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.

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 (ΔE(ST)) in diradicals. A theory for qualitatively predicting the ground states of diradicals and the use of Negative Ion Photoelectron Spectroscopy (NIPES) for measuring ΔE(ST) are described. The application of this theory, ab initio calculations, and NIPES to the prediction and measurement of ΔE(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(8 h) cyclooctatetraene (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 carbonyl stretching frequency in the singlet state of OXA and to establish that D(8h) COT violates the strictest version of Hund's rule.

[1]  N. Gritsan,et al.  The interplay of theory and experiment in the study of phenylnitrene. , 2000, Accounts of chemical research.

[2]  R. N. Mcdonald,et al.  Electron photodetachment of the phenylnitrene anion radical: EA, .DELTA.H.degree.f, and the singlet-triplet splitting for phenylnitrene , 1993 .

[3]  D. Hrovat,et al.  Ab Initio calculations of the potential surfaces for rearrangement of methylenecyclopropane and 2,2-difluoromethylenecyclopropane. Why do the geminal fluorines have little effect on lowering the activation energy?† , 1999 .

[4]  Anna I Krylov,et al.  Spin-conserving and spin-flipping equation-of-motion coupled-cluster method with triple excitations. , 2005, The Journal of chemical physics.

[5]  W. C. Lineberger,et al.  Negative Ion Photoelectron Spectroscopy Studies of Organic Reactive Intermediates , 1999 .

[6]  W. T. Borden,et al.  Ab initio calculations predict a singlet ground state for tetramethyleneethane , 1987 .

[7]  David A. Hrovat,et al.  CASSCF calculations find that a D8h geometry is the transition state for double bond shifting in cyclooctatetraene , 1992 .

[8]  E. Davidson,et al.  Some aspects of the potential surface for singlet trimethylenemethane , 1977 .

[9]  M. Newton,et al.  Potential energy surfaces of cyclobutadiene: ab initio SCF and CI calculations for the low-lying singlet and triplet states , 1978 .

[10]  A. Berinstain,et al.  2,3,5,6-Tetrakis(methylene)-1,4-cyclohexanediyl (1,2,4,5-tetramethylenebenzene), a disjoint non-Kekule singlet hydrocarbon biradical , 1993 .

[11]  W. L. Jorgensen,et al.  Solvent Effects on the Ring Opening of Cyclopropanones to Oxyallyls: A Combined ab Initio and Monte Carlo Study , 1994 .

[12]  K. Jordan,et al.  Theoretical study of the low-lying triplet and singlet states of diradicals: prediction of ground-state multiplicities in cyclic analogs of tetramethyleneethane , 1992 .

[13]  E. Davidson,et al.  Ab initio study of m-benzoquinodimethane , 1983 .

[14]  J. F. Harrison,et al.  The electronic structure of methylene , 1969 .

[15]  P. Vogel,et al.  A Kinetically Stable Singlet-State of 1,2,4,5-Tetramethylenebenzene , 1992 .

[16]  W. T. Borden.  Can a square or effectively square singlet be the ground state of cyclobutadiene , 1975 .

[17]  R. Celotta,et al.  Molecular Photodetachment Spectrometry. I. The Electron Affinity of Nitric Oxide and the Molecular Constants of NO , 1972 .

[18]  M. Murcko,et al.  The effects of heteroatom substitution on the singlet–triplet energy differences in diradicals—ab initio calculations of ΔEST in meta-benzoquinomethane and in 1,3-naphthoquinomethane , 1998 .

[19]  V. Staemmler,et al.  A theoretical study of the structure of cyclobutadiene , 1977 .

[20]  Eileen P. Clifford,et al.  Photoelectron spectroscopy of the CH3N− ion , 1999 .

[21]  W. C. Lineberger,et al.  Photoelectron spectroscopic study of the oxyallyl diradical. , 2011, The journal of physical chemistry. A.

[22]  Anna I Krylov,et al.  The effect of substituents on electronic states' ordering in meta-xylylene diradicals: qualitative insights from quantitative studies. , 2005, Journal of Chemical Physics.

[23]  P. Wenthold,et al.  Photoelectron spectroscopy of chloro-substituted phenylnitrene anions. , 2009, The journal of physical chemistry. A.

[24]  D. Hrovat,et al.  MCSCF and CASPT2N Calculations on the Excited States of 1,2,4,5-Tetramethylenebenzene. The UV-Vis Spectrum Observed Belongs to the Singlet State of the Diradical , 1994 .

[25]  P. Wenthold,et al.  Topological control of spin states in disjoint diradicals. , 2010, The journal of physical chemistry. A.

