Nicholas J. T u r d Columbia University New York, 10027
The Triplet State
Triplet states are now important intermediates of organic chemistry. I n addition to the wide range of triplet molecules available via photochemical excitation techniques (1) numerous molecules exist in stable triplet ground states, e.g., oxygen molecules. Theoretical calculations, furthermore, make predictions 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. I n spite of the increasing significance of the triplet state to organic chemistry, the fundamental nature of triplets and their distinction from biradicals is not always clear to the student. It is the purpose of this paper to call attention to the generally accepted definition of the triplet state, to review the experimental tests for distinguishing triplets from other reactive species, and to discuss some properties of triplet molecules. Definition of a Triplet State
A molecule exists in a triplet state when its total spin angular momentum quantum number S is equal to one. This definition of a triplet does not generally elicit a clear physical description of a triplet state to an average chemist who does not work with quantum mechanics except a t the descriptive level. Perhaps the best definition of a triplet state for the average chemist is the following: a triplet is a paramagnetic even-electron species which possesses three distinct but energetically similar electronic states as a result of the magnetic interaction of two unpaired electron spins. The several important terms of this definition allow some insight as to the essential features of a triplet. First of all, a triplet i s paramagnetic, and should thus display this property in a magnetic field. This paramagnetism serves as the basis for experimental magnetic susceptibility (6) and electron spin resonance studies (5) of the triplet state. However, we can imagine many paramagnetic odd electron species which are not triplets, e.g., nitric oxide. Thus, the criterion that a triplet must also be an even electron species is apparent. Even here, we can imagine paramagnetic, even electron species which possess (a) only two distinct electronic states or (b) five or more electronic states. The former occurs when the paramagnetism results from two electrons which act as two independent odd electrons. For example, two carbon radicals separated by a long saturated chain will behave as two doublet states if there is sufficient separation to prevent spin interactions. Five or more electronic states result when four or six parallel electronic spins interact (to yield quintet and septet states, respectively). One can now see that conceptual difficulties may 2
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arise in differentiating a biradical state (i.e., a species possessing two independent odd electron sites) from a triplet. Suppose two carbon radicals are separated by a long methylene chain as in I.
If the methylene chain is sufficiently long and the odd electron centers are so far removed from one another that they do not interact (magnetically and electronically) with one another then the system is a doublet of doubleis, i.e., two independent odd electrons or a true biradical. If the methylene chain should be folded (11) so that the odd electrons begin to interact (magnetically and electronically) with one another, then at some distance, R, between the -CH2 groups the doublet of doublets will become a triplet state. This state will result from the fact that the spin of the electron on carbon A is no longer independent of the spin on carbon B. Since the spins are quantized the following selection rule obtains: No. of spin states = 2 1 S I
+1
where S is the sum of the spin quantum numbers for the two electrons. This means that either three spin states (if S = 1 or -1, i.e., spins of both electrons on CAand Ce are the same) or one spin state (if S = 0, i.e., spin of the electron of CAis paired with that of CB) result. The former describes a triplet state and the latter a singlet state. Right away y e see a difficulty in terminology: The "tridet state" i s not one state but three states even i n the absence of an ezternal magnetic field. Indeed, under favorable conditions transitions may be observed between triplet levels a t zero external magnetic field. The effect of an external magnetic field is to further split the triplet levels and allow transitions between them to be more easily detected. Properlies of a Triplet State
A triplet may result whenever a molecule possesses two electrons which are both orbitally unpaired and spin unpaired. Orbital unpairing of electrons results when a molecule absorbs a photon of visible or ultraviolet light. Direct formation of a triplet as a result of this photon absorption is a very improbable process IAlfred P. Sloan Fellow, 1966-68. The author gratefully acknowledges the generous support of this work by the Air Force Office of Scientific Research (Grant AFOSR1000-66) and the National Science Foundation (Grant NSF-GP-4280).
since both the orbit and spin of the electron would have to change simultaneously. Thus, a singlet state is generally formed by absorption of light. However, quite often the lifetime of this singlet state is sufficiently long to allow the spin of one of the two electrons to invert, thereby producing a triplet. We shall now consider the ways in which such a species is unambiguously cbaracterized (see Fig. 1).
Figure 1.
Simple MO description of singleh and triplab.
