The interaction of NO(X2Π) with H2: Ab initio potential energy surfaces and bound states

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Two-color polarization spectroscopy measurements of Zeeman state-to-state collision induced transitions of nitric oxide in binary gas mixtures

We investigated collision induced transitions in the (0, 0) band of the A2Σ+-X2Π electronic transition of nitric oxide (NO) using two-color polarization spectroscopy (TCPS). Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295 K and 1 atm, were obtained with the pump beam tuned to the R11(11.5) and OP12(1.5) transitions. The buffer gases were He, Ar, and N2. The probe was scanned while the pump beam was tuned to the line center. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. A model for collisional transfer from an initial to a final Zeeman state was developed based on the difference in cosine of the rotational quantum number J projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the A2Σ+ level of NO is almost zero for rotational quantum numbers ≥8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra.

An ab initio study of the rovibronic spectrum of sulphur monoxide (SO): diabatic vs. adiabatic representation

We present an ab initio study of the rovibronic spectra of sulphur monoxide (³²S¹⁶O) using internally contracted multireference configuration interaction (ic-MRCI) method and aug-cc-pV5Z basis sets. It covers 13 electronic states X³Σ^-, a¹Δ, b¹Σ⁺, c¹Σ^-, A''³Σ⁺, A'³Δ, A³Π, B³Σ^-, C³Π, d¹Π, e¹Π, C'³Π, and (3)¹Π ranging up to 66 800 cm^-1. The ab initio spectroscopic model includes 13 potential energy curves, 23 dipole and transition dipole moment curves, 23 spin-orbit curves, and 14 electronic angular momentum curves. A diabatic representation is built by removing the avoided crossings between the spatially degenerate pairs C³Π-C'³Π and e¹Π-(3)¹Π through a property-based diabatisation method. We also present non-adiabatic couplings and diabatic couplings for these avoided crossing systems. All phases for our coupling curves are defined, and consistent, providing the first fully reproducible spectroscopic model of SO covering the wavelength range longer than 147 nm. Finally, an ab initio rovibronic spectrum of SO is computed.

Experimental and theoretical investigation of resonances in low-energy NO-H2 collisions

The experimental characterization of scattering resonances in low energy collisions has proven to be a stringent test for quantum chemistry calculations. Previous measurements on the NO-H₂ system at energies down to 10 cm^-1 challenged the most sophisticated calculations of potential energy surfaces available. In this report, we continue these investigations by measuring the scattering behavior of the NO-H₂ system in the previously unexplored 0.4 cm^-1-10 cm^-1 region for the parity changing de-excitation channel of NO. We study state-specific inelastic collisions with both para- and ortho-H₂ in a crossed molecular beam experiment involving Stark deceleration and velocity map imaging. We are able to resolve resonance features in the measured integral and differential cross sections. Results are compared to predictions from two previously available potential energy surfaces, and we are able to clearly discriminate between the two potentials. We furthermore identify the partial wave contributions to these resonances and investigate the nature of the differences between collisions with para- and ortho-H₂. Additionally, we tune the energy spreads in the experiment to our advantage to probe scattering behavior at energies beyond our mean experimental limit.

Probing the location of the unpaired electron in spin-orbit changing collisions of NO with Ar

Understanding the molecular forces that drive a reaction or scattering process lies at the heart of molecular dynamics. Here, we present a combined experimental and theoretical study of the spin-orbit changing scattering dynamics of oriented NO molecules with Ar atoms. Using our crossed molecular beam apparatus, we have recorded velocity-map ion images and extracted differential and integral cross sections of the scattering process in the side-on geometry. We observe an overall preference for collisions close to the N atom in the spin-orbit changing manifold, which is a direct consequence of the location of the unpaired electron on the potential energy surface. In addition, a prominent forward scattered feature is observed for intermediate, even rotational transitions when the atom approaches the molecule from the O-end. The appearance of this peak originates from an attractive well on the A' potential energy surface, which efficiently directs high impact parameter trajectories towards the region of high unpaired electron density near the N-end of the molecule. The ability to orient molecules prior to collision, both experimentally and theoretically, allows us to sample different regions of the potential energy surface(s) and unveil the associated collision pathways.

An accurate 5D potential energy surface for H3O+-H2 interaction

Modeling of the observational spectra of H₃O⁺ allows for a detailed understanding of the interstellar oxygen chemistry. While its spectroscopy was intensively studied earlier, our knowledge about the collision of H₃O⁺ with the abundant colliders in the interstellar medium is rather limited. In order to treat these collisional excitation processes, it is first necessary to calculate the potential energy surface (PES) of the interacting species. We have computed the five-dimensional rigid-rotor PES of the H₃O⁺-H₂ system from the explicitly correlated coupled-cluster theory at the level of singles and doubles with perturbative corrections for triple excitations [CCSD(T)-F12] with the moderate-size augmented correlation-consistent valence triple zeta (aug-cc-pVTZ) basis set. The well depth of the PES is found to be rather large, about 1887.2 cm^-1. The ab initio potential was fitted over an angular expansion in order to effectively use it in quantum scattering codes. As a first application, we computed dissociation energies for the different nuclear spin isomers of the H₃O⁺-H₂ complex.

Correlations in rotational energy transfer for NO-D2 inelastic collisions

We present a combined experimental and theoretical study of state-to-state inelastic collisions between NO (X ²Π_1/2, j = 1/2, f) radicals and D₂ (j = 0, 1, 2, 3) molecules at collision energies of 100 cm^-1 and 750 cm^-1. Using the combination of Stark deceleration and velocity map imaging, we fully resolve pair-correlated excitations in the scattered molecules. Both spin-orbit conserving and spin-orbit changing transitions in the NO radical are measured, while the coincident rotational excitation (j = 0 → j = 2) and rotational de-excitation (j = 2 → j = 0 and j = 3 → j = 1) in D₂ are observed. De-excitation of D₂ shows a strong dependence on the spin-orbit excitation of NO. We observe translation-to-rotation energy transfer as well as direct rotation-to-rotation energy transfer at the lowest collision energy probed. The experimental results are in good agreement with cross sections obtained from quantum coupled-channels calculations based on recent NO-D₂ potential energy surfaces. The observed trends in the correlated scattering cross sections are understood in terms of the NO-D₂ quadrupole-quadrupole interaction.

Structural characterization of the NO(X2Π)-N2O complex with mid-infrared laser absorption spectroscopy and quantum chemical calculations

Both positive and negative ions of N₃O₂ have been observed in various experiments. The neutral N₃O₂ was predicted to exist either as a weakly bound NO·N₂O complex or a covalent molecule. The rovibrational spectrum of the NO(X²Π)-N₂O complex has been measured for the first time in the 5.3 µm region using distributed quantum cascade lasers to probe the direct absorption in a slit-jet supersonic expansion. The observed spectrum is analyzed with a semi-rigid asymmetric rotor Hamiltonian for a planar open-shell complex, giving a bent geometry with an a-axis-NO angle of about 21.9°. The vibrationally averaged ²A'-²A″ energy separation is determined to be ε = 144.56(95) cm^-1 for the ground state, indicating that the electronic orbital angular momentum is partially quenched upon complexation. Geometry optimizations of the complex restricted to a planar configuration at the RCCSD(T)/aug-cc-pVTZ level of theory show that the ²A″ state is more stable than the ²A' state by about 110 cm^-1 and the N atom of NO points to the central N atom of N₂O at the minimum of the ²A″ state.

Scattering resonances in bimolecular collisions between NO radicals and H2 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.

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 (X²Π_1/2, 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.