Tijs Karman

Quantum mechanical calculation of the collision-induced absorption spectra of N2–N2 with anisotropic interactions

We present quantum mechanical calculations of the collision-induced absorption spectra of nitrogen molecules, using ab initio dipole moment and potential energy surfaces. Collision-induced spectra are first calculated using the isotropic interaction approximation. Then, we improve upon these results by considering the full anisotropic interaction potential. We also develop the computationally less expensive coupled-states approximation for calculating collision-induced spectra and validate this approximation by comparing the results to numerically exact close-coupling calculations for low energies. Angular localization of the scattering wave functions due to anisotropic interactions affects the line strength at low energies by two orders of magnitude. The effect of anisotropy decreases at higher energy, which validates the isotropic interaction approximation as a high-temperature approximation for calculating collision-induced spectra. Agreement with experimental data is reasonable in the isotropic interaction approximation, and improves when the full anisotropic potential is considered. Calculated absorption coefficients are tabulated for application in atmospheric modeling.

Communication: Multiple-property-based diabatization for open-shell van der Waals molecules

We derive a new multiple-property-based diabatization algorithm. The transformation between adiabatic and diabatic representations is determined by requiring a set of properties in both representations to be related by a similarity transformation. This set of properties is determined in the adiabatic representation by rigorous electronic structure calculations. In the diabatic representation, the same properties are determined using model diabatic states defined as products of undistorted monomer wave functions. This diabatic model is generally applicable to van der Waals molecules in arbitrary electronic states. Application to locating seams of conical intersections and collisional transfer of electronic excitation energy is demonstrated for O2 - O2 in low-lying excited states. Property-based diabatization for this test system included all components of the electric quadrupole tensor, orbital angular momentum, and spin-orbit coupling.

Collision-induced absorption with exchange effects and anisotropic interactions: theory and application to H2 - H2.

We discuss three quantum mechanical formalisms for calculating collision-induced absorption spectra. First, we revisit the established theory of collision-induced absorption, assuming distinguishable molecules which interact isotropically. Then, the theory is rederived incorporating exchange effects between indistinguishable molecules. It is shown that the spectrum can no longer be written as an incoherent sum of the contributions of the different spherical components of the dipole moment. Finally, we derive an efficient method to include the effects of anisotropic interactions in the computation of the absorption spectrum. This method calculates the dipole coupling on-the-fly, which allows for the uncoupled treatment of the initial and final states without the explicit reconstruction of the many-component wave functions. The three formalisms are applied to the collision-induced rotation-translation spectra of hydrogen molecules in the far-infrared. Good agreement with experimental data is obtained. Significant effects of anisotropic interactions are observed in the far wing.

Imaging diffraction oscillations for inelastic collisions of NO radicals with He and D-2

We present state-to-state differential cross sections for collisions of NO molecules (X2Π1/2,j=1/2,f) with He atoms and ortho-D2 (j = 0) molecules as a function of collision energy. A high angular resolution obtained using the combination of Stark deceleration and velocity map imaging allows for the observation of diffraction oscillations in the angular scattering distributions. Differences in the differential cross sections and, in particular, differences in the angular spacing between individual diffraction peaks are observed. Since the masses of D2 and He are almost equal and since D2(j = 0) may be considered as a pseudo-atom, these differences directly reflect the larger size of D2 as compared to He. The observations are in excellent agreement with the cross sections obtained from quantum close-coupling scattering calculations based on accurate ab initio NO-He and NO-D2 potential energy surfaces. For the latter, we calculated a new NO-D2 potential energy surface.

Potential energy and dipole moment surfaces of the triplet states of the O2(X3Σg−) − O2(X3Σg−,a1Δg,b1Σg+) complex

We compute four-dimensional diabatic potential energy surfaces and transition dipole moment surfaces of O2-O2, relevant for the theoretical description of collision-induced absorption in the forbidden X3Σg- → a1Δg and X3Σg- → b1Σg+ bands at 7883 cm-1 and 13 122 cm-1, respectively. We compute potentials at the multi-reference configuration interaction (MRCI) level and dipole surfaces at the MRCI and complete active space self-consistent field (CASSCF) levels of theory. Potentials and dipole surfaces are transformed to a diabatic basis using a recent multiple-property-based diabatization algorithm. We discuss the angular expansion of these surfaces, derive the symmetry constraints on the expansion coefficients, and present working equations for determining the expansion coefficients by numerical integration over the angles. We also present an interpolation scheme with exponential extrapolation to both short and large separations, which is used for representing the O2-O2 distance dependence of the angular expansion coefficients. For the triplet ground state of the complex, the potential energy surface is in reasonable agreement with previous calculations, whereas global excited state potentials are reported here for the first time. The transition dipole moment surfaces are strongly dependent on the level of theory at which they are calculated, as is also shown here by benchmark calculations at high symmetry geometries. Therefore, ab initio calculations of the collision-induced absorption spectra cannot become quantitatively predictive unless more accurate transition dipole surfaces can be computed. This is left as an open question for method development in electronic structure theory. The calculated potential energy and transition dipole moment surfaces are employed in quantum dynamical calculations of collision-induced absorption spectra reported in Paper II [T. Karman et al., J. Chem. Phys. 147, 084307 (2017)].

