Journal of Molecular Spectroscopy 318 (2015) 84–90 Contents lists available at ScienceDirect Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms A variationally calculated room temperature line-list for H2O2 Ahmed F. Al-Refaie a, Roman I. Ovsyannikov b, Oleg L. Polyansky a, Sergei N. Yurchenko a, ⇑ Jonathan Tennyson a, a Department of Physics and Astronomy, University College London, London WC1E 6BT, UK b Institute of Applied Physics, Russian Academy of Sciences, Ulyanov Street 46, Nizhny Novgorod 603950, Russia article info abstract Article history: A room temperature line list for hydrogen peroxide is computed using a high level ab initio potential Received 2 September 2015 energy surface by Małyszek and Koput (2013) with a small adjustment of the equilibrium geometry In revised form 4 October 2015 and height of the torsional barrier and a new ab initio dipole moment surface (CCSD(T)-f12b/aug-cc-pv Accepted 5 October 2015 (T+d)Z). In order to improve further the ab initio accuracy, the vibrational band centers were shifted to Available online 8 October 2015 match experimental values when available. The line list covers the wavenumber region up to À1 8000 cm with the rotational excitations J 6 40. Room temperatures synthetic spectra of H2O2 are gen- Keywords: erated and compared to the spectra from the HITRAN and PNNL-IR databases showing good agrement. Hydrogen peroxide Ó 2015 Elsevier Inc. All rights reserved. Dipole moment Infrared Transition dipole Vibration HOOH Intensity Variational calculations 1. Introduction bending respectively, m2 represents the O–O stretch and the m4 mode represents the torsional excitation and is commonly repre- Hydrogen peroxide is a trace species in Earth [1–3] atmospheric sented in literature as n. chemistry and plays a role in stratospheric ozone production. The HITRAN 2012 database [11] only contains transitions for À1 There have been multiple detections of H2O2 in the Martian atmo- hydrogen peroxide below 1800 cm . This region covers the tor- sphere [4–7], where it is possibly formed by triboelectricity in dust sional, O–H bending modes and O–O stretch but misses the O–H devils and dust storms [6] and it may well act as an agent in the stretches at the 3750 cmÀ1 region. Only a few studies deal with oxidization of the Martian surface. A recent detection in the inter- spectra of H2O2 in the mid-infrared and near-infrared [12–14] stellar medium [8] gives insight to the formation of water in space. regions. Available experimental studies mostly concern torsional Finally H2O2 has been detected in the atmosphere of Europa [9] in rovibrational transitions involving the ground and excited states À1 the 3.5 lm(2587 cm ) region. [15], and the m3 [16] and m6 [14] vibrational modes. Whilst there Hydrogen peroxide is an asymmetric prolate rotor molecule. Its are ample data available in the literature for the torsional and most interesting characteristic is that it is the simplest molecule bending bands, the fundamental stretching modes are more diffi- that exhibits internal (torsional) rotation. This gives it a double- cult to obtain accurate term values for. The O–H stretching modes, minimum in its torsional potential as well as two alignments of m1 and m5, in particular have been especially problematic. The sep- the O–H bonds: cis and trans. The torsional mode therefore con- aration between the two bands is about 8–10 cmÀ1 and torsional tains four ‘sub-levels’ for each excitation and requires an additional splitting from the double minimum of the potential gives rise to internal-rotation quantum number (s ¼ 1; 2; 3; 4) [10] to properly doubling [17] in the form of ‘quasi’-degenerate states [18] that characterize it. It also only exhibits c-type transitions which conse- are difficult to resolve accurately. Olsen et al. [15] give an estimate À1 À1 quently means it has no pure rotational transitions. H2O2 has six of 3610–3618 cm for m5 and 3601–3617 cm for m1 whilst a À1 vibrational modes: m1 and m5 represent the symmetric and asym- Raman study gives a lower value of 3607 cm [17] for the m1 metric O–H stretching respectively, m3 and m6 represent the O–H band-center but determining the accuracy to better than 0.1 cmÀ1 is difficult. A theoretical line-list may provide a way of À1 ⇑ Corresponding author. characterizing the confusing spectra of H2O2 above 1800 cm E-mail address: [email protected] (J. Tennyson). but so far none have been produced. http://dx.doi.org/10.1016/j.jms.2015.10.004 