Vibrational excitation of NH3 and H2O induced by collisions

Vibrational excitation of NH3 and H2O induced by collisions Water in the Universe - Oct. 2025 Jérôme Loreau Department of Chemistry KU Leuven Outline Introduction Part 1: Ro-vibrational excitation in NH3 - He collisions Part 2: Vibrational excitation in H2O - H2 collisions Introduction Why study collisional excitation? •Interpret observations in astrophysical media where local thermodynamics conditions are not fulfilled •Rate coefficients used as input in radiative transfer models •Requires data for collisions of molecules with He/H2 over wide range of temperatures k(T) 1 2 A21 C21 C12 B21 B12 <latexit sha1_base64="Ac+qHpqY4ZQITGi2Ed18gwtdamU=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9kUQY+lXjxWsB/QLiWbZtvYbLIkWaEs/Q9ePCji1f/jzX9j2u5BWx8MPN6bYWZemAhurO9/e4WNza3tneJuaW//4PCofHzSNirVlLWoEkp3Q2KY4JK1LLeCdRPNSBwK1gknt3O/88S04Uo+2GnCgpiMJI84JdZJ7cYgw7XZoFzxq/4CaJ3gnFQgR3NQ/uoPFU1jJi0VxJge9hMbZERbTgWblfqpYQmhEzJiPUcliZkJssW1M3ThlCGKlHYlLVqovycyEhszjUPXGRM7NqveXPzP66U2ugkyLpPUMkmXi6JUIKvQ/HU05JpRK6aOEKq5uxXRMdGEWhdQyYWAV19eJ+1aFftVfH9VqTfyOIpwBudwCRiuoQ530IQWUHiEZ3iFN095L96797FsLXj5zCn8gff5A+/JjrI=</latexit> <latexit sha1_base64="Ac+qHpqY4ZQITGi2Ed18gwtdamU=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9kUQY+lXjxWsB/QLiWbZtvYbLIkWaEs/Q9ePCji1f/jzX9j2u5BWx8MPN6bYWZemAhurO9/e4WNza3tneJuaW//4PCofHzSNirVlLWoEkp3Q2KY4JK1LLeCdRPNSBwK1gknt3O/88S04Uo+2GnCgpiMJI84JdZJ7cYgw7XZoFzxq/4CaJ3gnFQgR3NQ/uoPFU1jJi0VxJge9hMbZERbTgWblfqpYQmhEzJiPUcliZkJssW1M3ThlCGKlHYlLVqovycyEhszjUPXGRM7NqveXPzP66U2ugkyLpPUMkmXi6JUIKvQ/HU05JpRK6aOEKq5uxXRMdGEWhdQyYWAV19eJ+1aFftVfH9VqTfyOIpwBudwCRiuoQ530IQWUHiEZ3iFN095L96797FsLXj5zCn8gff5A+/JjrI=</latexit> <latexit sha1_base64="Ac+qHpqY4ZQITGi2Ed18gwtdamU=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9kUQY+lXjxWsB/QLiWbZtvYbLIkWaEs/Q9ePCji1f/jzX9j2u5BWx8MPN6bYWZemAhurO9/e4WNza3tneJuaW//4PCofHzSNirVlLWoEkp3Q2KY4JK1LLeCdRPNSBwK1gknt3O/88S04Uo+2GnCgpiMJI84JdZJ7cYgw7XZoFzxq/4CaJ3gnFQgR3NQ/uoPFU1jJi0VxJge9hMbZERbTgWblfqpYQmhEzJiPUcliZkJssW1M3ThlCGKlHYlLVqovycyEhszjUPXGRM7NqveXPzP66U2ugkyLpPUMkmXi6JUIKvQ/HU05JpRK6aOEKq5uxXRMdGEWhdQyYWAV19eJ+1aFftVfH9VqTfyOIpwBudwCRiuoQ530IQWUHiEZ3iFN095L96797FsLXj5zCn8gff5A+/JjrI=</latexit> <latexit sha1_base64="Ac+qHpqY4ZQITGi2Ed18gwtdamU=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9kUQY+lXjxWsB/QLiWbZtvYbLIkWaEs/Q9ePCji1f/jzX9j2u5BWx8MPN6bYWZemAhurO9/e4WNza3tneJuaW//4PCofHzSNirVlLWoEkp3Q2KY4JK1LLeCdRPNSBwK1gknt3O/88S04Uo+2GnCgpiMJI84JdZJ7cYgw7XZoFzxq/4CaJ3gnFQgR3NQ/uoPFU1jJi0VxJge9hMbZERbTgWblfqpYQmhEzJiPUcliZkJssW1M3ThlCGKlHYlLVqovycyEhszjUPXGRM7NqveXPzP66U2ugkyLpPUMkmXi6JUIKvQ/HU05JpRK6aOEKq5uxXRMdGEWhdQyYWAV19eJ+1aFftVfH9VqTfyOIpwBudwCRiuoQ530IQWUHiEZ3iFN095L96797FsLXj5zCn8gff5A+/JjrI=</latexit> •Ubiquitous molecules in space (ISM, atmospheres, disks, etc) •Can be used as a probe of physical conditions •Constraints on nitrogen and oxygen chemistry •Prototypical systems for experimentalists (collisions, spectroscopy) Why NH3 and H2O? Previous works on collisional vibrational excitation of molecules (with QM methods, for astro) is limited: •Diatomic