25.6 First- and second-order properties for CCSD from expectation-value CC theory (XCCSD)

B. Jeziorski and R. Moszynski, *Int. J. Quantum Chem.*, **48**, 161 (1993);

T. Korona and B. Jeziorski, *J. Chem. Phys.*, **125**, 184109 (2006);

R. Moszynski, P. S. Zuchowski and B. Jeziorski, *Coll. Czech. Chem. Commun.*,
**70**, 1109 (2005);

T. Korona, M. Przybytek and B. Jeziorski, *Mol. Phys.*,
**104**, 2303 (2006),

T. Korona, *Theor. Chem. Acc.*, **129**, 15 (2011).

Note that properties obtained from the expectation-value expression with the coupled cluster wave
function **are not** equivalent to these derived from gradient or linear-response methods,
although the results obtained with both methods are quite similar. In XCC the exponential ansatz for the
wave function is utilized for the bra side, too.

For the first-order properties the one-electron operators
should be specified in the `EXPEC` card,
while for the second-order properties - in the `POLARI`
card. A density can be saved by specifying the `DM` card.

For the first-order properties
the option `XDEN=1` should be usually given.
Other options specify a type of the one-electron density, which can be either
the density directly derived from the expectation-value expression, see Eq. (8) of Paper 2,
or the modified formula, rigorously correct through the Møller-Plesser (MP) order, denoted
as
in Papers 1 and 2. In the first case the option
`PROP_ORDER`=*n* can be used to specify the approximation level for single and
double excitation parts of the so-called operator (see [2], Eq. (9));
, where
for a positive : all approximations to up to are used, and for a negative
only a density with obtained on the level will be calculated.
Another option related to the operator is
`HIGHW`=*n*, where ; if =0, some parts of and operators of a high MP order are
neglected. Below an example of a standard use of this method is given:

`CPROP`,`XDEN=1`,`PROP_ORDER`=-3,`HIGHW`=0

The combination above is also available by writing `EXPEC,XCCSD` after the `CCSD` card.
A cheap method denoted as XCCSD(3), obtained by a simplification of the original XCCSD formula,
is available by setting

`CPROP`,`XDEN=-21`

or by writing `EXPEC,XCCSD(3)` after the `CCSD` card.

In the second case the options `X3RESP=1` and the `CPHF,1` card (or alternatively the `EXPEC` card)
should be specified,

`CPROP`,`XDEN=1`,`X3RESP=1`;`CPHF,1`

For the second-order properties always the following options should be given:

`CPROP`,`PROPAGATOR=1`,`EOMPROP=1`

The recommended CCSD(3) model from Paper 4 requires that additionally the `PROP_ORDER=3` and `HIGHW=0` options
are specified.
Frequencies for dynamic properties (in atomic units)
should be given in variables `OMEGA_RE` (real parts)
and `OMEGA_IM` (imaginary parts). If one of these arrays is not given, it is filled with zeros.
Other options for the second-order properties involve

`OMEGAG`- (default 0.3). There are two linear-equation solvers,
`OMEGAG`is a minimum frequency, for which the second solver (working for large frequencies) is used. `DISPCOEF=`- if , calculate dispersion integrals for the van der Waals coefficients with
operators given in the
`POLARI`card, using as a number of frequencies for the numerical integration. In this case the frequency values given in`OMEGA_RE`and`OMEGA_IM`are ignored. If two molecules are calculated in the same script one after another, also the mixed dispersion integrals are calculated. The isotropic coefficient is stored in a variable`DISPC6`, the isotropic nonadditive coefficient - in a variable`DISPC9`. All necessary informations for the calculation of dispersion integrals are written to the ascii file*name.dispinfo*, where*name*is the name of the`MOLPRO`script. `THRPROPAG`- if given, use this threshold as a convergence criterion for the linear-equation solver for the first-order perturbed CCSD amplitudes.
`STARTT1`=*n*- various start options for the iterative linear-equation solver for the first-order perturbed CCSD amplitudes, the most useful is (zero start) and (start from the negative of the r.h.s. vector rescaled by some energetic factors dependent on the diagonal of the Fock matrix and the specified frequency).