Rovibrational states calculations of the H2O-HCN heterodimer with the multiconfiguration time dependent Hartree method.

Water and hydrogen cyanide are two of the most common species in space and the atmosphere with the ability of binding to form dimers such as H2O-HCN. In the literature, while calculations characterizing various properties of the H2O-HCN cluster (equilibrium distance, vibrational frequencies and rotational constants) have been done in the past, extensive calculations of the rovibrational states of this system using a reliable quantum dynamical approach have yet to be reported. In this work, we intend to mend that by performing the first calculation of the rovibrational states of the H2O-HCN van der Waals complex on a recently developed potential energy surface. We use the block improved relaxation procedure implemented in the Heidelberg MultiConfiguration Time-Dependent Hartree (MCTDH) package to compute the states of the H2O-HCN isomer, from which we extract the transition frequencies and rotational constants of the complex. We further adapt an approach first suggested by Wang and Carrington-and supported here by analysis routines of the Heidelberg MCTDH package-to properly characterize the computed rovibrational states. The subsequent assignment of rovibrational states was done by theoretical analysis and visual inspection of the wavefunctions. Our simulations provide a Zero Point Energy (ZPE) and intermolecular vibrational frequencies in good agreement with past ab initio calculations. The transition frequencies and rotational constants obtained from our simulations match well with the available experimental data. This work has the broad aim to propose the MCTDH approach as a reliable option to compute and characterize rovibrational states of van der Waals complexes such as the current one.

Temperature Dependence of the Electronic Absorption Spectrum of NO2.

The nitrogen dioxide (NO2) radical is composed of the two most abundant elements in the atmosphere, where it can be formed in a variety of ways including combustion, detonation of energetic materials, and lightning. Relevant also to smog and ozone cycles, together these processes span a wide range of temperatures. Remarkably, high-resolution NO2 electronic absorption spectra have only been reported in a narrow range below about 300 K. Previously, we reported [ J. Phys. Chem. A 2021, 125, 5519-5533] the construction of quasi-diabatic potential energy surfaces (PESs) for the lowest four electronic states (X̃, Ã, B̃, and C̃) of NO2. In addition to three-dimensional PESs based on explicitly correlated MRCI(Q)-F12/VTZ-F12 ab initio data, the geometry dependence of each component of the dipoles and transition dipoles was also mapped into fitted surfaces. The multiconfigurational time-dependent Hartree (MCTDH) method was then used to compute the 0 K electronic absorption spectrum (from the ground rovibrational initial state) employing those energy and transition dipole surfaces. Here, in an extension of that work, we report an investigation into the effects of elevated temperature on the spectrum, considering the effects of the population of rotationally and vibrationally excited initial states. The calculations are complemented by new experimental measurements. Spectral contributions from hundreds of rotational states up to N = 20 and from 200 individually-characterized vibrational states were computed. A spectral simulation tool was developed that enables modeling the spectrum at various temperatures─by weighting individual spectral contributions via the partition function, or for pure excited initial states, which can be probed via transient absorption spectroscopy. We validate these results against experimental absorption spectroscopy data at high temperatures, as well as via a new measurement from the (1,0,1) initial vibrational state.

The Low-Lying Electronic States of NO2: Potential Energy and Dipole Surfaces, Bound States, and Electronic Absorption Spectrum.

Nitrogen dioxide, NO2, is a free radical composed of the two most abundant elements in Earth's atmosphere, nitrogen and oxygen, and is relevant to atmospheric and combustion chemistry. The electronic structure of even its lowest-lying states is remarkably complex, with various conical intersections and Renner-Teller pairings, giving rise to complex and perturbed vibronic states. Here we report some analysis of the 18 molecular states of doublet spin-multiplicity formed by combining ground-state N(4Su) and O(3Pg) atoms. Three-dimensional potential energy surfaces were fit at the MRCI(Q)-F12/VTZ-F12 level, describing the lowest four (X̃, Ã, B̃, and C̃) electronic states. A properties-based diabatization procedure was applied to accommodate the intersections, producing energies in a quasidiabatic representation and yielding couplings that were also fit into surfaces. The low-lying vibrational levels on the ground X̃ state were computed and compared with experimental measurements. Compared to experiment, the lowest 125 calculated vibrational levels (up to 8500 cm-1 above the zero-point energy) have a root-mean-squared error of 16.5 cm-1. In addition, dipole moments for each of the lowest four electronic states-and the transition dipoles between them-were also computed and fit. With the coupled energy and dipole surfaces, the electronic spectrum was calculated in absolute intensity and compared with experimental measurements. Detailed structure in the experimental spectrum was successfully reproduced, and the total integrated intensity matches experiment to an accuracy of ∼1.5% with no empirical adjustments.

