An ab initio potential energy surface and vibrational states of MgH2(1 1A′)

A new permutation-symmetry-adapted machine learning diabatization procedure and its application in MgH2 system

This work introduces a new permutation-symmetry-adapted machine learning diabatization procedure, termed the diabatization by equivariant neural network (DENN). In this approach, the permutation symmetric and anti-symmetric elements in diabatic potential energy metrics (DPEMs) were simultaneously simulated by the equivariant neural network. The diabatization by deep neural network scheme was adopted for machine learning diabatization, and non-zero diabatic coupling was included to increase accuracy in the near degenerate region. Based on DENN, the global DPEMs for 1¹A' and 2¹A' states of MgH₂ have been constructed. To the best of our knowledge, these are the first global DPEMs for the MgH₂ system. The root-mean-square-errors (RMSEs) for diagonal elements (H₁₁ and H₂₂) and the off-diagonal element (H₁₂) around the conical intersection region were 5.824, 5.307, and 5.796 meV, respectively. The RMSEs of global adiabatic energies for two adiabatic states were 4.613 and 12.755 meV, respectively. The spectroscopic calculations of the 1¹A' state in the linear HMgH region are in good agreement with the experiment and previous theoretical results. The differences between calculated frequencies and corresponding experiment values are 1.38 and 1.08 cm^-1 for anti-symmetric stretching fundamental vibrational frequency and first overtone. The global DPEMs obtained in this work should be useful for further quantum mechanics dynamic simulations on the MgH₂ system.

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca6 H9 [N(SiMe3 )2 ]3 (pmdta)3 (pmdta=N,N,N',N'',N''-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n-1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.

Roaming Reactions and Dynamics in the van der Waals Region

Roaming reactions were first clearly identified in photodissociation of formaldehyde 15 years ago, and roaming dynamics are now recognized as a universal aspect of chemical reactivity. These reactions typically involve frustrated near-dissociation of a quasibound system to radical fragments, followed by reorientation at long range and intramolecular abstraction. The consequences can be unexpected formation of molecular products, depletion of the radical pool in chemical systems, and formation of products with unusual internal state distributions. In this review, I examine some current aspects of roaming reactions with an emphasis on experimental results, focusing on possible quantum effects in roaming and roaming dynamics in bimolecular systems. These considerations lead to a more inclusive definition of roaming reactions as those for which key dynamics take place at long range.

Theories and simulations of roaming

The phenomenon of roaming in chemical reactions has now become both commonly observed in experiment and extensively supported by theory and simulations. Roaming occurs in highly-excited molecules when the trajectories of atomic motion often bypass the minimum energy pathway and produce reaction in unexpected ways from unlikely geometries. The prototypical example is the unimolecular dissociation of formaldehyde (H₂CO), in which the "normal" reaction proceeds through a tight transition state to yield H₂ + CO but for which a high fraction of dissociations take place via a "roaming" mechanism in which one H atom moves far from the HCO, almost to dissociation, and then returns to abstract the second H atom. We review below the theories and simulations that have recently been developed to address and understand this new reaction phenomenon.

Selective gating to vibrational modes through resonant X-ray scattering

The dynamics of fragmentation and vibration of molecular systems with a large number of coupled degrees of freedom are key aspects for understanding chemical reactivity and properties. Here we present a resonant inelastic X-ray scattering (RIXS) study to show how it is possible to break down such a complex multidimensional problem into elementary components. Local multimode nuclear wave packets created by X-ray excitation to different core-excited potential energy surfaces (PESs) will act as spatial gates to selectively probe the particular ground-state vibrational modes and, hence, the PES along these modes. We demonstrate this principle by combining ultra-high resolution RIXS measurements for gas-phase water with state-of-the-art simulations.

Investigating dynamics of polyatomic molecules is difficult as their potential energy surfaces are multidimensional due to coupled degrees of freedom. Here the authors demonstrate a spatial selective gating technique to probe the different vibrational modes of water upon core-level excitation with X-rays.

A study of the water molecule using frequency control over nuclear dynamics in resonant X-ray scattering

We report a full analysis of the resonant inelastic X-ray scattering spectra of H₂O, D₂O and HDO.

