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), methylene (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 distinct 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 magnetic 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 important 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 interaction of unpaired spins and the fact that an unpaired spin shows a paramagnetic effect (is attracted) in a magnetic field. Absorption between triplet sublevels may be observed 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. sorption characteristics cannot be predicted accurately. Spin-orbital coupling is the interaction which "mixes" It would thus remain to be proven that the absorbing singlet and triplet states. It is of immense importance species is indeed a triplet and not some other transient to photochemists and is also fascinating in its own right. species. It might be noted that the implication of triplet states

Volume 46, Number 1, January 1969 / 3 in photosynthesis indirectly connects spin-orbital cou- with respect to electron spin-nuclear magnetic field in- pling with life as we know it. A brief qualitative de- teractions (because spin-paired electrons cancel each scription of this important mechanism would therefore other's effect). On the other hand, the field generated seem to be in order. by a paramagnetic material on the mabetic dipole of Quantum chemistry tells us that the rate'constant the electron is considerable. Thus, a high pressure of (probability) for interconversions (both radiative and oxygen (a ground state triplet) or nitric oxide (a ground radiationless) between singlet and triplet states will de- state doublet) is capable of enhancing singlet and triplet pend on the.extent of this "mixing" which in turn may interconversions. to the extent that So-TI absorption be described in terms of a mixing coefficient, becomes measurable. One of the most important fundamental problems in photochemistry which is yet to he resolved is the mechanism of radiationless decay of TI. The limiting life- Vso is the term which describes the interaction which time of TI is its inherent phosphorescence lifetime, usn- "flips" the electronic spin and E, - ET is the energy ally of the order of 1Q-10-2 see. However, very few difference between the singlet and triplet states involved triplets possess lifetimes longer than 10W4 sec in fluid in "mixing." Clearly, the smaller the energy gap be- solution. In rigid media at low temperatures the tween the interacting singlet and triplet states the larger triplet lifetimes approach, hut rarely achieve, their in- the quantity X. herent values. A trivial mechanism to explain these The interaction term Vg0is a typical quantum me- results is impurity diffusion controlled quenching chanical matrix element which describes the energy (oxygen being an efficient, ubiquitous culprit). In- (strength) of the spin-orbital coupling interaction. It deed, as experimenters take greater and greater pains to is believed that the interaction which causes the "spin "clean up" their systems, triplet lifetimes increase. flip" is relativistic in origin. Thus, the spinning elec- Extrapolated triplet lifetimes in liquid isopentane agree tron may be considered to generate a magnetic field be- fairly well with those at low temperature in rigid iso- cause it is a spinning and charged particle (a magnetic pentane. The actual values at 25T, are still of the dipole). The nucleus is likewise a spinning charged order of milliseconds, however. particle and generattes its own magnetic field. How- Examples of the intramolecular and intermolecular ever, the electron is also in orbit about the nucleus and heavy atom effectare given in Figures 4 and 5. by the laws of relativity, the nucleus may be considered to be in orbit about the electron. The net effect is that the magnetic field of the nucleus interacts with the mag- Singlets and Triplets: Differential Properties netic dipole of the spinning electron and applies a force Let us consider the excited singlet and triplet states or torque which causes it to "flip" direction. This cor- of the helium atom, i.e.,S~= (1s t ) (2s 4 ), TI = (Is t ) responds to the classical interaction which causes an ex- (2s t ). Because of the requirement of antisymme- ternal magnetic field to "flip" a magnetic dipole from trization of a total molecular wave function (7), the one orientation to another (see Fig. 3). Even from lowest triplet state and the lowest excited singlet state of He differ in energy and in electronic distribution. The energy separation is given by

where Es is the electronic energy of the lowest excited singlet state and E~isthe electronic energy of the lowest triplet state.

