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The Triplet State

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The Triplet State Nicholas J. Turd Columbia University Triplet New York, 10027 The State Triplet states are now important inter- arise in differentiating a biradical state (i.e., a species mediates of organic chemistry. In addition to the wide possessing two independent odd electron sites) from a range of triplet molecules available via photochemical triplet. Suppose two carbon radicals are separated by excitation techniques (1) numerous molecules exist in a long methylene chain as in I. stable triplet ground states, e.g., oxygen molecules. Theoretical calculations, furthermore, make predic- tions concerning the spin multiplicities of the ground states of many prototype organic molecules such as cyclobutadiene (s), trimethylene methane (S), methy- lene (4), etc., and indicate that they will be triplets. In spite of the increasing significance of the triplet state If the methylene chain is sufficiently long and the odd to organic chemistry, the fundamental nature of triplets electron centers are so far removed from one another and their distinction from biradicals is not always clear that they do not interact (magnetically and electron- to the student. It is the purpose of this paper to call ically) with one another then the system is a doublet of attention to the generally accepted definition of the doubleis, i.e., two independent odd electrons or a true triplet state, to review the experimental tests for dis- biradical. If the methylene chain should be folded tinguishing triplets from other reactive species, and to (11) so that the odd electrons begin to interact (mag- discuss some properties of triplet molecules. netically and electronically) with one another, then at some distance, R, between the -CH2 groups the doublet Definition of a Triplet State of doublets will become a triplet state. This state will A molecule exists in a triplet state when its total spin result from the fact that the spin of the electron on angular momentum quantum number S is equal to one. carbon A is no longer independent of the spin on carbon This definition of a triplet does not generally elicit a B. Since the spins are quantized the following selec- clear physical description of a triplet state to an av- tion rule obtains: erage chemist who does not work with quantum me- No. of spin states = 2 1 S I + 1 chanics except at the descriptive level. where S is the sum of the spin quantum numbers for Perhaps the best definition of a triplet state for the the two electrons. This means that either three spin average chemist is the following: a triplet is a para- states (if S = 1 or -1, i.e., spins of both electrons on magnetic even-electron species which possesses three as CAand Ce are the same) or one spin state (if S = 0, distinct but energetically similar electronic states a i.e., spin of the electron of CAis paired with that of CB) result of the magnetic interaction of two unpaired elec- result. The former describes a triplet state and the latter tron spins. The several important terms of this defini- a singlet state. tion allow some insight as to the essential features of a Right away ye see a difficulty in terminology: The triplet. First of all, a triplet is paramagnetic, and should "tridet state" is not one state but three states even in the thus display this property in a magnetic field. This absence of an ezternal magnetic field. Indeed, under paramagnetism serves as the basis for experimental favorable conditions transitions may be observed be- magnetic susceptibility (6) and electron spin resonance tween triplet levels at zero external magnetic field. studies (5) of the triplet state. However, we can The effect of an external magnetic field is to further imagine many paramagnetic odd electron species which split the triplet levels and allow transitions between are not triplets, e.g., nitric oxide. Thus, the criterion them to be more easily detected. that a triplet must also be an even electron species is ap- parent. Even here, we can imagine paramagnetic, Properlies of a Triplet State even electron species which possess (a) only two dis- tinct electronic states or (b) five or more electronic A triplet may result whenever a molecule possesses states. The former occurs when the paramagnetism two electrons which are both orbitally unpaired and results from two electrons which act as two independent spin unpaired. Orbital unpairing of electrons results odd electrons. For example, two carbon radicals sep- when a molecule absorbs a photon of visible or ultra- arated by a long saturated chain will behave as two violet light. Direct formation of a triplet as a result of doublet states if there is sufficient separation to prevent this photon absorption is a very improbable process spin interactions. Five or more electronic states re- IAlfred P. Sloan Fellow, 1966-68. The author gratefully sult when four or six parallel electronic spins interact acknowledges the generous support of this work by the Air Force (to yield quintet and septet states, respectively). Office of Scientific Research (Grant AFOSR1000-66) and the One can now see that conceptual difficulties may National Science Foundation (Grant NSF-GP-4280). 