Excited states and electronic structures of radicals, and their incorporation/representation in RMG

[alongd]

This issue is related to the recent efforts of including and better representing excited species (#171, #172). We have data for reactions of excited OH from the FFCM1 project (including thermo for OH):

CH(D)+O2<=>CO+OH*                             1.800E+11    0.000        0.00
H+O+M<=>OH*+M                                 5.450E+12    0.000        0.00
2OH+H<=>OH*+H2O                               1.450E+15    0.000        0.00
OH*<=>OH                                      1.450E+06    0.000        0.00
OH*+N2<=>OH+N2                                1.080E+11    0.500    -1238.00
OH*+O2<=>OH+O2                                2.100E+12    0.500     -482.00
OH*+H2O<=>OH+H2O                              5.920E+12    0.500     -861.00
OH*+H2<=>OH+H2                                2.950E+12    0.500     -444.00
OH*+CO2<=>OH+CO2                              2.750E+12    0.500     -968.00
OH*+CO<=>OH+CO                                3.230E+12    0.500     -787.00
OH*+CH4<=>OH+CH4                              3.360E+12    0.500     -635.00
OH*+Ar<=>OH+Ar                                1.250E+10    0.500        0.00
OH*+He<=>OH+He                                1.950E+09    0.500        0.00

However, I'm not sure whether we can represent OH* uniquely using AdjList. It is "vibrationally excited", and has the same electronic configuration as the ground state OH radical, see this paper for example.

It might be important for some cases when we compare predictions to experimental results, but perhaps it's not a must-have in RMG right now. In any case, it is worth a discussion.

[rwest]

Thanks for digging in to this. Whilst the paper you refer to shows there is such a thing as vibrationally excited OH, I'm not sure it's what most combustion kinetic modelers mean by OH.... See this paper for example http://pubs.acs.org/doi/abs/10.1021/jp035568j suggesting the OH in your first reaction CH(D)+O2<=>CO+OH* is the electronically excited A²Σ⁺

But what this means for adjacency list, I'm still not sure :)

I think I've seen this approach before:

OH
multiplicity 2
1 O u1 p2 c0 {2,S}
2 H u0 p0 c0 {1,S}

OH*
multiplicity 4
1 O u3 p1 c0 {2,S}
2 H u0 p0 c0 {1,S}

I've never really understood those A²Σ⁺ designations as well as I wish 🤔

[alongd]

I don't really understand the molecular term symbol either... :) So far I mainly looked at the 2S+1 multiplicity term. All the studies I've seen, including the one you suggested (Fujita 1982, Clyne 1979, Bechtel 1979, Smooke 1998, Carl 2003) refer to the OH ground state as X²Π and to the OH excited state as A²Σ⁺. I understand that both states have a multiplicity of 2. The Fujita paper refers to it as "the vibrationally excited OH radical in the electronic ground state". It could also be that there's a combustion-relevant electronic excited state which is a doublet as well, if one of the three unpaired electrons have an opposite spin to the other two(?).

I think Smooke's paper is most relevant to our case (I know Smooke has some very good CH4 models, and this specific paper deals with laminar diffusion flames). He describes OH as A²Σ⁺, however he also describes CH as A²Δ, where most other sources refer to CH* as a4Σ-...

So we have the following possibilities:

OH
multiplicity 2
1 O u1 p2 c0 {2,S}
2 H u0 p0 c0 {1,S}

OH* (option A - electronically excited)
multiplicity 4
1 O u3 p1 c0 {2,S}
2 H u0 p0 c0 {1,S}

OH* (option B - electronically excited, but still a doublet)
multiplicity 2
1 O u3 p1 c0 {2,S}
2 H u0 p0 c0 {1,S}

OH* (option C - vibrationally excited, no unique AdjList...)
multiplicity 2
1 O u1 p2 c0 {2,S}
2 H u0 p0 c0 {1,S}

Still looking into it.

[alongd]

We discussed the ground state vs. excited state of [C], [CH], [CH2] and [OH] with the RMG developers and Prof. Green. This issue might be a bit confusing, and certainly many of us (me included) weren't aware of the correct ground state of some of the species discussed here. I'll document here my current understanding of this issue, as well as our suggestions for implementation in RMG.

A general good source for radical structures is Molecular Spectra and Molecular Structure by Huber and Herzberg (e.g., see [CH] on p. 142).

In a nutshell (my current understanding), in Molecular Term Symbols X always refers to the ground state; A/B/C... refer to the 1st, 2nd, 3rd... excited states with the same multiplicity as the ground state; a/b/c... refer to the 1st, 2nd, 3rd... excited states with different multiplicities than the ground state. The upper-case number is the multiplicity. The capital Greek letter Σ or Π refers to the projection of the orbital angular momentum along the internuclear axis (i.e., Σ means that the electron's orbital angular momentum in question is parallel to the molecule axis, whereas Π means that it is perpendicular).

