| The exact two-component(X2C)method is a simple,accurate and efficient method that has been rapidly developed in the last dozen years for atomic-molecular quantum mechanics to calculate relativistic effects.In this study,some local approximations are used for the analytic derivative algorithm of X2C relativistic Hamiltonian to calculate the effective contact density,which improves the calculation efficiency but without losing accuracy.At present,the algorithm has been implemented by the independent program RelED developed by us.With the help of the utility,using molecular canonical or natural orbital information from various all-electronic scalar relativity density functional theory(DFT)or advanced ab initio calculations by modern quantum chemistry programs,one can obtain effective contact densities to study the M¨ossbauer isomer shifts.Using the analytic derivative algorithm of X2C relativistic Hamiltonian,the effective contact densities and isomer shifts of metal atoms in dozens of iron compounds and Hg Fn (n=1,2,4 and 6)molecules were studied.The obtained results show that 1)full consideration of static electron correlations can significantly improve the linear relationship between the theoretical57Fe effective contact densities and the experimental isomer shifts,and 2)the non-monotonous changes of the effective contact density in a series of HgFn compounds are mainly caused by the decrease of occupation number in Hg5d orbitals,which may reduce the screening effects to the 6s electrons.In addition,a full dimensional potential energy surface(PES)for the MnO++H2→H2O+Mn+ reaction was constructed,and the kinetic characteristics of the reaction was investigated by the Quasi-classical trajectory(QCT)method.The PES was fitted via the permutation invari-ant polynomial neural network(PIP-NN)fitting method based on a large number of(~34,000)ab initio points distributed in the entirely relevant configuration space,thus providing an accu-rate description of the stationary points,such as the minima,saddle points and the minimum energy path along the reaction path.On the newly constructed PES,we found two new stable points which has not been reported in earlier studies,and obtained the chemical reaction rate constants by QCT calculation.It is found that the rate constants is quite close to the experi-mental data,revealing the kinetic characteristics of the reaction at low temperatures. |