All posts by Raymond Firestone



The Fulminic Acid-Acetylene Cycloaddition is Not Concerted

Raymond A. Firestone
330 W 72 St., Apt 10A, New York, NY 10023

Revised November 1, 2017


Recently two important papers appeared from separate groups, both calculating by B3LYP/6-31G the reaction coordinate (RC) for the title reaction. Both concluded that concert obtains, although the formation of the first (C-C) bond was completed before the second bond (C-O) even began to form. The molecule after the first but before the second bond could only be a diradical. Why then concert? Because, said group 2, the interbond interval was so short, ~13 fs. The present manuscript rebuts concert on these grounds: (1) diradicals like this have often (≥45x) been intercepted, proving their independent existence; (2) there is no experimental evidence that the 13 fs interval is correct; (3) concert fails to explain why acetylenic dipolarophiles are not more reactive than ethylenic ones; (4) the Born-Oppenheimer principle says that electronic motion is immensely faster than nuclear motion, and that therefore no Woodward-Hoffmann transition state (TS) can exist on this RC; (5) in thermal reactions, RRKM requires activated molecules to undergo intramolecular vibrational redistribution (IVR) before bonding changes can occur, which takes ~500 – 1000 fs; (6) experimental measurement of bond formation times are 3 ns (Au-Au); in SN2 and carbonyl additions (C-C), ≥10 ns; even with photochemical activation (C-C), ~20 ps. All these facts are incompatible with concert, and fit diradicals.


The concerted mechanism for the Diels-Alder reaction (DA) has held sway since 1935.1 28 years later, Huisgen recognized 1,3-dipolar cycloadditions (1,3-DC) as a new class of reactions that appear to proceed in the same way, i.e.,  concerted.2 In 1937, Littman suggested on experimental grounds that the diradical mechanism might be a better one for the DA,3 and he has had several followers: Kistiakowsky,4  Walling5 and Firestone6 among others. In this mechanism, the rate-determining first step forms the diradical, whose energy is close to the Ea for this step. The second step, formation of the second bond by combination of the two radical centers, has an extremely low barrier.

The advent of the Woodward-Hoffmann Rules in 19657 seemed to end the discussion, for a symmetry-allowed concerted cycloaddition must be much faster than a stepwise one since the rate-determining step for concert has two more bonding electrons than that for diradicals, and also because a concerted transition state (TS) for either DA or 1,3-DC possesses some aromatic stabilization lacking in the stepwise path’s first TS.8 Moreover, the Woodward-Hoffmann Rules may allow but never demand concert.

The two bonding electrons present in the concerted TS but absent in the diradical provide ~80 Kcal/mol extra stabilization for concert, reduced to ~40 – 50 after adjustment for radical stabilization energies.8 This gives rise to an enormous factor, about 1030 in rate, that conclusively ensures that any given cycloaddition must be either concerted or stepwise, but never both mechanisms side by side.

The difference between the observed Ea and that for diradicals, subsequently named as energy of concert (Econ), tells us what that correct mechanism is. If Econ is large, it is concerted; if small, stepwise. Huisgen calculated from experimental data that Econ must be 37 – 58 Kcal/mol,9 and Firestone estimated, also from experimental data, ~43 Kcal/mol. So, the two opposite camps agree on this point.

Econs ranging from 12 to 30 Kcal/mol have also been derived from quantum mechanical calculations (QMC), e.g., 12.4,10,11 but these are suspect because they vary so widely, and because calculations unsupported by experiment are hypotheses, not facts. Although Econ is derived from one experimental number and another that is perforce only estimated, it is surprisingly easy to determine it precisely.8

There are now 45 experimentally verified—by direct physical interception—examples of DA and 1,3-DC that are unquestionably stepwise-diradical, and 43 more whose Econs are much too small for concert.8 These are 88 out of thousands of examples, the rest of which might or might not be concerted. There is no DA or 1,3-DC in the literature where experiment proves concert.

To be sure, proving concert experimentally is no simple matter, requiring mass balances of well over 99%. How high must they be? The most precise in the literature12 are 99.997% and 99.4%, but even these give rise to minimum Econs of only 3.5 and 1.7 Kcal/mol.8 Concert is still possible here, for no loss in stereospecificity could be detected, but it is certainly not proven.


