Found Chem
DOI 10.1007/s10698-017-9285-4
An alternative approach to unifying chemistry
with quantum mechanics
Vanessa A. Seifert1
The Author(s) 2017. This article is an open access publication
Abstract Harold Kincaid in Individualism and the Unity of Science postulates a model of
unity-without-reduction in order to accurately describe the relation between individualism
and macroeconomics. I present this model and apply it to the description of the relation
between chemistry and quantum mechanics. I argue that, when it comes to the description
of molecular structure, chemistry and quantum mechanics are unified in Kincaid’s sense.
Specifically, the two disciplines contribute to the formation of a unified body of knowledge
with respect to molecular structure.
Keywords Unity Supervenience Quantum mechanics
Introduction
The relation between chemistry and quantum mechanics is extensively debated1 in the
philosophy of chemistry. This is reasonable, considering the still vibrant debate in the
philosophy of science about the relation between sciences in general [for example Curd
and Cover (1998), Kellert et al. (2006), Dizadji-Bahmani et al. (2010), Bokulich (2008)].
The different positions presented in the philosophy of chemistry literature on this topic,
could be understood as forming a range of proposals that reside within two extremes. At
one extreme, chemistry is taken to be reduced to quantum mechanics so much so that, at
least in principle, quantum mechanics could substitute chemistry in the description,
1
For example Gavroglu and Simoes (2012), Hendry (2004, 2006b, 2010), Hendry et al. (2012), Hettema
(2014), Lombardi and Labarca (2005), Lombardi (2014), Needham (2010), Scerri (2012), Scerri and Fisher
(2016), Schummer (2014), Le Poidevin (2005), Ramsey (1997).
& Vanessa A. Seifert
vs14902@bristol.ac.uk
1
Department of Philosophy, University of Bristol, Cotham House, Bristol, UK
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V. A. Seifert
explanation and prediction of chemical phenomena (for a view that is around these lines
see Hettema 2012). At the other extreme, looking for a connection between the two
disciplines is not meaningful or useful since the research groups that employ chemical or
quantum mechanical descriptions have different research goals, employ different methods,
and develop substantially different or incompatible conceptions (for example Schummer
2014).2
The paper presents a novel position about the relation of chemistry and quantum
mechanics, that resides within the two extremes. Specifically, it presents Kincaid’s model
of unity and examines whether it applies for the case of chemistry’s and quantum
mechanics’ descriptions of molecular structure. The resulting conclusion is that chemistry
and quantum mechanics form a ‘‘integrated and interleveled’’ (Kincaid 1997) body of
knowledge about molecular structure.3
Sketching the content of the two disciplines
Before presenting Kincaid’s model, some initial clarifications are made. Firstly, the paper
doesn’t use the term ‘theory’ when referring to chemistry and quantum mechanics. Instead,
it refers to them as ‘disciplines’. Let me explicate why. Chemistry and quantum mechanics
involve the development of theoretical postulations and conceptions in order to describe,
explain and predict a particular domain of phenomena. Often, they specify, support or
explain those postulations via the use of mathematical models, visual representations,
experimental or semi-empirical methods. This aspect should not be excluded from a discussion of their relation. Firstly, because neglecting this would provide a distorted image of
how chemistry’s and quantum mechanics’ descriptions are formulated, and explained.
Secondly, because it would exclude important aspects of Kincaid’s model of unification;
namely of a unification that depends on the confirmatory, explanatory and heuristic
interaction of the two disciplines. In my view, the term ‘discipline’ captures more accurately the fact that models, representations etc. are taken into account when examining the
relation between chemistry and quantum mechanics.
Furthermore, the paper argues that if chemistry’s and quantum mechanics’ relation
complies to Kincaid’s model, then their respective descriptions of molecular structure can
be understood as forming a unified ‘body of knowledge’.4 ‘Body of knowledge’ refers not
only to the theoretical postulations and conceptions developed for the prediction and
explanation of a specific phenomenon. It also includes the mathematical models, visual
representations, approximations, semi-empirical methods and experimentations that are
involved in the description of that phenomenon.
Moreover, let me specify the main concepts postulated for the descriptions of molecular
structure, by reference to the two disciplines’ scales. ‘Scale’ refers to the particular time,
length or energy scale to which the objects of a discipline are relative. For example, at ‘‘the
2
There are also pluralist and emergentist understandings of chemistry that aren’t restricted to its
methodological or conceptual incompatibility with quantum mechanics. See for example Chang (2012),
Hendry (2006b), Lombardi and Labarca (2005).
3
Whether this sort of unification applies to descriptions of other chemical phenomena could possibly be
argued for, but isn’t pursued here.
