6 Å, there is a discontinuity in the curve
and a lower energy electronic state is followed for the remainder of the curve. This
electronic state is
5 B 2 , from the occupation of a B 1 orbital that is a combination of
an iron d orbital and an oxygen p orbital, and A 1 , B 2 , and B 1 orbitals, all of which
are iron d orbitals. This is a limitation inherent in using a restricted open shell
formulation to describe dissociation.
The Hückel initial guess is sufficient for points to converge from 1.4 to 2.1 Å,
however the curve is not continuous, especially beginning at 2.0 Å. From 2.2 to
2.5 Å, the optimized orbitals had to provide the initial guess in order for the
calculation to converge, and from 2.6 Å orbital rotations had to be restricted as well.
The calculated electronic ground state at the minimum is a
5 A 1 state. The occupation is in iron d orbitals of symmetry A 2 , A 1 , B 2 , and B 1 . At 2.0 Å, the electronic
state changes to
5 B 1 (the direct product of B 2 , A 1 , A 2 , and A 1 orbitals), with an
oxygen p x orbital included within the singly occupied orbitals. The excited state at
2.2 Å results from the occupation of an iron s orbital as well as an oxygen p x orbital
and is a
5 A 1 state. At 3.0 Å, the electronic state is still a
5 A 1 state, yet this is a result
of a combination of oxygen p x and p y orbitals being populated. The potential energy
curve generated by the Hückel guess demonstrates that, although the calculations
converged to an answer fairly easily, inspection of the singly occupied orbitals
shows that an excited state has been determined to be the ground state.
In addition to determining the equilibrium bond length from the minimum of the
calculated potential energy curve, gradient-drive geometry optimizations were
The Importance of Orbital Analysis
25
its construction, problems still arise when calculating a potential energy curve for
FeO (Fig. 18). Using the H core initial guess, only the points between 1.7 and 2.0 Å
converged successfully. From this point, however, the optimized orbitals from a
converged point were used as the initial guess for the next point on the curve with
orbital rotations restricted. Similar to the MOM method, this does ensure that the
calculated curve is constrained to one electronic state. However, with the exception
of a converged point at 2.6 Å, the points for the remainder of the curve past 2.2 Å
do not converge. Using the Hückel initial guess results in only two points that
converged, at 1.8 and 2.0 Å. With the optimized orbitals from these two points,
points at 1.7 and 1.9 Å were converged. For the remainder of the curve, however,
even utilizing the optimized orbitals as an initial guess did not provide a good
enough starting guess for the calculations to converge.
The M11 functional performed by far the best of the tested functionals in calculating the potential energy curve for FeO (Fig. 19). Using the H core initial guess a
curve was produced that was mostly smooth around the minimum with the
exception of a point at 1.55 Å. The calculated electronic state is
5 A 1, a state that
results from a combination of an A 2 , A 1 , B 2 , and B 1 orbitals, all of which are iron
d orbitals. The H core initial guess was sufficient for the points to converge from 1.4
to 1.64 Å. At 1.65 Å, the optimized orbitals were used for the starting guess, but it
was not necessary to restrict orbital rotations to reach convergence until points in
the IID region of the curve (specifically, 2.2, 2.3, 2.5, 3.2, and 3.3 Å). The point at
2.5 Å is a
5 A 2 electronic state, from the occupation of a B 1 , B 2 , and two A 1 orbitals,
all of which are still iron d orbitals. At 2.6 Å, there is a discontinuity in the curve
and a lower energy electronic state is followed for the remainder of the curve. This
electronic state is
5 B 2 , from the occupation of a B 1 orbital that is a combination of
an iron d orbital and an oxygen p orbital, and A 1 , B 2 , and B 1 orbitals, all of which
are iron d orbitals. This is a limitation inherent in using a restricted open shell
formulation to describe dissociation.
The Hückel initial guess is sufficient for points to converge from 1.4 to 2.1 Å,
however the curve is not continuous, especially beginning at 2.0 Å. From 2.2 to
2.5 Å, the optimized orbitals had to provide the initial guess in order for the
calculation to converge, and from 2.6 Å orbital rotations had to be restricted as well.
The calculated electronic ground state at the minimum is a
5 A 1 state. The occupation is in iron d orbitals of symmetry A 2 , A 1 , B 2 , and B 1 . At 2.0 Å, the electronic
state changes to
5 B 1 (the direct product of B 2 , A 1 , A 2 , and A 1 orbitals), with an
oxygen p x orbital included within the singly occupied orbitals. The excited state at
2.2 Å results from the occupation of an iron s orbital as well as an oxygen p x orbital
and is a
5 A 1 state. At 3.0 Å, the electronic state is still a
5 A 1 state, yet this is a result
of a combination of oxygen p x and p y orbitals being populated. The potential energy
curve generated by the Hückel guess demonstrates that, although the calculations
converged to an answer fairly easily, inspection of the singly occupied orbitals
shows that an excited state has been determined to be the ground state.
In addition to determining the equilibrium bond length from the minimum of the
calculated potential energy curve, gradient-drive geometry optimizations were
The Importance of Orbital Analysis
25