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The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to a quasirelativistic Hamiltonian matrix, that has the same electronic eigenstates as the original Dirac matrix. This transformation involves a matrix X, for which an exact identity is derived, and which can be constructed either in a noniterative way or by various(More)
The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to the matrix representation of a quasirelativistic Hamiltonian that has the same electronic eigenstates as the original Dirac matrix (but no positronic eigenstates). This transformation involves a matrix X, for which an exact identity is derived and which can be(More)
Starting point is the energy expectation value as a functional of the one-particle density matrix gamma and the two-particle density cumulant lambda(2). We decompose gamma into a best idempotent approximation kappa and a correction tau, that is entirely expressible in terms of lambda(2). So we get the energy E as a functional of kappa and lambda(2), which(More)
We start with some biographical notes on Erich Hückel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Hückel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We(More)
After a short historical account of the theory of the H3+ ion, two ab initio methods are reviewed that allow the computation of the ground-state potential energy surface (PES) of H3+ in the Born-Oppenheimer (BO) approximation, with microhartree or even sub-microhartree accuracy, namely the R12 method and the method of explicitly correlated Gaussians. The(More)
The k-particle irreducible Brillouin conditions IBCk and the k-particle irreducible contracted Schrödinger equations ICSEk for a closed-shell state are analyzed in terms of a Møller-Plesset-type perturbation expansion. The zeroth order is Hartree-Fock. From the IBC2(1), i.e., from the two-particle IBC to first order in the perturbation parameter mu, one(More)
of its components. This was found not to be true in general. Our final risk estimates, however, were hardly influenced by the existing deviations from additivity. Of much greater importance was the question how the UV-A component of sunlight contributed to the overall effect. In spite of some remaining uncertainties, our results for the physical(More)
Starting from the Nakatsuji theorem, a hierarchy of approximations is considered that begins with traditional coupled cluster theory with singles and doubles (CCSD) and proceeds via the ansatz of semigeneralized singles and doubles (CCSGSD), with operators of the types a(ab)(ic) and a(ka)(ij) included, to the generalized singles and doubles (CCGSD) ansatz(More)
We analyze the structure and the solutions of the irreducible k-particle Brillouin conditions (IBCk) and the irreducible contracted Schrödinger equations (ICSEk) for an n-electron system without electron interaction. This exercise is very instructive in that it gives one both the perspective and the strategies to be followed in applying the IBC and ICSE to(More)