Comment on Inverse problem from discrete spectrum in the D = 2 dimensional space (2014 Phys. Scr. 989 085201)

We analyse a method for the construction of the potential-energy function from the moments of the ground-state density. The sum rule on which some expressions are based appear to be wrong, as well as the moments and potential-energy functions derived for some illustrative examples.

A Comparative Study of Potential Energy Curves Analytical Representations for CO, N2, P2, and ScF in Their Ground Electronic States

In this study, a detailed comparative analysis of four different potential energy functions is elaborated. These potential energy functions namely are Morse, Deng-Fan, Varshni, and Lennard-Jones. Furthermore, a mathematical representation for long-range region is elucidated. As a study case, four diatomic molecules (CO, N2, P2, and ScF) in their electronic ground states were chosen. Subsequently, the corresponding dissociation energy as well as some spectroscopic parameters were calculated accordingly.

RO-VIBRATIONAL PARTITION FUNCTION AND MEAN THERMAL ENERGY OF THE IMPROVED WEI OSCILLATOR

In this paper, the improved Wei oscillator has been used to model the experimental Rydberg-Klein-Rees data of the X2 Σg+ state of N2+ diatomic ions. Average absolute deviation from the dissociation energy of 0.3211% and mean absolute percentage deviation of 0.6107% were obtained. These results are quite satisfactory since they are within error requirement rate of less than 1% of the Lippincott’s criterion. Using an existing equation in the literature for bound state ro-vibrational energy, expressions for ro-vibrational partition function and mean thermal energy were derived for the improved Wei oscillator within the context of classical physics. The formulas obtained for ro-vibrational partition function and mean thermal energy were subsequently applied to the spectroscopic data of N2+ (X2 Σg+) diatomic ions. Studies have revealed that the partition function of the system decreases monotonically with decrease in temperature and increases with increase in upper bound vibrational quantum number. On the other hand, the mean thermal energies of the diatomic ions show an initial sharp decrease when the temperature is decreased and afterwards remains fairly stable as the temperature is further lowered. The results obtained in this work may find suitable applications in astrophysics were potential energy functions are required to model experimentally determined potential energy data with high precision. The work may also be useful in many other areas of physics which include: chemical physics, molecular physics, atomic physics and solid-state physics

Automatically Constructed Neural Network Potentials for Molecular Dynamics Simulation of Zinc Proteins

The development of accurate and efficient potential energy functions for the molecular dynamics simulation of metalloproteins has long been a great challenge for the theoretical chemistry community. An artificial neural network provides the possibility to develop potential energy functions with both the efficiency of the classical force fields and the accuracy of the quantum chemical methods. In this work, neural network potentials were automatically constructed by using the ESOINN-DP method for typical zinc proteins. For the four most common zinc coordination modes in proteins, the potential energy, atomic forces, and atomic charges predicted by neural network models show great agreement with quantum mechanics calculations and the neural network potential can maintain the coordination geometry correctly. In addition, MD simulation and energy optimization with the neural network potential can be readily used for structural refinement. The neural network potential is not limited by the function form and complex parameterization process, and important quantum effects such as polarization and charge transfer can be accurately considered. The algorithm proposed in this work can also be directly applied to proteins containing other metal ions.