Density functional theory parametrization

The determination of the electronic structure of lanthanide-doped materials and the prediction of the optical properties are not trivial tasks. The standard ligand field models lack predictive power and undergoes parametric uncertainty at low symmetry, while customary computation methods, such as DFT, cannot be used in a routine manner for ligand field on lanthanide accounts. The ligand field density functional theory (LFDFT) algorithm23-30 consists of a customized conduct of nonempirical DFT calculations, extracting reliable parameters that can be used in further numeric experiments, relevant for the prediction in luminescent materials science.31 These series of parameters, which have to be determined in order to analyze the problem of two-open-shell 4f and 5d electrons in lanthanide materials, are as follows. 

It is seen from this comparison that the geometrical parameters obtained by the IPM and by the density functional theory (DFT) methods are close. It is enough to multiply re by 1.44 to obtain the same C H O distance for the TS calculated by the DFT method. The following parametric equations were proposed for the estimation of the C—H, O—H, and C—O distances in the reaction center of TS for reactions ROO + RH in the IPM method [34,35],... 

In this paper we present preliminary results of an ab-initio study of quantum diffusion in the crystalline a-AlMnSi phase. The number of atoms in the unit cell (138) is sufficiently small to permit computation with the ab-initio Linearized Muffin Tin Orbitals (LMTO) method and provides us a good starting model. Within the Density Functional Theory (DFT) [15,16], this approach has still limitations due to the Local Density Approximation (LDA) for the exchange-correlation potential treatment of electron correlations and due to the approximation in the solution of the Schrodinger equation as explained in next section. However, we believe that this starting point is much better than simplified parametrized tight-binding like s-band models. 

There has been much recent progress in the application of density functional theory (DFT) to the calculation of shift tensors, and several methods are presently available. The sum-over-state (SOS) DFT method developed by Malkin et al. (70) does not explicitly include the current density, but it has been parametrized to improve numerical accuracy. Ziegler and coworkers have described a GIAO-DFT method (71) that is available as part of the Amsterdam density functional package (72). An alternate method developed by Cheeseman and co-workers (73) is implemented in Gaussian 94 (74). 

M. R. A. Blomberg, P. E. M. Siegbahn, and M. Svensson,/. Chem. Phys., 104, 9546 (1996). Comparisons of Results from Parametrized Configuration Interaction (PCI-80) and from Hybrid Density Functional Theory with Experiments for First Row Transition Metal Compounds. 

The Kohn-Sham-Gaspar potential derived from density-functional theory has a similar expression for V c with Xa = 2/3, and only took into account exchange [20],[40]. To include correlation, several forms were proposed for / , with parameters obtained from fits to RPA calculations or more accurate Monte Carlo simulations [41] and different spin interpolations. The current version of the DVM code contains altogether nine choices of Vje, the preferred form being the Vosko, Wilk and Nusair [42] parametrization of the Ceperley and Alder Monte Carlo simulations [43]. 

Over the years, several computational methods have been developed. The variational theory can be used either without using experimental data other than the fundamental constants (i.e., ab initio methods) or by using empirical data to reduce the needed amount of numerical work (i.e., semiempirical data methods). There are various levels of sophistication in both ab initio [HF(IGLO), density functional theory (DFT) GIAO-MP2, GIAO-CCSD(T)] and semiempirical methods. In the ab initio methods, various kinds of basic sets can be employed, while in the semiempirical methods, different choices of empirical parameters and parametric functions exist. Tire reader is referred to reviews of the subject. ... 

Starting point is QM calculation within the framework of density-functional theory (DFT) (Hohenberg and Kohn, 1964 Kohn and Sham, 1965 Payne et al., 1992). DFT-based energy calculations can be used to evaluate the parameters of classical interatomic interaction potentials, which can be used to perform MS, MC, and MD simulations such ab initio potential parametrization is a key to improving the transferability of the classical force field. In Fig. 1, an interatomic potential energy function for Si-H interactions is given as an example of such a parametrization (Ohira et al., 1995). 

Grimme S (2004) Accurate description of van der Waals complexes by density functional theory including empirical corrections. J Comput Chem 25 1463-1473 Grimme S, Antony J, Ehrhch S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DET-D) for the 94 elements H-PU. J Chem Phys 132 154104... 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

With the development of current theories of electronic structure, such as multireference ab initio approaches and in particular density-functional theory (DFT), the appealing ligand-field approach became displaced by these approaches theoretically well justified but chemically less transparent and less readily analyzed and interpreted (but see Ref [3] as an exception). In contrast, the parametric strucmre of ligand-field theory and the need of experimental data to allow adjustment of these parameters makes this model a tool for interpretation rather than for predictions of electronic properties of transition-metal complexes. A proposed DFT-supported ligand-field theory (LFDFT) enables one to base the determination of LF parameters solely on DFT calculations from first principle [3-6]. This approach is equally suitable to predict electronic transitions [4] and, with appropriate account of spin-orbit coupling [5], one is able to calculate with satisfactory accuracy g- and A-tensor parameters [6]. 

As one moves towards the realm of condensed matter physics, the hope of a wavefunction-based theory involving an exact treatment of spin-jK>larisation and exchange fades. Most modem work in this field is carried out within the density functional theory (DFT) introduced by Hohenbei, Kohn and Sham [1,2], in which the electron density tak i on the role of the primary variable. This allows scope for any number of s roximate treatments of electronic exchange and correlation, so that calculations for even the largest s> tems become tractable. Insofar as spin-polarisation is included, it is tinted in a parametric maimer, making use of exact results obtained for the homogeneous electron gas. 

For scientific theories, being exact in principle seems to be a nice euphemism for being approximate in practice. Density-functional theory suffers from the same fate, and any DFT calculation can only be as reliable as the incorporated parametrization scheme for exchange and correlation. Indeed, the search for reliable exchange-correlation functionals is the greatest challenge to DFT. 

There have been two approaehes for parametrization of semiempirieal methods. One approach aims at reproducing ab initio MO calculations with the same minimal basis set. This approach is taken in the method of partial retention of diatomic differential overlap (PRDDO). " " The second approach aims at reproducing experimental data and/or high-level ab initio or density functional theory (DFT) calculations. Severe limitations of low-level ab initio ealeulations are well known now, especially for TM species. " As a result, parametrizations of modern semiempirical SCF MO methods follow the seeond approaeh. 

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