Vibrational and rotational population distributions of MgH(v"=0 and 1) produced in the reaction of Mg(3s3p 1P1) with H2

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.

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.

Reaction pathway for the nonadiabatic reaction of Ca(4s3d 1D)+H2-->CaH(X 2Sigma+)+H

The reaction pathway and the nascent CaH product distribution in the reaction Ca(4s3d (1)D)+H(2)-->CaH(X (2)Sigma(+))+H are obtained using a pump-probe technique. The Ca atom is first prepared in the 3 (1)D state by a two-photon absorption, and then in brief time delay the laser-induced fluorescence of the reaction product CaH is monitored. The CaH(v=0,1) distributions appear to be single peaked, as characterized by Boltzmann rotational temperature of 807+/-38 K (v=0) and 684+/-77 K (v=1). The vibrational population ratio of CaH(v=0)/CaH(v=1) is determined to be 3.3+/-0.1, while the v=2 population is not detectable. The fractions of the available energy partitioning into rotation, vibration, and translation are estimated to be 0.36+/-0.05, 0.28+/-0.04, and 0.36+/-0.05, respectively. With the aid of the potential energy surfaces calculations, the current reaction should favor a near C(2v) collision configuration. The temperature dependence measurement yields a positive slope, indicative of the reaction occurrence without any potential barrier. The colliding species are anticipated to follow an attractive 1B(2) (or 2A') surface and then transit nonadiabatically to the reactive ground state surface.

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

A three-dimensional global potential energy surface for the ground electronic state of MgH(2) is constructed from more than 3000 ab initio points calculated using the internally contracted multireference configuration interaction method with the Davidson correction at the complete basis set limit. Low-lying vibrational energy levels of MgH(2) and MgD(2) are calculated using the Lanczos algorithm, and found to be in good agreement with known experimental band origins. The majority of the vibrational energy levels up to 8000 cm(-1) are assigned with normal mode quantum numbers. However, our results indicate a gradual transition from a normal mode regime for the stretching vibrations at low energies to a local mode regime near 7400 cm(-1), as evidenced by a decreasing energy gap between the (n(1),0,0) and (n(1)-1,0,1) vibrational states and bifurcation of the corresponding wave functions.

Reaction pathway and potential barrier for the CaH product in the reaction of Ca(4s4p 1P1)+H2→CaH(X 2Σ+)+H

The nascent CaH product in the reaction Ca(4s4p1P1) + H2 --> CaH(X2Sigma+) + H is obtained using a pump-probe technique. The CaH(v = 0,1) distributions, with a population ratio of CaH(v = 0)/CaH(v = 1) = 2.7+/-0.2, may be characterized by low Boltzmann rotational temperature. According to Arrhenius theory, the temperature dependence measurement yields a potential barrier of 3820+/-480 cm(-1) for the current reaction. As a result of the potential energy surfaces (PES) calculations, the reaction pathway favors a Ca insertion into the H2 bond along a (near) C2v geometric approach. As the H2 bond is elongated, the configurational mixing between the orbital components of the 4p and nearby low-lying 3d state with the same symmetry makes significant the nonadiabatic transition between the 5A' and 2A' surface in the repulsive limbs. Therefore, the collision species are anticipated to track along the 5A' surface, then undergo nonadiabatic transition to the inner limb of the 2A' surface, and finally cross to the reactive 1A' surface. The observed energy barrier probably accounts for the energy requirement to surmount the repulsive hill in the entrance. The findings of the nascent CaH product distributions may be reasonably interpreted from the nature of the intermediate structure and lifetime after the 2A'-1A' surface transition. The distinct product distributions between the Ca(4 1P1) and Mg(3 1P1) reactions with H2 may also be realized with the aid of the PES calculations.