[C]

The ground state for [C] is X³P₀ (i.e., with one lone pair). The excited state than I suspect is relevant to us (combustion) is the singlet form - C(S) with two lone pairs - rather than the quintet form with four unpaired electrons. However, like any other species, this specific excited state should be verified for each case with the library's source. There's no problem to implement all states in RMG.

Sources: Mebel 2002, Towson University Chemistry Tutoring Center, Wikipedia on atomic carbon.

[CH]

The ground state for [CH] is X²Π (i.e., with one lone pair). Excited states could be doublets as well (A²Δ, B²Σ⁻, C²Σ⁺) or a quartet (a⁴Σ⁻). When studying flames with laser-induced fluorescence (Long & Smooke 1998) the excited and measured [CH]* state refers to A²Δ. It is very reasonable that in FFCM and similar projects [CH]* was measured using this technique, and therefore the correct representation is A²Δ in these RMG libraries (should be verified, though). Unfortunately, currently we don't have a unique representation for this excited state in RMG.

• One idea was to add an optional flag to the AdjList. This won't make the excited state react differently in RMG, but will at least differentiate between the states, making them two unique species.
• Another (simpler) approach would be to append the [CH] + M <=> [CH]* + M reactions from FFCM to the final Chemkin file if one is interested in comparing RMG's predictions to experimentally measured [CH]*. Of course, in this manner we don't capture the effect of [CH]* on the model generation, but arguably we could be capturing the bulk part of the [CH] <=> [CH]* transitions.

Since currently there is no such (urgent) need, we will simply comment the FFCM kinetic library appropriately to reflect the second option. But everyone's welcome to pick up this glove.

Sources: Long and Smooke 1998, M.C. Lin 2000, Pryor 1980, Baluja 2001, Wikipedia on Methylidyne radical,

[CH2]

The ground state for [CH2] is X³B₁ (i.e., bi-rad with no lone pairs). The "main" excited state is a¹A₁ (i.e., singlet with a lone pair). This case is simple to implement in RMG.

Sources: Pullman 1977, Wikipedia on Methylene (compound).

[OH]

The ground state for [OH] is X²Π (mono-rad, multiplicity 2). The "main" excited state is A²Σ⁺ (mono-rad, multiplicity 2 as well). The difference between these states is the projection of the orbital angular momentum along the internuclear axis. In the ground state, it is perpendicular to the internuclear axis. In the excited state (marked with A to denote it's the first excited state with the same multiplicity as the ground state) it is parallel to the internuclear axis. Therefore there's a spatial interaction between the unpaired electron and the oxygen lone pair\s, which causes this excited state to be ~100 kcal/mol higher in energy than the ground state. The OH* does not occur in combustion (in a significant amount), unless a laser excitation measurement is conducted. It does, naturally, react differently than the ground state.

The case here is similar to the [CH]* case described above, and there's currently no unique representation for [OH]* in RMG. We do have the various [OH] + M <=> [OH]* + M transitions from FFCM, which can be appended post mechanism generation. Currently we will not add [OH]* to RMG (we'll comment the FFCM library accordingly like the [CH]* case)

Sources: Carl 2003, Long and Smooke 1998, Bechtel 1979, Clyne 1979, Fujita 1982.

[rwest]

Thanks for taking the time to write this up clearly!

[rwest]

One thought: when we redesigned the adjacency list syntax, we imagined that additional keywords could be added in a similar fashion to "multiplicity". Eg. one could have

OH
multiplicity 2
1 O u1 p2 c0 {2,S}
2 H u0 p0 c0 {1,S}

and

OH*
multiplicity 2
excitedelectronicstate 1
1 O u1 p2 c0 {2,S}
2 H u0 p0 c0 {1,S}

or even

OH*
multiplicity 2
orbitalangularmomentum sigma+
1 O u1 p2 c0 {2,S}
2 H u0 p0 c0 {1,S}

So I think representation is easily fixed without breaking current adjacancy lists.

What to do with estimating its properties and reactivity etc. I'm not sure. We could just say anything in an excitedelectronicstate is not (subgraph)isomorphic with anything unless that is explicitly in the same excitedelectronicstate, thus preventing it from matching thermo estimates, reaction templates, etc. except where specifically included in a library.

Thoughts?

[alongd]

I like this approach.

Also, we might want to use a different library for the excited states that are only available once a laser is fired in an experimental system, so we won't generate [OH]* and [CH]* for normal runs.

[alongd]

For excited species with (currently) identical adjLists to the ground state we'd like to implement something like:

OH(A2Sp)
multiplicity 2
molecularTermSymbol A2Sigma+
1 O u1 p2 c0 {2,S} 
2 H u0 p0 c0 {1,S}

as @rwest suggested