The following complete article may be found under :
Del Re, Guiseppe : Ontological Status of Molecular Structure,
HYLE, 4, 81-103 (1998).
Ontological Status of Molecular Structure
Giuseppe Del Re
Cattedra di Chimica teorica, Università di Napoli «Federico II»,
Via Mezzocannone 4, I-80134 Naples, Italy; G.Delre@agora.stm.it
Abstract: Molecular structure (MS) has been treated as a convention or an
epiphenomenon by physicists and quantum chemists interpreting the
mathematicai formalism of quantum mechanics as the essential reality
criterion in
the submicroscopic world (R2 world). This paper argues that,
(a) even in the
R2 world there is a class of entities which are real per se even though they cannot be separated from their material support, and MS may belong to that class;
(b) MS actualizes a particular molecule from the many potentialities of a given
set of nuclei and electrons, all present in the same Schrödinger equation;
(c)
MS is a fact established in the XIXth century, albeit as a result of
circumstantial evidence (because of its belonging to the R2 world);
(d) the fact that MS is
known, as all objects of the atomic world, in terms of analogies with
macroscopic models, is not valid grounds for questioning its reality;
(e) MS is a set
of topological as well as geometrical relations. All along the discussion,
observability according to Bohr, Heisenberg, Feynman is taken as the essential
criterion of reality in the R2 world. On its basis, quantum mechanics is by no
means in conflict with the reality of molecular structure and shape. On the
other hand, the question of the minimum lifetime required for a MS proper to
exist should be left open, pending a detailed analysis of measurement
techniques.
Keywords : ontology, molecular structure, quantum mechanics, analogy,
observability.
Introduction
Tradition has it that Paul Dirac, after casting quantum mechanics into his well
known formalism, echoed Shakespeare by saying: «the rest is chemistry.» He
apparently thought that chemistry is only a sort of scientific cuisine. Also
Werner Heisenberg, though a man of great culture, was mistaken about the
program and field of inquiry of chemistry, for he suggested that chemistry
had merged with physics into quantum mechanics by bringing the atom to
the latter;1 the mistake being, of course, that if chemistry has
anything to do
with atoms, it is because they are the building blocks of molecuLes.
Other founding fathers of quantum mechanics certainly knew better: in
particular, Born and Oppenheimer considered it extremely important for the
validation of the new-born quantum mechanics that it should be proven that,
despite the uncertainty principle, the new theory was perfectly compatible
with the empirically founded notion of chemical structure. Also the work of
Heitler, Hückel, Slater, Pauling, Hund, and others was aimed at finding out if
quantum mechanics could account for the known building rules of molecules
and possibly extend their scope. This was done by introducing special, ad hoc
assumptions into a quantum mechanical perturbational
treatment.3
However, curiously enough, in later years the belief spread, especially
among chemists, that, in the world of atoms and molecules, real is what is
explicitly contained in the equations of quantum mechanics. It is not
surprising, therefore, that ideas (probably inspired by theories
of atomic nuclei) according to which the chemical bond is a convention,
and molecular structure
is merely a property of chemical formulas were received with indifference: the
great battle against such conventionalists as the great chemists Ian Berzelius
and Wilhelm Ostwald seemed to have been won in vain.
Yet, after almost a century of hard work and debates, by about 1900 the
organic chemists had reached the conclusion that structure is the
fundamental fact of the world of molecules; in the long run,
therefore, further progress
in our understanding of the physical world might be seriously hindered by
the existing uncertainty about the epistemological and ontological status of
molecular structure and related concepts.
This situation has prompted the reflections presented in this paper, which
is intended as a contribution towards the re-establishment of consistency
with historical facts and a critical analysis of the reasons why even the
founders of quantum mechanics considered molecular structure, bonds, valence as
ascertained properties of matter.
Our exposition will be divided into four parts.
In part A we shall consider
judgments of existence on things which cannot be isolated from their
material support (second class entities);
in part B we shall look at the status of the
latter in the picture of the physical world suggested by recent advances of
science;
in part C we shall pause on the history of molecular structure, to
show how it came to be considered a fact before quantum mechanics;
in part
D we shall see on what grounds and in what sense molecular structure is
more than ever a second class entity whose presence in molecules is a fact
which characterizes molecules as distinct from atom clusters and other
particle aggregates. The last part will demand a brief tour into the quantum
mechanical theory of time-dependent states.
