An efficient algorithm is presented for evaluating the analytical nuclear gradients of density-fitted four-component relativistic Dirac-Fock theory as an initial step toward realizing large-scale geometry optimization of heavy-element complexes. Our algorithm employs kinetically balanced 2-spinor basis functions for the small components. The computational cost of nuclear gradient evaluation is ...

GCM study of hexadecapole correlations in superdeformed 194 Hg. Abstract The role of hexadecapole correlations in the lowest superdeformed band of 194 Hg is studied by self consistent mean field methods. The generator coordinate method with particle number projection has been applied using Hartree-Fock wave functions defined along three different hexadecapole paths. In all cases, the ground sta...

The GW approximation is nowadays being used to obtain accurate quasiparticle energies of atoms and molecules. In practice, the GW approximation is generally evaluated perturbatively, based on a prior self-consistent calculation within a simpler approximation. The final result thus depends on the choice of the self-consistent mean-field chosen as a starting point. Using a recently developed GW c...

We review Fock space based quantum probability and in particular the theory of stop times based on it. In the Fock space H = F(L2(R+)), a stop time may be defined as as a positive self-adjoint operator T = ∫ R+ λ dE(λ) whose spectral resolution (E(λ):λ ∈ R+) is adapted to the natural filtration based on the splittings F(L(R)) = F(L([0, λ[)⊗F(L([λ,∞[) Then if K is one of the basic quantum martin...

We analyze microscopic many-body calculations of the nuclear symmetry energy and its density dependence. The calculations are performed in the framework of the Brueckner–Hartree–Fock and the Self– Consistent Green’s Functions methods. Within Brueckner–Hartree–Fock, the Hellmann–Feynman theorem gives access to the kinetic energy contribution as well as the contributions of the different componen...

In this chapter we introduce the fundamental concepts behind the Green Function Theory. We start from a description of the second quantization method and then, after introducing the ensemble average of an operator, we define the main object of the theory, the Green function. Further on, after obtaining the equation of motion for the Green function, we introduce the self-energy operator and we d...

As is known [1], for odd number of electrons the Hartree Fock method of self-consistent field gives the equation, calculation with which help is connected to a problem of diagonalizing a matrix Lagrange multiplier. It results to possible noncommutativity of a Fock operator with the operator density matrix (a projector on subspace of orbitals for electron in a atomic core) and, hence, to absence...

A controlled trial was conducted to investigate the effect of a brief mindfulnessbased intervention on the frequency, and difficulty in “letting go” of anxious selfstatements. Each day for a week participants in the treatment group (n = 28) listened to the Leaves on a Stream mindfulness exercise (LeJeune, 2012), while those in the control group (n = 29) listened to a passage of prose of equal d...