In the past decade, two major research groups have analyzed reaction (1) by quantum mechanical calculations (QMC) using the B3LYP/6–31G method. Both pronounced this particular (hypothetical) 1,3-DC to be concerted:
   HC=N=O + acetylene —> isoxazole   (1)
However, perusal of their data reveals that in both studies the C–C and C–O bonds are calculated to form sequentially, not simultaneously. That means that they cannot be concerted. In the first,13 the new C-C bond forms to completion before the C–O bond even begins to form. The only possible structure for the interim species is a diradical.

The second paper,14 however, depicts the same scenario—stepwise—but declares it a concerted cycloaddition because the time gap between formation of the two new bonds in reaction (1) is calculated to be only 13 – 15 fs, i.e., less than one vibration-time. Other cycloadditions within a group of 18 related cases had calculated time gaps ranging from 0 to 15 fs. A subsequent paper described a similar scenario for DA.15,16

Could this14 apply to all 1,3-DCs and DAs? No, because in most of the cited 88 examples8 a diradical was intercepted in some way: rotation within the dienophile (15 examples), intramolecular H transfer (26 examples), loss of a small molecule (3 examples), capture by a free-radical trap (1 example), or consequences of singlet-triplet interconversion by means of a nearby heavy atom (17 examples). The total here is 62, but only 45 count as interceptions because the many heavy atom interceptions are already counted elsewhere. There is an 18th highly probable example.18

Interception proves the independent existence of diradicals for long enough—much longer than 15 fs—to be diverted to another pathway. Other examples exist in which concert is impossible because Econ is too small, or zero, sometimes even less than zero which makes concert absurd.8 Therefore, the scenario in reference 14 cannot be true in these 88 cases.14 It is also weak because this QM method “has systematic errors for hetero systems”.18 A striking new case of Econ <0 is a group of DAs where [2+2] cycloadducts are the sole product at room temperature, and [2+4] products only appear >90°.19

Another drawback in the fs argument is that it has no experimental support. No one has actually measured the time lapse between bonds 1 and 2. Without that it’s a hypothesis and no more. However, in some other reactions people have experimentally determined the time to form bonds, which turns out to be much longer than 13 – 15 fs (v.i.).

Furthermore, even the hypothesis is on shaky ground. References 13 and 14 are not the last word in these calculations.13,14 A third group of theoreticians, using the same method, reached the opposite conclusion, i.e., that these cycloadditions are stepwise-diradical.20 This makes it even more imperative to settle the question with hard facts.8

Acetylenic Dipolarophiles. In reaction (1) the authors recognized a problem in that the calculated Eas were the same for both ethylenic and acetylenic dipolarophiles.14 There was no kinetic advantage for acetylenes, a paradox because the cost of opening a triple bond is much less than that of a double bond. Furthermore, there was no kinetic advantage when the cycloadduct was aromatic.21 Parallel results were reported for cycloaddition of hydrazoic acid to ethylene and acetylene, and formaldimine and HCN.22 This problem was also remarked elsewhere,23 for it had been experimentally observed >50 years ago.

This conflicts with concert,6,24 for it would be easier by ~10 Kcal/mol to break an acetylenic than an ethylenic pi-bond. In addition, when the cycloadduct is aromatic, it should have a further ~10 Kcal/mol lowering of the Ea for concert, where there is only a single TS whose properties are derived from both the reactants and the product.

If concert obtained, and we assumed that only half of each of the two 10 Kcal/mol advantages for the acetylene is present in the Ea, acetylenes should be >10,000,000x more reactive than olefins. But they are not. Half of each advantage is reasonable since the TS in one typical 1,3-DC is about halfway down the RC.18,25

Why does this problem not apply to diradicals? Because here there are two sequential TSs, the first rate-determining. At this TS (virtually identical with the diradical), the entire acetylenic pi-bond is consumed, favoring it over an ethylene by the full 10 Kcal/mol. However, this diradical contains a vinylic radical that has 10 Kcal/mol more strain energy than a saturated one. So, they cancel exactly.24 As for aromaticity, it plays no role here because its inception is delayed to the second TS, after the rate-determining first TS. So, on the diradical pathway double—and triple—bonded dipolarophiles should both react at similar rates, aromatic or not, which they do.

