Chapter 17
Coupled-Cluster Methods for
Generalized Excitations
The extension of the coupled-cluster (CC) method, originally devised for groundstates [1, 2], to the treatment of (generalized) electronic excitations is based on CE
states in which the CC ground-state parametrization is used. To deal with the nonorthogonality of the CE states and, even more importantly, to obtain tractable secular
equations, one introduces, as a second expansion manifold, the set of associated
biorthogonal states. The corresponding mixed or biorthogonal (B) representation of
the (shifted) hamiltonian gives rise to the non-hermitian BCC secular matrix.
This BCC secular problem lies at the core of the excited-state CC methodology,
which comprises two historically independent developments or brands, namely the
CCLR (coupled-cluster linear response) theory (see [3] and references therein) and
the EOM- CC (equation-of-motion coupled-cluster) approach (see [4] and references
therein). A closely related method is the SAC- CI (symmetry-adapted cluster configuration interaction) scheme [5]. For comprehensive presentations of ground- and
excited-state CC theory, the reader is referred to textbooks [6, 7] and review articles [8–10].
In this chapter, we give an introduction into the BCC concept and review in
particular the order relations and separability properties of the BCC secular equations.
We here refer to the extensive analysis given in Ref. [11] which may be consulted
for further details.
17.1 Ground-State Coupled-Cluster Formulation
In the CC approach, the ground state is represented in the form of an exponential
operator acting on the HF ground state | 0 :
|
cc
0 = e
ˆ
T
| 0
(17.1)
© Springer Nature Switzerland AG 2018
J. Schirmer, Many-Body Methods for Atoms, Molecules and Clusters, Lecture
Notes in Chemistry 94, https://doi.org/10.1007/978-3-319-93602-4_17
255
Coupled-Cluster Methods for
Generalized Excitations
The extension of the coupled-cluster (CC) method, originally devised for groundstates [1, 2], to the treatment of (generalized) electronic excitations is based on CE
states in which the CC ground-state parametrization is used. To deal with the nonorthogonality of the CE states and, even more importantly, to obtain tractable secular
equations, one introduces, as a second expansion manifold, the set of associated
biorthogonal states. The corresponding mixed or biorthogonal (B) representation of
the (shifted) hamiltonian gives rise to the non-hermitian BCC secular matrix.
This BCC secular problem lies at the core of the excited-state CC methodology,
which comprises two historically independent developments or brands, namely the
CCLR (coupled-cluster linear response) theory (see [3] and references therein) and
the EOM- CC (equation-of-motion coupled-cluster) approach (see [4] and references
therein). A closely related method is the SAC- CI (symmetry-adapted cluster configuration interaction) scheme [5]. For comprehensive presentations of ground- and
excited-state CC theory, the reader is referred to textbooks [6, 7] and review articles [8–10].
In this chapter, we give an introduction into the BCC concept and review in
particular the order relations and separability properties of the BCC secular equations.
We here refer to the extensive analysis given in Ref. [11] which may be consulted
for further details.
17.1 Ground-State Coupled-Cluster Formulation
In the CC approach, the ground state is represented in the form of an exponential
operator acting on the HF ground state | 0 :
|
cc
0 = e
ˆ
T
| 0
(17.1)
© Springer Nature Switzerland AG 2018
J. Schirmer, Many-Body Methods for Atoms, Molecules and Clusters, Lecture
Notes in Chemistry 94, https://doi.org/10.1007/978-3-319-93602-4_17
255