The Importance of Orbital Analysis
Rebecca Weber, George Schoendorff and Angela K. Wilson
Abstract It has long been known that there are multiple solutions to the
self-consistent Hartree-Fock equations. This can be problematic if careful attention
is not given to the orbital occupation and electronic state in the converged wave
function. The issues with convergence have been demonstrated through the calculation of potential energy curves for O 2 , F 2 , Cl 2 , Br 2 , LiF, NaCl, CaO, MgO,
ScO, FeO, TiO, YO, and ZrO. Hartree-Fock (HF) calculations were used to compute the points on the potential energy surface, with dynamic electron correlation
included through the use of the completely renormalized coupled cluster, including
singles, doubles, and perturbative triples [CR-CC(2,3)]. Even in regions with little
to no multireference character, as determined by the T 1 /D 1 diagnostics, HF does not
always converge to the ground electronic state. As HF provides the reference wave
function for CR-CC(2,3), and other post-Hartree-Fock ab initio methods, treatment
of electron correlation does not necessarily result in a smooth potential energy
curve, especially if HF is unable to produce a smooth curve. Even the convergence
rate of multireference methods can be affected as the initial orbitals that form the
basis for multireference calculations are frequently obtained from HF calculations.
Keywords Hartree-Fock Á Electronic states Á Wavefunction Á Coupled cluster Á
Diatomic Á Potential energy curve Á Ground state Á Excited state
1 Introduction
In the early days of computational chemistry, it was routine to check the stability of
the optimized Hartree-Fock (HF) wave function. As the field of computational
chemistry has grown to include more neophytes utilizing a theoretical approach in
R. Weber Á G. Schoendorff Á A.K. Wilson (&)
Department of Chemistry, Center for Advanced Scientific Computing and Modeling
(CASCaM), University of North Texas, Denton, TX 76203-5017, USA
e-mail: akwilson@unt.edu
© Springer International Publishing Switzerland 2015
M.A.C. Nascimento et al. (eds.), Frontiers in Quantum Methods and Applications
in Chemistry and Physics, Progress in Theoretical Chemistry and Physics 29,
DOI 10.1007/978-3-319-14397-2_1
3
Rebecca Weber, George Schoendorff and Angela K. Wilson
Abstract It has long been known that there are multiple solutions to the
self-consistent Hartree-Fock equations. This can be problematic if careful attention
is not given to the orbital occupation and electronic state in the converged wave
function. The issues with convergence have been demonstrated through the calculation of potential energy curves for O 2 , F 2 , Cl 2 , Br 2 , LiF, NaCl, CaO, MgO,
ScO, FeO, TiO, YO, and ZrO. Hartree-Fock (HF) calculations were used to compute the points on the potential energy surface, with dynamic electron correlation
included through the use of the completely renormalized coupled cluster, including
singles, doubles, and perturbative triples [CR-CC(2,3)]. Even in regions with little
to no multireference character, as determined by the T 1 /D 1 diagnostics, HF does not
always converge to the ground electronic state. As HF provides the reference wave
function for CR-CC(2,3), and other post-Hartree-Fock ab initio methods, treatment
of electron correlation does not necessarily result in a smooth potential energy
curve, especially if HF is unable to produce a smooth curve. Even the convergence
rate of multireference methods can be affected as the initial orbitals that form the
basis for multireference calculations are frequently obtained from HF calculations.
Keywords Hartree-Fock Á Electronic states Á Wavefunction Á Coupled cluster Á
Diatomic Á Potential energy curve Á Ground state Á Excited state
1 Introduction
In the early days of computational chemistry, it was routine to check the stability of
the optimized Hartree-Fock (HF) wave function. As the field of computational
chemistry has grown to include more neophytes utilizing a theoretical approach in
R. Weber Á G. Schoendorff Á A.K. Wilson (&)
Department of Chemistry, Center for Advanced Scientific Computing and Modeling
(CASCaM), University of North Texas, Denton, TX 76203-5017, USA
e-mail: akwilson@unt.edu
© Springer International Publishing Switzerland 2015
M.A.C. Nascimento et al. (eds.), Frontiers in Quantum Methods and Applications
in Chemistry and Physics, Progress in Theoretical Chemistry and Physics 29,
DOI 10.1007/978-3-319-14397-2_1
3