0022-2852/Ó 2015 Elsevier Inc. All rights reserved. A.F. Al-Refaie et al. / Journal of Molecular Spectroscopy 318 (2015) 84–90 85 In this work we present a room temperature line list generated the kinetic energy expansion order is 6 and the potential expansion using the variational approach TROVE [19,20] based on a high order is 8. quality ab initio potential energy [21,22] and new dipole moment A symmetry-adapted basis-set is constructed by a multi- surfaces. step contraction scheme that is truncated via polyad number Pmax ¼ 42 [22]. The primitive vibrational basis-set is constructed by solving the 1D Schrodinger equation for each basis-function 2. Method /v ðf Þði ¼ 1; 2; ...; 6Þ associated with the vibrational quantum i i number v via the Numerov–Cooley method [31,32] for each mode The accuracy of the line positions is determined by the quality i allowed by the polyad P: of the PES. The PES is based of the high-accuracy ab initio calcula- tions of Małyszek and Koput [21]. The PES was computed using the P ¼ 4v1 þ 8ðv2 þ v3 þ v4 þ v5Þþv6 6 Pmax: ð2Þ CCSD(T)-F12 method with parts of the PES utilizing aug-cc-pV7Z The six dimensional co-ordinate space is then divided into four basis-sets. These calculations can be considered state-of-the-art reduced subspaces: ðf Þ; ðf ; f Þ; ðf ; f Þ and ðf Þ based on symme- for this problem. We include the small adjustment to the ab initio 1 2 3 4 5 6 try. The reduced Hamiltonian is solved using the primitives /v as equilibrium geometry and height of the torsional barrier proposed i basis-functions to obtain the contracted vibrational basis-functions by Polyansky et al. [22]. The PES boasts a root-mean-squares (rms) À U ðf Þ, U ðf ; f Þ; U ðf ; f Þ and U ðf Þ. These basis-functions difference of 0.02 cm 1 for rotational levels up to J ¼ 35 within n1 1 n2 2 3 n3 4 5 n4 6 D low-lying vibrational states [22]. are then symmetrised according to the 2h(M) Molecular Group The rovibrational energies were calculated using the TROVE symmetry [33] and the final vibrational basis-set is formed from [19] computer suite. TROVE is a variational nuclear-motion solver the product of the four contracted basis-functions which are and can be employed in all steps of line-list production for mole- truncated via Eq. (2) and symmetrized again. The general form of cules of arbitrary structure. It has been successful to produce hot the Hamiltonian operator is: X X line lists for CH4 [23],PH3 [24],H2CO [25] and room temperature 1 1 H ¼ Hv þ J GabJ þ ðp Gka þ Gakp ÞJ ; ð3Þ ones for PH [26] and SO [27]. TROVE was also used to simulate ib a b k k a 3 3 2 ab 2 ak a room temperature spectrum for another non-rigid, chain mole- cule HSOH based on a high level ab initio potential energy and where Ja and pk are the rotational and vibrational momentum oper- dipole moment surfaces [28,29]. ators respectively and Hvib is the pure vibrational (J ¼ 0) Hamilto- Within TROVE, the nuclear-motion Hamiltonian is represented nian given as: as an expansion around a reference configuration where the bond X ¼ 1 þ þ ; ð Þ lengths for the O–O bond (R), the O–H1 bond (r1), the O–H2 bond Hvib pkGklpl V U 4 2 kl (r2) and the bond angles for O–H1 (h1) and O–H2 (h2) are frozen at their equilibrium and the torsional angle s varies on a grid of where Gab are kinetic energy factors, U is a pseudo-potential [19] ° ° 10,000 values ranging from 0 to 720 . The internal co-ordinates and V is the molecular potential energy. The contracted Hamilto- are described in Fig. 1. nian is solved up to an energy eigenvalue threshold of TROVE utilizes an approximate kinetic energy operator (KEO). 24,000 cmÀ1. A final contraction step can be performed by solving Comparisons with exact KEO codes such as WAVR4 [30] show the J ¼ 0 problem given by Eq. (4) and replacing the bulky primitive TROVE converging just as well [22] whilst being less computation- vibrational basis-sets with the more compact J ¼ 0 wavefunctions. ally demanding. Convergence is obtained for expansion orders This has the added benefit of making the computation of the between 6 and 8 [19]. Hamiltonian matrix elements for J > 0 more efficient as the Hvib Here, the kinetic energy is expanded around the reference contribution becomes: geometry in terms of five linearized co-ordinates of the form: C C hW j jW 0 i¼ d 0 ; ð Þ J¼0;i Hvib J¼0;i Ei i;i 5 f ¼ l À e; ð Þ i xi xi 1 l e where xi and xi represents linearized version and equilibrium Table 1 geometry of the bond lengths and angles respectively.