State-to-State Differential Cross Sections for Inelastic Collisions of NO Radicals with para-H2 and ortho-D2

We present state-to-state differential cross sections for collisions of NO molecules (X2Π1/2, j = 1/2f) with para-H2 and ortho-D2 molecules, at a collision energy of 510 and 450 cm–1, respectively. The angular scattering distributions for various final states of the NO radical are measured with high resolution using a crossed molecular beam apparatus that employs the combination of Stark deceleration and velocity map imaging. Rotational rainbows as well as diffraction oscillations are fully resolved in the scattering images. The observed angular scattering distributions are in excellent agreement with the cross sections obtained from quantum close-coupling scattering calculations based on recently computed NO–H2 potential energy surfaces, except for excitation of NO into the j = 7/2f channel. For this particular inelastic channel, a significant discrepancy with theory is observed, despite various additional measurements and calculations, at present, not understood.

Line-shape theory of the X3Σg−→a1Δg,b1Σg+ transitions in O2–O2 collision-induced absorption

We derive the theory of collision-induced absorption for electronic transitions in the approximation of an isotropic interaction potential. We apply this theory to the spin-forbidden X3Σg-→a1Δg and X3Σg-→b1Σg+ transitions in O2-O2, which are relevant for calibration in atmospheric studies. We consider two mechanisms for breaking the spin symmetry, either by the intermolecular exchange interaction between paramagnetic collision partners or by the intramolecular spin-orbit coupling. The calculations for the exchange-based mechanism employ the diabatic potential energy surfaces and transition dipole moment surfaces reported in Paper I [T. Karman et al., J. Chem. Phys. 147, 084306 (2017)]. We show that the line shape of the theoretical absorption spectra is insensitive to the large uncertainty in the electronic transition dipole moment surfaces. We also perform calculations using a simple model of the alternative mechanism involving intramolecular spin-orbit coupling, which leads to absorption intensities which are well below the experimental results. The relative intensity of this spin-orbit-based mechanism may impact the relative contribution to the absorption by collisions with diamagnetic collision partners, such as the atmospherically relevant N2 molecule. We furthermore show that both the line shape and temperature dependence are signatures of the underlying transition mechanism.

Observation of correlated excitations in bimolecular collisions

Although collisions between atoms and molecules are largely understood, collisions between two molecules have proven much harder to study. In both experiment and theory, our ability to determine quantum-state-resolved bimolecular cross-sections lags behind their atom–molecule counterparts by decades. For many bimolecular systems, even rules of thumb—much less intuitive understanding—of scattering cross sections are lacking. Here, we report the measurement of state-to-state differential cross sections on the collision of state-selected and velocity-controlled nitric oxide (NO) radicals and oxygen (O2) molecules. Using velocity map imaging of the scattered NO radicals, the full product-pair correlations of rotational excitation that occurs in both collision partners from individual encounters are revealed. The correlated cross sections show surprisingly good agreement with quantum scattering calculations using ab initio NO−O2 potential energy surfaces. The observations show that the well-known energy-gap law that governs atom–molecule collisions does not generally apply to bimolecular excitation processes, and reveal a propensity rule for the vector correlation of product angular momenta.Collisions between atoms and molecules are largely understood; however, our understanding of collisions between two molecules is lacking because they are significantly harder to study, Now, correlated rotational excitations have been observed in inelastic collisions between NO and O2 molecules. It is shown that the energy-gap law that governs atom–molecule collisions does not generally apply to bimolecular excitation processes.

Scattering resonances in bimolecular collisions between NO radicals and H-2 challenge the theoretical gold standard

Over the last 25 years, the formalism known as coupled-cluster (CC) theory has emerged as the method of choice for the ab initio calculation of intermolecular interaction potentials. The implementation known as CCSD(T) is often referred to as the gold standard in quantum chemistry. It gives excellent agreement with experimental observations for a variety of energy-transfer processes in molecular collisions, and it is used to calibrate density functional theory. Here, we present measurements of low-energy collisions between NO radicals and H2 molecules with a resolution that challenges the most sophisticated quantum chemistry calculations at the CCSD(T) level. Using hitherto-unexplored anti-seeding techniques to reduce the collision energy in a crossed-beam inelastic-scattering experiment, a resonance structure near 14 cm−1 is clearly resolved in the state-to-state integral cross-section, and a unique resonance fingerprint is observed in the corresponding differential cross-section. This resonance structure discriminates between two NO–H2 potentials calculated at the CCSD(T) level and pushes the required accuracy beyond the gold standard.Calculations at the theoretical gold standard generally yield accurate results for a variety of energy-transfer processes in molecular collisions. Using anti-seeding methods in a crossed-beam inelastic scattering experiment, a resonance structure is clearly resolved for NO–H2 collisions, pushing the required accuracy for theoretical potentials beyond the gold standard.

Publisher Correction: O2−O2 and O2−N2 collision-induced absorption mechanisms unravelled

In the version of this Article originally published, Figures 3 and 4 were erroneously swapped, this has been corrected in all versions of the Article.