4
Kincaid employs the term ‘theory’ when presenting his model of unity-without-reduction. Also, the term
‘body of knowledge’ is an added element that is proposed here. The paper slightly differentiates itself from
Kincaid’s original unificatory model, without however distorting its core thesis.
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An alternative approach to unifying chemistry with quantum…
quantum scale there are no cats; at scales appropriate for astrophysics there are no
mountains (..)’’ (p. 199, Ladyman and Ross 2007).
In chemistry, the time and length scale within which the chemical objects are defined is
not particularly fine grained. Chemical phenomena are described with reference to objects
of substantially different time and length scales; atoms, molecules and electrons are relative to a different time and length scale compared to, say, grams of iron reacting with
oxygen gas. Since the paper is concerned with the description of molecular structure, it
only focuses on the former scale.
Specifically, chemistry tracks molecular structure by reference to molecules, atoms,
chemical bonds, electrons and nuclei. The structure of the molecule is described in terms of
the characterisation of the atoms that make it up, and in terms of the interactions that take
place between them (namely via the chemical bond). In quantum mechanics, the basic
entities employed are nuclei and electrons. The Schrödinger equation describes the
movement and energies of each of the participating nuclei and electrons and then, by
employing approximate models, one can calculate the behaviour of the aggregate that they
form.
Two points are worth specifying based on the above. First, chemistry and quantum
mechanics describe molecular structure in partially overlapping (thus distinct) scales.
Second, although certain entities belong to the scale of both disciplines (i.e. electrons and
nuclei), those entities have different epistemic significance in the two descriptions.
Chemistry refers to electrons and nuclei in order to explain molecular structure, but does
not provide a complete descriptive and explanatory account of those entities. On the other
hand, quantum mechanics is in the business of explaining and describing electrons and
nuclei. In fact, while electrons and nuclei are employed in chemical descriptions of
molecular structure, they are taken in the context of their characterisation in quantum
descriptions. Chemistry employs descriptions of atomic structure in order to describe and
explain molecular structure, and as such, those descriptions are taken as already established
postulations that have been supported in quantum mechanics.5
The next section presents the seven criteria that make up Kincaid’s model of unity, and
argues that they hold with respect to the two disciplines’ descriptions of molecular
structure.
The seven elements of Kincaid’s unity
Kincaid proposed a non-reductive model in order to argue for the unification of individualism and macroeconomics. Interestingly, a similar unificatory view was held by Pierre
Duhem for the relation of chemistry to physics (Needham 2010). Although Duhem did not
extensively develop the requirements of such a unification, Duhem’s unity is based on a
non-reductive, heuristic and explanatory interdependence between the two sciences (p. 166
Needham 2010); something that Kincaid explicitly requires in order for his model to hold.
The model is defined via seven elements6 which, if they hold with respect to the two
descriptions of molecular structure, establish unity and support the existence of a unified
5
Although the determination of chemical and quantum scales implies some sort of integration of quantum
mechanical postulates to chemical descriptions, I don’t elaborate on this point until Kincaid’s model is fully
presented.
6
The model also explicitly rejects reducibility and strong emergence. This aspect of the model isn’t
currently examined due to limited word length.
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V. A. Seifert
body of knowledge about molecular structure. These elements define unification in Kincaid’s sense, but also act as criteria for this unification to hold. According to Kincaid, the
first three elements (namely (1), (2), (3) below) suffice for unity to hold. If it is possible to
support the other four criteria as well (namely (4), (5), (6), (7) below), then the position is
more strongly defended. Let us examine each element in detail.
(1)
The higher-level entities, postulated by chemistry for the description of molecular
structure, are either composed of, or token identical to the entities postulated by the
quantum mechanical description of molecular structure. (p. 66, Kincaid 1997)
The paper’s interest lies in the relation of the two disciplines with respect to their
descriptions of molecular structure. In this context, it is warranted to restrict the
examination of the first criterion only to the higher level entities that are involved in the
chemical description of molecular structure; namely atoms, molecules and chemical
bonds.
Firstly, some clarifications about the main terms need to be stated. By the term ‘entity’
the paper doesn’t include properties7; namely attributes, characteristics, features or qualities that can be postulated or attributed to things (Orilia and Swoyer 2016). Chemical
properties that are involved in the description of molecular structure such as bond energy,
bond length etc. do not fall under Kincaid’s first criterion but are addressed within the third
criterion (namely (3)).
