First and Second Amendment

First Amendment

In offering these considerations as

My theory of the stability of the molecule assumes that the quantum jump or ’lift’ changes the configuration of the same atoms.

An isomeric molecule is a molecule composed of the same atoms in a different arrangement.

In biology:

• this is a different ‘allele’ in the same ’locus’
• the quantum jump is a mutation

We should not imagine that:

• only in its very lowest state does our group of atoms form a molecule.
• the next higher state is ‘something else’.

Actually, the lowest level is followed by a crowded series of levels which do not involve any appreciable change in the configuration as a whole, but only correspond to those small vibrations among the atoms which we have mentioned above.

They, too, are ‘quantized’, but with comparatively small steps from one level to the next. Hence the impacts of the particles of the ‘heat bath’ may suffice to set them up already at fairly low temperature. If the molecule is an extended structure, you may conceive these vibrations as high-frequency sound waves, crossing the mole- cule without doing it any harm.

Fig. I I. The two isomers of propyl-alcohol.

So the first amendment is not very serious: we have to disregard the ‘vibrational fine-structure’ of the level scheme.

The term ’next higher level’ has to be understood as meaning the next level that corresponds to a relevant change of configuration.

The second amendment is far more difficult to explain, because it is concerned with certain vital, but rather compli- cated, features of the scheme of relevantly different levels.

The free passage between two of them may be obstructed, quite apart from the required energy supply; in fact, it may be obstructed even from the higher to the lower state. Let us start from the empirical facts. I t is known to the chemist that the same group of atoms can unite in more than one way to form a molecule.

Such molecules are called isomeric (‘consisting of the same parts’; laOe; == same, Jl£pOe; == part). Isomerism is not an exception, it is the rule. The larger

Fig. 12. Energy threshold (3) between the isomeric levels (I) and (2).

The arrows indicate the minimum energies required for transition. the molecule, the more isomeric alternatives are offered. Fig. I I shows one of the simplest cases, the two kinds of propyl- alcohol, both consisting of 3 carbons (C), 8 hydrogens (H), I oxygen (0). I The latter can be interposed between any hydrogen and its carbon, but only the two cases shown in our figure are different substances. And they really are.

All their physical and chemical constants are distinctly different. Also their energies are differen t, they represen t ‘different levels’ . The remarkable fact is that both molecules are perfectly stable, both behave as though they were ’lowest states’. There are no spontaneous transitions from either state towards the other.

The reason is that the 2 configurations are not neighbouring configurations.

The transition from one to the other can only take place over intermediate configurations which have a greater energy than either of them.

To put it crudely, the oxygen has to be extracted from one position and has to be inserted into the other. There does not seem to be a way of doing that without passing through configurations of con- siderably higher energy.

The state of affairs is sometimes I Models, in which C, Hand 0 were represented by black, white and red wooden balls respectively, were exhibited at the lecture. I have not reproduced them here, because their likeness to the actual molecules is not appreciably greater than that of Fig. I I. figuratively pictured as in Fig. 12, in which 1 and 2 represent the two isomers, 3 the ’threshold’ between them, and the two arrows indicate the ’lifts’, that is to say, the energy supplies required to produce the transition from state 1 to state 2 or from state 2 to state I, respectively.

We can give our ‘second amendment’, which is that transitions of this ‘isomeric’ kind are the only ones in which we shall be interested in our biological application.

It was these we had in mind when explaining ‘stability’ on pp. 4g-51 . The ‘quantum jump’ which we mean is the transition from one relatively stable molecular configuration to another. The energy supply required for the transition (the quantity denoted by HI) is not the actual level difference, but the step from the initial level up to the threshold (see the arrows in Fig.12).

Transitions with no threshold interposed between the initial and the final state are entirely uninteresting, and that not only in our biological application.

They have actually nothing to contribute to the chemical stability of the molecule. Why? They have no lasting effect, they remain unnoticed. For, when they occur, they are almost immediately followed by a relapse into the initial state, since nothing prevents their return.