What General Chemistry
Students Know (and Don’t
Know) About Quantum
Concepts in Chemistry
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry:
The Team
Peter Garik (presenting), Boston University
(garik@bu.edu)
Peter Carr, BU
Alan Crosby, BU
Dan Dill, BU
Yehudit Judy Dori,
Technion, Israel
Haim Eshach,
Ben Gurion University,
Israel
Luciana Garbayo, BU
Alexander Golger, BU
Morton Z. Hoffman, BU
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
This project is funded by the U.S
Department of Education’s Fund for the
Improvement of Post Secondary
Education (FIPSE).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
The objectives of our FIPSE project are
• to find ways to introduce quantum
concepts into the chemistry curriculum;
• to design software that will support the
teaching of quantum concepts; and,
• to evaluate the success of our software
and curricular activities in supporting
student learning of quantum concepts.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
Why teach quantum concepts at an early
stage in the chemistry curriculum?
The epistemology of a mature science relies
upon foundational models for its research
program.
Such models provide a unifying perspective
on the physical world and support the best
insights and reasoning that we can
currently achieve.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
For cosmology, it is the inflationary theory of
the universe.
For geology, it is plate tectonics.
For biology, it is Darwinian evolution.
Quantum Concepts in Chemistry
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Quantum Concepts in Chemistry
For chemistry, one of the foundational models is
unarguably the quantum theory of atomic
structure and electronic behavior.
The pedagogical issue is where does it belong in
the curriculum?
Quantum concepts appear burdened with
additional abstractions (including mathematics)
that make them first appear forbidding to teach.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
We argue that the unifying power of
quantum concepts is so great, and their
utilization for modern chemistry so
extensive, that finding ways to
successfully introduce them at an early
point in chemistry education is our
obligation to the students.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
What are quantum concepts in chemistry?
The principal quantum topics in chemistry
are:
1) The description of electrons and how
they behave in the presence of other
charges.
2) The description of the interaction of
radiation with matter, and primarily with
electrons.
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Quantum Concepts in Chemistry
Historically quantum concepts grew out of
analogies to electromagnetic theory. Since
the interaction of radiation with matter is a
key concept in chemistry (spectroscopy), it
is traditionally taught.
The properties of electromagnetic waves
provide an early access point for what we
refer to as “Quantum Readiness.”
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
•
•
What is a wave?
What is an electromagnetic wave?
– Is there an associated electric field
– Is there an associated magnetic field
•
•
What is the relationship between
amplitude and intensity?
What is constructive and destructive
interference?
Quantum Concepts in Chemistry
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Quantum Concepts in Chemistry
• How does the phase of a wave vary with
time and space?
• How does a light wave interact with a
charged particle?
• What is a photon?
• How do charged particles interact?
Students prepared with these concepts
should have analogies for understanding
quantum phenomena.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
What are the quantum concepts that we
would like students to master?
• The delocalization of the electron and its
description by a probability amplitude.
• The quantization of energy levels.
• The pairing of a wave function with an
energy.
• Constructive and destructive interference.
• The Pauli Exclusion Principle.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Quantum Concepts in Chemistry
• The transition in energy levels associated
with absorption and emission of radiation.
•The geometry of atomic and molecular
orbitals.
• The atomic structure that arises from the
Aufbau Principle.
• The molecular structure that arises from
bonding orbitals and hybridization.
Quantum Concepts in Chemistry
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Evaluating Students’ Conceptual
Understanding of Quantum
Concepts
As a first step to determining how students
learn quantum concepts, we engaged in
a qualitative research project.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Theoretical Background and
Methodology
• We base our qualitative research
approach of using interviews on the
empirical result from misconceptions
research that, in assessing a population of
students’ understanding of a scientific
phenomenon, the number of different
conceptions observed saturates quickly
(Wandersse, Mintzes and Novak 1994).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Theoretical Background and
Methodology
• For our interpretive work reading the
interviews, we adopted a perspective
based on a dynamics systems approach
proposed by Smith, diSessa and
Roschelle (1993), diSessa and Sherin
(1998), and by Petri and Niedderer (1998).
Quantum Concepts in Chemistry
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Theoretical Background and
Methodology
– We look for phenomenological primitives or
cognitive elements/tools that students employ
in order to construct their understanding.
– We expect to find cognitive attractors –
recurring misconceptions expressed by the
students.
– We further expect to find stable cognitive
elements, the deep seated convictions upon
which students rely for their interpretations.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Theoretical Background and
Methodology
To further understand students’ reasoning, we
adopt a modified ontological categorization
scheme following Chi and Slotta (1993). They
categorize entities as matter (objects), processes,
and mental states. This can be useful. For
example, if a student thinks that a photon is an
“object”, then with it comes a host of associations
such as the photon energy object collides with an
electron and knocks it to another orbital.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Theoretical Background and
Methodology
We add to these ontological categories the
field category in order to have a sensible
ontology for quantum entities.
