Multi-arrangement quantum dynamics in 6D: cis–trans isomerization and 1,3-hydrogen transfer in HONO

doi:10.1016/j.chemphys.2004.06.038

Chemical Physics

Volume 304, Issues 1–2, 13 September 2004, Pages 79-90

https://doi.org/10.1016/j.chemphys.2004.06.038 Get rights and content

Abstract

The overtone spectrum and wave packet dynamics of nitrous acid (HONO) are studied with a global six-dimensional potential energy function interpolated directly from density functional calculations together with the corresponding dipole hypersurfaces. The quantum dynamics for the cis–trans isomerization and the symmetric 1,3-hydrogen transfer are treated in full dimensionality in terms of the generalized Z-matrix discrete variable representation. For the quantum mechanical description of complicated rearrangements a new approach to multi-arrangement quantum dynamics is introduced and applied to the symmetric hydrogen exchange tunneling in cis-HONO. The cis–trans isomerization is found to be dominated by adiabatic barrier crossing with only minor tunneling contributions, but with pronounced mode selectivity. The OH-stretching overtones of trans-HONO are adiabatically almost completely separated from the OH torsional dynamics with extremely slow intramolecular energy redistribution. The 1,3-hydrogen transfer, by contrast, proceeds largely via coherent tunneling even significantly below the barrier. The process is clearly non-adiabatic (at least in terms of valence coordinates) but remains highly state specific. While the absorption spectrum of trans-HONO remains largely unaffected, OH-stretching overtones of cis-HONO (above the barrier between 2ν_OH and 3ν_OH) decompose into highly fragmented absorption patterns with corresponding tunneling periods on the picosecond time scale.

Introduction

In the limit of sufficiently high excitation energies even semi-rigid vibrations undergo large amplitudes eventually leading to chemical reactions. Such processes range from conformational changes to the rearrangement of chemical bonds even in the case of strictly bound state dynamics. The spectroscopy of high overtones thus allows in principle to follow how vibrational motion eventually translates into structural change and chemical reactions, i.e. the intramolecular energy redistribution as a primary step of unimolecular reactions. But only a detailed model of the dominant dynamical processes allows to translate experimental spectroscopic observations into an explicit picture of the molecular motion, which is the main subject of this contribution. From a chemist’s point of view arguably the most intriguing aspect concerns the relation between the dynamical behaviour of a molecule and certain structural features.

With its very light mass and the ensuing dynamical consequences (delocalization, tunneling) the motion of hydrogen atoms in different molecular environments deserves special attention. As a compromise between complexity and theoretical (or rather numerical) accessibility tetratomic molecules afford the most suitable model systems. The role of nitrous acid (HONO) in atmospheric chemistry has received considerable attention in recent years. The resulting large body of experimental information on its spectroscopy, photochemistry, and reaction kinetics makes it a particularly attractive model system for the interplay between intramolecular dynamics and chemical reactions. For example, HONO is the smallest stable molecule showing cis–trans isomerism.

Beyond “conventional” photodissociation via electronic excitation the possibility of IR induced photochemistry via high vibrational overtones [1], [2], [3] offers a particularly intriguing aspect as it might contribute significantly to the OH balance of the atmosphere [4] (see also [5], [6] and references cited therein). Other interesting dynamical processes include the cis–trans isomerization [7] and the (as yet unobserved) intramolecular hydrogen exchange, which makes the two oxygen atoms equivalent. The state of the theoretical investigation of HONO in its electronic ground state has recently been reviewed by de Maré and Moussaoui [8]. The stationary points on the potential energy hypersurface (PES) have been characterized in terms of their equilibrium (r_e) structure and corresponding harmonic wavenumbers (ω_e) on various levels of theory up to CCSD(T) [9], [10], [11]. Very recently, Richter et al. [11] have reported anharmonic calculations and wavepacket dynamics on a new (CCSD(T)/cc-pVQZ) potential energy hypersurface for the cis–trans isomerization at low excitations (⩽4000 cm⁻¹).

As a first step towards a complete characterization of the quantum dynamics of nitrous acid in its electronic ground state a previous contribution [12] reported the results of fully coupled quantum calculations of the IR absorption spectrum up to very high (“chemically significant”) excitation energies of almost ≈20,000 cm⁻¹. The underlying potential energy and electric dipole hypersurfaces had been interpolated directly from ab initio data (“direct dynamics”) encompassing all the major dynamical processes (cis–trans isomerization, tautomerization). The present contribution focusses on the quantum dynamical aspects of these results with particular emphasis on the influence of vibrational excitation on the reactive dynamics (mode selectivity, adiabaticity). The previous treatment is extended to include the hydrogen exchange tunneling of cis-HONO (equivalent to the O-atom exchange) introducing a new computational approach to multi-arrangement quantum dynamics.