Part A: Ontological status of relational
entities
A.1 Foundations
We accept the strong-realism axiom, according to which there are things,
events and processes independent of our own existence and will, and they can
be individually known by us, within limits imposed by otxr scnses and brain,
as existing and distinct from other objects.
We also accept the classical view that ordinary intuitive existence
judgments can be taken as starting points for a critical analysis, needed
anyway to
determine, as the case may be, either what precisely an existence judgment
applies to, or why it is mistaken.
As is well known, realism was challenged by philosophers since the birth
of philosophy 3. In modern science a sort of idealistic approach to
what science studies has been built on the difficulties quantum mechanics has
with
the role of the observer in experiments. Actually, there is much to say in
favor of the possibility that a careful distinction between ‘observer‘ and
‘perceiving subject‘ would remove the reality issue from the overfull
epistemological agenda of theoretical physics. However that may be,
the neopositivistic view of science was very popular for a time. However,
inconsistencies
turned out, and it would now seem that scientists prefer to believe that what
they study is reality.
A double classification of real entities is essential for our study. The
first
one is that between first class (FC) entities, 4 i.e. objects
existing per se (say, a
tree or a molecule), and second class (SC) entities (say,
the psyche of a dog or
a man), which presuppose a ‘carrier‘, even though they can be treated, within
certain limits, as if they were FC entities.5
The second distinction is between
entities directly and indirectly accessible to sensible experience — which
Schummer6, following Harré, calls R1 and R2 entities,
respectively. In this
paper, R1 is used for entities which can be perceived as such, R2 for entities
believed to exist because of analogical and logical evidence similar in nature
to
that by which a judge may condemn a man as the author of a crime.
A.2 Aspects of existence judgments
A few examples of entities on which a judgment of existence is made are
listed below to attract attention to points relevant to the chemical structure
problem. They are given in pairs: the latter member of each pair is similar to
the former but involves R2 entities.
1a: A quartz crystal AND a benzene crystal.
1b: Flour AND the chemical substance benzene.
• Example 1a compares a standard reality judgment with one still
bearing on directly perceived objects but partly based on indirect
evidence, possibly in the form of reports accepted by general
consensus.
• Example 1b is parallel to 1a, but refers to entities whose existence
no one would deny, and yet are partly abstract, for they can be
experienced as pieces with a variety of shapes and sizes, not
isolated ‘in the laboratory‘ as such.
2: A microscopic mite AND a benzene molecule.
• A molecule is a typical example of what Harré and Schummer call
R2 entities; a microscopic mite is an intermediate example, which
differs from a molecule inasmuch as it finds an immediate model
by analogy with direct experience.
3a: A computer program in general AND a computer program for the benzene
normal modes.
3b: Organization AND a benzene-producing organization.
• A computer program is an SC entity which can be ‘transferred‘
from one computer to another, and can be stored on all sorts of
material supports.
• Organization is a property of a whole which cannot be reduced to
the properties of its parts, for the behavior of each part depends
on those of the others and on the aims of the whole. The very
special nature of organization is recognized from linguistic usage,
which treats ‘an organization‘ as an entity per se.
• Both a program and an organization pattern are cases of
information, but it remains to be seen if organization is transferable,
as is
the case in general with information.
4a: A pattern in a carpet AND miscible liquid layers.
4b: A solid-state radio set AND crystal structure.
• SC entities come into existence (‘emerge‘) as a result of the
arrangement or interconnection of certain parts of a whole, but are
not the parts, even though they can be traced back to specially
situated or connected R1 or R2 entities;
• important SC entities of this type are associated to wholes whose
behavior results from special relations among many interacting
parts, ranging from tight dynamical cooperation of the parts (case
of a radio set) to persistent ordering due to weak pairwise inter-
actions (case of a crystal structure).
