The synergy between qualitative theory, quantitative calculations, and direct experiments in understanding, calculating, and measuring the energy differences between the lowest singlet and triplet states of organic diradicals

Abstract

This Perspective describes research, carried out in the authors' labs over the past forty years, aimed at understanding, predicting, and measuring the singlet-triplet energy differences ( ST ) in diradicals. A theory for qualitatively predicting the ground states of diradicals and the use of Negative Ion Photoelectron Spectroscopy (NIPES) for measuring  ST are described. The application of this theory, ab initio calculations, and NIPES to the prediction and measurement of  ST in a wide variety of organic diradicals is detailed. Among the diradicals that are discussed in this Perspective are HN, CH 3 N, PhN, CH 2 , trimethylenemethane (TMM), oxyallyl (OXA), meta-benzoquinodimethane (MBQDM), meta-benzoquinone (MBQ), tetramethyleneethane (TME), 1,2,4,5-tetramethylenebenzene (TMB), and D 8h cyclooctateraene (COT). All of these diradicals have been studied in one and, in most cases, in both of the authors' laboratories. The studies of OXA and D 8h COT were, in fact, collaborations between the research groups of the authors. These two projects both took advantage of the ability of NIPES to provide information about transition states. Transition-state spectroscopy was used to measure the cabonyl stretching frequency in the singlet state of OXA and to establish that D 8h COT violates the strictest version of Hund's rule. However, in some cases, it is not qualitative theories but the results of high-level calculations that motivate experimentalists to test how quantitatively accurate the calculations are. In other cases calculations are performed to see how well they reproduce experimental results that have already been obtained. When the results of calculations and experiments are found to be at odds with each other, additional experiments and/or calculations almost inevitably follow.Investigations of the energy differences between the lowest singlet and triplet state (E ST ) of organic diradicals 1 have provided many illustrations of the above types of synergies. Qualitative theories have resulted in computational and/or experimental tests, and calculations and experiments have not only stimulated each other but, in some cases, also led to the development of qualitative theories.For example, in response to the results of experiments and calculations on cyclobutadiene and trimethylenemethane, one of the coauthors of this review (WTB) helped to develop a qualitative theory, which allows the qualitative prediction of the approximate size and sign of

Close relation between quantum interference in molecular conductance and diradical existence

“…Borden and coworkers (28)(29)(30) showed that, in disjoint π-diradicals, the open-shell singlet and triplet states can generally be expected to be close in energy, but higher-order effects can often make the open-shell singlet state more stable than the triplet state [which, interestingly, is a violation of Hund's rule (31)]. On the other hand, nondisjoint diradicals generally have a triplet ground state.…”

“…On the other hand, nondisjoint diradicals generally have a triplet ground state. Borden and coworkers also provided a simple method to determine whether a diradical is disjoint or nondisjoint based on the starring procedure (28,30). If, in a diradical, the number of starred carbons (N S ) is equal to that of unstarred carbons (N U ), then the NBMOs can be chosen to be disjoint, with one NBMO confined to the starred set of atoms and the other to the unstarred set.…”

Chapter 2: Organic Molecules, Radicals, and Spin States

“…A detailed description of the apparatus, along with a landmark application to the evaluation of the singlettriplet gap in methylene and its deuterated isotopomer was reported in 1985 [87]. Access to high quality data for gas phase species, attended by the development of computational methods and theories capable of describing high-spin systems has advanced understanding substantially [88].…”

Negative Ion Photoelectron Spectroscopy Confirms the Prediction that 1,2,4,5-Tetraoxatetramethylenebenzene Has a Singlet Ground State

“…The 20 K NIPE spectra of TOTMB •− at 266 and 193 nm ( Figure S1); frequency assignments of symmetric vibrational modes for the 1 A g and 3 B 1u states of TOTMB ( Figure S2); stick spectrum in Figure 2, convoluted using Gaussian line shapes with fwhm of 25, 20, and 30 meV, superimposed on the experimental 266 nm spectrum ( Figures S3−S5); spin densities and bond lengths in TMB and TOTMB ( Figure S6); and optimized geometries, vibrational frequencies, and energies for the 1 UB3LYP/aug-cc-pVTZ//UB3LYP/aug-cc-pVTZ c 1.05 d 9.2 e CASPT2/aug-cc-pVDZ//CASSCF/aug-cc-pVDZ 1.17 6.1 CASPT2/aug-cc-pVDZ//CASPT2/aug-cc-pVDZ 1.18 6.1 CASPT2/aug-cc-pVTZ//CASPT2/aug-cc-pVDZ 1.28 6.2 CASPT2/aug-cc-pVQZ//CASPT2/aug-cc-pVDZ 1.32 6.3 a Adiabatic EA. b Negative sign for ΔE ST indicates that the singlet is lower in energy than the triplet.…”