Also, by ‘composed’ the paper refers to a part-whole relation8 between entities. This
relation is not merely an aggregative relation, in the sense of a thousand grains of sand
composing a heap. Rather, it also includes the possibility that the whole is partially
determined by the physical interactions9 between those parts. In other words, composition
is not restricted to a material, aggregative composition of the parts; it includes their
respective physical interactions as well.
Consider then the atom. The atom is the most basic constitutive unit in chemistry. It is
understood as comprised of a nucleus (i.e. a number of protons and neutrons) and of a
number of negatively charged electrons that surround it. The entities that compose
chemistry’s atom (i.e. protons, neutrons and electrons), are the lower-level entities that are
postulated by quantum mechanics. The manner in which lower level entities make up the
atom according to quantum mechanics, is fully accepted by chemistry. For example,
chemistry accepts that electrons move in a wave-like manner around the nucleus and that,
due to the pull of the nucleus, electrons are confined to have particular energies (i.e. to be
quantised), and to move within certain boundaries around the nucleus.
The aforementioned image of the atom has direct consequence for chemistry’s
description of molecules. A molecule represents a group of atoms that are arranged in a
particular manner in space and are held together via chemical bonds. Therefore, based on
the image of the atom, the molecule is ultimately composed of quantum mechanical
entities as well; namely nuclei and electrons.
7
This is a plausible interpretation of Kincaid’s requirement about ‘entities’, since Kincaid presents a
separate criterion that pertains to ‘properties’ (i.e. the requirement of supervenience in ‘‘Chemical properties
supervene on quantum mechanical properties (p. 66, Kincaid 1997)’’ section).
8
The paper doesn’t examine the philosophical debates concerning the nature of part-whole relations.
9
Physical interactions are gravitational, electromagnetic, strong nuclear and weak nuclear interactions. In
the case of the quantum mechanical description of molecules, the interactions with the largest effect are
electromagnetic in nature, so the paper primarily refers to this type.
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An alternative approach to unifying chemistry with quantum…
Concerning the chemical bond, there has been extensive debate [for example Hendry
(2006a), Weisberg (2008)] about whether it refers to a material part of a molecule or to a state
of energetic stability of molecules. Specifically, the structural conception takes that chemical
bonds are material parts that signify the spatial relationship between a pair of atomic nuclei
within a molecule (p. 917, Hendry 2006a). The energetic conception takes chemical bonding
to signify ‘‘facts about energy changes between molecular or supermolecular states.’’ (p. 919,
Hendry 2006a). The paper doesn’t defend a particular conception of the chemical bond; rather
it argues that under either of the two conceptions, Kincaid’s criteria are satisfied.
Specifically, the structural conception of the chemical bond understands it as a material part
of molecules and thus as a higher level entity. Therefore, for Kincaid’s model to be correct, the
(structural) chemical bond should be either composed of or token identical to lower-level
entities. Indeed this is the case. In chemistry it is represented as being the material part within the
molecule that links atomic centres through the interaction of each atom’s outer shell electrons.
Electrons are part of the structural chemical bond, in the sense that they contribute, via their
mutual interaction, to the stability that is achieved between the participating atomic centres, and
consequently, to the stability of the entire molecule. Quantum mechanics describes the structural chemical bond in terms of the wave function of the participating lower level entities which
specifies their interaction and behaviour. In this context, the structural chemical bond is indeed
composed of the electrons and their interactions, both between each other and with the
respective nuclei (that make up the atomic centres in the chemical level). However, it should be
noted that, at the quantum level, the structural chemical bond in not composed of electrons in an
aggregative individualistic manner; rather they compose it in the sense that they are ‘‘occupancies of non arbitrary partitions of the full electronic wave function that can be associated
with the bond’’ (p. 918, Hendry).
Concerning the energetic conception, even if the chemical bond refers to a set of
energetic properties of the entire molecule, Kincaid’s account is not challenged. This is
because, the energetic chemical bond (understood as a property) is supervenient on
quantum mechanical properties. This argument is elaborated in criterion (3).
(2)
Chemistry and quantum mechanics are logically compatible (p. 66, Kincaid 1997)
Logical compatibility demands that chemistry and quantum mechanics do not make
contradictory claims. In order to support the logical compatibility of chemistry and
quantum mechanics, the paper makes a counterfactual claim and a socio-historical one.
The counterfactual claim states that, if chemistry assumed forces that are not postulated by
quantum mechanics, i.e. forces that are independent and different from the four main
forces postulated in the totality of physics, then indeed, this would suffice to claim that
chemistry is incompatible with quantum mechanics. Since however there are not such
chemical forces (on the contrary the forces postulated in the explanation of chemical
behaviour are all physical), then there is no such logical incompatibility.
