Efficient Fourth-Order Split Operator for Solving the Triatomic Reactive Schrödinger Equation in the Time-Dependent Wavepacket Approach

2014 ◽  
Vol 118 (42) ◽  
pp. 9801-9810 ◽  
Author(s):  
Wentao Li ◽  
Dong H. Zhang ◽  
Zhigang Sun
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Split Operator

A FOURTH ORDER REAL-SPACE ALGORITHM FOR SOLVING LOCAL SCHRÖDINGER EQUATIONS

2003 ◽  
Vol 17 (28) ◽  
pp. 5459-5463 ◽  
Author(s):  
E. KROTSCHECK ◽  
J. AUER ◽  
S. A. CHIN
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Evolution Operator ◽  
Real Space ◽  
Imaginary Time ◽  
Split Operator ◽  
Normalisation Factor ◽  
Local Potentials ◽  
Positive Coefficients

We describe a rapidly converging algorithm for solving the Schrödinger equation with local potentials in real space. The algorithm is based on evolving the Schrödinger equation in imaginary time by factorizing the evolution operator e -εH to fourth order with purely positive coefficients. The states |ψj> and the associated energies extracted from the normalisation factor e -εEj converge as [Formula: see text]. Our algorithm is at least a factor of 100 more efficient than existing second order split operator methods. We apply the new scheme to a spherical jellium cluster with 20 electrons. We show that the low-lying eigenstates converge very rapidly and that the algorithm does not lose any of its effectiveness for very steep potentials.

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