Clearly, the acetylene-ethylene question in 1,3-DCs contradicts concert. This question, first discussed in 1968,6 is also recognized in reference 21, but without explanation.21

Sequence of Bond Formation. Now consider the species that exists immediately after completion of the first bond but before inception of the second bond according to reference 14.14

The first bond has a normal length, but the gap between the C and the O not yet joined together must be longer than a normal bond; otherwise it would already be the second bond. The as-yet-nonexistent second bond cannot be conflated with the C-O bond in the product because the Born-Oppenheimer approximation26 teaches that the lightweight electrons, whose mass is 1/29440 that of an O nucleus and 1/23920 of a CH unit, move so much faster than O atoms or CH units that they assume new equilibrium positions essentially instantaneously at every new point in space traversed by the heavier atoms as they move, relatively slowly, to their new bonding positions. The electrons follow, and cannot precede, the heavy atoms. At this instant—this very fs—the molecule is a diradical. The electrons cannot move into position for bond 2 during formation of bond 1, because the heavy atoms aren’t there yet,26 so there must be two successive TSs. At no time is there an aromatic Woodward-Hoffmann TS, and concert is ruled out. The time interval between formation of bonds 1 and 2 must be long enough to permit interception of the diradical (v.s.).

Time Required for Bond Formation. How long does it take to form the second bond? In 1922 Lindemann pointed out that since collisions are the means for energizing molecules to cross the activation barrier in either direction, bond formation or cleavage cannot occur within a time as short as a single vibration (1013/sec), for if it did, collisions (1010/sec) would be rate-determining, which would make all such reactions second order, not first.27 But first order reactions do occur. This is known as the Uni-molecular Anomaly. Collisions reversibly activate molecules to high vibrational states, and these are what go ahead to the product, but it takes a lot longer than 10-13 sec (100 fs). Reaction times of 13 – 15 fs would abolish uni-molecular kinetics.

Lindemann’s insight strongly influenced the evolution of chemical kinetics, and modern RRKM theory28 holds that intramolecular vibrational energy redistribution (IVR) in molecules whose energy is ~ Ea is always completed before further changes in bonding can occur (ergodic behavior). IVR is normally ~0.5 – 1 ps,29 i.e., 500 – 1000 fs, so bond formation must take longer than this. Large molecules (>3 – 4 atoms) obey RRKM,30,31 i.e., long reaction times relative to IVR. Thus, reaction times as short as 13 fs cannot be correct.

Nonergodic behavior—reaction times faster than IVR—is indeed seen,29 but only under special conditions: a very weak breaking bond (e.g., Van der Waals dimers), or pressures >100 atm, 31 or with ultrashort activation pulses to energies far above Ea.29 None of these conditions applies to reaction (1). Normally it is collisions, not , that elevate reactants to energies ~ Ea, but never far above Ea.

Time Delay in Unimolecular Reactions. Consider an intramolecular 1,3-DC in detail. The reactant is vibrationally activated by collision. If subsequent events occurred in a few fs, the overall transformation would be second order: first order in both reactant and solvent. Unimolecular kinetics can exist only if the first vibrationally activated reactants live long enough for most of them to be deactivated by another collision while a few other activated molecules eventually go on to product. That’s tens of ps, not fs.

Time Delay in Bimolecular Reactions. I chose an intramolecular 1,3-DC to begin discussion of time delay in order to utilize the Unimolecular Anomaly. Many examples now exist of bimolecular reactions, where energetic but very short interaction times where the reactants fly apart, proceed at very low rates. Second order reactions are not bound by the Anomaly, but it is likely that they also involve collisional activation, followed by reaction of vibrationally activated molecules. Some examples:

In 1968 Bauer reported the pericyclic reaction (2)
   H2 + ND <—> HD + ND2H   (2)  
at 700°C in a shock tube.32 As with unimolecular reactions, the exchange does not take place directly via translational energy (ET) even though there’s enough ET to surmount the barrier, for the kinetic expression is first order in ND3 and in Ar, but zero order in H2. Clearly, ND3 is vibrationally activated by collision with Ar, and then reacts with cold H2. Bauer and his associates reported many similar examples. Similarly, high ET was unable to induce reaction between vibrationally cold HI + DI, but if one partner had high EV reaction took place.33

D + H2 reaction slows down as ET rises above Ea because the collision time becomes too short.34 Similarly, with Li + HF (EV = 0) in crossed beams, the rate rises sharply as ET goes down.35

In all these cases, short reaction times are less productive than long ones. Fs reaction times are much too short. Nowadays there are many more examples.