This argument by itself does not suffice to support the logical compatibility of chemistry
and quantum mechanics. However, it acts as a positive indication in favour of the logical
compatibility of the two disciplines. Proceeding in a similar manner by examining all other
possible counterfactual claims will prove impractical and perhaps even untenable.
Therefore, I support the claim by invoking the following socio-historical argument.
The development of quantum chemistry10 does imply that the two disciplines must be
logically compatible, for if they weren’t, firstly, such a sub-discipline would not exist, and
10
Quantum chemistry is the sub discipline of chemistry that applies quantum models for the description,
prediction and explanation of chemical phenomena.
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V. A. Seifert
secondly, this would necessarily lead to the amendment or rejection of one of the two
theories, or at least to the recognition of an anomaly in one of them.11 This is supported by
the fact that in cases where the chemical description was incomplete or implicitly promoting an incompatible image with respect to quantum mechanics, chemistry has revised
its postulations and incorporated quantum mechanics’ main theses.12
The most striking example of the above is how chemistry’s image of the atom significantly changed with the incorporation of quantum mechanics’ postulations about the
wave-like manner of entities, the quantisation of energy levels, and spin. I briefly present
this example by focusing on three particular events.
Firstly, quantum mechanics’ postulations of the wave-like manner of entities affected
and influenced chemistry’s image of the atom. The proposition that entities do not only
behave as particles but also as waves had a direct effect on the way atoms were perceived
and on how their inner structure could be described. In this context, Schrödinger formulated the second-order differential equation that would describe the behaviour of a particle
in terms of its wave-like characteristics. Specifically, electron behaviour was described in
terms of the Schrödinger equation which is the mathematical representation of the trajectory of electrons. Added to this is the de Broglie relation which calculates the wave
length of the electrons and relates it to their momentum via Planck’s constant, h.
Secondly, Planck’s proposal that the amount of energy emitted from a blackbody in
thermal equilibrium is discrete and not continuous, had a significant effect on the model of
the atom as well. Specifically, Bohr incorporated Planck’s conclusion (p. 262–269, Pullman 1998) in his model of the atom, by postulating stable electron orbits around the
nucleus and by suggesting that, when an electron occupying a specific orbit ‘jumps’ onto
another orbit, it either releases or absorbs a discrete amount of energy.
Thirdly, the Schrödinger equation brought in a natural way Bohr’s image of the atom
since it generated and specified Bohr’s three quantum numbers (p. 277, Pullman 1998).
Bohr’s quantum numbers that were ‘‘associated with the size, shape, and spatial orientation’’ (p. 268, Pullman 1998) of the orbits, were now inferred by quantum mechanics
instead of merely being postulated.
In conclusion, the aforementioned events illustrate that developments in quantum
mechanics were not only accepted by chemistry but were incorporated in chemical
descriptions and explanations of atomic and molecular behaviour. This reveals the success
and continuous effort to preserve the logical compatibility of the two theories.
(3)
Chemical properties supervene on quantum mechanical properties (p. 66, Kincaid
1997)
Kincaid understands supervenience in the sense that fixing a set of lower level properties
fixes any higher level property (p. 72, Kincaid 1997). What Kincaid means by ‘fix’ is not
entirely clear, so the paper assumes an understanding of supervenience that is compatible
with Kincaid’s model. The paper presents the basic points derived from Kincaid’s
understanding of supervenience and then provides a definition of the term that is compatible with Kincaid’s understanding of supervenience.
11
Logical compatibility should not be confused with other sorts of compatibilities, like conceptual or
methodological compatibility. These incompatibilities could be argued for, however, they do not challenge
the fact that the two disciplines are logically compatible. (For more on conceptual compatibility see
Schummer 2014).
12
See Gavroglu and Simoes (2012) for an account of how the development of quantum mechanics affected
chemistry and resulted to the formation of quantum chemistry.
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An alternative approach to unifying chemistry with quantum…
The basic points that constitute Kincaid’s understanding of supervenience are the
following;
I.
II.
III.
IV.
V.
Supervenience does not ensure the existence of bridge laws, identity relations or
definitions that connect lower level with higher level properties. Specifically, it is
not required that one is able to describe the specific relationship between chemical
and quantum properties. Supervenience does not provide any systematic way of
describing such relations, it merely postulates that some sort of relation between
the quantum and chemical ontology exists.
It is possible for a lower level property to fix or determine more than one higher
level property. In fact, it might be the case that the way higher and lower level
properties cut up the world is very different, making it possible for a property of a
higher level theory never to be equivalent to one or more properties of the lower
level theory. Therefore, it is not required that a specific chemical property is related
to a specific quantum property.
