Some thoughts on analysis of far infrared spectra A.R.W. McKellar National Research Council of Canada

Useful resource for spectroscopy software: ( thanks to Zbigniew Kisiel)

Combination differences An important concept, which you are all familiar with. Especially valuable with high quality spectra (e.g. CLS)! a b c d a, b, c, d are four line positions. (a – b) = (d – c)

Combination differences The number of combination differences varies greatly depending on the type of spectrum. We can use the concept ‘internally’ (i.e. with a completely new spectrum). Or ‘externally’, with previously known information (e.g. we already know ground state parameters and hence energy levels). There are also more complicated energy loops …

Combination differences Simple example using known ground state to assign unknown upper state. Acrolein (CH 2 CHCHO), combination band. We have some predicted approximate line positions. They may not be perfect, but the errors will all be the same because the ground state levels are accurately known. 34 2,33 – 34 1, ,33 – 34 3, ,33 – 35 3, Draw 3 plots exactly centered on these positions

Combination differences 34 2,33 – 34 1, ,33 – 34 3, ,33 – 35 3,33 Simple example using known ground state to assign unknown upper state. (this is the principle used in the ASAP program).

Two general approaches to assigning spectra (but they are not mutually exclusive!) 1.Find patterns (related lines) and then figure out what they are. ‘Patterns’ often means equally-spaced series, and Loomis –Wood plots are a way to find such series. 2.Guess parameters, simulate spectrum, try to match with observed spectrum. This approach is now more practical than formerly thanks to computers and graphical interfaces. We don’t need any help to find a series here But we might like some help here

The Loomis-Wood idea. Plot the same spectrum many times with a constant offset equal to an expected series interval. This molecule (acrolein) has A = B = C = cm -1 The interval here is 0.32 cm -1 which is  (B + C)

It’s not necessary to plot the actual spectrum. You can simply have a line list and plot dots on horizontal lines which are offset by an interval. If you have a line list with intensities, you can plot bigger dots (or triangles) for stronger lines. With this approach, it’s easier to have many rows. The offset interval does not have to be constant. It can change in a regular manner.

Another plot for acrolein A = B = C = cm -1 The interval here is 2.75 cm -1 which is  2(A – ½(B + C)) = 2.86 Here the recurring feature is not a single line, but rather a whole Q-branch.

The Loomis –Wood idea is thus an aid to pattern recognition, where the ‘pattern’ is a series of features with some sort of regular spacing. The second approach is simulation. What do we already know about the molecule(s) responsible for the spectrum? 1.Nothing? Then guess the composition,  structure,  rotational constants. 2.Ground state parameters? We have to guess upper state parameters.

Example: Weakly-bound trimer C 2 H 2 – (N 2 O) 2 We have a supersonic jet spectrum using a helium / acetylene / nitrous oxide mixture. A new band is observed in the N 2 O 1 region which requires both C 2 H 2 and N 2 O, but is NOT the C 2 H 2 – N 2 O dimer.

Example: Weakly-bound trimer C 2 H 2 – (N 2 O) 2 Maybe this band is due to a trimer? So we calculate possible (C 2 H 2 ) 2 – N 2 O and C 2 H 2 – (N 2 O) 2 structures and rotational parameters. One result is the file “ ppmm4-0120example.out ”.

Example: Weakly-bound trimer C 2 H 2 – (N 2 O) 2 Start with the (calculated) lowest energy isomer of C 2 H 2 – (N 2 O) 2. To obtain rotational constants, we use the handy program PMIFST, with Cartesian atom coordinates from ppmm4-0120example.out. The C 2 symmetry axis is the b-axis, and the N 2 O have significant projections on the a- and c-axes.

Example: Weakly-bound trimer (C 2 H 2 ) 2 – N 2 O Now we try PGOPHER, with files N2O-C2H2example.ovr and N2O- C2H2example.pgo

Example: Benzene Recently we observed a supersonic jet spectrum using a helium / nitrous oxide / benzene mixture. A new band was observed in the N 2 O 1 region. What is it?!!