Even paramagnetism is not an infallible probe for a triplet state since free radicals which are also paramagnetic are often produced by the absorption of light. It appears that electron spin resonance (esr) is probably the most powerful single method for establishing that a molecule is in its triplet state. The nature of the (esr) signals may be predicted and fit to the following theoretical equation which describes the magnetic spin interactions and expected absorptions H = goH.S + D S + E ( S 2 - 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 9 d . 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 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 ( I j ) . The triplet, like any other electronic state, may be excited to upper electronic states of the same spin as the result of light absorption. I n favorable cases this may be observed by the method of flash spectroscopy (If). 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 symmetrically related emission of light from a triplet returning to a ground state is likewise improbable. Indeed, it takes the triplet states of some aromatic molecules an average of about 50 sec to emit light. This phenomenon is known as phosphorescence and is to be contrasted with fluorescence, the emission of light from an excited singlet state returning to a singlet ground state, a process which often occurs in nanoseconds. Althrmgh phosphorescence (long lived emission) was the first method employed to study triplets, it is not a specific device for establishing whether a long-lived emission occurs from a triplet. For instance, examples are known for which the slow combination of positive and negative sites will generate excited molecules which emit light. I n this case the combination reaction may be rate determining for light emission. Similarly, absorption from one triplet to another is not a specific method since the precise triplet-triplet absorption characteristics cannot be predicted accurately. It would thus remain to be proven that the absorbing species is indeed a triplet and not some other transient species.
Figure 2. The triplet rtote resulting fmm ond (bl win-exRrnd Rcld interactions.
la) spin-spin dipolar
interoctionr
Thus, from a study of the behavior of a triplet in a magnetic field, information on the electronic distribution in this excited state is obtained. In favorable cases, the nuclear geometry of the triplet may be derived. Other Tests for Triplets: Spin Orbital Coupling
I n addition to the above criteria for triplets, the response of the slow emission of a molecule to certain internal and external perturbations may provide additional evidence that the emission is phosphorescence and therefore arises from a triplet. The basic question which concerns us here is, "How do forbidden transitions occur"? Quantum mechanics provides a mechanism by assuming that the actual molecule does not contain "pure" states. Thus, each singlet is endowed with a certain extent of triplet character and vice-versa. This is a form of "mixing" states and requires a suitable interaction (perturbation) without which the states would remain pure. Spin-orbital coupling is the interaction which "mixes" singlet and triplet states. It is of immense importance to photochemists and is also fascinating in its own right. It might be noted that the implication of triplet states Volume 46, Number 1 , January 1 9 6 9
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in photosynthesis indirectly connects spin-orbital coupling with life as we know it. A brief qualitative description of this important mechanism would therefore seem to be in order. Quantum chemistry tells us that the rate'constant (probability) for interconversions (both radiative and radiationless) between singlet and triplet states will depend on the.extent of this "mixing" which in turn may be described in terms of a mixing coefficient,
Vso is the term which describes the interaction which "flips" the electronic spin and E, - ET is the energy difference between the singlet and triplet states involved in "mixing." Clearly, the smaller the energy gap between the interacting singlet and triplet states the larger the quantity X. The interaction term Vg0is a typical quantum mechanical matrix element which describes the energy (strength) of the spin-orbital coupling interaction. It is believed that the interaction which causes the "spin flip" is relativistic in origin. Thus, the spinning electron may be considered to generate a magnetic field because it is a spinning and charged particle (a magnetic dipole). The nucleus is likewise a spinning charged particle and generattes its own magnetic field. However, the electron is also in orbit about the nucleus and 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 magnetic dipole of the spinning electron and applies a force or torque which causes it to "flip" direction. This corresponds to the classical interaction which causes an external magnetic field to "flip" a magnetic dipole from one orientation to another (see Fig. 3). Even from