Experimental Measurement of Bond Formation Times. A recent publication describes the measurement of the time it takes to form a single Au-Au bond between two Au(CN)2 moieties. It takes 3 ns, i.e., 3×106 fs.36 Gold is not a special case, for similar times are also typical with small organic molecules.

When bond formation in a simple SN2 occurs with excess vibrational energy (EV), bonds form faster than IVR (non-RRKM). Even then, however, reaction times are ~20 ps37 or tens of ps,38 about a thousand times longer than 13 fs. In other SN2 and carbonyl additions where RRKM is obeyed and IVR is complete, reaction times are ≥10 ns.37

A bond-breaking reaction, cyclohexadiene —> 1,3,5-hexatriene, was initiated by 267 nm irradiation and tracked by X-ray scatter, finding an 80 fs bond-breaking time. The huge excess of energy instantaneously absorbed ensured nonergodic behavior, so had purely thermal activation been used, the reaction time would have surely been longer than IVR, i.e., >>80 fs.39

The diradical formed thermally from fulminic acid + acetylene has no excess EV and therefore cannot proceed to cycloadduct faster than IVR (~0.5 – 1 ps). Furthermore, it is not necessarily formed in a perfect conformation to make the second bond. It must first alter atomic positions which also takes time. We know that spin-paired diradicals often last long enough to rotate, even as much as 180°, before forming the second bond.8 Therefore, formation of a second covalent bond cannot occur in only 13 fs.


Two quantum chemistry groups have calculated the mechanism of fulminic acid-acetylene cycloaddition, proposing concert although their own data show a stepwise mechanism with a short-lived diradical intermediate. A third group takes the opposite position, casting doubt on all QM conclusions. However, group 2 espouses concert because of the very short (13 – 15 fs) lifetime of the diradical, a calculated but not experimentally supported time interval.

But a diradical is still a diradical regardless of its life-time. The Born-Oppenheimer Principle holds that electrons move so much faster than atoms that formation of each of the two new bonds is an independent event.

The concerted hypothesis is also disproved by numerous experiments showing that the intermediate diradicals can be intercepted, and therefore must exist independently, as well as others where Econ is too low to permit concert. In science, experiment not theory is paramount.

Furthermore, the calculated 13 – 15 fs delay is much too short to comply with the Lindemann principle and RRKM, and several experimental measurements of bonding times range from thousands to millions of fs.

Finally, one may ask why molecules in symmetry-allowed cycloadditions follow the higher-Ea diradical pathway. The simplest answer is that something else not yet recognized prevents concert. Discovery of the orbital symmetry rules—which in no way are opposed in this paper—does not mean that there are no other sets of rules. More on this anon.

Corresponding Author

RC, Reaction Coordinate; DC, Dipolar Cycloadditions; DA, Di-els-Alder; RRKM, Rice-Ramsburger-Kappel-Marcus.


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(10) Wilsey, S.; Houk, K. N.; Zewail, A. H.  J. Am. Chem. Soc. 1999, 121, 5772. This group also said that the “stepwise mechanism is much higher in E<sub>a</sub>”.<sup>11</sup>
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(16) For the simplest possible DA, similar QM calculations found the same diradical arising from three different reactants (ethylene + butadiene, vinyl cyclobutene, and cyclohexene, all with the same energy). This is a clear-cut diradical mechanism with no fs implications of concert.17
(17) Northrop, B. H.; Houk, K. N. J. Org. Chem. 2006, 71, 3.
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(25) It’s not so obvious why half of the aromatic resonance energy exists at the TS. Since pi bonds have sideways overlap of the orbitals while sigma bonds overlap end-to-end, it seems logical that bond strength should fall off faster in pi bonds than sigma bonds as they are stretched in the TS. I put this question to Dr. Ming-Hong Hao at Boehringer Ingelheim, who found that as a C=C bond is stretched, both the pi and sigma bonds fall away at the same rate, expiring at 3.15 Å. He used DFY/B3LYP with 6-31**++ basis set. Orbital energies were analyzed using natural bond order package in the Jaguar program. The following data also show preservation of the pi-bond at large distance [Schmid, M. W.; Truong, P. N.; Gordon, M. S. J. Am. Chem. Soc. 1987, 109, 5217]:

