Kroll method

Malkin, L, Malkina, O.L. and Malkin, V.G. (2002) Relativistic calculations of electric field gradients using the Douglas—Kroll method. Chemical Physics Letters, 361, 231-236. 

Preparation. It is made by the Kroll method that involves the reaction of chlorine and carbon upon baddeleyite (Zr02). The resultant zirconium tetrachloride, ZrCl4,... 

The FFC process, named after its discoverers, takes only 24 hours to make the same amount of titanium metal that takes the Kroll method a week or more to produce. It could increase the output of titanium from 60,000 tonnes a year to a million tonnes. The method can also produce titanium alloys. 

Titanium owes its great importance due to its excellent mechanical and corrosion performance. Titanium is produced by reduction of TiCl with magnesium (Kroll method) or sodium (Hunter method). As the cost of Hunter method is higher than Kroll method, Kroll method is considered the most efficient method for titanium electrodeposition. 

By using the general power series expansion for U all the infinitely many parametrisations of a unitary transformation are treated on equal footing. However, the question about the equivalence of these parametrisations for application in the Douglas-Kroll method, which represents a crucial point, is more subtle and will be analysed in the next section. It is especially not clear a priori, if the antihermitean matrix W can always be chosen in the appropriate way the mandatory properties of W, i.e., its oddness, antihermiticity and behaviour as a correct power in the external potential, have to be checked for every single transformation Ui of Eq. (73). 

K. M. Neyman, D. I. Ganyushin, A. V. Matveev, V. A. Nasluzov. Calculation of Electronic g-Tensors Using a Relativistic Density Functional Dougjas-Kroll Method. /. Phys. Chem. A, 106 (2002) 5022-5030. 

In preceding sections we have discussed several different relativistic methods four-component Dirac—Fock with and without correlation energy, the second-order Douglas—Kroll method, and perturbation methods including the mass—velocity and Darwin terms. The relativistic effective core potential (RECP) method is another well-established means of accounting for certain relativistic effects in quantum chemical calculations. This method is thoroughly described elsewhere - anJ is basically not different in the relativistic and... 

The calculations were performed with several different levels of correlation treatment Hartree-Fock (HF), configuration interaction with single and double excitations (SDCI), Multiconfiguration self consistent field (CAS), and multireference configuration interaction (MRCI). Relativistic efferts were accounted for using either the Douglas-Kroll method or a relativistic effective core potential approach (RECP). 

Nakajima, T., Hirao, K. Numerical illustration of third-order Douglas-Kroll method Atomic and molecular properties of superheavy element 112. Chem. Phys. Lett. 329, 511-516 (2000)... 

The metal was a laboratory curiosity until Kroll, in 1946, showed that titanium could be produced commercially by reducing titanium tetrachloride with magnesium. This method is largely used for producing the metal today. The metal can be purified by decomposing the iodide. 

Fig. 10(a) presents a comparison of computer simulation data with the predictions of both density functional theories presented above [144]. The computations have been carried out for e /k T = 7 and for a bulk fluid density equal to pi, = 0.2098. One can see that the contact profiles, p(z = 0), obtained by different methods are quite similar and approximately equal to 0.5. We realize that the surface effects extend over a wide region, despite the very simple and purely repulsive character of the particle-wall potential. However, the theory of Segura et al. [38,39] underestimates slightly the range of the surface zone. On the other hand, the modified Meister-Kroll-Groot theory [145] leads to a more correct picture. 

Zirconium, too, is produced commercially by the Kroll process, but the van Arkel-de Boer process is also useful when it is especially important to remove all oxygen and nitrogen. In this latter method the crude zirconium is heated in an evacuated vessel with a little iodine, to a temperature of about 200° C when Zrl4 volatilizes. A tungsten or zirconium filament is simultaneously electrically heated to about 1300°C. This decomposes the Zrl4 and pure zirconium is deposited on the filament. As the deposit grows the current is steadily increased so as to maintain the temperatures. The method is applicable to many metals by judicious adjustment of the temperatures. Zirconium has a high corrosion resistance and in certain chemical plants is preferred to alternatives such as stainless... 

Since working with the full four-component wave function is so demanding, different approximate methods have been developed where the small component of the wave function is eliminated to a certain order in 1/c or approximated (like the Foldy-Wouthuyserd or Douglas-Kroll transformations thereby reducing the four-component wave function to only two components. A description of such methods is outside the scope of this book. 

Though the element was discovered in 1789 it was not prepd in the pure state until 1914. It may be prepd commercially by the reaction of zirconium chloride with magnesium (the Kroll process) and other methods. The principle ore is zircon, deposits of which are found in the USA, Australia and Brazil. A number of special properties, such as exceptional resistance to corrosion and a low absorption cross section, have led to the use of Zr or alloys contg Zr, in many... 

If not otherwise stated the four-component Dirac method was used. The Hartree-Fock (HF) calculations are numerical and contain Breit and QED corrections (self-energy and vacuum polarization). For Au and Rg, the Fock-space coupled cluster (CC) results are taken from Kaldor and co-workers [4, 90], which contains the Breit term in the low-frequency limit. For Cu and Ag, Douglas-Kroll scalar relativistic CCSD(T) results are used from Sadlej and co-workers [6]. Experimental values are from Refs. [91, 92]. 

We extend the method over all three rows of TMs. No systematic study is available for the heavier atoms, where relativistic effects are more prominent. Here, we use the Douglas-Kroll-Hess (DKH) Hamiltonian [14,15] to account for scalar relativistic effects. No systematic study of spin-orbit coupling has been performed but we show in a few examples how it will affect the results. A new basis set is used in these studies, which has been devised to be used with the DKH Hamiltonian. 

Molecules are more difficult to treat accurately than atoms, because of the reduced symmetry. An additional complication arises in relativistic calculations the Dirac-Fock-(-Breit) orbitals will in general be complex. One way to circumvent this difficulty is by the Douglas-Kroll-Hess transformation [57], which yields a one-component function with computational effort essentially equal to that of a nonrelativistic calculation. Spin-orbit interaction may then be added as a perturbation, implementation to AuH and Au2 has been reported [58]. Progress has also been made in the four-component formulation [59], and the MOLFDIR package [60] has been extended to include the CC method. Application to SnH4 has been described [61] here we present a recent calculation of several states of CdH and its ions [62], with one-, two-, and four-component methods. 

Kroll, H., Maurer, H., Stockelmann, D., Becker, W., Fulst, J., Kriisemann, R., et al. (1992). Simulation of crystal structures by a combined distance-least-squares valence-rule method. Zeit. Kristallogr. 199, 49 66. 

Bioinorganic systems often contain heavy elements that need to be treated with an explicit relativistic method. It is now possible to carry out an explicit relativistic electronic structure calculation on the fly (152). The scalar-relativistic Douglas - Kroll - Hess method was implemented by us recently in the BOMD simulation framework (152). To use the relativistic densities in a non-relativistic gradient calculations turned out to be a valid approximation of relativistic gradients. An excellent agreement between optimized structures and geometries obtained from numerical gradients was observed with an error smaller than 0.02 pm. 

---