While conventional coupled-cluster and equation-of-motion methods allow one to
tackle electronic structure ranging from well-behaved closed shell molecules to
various open-shell and electronically excited species,^{Krylov:2008}
meta-stable electronic states, so-called resonances, present a difficult case
for theory. By using complex scaling and complex absorbing potential
techniques, we extended these powerful methods to describe auto-ionizing
states, such as transient anions, highly excited electronic states, and
core-ionized species.^{Bravaya:2013, Jagau:2014, Jagau:2017} In addition,
users can employ stabilization techniques using charged sphere and scaled
atomic charges options.^{Kus:2012} These methods are only available within
CCMAN2. The complex CC/EOM code is engaged by COMPLEX_CCMAN;
the specific parameters should be specified in the *$complex_ccman* section.

COMPLEX_CCMAN

Requests complex-scaled or CAP-augmented CC/EOM calculations.

TYPE:

LOGICAL

DEFAULT:

FALSE

OPTIONS:

TRUE
Engage complex CC/EOM code.

RECOMMENDATION:

Not available in CCMAN. Need to specify CAP strength or complex-scaling parameter
in *$complex_ccman* section.

The *$complex_ccman* section is used to specify the details of the
complex-scaled/CAP calculations, as illustrated below. If user specifies
CS_THETA, complex scaling calculation is performed.

$complex_ccman CS_THETA 10 Complex-scaling parameter theta=0.01, r->r exp(-i*theta) CS_ALPHA 10 Real part of the scaling parameter alpha=0.01, ! r->alpha r exp(-itheta) $end

Alternatively, for CAP calculations, the CAP parameters need to be specified.

$complex_ccman CAP_ETA 1000 CAP strength in 10-5 a.u. (0.01) CAP_X 2760 CAP onset along X in 10^-3 bohr (2.76 bohr) CAP_Y 2760 CAP onset along Y in 10^-3 bohr (2.76 bohr) CAP_Z 4880 CAP onset along Z in 10^-3 bohr (4.88 bohr) CAP_TYPE 1 Use cuboid cap (CAP_TYPE=0/2 will use spherical/Voronoi CAP) $end

The CAP_TYPE field specifies the type of the CAP. The current
options are: spherical CAP (CAP_TYPE = 0), cuboid CAP
(CAP_TYPE = 1), and Voronoi’s^{Sommerfeld:VC:2015} CAP
(CAP_TYPE = 2). In the calculations with Voronoi’s CAP, the onset is
specified by the CAP_X variable.

CS_THETA is specified in radian$\times $ 10${}^{-3}$. CS_ALPHA, CAP_X/Y/Z are specified in a.u.$\times $ 10${}^{-3}$, i.e., CS_THETA = 10 means $\theta =0.01$; CAP_ETA is specified in a.u.$\times {10}^{-5}$. The CAP is calculated by numerical integration, the default grid is 000099000590. For testing the accuracy of numerical integration, the numerical overlap matrix is calculated and compared to the analytical one. If the performance of the default grid is poor, the grid type can be changed using the keyword XC_GRID (see Section 5.5 for further details). When CAP calculations are performed, CC_EOM_PROP = 1 by default; this is necessary for calculating first-order perturbative correction.

Advanced users may find the following options useful. Several ways of
conducing complex calculations are possible, *i.e.*, complex scaling/CAPs can be
either engaged at all levels (HF, CCSD, EOM), or not. When applied at post
Hartree-Fock level, CAP can either be added to all blocks of the Fock matrix or
restricted to the virtual-virtual block only. The latter approach, known as
projected CAP ^{Santra:2002}, improves the stability of the calculation
results with respect to CAP onset by reducing a CAP-induced perturbation on the
target states through the occupied orbital space.

CAP projection is currently implemented only for EE/EA calculations and is
invoked by setting PROJ_CAP key in the *$complex_ccman* section as
follows. PROJ_CAP = 1 deploys CAP/EOM-CCSD with projected CAP added
at the CCSD and EOM steps. PROJ_CAP = 2 deploys CAP/EOM-CCSD/MP2/MP2T
with projected CAP added at the EOM step. The latter implies that
$T$-amplitudes (Sec. 7.9.2) are obtained from a real-valued
calculation (for zero CAP strength) and can be reused to generate complex
eigenvalue trajectories by specifying ETA_STEP and NSTEPS
parameters in *$complex_ccman*.

By default, if COMPLEX_CCMAN is specified, the EOM calculations are conducted using complex code. Other parameters are set up as follows:

$complex_ccman CS_HF = true CS_CCSD = true $end

Alternatively, the user can disable complex HF. These options are experimental and should only be used by advanced users. For CAP-EOM-CC, only CS_HF = TRUE and CS_CCSD = TRUE is implemented.

Non-iterative triples corrections are available for all complex scaled and CAP-augmented CC/EOM-CC models and requested in analogy to regular CC/EOM-CC (see Section 7.9.23 for details).

Molecular properties and transition moments are requested for complex scaled or CAP-augmented CC/EOM-CC calculations in analogy to regular CC/EOM-CC (see Section 7.9.18 for details). Natural orbitals and natural transition orbitals can be computed and the exciton wave-functions can be analyzed, similarly to real-valued EOM-CCSD (same keywords are used to invoke the analysis). Analytic gradients are available for complex CC/EOM-CC only for cuboid CAPs (CAP_TYPE = 1) introduced at the HF level (CS_HF = TRUE), as described in Ref. Benda:2017. The frozen core approximation is disabled for CAP-CC/EOM-CC gradient calculations. Geometry optimization can be requested in the same way as in regular CC/EOM-CC (see Section 7.9.18 for details).