Spin-orbit coupled diabatic potential energy surfaces for quantum dynamics

• Applicant: Professor Dr. Wolfgang Eisfeld
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2014 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 251392548

• Final Report Year: 2022

Final Report Abstract

The aim of the present project was the development of fully coupled diabatic potential energy surface (PES) models for methyl and phenyl iodide (CH3 I and PhI) in order to study the quantum dynamics of the photodissociation processes. These models have to account for both derivative and spin-orbit (SO) coupling and must be based on accurate electronic structure reference data. A new approach has been developed called Effective Relativistic Coupling by Asymptotic Representation (ERCAR) that yields the desired fully coupled PES models after diabatising SO free reference data. This method is key because the accurate and robust ab initio computation of fine structure energies is computationally by far too demanding for the present cases and a huge number of data points are required for fitting the model parameters. The central idea of the ERCAR method is to express the molecular electronic Hamiltonian in diabatic basis states, which are direct products of atomic states of iodine, carrying all the SO coupling effects, and molecular fragment states. This results in a model of a standard diabatic matrix for the Coulomb Hamiltonian plus a constant atomic SO matrix, which is determined analytically. This method was demonstrated to yield very accurate results for the fine structure states if accurate SO free reference data is represented sufficiently well by the diabatic Coulomb model. Two main problems had to be solved during this project. The first is the ab initio determination of the reference data for a fairly large number of electronic states. It turned out very difficult and time consuming to fine tune the setup of the ab initio calculations such that diabatisable data could be acquired. Therefore, the data acquisition for the full-dimensional models is still work in progress. The second problem is the diabatisation of a fairly large number of states including states for which no ab initio data can be computed throughout the nuclear configuration space (NCS). However, such states turn out to be relevant for the representation of the SO operator. As a solution, a new diabatisation method was developed, which combines a standard diabatisation by ansatz based entirely on adiabatic energies with a specific block-diagonalisation approach of the adiabatic wave functions and thus is called hybrid diabatisation. This very powerful diabatisation approach is widely applicable to many molecular systems and in the present case it is key to success. The hybrid diabatisation of the CH3 I data in a basis of asymptotic reference states yields excellent results and so far a 3D model is available, which is currently extended for the remaining degrees of freedom. By contrast, a comparable diabatisation of PhI data fails because no sufficient asymptotic basis could be found to represent the adiabatic states at short distance. The difference between these two systems is that in CH3 I all relevant electronic excitations are among the iodine orbitals while in PhI these excitations are among the phenyl orbitals. This problem was solved by a newly developed extension to the hybrid diabatisation. So called compensation states are defined and added to the diabatic basis such that a sufficient representation of the adiabatic states of interest becomes possible throughout the NCS. It turns out that these compensation states basically do not contribute to the SO coupling and thus can be used within the ERCAR approach. The hybrid diabatisation with compensation states yields a 1D ERCAR model for PhI in excellent agreement with available ab initio data for the fine structure states. The extension of this model to more degrees of freedom is work in progress. One more important development was improving the accuracy of our diabatic models by using artificial neural networks (ANNs). This ANN diabatisation utilizes a reference model that yields a qualitatively correct result, which is tuned by the ANN to improve the accuracy. This approach is very general and was tested initially for the extremely complicated quantum dynamics of NO3 , yielding results in unprecedented agreement with experiment. The application to PhI improved the accuracy of the energy data by up to two orders of magnitude. This ANN approach also solves many problems of the previous approach to expand the diabatic matrices in higher order Taylor series. The robustness of this ANN diabatisation seems very promising for future work.

Publications

• A new approach for the development of diabatic potential energy surfaces: Hybrid blockdiagonalization and diabatization by ansatz. J. Chem. Phys., 2016, 145, 184108
  N. Wittenbrink, F. Venghaus, D. Williams and W. Eisfeld
  
• Block-diagonalization as tool for the robust diabatization of high-dimensional potential energy surfaces. J. Chem. Phys., 2016, 144, 114110
  F. Venghaus and W. Eisfeld
  
• Development of multi-mode diabatic spin-orbit models at arbitrary order. J. Chem. Phys., 2016, 148 094102
  T. Weike and W. Eisfeld
  
• An improved spin-orbit coupling model for use within the effective relativistic coupling by asymptotic representation (ERCAR) method. J. Chem. Phys., 2017, 146, 144110
  N. Wittenbrink and W. Eisfeld
  
• Extension of the effective relativistic coupling by asymptotic representation (ERCAR) approach to multi-dimensional potential energy surfaces: 3D model for CH3 I. J. Chem. Phys., 2018, 148 094102
  N. Wittenbrink and W. Eisfeld
  
• Neural network diabatization: A new ansatz for accurate high-dimensional coupled potential energy surfaces. J. Chem. Phys., 2018, 149 204106
  D. M. G. Williams and W. Eisfeld
  
• Diabatic neural network potentials for accurate vibronic quantum dynamics – The test case of planar NO3. J. Chem. Phys., 2019, 151, 164118
  David M. G. Williams and Wolfgang Eisfeld
  
• Complete Nuclear Permutation Inversion Invariant Artificial Neural Network (CNPI-ANN) Diabatization for the Accurate Treatment of Vibronic Coupling Problems. J. Phys. Chem. A, 2020, 124, 7608
  David M. G. Williams and Wolfgang Eisfeld
  
• A general method for the development of diabatic spin-orbit models for multi-electron systems. J. Chem. Phys., 2022, 156 054115
  F. Fritsch, T. Weike, and W. Eisfeld