Speaker
Description
Background
Titan's atmosphere is composed mostly of N$_2$ with small amounts 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. 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 excited states.[1]
\begin{equation}
\textrm{CN(X }^2\Sigma^+_g\textrm{) + M }\leftrightarrow \textrm{ CN(A }^2\Pi, B ^2\Sigma^+_g \textrm{) + M } \hspace{2cm} 1
\end{equation}
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. To this end, we have calculated single point energies and state couplings for the CNN states that correspond to the ground and first excited states of CN by solving the Schr\"{o}dinger equation under the Born-Oppenheimer approximation. These energies were fit to functional forms to produce Potential Energy Surfaces (PESs). The PESs are made up of three pairwise diatomic terms, fit with physics based functions, and one three-body interaction term, fit using a parametrically managed neural network. Following the Compatibilization by Deep Neural Network (CDNN) approach of Meng et al, this neural network simultaneously discovers a diabatic basis and couplings for the states.[4] In such a diabatic basis, the state couplings are smooth and well behaved, and the adiabatic basis can be easily recovered if necessary. Nonadiabatic dynamics calculations using either basis can now be performed to 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 use the electronic structure code MPEC to calculate ab initio single point energies using the Improved Internally Contracted Multi Reference Configuration Interaction with Single and Double excitations (i$^2$c-MRCI(SD)) method.[5] Such calculations require reference orbitals, which we generated using the Complete Active Space Self Consistent Field (CASSCF) method.
There are Quintet A'' and Triplet A'' manifolds for CNN that link the CN(X,A,B)+N($^4$S$_o$) states. Reference orbitals were generated for the lowest 24 states of both of these symmetries at a large number of geometries of the CNN system using CASSCF. In these calculations we used augmented-correlation-consistent-polarized-Valence-Triple-Zeta (aug-ccpVTZ) basis sets for each atom, and an active space consisting of 9 orbitals. The 1s and 2s orbitals for each atom were kept doubly occupied, and the remaining 8 electrons are distributed across the 9 active orbitals. The CASSCF reference orbitals were then used in i$^2$c-MRCI(SD) calculations, where excitations were allowed out of all 2s and 2p orbitals.
Functional Forms
The triatomic CNN energies were fit in a manner similar to Meng et al, where the three body potential is expressed as a sum of three pairwise additive terms, fit with physics-based functions as described in Ref. 6, and a three body interaction term fit with a deep neural network.[4]
Dynamics Simulations
Nonadiabatic dynamics calculations using the CN$_2$ surfaces described here are currently in progress. Both Tully's Fewest Switches Surface Hopping (FSSH) and the Coherent Switching with Decay of Mixing (CSDM) methods are being used to determine rate coefficients for reaction 1 and others.[7,8]
Results
While dynamics calculations are still in progress, the fit PESs already illustrate important features of the CNN system. For the lowest two Quintet A'' states there are more avoided crossings at lower energies for collinear geometries than for perpendicular bisector geometries. 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 has produced ab initio PESs that describe the CNN complex and allow nonadiabatic dynamics simulations of CN (de)excitation by N atoms. Data from high-level electronic structure calculations were fit and diabatized with a parametrically managed neural network. The topology of these fits suggests that collisional (de)excitation of CN by N atoms is likely to proceed through collinear geometries. Thorough analysis of dynamics calculations will show the relative importance of different reaction pathways and 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
- 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.
- Aaron M Brandis and Brett A Cruden. “Titan Atmospheric Entry Radiative Heating”. In: 47th AIAA Thermophysics Conference. 2017, p. 4534.
- 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.
- Qinghui Meng et al. “Automated Learning of a Dense Manifold of Electronic States and Electronic Energy Transfer and Reactions in Singlet O Collisions with N$_2$”. In: Research (2026), p. 0992.
- David W Schwenke. “Introducing MPEC: Massively Parallel Electron Correlation”. In: The Journal of Chemical Physics 158.8 (2023).
- 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.
- John C Tully. “Molecular Dynamics with Electronic Transitions”. In: The Journal of Chemical Physics 93.2 (1990), pp. 1061–1071.
- Chaoyuan Zhu et al. “Coherent Switching with Decay of Mixing: An Improved Treatment of Electronic Coherence for Non-Born–Oppenheimer Trajectories”. In: The Journal of Chemical Physics 121.16 (2004), pp. 7658–7670
Summary
The electric excitation of CN via collision with N atoms plays an important role in the population of radiating species in shock layers around craft entering Titan's atmosphere, but data for the relevant reaction rates is lacking. This work constructed Potential Energy Surfaces of CNN to study these reactions directly. These new PESs enable calculations of these reaction rates that will improve predictions of radiative heat flux from computational fluid dynamics simulations.