Theoretical investigation of the H + HD → D + H2 chemical reaction for astrophysical applications: A state-to-state quasi-classical study.

We report a large set of state-to-state rate constants for the H + HD reactive collision, using Quasi-Classical Trajectory (QCT) simulations on the accurate H3 global potential energy surface of Mielke et al. [J. Chem. Phys. 116, 4142 (2002)]. High relative collision energies (up to ≈56 000 K) and high rovibrational levels of HD (up to ≈50 000 K), relevant to various non thermal equilibrium astrophysical media, are considered. We have validated the accuracy of our QCT calculations with a new efficient adaptation of the Multi Configuration Time Dependent Hartree (MCTDH) method to compute the reaction probability of a specific reactive channel. Our study has revealed that the high temperature regime favors the production of H2 in its highly rovibrationnally excited states, which can de-excite radiatively (cooling the gas) or collisionally (heating the gas). Those new state-to-state QCT reaction rate constants represent a significant improvement in our understanding of the possible mechanisms leading to the destruction of HD by its collision with a H atom.

Rotationally inelastic scattering of O3-Ar: state-to-state rates with the multiconfigurational time dependent Hartree method.

The Chapman cycle, proposed in 1930, describes the various steps in the ongoing formation and destruction of stratospheric ozone. A key step in the formation process is the stabilization of metastable ozone molecules through collisions with a third body, usually an inert collider such as N2. The "ozone isotopic anomaly" refers to the observation of larger-than-expected atmospheric concentrations for certain ozone isotopologues. Previous studies point to the formation steps as the origin of this effect. A possibly key aspect of the ozone formation dynamics is that of the relative efficiencies of the collisional cooling of different isotopologues. Although the substitution of low-abundance 18O for 16O in O3 molecules corresponds to a relatively small net change in mass, related to this are some subtleties due to symmetry-breaking and a resulting more than doubling of the density of allowed states governed by nuclear-spin statistics for bosons. Recently, a highly accurate 3D potential energy surface (PES) describing O3-Ar interactions has been constructed and used to benchmark the low-lying rovibrational states of the complex. Here, using this new PES, we have studied the collisional energy-transfer dynamics using the MultiConfiguration Time Dependent Hartree method. A study of the rotationally inelastic scattering was performed for the parent 16O16O16O-Ar system and compared with that of the 16O16O18O-Ar isotopologue. The state-to-state cross-sections and rates from the 00,0 initial state to low lying excited states are reported. Analysis of these results yields insight into the interplay between small changes in the rotational constants of O3 and the reduced mass of the O3-Ar collision system, combined with that of the symmetry-breaking and introduction of a new denser manifold of allowed states.

State-to-state inelastic rotational cross sections in five-atom systems with the multiconfiguration time dependent Hartree method.

We present a MultiConfiguration Time Dependent Hartree (MCTDH) method as an attractive alternative approach to the usual quantum close-coupling method that approaches some computational limits in the calculation of rotational excitation (and de-excitation) between polyatomic molecules (here collisions between triatomic and diatomic rigid molecules). We have performed a computational investigation of the rotational (de-)excitation of the benchmark rigid rotor H2O-H2 system on a recently developed Potential Energy Surface of the complex using the MCTDH method. We focus here on excitations and de-excitations from the 000, 111, and 110 states of H2O with H2 in its ground rotational state, looking at all the potential transitions in the energy range 1-200 cm-1. This work follows a recently completed study on the H2O-H2 cluster where we characterized its spectroscopy and more generally serves a broader goal to describe inelastic collision processes of high dimensional systems using the MCTDH method. We find that the cross sections obtained from the MCTDH calculations are in excellent agreement with time independent calculations from previous studies but does become challenging for the lower kinetic energy range of the de-excitation process: that is, below approximately 20 cm-1 of collision energy, calculations with a relative modest basis become unreliable. The MCTDH method therefore appears to be a useful complement to standard approaches to study inelastic collision for various collision partners, even at low energy, though performing better for rotational excitation than for de-excitation.

