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 , 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:
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