Part B: Levels of reality and the role of
analogies
B. 1 The nature of the physical world
The traditional expression ‘physical world‘ covers all that can be detected
directly or indirectly by our five senses. The above examples show that the
claim that the whole physical world is nothing but ‘atoms and quanta‘ is as
untenable as the claim that airplanes, tractors, cars, trains, bridges,
etc., are
but the materials of which they are made. That is to say, a given collection of
atoms and quanta — or indeed of fundamental particles — can in general form
an incredibly large number of different physical systems, each with its own
identity and specific properties.
In principle, the possible existence and properties of those systems can be
quantitatively predicted from the properties of
the constituent particles. To
that end, however, the physical conditions which correspond to existence and
the nature of the properties must be known or guessed, unless they are
simply sums of corresponding properties of the parts; moreover, the collection
of particles from which a system arises contains part of information about
that system only potentially. In other words, information about possible
wholes is partly either latent or not uniquely specified
in the constituents,
meaning by ‘latent‘ that the problem remains of knowing which global
properties are possible that are not sums of the properties of the parts,
and by ‘not
uniquely specified‘ the fact that a specific system of n given particles is
formed by selection out of many possibilities.
A chemical example of such a selection process is the sequence of
operations by which one isomer is selected out of many. For example, given six
carbon atoms and six hydrogen atoms, the rules of valency predict 217
different molecules (and hence 217 different chemical substanccs)
formed with the
same atoms (‘isomers‘). Although a much greater number of aggregates of
the same number and species of atoms can be imagined, no chemist has any
doubt that those 217 and only those 217 can be synthesizcd, the reserves
being that some of the possible molecules can be relatively unstable bccause
of steric hindrance or bond bending, and therefore they might have to be
isolated under very special conditions, say, very low temperatures; and some
isomers may be equivalent forms of the same molecule (cf. our comment on
the Kekulé structures at the end of Sect. D.4).
Starting from the 42 electrons and the 12 nuclei of benzene, the only way
to predict theoretically the possible ‘existence‘ of those
substances consists in:
(a) declaring that there is a molecule when there is a chemically stable
configuration, i.e. one corresponding to a free-energy minimum such
that its lifetime with respect to spontaneous isomerization is
sufficiently long for chemical observation;7
(b) writing down the Hamiltonian operator for the given nuclei and
electrons;
(c) trying to solve the Schrödinger equation by a numerical quantum
mechanical exploration of the whole 162-dimensional energy
hypersurface defined by the 42 electrons and 12 nuclei, with the vibrational
analysis required for entropy computations.
Such a procedure is possible in principle with a sufficiently powerful
computer, but it is conceptually similar to (and not as reliable as) an empirical
search for the isomers of benzene not guided by the laws of valency;
moreover, since the information contained in the chemical formula according to
the theory of valency also concerns chemical reactivity, further ad hoc criteria
would be necessary.
In conclusion, the criteria of existence of molecules are provided by the
building laws formulated in the theory of valency quite independently of the
fact that quantum mechanical computations lead to the same molecules if the
right input data and definitions are provided.
B.2 Two examples of complex systems
What we have seen so far seems strongly to suggest that the aporias and
limitations of physicalistic reductionism (‘the world is nothing but atoms and
quanta‘) require the adoption of a new general picture of the physical world
as a system made of (sub-) systems of different orders of size and degrees of
complexity. The subsystems in question range from tightly integrated ones to
weakly interacting ones which still have an identity of their own.
A molecule and a cell provide two concrete reference examples for our
further reflections.
a) A molecule
A molecule is a collection of electrons and nuclei, and can be described as
such. However, as seen on the case of benzene, a description at this level
leaves a large number of possibilities open, because — at variance with a plasma
or an atom cluster — the way in which the electrons and nuclei are put
together matters, and the ‘connections‘ (chemical bonds) determine the
properties of the whole. Moreover, at variance with the physicists‘ liquid-
drop model, a molecule appears to be a persistent entity, whose demolition
requires ad hoc conditions or processes.
The boom of research on molecules of the fullerene class after their
discovery in 1985 was due precisely to the fact that, thought at first to be just
amorphous clusters of carbon atoms, on closer inspection they turned out to
have properties not explicable by the liquid-drop model or by analogy with a
tiny crystal, but explicable if they had a quasi-rigid structure.