Supervenience is not refuted if the lower level predicates that describe lower level
properties are derived through the use of ad hoc information from higher level
predicates of the respective higher level description of that system. It is irrelevant
whether the description of lower level entities and properties is facilitated by
information provided from the description of the respective higher level entities
and properties that are composed or supervenient upon them.
It allows multiple realisability; namely it is possible for two systems to differ with
respect to their lower level properties, while not differing with respect to their
higher level properties. In terms of our discussion, this amounts to allowing the
possibility of two entities differing with respect to some set of their quantum
properties, while not differing with respect to their chemical properties.13
Supervenience is not taken to be a necessitation relation between higher and lower
level properties; it is not the case that a change in the chemical properties of an
entity necessitates a specific change in the quantum properties of that entity. It
merely postulates that there is a change in quantum properties, when there is a
change in chemical properties. Whether this is necessitation relation between
higher and lower level properties, or a relation of a different modal force is not
examined and our account of supervenience allows for different interpretations of
that relation.
Supervenience then is an ontological position with regard to the relation between
chemical and quantum mechanical properties. It postulates the existence of a relation
between chemical and quantum mechanical properties, such that when any chemical
property of a molecule (say its structure) changes, then it is always the case than one or
more of the quantum mechanical properties of its composing (or token identical) lower
level elements have changed as well. However, this does not entail, neither that this is a
one-to-one relation, nor that such a relation be epistemically describable by the chemical or
quantum formulation (see point I). More importantly, it doesn’t have to be the case, for
supervenience to hold, that one is able to pin point which specific set of properties as
described in the quantum mechanical formalism correspond or (at least) change when a
chemical property changes.
13
Whether this is the case between chemical and quantum properties does not challenge our understanding
of supervenience, so the paper doesn’t examine whether multiple realisability holds.
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V. A. Seifert
A sufficient, though not necessary, argument for supervenience would be to show that
when the complete chemical description of a molecule changes, then its relevant complete
quantum mechanical description changes as well. Notice that this sort of epistemic support
of supervenience rests on the assumption that both descriptions are complete in their
characterisation of a molecule. That is, it is not the case that either the chemical or the
quantum mechanical description miss out in describing some chemical or quantum
mechanical property, process or interaction that takes place within the system; the system
is fully described within the context of the chemical and quantum mechanical
formulations.
Although this is a possible strategy to follow in order to defend supervenience, it will
not be elaborated here, mainly due to restrictions in the length of the paper. Instead, it is
argued that rejecting supervenience would lead to conclusions that are not supported by the
our best current chemistry and quantum mechanics.
Let us suppose then that supervenience does not hold. It follows that there is at least one
higher level property of a system that, when it changes, there is no lower level property of
the system that changes; the system remains invariant on the lower level. In this case, this
would amount to claiming that when a chemical property of a system changes, none of its
quantum mechanical properties change. Epistemically this would be reflected by the fact
that the (complete) quantum mechanical description of the system remains the same as
before the change in the chemical description.
Although supervenience is not here defined in terms of determination or realisation,
from its rejection it follows that there are at least some aspects of the higher level behaviour of a system (i.e. property, interaction, process) that is not determined or realised by
its lower level entities and their respective interactions; they are in principle inexplicable
by any sort of description of its lower level entities and properties. For chemical properties
this can be stated as followed: there is at least one chemical property of the system that is
not determined by the existence, interactions and properties of its composing quantum
parts (i.e. electrons and nuclei). It is not only that the change in a chemical property has not
been detected in the quantum description; most importantly, such a change is ontologically
undetermined by any lower level set of properties of its parts.
Do our best current physical and chemical formulations of molecular structure allow for
the possibility of such a view of molecules? Although we do not take supervenience as
self-evidently true, nor do we deny that it is questionable whether and to what extent it can
be maintained when considering for example the mind–body relation (p. 96, Dupré 1993),
within the context of chemistry and quantum mechanics it is safe to argue that the rejection
of supervenience would lead to the acceptance of a thesis that is scientifically dubious.
Firstly, there is no positive scientific evidence that molecules behave in a manner that is
totally independent from the perspective of quantum mechanics; rather the contrary. The
only evidence that has been presented is negative [for example Hendry (2006b) and
Hendry (2010)] in the sense of presenting specific and unique cases of chemical properties
whose changes have not (supposedly) been epistemically recovered in the quantum
mechanical description. Even if, for example, we accept that isomers cannot be differentiated quantum mechanically with respect to some of their structural properties, changes to
the majority of chemical properties (whether structural or not) are in fact reflected in
changes in the wave function of the respective system. The fact that only some structural
changes may not be described quantum mechanically should be regarded as evidence in
favour of supervenience rather than as evidence against it, especially if one considers the
array of alternative epistemic justifications that have been provided in order to explain such
‘failures’ of the quantum formalism [see for example Scerri (2012)].
