The Philosophy of Computational Quantum Chemistry
From Dr. Buyong Ma , Ph.D
Dissertation of University of Georgia, March, 1995
The advances of computational approach to chemical problems are
remarkable. It has been gradually clear that computer may be the instruments of
new experimental methodology, i.e., computer experiment, which means that
computer together with appropriate software form a fundamental extension of our
means to obtain experimental information[1,2]. The philosophical significance of
such scientific practice, especially computational quantum chemistry, remains to
be evaluated and appreciated. A careful examination of the newly advanced
scientific discipline may enrich our understanding about some problems of
philosophy of science, for instance, the relationship between theory and
observation and cognitive models of science. Vise verse, a philosophical
consideration of computational quantum chemistry might help us get fully
appreciation about computational quantum chemistry.
of computational chemistry is somewhat arbitrary and subjective. The following
are examples which are of interest to the present introduction.
I. The theoretical nature of computational quantum Chemistry
Hopfinger: Quantitatively modeling of chemical behavior on a computer by the
formalism of theoretical chemistry.
2. Schlyer: Attempts to model all
aspects of real chemistry as closely as possible by using calculations rather
3. Clark: use of molecular mechanics along with
semiempirical and ab initio molecular orbital theory to determine structures and
properties of molecules.
Therefore, according to above definitions there are
three characteristics for computational chemistry:
A. obtaining chemical
information (structure, property and their relationship) by calculation rather
then experiment (for comparison with physical experiment, see flow charts
B. The heart of computational chemistry is the formalisms of the
theories in chemistry, which include classical, quantum, and statistical
mechanics and other aspects of molecular physics, chemical physics, and physical
C. There are different branch of computational chemistry,
depending on the formalism of the theoretical chemistry employed. For example,
computational quantum chemistry use quantum mechanics rigorously while
semiempirical method less rigorously (incorporating of empirical determination
of two electron integral involved in solving shrodinger's equation. Molecular
mechanics and dynamic base on the formalism of classical mechanics and
incorporating parameters gotten from experiment or other theoretical method.
According to May Jo Nye, there are two conceptual core in chemistry. (1)
Dynamics, namely, the mechanism of chemical reactivity. and (2) Chemical
'species' and chemical 'constitutions'. In short the central problem in
chemistry is the structures, properties and their relationships of matter
(molecules). The structures of molecule involve two aspects, namely qualitative
structures (nucleus arrangement, electronic structures, etc.) and quantitative
structures. The properties of molecule also have two aspects, name chemical
properties (reactivity for example) and physical property. It is the intention
of computational chemistry to deal with the central problem in chemistry.
The theory of computational quantum chemistry may be briefed as follow: A
molecule in a particular electronic state may exist with various configurations
of its nuclei, each configuration in spaces corresponding to a particular
potential energy of the system. A map of the potential energy versus nuclear
configuration for a given electronic state is called a potential energy surface.
The ideas of molecular structure, energetics and dynamics are unified by the
potential energy surfaces. The potential energy surfaces of a molecule can be
constructed by the formalism of quantum mechanics. Therefore, the information of
the structure and properties of the molecules can be calculated by the formalism
of quantum mechanics and the information about their relationship may be
A flow chart of computational quantum chemistry in practice may be as
Note here, in the process of determining molecular
structure and properties, no real substance are involved, in contrast to a
physical experiment, for which the flow chart may be that in Figure 1b.
II. The philosophical background of the critics of computational (quantum)
Chemistry Dirac made his famous manifesto 50 years ago:
underlying physical laws necessary for the mathematical theory of a large part
of physics and the whole of chemistry are thus completely known, and the
difficulty is only that the exact application of these laws leads to equations
much too complicated to be soluble.
Today this difficulty has been
circumvented due the joint advance of computer and theoretical methods. However,
another difficulty -- conceptual difficulty still stand. Even today many
chemists are uncomfortable with the thought of using a digital computer as an
investigative tool. Many are skeptical. Some are uninformed or even prejudiced.
