Ab Initio Quantum Chemical Investigation of the Spin States of Some Fused Ring Systems

Abstract

The ground-state spins of seven diradicals belonging to the fused ring system have been investigated by ab initio restricted and unrestricted formalisms. The systems under study are (1) 4-oxy-2-naphthalenyl methyl, (2) 1,8-naphthalenediylbis(methyl), (3) 8-imino-1-naphthalenyl methyl, (4) 1,8-naphthalenediylbis(amidogen), (5) 8-methyl-1-naphthyl carbene, (6) 8-methyl-1-naphthalenyl imidogen, and (7) 8-methyl-1-naphthyl diazomethane. Out of the seven molecules, only 1 was theoretically investigated earlier. To our knowledge, for 2-7, this work represents the first ab initio investigation. A variety of basis sets have been employed in these calculations. For each spin state, the molecular geometry has been fully optimized at the unrestricted Hartree-Fock (UHF) level using the STO-3G, 4-31G, 6-311G(d), and 6-311G(d,p) basis sets. The UHF optimized geometries have been used for Møller-Plesset (MP) and coupled cluster (CC) calculations as well as the density functional (UB3LYP) treatment. Results in the unrestricted formalism have been given only at UHF and UB3LYP levels for the 6-311G(d) basis. The UHF calculations yield an unrealistically large singlettriplet (S-T) splitting. Splittings calculated with different bases disagree seriously. The S-T gap is smaller in the split-valence bases. The basis set truncation error can be considerably overcome by calculations involving electron correlation. For these diradicals, any meaningful result would require larger bases with polarization functions. Apart form this difficulty, the optimized geometry turned out to be highly spin-contaminated. The spin-contamination can be significantly reduced by the density functional UB3LYP treatment. Nevertheless, for most of the diradicals, the UB3LYP method did not yield a systematic trend. To avoid spin contamination completely, we have repeated computations in the restricted (open-shell) Hartree-Fock framework. Geometry optimizations were carried out using p) bases at the R(O)HF level and 6-311G(d,p) basis at the R(O)B3LYP level for each spin state. The R(O)B3LYP/6-311G(d,p) optimized geometry yields the best total energy for each spin state and hence the most reliable S-T energy difference. Molecules 1-6 are found as ground-state triplets. The calculated results are in agreement with the available experimental findings. Molecules 3 and 7 have widely different geometries in the singlet and triplet states. The calculations using 6-311G(d) and 6-311G(d,p) basis sets show that in molecule 3 the substituents of naphthalene are -NH 2 and -CH in singlet but -NH and -CH 2 in triplet. The two optimized geometries are tautomeric forms. Molecule 7 is expected to be either a ground-state triplet with a very little S-T gap or a ground-state singlet. This prediction is borne out by the computed results. The R(O)B3LYP/6-311G(d,p) calculation yields a S-T splitting of -21.9 kcal mol -1 . The singlet state becomes stabilized by forming an additional condensed ring. The UHF spin density plots obtained from the 4-31G optimized geometries manifest the ...

Calculations of the Relative Energies of the Low-Lying Electronic States of 2-Methylenedihydrophenalene-1,3-diyl: Effects of a 1,8-Naphtho Bridging Group on Trimethylenemethane and of a Vinylidene Bridging Group on 1,8-Naphthoquinodimethane

“…These findings suggest that triplets are probably also the ground states of 2 and 4 , or at least are very close in energy to the ground states. However, to the best of our knowledge, the singlet−triplet energy separations in 2 and 4 have neither been reliably calculated nor accurately measured.…”

The Triplet–Singlet Gap in the m-Xylylene Radical: A Not So Simple One

“…On the other hand, one must also realize that this type of CASSCF/CASPT2 calculations become rapidly intractable when the size of the molecule increases, even moderately. DFT-based calculations offer a very attractive alternative, and there is abundant literature in related systems indicating that the popular B3LYP and similar hybrid functionals tend to provide values close to the experimental one, − although the semiempirical flavor of hybrid functionals makes one wonder if the right answer comes from the right reason, a long-standing question in modern electronic structure theory. Nevertheless, the complexity of the electronic structure of MBQDM revealed by the CASPT2 and EOM-SF-CCSD calculations commented above may also appear to be difficult for DFT-based methods.…”

Variational fractional-spin density-functional theory for diradicals

“…Accurate predictions of the singlet-triplet (ST) energy gaps remains a challenge for conventional density-functional theory because of the multireference nature of the singlet state. 12,13 Therefore, most computational studies involving singlet diradicals utilize ab initio multireference methods, such as complete active space self-consistent field (CASSCF), [14][15][16] complete active space with second-order perturbation theory, 17,18 or multireference coupled cluster theory. 19,20 Unfortunately, all these multireference ab initio methods are extremely computationally demanding for large systems.…”

“…Direct application of DFT usually takes the form of unrestricted calculations and is complicated with spin contamination that leads to overstabilization of singlet states similar to unrestricted Hartree-Fock calculations. 14,15,21,22 Many efforts have been devoted to understanding and correcting spin contamination, 15,[23][24][25][26] and a factor-of-2 correction is normally needed. 27 One can also use spin-projection to improve the accuracy of unrestricted methods for calculating ST gaps, 21, 28-30 but it is not a self-consistent approach and does not provide satisfactory densities.…”