with respect to electron spin-nuclear magnetic field interactions (because spin-paired electrons cancel each other's effect). On the other hand, the field generated by a paramagnetic material on the mabetic dipole of the electron is considerable. Thus, a high pressure of oxygen (a ground state triplet) or nitric oxide (a ground state doublet) is capable of enhancing singlet and triplet interconversions. to the extent that So-TI absorption 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 lifetime of TI is its inherent phosphorescence lifetime, usnally of the order of 1Q-10-2 see. However, very few triplets possess lifetimes longer than 10W4 sec in fluid solution. I n rigid media a t low temperatures the triplet lifetimes approach, hut rarely achieve, their inherent values. A trivial mechanism to explain these results is impurity diffusion controlled quenching (oxygen being an efficient, ubiquitous culprit). Indeed, as experimenters take greater and greater pains to "clean up" their systems, triplet lifetimes increase. Extrapolated triplet lifetimes in liquid isopentane agree fairly well with those a t low temperature in rigid isopentane. The actual values a t 2 5 T , are still of the order of milliseconds, however. Examples of the intramolecular and intermolecular heavy atom effectare given in Figures 4 and 5. Singlets and Triplets: Differential Properties
Let us consider the excited singlet and triplet states of the helium atom, i . e . , S ~= (1s t ) (2s 4 ), TI = (Is t ) (2s t ). Because of the requirement of antisymmetrization of a total molecular wave function (7), the 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 ~ i the s 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
charge on the nucleus the stronger the nuclear magnetic field and, for certain orbitals, the closer the electrons tend to get to 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 orahability of being on the nucleus, or tends to localize at or penetrate one nucleus) the greater the interaction of the elect,ron and the nucleus
I n 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 spinning electron. I n diamagnetic molecules the interaction of the magnetic dipole of one electron with the spin dipole of another electron tends to be negligible 4
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+ T1
Absorption
- -
Figure 4. lntramolecvlar h e w y atom effect on on absorption spectrum. hv TI ohsorption is greatly enhanced by insertion The intensity of So of a heavy atom on the oromatt framework. The heavy atom increases 7, absorption to become siperispin orbital coupling and covrer 50 mentally signiRcant.
+
photochemical behavior (8). For example, the SI state of butadiene undergoes valence isomerization to bicyclobutane and cyclobutene (9) while the TI state prefers to dimeriae (10).
hJ
"0°"
Pure tiquid
I n practice ( I I ) , a TI state is not populated directly hut generally forms as a result of a radiationless transition from S,, which can he easily populated by photochemical excitation with visible or ultraviolet light.
1
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.
I n addition, Figure 7.
where rlzis the separation of electron 1and 2. The term Ksr represents the self-repulsion of the two electrons in the 1s and 2s orbitals. Since repulsion alT 0 and EB ways results in an increase in energy, K ~ > ET > 0. Since the description of SIand TI given above can be generalized to include molecules, i t turns out that for a given excited configuration of electrons, the singlet state is always of higher energy than the corresponding triplet state. Quantum mechanics leads us to the non-intuitive conclusion that in the triplet state electrons exhibit an avoidance tendency relative to the electrons in the corresponding singlet state. Pictorially this situation is described in Figure 6. I n (A) the TI state is shown having the 1s and 2s electrons spacially distinct, i.e., el and ez tend to avoid one another. I n (B) the electrons have their spins in phase and tend to occupy the same regions of space, thereby causing greater electronic repulsion in SIthan TI. The fact that S1and TI possess different energy and electronic distribution suggests that they should also possess different photochemistry. Indeed, numerous examples are known for which a SI and TI state of the same molecule demonstrate substantial differences in
-
Indired photochemical excitation of TI via SI.
Some examples of singlet and triplet parameters are listed in the table. It can he seen that a wide range of values exists for the energies, triplet yields, and triplet decay constants. Singlets and Triplets of Ketones
As an example of the differences in Sl and TI which may exist for a molecule, consider formaldehyde (12). An analysis of the vibrational structure of formaldehyde absorption and emission spectra allows conclusions to he made concerning the properties of S1and TI. Below are listed some of these properties which are compared to those of SO.
So, stable
planar
rco = 1.21 & . = 2.5 D E =0 p.
SL TI pyrimidal, -25' out pyrimidal, -35' out of plsne . of plane r,. = 1.31 A T,, = 1.32 A p,o = 1.5 D p. a 1.5 D El 83 kcdlmol6 E8 72 kcal/mole
--
N
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; Figure 6.
Pictorial description of the
SI ond TI
strrter of helium.
c;-g
6 +6
xD --. ,c-9
Volume 46, Number
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I, Januory 1969 / 5
Excited State Parameters for Some Organic Molecules Molaoule
Ex'
En'
T
kid
ka'
. ;Energy of l o w e t vibratiqnal level in kcal/mole. FIu0re8oenoe y~eldam flu~dsolution at 25'C. 'Triplet yields. d F I ~ ~ r e s c e ndecay ~ e constants (XI09 iin aeo-I. 'Triplet deohy oonstant. in fluid ~olutionat 2S°C.