They do not believe that theory is capable of making accurate predictions of
The reluctance of chemists' acceptance of computational
chemistry may have several reasons due to its theoretical nature. The strongest
resistance comes from the refutation to reduce chemistry to physics. In the
regards of the applicability of quantum mechanics to chemistry, some chemists4
argued that molecular structure is a classical idea, foreign to the principles
of pioneer quantum mechanics that neither gives a correct nor a consistent
description of molecules (due to the Born-Oppenheimer approximation). For some
chemists, the emphasis on environment and on the molecule acting in an
environment is not trivial, for it lies at the heart of the conceptual aims and
problems of the chemical discipline. They resist the quantum mechanical
reduction of chemical molecule to an isolated physical molecule. Of course, the
reductionism of philosophy of science (specifically, the reduction of chemistry
to physics here) will be a arguing topic forever. Nevertheless, the successes
and practices of computational quantum chemistry indicate that there is a place
in chemistry for a gentle form of reductionism.
The most revolutionary aspect of computational chemistry, as may be seen from
the above flow charts, is that the computational chemistry does not study matter
(molecules) directly, in contrast to the traditional descriptive practice in
chemistry. In this regard, the resistance are understandable. For example, one
simple question may be how is it possible to obtain knowledge from complex
molecular world by mathematics fitting rather than observing the molecular world
directly. There may be a misunderstanding of the relationship between theory and
phenomena, which constituted a philosophical motivation for such resistance. I
do not mean to argue whether a philosophical belief may affect scientific
acceptance substantially. The fact is that the emphasis of
observational/descriptive nature of chemistry actually reflected the opinions of
received view of (positivistic) philosophy of science, which privileges
observation over theory.[7,8,9] According to the received view of (positivistic)
philosophy of science, observation yield factual knowledge (neutral body of
facts). Theory then may be logically reconstructed (inductively) from factual
knowledge. The factual knowledge can be used inductively to confirm or
disconfirm laws or theories.
These resistances, if formulated in the
language of the received view of (positivistic) philosophy of science, would be
sound like this: quantum mechanics is logically probable (or wrong) for
chemistry since the chemical molecule is not an isolated physical molecule.
Furthermore, the practice of computational quantum chemistry contracts the
principle that the scientific knowledge should be obtained from observation.
The received view of (positivistic) philosophy of science reigned the philosophy
of science before 1960s. However, since 1960s, received view of (positivistic)
philosophy of science has been beaten to death by the following
1. There is no observation/theory distinction; and
observation involves theory, i.e. it is theory-laden. Therefore, there is no
neutral body of facts, from which the theory may be constructed logically, and
against which the relative merits of competing theories can be assessed.
the received view of (positivistic) philosophy of science obscured the
relationship between theory and phenomena.
3. theories can not be logically
assessed at a time through their observational consequences by means either of
confirmation, verification, or falsification. theory evaluation is a complex
matter involving many factors beyond the idealized logic of justification.
Theory often do not even purport to be true but rather are introduced as an
"idealization", an "abstraction", a "simplification", a "model", or even as a
The implication of applying the above arguments against the
resistance of computational chemistry is obvious. Interestingly, the successes
of computational quantum chemistry coincident with the fallen of the received
view of (positivistic) philosophy of science and the rising of 'new philosophy
of science', among which the semantic conception (model-theoretic view) of
theories is most widely held now[8,9]. One of the reasons accounting for the
failure of the received view of philosophy of science is that it primarily
concern about the analysis of the product of science, for example, scientific
statements (stating from linguistic analysis), rather than examining the history
or the practice of scientific activity. The study of the history of science has
led revolution in philosophy of science. However, the examination of
contemporary scientific practice has limited in the areas of bioscience and
psychology (opposite to another extreme of examining only physics in early this
century). As a result, the practice of chemical research, which constitute an
important linkage from physics to bioscience, has been virtually neglected,
except for few studies. So it is the very time for us to consider a new
philosophical examination of chemistry, particularly computational quantum
chemistry here. As I will illustrated in the following sections, the practice of
computational quantum chemistry strongly support the semantic conception of
theory; and the semantic conception of theory is a powerful tool to examine the
philosophical significance of computational quantum chemistry.