Figure 3. Diagram representing the spin-orbital coupling of slsctmn and nvclevr which causes "spin-Rip." this oversimplified picture we would expect the degree of spin-orbital coupling to depend on:

) The nuclear charge (heavy atom effect), since the larger the 0 + T1 charge on the nucleus the stronger the nuclear magnetic field and, for certain orbitals, the closer the electrons tend to get to Absorption the nucleus 2) The particular orbital of the electron, since if the orbit has "s"-character (in which case the elect.ron has a finite oraha- bility of being on the nucleus, or tends to localize at or pene- trate one nucleus) the greater the interaction of the elect,ron and the nucleus In addition to these effects the symmetry of the mixing states determines the magnitude of A. Vs0 represents the interaction of any magnetic field with the Figure 4. lntramolecvlar hewy atom effect on on absorption spectrum. spinning electron. In diamagnetic molecules the inter- The intensity of So + hv - TI ohsorption is greatly enhanced by insertion action of the magnetic dipole of one electron with the of a heavy atom on the oromatt framework. The heavy atom increases spin orbital coupling and covrer 50 - 7, absorption to become siperi- spin dipole of another electron tends to be negligible mentally signiRcant.

4 / journal of Chemicol Education photochemical behavior (8). For example, the SI state of butadiene undergoes valence isomerization to bicy- clobutane and cyclobutene (9) while the TI state prefers to dimeriae (10).

In practice (II), a TI state is not populated directly hut generally forms as a result of a radiationless transi- tion from S,, which can he easily populated by photo- "0°" hJ Pure tiquid 1 chemical excitation with visible or ultraviolet light.

LIGHT ABSM(PTI0N

Figure 5. lntermolecvlor heovy otom effect on the obsorptim spechum of 1-chlomnophtholens. When the iodine atom of ethyl iodide collides with the 1.chlommphtholene it induces stronger spin-orbital coupling in the latter ond enhances the So -+ TI absorption pmeess.

In addition, Figure 7. Indired photochemical excitation of TI via SI. where rlzis the separation of electron 1 and 2. Some examples of singlet and triplet parameters are The term Ksr represents the self-repulsion of the two listed in the table. It can he seen that a wide range of electrons in the 1s and 2s orbitals. Since repulsion al- values exists for the energies, triplet yields, and triplet ways results in an increase in energy, K~T> 0 and EB - decay constants. ET > 0. Since the description of SI and TI given above Singlets and Triplets of Ketones can be generalized to include molecules, it turns out that for a given excited configuration of electrons, the As an example of the differences in Sl and TI which singlet state is always of higher energy than the corre- may exist for a molecule, consider formaldehyde (12). sponding triplet state. Quantum mechanics leads us to An analysis of the vibrational structure of formaldehyde the non-intuitive conclusion that in the triplet state absorption and emission spectra allows conclusions to electrons exhibit an avoidance tendency relative to the he made concerning the properties of S1 and TI. Below electrons in the corresponding singlet state. Pictori- are listed some of these properties which are compared ally this situation is described in Figure 6. In (A) the to those of SO. TI state is shown having the 1s and 2s electrons spa- cially distinct, i.e., el and ez tend to avoid one another. In (B) the electrons have their spins in phase and tend to occupy the same regions of space, thereby causing greater electronic repulsion in SI than TI. So, stable SL TI The fact that S1 and TI possess different energy and planar pyrimidal, -25' out pyrimidal, -35' out electronic distribution suggests that they should also of plsne . of plane rco = 1.21 .& T,, = 1.32 A r,. = 1.31 A possess different photochemistry. Indeed, numerous p. = 2.5 D p,o = 1.5 D p. a - 1.5 D examples are known for which a SI and TI state of the E = 0 El N 83 kcdlmol6 E8 - 72 kcal/mole same molecule demonstrate substantial differences in For many ketones, SI and TI are derived from n,s* excitation. These states may he described as ones in which the electron excitation is essentially localized on the carbonyl function. We'may approximate an n,s* state in atomic orbital terms as:

or in valenc: bond terms as; xD ;c-g --. ,c-9 - - 6 Figure 6. Pictorial description of the SI ond TI strrter of helium. +6

Volume 46, Number I, Januory 1969 / 5 Excited State Parameters for Some Organic Molecules The nature of triplets may be probed by emission