Finally, we follow Lawson (1993) by
including chunking as an important
component in explaining the way that our
minds organize what we learn.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Design and Procedures
1) We interviewed students prior to, and
subsequent to, instruction on quantum
concepts.
2) Students were selected from a pool of
volunteers taking the honors general
chemistry course at a research
university.
Quantum Concepts in Chemistry
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Design and Procedures
• The students were all freshman in their
second semester.
• This was an elite group of students: they
had passed a placement test to enroll in
the honors course for science majors.
• Most students were chemistry or science
concentrators.
Quantum Concepts in Chemistry
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Design and Procedures
• Students were selected for the interviews to
produce an even grade distribution.
• Each interview was conducted based on the
same set of questions (an interview guide
approach).
• To the extent possible, the interviews were
clinical in nature – in a Piagetian fashion. The
interviewers flexibly probed the individual
student’s responses to elicit deeply held
convictions.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Design and Procedures
• As an aid to better elicit explanations from the
participants, experiments were done during the
interview (double slit interference pattern,
hydrodgen discharge tube with grating, strong
magnets).
• In conducting the interviews prior to instruction,
an assumption was made that students would
have had exposure to quantum concepts in their
high school chemistry courses.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings
Our findings in our pre-instruction interviews are
confirmatory of prior physics education research, and some
echo our earlier findings with high school students (Eshach
and Garik 2001).
• 1) In describing the structure of the hydrogen atom, most
students began with descriptors reminiscent of the Bohr
model (orbit, circular region) but in further conversation
they described and drew pictures with elements of an
electron cloud model, albeit one frequently characterized
by a rapidly moving particle. Such transitional descriptions
of the H-atom agree with the reports of Petri and Niedderer
(1998), Müller and Wiesner (2002), Mashhadi (1996), and
Ireson (2000).
Quantum Concepts in Chemistry
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Findings
• 2) Students knew that both light and electrons
possessed wave-like properties. However, some
believed that this referred to the trajectory of
these as particles in space, a previously
described cognitive attractor (Ireson 2000;
Müller and Wiesner 2002; Olsen 2002).
• 3) In discussing interference of light waves,
students referred to waves as if they were
objects, as opposed to being dynamic events
(Wittmann 2001).
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings
• 4) The confusion of students about the
properties of electromagnetic waves is
apparent from the fact that they were
unaware that there is an electric field
component to radiation. This was
uniformly true in our pre-instruction
interviews.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings (and Disclaimer)
Many topics were covered in the preinterviews. The post-interviews tended to be
more focused as learning of specific items
were investigated.
At the risk of mischaracterizing what these
very bright and very well taught students
accomplished, we will now focus on two
areas in which they encountered difficulty.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings
A key quantum concept is that atomic
orbitals are stationary quantum states
characterized by two quantities: a wave
function and an energy (ψ, E).
As we see from the following responses,
students wrestle mightily with this apparently
simple idea.
Quantum Concepts in Chemistry
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Findings: Orbital/Energy Level
S1.112.post
P: What is an orbital?
S: An orbital is the space where the electron is probably going to be, and it’s
defined by a wave that fits with the Schrödinger... Or that meets the solution for
the Schrödinger Equation.
P: You say the space that an electron is going to be. That is an orbital?
S: Well, okay, let me rephrase this, hopefully clearer. An orbital is an area of
space that satisfies the Schrödinger Equation, and has a specific energy that
satisfies that equation, and within that area in space, each point in space has a
probability that the electron may be at that point in space, and an orbital is all
the points in space that satisfy that energy.
P: What is an energy level?
S: An energy level is a specific energy that satisfies the Schrödinger equation,
that’s a possible solution for that equation, and you can have many points in
space that will satisfy that energy, and all the points that satisfy that energy
make up the orbital that’s in that energy level.
P: So, what is the connection between an energy level and an orbital?
S: Orbitals are at specific energy levels.
Quantum Concepts in Chemistry
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Findings: Orbital/Energy Level
S2.112.post
S: Energy level. This is word, this is the phrase that I just really don’t
like. An energy level represents the difference between two orbitals as
far one electron moves from one orbital to another. I can’t say this still.
The electron moves from one orbital to another that difference is known
as a quote, unquote, energy level. I left you saying last time saying that
I don’t think that is good word for it, but I never, I thought about it for a
long time actually. I spent most of the day thinking about it, and I
couldn’t come up with a phrase that accurately described it. And, it’s, I
think, energy state is better because it describes the state of the
electron, the electron is in the excited state, it’s not where it is normally
at. But then when you start saying state, students start thinking ‘is it a
solid, liquid, or gas?’ and there’s too many overlapping words in
chemistry. It makes things very confusing. But, an energy level is just
the difference between two orbitals of an atom.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings: Orbital/Energy Level
S3.112.post
S: An orbital is… It’s actually just another name for the wave function,
which is the probability of finding an electron in a certain shape and
area, distance away from the nucleus.