Section snippets

Ab initio potential energy hypersurface

The potential energy hypersurface used in this study for the electronic ground state of nitrous acid was derived by successively averaged spline interpolation (SASI) from about one million energies calculated at the B3LYP/6-31G^∗∗ level of density functional theory. As shown in [12] by extensive comparison with higher level ab initio calculations this level of theory provides a reasonable compromise between accuracy and cost (see also [8], [13]). All physically important qualitative features of

Vibrational eigenvalues and wave packet dynamics

The vibrational eigenvalues and eigenfunctions were calculated in terms of the Near variational PODVR (NvPODVR) proposed by Wei [14]. Within the generalized Z-matrix DVR formalism [15] the vibrational Hamiltonian is given in terms of the generalized coordinates q_k and their conjugate momenta ${\hat{p}}_{k} = - ı ℏ \partial / \partial q_{k}$ $\hat{H} = \frac{1}{4} (\sum_{k, l} \{{\hat{p}}_{k} {\hat{p}}_{l}, G_{kl}\} + ℏ^{2} \frac{\partial^{2} G_{kl}}{\partial q_{k} \partial q_{l}}) + u + V,$ where {A, B} = AB + BA is the anti-commutator of A and B. The vibrational elements of the contravariant metric tensor, G_kl, are calculated from the atomic

Results

The calculated overtone absorption spectrum of cis- and trans-HONO up to about 20,000 cm⁻¹ has already been presented in a previous contribution [12]. The following discussion of results will therefore concentrate on reactive intramolecular processes involving these isomers. Fig. 1 illustrates the minimum energy path for the H atom orbiting around the heavy atom ONO frame. The potential energy profile clearly identifies three major processes: The 1,3-H atom transfer in cis-HONO (in-plane), the

Conclusions

Using global potential energy and electric dipole moment hypersurfaces interpolated directly from quantum chemical calculations allowed the simultaneous study of the spectroscopy and wave packet dynamics of nitrous acid in full dimensionality. With the potential covering the essentially complete configuration space accessible below about 20,000 cm⁻¹ the two major rearrangement processes were investigated in detail, viz. the cis–trans isomerization and the intramolecular 1,3-hydrogen transfer in

Acknowledgements

The author thanks H.-D. Meyer and P. Rosmus for sharing their results prior to publication. This work has been supported financially by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 357.