Development of a potential energy surface for the O3-Ar system: rovibrational states of the complex.

The cycle of formation and destruction of ozone is an important process in the atmosphere. A key step in the formation process is the stabilization of a metastable ozone molecule, which occurs through energy transfer: usually a highly excited ozone molecule loses the excess energy through inelastic collisions with a third body (M). However, the details of this energy transfer mechanism are still not well known and one of the reasons has been the lack of an accurate potential energy surface (PES). In theoretical studies, Ar is often selected as the third body when considering O3-M dynamics. However, electronic structure calculations have not previously been reported for the complex. In this paper we benchmark the electronic structure for this system, and present our first steps towards constructing a fully flexible 6D PES by obtaining a 3D PES in the rigid rotor approximation. For this purpose, to benchmark the non-bonded interactions, we performed ab initio electronic structure calculations using explicitly-correlated coupled-cluster theory extended to the complete basis set limit (CCSD(T)-F12b/CBS). A multireference-based protocol suitable to describe the 6D flexible system was developed using the explicitly-correlated multi-reference configuration interaction (MRCI-F12) method. Subsequently, we used the AUTOSURF code to construct 3D PESs for each of the two methods with global root-mean-squared errors of less than 1 cm-1. The PES is characterized by two equivalent wells on either face of the ozone molecule consistent with the symmetry of the system. Calculations of the rovibrational levels for the complex using the Multiconfigurational Time Dependent Hartree (MCTDH) method provide insight into the states and dynamics of the system. Based on symmetry analysis, the allowed states and transitions were obtained: the transition frequencies and calculated rotational constants were then compared with previously reported experimental measurements. The isotopic effect was also studied using the 16O18O16O and 16O16O18O isotopologues. Roughly a doubling in the density of allowed states is observed when the symmetry of the ozone molecule is broken.

Dynamical interference in the vibronic bond breaking reaction of HCO.

First-principles treatments of quantum molecular reaction dynamics have reached the level of quantitative accuracy even in cases with strong non-Born-Oppenheimer effects. This achievement permits the interpretation of puzzling experimental phenomena related to dynamics governed by multiple coupled potential energy surfaces. We present a combined experimental and theoretical study of the photodissociation of formyl radical (HCO). Oscillations observed in the distribution of product states are found to arise from the interference of matter waves-a manifestation analogous to Young's double-slit experiment.

The rotational spectrum and potential energy surface of the Ar-SiO complex.

The rotational spectra of five isotopic species of the Ar-SiO complex have been observed at high-spectral resolution between 8 and 18 GHz using chirped Fourier transform microwave spectroscopy and a discharge nozzle source; follow-up cavity measurements have extended these measurements to as high as 35 GHz. The spectrum of the normal species is dominated by an intense progression of a-type rotational transitions arising from increasing quanta in the Si-O stretch, in which lines up to v = 12 (∼14 500 cm-1) were identified. A structural determination by isotopic substitution and a hyperfine analysis of the Ar-Si17O spectrum both suggest that the complex is a highly fluxional prolate symmetric rotor with a vibrationally averaged structure between T-shaped and collinear in which the oxygen atom lies closer to argon than the silicon atom, much like Ar-CO. To complement the experimental studies, a full dimensional potential and a series of effective vibrationally averaged, two-dimensional potential energy surfaces of Ar + SiO have been computed at the CCSD(T)-F12b/CBS level of theory. The equilibrium structure of Ar-SiO is predicted to be T-shaped with a well depth of 152 cm-1, but the linear geometry is also a minimum, and the potential energy surface has a long, flat channel between 140 and 180°. Because the barrier between the two wells is calculated to be small (of order 5 cm-1) and well below the zero-point energy, the vibrationally averaged wavefunction is delocalized over nearly 100° of angular freedom. For this reason, Ar-SiO should exhibit large amplitude zero-point motion, in which the vibrationally excited states can be viewed as resonances with long lifetimes. Calculations of the rovibrational level pattern agree to within 2% with the transition frequencies of normal and isotopic ground state Ar-SiO, and the putative K a = ±1 levels for Ar-28SiO, suggesting that the present theoretical treatment well reproduces the salient properties of the intramolecular potential.