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An alternative approach to unifying chemistry with quantum…
The fourth criterion of Kincaid’s model is focused on exactly this point (i.e. (4)). It
requires that there is sufficient scientific evidence that could inductively support that higher
level properties supervene upon lower level ones.
(4)
It is possible to inductively support supervenience by citing examples of quantum
mechanical mechanisms that fix or realise higher level properties (p. 66, Kincaid
1997)
The support of supervenience can be strengthened by citing examples of mechanisms that
illustrate how the chemical properties are fixed or determined by the properties of lowerlevel entities. Kincaid does not require that there is a complete set of mechanisms in the
quantum description that realise or bring about the complete set of higher-level properties;
he merely wishes to support supervenience by pointing out that there exist examples of
mechanisms that illustrate his point. The most striking perhaps quantum mechanism is the
one used to define the orbital structure of atoms in chemistry.
This mechanism is based on Schrödinger’s specification of the three quantum numbers
and on Pauli’s exclusion principle that specifies the fourth quantum number. It outlines the
building rules with which chemists are able to specify the electron configuration of atoms,
and consequently it provides the basis for specifying what kind of bonds different types of
atoms can form, and with what type of atoms that could be.
The electron configuration of an atom is a ‘‘list of all its occupied orbitals, with the
number of electrons that each one contains’’ (p. 33, Atkins and Jones 2010). This list is
completed by following certain building rules that are based on Schrödinger’s solution of
the wave function for the hydrogen atom, and on Pauli’s Principle. Specifically, atomic
orbitals refer to one-electron orbital eigenfunctions which are ‘‘based on the attraction of
the nucleus for the electron we are considering plus the average repulsion of all the other
electrons’’ (p. 13, Mulliken 1967). The shape and size of the area that the electron is most
probably occupying around the nucleus is designated by the four quantum numbers.
The first quantum number is the principle quantum number,14 which represents the
energy and size of the atomic shell. This classification of orbitals into atomic shells is
further sub-divided because an electron can occupy an atomic shell by orbiting around in
various forms. These different forms are captured by the notion of subshell, and each
subshell is represented by the angular momentum quantum number, l. In chemistry, one
writes down the shell and subshell that an electron occupies, in terms of the value of the
principle quantum number (n) and the letters s,p,d,f that correspond to the values of the
angular momentum quantum number (l). So, for example 1 s represents a subshell of the
s-form that occupies the lowest atomic shell, 2p represents the p subshell in the second
atomic shell etc.
Moreover, from the quantum calculation of the probability density of finding an electron
at a particular subshell, it turns out that not all atomic shells allow all forms of subshells (p.
33, Atkins and Jones 2010). This is because for example, the wave function of a p-electron
vanishes at its nucleus. That is why, in shell-1 an electron will be found to occupy only an
s-subshell, and not a p- or f-subshell. Keeping this in mind, quantum mechanics has posited
a ranking of orbitals of the following form:
1s \ 2s \ 2p \ 3s \ 3p \ 3d\
14
I follow the technical notation of Atkins and Friedman (2005) and Atkins and Jones (2010).
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V. A. Seifert
The third feature required to specify the orbital of an electron is the magnetic quantum
number, ml. The value of ml specifies the individual orbitals within a subshell and represents the different direction of each orbital within that subshell.
The last element for a complete description of the electrons’ orbitals, is derived from
Pauli’s Principle. Pauli introduced a rule according to which a maximum of two electrons
can occupy one orbital; namely an orbital with a specific set of (n,l, ml) numbers. These
two electrons are viewed as if moving on opposite directions on the orbital and they are
represented uniquely in chemistry by one more quantum number, namely spin (which takes
two possible values; ?1/2, -1/2).
In sum, the possible values of the three quantum numbers, together with their subshell
ranking and the Pauli Principle, act as building rules that chemists use in order to write the
electron configuration of an atom. By following those rules, it is possible to represent the
orbitals that the electrons of a particular atom will occupy in terms of them having
particular size, shape and orientation. So, for example, the hydrogen atom has one electron.
