We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m...We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.展开更多
Benzothiazole (BTH) and its derivatives are organic molecules with biologic actions. Because of their many applications, they are produced on a massive scale and used in a number of environmental compartments. Their d...Benzothiazole (BTH) and its derivatives are organic molecules with biologic actions. Because of their many applications, they are produced on a massive scale and used in a number of environmental compartments. Their discharge into water produces environmental problems, exposing our environment to public health problems. A solution that can contribute to their deterioration is becoming a necessity. For this reason, a conceptual analysis of the reactivity of benzothiazole and four of its compounds was undertaken in order to investigate certain aspects of their biodegradability. A theoretical investigations of the compounds studied were conducted in the gas and water phases with the most widely used density functional theory method, Becke-3-Parameter-Lee-Yang-Parr (B3LYP) with 6-31G+ (d, p) basis. Reactivity study calculated global indices of reactivity revealed that 2-SCH3_BTH is the most reactive. Dipole moment values analysis reveals that 2-NH2_BTH is the most soluble in water, while the lipophilicity shows that 2-NH2_BTH is the most hydrophilic compound. Thermodynamic parameters values reflect that reactions are respectively exothermic and spontaneous. By analyzing an Electrostatic Molecular Potential (EMP) map, researchers can pinpoint reactive sites on a molecule and anticipate its reactivity. This assessment is further enhanced by incorporating global and local reactivity descriptors. Additionally, an exploration of frontier molecular orbitals offers valuable insights into the molecule’s charge transfer characteristics. Moreover, a combined examination of internal and external molecular interactions unveils hyperconjugative interactions arising from charge delocalization, as elucidated through natural bond orbital (NBO) analysis.展开更多
基金Project supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20220917)the National Natural Science Foundation of China (Grant Nos.12001213 and 12302035)。
文摘We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
文摘Benzothiazole (BTH) and its derivatives are organic molecules with biologic actions. Because of their many applications, they are produced on a massive scale and used in a number of environmental compartments. Their discharge into water produces environmental problems, exposing our environment to public health problems. A solution that can contribute to their deterioration is becoming a necessity. For this reason, a conceptual analysis of the reactivity of benzothiazole and four of its compounds was undertaken in order to investigate certain aspects of their biodegradability. A theoretical investigations of the compounds studied were conducted in the gas and water phases with the most widely used density functional theory method, Becke-3-Parameter-Lee-Yang-Parr (B3LYP) with 6-31G+ (d, p) basis. Reactivity study calculated global indices of reactivity revealed that 2-SCH3_BTH is the most reactive. Dipole moment values analysis reveals that 2-NH2_BTH is the most soluble in water, while the lipophilicity shows that 2-NH2_BTH is the most hydrophilic compound. Thermodynamic parameters values reflect that reactions are respectively exothermic and spontaneous. By analyzing an Electrostatic Molecular Potential (EMP) map, researchers can pinpoint reactive sites on a molecule and anticipate its reactivity. This assessment is further enhanced by incorporating global and local reactivity descriptors. Additionally, an exploration of frontier molecular orbitals offers valuable insights into the molecule’s charge transfer characteristics. Moreover, a combined examination of internal and external molecular interactions unveils hyperconjugative interactions arising from charge delocalization, as elucidated through natural bond orbital (NBO) analysis.