Toward Understanding the Roaming Mechanism in H + MgH → Mg + HH Reaction

The roaming mechanism in the reaction H + MgH →Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio three-dimensional ground electronic state potential energy surface. The reaction dynamics are explored by running trajectories initialized on a four-dimensional dividing surface anchored on three-dimensional normally hyperbolic invariant manifold associated with a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase space where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. The complex forming trajectories in the HMgH well can either return to the radical channel or "roam" to the MgHH minimum from where the molecule may react.

Separability of tight and roaming pathways to molecular decomposition

Recent studies have questioned the separability of the tight and roaming mechanisms to molecular decomposition. We explore this issue for a variety of reactions including MgH(2) → Mg + H(2), NCN → CNN, H(2)CO → H(2) + CO, CH(3)CHO → CH(4) + CO, and HNNOH → N(2) + H(2)O. Our analysis focuses on the role of second-order saddle points in defining global dividing surfaces that encompass both tight and roaming first-order saddle points. The second-order saddle points define an energetic criterion for separability of the two mechanisms. Furthermore, plots of the differential contribution to the reactive flux along paths connecting the first- and second-order saddle points provide a dynamic criterion for separability. The minimum in the differential reactive flux in the neighborhood of the second-order saddle point plays the role of a mechanism divider, with the presence of a strong minimum indicating that the roaming and tight mechanisms are dynamically distinct. We show that the mechanism divider is often, but not always, associated with a second-order saddle point. For the formaldehyde and acetaldehyde reactions, we find that the minimum energy geometry on a conical intersection is associated with the mechanism divider for the tight and roaming processes. For HNNOH, we again find that the roaming and tight processes are dynamically separable but we find no intrinsic feature of the potential energy surface associated with the mechanism divider. Overall, our calculations suggest that roaming and tight mechanisms are generally separable over broad ranges of energy covering most kinetically relevant regimes.

Spectroscopic Properties of MgH2, MgD2, and MgHD Calculated from a New ab Initio Potential Energy Surface

A three-dimensional potential energy surface for the ground electronic state of MgH2 has been constructed from 9030 symmetry-unique ab initio points calculated using the icMRCI+Q method with aug-cc-pVnZ basis sets for n=3, 4, and 5, with core-electron correlation calculated at the MR-ACPF level of theory using cc-pCVnZ basis sets, with both calculations being extrapolated to the complete basis set limit. Calculated spectroscopic constants of MgH2 and MgD2 are in excellent agreement with recent experimental results: for four bands of MgH2 and one band of MgD2 the root-mean-square (rms) band origin discrepancies were only 0.44 and 0.06 cm(-1), respectively, and the rms relative discrepancies in the inertial rotational constants (B[v]) were only 0.0196% and 0.0058%, respectively. Spectroscopic constants for MgHD were predicted using the same potential surface.

An accurate ab initio potential energy surface and calculated spectroscopic constants for BeH2, BeD2, and BeHD

A three-dimensional potential energy surface for the ground electronic state of BeH(2) has been determined by three-dimensional spline interpolation over 6864 symmetry-unique ab initio points calculated at the icMRCI/aug-cc-pV5Z level and corrected for core-electron correlation computed at the MR-ACPF/cc-pCV5Z level. Calculated spectroscopic constants of BeH(2) and BeD(2) are in excellent agreement with recent experimental results: for 11 bands of BeH(2) and 5 bands of BeD(2) the root mean square (rms) band origin discrepancies were only 0.15(+/-0.09) and 0.46(+/-0.19) cm(-1), respectively, and the rms relative discrepancies in the inertial rotational constants (B([v])) were only 0.028% and 0.023%, respectively. Spectral constants for BeHD were predicted using the same potential surface. The effect of different interpolation methods on predicted potential function values and on the calculated level energies and spectroscopic constants has been examined.