molecules + He, H2 (ex: CO, SO, CN, HCl, H2, …) •Linear molecules + He, H2 (HCN, C3, … , Stoecklin et al.) •Polyatomic molecules: H2O + H2 (Stoecklin et al.; Wiesenfeld), CH3OH + He (Pottage et al.), CO2 + He (Selim et al.), CH3 + He (Ma et al.), NH3 + He (Loreau and van der Avoird) Grant et al, ApJL 947 L6 (2023) Understand spectra from high-T environments: disks, AGB stars,… Why study ro-vibrational excitation? Challenges for ro-vibrational excitation with QM methods: •Construction of the PES (increased dimensionality) •Increased number of coupled equations (more internal states available) •Rovibrational excitation of molecules by H2 is expected to be very different than by He •At high temperatures data for collision with H2 (j > 0) is also needed Alternatives to fully QM (close-coupling, CC): •QM + decoupling (coupled states, CS + nearest neighbour) •vibrational close-coupling rotational infinite-order-sudden (VCC-IOS) •Multichannel distorted-wave Born approximation •QCT •… •Need to benchmark approximations! =R1X ↵ |↵i↵(R) ~2 2µ d2↵ dR2+X ↵0 h↵0|HA+HB+V+ L2 2µR2|↵i↵=E↵ <latexit sha1_base64="F52NcJyK23j1mCGcw+8mYEKKds8=">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</latexit> <latexit sha1_base64="F52NcJyK23j1mCGcw+8mYEKKds8=">AAACpHicbVHLjtMwFHXCawiPKbBkc6ECIVVUSYUEC5AGEKKLWXSAdkaq28hxnMYa24lsB6my8mX8BTv+BreJxDy40pWOz3363KwW3Ng4/hOEN27eun3n4G507/6Dh4eDR48Xpmo0ZXNaiUqfZcQwwRWbW24FO6s1IzIT7DQ7/7yLn/5k2vBK/bDbmq0k2ShecEqsp9LBr9e40IQ6XGZEryetm2DZtB2XryeAaclTTERdEmhd/s2nRCPAppGp6+g1rjWXrMWCqI1gcInFfraFafpxNE0/wQgW3rvmDmcFHLf7keBnwq41dPldC6z7hv9WiD58ufBKB8N4HO8NroOkB0PU2ywd/MZ5RRvJlKWCGLNM4tquHNGWU8HaCDeG1YSekw1beqiIZGbl9iK38MIzORSV9q4s7NmLFY5IY7Yy85mS2NJcje3I/8WWjS3erRxXdWOZot2gohFgK9hdDHKuGbVi6wGhmvtdgZbEa2j9XSMvQnL1y9fBYjJO4nFy8mZ49L6X4wA9Rc/RK5Sgt+gITdEMzRENngVfg1lwEr4Mj8Pv4bxLDYO+5gm6ZOH6L6qqzlQ=</latexit> <latexit sha1_base64="F52NcJyK23j1mCGcw+8mYEKKds8=">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</latexit> <latexit sha1_base64="F52NcJyK23j1mCGcw+8mYEKKds8=">AAACpHicbVHLjtMwFHXCawiPKbBkc6ECIVVUSYUEC5AGEKKLWXSAdkaq28hxnMYa24lsB6my8mX8BTv+BreJxDy40pWOz3363KwW3Ng4/hOEN27eun3n4G507/6Dh4eDR48Xpmo0ZXNaiUqfZcQwwRWbW24FO6s1IzIT7DQ7/7yLn/5k2vBK/bDbmq0k2ShecEqsp9LBr9e40IQ6XGZEryetm2DZtB2XryeAaclTTERdEmhd/s2nRCPAppGp6+g1rjWXrMWCqI1gcInFfraFafpxNE0/wQgW3rvmDmcFHLf7keBnwq41dPldC6z7hv9WiD58ufBKB8N4HO8NroOkB0PU2ywd/MZ5RRvJlKWCGLNM4tquHNGWU8HaCDeG1YSekw1beqiIZGbl9iK38MIzORSV9q4s7NmLFY5IY7Yy85mS2NJcje3I/8WWjS3erRxXdWOZot2gohFgK9hdDHKuGbVi6wGhmvtdgZbEa2j9XSMvQnL1y9fBYjJO4nFy8mZ49L6X4wA9Rc/RK5Sgt+gITdEMzRENngVfg1lwEr4Mj8Pv4bxLDYO+5gm6ZOH6L6qqzlQ=</latexit> NH3 - He collisions with CC Vibrationally-excited NH3 in space: •Six vibrational modes: umbrella bend (~10.5 m), asymmetric bend (~6.1 m), symmetric stretch (~3 m), asymmetric stretch (~2.9 m) •Observed in circumstellar enveloppes, protostars and star-forming regions, (protoplanetary disks?). The mode is the most relevant. •In circumstellar enveloppes, [NH3] is much higher than predicted; in protoplanetary disks it is lower… New observations with JWST? •No rate coefficients for excitation by He or H2… v2 μ μ μ μ v2 Wong et al., A&A 612 A48 (2018) Pontoppidan et al., ApJ 874 92 (2019) Open questions: -Does the umbrella motion impact pure rotational transitions in v = 0? (assumption: no) -Are the rate coefficients for rotational excitation in v = 1 identical to v = 0? (assumption: yes) -What is the magnitude of the v = 1 0 rate coefficients? (assumption: ~20 times smaller than v = 0 0) -Can we use NH3 - He collisions as a test case towards NH3 - H2 collisions? 