These descriptions make certain stereoelectronic predictions concerning the reactivity of the n,a* state. Unfortunately, this model does not predict differences which should result from spin differences. Evidence exists, however, that SI and TI may have different reactivities toward the same reaction, even though both are n,s*. For example, acetone singlets are much less reactive toward hydrogen abstraction from tri-n-hutyl stannane than acetone triplets (IS).
The nature of triplets may be probed by emission 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). Literature Cited
(1) (a) TURRO,N. J., "Molecular Photochemistry," W. A. J.. Beniamin Co.. New York. N. Y.. 1965: CALVERT. . ~ N D . P I J.'N., ~, JR., "~hotochemistry,'" John whey; New York, N. Y., 1966. (b) REID, C., "Excited States in Chemistry and Biology," Butterworth, London, 1957. (c) EI~SAYED, M. A,, Accounts qf Chemical Research, 1 , 8
,-"".,. 110fi7\
(d) LOWER,S. K., AND EI~SAYED, M. A,, Chem. Rev., 66,199 (1966). (e) WAGNER, P. J., AND HAMMOND, G. S. in "Advances in Photochemistry," (Editors: NOYES,W. A,, JR., HAMMOND, G. S., AND PITTS,J. N., JR.), Vo1. 5, Interscience (division of John Wiley & Sons, Inc.) New York, 1968, p. r)l
(f)PORTER,G., Proc. Chem. Soe., 291 (1959). (g) LEWIS,G. N., AND KASHA,M., J. Am. Chem. Soc., 66,
- I@+ (CH~)~COH + fnBuh SnH k - 10" + ( ~ B USnH ) ~ -+ (CH~)~COH k
(CHakCOa (CHz)&O'
Whether a different reactivity between 81and TI of the same configuration will be general cannot be answered now, but will probably be the subject of much future work. Summary
The "three state" character of triplets is not of significance to the chemistry of these species. However, conservation of spin may inhibit certain chemical reactions which require a "spin flip" in going from reactants to products. Also, the inherent improbability of a spin flip from a triplet to form a singlet, enhances the lifetime of the former and thereby increases the probability that it will survive long enough (relative to excited singlets) to undergo a chemical reaction. Although the inherent character of triplets is such that the two spin-unpaired electrons tend to "avoid" each other, triplets are not necessarily biradicals in the sense of two chemically independent odd electron centers.
6 / Journal o f Chemical Educafion
2100 (1944). (h) XASHA,M., Chem. Rev., 41, 401 (1948). G., Photo(i) MCGLYNN, S. P., SMITH,F. J., A N D CILENTO, ehem. -Phatobio.., 3 ~ . 269 ~. , 11964). ~ -.--, ( j ) THOMPSON, C., Quart. Rev., 22, 45 (1968). (k) MCGLYNN,8. P., KINOSHITA,M., A N D ALUMI, T., "Molecular Spectroscopy of the Triplet State," PrenticeHall, Inc., Englewood, New Jersey, 1968. 3. D., AND PETTIT, R., J. Am. WATTS, L., FITZPATRICK, Chem. Soc., 88, 623 (1966). D o w ~P., , J . Am. Chem. Soe., 88, 2587 (1966). KIRMSE,W., "Carbene Chemistry," Academic Press, New York., 1964. - HUTCHINSON, C. A,, JR., AND MAGNUM, B. W., J. Chem. Phys., 32, 1261 (1960). M., AND KASHA, M., J . Chem. Phya., LEWIS,G. N., CALVIN, 17, 804 (1949). DEKE, R. H., AND WITTKE,J. P., "Introduction to Quantum Mechanics." Addison-Wesley, .. Readine. -. Mass.. 1960. p. 318. Review: TURRO,N. J., DALTON, 3. C., AND WEISS,D. S., Org. Photochem., 2, in press. R., J. Am. Chem. Soc., 85, 4045 (1963). SRINIYASAN, G. S., TURRO,N. J., AND FISCHER,A,, J . Am. HAMMOND, Chem. Soc., 83, 4674 (1961). Review: TURRO,N. J., Chem. Eng. News, 45, 84 (1967). D. G., Adu. Phgs. Org. BRAND, 3. D. C., AND WILLIAMSON, Chem., 1, 365 (1963). WAGNER,^. J., J . Am. Chem. Soc., 89, 2503 (1967). ~
(2) (3) (4)
(8) (9) (10) (11) (12) (13)
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