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.
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 density 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