III. Theory and phenomena: a semantic conception (model-theoretic view) of
theoryAccording to the semantic conception of theories8, scientific
theories are not linguistic entities, but rather set-theoretic entities. The
heart of a theory is an extralinguistic theory structure. Theory structures
variously are characterized as set-theoretic predicates, state space and
relational systems. When one propounds a theory, one specifies the theory
structure and asserts a theoretical hypothesis claiming that real-world
phenomena (or a particular real-world phenomenon) stand(s) in some mapping
relationship to the theory structure whereby that structure models the dynamic
behavior of the phenomena or phenomenon. The following analysis will be helpful
to understand the semantic conception of theory and its use for examining the
practice of computational quantum chemistry.
A. Intended scope of the theory:
Theory are formulated to characterize a
class of phenomena known as the "intended scope of the theory" perhaps, say, the
class of all mechanical phenomena of interacting bodies.
B. physical system:
The theory does not attempt to characterize the phenomena in all their
complexity, but only attempts to do so in terms of a few parameters abstracted
from the phenomena. In effect, what the theory does is directly describe the
behavior of abstract system, known as physical system, whose behaviors depend
only on the selected parameters. However, these physical systems are abstract
replicas of actual phenomena, being what the phenomena would have been if no
other parameters exerted an influence. Thus by describing the physical systems,
the theory indirectly gives a counterfactual characterization of the actual
C. theory-induced physical system:
As illustrated below,
corresponding a theory, there is a theory-induced physical system, which
correspond in the manner as that between phenomena and physical system. In
propounding the theory we are claiming that the class of theory-induced physical
system is identical with the class of causally possible physical system for the
theory. If the theory is empirically true, then these two classes are identical;
and if they are not identical, the theory is empirically false.
Although theories directly determine only the class of
theory-induced physical system, they can be used to predict phenomena in the
following manner: suppose the theory is one whose laws are deterministic laws of
succession and that we wish to predict the subsequent behavior of some
phenomenon at t'. By means of one's experimental methodology it is determined
what physical system state corresponds to the phenomenon at some prior time t.
Then, using some formulations of the theory, one determines which theory-induced
physical system characterizes the behavior of a physical system in state s at
time t; Determine the physical system in question indicates a sequence of states
the physical system subsequently will assume, and from that sequence one
determines what state s' the physical system will be in at t'. If the theory is
empirically true, then s' will correspond to the phenomena in question at t'
that is, s' indicates what the phenomenon would be at t', if its parameters were
the only ones affecting the phenomenon and the phenomenon were to meet the
idealized conditions imposed by the theory. Then by the experimental
methodology, one determines the actual phenomenon p' which should correspond to
According the analysis above, the formalism of
computational quantum chemistry may be reformulated in the semantic conception
to get insight into the philosophical significance of such practice.
dealing with the chemical phenomena, we define the corresponding physical system
of chemical phenomena as the molecules and their collection ( intended scope of
computational chemistry and its physical system).
2. the theory-induce
physical system for the computational quantum chemistry is the molecules and
their collections as well.
3. the theory of computational quantum chemistry
is empirically true and the theory-induce physical system constituted of
molecules and their collection is identical to the physical system constituted
of molecules and their collections, which corresponding to the chemical
4. The mathematical models or theoretical formulation of the
molecular system are molecular quantum mechanics and statistical mechanics etc.
5. By using the theoretical formulation, we may describe and predict the
behavior of theory induced molecular system, which corresponds to the real
IV. The Successes and Philosophical significance of computational quantum
chemistry: methylene paradigm and other examplesA. reliability of
application of molecular quantum mechanics in chemistry
In applying semantic
analysis of computational quantum chemistry, an important question about
applicability of quantum mechanics to chemistry is the reliability of
'prediction' . The question may be of two aspects: (1) how close are the
physical systems (theory-induced physical systems) to the chemical phenomena?
(2) how good is the mathematics description of the theory-induced physical
Coulson's generation of quantum theoretical chemists were struck by
the fact that the mathematical physics of quantum mechanics did not result in
fundamental breakthroughs or discoveries in chemistry. Even Mullican claimed
that his initial work in quantum mechanics 'interpreted' rather than
'discovered' chemical facts.
Allberte Pullman4 commented in 1970; "while
it is certainly indispensable that theoretical chemist constantly try to improve
the values of the size they calculated and more and more approach exact energy
values .... quantum chemistry risk giving the impression that its essential goal
is reproducing by uncertain methods known results, in contrast to all other
sciences whose goal is to use well-defined methods for the research of unknown
Ironically, it is in 1970 this 'more and more approach exact energy values lead
to a breakthrough in theoretical chemistry. This breakthrough is not the
theoretical method, rather it established first time that molecular quantum
mechanics could yield accurate results to challenge experiment and is very
significant from the view of point of philosophy of science. The case indicated
here is the famous methylene paradigm.