Not covered 87-98 incl.
Continued : Ontological Status of
Molecular Structure, page 99
interacts with any other particle, the ammonia molecule always behaves as a
pyramidal structure; the planar stationary states are useful mathematical
intermediates, and could be attributed a physical meaning only when time periods
far longer than the inversion period are considered, as when a microwave
photon is emitted or absorbed.26
Note that the potential energy profile for
ammonia inversion is a double well, with energy minima corresponding to the
two pyramidal configurations.
The case of the Kekulé ‘structures‘ of benzene introduced in the chemical
resonance theory should be mentioned, because confusion may arise from the
fact that there the term ‘structure‘ stands for ‘bond arrangement‘, the nuclear
frame being ignored. As such, those structures correspond to degenerate
electronic states associated to the same nuclear configuration. In that sense
they are crude approximations of structures predicted by the chemical theory
of molecular structure, which should have alternating short and long bonds.
If thus redefined, they show the real nature of the major contribution of
quantum mechanics to the theory of chemistry: the two degenerate
structures, at variance with the case of ammonia, do not correspond to energy
minima, and it is their 50—50 linear combination which does so; consequently,
out of the 217 isomers mentioned above, at least the two corresponding to a
distorted hexagon alternating (long) single and (short) double bonds are only
realized as extremes of a vibration; therefore, in accordance with the above
analysis, they cannot be treated as representations of a genuine molecule.
Even a perturbation would not normally stabilize them — at variance with the
case of ammonia —‚ because the energy required is large.
In sum, doubts about the existence of molecular structure and molecular
shape (except as regards resonance of electronic structures) seem to be due to
a misunderstanding: it is not the mathematics of quantum mechanics that
determines what exists and what does not exist in the world of FC and SC R2
entities, but their experimental observability. This point, as it seems, should
be taken as a starting point for reflections on molecules and their structure, in
full agreement with Bohr‘s Kopenhagener Geist der Quantentheorie. As to its
implications for the ontology of the world of molecules, the above discussion
is only a first exploration, which should be followed by quite a subtle and
intricate technical discussion.
D.4 Status of molccular structure and bonds
Apart from our last remark, we have reached a general conclusion which can
be summarized as follows:
Molecular structure is a static topological and geometrical order principle
which belongs to the reality of a molecule, indeed is what distinguishes a
particular molecule from all other clusters and molecules consisting of
the same
atoms. It is a "principle" in the following sense: it is a unitary SC entity to
which a variety of observable molecular properties belong; it can only be#
observed, as any other entity, through properties which depend on it;
indeed, the
latter belong to it, in the sense that, (a), they are inseparable, (b) they
vanish as
soon as the structure disappears, (c), they all change more or less dramatically
if the structure changes.
What is the status of molecular structure from the complexity viewpoint?
This question arises from the analysis of example 4b of Sect. A.2, where we
have suggested that what makes a whole a whole may range from a set of
essentially additive properties to something entirely new with respect to the
parts, having properties of its own (organization). It would seem that it has
already something in common with organization; to be sure, it is not related
to actual exchange of information, but it makes a molecule behave as a whole,
as is shown immediately by the remark that, at variance with a crystal,
cleavage of a bond yields molecuies (radicals or ions, in general)
having completely
different properties. This is the reason why it is a ‘principle‘; and the
qualification ‘static‘ used above is a concise way of telling that it does
not correspond, as the organization of a ccli (exampie b, Sect. B.2),
to an internal
activity capable of adaptation to a changing cnvironment.
This consideration completes as it were the evidence in favor of the claim
that, far from being a property of symbolic diagrams, molecular structure is a
real SC entity which cannot be reduced to ‘atoms and quanta‘. There remain,
of course, many subordinate qucstions, the most important one being the
existence of the chemical bond. To answer this question in detail it would be
necessary to retread the path foiiowed for structure; we only recall here that,
as the analogy by which structure becomes intelligible to us is that with the
stick-and-ball, or, better, spring-and-ball model of a molecule, so also a bond
as an SC entity must be defined by means of an analogy (a privileged
connection analogous to a quasi-rigid spring but, for one thing, not isoiable) to
which corrections and reservations are added.
