Exact two-component method

The role and importance of relativistic effects in the chemistry is already widely acknowledged. The problem which remains is the choice of the best method for the calculation of these effects. In advanced calculations they need to be spin-free or spin-dependent algorithms. One of the most exact two-component method is the infinite order two-component lOTC theory implemented in its spin-free version into... 

From the Modified Dirac Equation to Exact-Two-Component Methods... 

So far, we have discussed the three variants of exact-decoupling methods. In principle, they are all exact two-component methods when employing the full electrostatic potential V. However, in practice, approximations are introduced in order to increase the efficiency (ideally without compromising the accuracy). The discussion to follow continues according to Ref. [16] and is independent of how the exact-decoupling transformation U is obtained. It therefore holds for all exact-decoupling methods. 

M. Barysz, A. J. Sadlej. Two-component methods of relativistic quantum chemistry from the Douglas-KroU approximation to the exact two-component formalism. /. Mol. Struct. (THEOCHEM), 573(1-3) (2001) 181-200. 

Component Methods of Relativistic Quantum Chemistry from the Douglas-Kroll Approximation to the Exact Two-Component Formalism, (b) M. Barysz, J. Chem. Phys., 114,9315 (2001). Systematic Treatment of Relativistic Effects Accurate through Arbitrarily High Order in ot. ... 

There has been much excitement in the relativistic quantum chemistry community regarding the possibility of constructing a formally exact two-component Hamiltonian for molecular calculations [50-56], as outlined in several review articles recently [56-59]. To be specific, an exact Hamiltonian can be constructed relatively straightforwardly at the one-electron level. Many-electron effects can be built into the approach in a pragmatic way with the help of model potentials [60-62]. For perspectives on a systematic incorporation of electron correlation into relativistic quantum chemical methods with many-electron wavefunctions, see Kutzelnigg [58] Liu [59] Saue [56] Saue and Visscher [63]. For a perspective on DFT, see van Wiillen [64]. 

X2C ( eXact 2-Component ) is an umbrella acronym [56] for a variety of methods that arrive at an exactly decoupled two-component Hamiltonian, with X2C referring to one-step approaches [65]. Related methods to arrive at formally exact two-component relativistic operators are, for example, infinite-order methods by Barysz and coworkers (BSS = Barysz Sadlej Snijders, lOTC = infinite-order two-component) [66-69] and normalized elimination of the small component (NESC) methods [70-77]. We discuss here an X2C approach as it has been implemented in a full two-component form with spin-orbit (SO) coupling and transformation of electric property operators to account for picture-change (PC) corrections [14],... 

Sun Q, Xiao Y and Liu W 2012 Exact two-component relativistic theory for NMR parameters General formulation and pilot application. J. Chem. Phys. 137(17), 174105—20. van Lenthe E 1996 The ZORA Equation PhD thesis Vrije Universiteit Amsterdam, Netherlands. He6 BA, Marian CM, Wahlgren U and Gropen O 1996 A mean-field spin-orbit method applicable to correlated wavefunctions. Chem. Phys. Lett. 251, 365—371. 

Future important contributions of heats of immersion will be made in the field of solution adsorption despite the necessity for more exacting experimentation. The common problem in solution adsorption has been to define the nature and extent of the interface between solid particles and mixed liquids. Specifically, more information is needed concerning the orientation and solvation of adsorbed molecules as well as the composition and practical boundary of the adsorbed phase. Direct adsorption measurements yield only net changes in concentration and indirect approaches must be taken (66). Much can be learned, however, by measuring the heats of immersion of powders into two component solutions of varying composition where the adsorption of one component is predominant. This technique, also, is the only available method for measuring the heat of adsorption of... 

The phase equilibria and diagrammatic structures in a two-component system are illustrated in Figure 7 (12). The phase diagrams have often been determined by inspection with the naked eye. More exact methods include x-ray and NMR analysis, density measurements, separation by high-speed centrifugation or differential thermal analysis. 

From these studies it is clear that damage to DNA is broader than initially expected from the two-component model since products on aU four bases and the sugar moiety have been proposed. These proposals include sugar and phosphate radicals despite early failures to detect radicals in the backbone of the DNA double helix. More work is requited in order to determine the exact identity of the radical products since structural information is difficult to obtain through the methods implemented thus far. 

The development of theory for reliable calculations of chemical dynamics has two components the construction of accurate, ab initio, multidimensional potential energy surfaces (PESs) and the performance of reactive scattering calculations, either by time-independent (TI) or time-dependent (TD) methods, on these surfaces. Accurate TI quantum methods for describing atom-diatom reactions, in particular for the benchmark H + H2 reaction, have been achieved since 1975.[1,2,3] Many exact and approximate theories have been tested with the H + H2 reaction.[4,5]... 

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