Abstract. Wepresentinthispaperamodi®cationofthe selection procedure, within the CIPSI algorithm, specif- ically intended for the calculation of one-electron properties. In this new procedure the determinants are selected following their contribution to a certain one-electron property. As test cases we report the calculation of the electric dipole of carbon monoxide and of the hyper®ne coupling constants of the CH 3 radical. Key words: Multireference CI ± Perturbation CI ± CIPSI ± One-electron properties Introduction Inthelastdecadesalargeeorthasbeendevotedtothe development of post Hartree-Fock methods for the accurate calculation of electronic energies and wave- functions. Dierent criteria are used to evaluate the accuracy of the wavefunction such as, for instance, the energy variational principle for variational calculations or the norm of the perturbation correction to the wavefunctioninperturbationcalculations.Thesecriteria are the basis for the construction of iterative strategies which allow a progressive improvement of the accuracy ofthecalculation,asinthecaseoftheMRDCI[1]and CIPSI[2]methods.Oncethewavefunctionisknown,the physical properties can be calculated as the mean value oftheassociatedoperatoronthewavefunction.Weshall consider here only one-electron properties. Following thisapproachitisquitediculttocontroltheaccuracy ofthevalueobtainedforthephysicalproperty.Indeedit is not guaranteed that determinants or con®gurations) whichgivelargecontributionstotheenergyortolarge changes in the wavefunction) do the same for a certain one-electronproperty.Alimitingcasecanbeconceived, where the determinantal space can be divided in two dierentsets:the®rstcontainingthedeterminantswhich contributetotheenergywithanegligiblecontributionto the one-electron property and the complementary space containingthedeterminantsneededtocorrectlydescribe the one-electron property. In this case, in order to have an accurate value of the property, one should approach the full CI FCI) limit for the energy and thus perform verylargeCIcalculations.Usuallythesituationisnotso dramatic, but a slow convergence of the properties with respect to the number of determinants used in the CI is oftenobserved.Wepresentinthenextsectionthebasisof anewselectionprocedurewithintheframeoftheCIPSI [2,3,4,5]algorithmwhichallowsthedeterminantsgiving alargecontributiontothedescriptionoftheone-electron property to be identi®ed. In order to test the new approachandtocompareitwiththeselectionprocedure used for the energy calculation which, in its original formulation [2] as well as in successive reelaborations [6,7],isbasedonthecontributionstothewavefunction, wereportbelowtwotestcases:theelectricdipoleofCO andthehyper®necouplingconstantsofCH 3 . Method In recent papers [6, 7] parts I and II of this series) we have revised the original CIPSI algorithm. Brie¯y one identi®esavariationalspacecalled S whichcontainsthe most important determinants describing the electronic states under investigation. The Hamiltonian projected onto S is diagonalized and the eigenstates are taken as zero-order descriptions of the true wavefunctions ^ P ^ H ^ P W 0 m   E  E MR m W 0 m   E 1 ^ P  X N 2S N j i N h j W 0 m   E  X N 2S C m N N j i 2 The contributions of the determinants not belonging to S are evaluated by a second-order Rayleigh- Correspondence to: C. Angeli e-mail: anc@dns.unife.it Regular article Multireference perturbation CI IV. Selection procedure for one-electron properties Celestino Angeli, Renzo Cimiraglia Dipartimento di Chimica, UniversitaÁ di Ferrara, Via Borsari 46, 44100 Ferrara, Italy Received: 20 August 2000 /Accepted: 2 October 2000 /Published online: 21 December 2000 Ó Springer-Verlag 2000 Theor Chem Acc 2001) 105:259±264 DOI 10.1007/s002140000212