Influence of Renner-Teller Coupling between Electronic States on H + CO Inelastic Scattering.

We examine the excitation of carbon monoxide from its rovibrational ground state via collisions with a hydrogen atom. Calculations employ the Multi-Configuration Time-Dependent Hartree method and treat the nonadiabatic dynamics with the inclusion of both the ground and the Renner-Teller coupled first excited electronic states. For this purpose, a new set of recently presented global HCO Potential Energy Surfaces (PESs) that cover the 0-3 eV range of energy is used. The results obtained here considering only the ground state (without the Renner-Teller coupling) are in qualitative agreement with those available in the literature. The Renner-Teller effect is known to have an important effect on the spectroscopy of the system, and its inclusion and effects on the dynamics for the processes described in this paper are fairly significant also. The results of this study indicate that for certain very particular initial conditions rather dramatic effects can be observed.

A new set of potential energy surfaces for HCO: Influence of Renner-Teller coupling on the bound and resonance vibrational states.

It is commonly understood that the Renner-Teller effect can strongly influence the spectroscopy of molecules through coupling of electronic states. Here we investigate the vibrational bound states and low-lying resonances of the formyl radical treating the Renner-Teller coupled X̃(2)A(') and Ã(2)A(″) states using the MultiConfiguration Time Dependent Hartree (MCTDH) method. The calculations were performed using the improved relaxation method for the bound states and a recently published extension to compute resonances. A new set of accurate global potential energy surfaces were computed at the explicitly correlated multireference configuration interaction (MRCI-F12) level and yielded remarkably close agreement with experiment in this application and thus enable future studies including photodissociation and collisional dynamics. The results show the necessity of including the large contribution from a Davidson correction in the electronic structure calculations in order to appreciate the relatively small effect of the Renner-Teller coupling on the states considered here.

Calculated vibrational states of ozone up to dissociation.

A new accurate global potential energy surface for the ground electronic state of ozone [R. Dawes et al., J. Chem. Phys. 139, 201103 (2013)] was published fairly recently. The topography near dissociation differs significantly from previous surfaces, without spurious submerged reefs and corresponding van der Waals wells. This has enabled significantly improved descriptions of scattering processes, capturing the negative temperature dependence and large kinetic isotope effects in exchange reaction rates. The exchange reactivity was found to depend on the character of near-threshold resonances and their overlap with reactant and product wavefunctions, which in turn are sensitive to the potential. Here we present global "three-well" calculations of all bound vibrational states of three isotopic combinations of ozone ((48)O3, (16)O2 (18)O, (16)O2 (17)O) for J = 0 and J = 1 with a focus on the character and density of highly excited states and discuss their impact on the ozone isotopic anomaly. The calculations were done using a parallel symmetry-adapted Lanczos method with the RV3 code. Some comparisons were made with results obtained with the improved relaxation method implemented in the Heidelberg multi-configuration time-dependent Hartree code.

Vibrational energy levels of the simplest Criegee intermediate (CH2OO) from full-dimensional Lanczos, MCTDH, and MULTIMODE calculations.

Accurate vibrational energy levels of the simplest Criegee intermediate (CH2OO) were determined on a recently developed ab initio based nine-dimensional potential energy surface using three quantum mechanical methods. The first is the iterative Lanczos method using a conventional basis expansion with an exact Hamiltonian. The second and more efficient method is the multi-configurational time-dependent Hartree (MCTDH) method in which the potential energy surface is refit to conform to the sums-of-products requirement of MCTDH. Finally, the energy levels were computed with a vibrational self-consistent field/virtual configuration interaction method in MULTIMODE. The low-lying levels obtained from the three methods are found to be within a few wave numbers of each other, although some larger discrepancies exist at higher levels. The calculated vibrational levels are very well represented by an anharmonic effective Hamiltonian.

Resonances of HCO Computed Using an Approach Based on the Multiconfiguration Time-Dependent Hartree Method.

