referred to as the H core guess, following the nomenclature in GAMESS [13]. While
this initial guess is usually fairly poor, it has the advantage of being implemented in
most computational codes [5]. Another common approach is to use the guess
generated by a semi-empirical procedure such as Extended Hückel Theory (referred
to in this paper as the Hückel guess) and projected onto the current basis. The initial
guess provided by Hückel theory is generally superior to that provided by H core , yet
can still have difficulty assigning the initial electronic configuration based on the
orbital population [13]. Another approach that can be useful, especially when
calculating a potential energy curve, is to use the optimized orbitals from a nearby
point on the potential energy surface, as is done automatically during a gradient
driven geometry optimization.
As Hartree-Fock does not account for electron correlation beyond mean field
correlation, a myriad of correlated electron methods have been developed that are
based upon a Hartree-Fock reference wave function. Configuration interaction (CI),
coupled cluster (CC), and many body perturbation theory are examples of such
theories designed to recover electron correlation energy. Full CI calculations do not
depend on the quality of the reference wave function, yet full CI with an appropriately large basis set quickly becomes computationally intractable. Because of this
increase in computational cost (in terms of memory and CPUs required for the
calculation), more approximate methods are used. An example of a more approximate method would be coupled cluster including single and double excitations,
with perturbative triples [CCSD(T)]. Although truncated, CCSD(T) has been shown
to calculate ground state properties such as heats of formation, at times achieving
more accurate results (i.e. closer to results achieved by full CI) than less approximate methods such as CCSDT [14].
However, the accuracy of truncated correlated methods can be sensitive to the
choice of the reference wave function. CCSD(T) is a single reference post-HartreeFock method, generally based upon a HF wave function. If the reference wave
function as determined by HF corresponds to an excited state determinant, truncated
correlated methods are not necessarily able to produce the correct ground state.
Even single reference theories such as the completely renormalized coupled cluster
method, including singles, doubles, and perturbative triples [CR-CC(2,3)] that have
been shown to treat some multireference problems [15, 16] (i.e. bond breaking,
singlet-triplet gaps in biradical systems, and other systems with strong static correlation) still are subject to the limitations of the reference wave function. Furthermore, while it is possible to converge to a ground state wave function while
using an excited state reference, the amplitudes can be much more challenging to
converge.
There are other single-reference methodologies that use more than one determinant within their formulation, for example the spin flip method [17, 18]. The spin
flip method and its variants use multiple determinants (the reference state and
additional excited states that result from a spin flip of an electron) and are able to
better describe events such as bond breaking. The description of the reference state
can increase to higher correlated methods, yet this would increase the computational cost involved within the calculation. Additionally, for the simplest version of
6
R. Weber et al.
this initial guess is usually fairly poor, it has the advantage of being implemented in
most computational codes [5]. Another common approach is to use the guess
generated by a semi-empirical procedure such as Extended Hückel Theory (referred
to in this paper as the Hückel guess) and projected onto the current basis. The initial
guess provided by Hückel theory is generally superior to that provided by H core , yet
can still have difficulty assigning the initial electronic configuration based on the
orbital population [13]. Another approach that can be useful, especially when
calculating a potential energy curve, is to use the optimized orbitals from a nearby
point on the potential energy surface, as is done automatically during a gradient
driven geometry optimization.
As Hartree-Fock does not account for electron correlation beyond mean field
correlation, a myriad of correlated electron methods have been developed that are
based upon a Hartree-Fock reference wave function. Configuration interaction (CI),
coupled cluster (CC), and many body perturbation theory are examples of such
theories designed to recover electron correlation energy. Full CI calculations do not
depend on the quality of the reference wave function, yet full CI with an appropriately large basis set quickly becomes computationally intractable. Because of this
increase in computational cost (in terms of memory and CPUs required for the
calculation), more approximate methods are used. An example of a more approximate method would be coupled cluster including single and double excitations,
with perturbative triples [CCSD(T)]. Although truncated, CCSD(T) has been shown
to calculate ground state properties such as heats of formation, at times achieving
more accurate results (i.e. closer to results achieved by full CI) than less approximate methods such as CCSDT [14].
However, the accuracy of truncated correlated methods can be sensitive to the
choice of the reference wave function. CCSD(T) is a single reference post-HartreeFock method, generally based upon a HF wave function. If the reference wave
function as determined by HF corresponds to an excited state determinant, truncated
correlated methods are not necessarily able to produce the correct ground state.
Even single reference theories such as the completely renormalized coupled cluster
method, including singles, doubles, and perturbative triples [CR-CC(2,3)] that have
been shown to treat some multireference problems [15, 16] (i.e. bond breaking,
singlet-triplet gaps in biradical systems, and other systems with strong static correlation) still are subject to the limitations of the reference wave function. Furthermore, while it is possible to converge to a ground state wave function while
using an excited state reference, the amplitudes can be much more challenging to
converge.
There are other single-reference methodologies that use more than one determinant within their formulation, for example the spin flip method [17, 18]. The spin
flip method and its variants use multiple determinants (the reference state and
additional excited states that result from a spin flip of an electron) and are able to
better describe events such as bond breaking. The description of the reference state
can increase to higher correlated methods, yet this would increase the computational cost involved within the calculation. Additionally, for the simplest version of
6
R. Weber et al.