[26]  W. C. Lineberger,et al.  PHOTOELECTRON SPECTROSCOPY OF M-XYLYLENE ANION , 1997 .

[27]  Seung Joon Kim,et al.  Phenylnitrene: energetics, vibrational frequencies, and molecular structures , 1992 .

[28]  M. Winkler.  Singlet-triplet energy splitting and excited states of phenylnitrene. , 2008, Journal of Physical Chemistry A.

[29]  V. Staemmler.  Ab initio calculation of the lowest singlet and triplet states in CH2, CHF, CF2, and CHCH3 , 1974 .

[30]  J. R. Butler,et al.  Photofragmentation of arylmethylenecycloprppanes to alkylidenecarbenes , 1970 .

[31]  W. Hase,et al.  A bimolecular mechanism for ketene photodissociation in the near ultraviolet , 1977 .

[32]  S. Peyerimhoff,et al.  ab initio Study on the Stability and Geometry of Cyclobutadiene , 1968 .

[33]  D. Craig.  Electronic levels in simple conjugated systems, I. Configuration interaction in cyclobutadiene , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[34]  Ernest R. Davidson,et al.  The Importance of Including Dynamic Electron Correlation in ab initio Calculations , 1996 .

[35]  H. Jiao,et al.  Stability of Tetraoxocyclobutane Revised: Perturbation Theory and Density Functional Scheme , 2001 .

[36]  W. Goddard,et al.  Ab initio studies on the singlet–triplet splitting of methylene (CH2) , 1977 .

[37]  A. Ovchinnikov.  Multiplicity of the ground state of large alternant organic molecules with conjugated bonds , 1978 .

[38]  A. Berinstain,et al.  Photochemical generation and preparative capture of 1,2,4,5-tetramethylenebenzene in fluid solution. Nanosecond time-resolved spectroscopic determination of absolute rates of dimerization and oxygen trapping of a disjoint singlet hydrocarbon biradical , 1992 .

[39]  V. Staemmler.  Ab initio calculations on small hydrides including electron correlation , 1973 .

[40]  W. Goddard,et al.  Generalized valence bond description of bonding in low-lying states of molecules , 1973 .

[41]  P. Wenthold,et al.  Regioselective synthesis of biradical negative ions in the gas phase. Generation of trimethylenemethane, m-benzyne, and p-benzyne anions , 1994 .

[42]  W. C. Lineberger,et al.  The photoelectron spectrum of CCl2-: the convergence of theory and experiment after a decade of debate. , 2009, Physical chemistry chemical physics : PCCP.

[43]  H. C. Longuet-Higgins,et al.  Some Studies in Molecular Orbital Theory I. Resonance Structures and Molecular Orbitals in Unsaturated Hydrocarbons , 1950 .

[44]  D. Neumark.  Transition-state spectroscopy via negative ion photodetachment , 1993 .

[45]  W. C. Lineberger,et al.  Laser photoelectron spectrometry of CH , 1975 .

[46]  D. Hrovat,et al.  Ab initio calculations of the singlet-triplet energy difference in phenylnitrene , 1992 .

[47]  R. Baseman,et al.  Trimethylenemethane. Experimental demonstration that the triplet state is the ground state , 1976 .

[48]  C. Bender,et al.  C2υ Potential Energy Surfaces for Seven Low‐Lying States of CH2 , 1971 .

[49]  F. Anet,et al.  The Rate of Bond Change in Cycloöctatetraene , 1962 .

[50]  M. Platz,et al.  Electron spin resonance spectroscopy of the triplet state of m-xylylene , 1983 .

[51]  D. Hrovat,et al.  Violations of Hund's rule in molecules — where to look for them and how to identify them , 1997 .

[52]  R. Gleiter,et al.  Reinvestigation of the ordering of the low-lying electronic states of cyclobutanetetraone with CASPT2, CCSD(T), G3B3, ccCA, and CBS-QB3 calculations , 2009 .

[53]  Ernest R. Davidson,et al.  Effects of electron repulsion in conjugated hydrocarbon diradicals , 1977 .

[54]  A. Gold,et al.  Trimethylenemethane. Proton Hyperfine Splitting , 1968 .

[55]  W. C. Lineberger,et al.  Transition-State Spectroscopy of Cyclooctatetraene , 1996, Science.

[56]  S. Shaik,et al.  Tetramethyleneethane (TME) Diradical: Experiment and Density Functional Theory Reach an Agreement , 1999 .

[57]  R. Caballol,et al.  The Controversial Ground State of Tetramethyleneethane. An ab Initio CI Study , 2000 .

