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Systems of particles with a low binding energy and a wave function that is widely distributed in space are considered in this work. The study of these systems is not an easy task and requires different approaches, solution methods and additional computational recourses. Extensive studies of weakly bound systems have been conducted in recent times [1,2,3].
The goal of the work is the development and implementation of the discrete variables representation method [4,5], which allows to carry out calculations with smaller computing resources without loss of accuracy, reduce the calculation runtime, and as a result, conduct scientific research faster and with lower financial costs. Initially, the method was developed and implemented for systems with zero orbital momentum; the decomposition was performed according to functions constructed from Legendre polynomials.
The algorithm was generalized to perform high accuracy and quick calculation for systems with non-zero total orbital momentum. Also in order to perform calculations faster, the discrete-variable representations (DVR) of different kinds are used in this work.
The DVR method is based on constructing function with the well known functions such as Legendre polynomials $P_n$:
$\varphi_i(z) = \frac{P_n(z)}{P_n^{\prime}(z_i)(z-z_i)}$, $\varphi_i(z_k)=\delta_{ik}$,
where $z_k$ are defined by $P_n(z_k)=0$. Due to the properties of the DVR functions the calculations of the potential energy may be simplified. That allows to gain speed and accuracy for solving the problem.
Algorithm was used to calculate binding energies of the systems Ne$_3$, He$_3$, Li—He$_2$. The method allows to decrease runtime significantly without loss of accuracy.
References
[1] Yuan, J., Lin, C. D.: J. Phys. B: At. Mol. Opt. Phys. 31, 647 (1998).
[2] Baccarelli, I. et al.: Phys. Chem. Chem. Phys. 2, 4067 (2000).
[3] Kolganova, E.A.: Few-Body Systems 58, 57 (2017).
[4] Baye, D.: Phys. Rep. 565, 1107 (2015).
[5] Shizgal, B.: Spectral Methods in Chemistry and Physics. Springer, Nether-
lands (2015).