It must be the case that the lowest energy shells are occupied first; so hydrogen’s electron
occupies shell-1. Also, we know that in shell-1 the electron moves necessarily in an
s-subshell, namely spherically around the nucleus. So, the electron of a hydrogen atom
occupies orbital 1 s. For the carbon atom, which has six electrons, two electrons will
occupy shell-1 on an s-subshell with opposite spin (due to Pauli’s Principle), two more will
occupy shell-2 on an s-subshell, and the other two will occupy shell-2 on a p-subshell.
Which orbital must be filled first is indicated by the aforementioned ranking of orbitals
(1 s \ 2 s \ 2p \ 3 s \ 3p \ 3d \ ).
This mechanism illustrates how certain chemical properties of atoms and molecules
supervene on quantum properties of electrons and nuclei. The number of electrons that fill
the last atomic orbital and the particular quantum characteristics of the atomic orbital (in
terms of the quantum numbers that specify it), realise the overall structure of the atom, and
subsequently its chemical behaviour. This is particularly important for the chemical
description of atoms and molecules since, specifying the structure of each atom that
participates in the formation of a molecule, defines and explains the particular bonds that
are formed with other atoms within the molecule as well as those bonds’ properties, and
thus contribute to the explanation and prediction of the structure and reactivity of the
molecule.
(5)
Both chemistry and quantum mechanics heuristically depend on each other (p. 66,
Kincaid 1997)
For the two theories to be considered as ‘heuristically dependent’ upon each other, the
paper takes that it should be the case that both quantum mechanics and chemistry;
i.
ii.
have enriched or influenced the research questions that concern the other discipline
have developed tools, methods or models that have accommodated the research
questions of the other discipline.
Indeed, the relation of chemistry and quantum mechanics has illustrated such a heuristic
interdependence and has enriched the research questions of both theories. Quantum
mechanics led chemists to further investigate the structure of atoms and to incorporate in
the chemical description quantum mechanical postulations about the structure of atoms.
Conceptual issues such as the nature of the chemical bond still maintain a lively debate
among chemists and physicists, since quantum mechanics revealed the existence of factors
that affect the conceptual understanding of basic chemical concepts. On the other hand,
chemistry also raised questions that enriched quantum mechanical research; different
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An alternative approach to unifying chemistry with quantum…
quantum models are continuously being developed in order to expand the quantum
mechanical description to various kinds of entities (i.e. atoms, diatomic molecules, polyatomic molecules, metals etc.).
Moreover, the history of quantum chemistry reveals a continuous exchange of tools,
methods and models in the effort to satisfy explanatory and predictive needs of both sides.
Chemists have gained a substantial amount of quantitative and qualitative information
concerning molecular structure by quantum models that solve, via approximations and
idealisations, the Schrödinger equation for different types of atoms or molecules. Certain
techniques manage to give us accurate descriptions of small molecules, whereas others are
more successful in describing larger (polyatomic) molecules, or types of matter such as
metals (see Hoffman 1990). Moreover, through the development of the Molecular Orbital
approach, quantum chemists developed novel visual representations of molecular orbitals
that enriched chemistry’s understanding of molecular structure in organic chemistry.
All in all, exploring the history of the development of chemistry, quantum mechanics
and computation illustrates how those disciplines of scientific investigation have utilised
each others’ models in order to expand their research and to accommodate their
explanatory, heuristic and predictive needs (see Gavroglu and Simoes 2012). Currently,
this interdependence between chemistry and quantum mechanics has been extended in a
wide range of sub-disciplines, where quantum mechanical models are used in material
science, drug design etc. (p. 245, Matta 2013). Although those needs may be different for
each discipline, this does not mean that the models they use are not provided by other subdisciplines. In this sense, Kincaid’s criterion is fulfilled.
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Chemistry and quantum mechanics confirmationally depend on each other (p. 66,
Kincaid 1997)
Chemistry and quantum mechanics are confirmationally dependent in two ways. Firstly,
the results of chemical experimentation have played a vital role both in the development
and in the evaluation of quantum models. The quantitative results of quantum models are
compared with experimental results so as to see how accurate the model is and to what
direction changes need to be made within the model so as to minimise error. Those
experimental results are provided through the work of experimental chemists who, with the
use of spectroscopical and other techniques, calculate chemical properties. This aspect of
confirmational interdependence is illusttrated in (Weisberg 2008), who evaluates the
predictive success of different quantum models by comparing the calculation of the dissociation energy and the equilibrium distance of atomic nuclei in quantum models, with the
respective results of chemists’ experimental calculation of the dissociation energy and
bond length.
Secondly, novel predictions of chemical phenomena have been made with the help of
quantum mechanics. For example, the specification of atomic structure by quantum
mechanics helped chemists understand spectroscopic results and thus predict novel elements, in accordance to the periodic table (p. 213, Needham 2004). Moreover, quantum
models have made novel predictions about, among others, pericyclic reactions (p. 1057,
Hendry 2004), large molecules, and metals, enriching thus chemical knowledge and corroborating chemistry’s theoretical postulations.