D.5 Structures and formulas
In the work already cited, Schummer pointed out that structural formulas
may be looked at as analogical representations (which stand for molecules in
virtue of an analogy) helping chemists to keep track of the static and dynamic
properties of molecules.27
This view has its merits, for it emphasizes that the
chemists do not work with mathematical symbols, as the physicists do, but
with schematic topological and geometrical representations of molecules. It
might be misieading, however, to think that structural formulas are only a
reminder of molecular properties. Indeed, since the beginning there was great
emphasis on their faithfulness to the spatial arrangement of atoms and bonds.
Nowadays, the formula as a simplified but essentially correct representation
of a molecule in space is the tool for designing new, strange molecules
(‘supermolecules‘)28 and for understanding the role of configurations
in biochemical processes.
Apart from the great historical events (such as the discovery of the
biochemical significance of protein and DNA conformations), suffice it to
mention that in a single issue of Nature, chosen at random from a bookshelf,
we found formulas used both to represent schematically the conformations
of immunoglobulin29 and to show how certain supermolecules could be
obtained by inserting two independent cyclic molecules one into the other (as
cham rings, ‘catenanes‘).30 We add that geometry-dependent features
like
Bayer strains characterize molecules which are comparatively unstable and/or
highly reactive: eg. (in today‘s formulas) a hydrocarbon molecule represented
by a triangle on paper is more ‘strained‘ than one represented by a pentagon,
because the angles are 60° instead of 108°.
Thus, a structural formula can be interpreted as a representation of a
molecule with its structure in the same way as a drawing of a person can be
used to discuss the difference in profile between that person and another. As
said, this consideration is not in contrast with the use of chemical formulas as
‘thinking aids‘, but it should be kept in mind in order not to fall into traps
like misunderstanding the meaning and epistemological status of the Born-
Oppenheimer approximation (Sect. D. 1).
Notes
1 W. Heisenberg, Physics and Philosophy, Harpers & Bros.,
New York 1958.
2 See Sect. D.1 for references.
3 The literature on this point is next to infinite;
suffice it to recall two books which
we consider representative of the situation of ontology today:
W.O. Quine, From
a logical point of view‘, Harvard Univ. Press, Harvard/Mass 1953, 1961; H.
Putnam, The many faces of Realism,
Open Court, La Salle/Ill. 1987. A critical
study of realism in science with emphasis on chemistry has been given by J.
Schummer, Realismus und Chemie, Königshausen & Neumann,
Würzburg 1996.
4 Called substances in the Aristotelian tradition.
5 The ontological status of entities like a pure number
or an idea will not be explicitiv considered here.
6 Op. cit., p. 13.
7 An energy barrier with walls higher than about 150 kJ/mole will usually do. By
‘energy‘ one means here one of the thermodynamical functions E-TS or H-TS,
viz internal energy E or enthalpy H minus the temperature
T times the entropy S,
because they represent the energy which matters for chemical reactions. For a
recent discussion and references cf ‘A controversy about the Gibbs function‘,
in:
Journal Chemical Education, 73 (1996), 384-412.
8 As is weil known, except in borderline cases molecular biologists
do not consider
the molecular nature of enzymes as part of their subject,
for their problems always
bear on how the enzymes interact, cooperate and maybe change into one another
or form new enzymes to perform certain tasks in a cell.
9 Schummer rightly calls these objects Bausteine, building blocks,
although he
adopts an essentially topological definition of molecular structure
(op. cit., pp. 254, 268).
10 Robert Boyle: The sceptical chymist (1661), chap. 6.
11 Cf. F.A.v. Kekulé: Berichte der Deutschen Chemischen
Gesellschaft, 23 (1890),
1302. Trans. into English by O.T. Benfey,
Journal of Chemical Education, 35
(1958), 21-23.
12 L. Paoloni: I contesti della scoperta della struttura molecolare. IV. Un caso
esemplare: la rappresentazione del benzene 1865-1932.
