DV-DFS method

The present results show that the DV-DFS method is applicable to calculations of potential energy curves for such a heavy and complicated system as uranyl nitrate dihydrate. It may also be useful to derive first-principles potential energy curves for the MD simulations. The electronic structure and MD results will be valuable for understanding dynamical properties of actinide ions in solution and for molecular design of novel extractants for selective separation of actinides. 

The aim of the present work is to perform a detailed theoretical study of the electronic structures of actinyl nitrates. Relativistic effects are remarkable in the electronic structure and chemical bonding of heavy atoms such as actinide elements[6j. In our previous study, we applied the relativistic discrete variational Dirac-Fock-Slater(DV-DFS) method to study of the electronic structure of uranyl nitrate dihydrate[7]. The accuracy of the DV-DFS method was demonstrate by its ability to reproduce the uranyl nitrate dihydrate experimental X-ray photoelectron spectrum. 

In the present investigation we will use the DV-DFS method to armpare uranyl, neptunyl and plutonyl nitrate dihydrates from the viewpoint of their partial densities of states due to the An components. We discuss the similarity and difference in the electronic structures of these actinide nitrate dihydrates in order to estimate their stabilities. We also apply population analysis to confirm how far the An electrons contribute to the chemical bonding between the actinide and donor oxygen atoms. Finally, we compare the bonding nature between the... 

Figure 2 shows the valence energy level structures for the actinyl nitrate dihydrates obtained from the relativistic DV-DFS method. The highest occupied molecular orbitals (HOMO) are shown connected with broken lines as are the lowest unoccupied molecular orbitals (LUMO). These energy level... 

We have performed relativistic calculations on hexavalent uranyl, neptunyl and plutonyl nitrate dihydrates using the DV-DFS method. The valence energy level structures were similar to each other except for the HOMO level. The An 5f electrons of Np and Pu occupy the antibonding states and they contribute to the decrease in the bonding interaction between the actinide atoms and the oxygen atom of the water molecules. 

With these initial values of the yt and <, initial values of the can be calcu by Eq. (12.44). The Pf and < values are already available from the prelim DEW P and BUBL P calculations. Equations (12.41) and (12.42) now p initial values of F = F0 and dF/dV = (dF/dV)0. The initial value of V comes from the preceding step. These values are substituted into Eq. (1 which represents Newton s method, and repeated application of this equ leads to the value of V for which Eq. (12.41) is satisfied for the present es of the Kj. The remaining calculations serve to provide new estimates of and d>, from which to reevaluate the Kt. The sequence of steps is repeated there is no significant change in results from one iteration to the next, first application of Newton s method, the starting value V0 in subsequent ite is simply the most recently calculated value. Once the value of V is estab ... 

The DV-DFS molecular orbital(MO) method is based on the Dirac-Fock-Slater approximation. This method provides a powerful tool for the study of the electronic structures of molecules containing heavy elements such as uranium[7,8,9,10]. The one-electron molecular Hamiltonian in the Dirac-Fock-Slater MO method is written as... 

In a continuous flow method, the volume flow rate over the surface of the solid is given by dV/df, so that differentiation of Eq. (23) leads to... 

Since dF/dV is always negative, the F vs. V relation is monotonic, and this makes Newton s method (App. E), a rapidly converging iteration procedure, well suited to solution for V. Newton s method here gives... 

Equilibrium is really attained by minimizing the free energy (dF/dV =0) but if both dominant terms of the free energy are power laws in concentration, then the scaling method used here is correct up to a numerical prefactor. 

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