Pure Rotational Spectroscopy of Asymmetric Tops
in the Undergraduate Classroom or Laboratory
A. J. Minei
College of Mount St. Vincent, Riverdale, NY
S. A. Cooke
Purchase College SUNY, Purchase, NY
Context:
 Atkins and De Paula “Physical Chemistry”
 Section 12-4: “The Rotational Energy Levels”
 (a) Spherical rotors
 (b) Symmetric rotors
 (c) Linear rotors
 (d) Degeneracies and the Stark effect
 (e) Centrifugal distortion
Context:
 McQuarrie and Simon
“Physical Chemistry: A Molecular Approach”
 Section 13-8: “The Rotational Spectrum of a Polyatomic Molecule
Depends on the Principal Moments of Inertia of the Molecule”
 “There are no simple expressions for the energy levels of an
asymmetric top molecule. Generally, their rotational spectra are
fairly complicated and do not exhibit any simple pattern”
 Section 13-9: “…vibrational spectra of polyatomic molecules turn
out to be easily understood in terms of the HO approximation. The
key point is the introduction of normal coordinates, which we discuss
in this section”.
Hypotheses:
 Pure rotational spectra from asymmetric tops do contain
easily recognizable patterns. (Low frequency and low
temperature helps!).
 These patterns are identifiable by undergraduate students.
 A “top down” approach to teaching rotational spectroscopy of
asymmetric tops can follow a traditional pedagogic method
in chemistry for teaching NMR and IR spectroscopy.
Related work
 Gordy and Cook, Chapter 7.5
 “Assignment and Analysis of Complex Rotational Spectra”, Z.Kisiel, in:
J.Demaison et al. (Eds.), Spectroscopy from Space, Kluwer Academic
Publishers, Dordrecht, 2001, pp.91-106.
 Pollnow and Hopfinger, J. Chem. Ed. 1968, p 528.
 Nick Walker et al. Rotational Spectroscopy –Wikipedia page
 Probably everyone in this room has contributed to this field!
Background
 It is useful if the student is familiar with VSEPR theory and
electronegativity.
 Quantum numbers J, K-1, K+1
 Rotational constants A, B, C.
Patterns: a-type R-branch
Separation between groups = (B + C)
Center of group = (B + C) × (J+1)
Span of group = (B - C) × (J+1)
What about A?
“Asymmetry” = Asym
Asym = (center K-1= 0) – (left K-1 = 1)
“Reduced” Asymmetry, 
= Asym / [(B-C)×J]
Patterns: a-type R-branch
2𝐵 − 𝐶 + 𝐶𝜅
𝐴=
𝜅+1
Patterns: b-type R-branch, K-1 = 0,1
Patterns: b-type R-branch, K-1 = 2,3
Often, K-1 = 2 splitting
(𝐵 − 𝐶) × 𝐽′ × 𝐽′′
≈
2
Patterns: c-type Q-branch
These patterns are typically spaced by
≈ 2𝐴 − (𝐵 + 𝐶)
SpecFitter – A multiplatform Java program for the pedagogic
fitting of spectra
a-type helper app:
1
2
3
4
5
10000
A
1553.380(222)
20000
B
325.07774( 61)
30000
C
311.26018( 66)
200 -DeltaJ
-0.01652( 87)E-03
1100 -DeltaJK
-0.0609( 40)E-03
2,2,3,3-tetrafluoropropyl trifluoroacetate
Lab activity – Purchase College
9 Students at Purchase College
performed the “Assignment Lab”
successfully.
6 Biochemistry majors
2 Chemistry majors
1 Senior citizen
c-type spectrum
≈ 2𝐴 − 𝐵 + 𝐶 = 1885 MHz
𝐵 + 𝐶 = 1065 MHz
Therefore A = 1475 MHz
Alternative operation mode
Peak picking subroutine
Can’t pgopher, JB95 and AABS do all this?
Yes.
Distinctions:
SpecFitter is:
(1)Specifically aimed at learning how to fit pure rotational spectra
(2)Potentially multiplatform (Windows, Mac, Linux)
(3)Open source
(4)A “one window” application, “MouseEvent” driven
Class Evaluations
 Sample sizes
 6 students from Manhattanville College (concurrently in
PChem 2 – QM).
 4 students from College of Mount St. Vincent (concurrently in
PChem 2 – QM).
 12 students from Wesleyan University (concurrently in Stew
Novick’s High resolution spectroscopy class).
 Total of 22 respondents for pre-activity questionnaire, 19
respondents for post-activity questionnaire.
Pre-activity questionnaire

Have you previously assigned/analyzed a microwave
spectrum?


Yes – 9 No – 13
Post-activity questionnaire

Do you feel more confident in analyzing microwave spectra?


Yes – 17 No – 1 “Sorta” – 1
Are you more interested in microwave spectroscopy after the
class than before?


Yes – 16 No – 2 “Somewhat” – 1
Do you think the software presented is helpful in assigning
asymmetric molecular microwave spectra?


Yes – 19 No – 0
Conclusion:
Numerous undergraduate students have demonstrated that
asymmetric molecular rotational spectra can be analyzed
using a “top down” approach.
Thanks:
Students at the four institutions for participating.
The Southern New England Microwave Spectroscopy
Consortium for encouraging conversations.