Ž . Chemical Physics 225 1997 197–202 New algorithms for an individually selecting MR-CI program M. Hanrath, B. Engels ) Institut fur Physikalische und Theoretische Chemie, UniÕersitat Bonn, Wegelerstrasse 12, 53115 Bonn, Germany ¨ ¨ Received 9 May 1997 Abstract In the present work we discuss the main features of new algorithms to do individually-selecting MR-CI calculations. Employing a new program package we are able to perform calculations including more than two million selected Ž . configuration state functions CSFs as a matter of routine. A test calculation on the C molecule including about 2.3 mill. 6 selected CSFs takes about 54 minutes on a PentiumPro for one iteration within the Davidson procedure. This enables one to study more complicated and larger systems with a higher accuracy than before. q 1997 Elsevier Science B.V. 1. Introduction The CI method is able to describe the electronic structures of molecules which cannot be qualitatively described by a single configuration wave function. Examples are biradicals or molecules in electroni- cally excited states. Widely used is the MR-CI method which includes all single and double excita- tions with respect to a set of reference configura- tions. In new treatments of the MR-CI problem the wx direct CI method as proposed by Roos 1 is used. wx wx The development of GUGA 2 and SGA 3 meth- ods have yielded in efficient algorithms which allow the handling of very large MR-CI spaces. However, despite those algorithms, the calculations become very time consuming if the size of the problem exceeds several million configurations. In order to reduce the cost of the calculations several truncations of the MR-CI expansion were developed. One successful approach is the internally wx contracted MR-CI proposed by Meyer 4 and effi- ) Corresponding author. wx ciently formulated by Knowles and Werner 5 . An- other possibility to truncate the problem is a method called individually selecting MR-CI. In this method the whole MR-CI space is scanned and only those configurations, which are found to be important are included in the secular equation, i.e. are handled variationally. The influence of all other configura- tions of the MR-CI space on the total energy is obtained by perturbation theory. This idea was re- fined and extensively used by Peyerimhoff and w x Buenker 6,7 . It led to the MRD-CI program pack- wx age 8 which is widely used by various groups. Based on the MRD-CI approach the groups of Peyer- imhoff and Buenker studied various problems in theoretical chemistry for example the spectroscopic w x properties of molecules 9–11 or the description of w x reaction mechanisms 12,13 . The idea of the indi- vidually selecting MR-CI method was also used by w x Whitten and Hackmeyer 14 , in the CIPSI program w x of Malrieu and coworkers 15 , in the MELDF pro- w x gram of Davidson and coworkers 16 and more w x recently in the program of Harrison 17 . Within the individually selecting MR-CI the size 0301-0104r97r$17.00 q 1997 Elsevier Science B.V. All rights reserved. Ž . PII S0301-0104 97 00241-3