A. J. Minei College of Mount St. Vincent, Riverdale, NY S. A. Cooke Purchase College SUNY, Purchase, NY Pure Rotational Spectroscopy of Asymmetric Tops in the Undergraduate Classroom or Laboratory

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 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 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] Separation between groups = (B + C)

Patterns: a-type R-branch

Patterns: b-type R-branch, K -1 = 0,1

Patterns: b-type R-branch, K -1 = 2,3 Often, K -1 = 2 splitting

Patterns: c-type Q-branch These patterns are typically spaced by

SpecFitter – A multiplatform Java program for the pedagogic fitting of spectra

a-type helper app: A (222) B ( 61) C ( 66) DeltaJ ( 87)E DeltaJK ( 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

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.