— Contexts of the discovery
of molecular structure. IV. An exemplary case: the representation of benzene
1865-
1932‘ (in Italian),
in: P. Riani and G. Villani (eds.), Lecture notes for the Summer
School on the methodological and epistemological foundations, history and
teaching of
chemistiy, ICQEM-CNR, Pisa 1996. For copies contact Istituto di Chimica
Quantistica ed Energetica Molecolare, via Risorgimento 35, I-56126 Pisa, Italy.
Also the preceding lectures by Paoloni, in the same book,
are of the greatest interest.
12a Both quotations are reported by Paoloni, loc. cit., Note 12.
13 We are not taking here a precise position, but we are inclined to agree with the
analysis made by C. Fabro, Percezione e Pensiero
— Perception and Thought.
Morcelliana, Brescia 1962, chap. 1, where he compares W. Köhler‘s Gestalttheorie
with the Aristotelian view about knowledge of sensible reality.
14 Cf Schummer, Op. cit., p. 246f.
15 A review can be found in the famous paper by F. Hund,
Zeitschrift für Physik, 73 (1932), 1-30.
16 M. Born and J.R. Oppenheimer, Annalen der Physik, 84 (1927), 457. A slightly dif-
ferent presentation is given by J.C. Slater, Quantum Theory of Molecules
and
Solids, McGraw-Hill, New York 1963, Vol. 1, App. 2.
Slater correctly speaks of
the B-O approximation as a ‘theorem‘.
A more detailed presentation is given by A.
Messiah, Mécanique Quantique, Dunod, Paris 1959.
17 M. Born and W. Heisenberg, Annalen der Physik, 74 (1924), 1.
18 This value applies to the maximum-amplitude
(the y-mode of the ring at 405 cm-1),
excited with one quantum (7.4% probability at room temperature); the majority
of the atoms are in the vibrational ground state, with a maximum uncertainty of
0.06 Å on their positions.
The bond lengths are 1.40 and 1.00 Å for CC and OH,
respectively. Although computed from the harmonic oscillator wavefunctions, this
illustrates the general B-O theorem, according to which the amplitude of the
nuclear motions about their equilibrium positions in the first
vibrational excited state
is ca. 1/10 of bond distances or less; in the ground vibrational state
it is far smaller, of course.
19 R. G. Woolley, Journal of the American Chemical Society,
100 (1978), 1073-1078.
Cf. Schummer, op. cit., p. 164.
20 For excited states molecular structure is not yet easily observable,
but there is already sufficient experimental evidence to prove
that the same notion applies; anyway an extension of the considerations
given below is possible.
21 Certain organic molecules are found in coal, and are likely to have
persisted since the Carboniferous, millions of years ago.
22 This is a crude way of stating the famous Mach principle in quantum mechanical
language.
23 This remark is not superfluous, because such popular philosophers of
sciencc as K. R. Poppcr apparently saw in continuous change
an argument for claiming that
what is real is only events and processes.
24 We shall discuss elsewhere the problem posed by the fact that
the lifetime as defined here is temperature and environment dependent.
25 The essential points are given by R. Feynman, Lectures in Pbysics,
Eddison-
Wesley, Reading/Mass. 1963, part III, chap. 8, in his treatment of the ammonia
maser.
26 This point is related to the general epistemological framework of quantum
mcchanics. A brief but masterful discussion is to be found in
W. Heisenberg‘s The physical principles of quantum theory
(translation from German), Univ. of Chicago
Press, Chicago 1930, chap. IV, p. 65.
27 Schummer, op. cit., p. 243ff.
28 Cf V. Balzani, F. Scandola: Supramolecular Photochemistry,
Ellis-Horwood, New York-London 1991.
29 C. Chothia et al.,Nature, 342 (1989), 877-883.
30 R. Pease, ibid. pp. 859-60.
Giuseppe Del Re:
Cattedra di Chimica teorica, Università di Napoli «Federico II», Via
Mezzocannone à, I-80134 Naples, Italy; G.Delre@agora.stm.it
Last updated : Apr. 15, 2002 - 16:05 CET
