Chemieal Physies 87 (1984) 215-221 North-Holland, Amsterdam 215 MULTICONFIGURATION COUPLED-CLUSTER CALCULATIONS FOR EXCITED ELECTRONIC STATES: APPLlCATIONS TO MODEL SYSTEMS Ajit BANERJEE and Jack SIMONS Chemis/ry Department, Universi/y oj Utah, Salt Lake City. Utah 84112, USA Reeeived 12 September 1983 A multieonfigurational eoupled-cluster method previously developed in our laboratory is used to study excited states of the same spatial and spin symp1etry as the ground state. Applieations are made, with rather smali atomie orbital basis sets, to molecular systems whieh are highly eorrelated. These small-basis calculations are viewed on model ealculations whose value lies in the faet that one ean also obtain the exact (fuli configuration interaetion) energy in sueh eases. The results show that even though the eoupled-cluster equations may have many spurious solutions, one can locate solutions corresponding to the desired excited states by using proeedures similar to those utilized for ground states. To aehieve this success, one should include in the reference funetion all of the dominant eonfigurations of the state under eonsideration. Next, oneshould use the unique solution of the linearizedeoupled-cluster equations as the initial estimate to begin the solution of the non-linear eoupled-cluster equaCons. If the solution of these non-linear equations gives rise to one or more large t amplitudes one should repeat this proeedure but with the configuration eorresponding to the large / amplitude included in the referenee funetion. l. Introduction The coupled-cluster (CC) method [1-9] is rec- ognized to be a powerful tool for the computa- tional investigation of electronic properties of molecules. Within CC methods, the coupled-pair many-electron theory [2] (CP MET) is a wel1char- acterized and seemingly quite reliable approxima- tion for the calculation of ground-state wavefunc- tions for. systems where the Hartree-Fock single determinant is the dominant configuration. More recent1y, open-sheIl CC methods [4-9] have been developed which al1ow one to study systems with wavefunctions requiring multiconfigurational de- scription. We recent1y applied our own coupled- cluster method [5- 7], which treats multiconfigura- tion reference states (which we refer to as the CCMC method) to the ground states of several closed- and open-shel1 systems [H2e~;), LieS). HeH2eAt), CH2eBt, lAt), and BeH2eA1)]. Of course, any method for the calculation of elec- tronic properties would be of limited value if 0301-0104/84/$03.00 <DElsevier Science Publishers B.V. (North-Hol1and Physics Publishing Oivision) excited electronic states of the same spatial and spin symmetry as the ground state could not be obtained with reasonably similar accuracy and ease. In this paper, we study such excited states using our CCMC method. In section 2 we briefly review our CCMC development and discuss the possibili- ties in which various coupled cluster methods might be expected to produce erroneous results. In sec- tion 3 the results of our CCMC calculations on the excited states of smaIl atomic-orbital basis treat- ments of CH2eA1) and BeH2eAI) are presented and analyzed. We stress that in both cases, the lAI states examined are not the lowest states of these symmetries. We are looking at excited states which have lower states of the same symmetry. The em- phasis of this pap~r lies in demonstrating that our CCMC method can be used on excited electronic states in exactly the same manner as on ground states. Our test systems are chosen to ilIustrate and test this emphasis. rather than to generate new chemical knowledge about these molecules.