HOW DO DIFFERENT FLUORINE SUBSTITUTION PATTERNS AFFECT THE ELECTRONIC STATE ENERGIES OF PHENYLNITRENE

Substituted phenylnitrenes, reacting out of their closed-shellsinglet (CSS) states, can serve as photoaffinity labeling reagents if they engage in bond insertion reactions.1-3 Such reactivity is similar to that exhibited by singlet phenylcarbene.4 However, the reactivity of unsubstituted CSS phenylnitrene (PhN) is dominated by unimolecular ring expansion to form didehydroazepine.4,5 Substituents on the aromatic ring are required for bimolecular insertion reactions to compete with ring expansion, e.g., polyfluorinated phenylnitrenes, which were first examined by Banks and Prakash.6,7 Platz has demonstrated that the barrier to ring expansion in 2,6-difluorophenylnitrene ((o,oF2)PhN) is increased by 3-5 kcal/mol compared to unsubstituted PhN.4,8 Platz has also shown that proper location of the fluorines on the aromatic ring is critical to this effect; 3,5difluorophenylnitrene ((m,m-F2)PhN), like PhN, undergoes ring expansion faster than it participates in insertion reactions.2-4 Elucidating the energies for different electronic states of PhN has been the goal of several experimental9,10 and theoretical11-13 studies. Theory and experiment are in good agreement on the relative ordering of the lowest energy states. The ground state is a triplet (A2), the first excited state is an open-shell singlet (A2) lying about 18 kcal/mol higher in energy, and higher still is the first CSS (1A1). No experimental number is available for the relative energy of the latter state, but reasonable quality singleand multireference configuration interaction (CISD+Q) calculations place it 31-39 kcal/mol above the triplet. The electronic configuration of this state is dominated by double occupation of the nitrogen p orbital that lies in the plane of the aromatic ring. The next higher lying CSS (2A1) is derived from double excitation of that pair of electrons out of the inplane p orbital and into the aromatic π system. Kim et al.12 have estimated the energy of this state to be about 52 kcal/mol above the triplet, but the errors associated with this calculation may be substantial (vide infra). The energy of this state bears on the ring expansion reactivity of PhN insofar as it correlates with the CSS ground state of didehydroazepine, i.e., the ring expansion is a Wagner-Meerwein shift of a C-C bond to the electron-deficient nitrogen using the empty in-plane p orbital. On the basis of this analysis, Platz has speculated that different fluorine substitution patterns may preferentially stabilize the 1A1 state and hence lead to higher activation barriers for ring expansion.4 Of course, a more complete explanation includes the recognition that there must be an avoided crossing in the state-symmetry correlation diagrams, but the crux of the argument remains a differential effect on the relative energies of the two CSS states (Figure 1). In order to address this question, we have employed density functional theory14 (DFT) to calculate15,16 the relative energies of the triplet and CSS states of PhN, (o,o-F2)PhN, (m,m-F2)PhN, and 4-fluorophenylnitrene (p-FPhN) and their corresponding didehydroazepines. To assess the quality of this level of theory, we have compared the DFT results for PhN to multireference second-order perturbation theory (CASPT2N)17,18 employing an eight-electron/eight-orbital active space and also to single-reference coupled cluster19 calculations including all single, double, and perturbative triple20 excitations (CCSD(T)). These calculations are summarized in Table 1. The gap between the A2 and 1A1 states for PhN appears to be well predicted by DFT. On the basis of the results for methylene, Roos has suggested that the CASPT2N level overstabilizes triplets relative to singlets by 3-5 kcal/mol.21 Our own calculations for various carbenes and nitrenium ions have shown similar overstabilizations of triplet states by up to 8 kcal/ mol.22 The CCSD(T) calculations also support the DFT results. Because of the size of PhN, calculations at this level were not performed using a triple-u basis. The larger stabilization of the triplet at this level of theory compared to DFT is consistent with lesser flexibility in the basis set and the observed tendency of CCSD(T) to overstabilize triplets relative to CSSs by 1-2 kcal/mol in carbenes and nitrenium ions.22 Similar levels of DFT have previously been shown to accurately predict singlet-