Journal of Physics A: Mathematical and Theoretical, 2020
In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Ry... more In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Rydberg) states is quantified by means of the Rényi and Shannon entropies of its momentum probability density. These quantities, which rest at the core of numerous fields from atomic and molecular physics to quantum technologies, are determined by means of a methodology based on the strong degree-asymptotics of a modified L q -norm of the Gegenbauer polynomials which control the wavefunctions of these states in momentum space. The leading term of these entropic quantities is found from first principles, i.e. by means of the Coulomb potential parameters (space dimensionality, the nuclear charge) and the states’s hyperquantum numbers, in a rigorous simple manner. It is shown that they fulfill a logarithmic growth scaling law with the principal hyperquantum number n which characterizes the Rydberg state.
Results are presented for a molecular dynamics simulation of melting of the water hexamer from th... more Results are presented for a molecular dynamics simulation of melting of the water hexamer from threedimensional configurations (the book, cage, and prism isomers). The interactions between water molecules are described using two rigid potentials-TIP4P and TIP5P. The isomer geometry is determined using the connectivity matrix of the H-bond network graph. It is found in a numerical experiment that the Lindemann index, which shows the fluctuations in the length of intermolecular bonds, behaves similarly for all the studied initial isomers of the cluster. The melting of the cluster is found to depend on the interaction potential used in the study. For the cluster's full energy, regions are identified which can be attributed to the premelting phase, which is dominated by the book isomer for TIP4P and ring isomer for TIP5P. The energy region attributed to the quasi-liquid phase of the cluster is shown to be characterized by isomers with ring and linear structures for both of the potentials.
... Elena D. Belega a , Corresponding Author Contact Information , E-mail The Corresponding Autho... more ... Elena D. Belega a , Corresponding Author Contact Information , E-mail The Corresponding Author , Evgeny A. Cheremukhin a , Pavel V. Elyutin b , E-mail The Corresponding Author and Dmitry N. Trubnikov a , E-mail The Corresponding Author. ...
This paper presents the results of dynamic behavior modeling of phase states (solid and liquid) o... more This paper presents the results of dynamic behavior modeling of phase states (solid and liquid) of water clusters ((H 2 O) 8 , (H 2 O) 10 , and (H 2 O) 12) by molecular dynamics method. The initial configurations of the clusters were cube for octamer, pentagonal prism for decamer, and fused-cube structure for dodecamer. The different analytical interaction potentials (TIPnP (n = 3, 4), SPC, and SPC/E) were applied to the phase dynamics of water octamer to choose the most appropriate potential for the study. The dynamic criteria based on the molecule's potential energy distribution were applied for identification of solid and liquid phases of decamer and dodecamer. The most probable conformers of decamer and dodecamer in different phases were obtained.
The partition functions and thermodynamic properties of small clusters of rare gas atoms. [The Jo... more The partition functions and thermodynamic properties of small clusters of rare gas atoms. [The Journal of Chemical Physics 100, 3843 (1994)]. Pavel V. Elyutin, Vladimir I. Baranov, Elena D. Belega, Dmitrij N. Trubnikov. Abstract. ...
The molecular dynamics method was used to analyze the dynamic characteristics of water clusters i... more The molecular dynamics method was used to analyze the dynamic characteristics of water clusters in the solid and liquid phase. A criterion is proposed for choosing the interaction potential, which is based on the distributions of the potential energy of cluster molecules in different phases. The connection of the obtained distributions with the dynamics and structure of the hydrogen bonds’ net of the cluster is shown.
Journal of Physics A: Mathematical and Theoretical, 2020
In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Ry... more In this work the momentum spreading of a multidimensional hydrogenic system in highly excited (Rydberg) states is quantified by means of the Rényi and Shannon entropies of its momentum probability density. These quantities, which rest at the core of numerous fields from atomic and molecular physics to quantum technologies, are determined by means of a methodology based on the strong degree-asymptotics of a modified L q -norm of the Gegenbauer polynomials which control the wavefunctions of these states in momentum space. The leading term of these entropic quantities is found from first principles, i.e. by means of the Coulomb potential parameters (space dimensionality, the nuclear charge) and the states’s hyperquantum numbers, in a rigorous simple manner. It is shown that they fulfill a logarithmic growth scaling law with the principal hyperquantum number n which characterizes the Rydberg state.
Results are presented for a molecular dynamics simulation of melting of the water hexamer from th... more Results are presented for a molecular dynamics simulation of melting of the water hexamer from threedimensional configurations (the book, cage, and prism isomers). The interactions between water molecules are described using two rigid potentials-TIP4P and TIP5P. The isomer geometry is determined using the connectivity matrix of the H-bond network graph. It is found in a numerical experiment that the Lindemann index, which shows the fluctuations in the length of intermolecular bonds, behaves similarly for all the studied initial isomers of the cluster. The melting of the cluster is found to depend on the interaction potential used in the study. For the cluster's full energy, regions are identified which can be attributed to the premelting phase, which is dominated by the book isomer for TIP4P and ring isomer for TIP5P. The energy region attributed to the quasi-liquid phase of the cluster is shown to be characterized by isomers with ring and linear structures for both of the potentials.
... Elena D. Belega a , Corresponding Author Contact Information , E-mail The Corresponding Autho... more ... Elena D. Belega a , Corresponding Author Contact Information , E-mail The Corresponding Author , Evgeny A. Cheremukhin a , Pavel V. Elyutin b , E-mail The Corresponding Author and Dmitry N. Trubnikov a , E-mail The Corresponding Author. ...
This paper presents the results of dynamic behavior modeling of phase states (solid and liquid) o... more This paper presents the results of dynamic behavior modeling of phase states (solid and liquid) of water clusters ((H 2 O) 8 , (H 2 O) 10 , and (H 2 O) 12) by molecular dynamics method. The initial configurations of the clusters were cube for octamer, pentagonal prism for decamer, and fused-cube structure for dodecamer. The different analytical interaction potentials (TIPnP (n = 3, 4), SPC, and SPC/E) were applied to the phase dynamics of water octamer to choose the most appropriate potential for the study. The dynamic criteria based on the molecule's potential energy distribution were applied for identification of solid and liquid phases of decamer and dodecamer. The most probable conformers of decamer and dodecamer in different phases were obtained.
The partition functions and thermodynamic properties of small clusters of rare gas atoms. [The Jo... more The partition functions and thermodynamic properties of small clusters of rare gas atoms. [The Journal of Chemical Physics 100, 3843 (1994)]. Pavel V. Elyutin, Vladimir I. Baranov, Elena D. Belega, Dmitrij N. Trubnikov. Abstract. ...
The molecular dynamics method was used to analyze the dynamic characteristics of water clusters i... more The molecular dynamics method was used to analyze the dynamic characteristics of water clusters in the solid and liquid phase. A criterion is proposed for choosing the interaction potential, which is based on the distributions of the potential energy of cluster molecules in different phases. The connection of the obtained distributions with the dynamics and structure of the hydrogen bonds’ net of the cluster is shown.
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