Infrared Emission Spectra and Equilibrium Structures of Gaseous HgH2 and HgD2

A detailed analysis of the high-resolution infrared emission spectra of gaseous HgH2 and HgD2 in the 1200-2200 cm(-1) spectral range is presented. The nu3 antisymmetric stretching fundamental bands of 204HgH2, 202HgH2, 201HgH2, 200HgH2, 199HgH2, 198HgH2, 204HgD2, 202HgD2, 201HgD2, 200HgD2, 199HgD2, and 198HgD2, as well as a few hot bands involving nu1, nu2, and nu3 were analyzed rotationally, and spectroscopic constants were obtained. Using the rotational constants of the 000, 100, 01(1)0, and 001 vibrational levels, we determined the equilibrium rotational constants (B(e)) of the most abundant isotopologues, 202HgH2 and 202HgD2, to be 3.135325(24) cm(-1) and 1.569037(16) cm(-1), respectively, and the associated equilibrium Hg-H and Hg-D internuclear distances (re) are 1.63324(1) A and 1.63315(1) A, respectively. The re distances of 202HgH2 and 202HgD2 differ by about 0.005%, which can be attributed to the breakdown of the Born-Oppenheimer approximation.

Ab Initio Prediction of the Potential Energy Surface and Vibrational−Rotational Energy Levels of Calcium Dihydride, CaH2

The equilibrium structure and potential energy surface of calcium dihydride, CaH(2), have been determined from large-scale ab initio calculations using the coupled-cluster method, CCSD(T), in conjunction with basis sets of quadruple- and quintuple-zeta quality. The CaH(2) molecule was found to be quasilinear. The HCaH bending potential function was predicted to be extraordinarily flat near the minimum, located at the HCaH angle of 164 degrees. The barrier to linearity was calculated to be just 6 cm(-1). The vibrational-rotational energy levels of various isotopomers were predicted using the variational method. The calculated vibrational fundamental frequencies are in good agreement with the results of matrix-isolation studies, and the other predicted spectroscopic constants can assist in the future detection of calcium dihydride in the gas phase.

A reliableab initiopotential energy surface and vibrational states for the ground electronic state of HgH2(XΣg+1)

A three-dimensional global potential energy surface for the ground (X (1)Sigma(+)(g))electronic state of HgH(2) is constructed from more than 13,00 ab initio points. These points are generated using an internally contracted multireference configuration interaction method with the Davidson correction and a large basis set. Low-lying vibrational energy levels of HgH(2), HHgD, and HgD(2) calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins. The majority of the vibrational energy levels up to 9000 cm(-1) are assigned with normal mode quantum numbers. Our results indicate a gradual transition for the stretching vibrations from the normal mode regime at low energies to the local mode regime near 9000 and 8000 cm(-1) for HgH(2) and HgD(2), respectively, as evidenced by a decreasing energy gap between the (0,0,n(3)) and (1,0,n(3)-1) vibrational states and bifurcation of the corresponding wave functions.

Infrared emission spectra and equilibrium bond lengths of gaseous ZnH2 and ZnD2

A detailed analysis of the high resolution infrared emission spectra of gaseous ZnH2 and ZnD2 in the 800-2200 cm(-1) spectral range is presented. The nu3 antisymmetric stretching fundamental bands of 64ZnH2, 66ZnH2, 67ZnH2, 68ZnH2, 64ZnD2, 66ZnD2 and 68ZnD2, as well as several hot bands involving nu1, nu2 and nu3 were rotationally analyzed, and spectroscopic constants were obtained. Rotational l-type doubling and l-type resonance, local perturbations, and Fermi resonances were observed in the vibration-rotation bands of both ZnH2 and ZnD2, and equilibrium vibrational frequencies (omega1, omega2 and omega3) were estimated. Using the rotational constants of the 000, 100, 01(1)0 and 001 vibrational levels, the equilibrium rotational constants (B(e)) of 64ZnH2 and 64ZnD2 were determined to be 3.600 269(31) cm(-1) and 1.801 985(25) cm(-1), respectively, and the associated equilibrium bond lengths (r(e)) are 1.524 13(1) angstroms and 1.523 94(1) angstroms, respectively. The difference between the r(e) values of 64ZnH2 and 64ZnD2 is about 0.01%, and is mainly due to the breakdown of the Born-Oppenheimer approximation.