Chemical Physics 133 (1989) 345-354 North-Holland, Amsterdam zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA AB INITIO CALCULATIONS FOR DIPOLE-FORBIDDEN TRANSITIONS IN NBr: RADIATIVE LIFETIMES OF THE b IX+ AND a ‘A STATES K. BHANUPRAKASH, Praphull CHANDRA ‘, Gerhard HIRSCH and Robert J. BUENKER Fachbereich 9-Theoretische Chemie, Bergische Universitdt GH Wuppertal, Gaussstrasse 20, D-5600 Wuppertal I, FRG Received 19 September 1988; in final form 9 February 1989 Spin-perturbed wavefunctions have been evaluated for the three lowest electronic states of NBr using the spin-orbit coupling Hamiltonian with MRD CI wavefunctions as the zeroth-order basis, and the radiative lifetimes of the a ‘A and b ‘X+ states have been determined. Comparison is made with available experimental data. In the case of the b ‘Z+-X ‘ZO,*, transition, the fir moment is found to be larger (by a factor of 7- 11) than the pL (whereby experiments indicate a factor of 15 or greater ). In the case of the a ‘A-X ‘Zz I transition the calculated value is about two hundred and sixty times smaller than an experimental value reported in a gas-phase study, but it agrees quite well with the value determined in matrices. The zero-field splitting based on spin-orbit coupling alone has been calculated to be 11.3 cm-‘, only 40-7096 of the available experimental results. Finally com- parison is made with the corresponding data for other nitrogen halides. 1. Introduction The x4x*2 configuration in diatomic nitrogen hal- ides gives rise to the three lowest-lying electronic states, i.e. X 3x-, a ‘A and b ‘C+. Optical transitions between these states are strongly forbidden due to the dipole selection rules. Nevertheless the presence of spin-orbit coupling, which becomes larger with in- creasing atomic number of the halogen species, low- ers these constraints and leads to weak radiative tran- sitions. In recent years there have been a number of studies on these spin-forbidden transitions, both the- oretical [ l-6 ] and experimental [ 7-20 1. Of particular interest in this connection is the NBr molecule, for which there are quite a few experimen- tal studies [ 13-201 but no ab initio study as yet. Spectroscopic analyses of the b ‘E+-X 3E- transition in the near-visible region have been reported by El- liot [ 13 ] and Milton et al. [ 14 1. Approximate values for the zero-field splittings were given by Milton et al. [ 141, who place the constant either at 17.4 or 20 cm-‘.Prittetal. [16] observedboththeb’C+-X3x- and a ‘A-X ‘E;- transitions. In reporting their molec- ’ Permanent address: Banaras Hindu University, Department of Chemistry, Varanasi, 22 1005, India. ular constants, preference is given to the larger of these two values for the zero-field splitting. The radiative rates for these NBr transitions have been measured by Coombe et al. [ 171 in the gas phase and by Becker et al. [ 18 ] in matrices. More recently Wildt and Fink [ 19 ] have remeasured the transition moments for the b-X transition, and Pritt [20] has reported a new value for the X spin-spin splitting of 24.76kO.22 cm-‘. In general there is disagreement over the value determined for the radiative lifetime of the a ‘A state, but that of the b ‘xc+ state seems to be better estab- lished experimentally. In light of the above experiments and the lack of any detailed theoretical calculations on the NBr mol- ecule, it seemed of interest to carry out an ab initio CI treatment of the pertinent states of NBr and to study in detail the transition probabilities and radia- tive lifetimes of these forbidden transitions. Also of interest in this study will be a comparison of NBr with other nitrohalides, i.e. with the results reported ear- lier for NF and NC1 [ 3 1. 2. Theory The basic computational technique employed is low-order perturbation theory, according to which the 0301-0104/89/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )