Infinite-order two-component

Barysz, M. and Sadlej, A.J. (2002) Infinite-order two-component theory for relativistic quantum chemistry. Journal of Chemical Physics, 116, 2696-2704. 

Ilias, M. and Saue, T. (2007) An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation. Journal of Chemical Physics, 126, 064102-1-064102-9. 

Abstract In this chapter I demonstrate a series of examples showing the importance of relativistic quantum chemistry to the proper description of variety of molecular and atomic properties including valence and core ionization potentials, electron affinities, chemical reactions, dissociation energies, spectroscopic parameters and other properties. An overview of basic principles of the relativistic quantum chemistry and the reduction of relativistic quantum chemistry to two-component form is also presented. I discuss the transition of the four-component Dirac theory to the infinite-order two-component (lOTC) formalism through the unitary transformation which decouples exactly the Hamiltonian. 

Keywords Relativistic effects Infinite-order Two-component theory Change of picture Back unitary transformation Ionization potentials Electron affinities Dissociation energies Hydrolysis Electric properties CEBE Strong bonds to gold... 

The Infinite-Order Two-Component (lOTC) method has been recently applied to the calculations of the valence and inner shell ionization potentials for the Ne, Ar, Kr, and Xe elements [34]. 

Since the infinite-order two-component theory is based on exact equations, it is obvious that it must reproduce all features of the positive-energy Dirac spectrum. However, the way this theory is used introduces the algebraic approximation. 

GAMES S is a program for ab initio molecular quantum chemistiy which can compute self-consistent field (SCF) wave functions ranging from restricted Hartree-Fock (RHF), ROHF, UHF, GVB, and MCSCF [47], Computation of the Hessian energy permits prediction of vibrational frequencies with IR or Raman intensities. Solvent effects may be modeled by the discrete Effective Fragment potentials or continuum models such as the polarizable continuum model [48]. Numerous relativistic computations are available, including infinite order two component scalar corrections, with various spin-orbit coupling options [49]. 

Abstract In this chapter I discuss some aspects of relativistic theory, the accuracy of the infinite order two-component relativistic lOTC method and its advantage over the infinite order Douglas-Kroll-Hess (DKHn) theory, in the proper description of the molecular spectroscopic parameters and the potential energy curves. Spin-free and spin dependent atomic mean filed (AMFI) two-component theories are presented. The importance of the quanmm electrodynamics (QED) corrections and their role in the correct description of the spectroscopic properties of many-electron atoms for the X-ray spectra is discussed as well. Some examples of the molecular QED calculations will be discussed here as well. 

In the present work we will focus mainly on the infinite order two-component method, lOTC. However, some comparison between the lOTC and DKHn methods will be also presented. So far the discussion has been focus on the block-diagonalization of the one-electron Dirac Hamiltonian. For the N electron system a Hamiltonian may be written as the sum of the one-electron transformed Dirac Hamiltonian plus the Coulomb electron-electron interaction and it is commonly used form of the relativistic Hamiltonian. 

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... 

This Hamiltonian can then be used variationally in quantum chemical calculations, since because of its derivation no negative energy states can occur. It should be anticipated that this Hamiltonian is conceptually equivalent to the infinite-order Douglas-Kroll-Hess Hamiltonian to be discussed in section 12.3, because both schemes do not apply any expansion in 1/c. Also the expressions for Ep and Ap are strictly evaluated in closed form within both approaches. However, whereas Douglas-Kroll-Hess theory yields analytic exressions for each order in V, the infinite-order two-component method summarizes all powers of V in the final matrix representation of/+. 

The four-component reference value has to be reproduced by the infinite-order two-component DKH scheme, and any finite-order DKH approximation should converge toward this reference with increasing order of decoupling. 

M. Barysz, L. Mentel, J. Leszczynski. Recovering four-component solutions by the inverse transformation of the infinite-order two-component wave functions. /. Chem. Phys., 130 (2009) 164114. 

D. Kgdziera, M. Barysz. Non-iterative approach to the infinite-order two-component (lOTC) relativistic theory and the non-symmetric algebraic Riccati equation. Chem. Phys. Lett., 446 (2007) 176-181. 

The geometry parameters were toh = 0.99192 A, HOH = 101.411°. The basis set consisted of the primitives Gaussian functions left uncontracted of Dunning s cc-pVDZ hydrogen and oxygen basis sets [35]. The infinite-order two-component (lOTC) relativistic Hamiltonian of Barysz and Sadlej [36] was employed... 

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],... 

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