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Efficient fourth-order split operator for solving the triatomic reactive Schrödinger equation in the time-dependent

Wentao Li1, Dong H Zhang, Zhigang Sun

  • 1Center for Theoretical and Computational Chemistry and State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences , Dalian 116023, China.

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The fourth-order split operator (4A6a) in the kinetic-potential-kinetic (TVT) form is recommended for reactive scattering calculations. This method demonstrates superior numerical efficiency in time-dependent quantum wavepacket simulations.

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Area of Science:

  • Computational Chemistry
  • Quantum Dynamics
  • Chemical Physics

Background:

  • Time-dependent quantum wavepacket methods are crucial for simulating reactive scattering.
  • Higher-order split operators offer improved accuracy but require careful selection.
  • Previous studies explored potential-kinetic-potential (VTV) forms for these operators.

Purpose of the Study:

  • To evaluate the efficiency of a fourth-order split operator (4A6a) in the kinetic-potential-kinetic (TVT) form.
  • To compare the performance of TVT split operators against VTV split operators in reactive scattering.
  • To recommend a reliable propagator for time-dependent quantum wavepacket calculations.

Main Methods:

  • Implementation of the fourth-order split operator (4A6a) in the TVT form.
  • Numerical simulations of several triatomic reactive scattering processes (H + H2, H + H2(+), H + NH, H + O2, F + HD).
  • Comparative performance analysis of TVT and VTV split operators.

Main Results:

  • The 4A6a operator in the TVT form exhibited optimal performance among tested higher-order split operators.
  • Consistent good numerical efficiency was observed for the recommended TVT 4A6a operator.
  • The TVT form demonstrated superior performance compared to the VTV form in the tested reactions.

Conclusions:

  • The fourth-order split operator (4A6a) in the TVT form is highly recommended for general use in reactive scattering calculations.
  • This propagator offers excellent numerical efficiency and can be reliably applied without extensive prior testing.
  • The TVT splitting strategy is advantageous for higher-order split operators in wavepacket dynamics.