The improved relaxation method with a complex absorbing potential (CAP) was used to compute resonance states of the formyl radical (HCO) using the Heidelberg multi-configuration time-dependent Hartree (MCTDH) program. To benchmark this approach, the same potential energy surface as was used in three other method development studies was used here. It was found that the MCTDH-based approach was able to accurately and efficiently compute 90 resonance states up to more than 1 eV above the dissociation limit. Extremely close agreement was obtained for energies and widths (lifetimes) calculated using MCTDH compared with those reported previously for three other CAP-based approaches that separately involved filter-diagonalization, a preconditioned complex-symmetric Lanczos algorithm, and a non-Hermitian real-arithmatic Lanczos method. The high accuracy achieved in this benchmark study supports the applicability of MCTDH to the study of resonances in larger systems in which increased dimensionality makes the efficiency of MCTDH advantageous.

Rotational Excitations in CO-CO Collisions at Low Temperature: Time-Independent and Multiconfigurational Time-Dependent Hartree Calculations.

The rotational excitation in collisions between two carbon monoxide molecules was studied while combining the use of both time-independent and time-dependent formalisms. All of the calculations made use of a recently published four dimensional PES for CO dimer. Time-independent scattering calculations were performed in the lower part of the collision energy range, thus limiting the number of open channels and computational cost. The PES features a low-energy path for geared motion that appears to affect the excitation propensities in low-energy collisions. For reactants colliding without initial rotational excitation, symmetric excitations (both monomers excited equally) are strongly favored. This behavior deviates significantly from an exponential gap model based on endo- or exoergicity. Comparable time-dependent calculations were performed in an extended energy range made feasible by the lower cost of those calculations. The wave packet propagation in the time-dependent approach was performed with the multiconfiguration time-dependent hartree (MCTDH) method and analyses via the flux method, and the Tannor and Weeks approach was used to calculate the transition probabilities in the energy range up to 1000 cm(-1). We deduce from the cross sections the corresponding reaction rates for temperatures between 10 and 250 K. MCTDH was found to yield well-converged results, where the methods overlap, validating the use of MCTDH as an efficient tool to study collision processes.

Ozone photodissociation: isotopic and electronic branching ratios for symmetric and asymmetric isotopologues.

We present new calculations of the branching ratios between the various electronic and isotopic photodissociation channels of ozone. Special emphasis is placed on the isotopic/isotopologue differences because the contribution of the ozone photodissociation to the oxygen isotope and ozone isotopologue enrichments or fractionations is important for atmospheric applications. These branching ratios, which depend on photon energy, have been calculated with a full quantum mechanical wavepacket propagation approach: the multiconfiguration time-dependent Hartree (MCTDH) method. Five ozone isotopologues are considered: three symmetric, (16)O(3) (noted 666), (16)O(17)O(16)O (676), and (16)O(18)O(16)O (686); two asymmetric, (16)O(2)(17)O (noted 667) and (16)O(2)(18)O (668). The 668 and 667 asymmetric isotopologues can dissociate into either 66 + 8 or 68 + 6 for 668 and into 66 + 7 or 67 + 6 for 667. In the ranges of the Chappuis and Hartley bands, the dissociation is very fast and electronic and isotopic branching ratios are obtained from the wavepacket fluxes through complex absorbing potentials (CAPs) located perpendicular to the dissociation channels of the potential energy surfaces (PESs) of the A (1)B(1) (Chappuis) and B 3(1)A' (Hartley/Huggins) electronic states. In the range of the Huggins band the dissociation is much slower and the isotopic branching ratios of 667 and 668 asymmetric isotopologues, (e.g; 668 → 66 + 8 or 86 + 6) are obtained from the ratios of two partial absorption cross sections corresponding to the selective excitation of one or the other of the two isomers of C(s) symmetry, which dissociate respectively into 66 + 8 and 86 + 6. We find that the photodissociation of the 668 asymmetric isotopologue favors the 68 + 6 channel with a propensity varying between 52% (Hartley) and 54% (Huggins) as a function of the photon energy. The electronic branching ratios to the singlet channel (O(3) + hυ → O((1)D) + O(2)((1)Δ)) are all close to 90% above ≈32,000 cm(-1). Below this energy, the singlet channel is energetically closed and only the triplet channel (O(3) + hυ → O((3)P) + O(2)((3)Σ)) is open. These branching ratios are required to calculate the photolysis rates of each ozone isotopologue, which in turn contribute to the atomic oxygen and the ozone isotopic enrichments in the atmosphere.

