ANALYSIS OF COUPLED-CLUSTER METHODS .4. SIZE-EXTENSIVE QUADRATIC CI METHODS QUADRATIC CI WITH TRIPLE AND QUADRUPLE EXCITATIONS

A procedure is developed that leads from CI to size-extensive CI (ECI) by stepwise cancellation of disconnected terms in the CI equations. T he ECI methods thus obtained are identical with the corresponding coup led cluster (CC) methods with the exception of CISD and CISDT, which c onvert to size-extensive quadratic CI (QCISD) and ECISDT. The latter m ethod has similar properties as CCSDT, but does not offer any signific ant time-savings as compared to CCSDT. Therefore, the idea of extendin g CI methods to size-extensive CI methods does not lead to a hierarchy of independent CC methods. However, the procedure of obtaining ECI me thods lays the basis for deriving QCI methods that are truly size-exte nsive. This is accomplished by (a) deleting the first linear term of t he p-fold CI excitation equations (p greater-than-or-equal-to 3) since this term always represents a disconnected term and (b) including jus t the connected part of appropriate quadratic correction terms in all but the energy equation. In this way, size-extensive QCISDT and QCISDT Q are obtained and their properties are discussed in comparison with Q CISD(T) and CCSDT.