Compound     Pi bond length    Å Pi bond energy, Kcal/mol]
CH2=CH2             1.34                    65.4
CH2=SiH2            1.70                     35.6
SiH2=SiH2            2.16                    22.7

Despite gradual weakening of bonds to Si going down the last column, 35% of the pi bond strength remains after stretching from 1.34 to 2.16 Å, which is the approximate gap between bond-forming atoms in pericyclic TSs.
(26) Born, M.; Oppenheimer, J. R. Ann. Der. Physik. 1927, 389, 457. The separation of electronic and nuclear motion holds even with the lightest nuclei, H + H2; Fleming, D. G. et al. Science 2011, 331, 448.
(27) Lindemann, F. A. Trans. Faraday Soc. 1922, 17, 598.
(28) Marcus, R. A. J. Chem. Phys. 1952, 20, 359.
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(38) Li, C.; Ross, P.; Szulejko, J. E.; McMahon, T. B. J. Am. Chem. Soc. 1996, 118, 9360.
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During a magnificent recent performance of Tschaikowsky’s opera “Eugene Onegin,” I suddenly realized that Lensky’s challenge to Onegin, ostensibly to get satisfaction for Onegin’s insulting behavior, has an entirely different motive. His idealized picture of his fiancéE Olga has been shattered by her behavior with Onegin on the dance floor. Whirling around with Onegin, she seems to revel in the distress she is causing Lensky, and the poet’s long-revered picture of her as his perfect, eternal love is destroyed. This he is unable to bear, and what he now desires is not satisfaction, but death at Onegin’s hands.
This is made clear during the duel. When the dueling-master says “Fire”, Onegin raises his weapon as quickly as he could, but Lensky is unnaturally slow in raising his, as though he had no desire to shoot Onegin, but instead awaited his own death. This behavior was not an invention of the opera’s director, for it is just as Pushkin wrote in his great poetic novel. So actually Lensky provokes the duel as a means of committing suicide.
There are many other instances in literature and drama of suicide by proxy. Suicide is forbidden by all religions and is also condemned as cowardly. One desiring death might not even consciously know that he is deliberately provoking someone else to kill him. But this is clear in Lensky’s case, and also in the following examples.
In Benjamin Britten’s opera “Billy Budd,” Billy is an impressed seaman who is sunny in disposition, handsome, happy with his shipmates and beloved by them all. In contrast, Claggart, the first mate, is ugly in his mien and his heart. He is envious of Billy’s goodness and popularity, and undoubtedly in love with him as well. His homosexual feelings are intolerable to one with his background, and he hates himself for that. Therefore, he commits suicide by provoking Billy mercilessly until Billy, good man though he is, finally loses control and kills Claggart. In this way Claggart not only ends his own life by another’s hand, but also gets revenge on Billy (who, of course, is hung for his crime) for existing.
A similar situation is found in the play “Streamers” by David Rabe. It takes place in an Army barracks in peacetime. The protagonists are a young recruit who comes from a small redneck town and a big-bodied, big-personality, happy black man from a city slum, a former gang member now gone straight.
The captain of the platoon is openly gay, and often invites one or another of the men to join him in bed. The men we see do not participate, although they all seem to be at ease with the captain, accepting him as he is. Trouble arises when the captain offers something to the black guy to accede to his wish even though he is straight. “What the hell, why not?” says the good-natured soldier. Nobody seems to mind except the small-town recruit, who becomes angry and tries to prevent them. Others try to cool him down, but fail. He verbally attacks the black soldier, who brushes him off. This increases the young man’s anger and he begins to physically attack the black man, who is hard to provoke but eventually fights back. The young man snatches a razor for a weapon, but then throws it away and pummels the big guy verbally and physically, eventually making him angry. As the fighting intensifies, the defender finally pulls out a knife and cuts the other on the palm of his hand. I took this as a gangland gesture of warning, an attempt to cool things before something serious happens. But this only goads the attacker to a frenzy of blows, and finally the defender stabs his attacker to death.
The question that arises is why the young recruit is so offended by the tryst arranged by two other men, given that it is none of his business? My answer is that the small-town boy suddenly realizes for the first time that he personally is gay having discovered, against his will, that he desires the captain for himself. He attacks the black man, not because he wants to replace him with the captain, which he could never do, but because his lifelong hatred of gays is turned against himself, and he can tolerate life no longer. That he wants to die and not win the fight is what impels him to throw away his own weapon even before the battle is joined.
