The vertical electronic spectrum of pyrrole: A second and third order n-electron valence state perturbation theory study Mariachiara Pastore, Celestino Angeli, Renzo Cimiraglia * Dipartimento di Chimica, Universita ` di Ferrara, Via Borsari 46, I-44100 Ferrara, Italy Received 3 February 2006; in final form 3 March 2006 Available online 10 March 2006 Abstract The vertical electronic spectrum of pyrrole is investigated by means of second and third order n-electron valence state perturbation theory. The three 1 A  1 , 1 B þ 2 and 1 A þ 1 p ! p  valence states, as well as the 3s, 3p and 3d p- and r-type Rydberg states, are considered. Particular attention is paid to the description of the valence states, where different active spaces of increasing size are used to improve the zero order wave function. For the Rydberg states and the covalent valence state ð 1 A  1 Þ, the perturbative results show a coherent trend and are in accordance with those of the previous high-level studies. For the two ionic valence states ( 1 B þ 2 and 1 A þ 1 ), rather large active spaces are required to get satisfactory results. Ó 2006 Elsevier B.V. All rights reserved. 1. Introduction In a great deal of chemically interesting phenomena as, for instance, the rupture of chemical bonds, transition states and excited electronic states, a single reference approximation is defective and a multireference approach is required. Building a wave function that includes all the configurations that are important in the qualitative descrip- tion of the system is essential to properly take into account the so-called statical correlation energy. In such cases, mul- tireference perturbation theory is a powerful and relatively inexpensive tool to improve the zero order results, recover- ing a large amount of the dynamical correlation energy. The most successful procedure is based upon the use of a zero order function of Complete Active Space Self Consis- tent Field (CAS-SCF) type followed by a second order per- turbative treatment, where the first order correction to the wave function is built in terms of contracted excitations applied to the reference function. The CASPT2 method, developed by Roos and cowork- ers [1], is nowdays the most popular MRPT: its application to many problematic test cases has provided results in good accordance with experiment. A few years ago, in our group, a new formulation of MRPT, called ‘n-electron valence state perturbation the- ory’ (NEVPT), was proposed [2–4], implemented and suc- cessfully tested [5]. Contrary to CASPT2, where the zero order Hamiltonian is a generalized Fock operator, the NEVPT2 approach makes use of an auxiliary Hamiltonian, proposed by Dyall [6], to define ^ H 0 . Dyall’s Hamiltonian is monoelectonic in the core and virtual orbitals but fully bielectronic in the active orbitals. This choice makes NEVPT size consistent and exempt from intruder states that, instead, often affect the CASPTT2 results. The latter formal requirement is most desirable in the study of excited states, which are more liable to be exposed to the presence of intruder states than the ground state. Although a second order treatment is able to provide a conspicuous fraction of the dynamical correlation, the evaluation of the third order correction to the energy can be very useful, as shown by Werner [7], without prohibitive computational costs, in order to check on the stability and convergency of the perturbation series. Recently, an efficient implementation of third order n-electron valence state perturbation theory (NEVPT3) 0009-2614/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.03.011 * Corresponding author. E-mail address: cim@unife.it (R. Cimiraglia). www.elsevier.com/locate/cplett Chemical Physics Letters 422 (2006) 522–528