Between 1962 and 1970 there was
essentially universal scientific agreement that the methylene molecule was
linear in its triplet ground state, as concluded by the brilliant spectroscopist
Gerhard Herzberg (the father of modern spectroscopy) from experiments described
in his Nobel Prize citation. The 1970 theoretical treatment by Bender and
Schaefer brought to bear on the methylene problem theoretical methods that had
been applied only to atoms and diatomic molecules. Their theoretical results,
which predicted that the methylene molecule was bent by 135ø, clashed with the
experimental conclusion. Indirect experimental evidence for such highly bent
methylene molecule came quickly, followed by a reinterpretation of the
spectroscopic studies to confirm the bent geometry predicted by theory. The
reliability of molecular quantum mechanical model for chemistry and a new role
for theory, "full partner with experiment" had been charted. The methylene
paradigm is only one example. Since 1970, computational quantum chemistry is
established as a well defined method and widely used as tool for searching of
unknown truth. In Professor Schaefer's group alone there are at least 23 cases
in which experimental conclusions were ultimately revised to conform to
B. Philosophical significance of computational quantum chemistry: theoretical
observer and theoretical experimentation as an inquiry method for nature.
philosophical significance of the practice of computational quantum chemistry
lies on its implication about the roles of theory and its interaction with
physical experiments. The conventional roles of theory were the explanation
(interpretation) and prediction function. However, the practice of
computational chemistry has go beyond simple prediction and suggests that the
theories also have experimental function. To mean the experimental function
here, I do not restrict to theoretical involvement in observation as the critics
of observation/theory distinction implied. The experimental function of theory
that I will try to advocate is its function as experimental tool obtain
information from nature. Let us take three kinds research problem in chemistry
for illustration: (1) Molecular structures and their spectroscopic constant. (2)
Spectroscopic experiments for chemical reactions: and (3) Synthetic chemistry.
The most and earliest success for the quantum chemistry is in the first
category, for example the methylene problem cited earlier. The ab initio
results are well established and accepted. Two examples may be see in chapters 2
and 5 in this dissertation. In the later case, our theoretical results disagreed
with experimental X-ray structure of tetraethynylmethane, new experimental
results followed up confirmed our theoretical results recently.
argued: 'Quantum mechanics gives perfect prediction for all spectroscopic
experiment. However, chemistry is not spectroscopy." Let us take the examples in
the second category with more elements of chemistry -- the dynamics and kinetics
of chemical reaction. One example of such practice is successful calculations of
thermochemical properties for chemical reactions. In Chapter 5, we will see the
accurate theoretical results about the bonding energies, the changes of
enthalpies, entropy, and free energies of hydration reactions of metaphosphate
anion. Other examples concern two of the fundamental hypothesis or principles
for the chemical reaction, namely potential energy surfaces and transitions
state theory. The successes of computational chemistry in the areas are
remarkable, and some of them may be seen in Professor Schaefer's list.[2c]
Let us take third category for further elaboration. According to the semantic
conception of theory, if the theory is empirically true the theory-induced
physical system replicates the phenomenal system. Therefore if the theory
induced physical system exist then there should exist a phenomenal system
corresponding to the theory-induced physical system (The successful prediction
of the existence of positron is a nice example). This philosophical belief is
well illustrated in the new research field of molecular design. In the field of
chemistry, the situation is more complex than in the case of fundamental
particles, because of the infinite number of the possible molecules. Theory can
be used to search the possible existence of new classes of molecules that might
be of scientific value and of value to society. For example drug design and
molecular electronics. Computational chemistry play a vital role in the
molecular design. The successes for such practice wait to be seen, since the
discipline is totally new and "the user of the (computer) programs lacked the
imagination to ask the right question". Nevertheless, a lot of successful
prediction of existence of small molecule have been appeared, one example is the
prediction about existence of a novel class of molecular complexes including
Li-H2O by Professor Schaefer's group.