2 / Journal of Chemical Educofion since both the orbit and spin of the electron would have Even paramagnetism is not an infallible probe for a to change simultaneously. Thus, a singlet state is gen- triplet state since free radicals which are also para- erally formed by absorption of light. However, quite magnetic are often produced by the absorption of light. often the lifetime of this singlet state is sufficiently long It appears that electron spin resonance (esr) is prob- to allow the spin of one of the two electrons to invert, ably the most powerful single method for establishing thereby producing a triplet. We shall now consider that a molecule is in its triplet state. The nature of the ways in which such a species is unambiguously cbar- the (esr) signals may be predicted and fit to the fol- acterized (see Fig. 1). lowing theoretical equation which describes the mag- netic spin interactions and expected absorptions H = goH.S + DS+ E(S2 - SNP) This particular equation is derived for the special case of molecules with a plane of symmetry and a symmetry axis perpendicular to that plane. However, the impor- tant general features of this equation are (a) the term 9d.S which describes the interaction of the external magnetic field (H) with the unpaired electron spin (8); the term DS,? + E(SS2- S,2) which describes (b) the Figure 1. Simple MO description of singleh and triplab. spin-spin dipolar interactions along the x, y, and z axes of the molecule. These are illustrated in Figure 2. Let us ask, "What are the general properties to be expected of a molecule in the triplet state?" Some of the more important physical properties are (a) Paramagnetism (b) Absorption between triplet sublevels (e) Electronic absorption from the lowest triplet to upper triplets (d) Electronic emission from the lowest triplet to a lower singlet ground state (if the triplet level is not the ground state) The paramagnetism of the triplet results from the in- teraction of unpaired spins and the fact that an un- paired spin shows a paramagnetic effect (is attracted) in a magnetic field. Absorption between triplet sublevels may be ob- served directly by the use of an electron spin resonance spectrometer (Ij). The triplet, like any other electronic state, may be excited to upper electronic states of the same spin as the result of light absorption. In favorable cases this may Figure 2. The triplet rtote resulting fmm la) spin-spin dipolar interoctionr be observed by the method of flash spectroscopy (If). ond (bl win-exRrnd Rcld interactions. For most organic molecules the lowest triplet state is an excited electronic state and may emit light and pass to the ground singlet state. Since light absorption to form a triplet from a singlet is improbable, the sym- Thus, from a study of the behavior of a triplet in a mag- metrically related emission of light from a triplet re- netic field, information on the electronic distribution in turning to a ground state is likewise improbable. In- this excited state is obtained. In favorable cases, the deed, it takes the triplet states of some aromatic mole- nuclear geometry of the triplet may be derived. cules an average of about 50 sec to emit light. This phe- nomenon is known as phosphorescence and is to be con- Other Tests for Triplets: Spin Orbital Coupling trasted with fluorescence, the emission of light from an In addition to the above criteria for triplets, the re- excited singlet state returning to a singlet ground state, sponse of the slow emission of a molecule to certain in- a process which often occurs in nanoseconds. ternal and external perturbations may provide addi- Althrmgh phosphorescence (long lived emission) was tional evidence that the emission is phosphorescence the first method employed to study triplets, it is not a and therefore arises from a triplet. specific device for establishing whether a long-lived emis- The basic question which concerns us here is, "How do sion occurs from a triplet. For instance, examples are forbidden transitions occur"? Quantum mechanics known for which the slow combination of positive and provides a mechanism by assuming that the actual negative sites will generate excited molecules which molecule does not contain "pure" states. Thus, each emit light. In this case the combination reaction may singlet is endowed with a certain extent of triplet char- be rate determining for light emission. acter and vice-versa. This is a form of "mixing" states Similarly, absorption from one triplet to another is and requires a suitable interaction (perturbation) not a specific method since the precise triplet-triplet ab- without which the states would remain pure.
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