Example: Benzene Didn’t seem to fit N 2 O-C 6 H 6 or any other weakly bound species we could think of! Could it be C 6 H 6 itself?? My knowledge of benzene is highly limited! Planar symmetric top. B = cm -1 ; C  B/2. Would be a perpendicular band.

Example: Benzene Yes! It turns out to be C 6 H 6 itself!! (So it didn’t require N 2 O in the expansion gas.) Thanks to PGOPHER, it was easy to figure this out without actually knowing much about degenerate vibrations of symmetric rotors in general, or about benzene in particular! [probably ]

Example: CO 2 Another example, to show how easy GOPHER is and how accurate CLS spectra are. A simple impurity shows up in our spectrum of acrolein at 200 K. It’s the 2 bending band of carbon dioxide.

Example: CO 2 PGOPHER is quite tolerant of the formatting of spectra for input (in this case, CO2-example.txt ). Once you have loaded a spectrum successfully, you can save it as an *.ovr file (overlay). To start with a new linear molecule, we use: File > New > Linear Molecule

Example: CO 2 Here are parameters (from 1980)

Example: CO 2 Now we’ll try a state-of-the-art fit, using our spectrum where CO 2 is just an unwanted impurity. (Impurities can be useful for absolute frequency calibration.)

Water! Ubiquitous in the far-IR. Intensities can be weird! Difficult to fit with standard Hamiltonians. The example file H2O.pgo may be useful for rough determination of water in your spectra. But don’t expect super accuracy!

Water! The water calculation also illustrates an inherent problem of calculating partition functions, especially when centrifugal distortion is large. To see this: View > Levels Colin can tell us more.

Molecules Diatomic Linear Symmetric rotor Spherical rotor Asymmetric rotor Paradoxically, the simplest (no degeneracies)

Perturbations Symmetry is the guide to which perturbations are possible between vibrational states. ‘Fermi-type’, or ‘anharmonic’ no rotational dependence ‘Coriolis-type’ a-, b-, c-type, OR higher order Matrix elements a-type (  K a = 0) G a k 2 G a = 2A  a b-type (  K a =  1) ½G b [J(J + 1) – k(k  1)] 1/2  = 0 to 1 c-type (  K a =  1)  ½G c [J(J + 1) – k(k  1)] 1/2

Acrolein 17, K a = 13  12 Q-branch. K a = 13 levels of 17 are crossed by K a = 13 of 4 18 at J = 30. There is an a-type Coriolis interaction (  K a = 0) with total magnitude  0.13 cm -1 (as you can see). 0.13/K 2 = 0.13/169  cm -1 actual fitted parameter is cm -1 This is a local perturbation

(J = 20 levels shown) Here is a more global c-type Coriolis perturbation (same molecule) K  9 of 17 pushed up by K  10 of 12 K  10 of 17 pushed down by K  11 of 12 (actually K = 7 of 4 18 )

Simulation (PGOPHER) as a learning tool PGOPHER is a lot smarter than me (not sure about you)

Simulation (PGOPHER) as a learning tool As an example, H 2 CO (formaldehyde) 2 band, H2CO-example-a.pgo. These are only approximate parameters – note the PGOPHER default asymmetric top is very similar. Ground A B C

Simulation (PGOPHER) as a learning tool H 2 CO 2 is an a-type band, so we’ll try that first But we can also learn what a b- or c-type band should look like. Illustrate a-type. Switch to b-type (whoops, have to have correct upper state symmetry)! Switch to c-type. Looks similar to b-type, so duplicate the molecule to illustrate the difference, with b- and c-type in different colors.

Simulation (PGOPHER) as a learning tool Another example, Cl 2 CS (thiophosgene) 2 band, Cl2CS-example-a.pgo. It’s isovalent with formaldehyde, but much heavier. Near-oblate instead of near-prolate. Again, these are only approximate parameters. Ground A B C For planar oblate top, A = B = 2C

Thiophosgene example, a-type band We see clumps of lines separated by 0.11 cm -1 (  B  2C)

Thiophosgene example, b- and c-type bands a- and b-type bands are quite similar (because A  B), just as b- and c-type bands were similar for H 2 CO