Comparison of the Huggins band for six ozone isotopologues: vibrational levels and absorption cross section.

By use of the 3(1)A' ab initio potential energy surface (PES) of ozone and the multi-configuration time-dependent Hartree program for wavepacket propagation, we have determined numerous eigenstates of this state for six ozone isotopologues. These bound vibrational levels are the upper levels of the Huggins band, which covers the range from 27,000 to ~33,000 cm(-1). This study extends our previous work on the Hartley band, which was limited to the range ~32,000-50,000 cm(-1). Four isotopologues, (16)O(3), (16)O(17)O(16)O, (16)O(18)O(16)O, and (18)O(3) (noted hereafter 666, 676, 686, and 888), are symmetric, and two are asymmetric, (17)O(16)O(2) and (18)O(16)O(2) (noted hereafter 667 and 668). The PES of the 3(1)A' state has two equivalent minima of C(s) symmetry located at ~27,000 cm(-1) above the X(1)A(1) ground state. The equilibrium geometry of these two minima is r(e(1)) = 2.28 a(0), r(e(2)) = 3.2 a(0), and θ(e) = 107°. The dissociation limit of this PES, which correlates to the O((1)D) + O(2) ((1)Δ) "singlet" channel, is about 4300 cm(-1) above the two minima. For the (16)O(3) isotopologue, the 120 lowest bound eigenstates have been calculated and partially assigned up to 800 cm(-1) below the dissociation limit. The 60 lower eigenstates are easily assignable in term of three normal modes, the "long" bond (ν(1)), the bending (ν(2)), and the "short" bond (ν(3)). A new family of wave functions, aligned along the dissociation channels, appears at 3782 cm(-1) above the 3(1)A' (0,0,0) level. The 3(1)A' vibrational levels and the corresponding intensity factors from the (000), (010), (100), and (001) levels of the X(1)A(1) ground state have been calculated for the six isotopologues. The Huggins absorption cross sections of the six isotopologues have been calculated from the 3(1)A' vibrational energy levels and the corresponding intensity factors. The rotational envelope of each vibronic band has been empirically described by an ad hoc function. The ratio of the Huggins cross section of each ozone isotopologue with one of (16)O(3) provides the fractionation factor of each ozone isotopologue as a function of the photon energy. These various fractionation factors will allow predicting enrichments due to photolysis by various light sources like the actinic flux.

Absorption cross section of ozone isotopologues calculated with the multiconfiguration time-dependent hartree (MCTDH) method: I. The Hartley and Huggins bands.

The absorption cross sections of 18 isotopologues of the ozone molecule have been calculated in the range of the Hartley-Huggins bands (27000-55000 cm(-1)). All 18 possible ozone isotopologues made with (16)O, (17)O, and (18)O have been considered, with emphasis on those of geophysics interest like (16)O(3) (17)O(16)O(2), (16)O(17)O(16)O, (18)O(16)O(2), and (16)O(18)O(16)O. We have used the MCTDH algorithm to propagate wavepackets. As an initial wavepacket, we took the vibrational ground state multiplied by the transition dipole moment surface. The cross sections have been obtained from the autocorrelation function of this wavepacket. Only two potential energy surfaces (PESs) and the corresponding transition dipole moment are involved in the calculation. The dissociating R state has been omitted. The calculations have been performed only for J = 0. The comparison with the experimental absorption cross sections of (16)O(3) and (18)O(3) has been performed after an empirical smoothing which mimics the rotational envelop. The isotopologue dependence of the cross sections of 18 isotopologues can be split into two energy ranges, (a) from 27000 to 32000 cm(-1), the Huggins band, which is highly structured, and (b) from 32000 to 55000 cm(-1), the main part of the cross section which has a bell shape, the Hartley band. This bell-shaped envelop has been characterized by a new analytic model depending on only four parameters, amplitude, center, width, and asymmetry. The isotopologue dependence of these parameters reveals the tiny differences between the absorption cross sections of the various isotopologues. In contrast to the smooth shape of the Hartley band, the Huggins band exhibits pronounced vibrational structures and therefore shows large isotopologue differences which may induce a significant isotopologue dependence of the ozone photodissociation rates under actinic flux.