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Different time propagation approaches have been developed to solve the von Neuman equation (equation 1). Different time propagation approaches are based on different ways to express the exponential term in equation 3. In the case of Chebyshev, the unitary operator is calculated using a polynomial series (equation 4).
The polynomial series is exponential in nature but it can be truncated when the desired convergence is reached. Each term in the series is smaller than the previous term. In this scheme Fock matrix is scaled to restrict all the eigenvalues (ε ) within -1 and +1 range. Each term of the series can be calculated using a recursive formula.
I have written a code that will add Chebyshev propagator in the RT-TDDFT module of NWChem software. All the features of RT-TDDFT module will be available with this propagator. All the details required for setting up the code is provided on the GitHub page (https://github.com/SoumenChem/Chebyshev ). Feel free to download and try the code. Please email me with your questions and suggestions at CHEMSGHOSH(at)GMAIL.COM.
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