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

First-order and frequency-dependent second-order properties, derived from the expressions based on the expectation value of a one-electron operator, can be obtained with the CPROP directive for the closed-shell CCSD method. For first-order properties obtained from the energy-derivative approach see section 24.11. The expectation-value methods utilized in the program are described in the following papers:

$[1]$ B. Jeziorski and R. Moszynski, Int. J. Quantum Chem., 48, 161 (1993);
$[2]$ T. Korona and B. Jeziorski, J. Chem. Phys., 125, 184109 (2006);
$[3]$ R. Moszynski, P. S. Zuchowski and B. Jeziorski, Coll. Czech. Chem. Commun., 70, 1109 (2005);
$[4]$ T. Korona, M. Przybytek and B. Jeziorski, Mol. Phys., 104, 2303 (2006),
$[5]$ 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 ${\cal O}(W^3)$ Møller-Plesser (MP) order, denoted as $\bar X(3)_{\rm resp}$ 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 $S$ operator (see [2], Eq. (9)); $n=\pm 2,\pm 3,\pm 4$, where for a positive $n$: all approximations to $S$ up to $n$ are used, and for a negative $n$ only a density with $S$ obtained on the $\vert n\vert$ level will be calculated. Another option related to the $S$ operator is HIGHW=n, where $n=0,1$; if $n$=0, some parts of $S_1$ and $S_2$ operators of a high MP order are neglected. Below an example of a standard use of this method is given:


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


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,


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


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

(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.
if $n>0$, calculate dispersion integrals for the van der Waals coefficients with operators given in the POLARI card, using $n$ 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 $C_6$ coefficient is stored in a variable DISPC6, the isotropic $C_9$ 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.
if given, use this threshold as a convergence criterion for the linear-equation solver for the first-order perturbed CCSD amplitudes.
various start options for the iterative linear-equation solver for the first-order perturbed CCSD amplitudes, the most useful is $n=0$ (zero start) and $n=7$ (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).
molpro@molpro.net 2019-06-16