Speaker
Description
Background
Titan's atmosphere is composed mostly of N$_2$ with a small amount of CH$_4$, and so, shock layers around craft entering Titan's atmosphere will contain a variety of molecules formed from H, C, and N atoms, including the cyanogen radical CN. Sensitivity analysis has shown that the radiative heat flux predicted by computational fluid dynamics (CFD) simulations of Titan entry has up to 14\% uncertainty due to the rate coefficients for collisional (de)excitation reactions that control the population of CN in its first and second excited states.[1]
$ \hspace{2cm} \textrm{CN}(\textrm{A} ^2\Pi) + \textrm{M} \longleftrightarrow \textrm{CN}(\textrm{B} ^2\Sigma^+_g) + \textrm{M} \hspace{3cm} \textrm{(1)} $
The red and violet emission bands from CN's first and second excited states, respectively, are known to be large sources of radiative heat flux on capsules entering Titan's atmosphere.[2,3] So, the simulated population of CN in its first and second excited states is very important, but, currently has some inherent uncertainty coming from the data for the rate coefficients for reaction (1).
The goal of the current work is to provide improved rate coefficient data for these reactions from first principles quantum chemistry calculations. The first step of this process is to calculate ab initio Potential Energy Surfaces (PESs) and state couplings that link the ground, first excited, and second excited states of CN. PESs are constructed by calculating single point energies and state couplings by solving the Schrodinger equation under the Born-Oppenheimer approximation. These energies and couplings can then be transformed to a diabatic basis where the state couplings are smoother, and fit with functional forms. Then, nonadiabatic dynamics calculations using the diabatic surfaces and couplings will determine the heavy particle (de)excitation rate coefficients at conditions relevant to shock layers around vehicles entering Titan's atmosphere.
Methodology
Electronic Structure Calculations
We focus first on heavy particle (de)excitation by nitrogen atoms, so our current structure calculations are of CNN. We use the new electronic structure code MPEC to calculate ab initio single point energies using the i$^2$c-MRCI(SD) method.[4] I$^2$c-MRCI(SD) calculations require reference orbitals, which we generated using the Multi Configuration Hartree Fock (MCHF) method to optimize a set of Complete Active Space (CAS) orbitals.
Preliminary calculations of N atoms and CN molecules showed that there are Quintet A'' and Triplet A'' manifolds for CNN that link the $\textrm{CN(X,A,B)+N(}^4\textrm{S}_\textrm{o}\textrm{)}$ states. Reference orbitals were generated for the lowest 14 states of both of these symmetries at a large number of geometries of the CNN system. To generate these orbitals, we used augmented-correlation-consistent-polarized-valence-triple-zeta (aug-ccpvtz) basis sets for each atom, and an active space consisting of the 2s orbital on the carbon atom and all the 2p orbitals for each atom. The 1s orbitals for each atom, and the 2s orbitals for the nitrogen atoms were kept doubly occupied. The i$^2$c-MRCI(SD) calculations for those states corresponding to $\textrm{CN(X,A,B)+N(}^4\textrm{S}_\textrm{o}\textrm{)}$ are currently in progress.
Functional Forms
The I$^2$c-MRCI(SD) energies of CN have already been fit to functions using repulsive, short range, and long range terms: $V(R_{C-N}) = V_{Rep} + V_{SR} + V_{LR}$ as described in Ref. [5].The triatomic energies will be fit in a similar manner, also discussed in Ref. [5].
Dynamics Simulations
Once the i$^2$c-MRCI(SD) energies and state couplings are completed, diabatized, and fit with functional forms, they can be used in nonadiabatic dynamics simulations of CN+N collisions that will use Tully's fewest switches surface hopping method to determine rate coefficients for reaction (1) and others.[6]
Results
The i$^2$c-MRCI(SD) calculations are still in progress, but the MCHF calculations already illustrate important features of the CNN system. While the calculations are not perfectly resolved at every geometry, they show important features of the adiabatic states they represent. There are several avoided crossings at intermediate distances of 3.5-6 a$_0$ for the first three Quintet A'' states at collinear geometries, while for the perpendicular bisector geometries there is only one avoided crossing near 2.4 a$_0$. These features indicate that the heavy particle (de)excitation in reaction (1) is more likely to occur through collinear geometries because the states of interest are more closely coupled there.
Conclusions and Further Work
This work will produce ab initio PESs that describe the CNN complex and allow nonadiabatic dynamics simulations of CN (de)excitation by N atoms. The electronic structure calculations to form the PESs are underway. Reference orbitals have been generated at a large number of triatomic geometries for the symmetries of interest and show multiple avoided crossings at collinear arrangements. This suggests that collisional (de)excitation of CN by N atoms is likely to proceed through these geometries. Once the PESs are completed, thorough analysis will show possible reaction pathways in detail, and nonadiabatic dynamics simulations will determine improved rate coefficients that can be used in CFD simulations to lower uncertainties in radiative heat flux predictions for atmospheric entry to Titan.
References
[1] Thomas K West IV et al. “Uncertainty Analysis of Radiative Heating Predictions for Titan Entry”. In: Journal of Thermophysics and Heat Transfer 30.2 (2016), pp. 438–451.
[2] Aaron M Brandis and Brett A Cruden. “Titan Atmospheric Entry Radiative Heating”. In: 47th AIAA Thermophysics Conference. 2017, p. 4534.
[3] LM Walpot et al. “Convective and Radiative Heat Flux Prediction of Huygens’s Entry on Titan”. In: Journal of Thermophysics and Heat Transfer 20.4 (2006), pp. 663–671.
[4] David W Schwenke. “Introducing MPEC: Massively Parallel Electron Correlation”. In: The Journal of Chemical Physics 158.8 (2023).
[5] Richard L Jaffe, David W Schwenke, and Marco Panesi. “Chapter 3: First Principles Calculation of Heavy Particle Rate Coefficients”. In: Hypersonic Nonequilibrium Flows: Fundamentals and Recent Advances. American Institute of Aeronautics and Astronautics, Inc., 2015.
[6] John C Tully. “Molecular Dynamics with Electronic Transitions”. In: The Journal of Chemical Physics 93.2 (1990), pp. 1061–1071.
Summary
The CN molecule is an important contributor to radiative heat flux in shock layers around vehicles entering Titan's atmosphere. Deficiencies in the current data for heavy particle (de)excitation rate coefficients of CN lead to uncertainties in the population of CN in its first and second excited states. This in turn leads to uncertainties in the radiative heat flux predicted by Computational Fluid Dynamics (CFD) simulations of Titan atmospheric entry. This work performs ab initio electronic structure calculations of the CNN complex to create Potential Energy Surfaces (PESs) that correlate to the ground and first and second excited states of CN. Preliminary electronic structure calculations have shown that there are six states of CNN (three Quintet A'' and three Triplet A'') correlating to asymptotes with these CN states and a ground state nitrogen atom. Initial calculations of these states suggest that heavy particle (de)excitation of CN by N atoms is likely to proceed through collinear geometries. Complete PESs will show all of the reaction pathways in detail, and will be used in nonadiabatic dynamics calculations to evaluate improved rate coefficients and reduce uncertainty in the radiative heat flux during Titan entry.
