A practical and efficient diabatization that combines Lorentz and Laplace functions to approximate nonadiabatic coupling terms

An ab initio diabatic study of rovibronic spectra of CN

An ab initio study of the rovibronic spectra for the cyano radical (CN) based on a diabatic representation is presented. This work considers 17 electronic states, 59 dipole moment curves, 88 spin-orbit coupling curves, and 30 electronic angular momentum coupling curves, which are obtained using the internally contracted multireference configuration interaction method including the Davidson correction (icMRCI + Q) with the aug-cc-pwCV5Z-DK basis set. The diabatic transformations are performed based on a property-based diabatization method to remove the avoided crossings for the D2Π-H2Π and b4Π-24Π pairs. Ab initio potential energy curves of the X2Σ+, B2Σ+, E2Σ+, A2Π, D2Π, H2Π, F2Δ and J2Δ electronic states are shifted to match the experimental electronic excitation energies and the equilibrium internuclear distances. The coupled nuclear motion Schrödinger equations are then solved to obtain the rovibronic spectra of CN for wavenumbers from 0 to 80 000 cm-1. At wavenumbers of 0-30 000 cm-1, our absorption cross sections agree well with available theoretical data. For wavenumbers above 30 000 cm-1, our cross sections are larger than previous data in view of the fact that the transitions involving high-lying electronic states are considered. This work provides an overall prediction of the rovibronic spectrum of CN. Our results are suitable for temperatures below 8000 K and could be useful for the investigations of planetary exploration.

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.

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.

Wavepacket propagations for the early time dynamics of proton-coupled electron transfer in the charge-transfer state of NH3Cl complex

A charge-transfer (CT) excited state of NH₃Cl, generated by photo-detachment of an electron from the anionic NH₃Cl^- precursor, can be represented as H₂N⁺-H-Cl^- and proceeds to two chemical reactions: one reaction generating NH₂ and HCl resulting from a proton transfer (PT) and the other reaction producing NH₃ and a Cl atom resulting from an electron transfer (ET); both are coupled to form a typical proton-coupled electron transfer (PCET) process. The early time dynamics of this CT were studied using time-dependent wavepacket propagation on three nonadiabatically coupled electronic states in a reduced three-dimensional space. The electronic states were treated using the XMS-CASPT2/aug-cc-pVTZ ab initio methodology. The population dynamics of the three coupled electronic states were analyzed in detail to reveal the initial stage of the PCET process up to ∼100 fs, while the branching ratio, χ = PT/(ET+PT), was determined after wavepacket propagations of up to 2000 fs. Another main result is the dependence of χ on the vibration levels of the initial precursor anion and the isotope substitution of the connecting H atom with deuterium and tritium. Our study reveals the detailed microscopic features of the PCET process embedded in the CT state of the NH₃Cl complex and certain systematic dependences of the branching ratio χ on the above factors.

Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only

A very simple equation, F_ij^App=[(∂²(V_i^a-V_j^a)/∂Q²)/(V_i^a-V_j^a)]^1/2/2, giving a reliable magnitude of non-adiabatic coupling terms (NACTs, F_ij's) based on adiabatic potential energies only (V_i^a and V_j^a) was discovered, and its reliability was tested for several prototypes of same-symmetry interstate crossings in LiF, C₂, NH₃Cl, and C₆H₅SH molecules. Our theoretical derivation starts from the analysis of the relationship between the Lorentzian dependence of NACTs along a diabatization coordinate and the well-established linear vibronic coupling scheme. This analysis results in a very simple equation, α=2κ/Δ_c, enabling the evaluation of the Lorentz function α parameter in terms of the coupling constant κ and the energy gap Δ_c (Δ_c=|V_i^a-V_j^a|_Qc ) between adiabatic states at the crossing point Q_C. Subsequently, it was shown that Q_C corresponds to the point where F_ij^App exhibit maximum values if we set the coupling parameter as κ=[(V_i^a-V_j^a)⋅(∂²(V_i^a-V_j^a)/∂Q²)]_Qc^1/2/2. Finally, we conjectured that this relation could give reasonable values of NACTs not only at the crossing point but also at other geometries near Q_C. In this final approximation, the pre-defined crossing point Q_C is not required. The results of our test demonstrate that the approximation works much better than initially expected. The present new method does not depend on the selection of an ab initio method for adiabatic electronic states but is currently limited to local non-adiabatic regions where only two electronic states are dominantly involved within a nuclear degree of freedom.