Infinite-order two-component method

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. 

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/+. 

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