In conclusion, we should note that the
nature of the computational chemical prediction has the component of
experimentation. The prediction process itself is a experimental process. This
is why some scientists call the computational chemistry as computer experiment.
As Professor Schaefer put out[2a], " computational quantum chemistry is a gentle
reductionist companion to experiment in the same sense that a powerful NMR
spetrosmeter can be a valuable companion to the synthetic organic or inorganic
chemist. We do not expect chemical concepts to flow out of the computer any more
than we expected chemical concepts to emerge directly from NMR machine. However,
when placed in the hands of a superb intuitive chemist, both devices provide the
data from which meaningful chemical understanding of nature may be
Here we should put it forward that the new role of theory
suggested by the practice of computational chemistry maybe termed as
'experimentation'. Recall that it has long been recognized the role of 'thought
experiment'. We should define two kinds of experimentation here, namely,
'theoretically experimentation; and 'physical experimentation' which is the
conventional and narrow mean of experimentation.
V. Save the Phenomena: the interplay between theoretical experimentation and
physical experimentation and the philosophical significance of a theoretical
observerMany scientists hold the belief that the goal of science is to save
phenomena. The phrase "save the phenomena" crystallizes Plato's conviction that
one of the primary tasks of science is to provide a model that would adequately
explain the perceivable world of the sense. For Plato there was an inseparated
relationship between science and philosophy. He saw the task of philosophy
(science/knowledge) to get beyond the realm of the physical (opinion) to the
ultimate or metaphysical realm.
The successes of computational quantum
chemistry suggested that many chemical phenomena are save by the model of
molecular quantum mechanics. Therefore, by applying the model to chemistry, a
scientist may perform the theoretical experiments to inquire into nature of
chemical world and be a theoretical observer of chemical phenomena.
Scientists need no convincing that (physical) experiment plays an essential
role in science. However, for philosophers of science, the well-known function
of (physical) experimentation is hypothesis testing and another function as
means of inquiry is less often discussed. For the interplay between theory
and experiment, most of the philosopher of science focused on the debate of
obervation/theory distinction and some of them (Van Fraasson, for example as
I know) go further to state that (physical) experimentation is the continuation
of theory construction by other means. Of course, it need no argument that
theory construction is the continuation of physical experimentation as well.
Given such philosophical background, how should we understand the interplay
between theoretical experimentation and physical experimentation? A new tool may
The cognitive revolution in philosophy of science is well under
way. One of the working assumption is that the fundamental premise of the
cognitive approach is that humans are subject to empirical study. Further more,
what distinguishes the study of cognition, as opposed to such other natural
human processes and ability as digestion is a focus on those aspects of human
activity that involve information gathering and processing. If we take the
perspective that science is a method of information gathering and processing,
then we can ask about the relative contributions of various kinds of
Humans constitute a self-organization system. Therefore,
scientific activity should have the characteristics of a self-organization
system, which is also a feedback system (as the following).
Here, for any input information, no matter that from
physical experimentation or theoretical experimentation, has to be evaluated by
comparison block. Conventionally, such feedback function is only performed by
physical experiments, i.e., theoretical results must be confirmed by experiment.
Often, however, the histories of physics and computational quantum chemistry
show that experimental results are both fallible and corrigible as well. It is
apparent that a theoretical experimentation, which performs comparison function
as well, will make such feedback system more complete and more efficient. A
phenomenon is saved only the information form this phenomenon has pass such
feedback system as output. Therefore, the interplay of theoretical
experimentation and physical experimentation is their dual roles as input
(inquiry) and comparison (testing).
The philosophical significance of a
theoretical observer of nature may be inferred from the analysis of Lorentz
observation process, which fit the interplay between theory and (physical)
It is important to note that, upon the inquiry into
nature, no matter whatever kind of operation they are officially designated,
they are in principle much more limited in the amount of information that they
can provided about the properties and relations of the object in the domain.
Therefore, we should to try to obtain the maximum amount of knowledge we may
obtained from this world. If we agree that theory represents our knowledge about
this world, then we can obtained the maximum amount of knowledge only when a
theoretician is an "direct observer" of the world, as suggested by the
relativistic model for general systems.
I appreciate helpful discussions with Dr. Y. Xie and Mr
G. Zhu. I thank Mr. David Sherrill for proof-reading this manuscript.
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