0.79 cm-1 35.2 cm-1 950 cm-1 V(𝜌) 𝜌 90° 112.1° (𝜌e) + + - - v=0 v=1 He Umbrella vibrational mode ( ) of NH3 : splitting of levels ν2 j± k •(mod 3): ortho states •(mod 3): para states •±: inversion •Due to nuclear spin statistics for k = 0 half the levels are missing •ortho-para conversion forbidden k=0 k6=0 Rotational states of NH3: 0 50 100 150 200 Energy (cm-1) 0010+ 2030+ 401121314111+ 21+ 31+ 41+ 22324222+ 32+ 42+ 334333+ 43+ 4444+ 5555+ k=0 k=1 k=2 k=3 Scattering of NH3 by He: quantum-mechanical close coupling (CC) method with 4D PES R ✓  ⇢ He Gubbels et al., JCP 136 074301 (2012) Approach 3: complete description of umbrella motion Hamiltonian for NH3-He includes explicit description of umbrella motion; =R1X ↵ |↵i↵(R) ϕ± v ˆ H=X i ˆ j2 i 2Iii(⇢)+ˆ T(⇢)+V(⇢) ~2 2µR @2 @R2R+1 2µR2(ˆ J2+ˆ j2 2ˆ j·ˆ J)+V(⇢,R,✓,') NH3 monomer ϕ± 0=1 2(δ(ρ−ρe)±δ(π−ρ+ρe)) + PES independent of ρ -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 50 60 70 80 90 100 110 120 130 wave function rho (deg) NH3 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 50 60 70 80 90 100 110 120 130 wave function squared rho (deg) NH3 ND3 184303-5 J. Loreau and A. van der Avoird J. Chem. Phys. 143, 184303 (2015) corresponding to the inversion motion, given by ˆ T(⇢)=1 2g1 4@ @⇢ I1 ⇢⇢g1 2@⇢g1 4,(4) where g(⇢)=IxxIyyIzzI⇢⇢ is expressed as a function of the principal inertia moments of ammonia and the moment of inertia I⇢⇢ associated with the umbrella motion.50 Vumb(⇢) is the double-well potential for the umbrella motion, with a barrier at ⇢=⇡/2. We used the same parametrization as in Ref. 25, Vumb(⇢)=k⇢ 2✓⇢⇡ 2◆2 +a⇢exp "b⇢✓⇢⇡ 2◆2#.(5) Due to tunnelling through the barrier, the first two vibrational states are split into doublets. The three parameters are fitted in order to reproduce the experimental v=0!1 transition frequency (949.9 cm1) as well as the splittings in the v=0 (0.79 cm1) and v=1 (35.2 cm1) states. The parameters for NH3–He are given in Ref. 25. For the other rare gases, we re-fitted the parameters to reflect the fact that the length of the N–H bonds used to compute the PES was slightly di↵erent. We used k⇢=92 026 cm1rad2, a⇢=23 383 cm1, and b⇢=3.205 rad2. For ND3, the splittings are smaller (0.053 cm1in the v=0 level) and the parameters are k⇢=93 170 cm1rad2,a⇢=23 349 cm1, and b⇢=3.236 rad2. In our calculations, we kept the four lowest states ± v(⇢) of the umbrella motion (where ±denotes the parity of the function under the inversion), corresponding to v=0 and v=1. We will compare the results obtained using the Hamiltonian (3) with those obtained with a model1,37 that approximates the ground tunneling states as symmetric or antisymmetric combinations of the