[58]  W. C. Lineberger,et al.  Methylene: A study of the X̃ 3B1 and ã 1A1 states by photoelectron spectroscopy of CH−2 and CD−2 , 1985 .

[59]  W. Marsden.  I and J , 2012 .

[60]  I. Shavitt.  Geometry and singlet−triplet energy gap in methylene: a critical review of experimental and theoretical determinations , 1985 .

[61]  W. C. Lineberger,et al.  Laser photoelectron spectrometry of NH−: Electron affinity and intercombination energy difference in NH , 1976 .

[62]  A. Matlin,et al.  Ab initio computational study of methano- and ethano-bridged derivatives of oxyallyl , 1990 .

[63]  W. Doering,et al.  Stereochemistry of the methylenecyclopropane rearrangement—II: Exclusion of the concerted 45° pivot mechanisms☆ , 1973 .

[64]  D. Hrovat,et al.  Ab initio calculations on 1,2,4,5-tetramethylenebenzene at geometries optimized by .pi.-CI calculations. Prediction of a singlet ground state for a disjoint diradical , 1986 .

[65]  Laser photoelectron spectrometry of methylene(1-). Singlet-triplet splitting and electron affinity of methylene , 1976 .

[66]  Werner Kutzelnigg.  Friedrich Hund and Chemistry , 1996 .

[67]  V. Staemmler,et al.  Violation of Hund's rule by spin polarization in molecules , 1978 .

[68]  R. Borrelli,et al.  Franck-Condon analysis of the SF6- electron photodetachment spectrum , 2007 .

[69]  Bradley A. Smith,et al.  TRIMETHYLENEMETHANE. COMPARISON OF MULTICONFIGURATION SELF-CONSISTENT FIELD AND DENSITY FUNCTIONAL METHODS FOR A NON-KEKULE HYDROCARBON , 1996 .

[70]  Josef Michl,et al.  Neutral and Charged Biradicals, Zwitterions, Funnels in S1, and Proton Translocation: Their Role in Photochemistry, Photophysics, and Vision , 1987 .

[71]  P. Dowd,et al.  Trimethylenemethane from Photolysis of 3-Methylenecyclobutanone , 1967 .

[72]  R. Borrelli,et al.  The electron photodetachment spectrum of c-C4F8-: a test case for the computation of Franck-Condon factors of highly flexible molecules. , 2008, The Journal of chemical physics.

[73]  P. Bunker,et al.  Analysis of the laser photoelectron spectrum of CH−2 , 1985 .

[74]  G. Herzberg.  The Bakerian Lecture, The spectra and structures of free methyl and free methylene , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[75]  Xuanyu Feng,et al.  Triplet Species from Dihydropyrrolo[3,4-d]pyridazines, the Diazene Precursors of N-Arenesulfonyl-3,4-dimethylenepyrroles , 1997 .

[76]  H. Schaefer,et al.  Methylene: A Paradigm for Computational Quantum Chemistry , 1986, Science.

[77]  K. Morokuma,et al.  Structure and stability of oxyallyl. An MCSCF study , 1984 .

[78]  W. C. Lineberger,et al.  Photoelectron spectra of dihalomethyl anions: testing the limits of normal mode analysis. , 2011, The Journal of chemical physics.

[79]  J. J. Grabowski,et al.  Anion-Molecule Approaches to Non-Kekulé Molecules: The Radical Anion of Tetramethyleneethane , 1993 .

[80]  Eileen P. Clifford,et al.  Properties of tetramethyleneethane (TME) as revealed by ion chemistry and ion photoelectron spectroscopy , 1998 .

[81]  J. F. Harrison.  Structure of methylene , 1974 .

[82]  W. C. Lineberger,et al.  Laser photoelectron spectroscopy of CH2−, and the singlet–triplet splitting in methylene , 1981 .

[83]  M. Hanack,et al.  Vinyl cations from solvolysis , 1970 .

[84]  H. Schwarz,et al.  Generation of the elusive meta-benzoquinone in the gas phase. , 2005, Angewandte Chemie.

[85]  M. B. Coolidge,et al.  Ab initio MCSCF and CI calculations of the singlet-triplet energy differences in oxyallyl and in dimethyloxyallyl , 1990 .

[86]  A. Krylov,et al.  Structure, vibrational frequencies, ionization energies, and photoelectron spectrum of the para-benzyne radical anion , 2008 .

[87]  G. Ellison,et al.  CASSCF and CASPT2 ab initio electronic structure calculations find singlet methylnitrene is an energy minimum , 2000 .

