DF method

Goh, S. K., Gallant, R. T., St-Amant, A., 1998, Towards Linear Scaling for the Fits of the Exchange-Correlation Terms in the LCGTO-DF Method via a Divide-and-Conquer Approach , Int. J. Quant. Chem., 69, 405. 

The density functional (DF) method has been successful and quite useful in correlating experimental results when model densities are used in the calculations. In fact, the equations characteristic of the DF method can be derived from a variational approach as Kohn and Sham showed some time ago. In this approach, when model densities are introduced, it is not always possible to relate such densities to corresponding wave functions this is the N-representability problem. Fortunately, for any normalized well behaved density there exists a Slater single determinant this type of density is then N-representable. The problem of approximately N-representable density functional density matrices has been recently discussed by Soirat et al. [118], In spite... 

Notwithstanding the beatiful results obtained with the DF method, this one appears to be much less successful in calculating transition states and barriers for hydrogen exchange and abstraction reactions [122], Parrinello and coworkers have voiced concerns about the accuracy ofDF theory with respect to chemical reactions in solution [121]. 

This situation changed drastically when it was discovered in the 1990s that density functional (DF) methods do a much better job of modeling force fields than (affordable) wave function based methods. Already within the local density approximation (LDA) of DF theory, vibrational frequencies were predicted with... 

The photoionisation spectrum of the OSO4 molecule is one example were we definitely see the relativistic influence. Fig. 5 compares the experimental results with our DVM-DFS method and extensive HF-CI calculations. The splitting of the 3tj levels (originating from the spin-orbit splitting of the 5d-wavefunctions of Os) are quite well-reproduced. 

The density functional(DF) method is one of the most promising tools for the calculation of structure and orientation in heterogeneous fluids near phase boundaries. Among many proposals for the application of DF method, that by Tarazona has been frequently used in the studies of interfaces and phase transitions in hard sphere systems. 

In the present study, the DF method is used to clarify the molecular orientation in fluids near two-dimensional solid-liquid interface. Our molecular model is the triatomic molecule shown in Figure 1. We expect that the results of the present study will give valuable information about the effect of molecular shape on the orientation of real molecules such as liquid crystals near the solid-fluid interface. 

Comparison is attempted between the results of density distribution calculated by the DF method and those from Monte Carlo(MC) simulation. The present. MG simulations have been... 

As a typical example, calculation has been made for density p(z,6) in the condition that bulk density p=0.5, d/a=0.2 and the bond angle a=90°. In Figure 2 are shown the results ol the present DF method(left) and Monte Carlo simulation (right). 

It is seen from the figure that the DF results give a smooth density distribution. Althougl the first peak of the density calculated by the DF method is higher than that obtained b] the MC method, the density p vs. tilt angle 0 relation shows qualitative agreement for eacl approach as seen in Figure 3(upper). 

Figure 3 The molecular density (solid line) and the length h(dotted line) between the center of the mass of molecule and the surface as a function of the tilt angle from the DF method Molecule with a = 90 (left) and molecule with a = 180 (right). Molecular density from MC c Jculation(broken line) is also given for comparison.

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. 

A model s limitations should be assessed from three different perspectives (1) overall model predictivity (model validation), (2) individual prediction confidence (applicability domain), and (3) chance correlation. These attributes can be more readily assessed in the consensus tree modeling such as the DF method than in other QSAR methods. Using DF as an example, we have found the following ... 

Take snapshots of the electronic structure at selected geometries and/or time intervals, with DF methods... 

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