“In the Valley of Elah,” written and directed by Paul Haggis, is a motion picture drawn from a real-life event. It received little attention, but is a riveting movie about war and guilt that provides a deeper understanding about what war veterans have to live with when they return home with horrible memories. Three buddies from the same town, who served together in Iraq, come home. They hang out together, carouse a lot and have difficulty adjusting to civilian life. Their parents and friends are unhappy, but say that they just need time to return to normal. Then one of them disappears. After days (or weeks) his body is found in a junk-strewn lot, partially eaten away by wild dogs. No one can tell how he got there.
One day in Iraq, this soldier had been at the wheel of a jeep in very dangerous territory. A young boy appeared in their path. His buddies insisted that he drive on at full speed, ignoring the boy who was surely a decoy intended to make them stop in an ambush, a tactic often used by the enemy. He did this, killing the boy, but then he could not drive on. He stopped, got out of the car and went over to the body for a few minutes before continuing to drive. There was no ambush. This incident haunted him constantly.
Slowly it emerges that this guy, one evening, started a fight with his comrades. It lasted hours. He became more and more enraged until finally one of them killed him, leaving his body where it was eventually found. Soon after, the buddy who killed him hangs himself.
This tragedy clearly emerges from the huge guilt that consumes the ex-soldier, becoming more and more unbearable until he commits suicide by inciting his buddy to kill him in an act of mercy. Then the buddy can take no more, and takes his own life.
In the play “Red Dog Howls” by Alexander Dinelaris, a young man living in the U.S. meets his old grandmother. She is a survivor of the Armenian holocaust who now lives comfortably in a beautiful, well-furnished apartment. She befriends him, inviting him to visit frequently for good food and company. She has one treasured object from the past, an embroidered pillow that somehow was not lost with everything else.
Although her behavior is in no way suspicious, it slowly dawns on him that the reason she has cultivated him is to induce him to kill her with this pillow. Apparently, her memories are more than she can bear, and death at her beloved grandson’s hands with the precious pillow is an attractive way to end her life. When he eventually realizes what she wants of him, he does it.
Among holocaust survivors, suicide many years later is not rare. One can speculate that they had memories of unforgettable horrors that could not be expunged, or even that some of them had done something shameful in a desperate urge to stay alive, such as stealing some food from a buddy, or blaming another for something they had done. Surely such things did happen.
In Thomas Mann’s great novel “The Magic Mountain,” the hard-souled Jesuit, Nafta, provokes a duel with Settembrini, the pure humanist. His motive is not clear since he has no quarrel with Settembrini other than their friendly, long-lasting debate about philosophy. At the duel, as soon as firing is allowed, Settembrini points his pistol straight upward and fires. Nafta is now free to kill Settembrini at will, but instead he goes into a rage and shoots himself in the head. One can but speculate on Nafta’s motive, but I have the feeling that, over their months of friendship and discussion, Nafta had felt morally bested by Settembrini and wanted to be killed by him because life was no longer worth living, and also to get revenge on him, since he would surely be accused of murder. When Settembrini refuses to kill him even at risk of his own life, Nafta has to do it himself.
An obvious example of suicide by proxy is Tristan in Wagner’s opera, “Tristan und Isolde.” When the protagonists’ tryst is discovered by the others, including his patron King Marke, Tristan is convinced that everything he lives for — Isolde — is lost to him forever. He sees death in Melot’s sword and, therefore, welcomes his attack, which mortally wounds Tristan. Back at home, it appears that he might recover, so upon Isolde’s entrance he makes sure his wound will be lethal by tearing off his bandages. Isolde also wants to die, but needs no help. All she has to do is sing the Liebestod.
One might cavil at some of the interpretations above, but not at the concept of death by proxy, for this occurs — probably more often than recorded — in real life. An article in Journal of Police Crisis Negotiations 9[2], 105-118, June 2009, by Brian F. Kingshott, entitled “Suicide by Proxy: Revisiting the Problem of Suicide by Cop” discusses suicide in which a police officer is deliberately provoked by the protagonist to use deadly force. In view of the high rate of suicide in the world, ~1 million/year, this cannot be a rare event.