P: What is an energy level?
S: An energy level is the radius, a certain set radius away from the
nucleus where electrons are found to be.
P: What is the relationship between an orbital and an energy level?
S: Orbitals are found in certain energy levels, so if there’s, in the first
energy level there’s the s orbital, which is spherically shaped, and
that’s, there’s a probability of finding it there, and then if you go into the
second orbital, in the middle there’s a node, a region where is just
doesn’t, you wont, you will not find the electron, when you get into
higher more complex atoms with more electrons.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings: Orbital/Energy Level
S4.112.post
P: What is the relationship between an orbital and an
energy level?
S: The energy level dictates, no actually not, actually it’s
no…[pause] Every orbital, that, like the different orbitals,
have different possible energy configurations…no, that’s
not what…I am not really sure how to explain it. Umm…I
know that they’re related, I just can’t really explain how.
Like, ah, as energy increases, the radius of the electron,
or the distance of the electron away form the nucleus
increases and generally speaking, the different, the more
complex, um orbital shapes also increase complexity as
energy does. I guess that the only way I can explain, I
can’t really think of any other way to say it.
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Findings
Another example of student confusion
emerged in discussions of what
electromagnetic radiation and photons are.
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(http://quantumconcepts.bu.edu)
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Findings: Nature of Light
S1.112.post
P: Okay. When you say that it’s electromagnetic radiation, can you elaborate on that?
What is electromagnetic?
S: It’s oscillating in energy, and that induces some sort of magnetic oscillation with it, but
electromagnetic radiation would be the, like, wave that’s oscillating in energy, I think.
P: It is said that light propagates as a wave. What is it that is waving?
S: Oh, I think it’s the energy. Yeah. Well, it’s the value of the wave function, and that is
related to energy.
P: And what is it that is oscillating?
S: The value of the wave function. So…
P: Could you put a… Could you label what your axis, or what your axes are?
S: Okay, well, if this an axis that is…We can label it x, we can label it anything, then
where it crosses this other axis is zero and the value of the function along that axis
equals to psi of the function, whatever the function…Or psi of the variable, whatever you
chose to call that axis, x, or r, or d.
P: Okay, what are the units for x, and what are the units for psi?
S: the units for x would be distance, so probably meters, or centimeters, however you
chose to measure it, and I’m pretty sure psi is unitless.
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Findings: Nature of Light
3.112
P: What is light?
S: It’s electromagnetic radiation.
P: What do you mean by electromagnetic, when you say
electromagnetic radiation?
S: Well, it’s… In wave form it’s electricity perpendicular to magnetic
waves.
P: Okay, but when you say electricity, what do you mean by electricity?
S: Just the charge of the electron.
P: Charge of the electron?
S: Uh huh.
P: So are there electrons present within an electromagnetic wave or
radiation?
S: Yes.
Quantum Concepts in Chemistry
(http://quantumconcepts.bu.edu)
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Findings: Nature of Light
S3.112.post
What’s waving?
S: It’s… It’s not really anything that’s in particular waving,
that’s just… Cause it’s… It’s actually found to be… There’s
the wave and particle duality, so it’s not really waving
necessarily. I mean, there’s a sine curve so I guess it
would be energy, if anything.
P: So you said the sine curve, and now you say energy.
How do you relate the sine curve to energy?
S: As it… As the wave propagates up and down its different
states, or different amounts of energy.
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Findings: Nature of Light
S4.112.post
P: Okay, can you tell me what light is?
S: Nope, still really don’t know. Just pretty much, packets of , well not packets of energy,
just straight up energy. Quantized energy. There.
(skip)
P: It is said that light propagates as a wave. Can you tell me what it is that is waving or
oscillating for a light wave?
S: The way it moves. It just goes in a wavelike fashion. And so, the traditional thought
that light is just a straight beam, the individual, well, theoretical, the quantity that they
quantify as a particle is moving in a wavelike fashion, not just straight.
(skip. What follows demonstrates that the above is a liberated conviction, and not
deeply held conviction.)
S: Light doesn’t really have a distinct form or shape. It’s just the wave that they say is just
a general, just a representation of…of what it could be. Not technically the actual
movement itself, it’s just a theoretical representation of what it could be, not technically
the actual movement itself. It is just a theoretical representation because we can’t
measure what it looks like or what it does. So, we just have to give some mathematical
computation to that to represent some sort of quantification of light itself.
During the course of the interview, this student interpreted the two-slit experiment
done in his presence with a HeNe-laser as showing a pattern of electron density.
