Basics of MARVEL

MARVEL Images

A MARVELous Analogy

Mapping a Train Network vs Mapping Energy Levels in a Molecule using MARVEL

You live in Liverpool Street. You want to know how long to get from Liverpool Street to any other station on the line but you are afraid of the tube and don’t get on it at all.

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All you have is friends that take random journeys on this rail system. E.g. one from Bond Street to Tottenham Court Road, one from Holland Park to Post Office etc.

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Your friends all give you their starting point and final destination and the time it took them. Some give you an estimated uncertainty (plus/minus 1 minute). Some you make a reasonable guess at.

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You get all the information, put it together and you get …. An inconsistent mess!

Turns out that:

- One friend thought he went to Chancery Lane but actually went to Wood Lane

- Another feel asleep part way through their journey and went to the end of the line & back before getting off.

- One friend had a broken watch

And so on.

You need to get rid of the bad data!

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Once you get rid of the bad data, you have a map with most of the information filled in, but…

- All your friends are Republicans, so nobody goes to Queen’s Road

- Two of your friends both live in Ealing Broadway, but go only to Marble Arch for work… but no-one else goes to Marble Arch at all (scared of marble)

So you end up with some missing parts of your map and some links that don’t connect with the rest of your network.

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After all of this, you have an incomplete map of stations and time to travel between them in 1920! Now, you can decide whether to conquer your fear of tubes… or just admire from afar!

Then they build another line...

You select a Zero Point, usually the ground state, and want to know the energy of all the other quantum states relative to the ground state.

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Experimentalists have measured differences in energy between two quantum states … not quite randomly, but there are selection rules, experimental limitations & scientific whims that influence which measurements are made.

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Experimentalists make mistakes… we must remove them.For each transition frequency, you need initial & final state quantum numbers (otherwise, the transition frequency they give you is useless).

You also use the uncertainty in the transition frequency.

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Experimentalists make mistakes… we must remove them.

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Your spectroscopic network will not be complete.

There will be orphan transitions and free-floating networks

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You have beautiful data that we can hopefully publish that will be fantastic and useful!

Then someone will run a new experiment, and we need to update our collation.

MARVEL

This software is used in the process of calculating theoretical spectroscopy data (linelists) and greatly aids the work the ExoMol group are doing to aid the characterisation of exoplanet atmospheres. In order to tell exactly how each molecule will react when light from the host star passes through a planets atmosphere, we need to use quantum mechanics and look very closely at the individual molecule.

Each group working on a MARVEL project will be assigned their own molecule of astrophysical interest. To date, these have been: methane (CH4), titanium oxide (TiO) [5], acetylene (C2H2) [6], hydrogen sulfide (H2S) and zirconium oxide (ZrO).
Each molecule will have so-called energy levels. These are a defined set of energies, dictated by the laws of quantum mechanics, of which a molecule can hold. The set of energies that are allowed is completely unique for each molecule. A molecule can have electronic, vibrational and rotational energy levels.
When a photon of light passes through a molecule, if it holds one of the unique amounts of energy related to the particular molecule, E, or frequency, f, (which are directly proportional to one another: E=hf, where h is Planck's constant. Note: the terms 'energy' and 'frequency' are sometimes used interchangeably) the molecule will absorb the photon and gain some internal energy.
Then energy states in order of highest to lowest:
- Electronic (energy of the electrons) - only for diatomics
- Vibrational (energy of the molecule vibrating as a whole, stretching and bending)
- Rotational (energy of the molecule rotating as a whole)
The region of importance for astronomical observations using Twinkle is in the IR (infra-red). For diatomics, this will mean electronic, vibrational and rotational transitions need to be considered, but for polyatomics (molecules with more than two atoms), only vibrations and rotations are important.
This gained energy will either cause the molecule to go up an electronic, vibrational or rotational energy level. The difference between these energy levels (called transition frequency, in units of wavenumber, \cm) can be measured experimentally; this has been happening in laboratories around the world for decades. There is therefore alot of information for each molecule which needs to be collected together and analysed.
The ORBYTS MARVEL group's aim is to search through published scientific literature from the last few decades for ALL transition frequencies that have been recorded. This is just the difference between energy levels. What is really needed is the value for each of the two energy levels involved in each recording - we call these upper and lower energies (the molecule has gone from the lower to the upper energy, as a result of absorbing a photon (small amount) of light of a specific frequency, unique to the molecule).
We take all these differences in energy (transition frequencies) and make sure the lower energy level and upper energy level are assigned with labels (which we call quantum numbers) which give the amount of e.g. rotation and vibration of the molecule. These quantum numbers start at 0 to indicate no rotation or vibration (or electronic excitation), and go up in steps of 1.

Once the differences between upper and lower energy levels have been collected and labelled, the data can be input into the MARVEL software. This software analyses all these and (assuming they all agree with each other) outputs a list of energy levels, which is the unique fingerprint for each molecule. It creates a network between these levels, shown in Figure \ref{graphic:para_network}. Here, each point represents and energy level and each line between them the transition which was measured experimentally.
The trouble with lots of different groups around the world measuring these transitions between energy levels (transition=upper energy level-lower energy level, in units of \cm) is that they do not always agree. Sometimes two different groups have labelled two different energy levels with the same label. Sometimes they agree but to within a defined error or uncertainty.
It is the job of the ORBYTS group to make sure that these differences between groups are identified and dealt with. Ultimately they will work towards getting a set of energy levels, with associated uncertainties, which can be published and used by ExoMol and other groups in their scientific research.

In an atom you have energy levels. When an molecule goes from an upper electronic energy level to a lower electronic energy level, a photon of light is emitted which has an wavelength/frequency (remember c = f and E = hf) corresponding to the difference in energy between the two electronic states.

Taking the case of a diatomic molecule, as well as electronic energy levels there are also vibrational and rotational energy levels. Thus when a molecule changes state its electronic, vibrational and rotational states can all change.

Interpreting Spectroscopic Data

For Rotational Levels:

P branch means J' = J" -1
Q branch means J' = J''
R branch means J' = J''+1

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