Triradicals and diradicals

We are fascinated by electronic structure and bonding in di- and tri-radicals, species with two and three unpaired electrons, respectively.


We investigate these systems in collaboration with Prof. Paul G. Wenthold from the Purdue University in Indiana. From the electronic structure point of view, triradicals are described as systems where three electrons are distributed over three (near)-degenerate orbitals, as shown in the diagram below. Due to the orbital near-degeneracies, triradicals have many low-lying electronic states. Moreover, their wave functions are multi-configurational and are very difficult to model. The SF method describes all the low-spin triradical states as the spin-flipping excitations from the high spin reference state.

Triradical determinants

By using a variety of SF models, we investigated bonding patterns that arise from the interaction of unpaired electrons. We have found that in the C6H3 isomers, the unpaired electrons form partial bonds between the radical centers that has distinct structural, spectroscopic, and thermochemical consequences. For example, the distances between the radical centers are contracted by 0.4 – 0.1 Å relative to the parent closed shell benzene molecule even in the high spin states. Energies of these partial bonds vary from 0.4 to up to 30 kcal/mol, which is about one third of a normal chemical bond. Currently, we are learning how to control the ground state multiplicity of triradicals and diradicals by substitutions—this is important for the design of plastic magnetic materials from these building blocks.

Benzene triradicals

Distance between radical centers in the m-benzyne diradical and the 1,3,5 tridehydrobenzene triradical. Bond contraction relative to the closed-shell parent molecule (benzene) reveals bonding interaction between the radical centers even in high-spin states.

Molecular orbitals of DMX

This picture shows molecular orbitals and low-lying electronic states of DMX. Note that the closed-shell doublet (12B2 state) in which electrons are distributed in accordance with the Aufbau principle is 2.5 eV above the ground state! Another likely candidate for the ground state, the quartet 14B2 state, is 0.5 eV above the open-shell doublet, thus violating Hund's rule.

Related Publications

236. P. Pokhilko, D. Izmodenov, and A. I. Krylov
Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets
J. Chem. Phys.  152, 034105 (2020) Abstract  PDF Supporting info

197. N. Orms and A. I. Krylov
Singlet-triplet energy gaps and the degree of diradical character in binuclear copper molecular magnets characterized by spin-flip density functional theory
Phys. Chem. Chem. Phys. 20, 13095 – 13662 (2018) Abstract  PDF Supporting info

194. N. Orms, D. R. Rehn, A. Dreuw, and A. I. Krylov
Characterizing bonding patterns in diradicals and triradicals by density-based wave function analysis: A uniform approach
J. Chem. Theo. Comp. 14, 638 – 648 (2018) Abstract  PDF 

193. A. Luxon, N. Orms, R. Kanters, A. I. Krylov, and C. Parish
An ab initio exploration of the Bergman cyclization
J. Phys. Chem. A 122, 420 – 430 (2018) Abstract  PDF 

189. E. Hossain, S.M. Deng, S. Gozem, A.I. Krylov, X.-B. Wang, and P.G. Wenthold
Photoelectron spectroscopy study of quinonimides
J. Am. Chem. Soc. 139, 11138 – 11148 (2017) Abstract  PDF 

96. P.U. Manohar, L. Koziol, and A.I. Krylov
Effect of a heteroatom on bonding patterns and triradical stabilization energies of 2,4,6-tridehydropyridine versus 1,3,5-tridehydrobenzene: Erratum
J. Phys. Chem. A 114, 6558 (2010) PDF 

95. V. Mozhayskiy, D.J. Goebbert, L. Velarde, A. Sanov, and A.I. Krylov
Electronic structure and spectroscopy of oxyallyl: A theoretical study
J. Phys. Chem. A 114, 6935 – 6943 (2010) Abstract  PDF Supporting info

91. C.A. Taatjes, D.L. Osborn, T.M. Selby, G. Meloni, A.J. Trevitt, E. Epifanovsky, A.I. Krylov, B. Sirjean, E. Dames, and H. Wang
Products of the benzene + O(3P) reaction
J. Phys. Chem. A 114, 3355 – 3370 (2010) Abstract  PDF Supporting info

75. P.U. Manohar, L. Koziol, and A.I. Krylov
Effect of a heteroatom on bonding patterns and triradical stabilization energies of 2,4,6-tridehydropyridine versus 1,3,5-tridehydrobenzene
J. Phys. Chem. A 113, 2591 – 2599 (2009) Abstract  PDF Supporting info

61. V. Vanovschi, A. I. Krylov, and P. G. Wenthold
Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion
Theor. Chem. Acc. 120, 45 – 58 (2008) Abstract  PDF 

52. L. Koziol, M. Winkler, K.N. Houk, S. Venkataramani, W. Sander, and A. I. Krylov
The 1,2,3-tridehydrobenzene triradical: 2B or not 2B? The answer is 2A!
J. Phys. Chem. A 111, 5071 – 5080 (2007) Abstract  PDF (164 kB) 

50. T. Wang and A. I. Krylov
Electronic structure of the two dehydro-meta-xylylene triradicals and their derivatives
Chem. Phys. Lett. 426, 196 – 200 (2006) Abstract  PDF (132 kB) 

43. L.V. Slipchenko and A.I. Krylov
Efficient strategies for accurate calculations of electronic excitation and ionization energies: Theory and application to the dehydro-meta-xylylene anion
J. Phys. Chem. A 110, 291 – 298 (2006) Abstract  PDF (150 kB) 

41. A. I. Krylov
J. Phys. Chem. A 109, 10638 – 10645 (2005) Abstract  PDF (180 kB) 

40. T. Wang and A. I. Krylov
The effect of substituents on electronic states ordering in meta-xylylene diradicals: Qualitative insights from quantitative studies
J. Chem. Phys. 123, 104304 (2005) Abstract  PDF (111 kB) 

37. T. E. Munsch, L. V. Slipchenko, A. I. Krylov, and P. G. Wenthold
Reactivity and Structure of the 5-Dehydro-m-xylylene Anion
J. Org. Chem. 69, 5735 – 5741 (2004) Abstract  PDF (180 kB) 

36. A. M. C. Cristian, Y. Shao, and A. I. Krylov
Bonding patterns in benzene triradicals from structural, spectroscopic, and thermochemical perspectives
J. Phys. Chem. A 108, 6581 – 6588 (2004) Abstract  PDF (151 kB) 

35. L. V. Slipchenko, T. E. Munsch, P. G. Wenthold, and A. I. Krylov
5-Dehydro-1,3-quinodimethane: A hydrocarbon with an open-shell doublet ground state
Angew. Chem. Int. Ed. 43, 742 – 745 (2004) Abstract  PDF (167 kB) 

32. L. V. Slipchenko and A. I. Krylov
Electronic structure of the 1,3,5-tridehydrobenzene triradical in its ground and excited states
J. Chem. Phys. 118, 9614 – 9622 (2003) Abstract  PDF (127 kB) 

29. L. V. Slipchenko and A. I. Krylov
Electronic structure of the trimethylenemethane diradical in its ground and electronically excited states: Bonding, equilibrium geometries and vibrational frequencies
J. Chem. Phys. 118, 6874 – 6883 (2003) Abstract  PDF (138 kB) 

28. Y. Shao, M. Head-Gordon, and A. I. Krylov
The spin-flip approach within time-dependent density functional theory: Theory and applications to diradicals
J. Chem. Phys. 118, 4807 – 4818 (2003) Abstract  PDF (185 kB) 

26. L. V. Slipchenko and A. I. Krylov
Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study
J. Chem. Phys. 117, 4694 – 4708 (2002) Abstract  PDF (237 kB)