We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.

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A simple experiment is described for the observation of transition from order to chaos in a near Hamiltonian and a strongly dissipative system. The system is a compass needle moving in an oscillating magnetic field. As the field amplitude is increased, period doubling is observed following the Feigenbaum scenario. New modes are also created by tangent bifurcations. The motion in the dissipative case appears to terminate in strange attractor-type chaotic motion.

The state selective, one- and two-determinantal versions of the recently proposed direct iterative approach to the solution of the generalized Bloch equation [H. Meißner and J. Paldus, J. Chem. Phys. 113, 2612 (2000); Part II] are applied to the ground and excited states of several test molecular ab initio models for which the exact full configuration interaction results are available. Both closed- and open-shell states of different spin multiplicity are considered, as well as the excited states belonging to the same symmetry species as does the ground state. The versatility and flexibility of this approach stems from the possibility of introducing the cluster expansion based approximations of highly excited clusters at various levels of the iterative scheme, leading to a sequence of approximations including both the configuration interaction and coupled cluster methods with singles and doubles as a special case. Both the reliability and the efficiency of these various approximations is examined, and potentially promising approximation schemes are identified.

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