Quantum Concepts in Chemistry
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Findings
These two examples of misconceptions both
revolve around a common problem: the
understanding of a wave function. In one case it
is the wave function for a particle with mass. In
the other it is for a massless particle, a photon.
The difficulties revealed suggest that a common
solution might be in order that emphasizes the
field nature of both the electron’s wave function
and the wave function of radiation.
Quantum Concepts in Chemistry
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Findings: Chunks
Chemistry education relies heavily on students
acquiring chunks of knowledge that can be drawn
upon quickly. There is chunked knowledge that
students need to learn about atomic structure
(principal quantum number, s, p, d, f), about the
Periodic Table (groups of elements, periodic
trends), and spectroscopy.
Here we provide an example of a successful
chunk, and then one that is less well founded.
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Findings
Based on our
interviews, some of the
chunks we heard were:
• light
• interference
• energy level
• orbital
•spectrum
•
•
•
•
•
•
atomic structure
H atom
He atom
Li atom
H2
molecular bonding
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Example: H-spectrum chunk
H-spectrum chunk
S: There’s…I don’t think I could draw it as electrons jumping within an
atom, just because all the… It would be hard to draw all the different
shapes of the orbitals, and everything, but if you wanted to draw, you
could draw, like, lines here, and this would be…The scale that this was
on would be increasing energy, and the first energy level would be
down here, very low energy, and that would be the n equals one energy
level, and then you’d somewhat further up have n equals two, and as
you increase, the energy levels get closer together, until eventually they
blend into a solid line up here, and when an electron jumps…This
would be n equals five. When an electron jumps down, if you put
energy in it, into an atom, to get an electron all the way up to a higher
energy level, and then it goes and falls back down into the n equals two
energy level, then there’s a certain energy that it emits, and energy is
equal to Plank’s constant times a certain frequency, and so, if you find
the frequency and convert that to a wavelength, you can find out that
these jumps, where an electron goes down from n equals five to two, n
equals four to n equals two, or n equals three to n equals two, all emit
energy that’s within the visible range, or visible light range. So that’s
what we just saw, was electrons going down an energy level, and the
atoms emitting light.
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Example: Interference Chunk
P: Do you think you could sketch for me what you mean by this destructive interference?
S: So just like in the experiment there’s two slits, the light passes through there, and then
you just go on from here and here, and it would meet at a central point, which is the wall,
so right here, and when it… That’s just one section of the sine curve. When it meets this
way, you get constructive interference, and if the amplitude of it was, say, plus one, plus
one, plus one, minus one, minus one, you’d get amplitude added up to a plus two, and
minus two. You have to get the intensity, which is square of that [ ] result and plus two
equals… And… This would result in zero, with a flat line, and that would result in the
square root of that and you’d get nothing. So that would be a dark region and that would
be a bright region.
P: Why would the interference between the two waves be different at different positions?
S: I’m not sure I understand it.
(skip)
P: Is there something that determines whether they meet and result in destructive
interference as opposed to meeting and resulting in constructive interference?
S: No. I don’t believe there is.
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Discussion
The honors students that we interviewed showed a
remarkably stronger understanding of the Born
interpretation of orbitals than we have found in the past.
Our prior experience, with high school students and
medical students (Eshach & Garik 2001 and 2002),
matched other reports in the literature that students
describe atomic structure as a composite of Bohr, de
Broglie, and electron cloud concepts.
Moreover, on the whole the students we interviewed
grasped the fundamental spectroscopic fact that the energy
of emitted radiation is the difference between energy levels,
as opposed to the energy of a level (Zollman 2002).
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Discussion
Nevertheless, these students exhibited a
series of misconceptions that are
enlightening for an education researcher.
Specifically, we observe that the lack of a
careful introduction to the properties of an
electromagnetic wave, specifically the fact
that there is an electric field, eventually led
to students’ confusion.
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Discussion
We further suggest that the confusion that
students evidenced about photons as
objects, and the relationship between
energy levels and orbitals, is a result of not
understanding the field nature of both
electromagnetic radiation and wave states of
matter.
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Discussion
Such incomplete conceptions can later manifest
themselves when chunks of knowledge are put to
the test. For example, the interference chunk
previously related at first sounds plausible.
However, it proves inoperative when tested for
predictions. The student apparently has
constructed the chunk with waves behaving as
objects. As such, he cannot predict where maxima
and minima should occur in an interference
pattern.
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Conclusion
Given the central nature of quantum concepts to modern
chemistry, the dearth of education research in how to teach
this subject is surprising. Many papers have appeared in J.
Chem. Ed. discussing methods of instruction that rely on
quantum principles, but evaluation of these methods is
seemingly missing.
It is our conviction that if properly approached, quantum
concepts are teachable from an early stage in the
undergraduate chemistry curriculum. We hope to follow-up
this current research with future work that supports the
design of successful curriculum.
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