Chemistry Reference
In-Depth Information
only have to focus on the (broad) set of structures M
p
, and can ignore many of the
finer points of structuralist theorising.
The question is now whether a
approach to the theory of
absolute reaction rates is capable of characterising the inter-theory relationships
appearing in Fig.
2.1
. I will now briefly, and largely informally, discuss the sort of
relationships that are at play.
conceptual spaces
'
'
1. The simplest relationship exists between the
'
statistical mechanics
''
quantum
mechanics
'
boxes and the theory of absolute reaction rates.
A
'
simple
'
quantum mechanics (of the type I argued that was used in quantum
chemistry) is characterised by a Hilbert space and a set of operators as a structure
2
s
Definition 2 (QM-S) x is a characterisation of a simple quantum mechanics,
(
x
2
2
s
)if
σ
A
;
,
A
,
1.
x
¼
S,
H
2.
is a system of particles;
3.
H
is a separable Hilbert space;
4.
J
A
is an operator on
H
;
σ A
is the spectrum of
A
.
5.
As was argued by Muller (
1998
,
2003
), quantum mechanics is not easily
characterisable in terms of a structuralist model, and,
in fact,
'
all quantum-
mechanical set-structures float in a sea of stories
(Muller
2003
, p. 198). As Muller
argues, many of the practical applications of quantum mechanics rely on specifi-
cations of
'
and the like which are fluidly adapted to the
situation at hand. All of these adaptations make up the
'
sea of stories
'
.
One such story is quantum chemistry. In Hettema (
2012a
) I characterised ab initio
quantum chemistry as a structure of structures, comprising of a molecular frame, an
electronic structure and an atomic basis set. The simple definition is as follows:
systems
,
measurement
'
'
'
'
Definition 3
x
is
a potential model
for
ab initio quantum chemistry
(
x
2
M
p
(QCAI)) if there are (sub)structures F, E and B, such that
1.
x
(F,E,B,);
2. F represents the molecular frame of the form R
¼
Z
;
3. E represents the electronic structure of the for
m
;
;
;
σ
; ʨ; A
P
e
;
r
;
M
;
4. B represents an atomic basis set of the form R
B
; ˇ; ʱ
For now, it is sufficient to recognise that the connections between a generic
(
) quantum mechanics and an ab initio quantum mechanics depend on the
moves discussed by G¨rdenfors and Zenker (
2011
) in the following sense.
simple
'
'
depends, in the terminology of
G¨rdenfors and Zenker, on a change of scale or metrics as well as the salience of
dimensions as well as on a change in the separability of dimensions. The
The specification of a molecular
frame
'
'
frame
'
'
