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High hydrostatic pressure destroys the strong ferromagnetism in YCo 5 . The transformation proceeds in a stepwise fashion, as a first-order phase transition ͑P crit = 18± 2 GPa͒, and is accompanied by an isomorphic ͑without change of symmetry͒ lattice collapse and a topological change of the Fermi surface. Accurate fullpotential density-functional calculations enable us to ascribe these phenomena to a quasi-one-dimensional 3d-like band, whose top under ambient pressure is situated ϳ0.1 eV below the Fermi level. Lattice compression drives the top of the nondispersive band-and the associated peak in the majority density of statesupward in energy, until they reach the Fermi level and the system becomes unstable. A similar transition at a somewhat higher pressure ͑23 GPa͒ is predicted for the isomorphous compound LaCo 5 .

Topological changes of the Fermi surface under pressure may cause anomalies in the lowtemperature elastic properties. Our density functional calculations for elemental Osmium evidence that this metal undergoes three such Lifshitz transitions in the pressure range between 70 GPa and 130 GPa. The related elastic anomalies are, however, invisibly weak. The critical pressures considerably exceed the values for recently measured and calculated anomalies in the pressure (P ) dependence of the hexagonal c/a lattice parameter ratio close to 25 GPa. We demonstrate that the latter anomalies are statistically not significant and that (c/a)(P ) can be fitted equally well by a smooth dependence.

Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E F evolves from G ≈ 3G 0 to G ≈ 1G 0 (G 0 = 2e/h 2 ). Formation of a true one-atom point contact, with G ≈ 1G 0 and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E F , and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range −3 ≤ E − E F ≤ 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear "gold molecule" between the electrodes, and a weak coupling of this "molecule" to the tips.

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We study the dependence of the intrinsic conductance of a nanocontact on its shape by using the recursion-transfer-matrix method. Hour-glass, torus, and spherical shapes are defined through analytic potentials, the latter two serving as rough models for ring-like and spherical molecules, respectively. The sensitivity of the conductance to geometric details is analyzed and discussed. Strong resonance effects are found for a spherical contact weakly coupled to electron reservoirs.