Molaoule Ex' En' T kid ka' studies, esr experiments, and the effects expected on spin-orbital coupling. The triplet state has taken its place as an important reactive intermediate of organic chemistry, and the vigorous exploration of this field is reflected in the burgeoning list of recent publications on this topic (I). . ;Energy of lowet vibratiqnal level in kcal/mole. Literature Cited FIu0re8oenoe y~eldam flu~dsolution at 25'C. 'Triplet yields. (1) (a) TURRO,N. J., "Molecular Photochemistry," W. A. dFI~~rescen~edecay constants (XI09 iin aeo-I. 'Triplet deohy oonstant. in fluid ~olutionat 2S°C. Beniamin Co.. New York. N. Y.. 1965: CALVERT.J.. .~ND.PI~,J.'N., JR., "~hotochemistry,'" John whey; New York, N. Y., 1966. These descriptions make certain stereoelectronic pre- (b) REID, C., "Excited States in Chemistry and Biology," dictions concerning the reactivity of the n,a* state. Butterworth, London, 1957. Unfortunately, this model does not predict differences (c) EI~SAYED,M. A,, Accounts qf Chemical Research, 1, 8 ,-"".110fi7\,. which should result from spin differences. Evidence (d) LOWER,S. K., AND EI~SAYED,M. A,, Chem. Rev., 66,199 exists, however, that SI and TI may have different reac- (1966). tivities toward the same reaction, even though both are (e) WAGNER,P. J., AND HAMMOND,G. S. in "Advances in n,s*. Photochemistry," (Editors: NOYES,W. A,, JR., HAM- MOND, G. S., AND PITTS, J. N., JR.), Vo1. 5, Interscience For example, acetone singlets are much less reactive (division of John Wiley & Sons, Inc.) New York, 1968, p. toward hydrogen abstraction from tri-n-hutyl stan- r)l nane than acetone triplets (IS). (f)PORTER, G., Proc. Chem. Soe., 291 (1959). (g) LEWIS,G. N., AND KASHA,M., J. Am. Chem. Soc., 66, k - I@ (CHakCOa fnBuh SnH + (CH~)~COH 2100 (1944). + - (h) XASHA,M., Chem. Rev., 41, 401 (1948). k - 10" (i) MCGLYNN,S. P., SMITH,F. J., AND CILENTO,G., Photo- (CHz)&O' (~BU)~SnH -+ (CH~)~COH + ehem.~ ~ ~~ -Phatobio.. ~~ ~~ ~~ ,~, 3. 269~. 11964).~ -.--, ~ Whether a different reactivity between 81and TI of the (j)THOMPSON, C., Quart. Rev., 22, 45 (1968). (k) MCGLYNN,8. P., KINOSHITA,M., AND ALUMI, T., same configuration will be general cannot be answered "Molecular Spectroscopy of the Triplet State," Prentice- now, but will probably be the subject of much future Hall, Inc., Englewood, New Jersey, 1968. work. (2) WATTS, L., FITZPATRICK,3. D., AND PETTIT, R., J. Am. Chem. Soc., 88, 623 (1966). Summary (3) Dow~,P., J. Am. Chem. Soe., 88, 2587 (1966). (4) KIRMSE,W., "Carbene Chemistry," Academic Press, New

The "three state" character of triplets is not of sig- York.,- 1964. - nificance to the chemistry of these species. However, HUTCHINSON,C. A,, JR., AND MAGNUM,B. W., J. Chem. conservation of spin may inhibit certain chemical reac- Phys., 32, 1261 (1960). LEWIS,G. N., CALVIN,M., AND KASHA,M., J. Chem. Phya., tions which require a "spin flip" in going from reactants 17, 804 (1949). to products. Also, the inherent improbability of a DEKE, R. H., AND WITTKE,J. P., "Introduction to Quan- spin flip from a triplet to form a singlet, enhances the tum Mechanics." Addison-Wesley,.. Readine.-. Mass.. 1960. lifetime of the former and thereby increases the prob- p. 318. (8) Review: TURRO,N. J., DALTON, 3. C., AND WEISS, D. S., ability that it will survive long enough (relative to ex- Org. Photochem., 2, in press. cited singlets) to undergo a chemical reaction. (9) SRINIYASAN,R., J. Am. Chem. Soc., 85, 4045 (1963). Although the inherent character of triplets is such (10) HAMMOND,G. S., TURRO,N. J., AND FISCHER,A,, J. Am. that the two spin-unpaired electrons tend to "avoid" Chem. Soc., 83, 4674 (1961). each other, triplets are not necessarily biradicals in the (11) Review: TURRO,N. J., Chem. Eng. News, 45, 84 (1967). (12) BRAND,3. D. C., AND WILLIAMSON,D. G., Adu. Phgs. Org. sense of two chemically independent odd electron cen- Chem., 1, 365 (1963). ters. (13) WAGNER,^. J., J. Am. Chem. Soc., 89, 2503 (1967).

6 / Journal of Chemical Educafion