[88]  W. C. Lineberger,et al.  Photoelectron spectroscopy of the trimethylenemethane negative ion , 1999 .

[89]  J. R. Butler,et al.  Thermal rearrangements of 2,2-diphenylmethylenecyclopropanes to indenes , 1970 .

[90]  Jiabo Li,et al.  Monoaza-analogs† of trimethylenemethane. Isoelectronic similarities and differences , 1998 .

[91]  F. Stuhl,et al.  Detection and quenching of NH(b 1Σ+) in the pulsed vacuum UV photolysis of NH3 , 1975 .

[92]  Y. Paik,et al.  Tetramethyleneethane, a ground-state triplet , 1986 .

[93]  A. Krylov,et al.  Electronic structure and spectroscopy of oxyallyl: a theoretical study. , 2010, The journal of physical chemistry. A.

[94]  C. A. Coulson,et al.  Note on the method of molecular orbitals , 1940, Mathematical Proceedings of the Cambridge Philosophical Society.

[95]  Lionel Salem,et al.  The Electronic Properties of Diradicals , 1972 .

[96]  G. Kennedy,et al.  Kinetics of methylene addition to cis- and trans-but-2-ene. Further evidence for the energy separation between triplet and singlet methylene , 1977 .

[97]  W. Doering,et al.  Stereochemistry of the methylenecyclopropane rearrangement : Feist's ester , 1970 .

[98]  S. F. Boys,et al.  Quantum Variational Calculations for a Range of C H 2 Configurations , 1960 .

[99]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[100]  Y. S. Lin,et al.  Ring Inversion and Bond Shift in Cyclooctatetraene Derivatives , 1964 .

[101]  E. Wasserman,et al.  EPR of CH2: a substiantially bent and partially rotating ground state triplet , 1970 .

[102]  P. Wenthold,et al.  Benzoylnitrene radical anion: A new reagent for the generation of M-2H anions , 2007, Journal of the American Society for Mass Spectrometry.

[103]  J. A. Berson.  A New Class of Non-Kekule Molecules with Tunable Singlet-Triplet Energy Spacings , 1997 .

[104]  W. C. Lineberger,et al.  The lowest singlet and triplet States of the oxyallyl diradical. , 2009, Angewandte Chemie.

[105]  W. Goddard,et al.  Theoretical Chemistry Comes Alive: Full Partner with Experiment , 1985, Science.

[106]  W. C. Lineberger,et al.  Laser photoelectron spectroscopy of vibrationally relaxed CH−2: A reinvestigation of the singlet–triplet splitting in methylene , 1984 .

[107]  W. C. Lineberger,et al.  Laser photoelectron spectrometry of the negative ions of silicon and its hydrides , 1975 .

[108]  A. West,et al.  Do High-Spin Topology Rules Apply to Charged Polyradicals? Theoretical and Experimental Evaluation of Pyridiniums as Magnetic Coupling Units , 1996 .

[109]  W. T. Borden.  Differences in expected stability of the triplet state in cyclic π-systems containing 4n electrons , 1969 .

[110]  H. C. Longuet-Higgins,et al.  The electronic structure of conjugated systems II. Unsaturated hydrocarbons and their hetero-derivatives , 1947, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[111]  W. T. Borden,et al.  Violations of Hund's Rule in Non-Kekule Hydrocarbons: Theoretical Prediction and Experimental Verification , 1994 .

[112]  W. Roth,et al.  Zur Energie‐Delle von Diradikalen; III1) 2,3,5,6‐Tetramethylen‐1,4‐cyclohexadiyl , 1991 .

[113]  J. F. M. Oth,et al.  Conformational mobility and fast bond shift in the annulenes , 1971 .

[114]  K. Jordan,et al.  Theoretical study of the low-lying triplet and singlet states of tetramethyleneethane: prediction of a triplet below singlet state at the triplet equilibrium geometry , 1993 .

[115]  H. Reisenauer,et al.  The Diradical 2,3,5,6-Tetramethylene-1,4-cyclohexanediyl (“1,2,4,5-Tetramethylenebenzene”)† , 1987 .

[116]  W. C. Lineberger,et al.  SINGLET-TRIPLET SPLITTINGS IN CX2 (X = F, CL, BR, I) DIHALOCARBENES VIA NEGATIVE ION PHOTOELECTRON SPECTROSCOPY , 1999 .

[117]  Eileen P. Clifford,et al.  Photoelectron spectroscopy of the phenylnitrene anion , 1992 .

[118]  R. Celotta,et al.  Molecular Photodetachment Spectrometry. II. The Electron Affinity of O2 and the Structure of O2 , 1972 .