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Chemistry and quantum mechanics contribute in the explanatory endeavours of each
other (p. 66, Kincaid 1997)
Kincaid does not specify in detail what he means by ‘explanation’ nor does he explicitly
support a particular philosophical model of explanation (i.e. deductive nomological, SR
123
V. A. Seifert
model, causal mechanical etc.). The paper retains this neutral position and understands
explanation in a naive, qualitative and scientistic sense. Specifically, it takes as explanatory
any narrative developed within the scientific literature and pedagogy, and employed by
working scientists in order to understand the phenomena which they examine.
In the context of such an understanding of ‘explanation’, the paper takes that Kincaid’s
seventh criterion holds with respect to chemistry and quantum mechanics. Specifically,
advances in quantum mechanics have enriched chemical explanations of molecular
structure and at times even led to their revision. This can be argued from an opposite
perspective as well; chemical explanations of molecular structure have been used in the
development of quantum models and have guided quantum chemists towards a more
accurate interpretation of the mathematical description of atoms and molecules (as this
manifests via the Schrödinger equation). In fact, genuine explanatory differences both
between different quantum models, and between quantum models and chemistry have
raised heated discussions in order to consolidate or review the explanatory account of one
or both of the sides.
There are several examples that illustrate this interdependence, among which are the
following;
• The use of the quantum mechanical account of atomic structure in the explanation of
the periodic table. As already illustrated, quantum mechanics provide chemists a
mechanism to specify and explain atomic structure in terms of electron configuration.
This proved particularly helpful in the explanation of the periodic table and of its
success in classifying chemical elements according to similar chemical and physical
properties (Scerri 2006). Despite the fact that the periodic table was constructed long
before the advent of quantum mechanics, quantum mechanics provides the explanation
of why the chemical elements belonging in specific vertical and horizontal columns
exhibit particular similarities.
• Quantum mechanics has enriched the understanding of molecular structure through the
explanatory conclusions derived by different quantum models that attempt to describe
molecular structure. For example, the development of the molecular orbital (MO)
approach in quantum mechanics has revealed the effect of electron delocalisation on
the overall stability of a molecule. Modern versions of the MO approach, like the
Hartree–Fock methods and the Configuration Interaction approach (CI), take into
account the repulsion of electrons, the ionic character of chemical bonds and the
mixing of higher energy states, revealing additional factors that enrich chemistry’s
understanding of basic chemical concepts pertained to molecular structure (Weisberg
2008).
• Quantum mechanical models have been developed with the help of theoretical
chemistry in the sense that the models are calibrated or corrected through the use of
chemical postulations or assumptions from chemistry (p. 183, Hendry 2010).
Concluding this section, there is sufficient evidence that supports the heuristic, confirmatory and explanatory interdependence of quantum mechanics and chemistry. This
epistemic interdependence, together with the satisfaction of supervenience and the logical
compatibility of the two theories, define the specific model of unification and, consequently, strongly support that quantum mechanics and chemistry are indeed unified in such
a way.
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An alternative approach to unifying chemistry with quantum…
Concluding remarks: the virtues of Kincaid’s unificatory model
Kincaid’s unificatory model is primarily an epistemic position regarding how different
disciplines formulate a unified body of knowledge that is continuously influenced and
developed through each discipline’s explanatory, confirmatory and heuristic advances.
Molecular structure is described, explained and predicted through the theoretical postulations and conceptions, but also the experimental and representational tools of both
quantum mechanics and chemistry, resulting in the formation of a unified body of
knowledge.
This understanding of unification is compatible with various epistemic and ontological
positions about chemistry and quantum mechanics. Although an enumeration of all the
alternatives is not currently possible, let me provide some examples. On the one hand, it is
possible to maintain the autonomy of the two disciplines, if one understands the term as
merely signifying the existence of distinct research groups with distinct research goals, that
employ independent methods, tools, models, or even conceptions. On the other hand, the
model is also compatible with the existence of local reductions between the two
descriptions; namely Kincaid’s unity is not refuted if, for example, certain properties of the
higher level description are connected via bridge laws to sets of lower level properties.
Concerning metaphysical issues, the supervenience thesis does not necessarily entail that
the higher level entities and properties are eliminable from reality (though this is also a
compatible position). One could still maintain that molecules exist and that their structure
is real, without contradicting Kincaid. These points however will be discussed on another
occasion.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made.
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