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New line intensities for the far infrared bands of the Trans- and Cis-conformer of nitrous acid (HONO), new determination of the Trans-Cis conformer barrier and its impact on the astrophysical detection of nitrous acid in protostellar clouds
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The first goal of this work is to improve the determination of the energy difference (ΔE_Cis-Trans) between the ground vibrational state of the Cis- and Trans-HONO conformers of nitrous acid. For this, high resolution spectra were recorded in the 50–200 cm⁻¹ spectral region at three different temperatures, 240, 270 and 296 K. The relative line intensities for the B-type transitions of pure rotational bands of Trans-HONO and Cis-HONO achieved from our measurements were combined in least squares fit computations to those measured previously by Sironneau et al. [Sironneau V, Flaud JM, Orphal J, Kleiner I, Chelin P. Absolute line intensities of HONO and DONO in the far-infrared and re-determination of the Energy Difference between the trans- and cis-species of nitrous acid. J Mol Spectrosc 2010;259:100–104]. In this way, we can significantly improve the accuracy on the HONO conformer energy difference, with a value for ΔE_Cis-Trans = 95.8 ± 9.2 cm⁻¹ compared to ^SIRΔE_Cis-Trans = 99 ± 25 cm⁻¹ in the previous study of Sironneau et al. The second goal is to generate a line list with “absolute” line intensities for the pure rotational bands in the far infrared region of Trans-HONO and Cis-HONO, with both A- and B-type transitions. This new line list proved to be more robust for an improved detection of HONO in astrophysical objects [Coutens A, Ligterink NFW, Loison JC, Wakelam V, Calcutt H, Drozdovskaya MN, Jørgensen JK, Müller HSP, Van Dishoeck EF, Wampfler SF. The ALMA-PILS survey: First detection of nitrous acid (HONO) in the interstellar medium. Astronomy & Astrophysics 2019;623:L13].
Absolute line intensities of HONO and DONO in the far-infrared and re-determination of the energy difference between the trans- and cis-species of nitrous acid
2010, Journal of Molecular Spectroscopy
Relative line intensities of trans- and cis-HONO and -DONO have been measured using absorption spectra in the far-infrared previously recorded by high-resolution Fourier-transform spectroscopy [A. Dehayem-Kamadjeu, O. Pirali, J. Orphal, I. Kleiner, P.-M. Flaud, J. Mol. Spectrosc. 234 (2005) 182–189]. These relative, experimental line intensities (120 lines for trans-HONO and 94 for cis-HONO, as well as 46 lines for trans-DONO and 31 for cis-DONO) were then least-squares fitted leading to the determination of “relative” permanent dipoles moments (b-component) and their rotational corrections for the trans- and cis-HONO and -DONO species. Then these “relative” permanent dipoles moments and their rotational corrections were scaled to the absolute values derived from Stark effect measurements [M. Allegrini, J.W.C. Johns, A.R.W. McKellar, P. Pinson, J. Mol. Spectrosc. 79 (1980) 446–454] and used to generate “absolute” line intensities. These “absolute” line intensities were used to derive the concentrations of the trans- and cis-species in the absorption cell. It was then possible, assuming thermodynamic equilibrium, to use the ratio of the concentrations of the trans- and cis-species to re-determine the energy differences (ΔE) between the ground vibrational states of trans- and cis-HONO: these energy differences are 99 ± 25 cm⁻¹ for HONO and 136 ± 30 cm⁻¹ for DONO. Finally applying zero-point-energy corrections we report an average value for ΔE_HONO of 107 ± 26 cm⁻¹. This value is in good agreement with previous experimental studies and with recent high-level ab initio calculations.
Rotational isomers of small molecules in noble-gas solids: From monomers to hydrogen-bonded complexes
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Molecular conformation, quantum tunneling, and hydrogen bonding play important roles in various photochemical processes. We have studied a number of small molecules possessing rotational isomerism (HONO, formic acid, acetic acid, etc.) isolated in noble-gas solid matrices. Selective vibrational excitation efficiently promotes the conformational change in the excited molecule, which allows preparation of higher-energy conformers. Stability of the higher-energy conformers is often limited by quantum tunneling of hydrogen as observed for some carboxylic acids (formic, acetic, etc.). The tunneling mechanism is supported by the strong H/D isotope effect and characteristic temperature dependence with a clear low-temperature limit. The reaction barrier height is an important factor in a tunneling process; however, other factors also play an essential role. The energy mismatch between the initial state of the higher-energy conformer and accepting state of the ground-state conformer is probably important. Hydrogen bonding can change tunneling decay rate of unstable conformers. The trans–cis formic acid dimer was prepared by vibrational excitation of the trans–trans form in neon and argon matrices. Tunneling decay of cis formic acid is substantially slower in the dimeric form compared to monomer, especially in solid neon. This stabilization effect is explained by a complexation-induced increase of reaction barrier, which is confirmed computationally. The complex between cis formic acid and water was prepared in an argon matrix and found to be stable at low-temperatures. These results show that intrinsically unstable conformational structures can be thermodynamically stabilized in asymmetrical hydrogen-bonded network. This effect occurs when the energy difference between conformers is smaller than the hydrogen bond interaction energy, which allows chemistry of unstable conformers to be studied.
The infrared-driven cis-trans isomerization of nitrous acid HONO III: A mixed quantum-classical simulation
2008, Chemical Physics
A mixed quantum–classical simulation of the IR-driven cis–trans isomerization of HONO in a Kr matrix at 30 K is presented, treating the hydrogen atom as quantum particle and the Kr matrix as well as intermolecular degrees of freedom of the ONO-body as classical. A new method is presented to time-propagate the coupled set of equations in a DVR basis in internal spherical coordinates, rather than in laboratory frame fixed cartesian coordinates. In spherical coordinates, a much more precise computation of the weak vibrational couplings is possible using a still manageable basis size. Good qualitative agreement between simulation and experiment is obtained, underestimating relaxation and isomerization rates by a modest factor ≈5. Upon matrix fluctuations, frequent curve crossings occur between the initially excited OH-stretch vibration and a closely lying combination mode of torsional and bending coordinate that lead to a transfer of population. The subsequent pathway of energy flow is deduced and discussed within a tier model, where trans-states, that belong to the second tier, are populated through a first tier of states that is composed of combinations of bending and torsional excitations. No specific energy pathway is revealed that would funnel the hydrogen atom directly towards the trans-side, hence the experimentally observed high cis → trans quantum yield of close to one probably has to be explained in a statistical scenario on a timescale much longer than that of the present simulation.
The ν4 bands at 11 µm: linelists for the Trans- and Cis- conformer forms of nitrous acid (HONO) in the 2019 version of the GEISA database
2022, Molecular Physics
Ab initio calculation of rovibrational states for non-degenerate double-well potentials: Cis-trans isomerization of HOPO
2020, Journal of Chemical Physics

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Multi-arrangement quantum dynamics in 6D: cis–trans isomerization and 1,3-hydrogen transfer in HONO

Abstract

Introduction

Section snippets

Ab initio potential energy hypersurface

Vibrational eigenvalues and wave packet dynamics

Results

Conclusions

Acknowledgements

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J. Chem. Phys.