Vibrational energies of some diatomic molecules for a modified and deformed potential

Abstract

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Achieving vibrational energies of diatomic systems with high quality by machine learning improved DFT method

“…The relative deviation (see eqn (9)) is used to measure the performance of ANN. For the test set consists of Na 35 Cl, 24 MgO and 12 C 16 O, the average relative deviation of the nal ANN model is 0.42%, the maximum relative deviation is 4.65%, the minimum relative deviation is 0.0000099%. On the sub-sample set, the average relative deviation is 1.10%, the maximum relative deviation is 15.92%, the minimum relative deviation is 0.0000038%.…”

“…A case in point is 24 MgO in Table 2. The task of the ANN is to learn the correct mapping relationship between input characteristic variables and system deviation E sys v .…”

“…18,21,22 (2) Data driven algorithms, such as empirical potential energy function and direct parameter formulas for energy levels. 23,24 The accuracy of data driven algorithms are higher than ab initio methods except that they are only applicable to some molecular systems which have superior-quality experimental data.…”

“…To obtain the best prediction, three widely used machine learning regression algorithms were tested with H 35 Cl as an example. Then, the best performing algorithm was used to predict the vibrational energy levels of 12 C 16 O, 24 MgO, and Na 35 Cl. Finally, the spectral quality of many systems ( 24 MgO, HF, N 2 , H 35 Cl, Na 35 Cl, 12 C 16 O, BeH, and SiN et al) were greatly improved.…”

Combining ab initio and machine learning method to improve the prediction of diatomic vibrational energies

“…Therefore, diatomic molecules energy structure are widely used in astrophysics, ultracold molecule, fundamental physical constants, chemical reaction manipulation and so forth [1][2][3][4][5][6][7][8][9]. From the computational perspective, there are two main strategies to obtain the vibrational energies: (1) ab initio method based on quantum mechanics principle deduction [10,11]; (2) data driven algorithm such as empirical potential energy function and direct parameter formulas for energy levels [12,13]. Ab initio method is universal, however, due to the complexity of quantum multi-body interaction (even diatomic molecules may involve hundreds of quantum objects), people have to model and approximate the wave function and Hamiltonian of the material according to the characteristics of the system, and make a subtle balance between the amount of calculation and the complexity of the model.…”