performed using the M11 functional as well, beginning with both the H core and
Hückel initial guesses. The optimized bond length determined using the H core initial
guess was 1.607 Å, the same as the bond length determined from the minimum of
the potential energy curve. The optimized bond length resulting from the Hückel
initial guess was 1.643, 0.036 Å longer than the bond length at the bottom of the
potential energy curve (also 1.607 Å). The experimental bond length is 1.626 Å, as
seen in Table 1. The H core -optimized bond length and the PEC-determined bond
lengths are all 0.019 Å too short, while the optimized bond length from the Hückel
guess is 0.017 Å too long.
These calculated curves demonstrate that DFT is not immune to the excited state
optimization problems either. While using a combination of DFT and the H core
initial guess, along with an initial bond length close to equilibrium, a correct bond
distance can be computed. However, using the Hückel guess can result in optimization to the wrong state and neither method is able to produce good initial
orbitals at large internuclear distances.
4 Conclusion
Potential energy curves for a set of diatomic molecules were calculated using
Hartree-Fock, CR-CC(2,3), and DFT with the B3LYP and PBE0 functionals. For
some systems, HF erroneously converged to an excited state instead of the ground
state of the molecule. Inspection of the optimized orbitals is imperative to determine
that the calculation has converged to the intended state. While optimization techniques such as the Newton-Raphson method will converge to a local minimum with
respect to the orbital coefficients, the initial orbital guess must be correctly populated as the Newton-Raphson method finds the nearest minimum rather than the
global minimum. The initial guess can be generated through several commonly
used options within computational chemistry software packages, but care must still
be taken that the correct orbitals are being populated. This requires analysis of the
converged orbitals.
In situations that contain parallel potential energy curves, convergence to an
excited state during a geometry optimization will not impact the optimized
geometry. Not every system has parallel potential energy curves, however, and
large deviations in the optimized geometries can be observed.
Even in cases of relatively small multireference character, such as for TiO, HF
can have difficulty converging to a single state. For molecules with significant
multireference character such as FeO, it is clearly more reasonable to use multireference methods of calculation. However, the SCF wave function provides a
basis for a multireference calculation as well, and the convergence rate of the
multireference calculation may depend on the quality of the SCF orbitals used. For
this reason, it is of utmost importance to review the optimized wave function and
ensure that the calculation has converged to the correct state.
26
R. Weber et al.
Hückel initial guesses. The optimized bond length determined using the H core initial
guess was 1.607 Å, the same as the bond length determined from the minimum of
the potential energy curve. The optimized bond length resulting from the Hückel
initial guess was 1.643, 0.036 Å longer than the bond length at the bottom of the
potential energy curve (also 1.607 Å). The experimental bond length is 1.626 Å, as
seen in Table 1. The H core -optimized bond length and the PEC-determined bond
lengths are all 0.019 Å too short, while the optimized bond length from the Hückel
guess is 0.017 Å too long.
These calculated curves demonstrate that DFT is not immune to the excited state
optimization problems either. While using a combination of DFT and the H core
initial guess, along with an initial bond length close to equilibrium, a correct bond
distance can be computed. However, using the Hückel guess can result in optimization to the wrong state and neither method is able to produce good initial
orbitals at large internuclear distances.
4 Conclusion
Potential energy curves for a set of diatomic molecules were calculated using
Hartree-Fock, CR-CC(2,3), and DFT with the B3LYP and PBE0 functionals. For
some systems, HF erroneously converged to an excited state instead of the ground
state of the molecule. Inspection of the optimized orbitals is imperative to determine
that the calculation has converged to the intended state. While optimization techniques such as the Newton-Raphson method will converge to a local minimum with
respect to the orbital coefficients, the initial orbital guess must be correctly populated as the Newton-Raphson method finds the nearest minimum rather than the
global minimum. The initial guess can be generated through several commonly
used options within computational chemistry software packages, but care must still
be taken that the correct orbitals are being populated. This requires analysis of the
converged orbitals.
In situations that contain parallel potential energy curves, convergence to an
excited state during a geometry optimization will not impact the optimized
geometry. Not every system has parallel potential energy curves, however, and
large deviations in the optimized geometries can be observed.
Even in cases of relatively small multireference character, such as for TiO, HF
can have difficulty converging to a single state. For molecules with significant
multireference character such as FeO, it is clearly more reasonable to use multireference methods of calculation. However, the SCF wave function provides a
basis for a multireference calculation as well, and the convergence rate of the
multireference calculation may depend on the quality of the SCF orbitals used. For
this reason, it is of utmost importance to review the optimized wave function and
ensure that the calculation has converged to the correct state.
26
R. Weber et al.