equilibrium structures, |±i=[f(⇢⇢e)±f(⇡⇢+⇢e)]/p2, where f(x)is a Dirac delta function localized at x=0. This model only requires the knowledge of the PES at the equilibrium angle ⇢=⇢e and has been shown to give accurate results11,25 by direct comparison with the “exact” method using Hamiltonian (3). However, at collision energies lower than the inversion splitting (0.79 cm1), this approximation is not expected to be valid. The inelastic scattering cross sections were computed using the quantum-mechanical close-coupling method, in which the total wave function is expanded as a sum of products of radial and angular functions. Upon integration over the angular coordinates, the Schrödinger equation leads to a set of coupled second-order di↵erential equations to be solved using appropriate boundary conditions.25 The total angular momentum Jand its projection Mon the space-fixed zaxis are conserved during the collision. The molecular symmetry group51 of inverting NH3, and also of the NH3–Rg complexes, is D3h(M). NH3has two nuclear spin configurations depending on the value of k, the projection of the angular momentum jon the symmetry axis of the molecule. Rotational levels with k=0,3,6,... (ortho-NH3) correspond to the A2representations, while levels for which kis not a multiple of 3 (para-NH3) correspond to the Erepresentations. The levels corresponding to the A1representations are forbidden by nuclear spin statistics. The di↵erent spin configurations cannot interconvert during collisions. In the case of ND3, there are no restrictions due to nuclear spin statistics, and states with k=0,3,6,... can correspond either to the A1or the A2representations, so that there are three nuclear spin modifications. The rotational levels of NH3and ND3are labeled as |jk±i, where ±refers to the symmetry under inversion. The lowest energy levels of NH3are shown in Fig. 2. B. Computational details The four lowest levels ± v(⇢)of the umbrella motion were calculated with the sinc-function discrete variable representation method.52 Tests were performed with six umbrella functions, which showed that our calculations are converged. The coupled equations were solved with the renormalized Numerov propagator for energies in the range 0.001–300 cm1. The size of the grid in R, its number of points, and the maximum value of the total angular momentum Jdepended on the collision energy as well as on the colliding partners. Numerous tests were performed to make sure that the cross sections were converged. At the lowest energies considered, a typical grid ranged from 4 a0to 100 a0, with the number of points increasing from about 200 for He to 600 for Xe. At the highest energies, we chose grids ranging from 4 a0 to 30 a0with about 150–200 points for the various rare gases. The maximum value of Jrequired to obtain converged cross sections increased with the reduced mass of the system. At the highest energy, 45 partial waves were required to converge the elastic cross sections for NH3–He, while for NH3–Xe that number increased to 175. The convergence was faster for the inelastic cross sections. The size of the angular basis set was truncated at jmax =7 for NH3and jmax =9 for ND3. C. Results For the reasons mentioned above, we will from now on focus on the initial state 11. Unless otherwise stated, the FIG. 2. Diagram of the lowest rotational energy levels of NH3labeled as jk±. The levels of ortho-NH3are shown in black while those of para-NH3 are shown in red. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 164.15.17.135 On: Thu, 12 Nov 2015 12:17:38 184303-5 J. Loreau and A. van der Avoird J. Chem. Phys. 143, 184303 (2015) corresponding to the inversion motion, given by ˆ T(⇢)=1 2g1 4@ @⇢ I1 ⇢⇢g1 2@⇢g1 4,(4) where g(⇢)=IxxIyyIzzI⇢⇢ is expressed as a function of the principal inertia moments of ammonia and the moment of inertia I⇢⇢ associated with the umbrella motion.50 Vumb(⇢) is the double-well potential for the umbrella motion, with a barrier at ⇢=⇡/2. We used the same parametrization as in Ref. 25, Vumb(⇢)=k⇢ 2✓⇢⇡ 2◆2 +a⇢exp "b⇢✓⇢⇡ 2◆2#.(5) Due to tunnelling through the barrier, the first two vibrational states are split into doublets. The three parameters are fitted in order to reproduce the experimental v=0!1 transition frequency (949.9 cm1) as well as the splittings in the v=0 (0.79 cm1) and v=1 (35.2 cm1) states. The parameters for NH3–He are given in Ref. 25. For the other rare gases, we re-fitted the parameters to reflect the fact that the length of the N–H bonds used to compute the PES was slightly di↵erent. We used k⇢=92 026 cm1rad2, a⇢=23 383 cm1, and b⇢=3.205 rad2. For ND3, the splittings are smaller (0.053 cm1in the v=0 level) and the parameters are k⇢=93 170 cm1rad2,a⇢=23 349 cm1, and b⇢=3.236 rad2. In our calculations, we kept the four lowest states ± v(⇢) of the umbrella motion (where ±denotes the parity of the function under the inversion), corresponding to v=0 and v=1. We will compare the results obtained using the Hamiltonian (3) with those obtained with a model1,37 that approximates the ground tunneling states as symmetric or antisymmetric combinations of the equilibrium structures, |±i=[f(⇢⇢e)±f(⇡⇢+⇢e)]/p2, where f(x)is a Dirac delta function localized at x=0. This model only requires the knowledge of the PES at the equilibrium angle ⇢=⇢e and has been shown to give accurate results11,25 by direct comparison with the “exact” method using Hamiltonian (3). However, at collision energies lower than the inversion splitting (0.79 cm1), this approximation is not expected to be valid. The inelastic scattering cross sections were computed using the quantum-mechanical close-coupling method, in which the total wave function is expanded as a sum of products of radial and angular functions. Upon integration over the angular coordinates, the Schrödinger equation leads to a set of coupled second-order di↵erential equations to be solved using appropriate boundary conditions.25 The total angular momentum Jand its projection Mon the space-fixed zaxis are conserved during the collision. The molecular symmetry group51 of inverting NH3, and also of the NH3–Rg complexes, is D3h(M). NH3has two nuclear spin configurations depending on the value of k, the projection of the angular momentum jon the symmetry axis of the molecule. Rotational levels with k=0,3,6,... (ortho-NH3) correspond to the A2representations, while levels for which kis not a multiple of 3 (para-NH3) correspond to the Erepresentations. The levels corresponding to the A1representations are forbidden by nuclear spin statistics. The di↵erent spin configurations cannot interconvert during collisions. In the case of ND3, there are no restrictions due to nuclear spin statistics, and states with k=0,3,6,... can correspond either to the A1or the A2representations, so that there are three nuclear spin modifications. The rotational levels of NH3and ND3are labeled as |jk±i, where ±refers to the symmetry under inversion. The lowest energy levels of NH3are shown in Fig. 2. B. Computational details The four lowest levels ± v(⇢)of the umbrella motion were calculated with the sinc-function discrete variable representation method.52 Tests were performed with six umbrella functions, which showed that our calculations are converged. The coupled equations were solved with the renormalized Numerov propagator for energies in the range 0.001–300 cm1. The size of the grid in R, its number of points, and the maximum value of the total angular momentum Jdepended on the collision energy as well as on the colliding partners. Numerous tests were performed to make sure that the cross sections were converged. At the lowest energies considered, a typical grid ranged from 4 a0to 100 a0, with the number of points increasing from about 200 for He to 600 for Xe. At the highest energies, we chose grids ranging from 4 a0 to 30 a0with about 150–200 points for the various rare gases. The maximum value of Jrequired to obtain converged cross sections increased with the reduced mass of the system. At the highest energy, 45 partial waves were required to converge the elastic cross sections for NH3–He, while for NH3–Xe that number increased to 175. The convergence was faster for the inelastic cross sections. The size of the angular basis set was truncated at jmax =7 for NH3and jmax =9 for ND3. C. Results For the reasons mentioned above, we will from now on focus on the initial state 11. Unless otherwise stated, the FIG. 2. Diagram of the lowest rotational energy levels of NH3labeled as jk±. The levels of ortho-NH3are shown in black while those of para-NH3 are shown in red. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 164.15.17.135 On: Thu, 12 Nov 2015 12:17:38 Approach 1: neglect umbrella motion no + - transitions Approach 2: model ground vibrational state as combination of equilibrium structures, and What is the magnitude of the v = 1 0 rate coefficients? Cross sections for NH3(v = 1, jk ) NH3(v’, j’k’ ) •Transitions which conserve the parity of the umbrella wave function (+ +, - -) have larger cross sections •Cross sections v = 1 0 are ~105 smaller than v = 1 1 jk = 2110-6 10-5 10-4 10-3 10-2 10-1 100 101 10 20 30 40 50 60 70 80 90 100 Cross section (10-16 cm2) Energy (cm-1) v’=1, j’k’ = 22v’=1, j’k’ = 22+ v’=0, j’k’ = 22v’=0, j’k’ = 22+ T = 150 K factor 3 Difference decreases as T increases Rotational transitions in v = 0 vs. in v = 1