Transmission coefficient and two-fold degenerate discrete spectrum of spin-1 bosons in a double-step potential

The scattering of spin-1 bosons in a nonminimal vector double-step potential is described in terms of eigenstates of the helicity operator and it is shown that the transmission coefficient is insensitive to the choice of the polarization of the incident beam. Poles of the transmission amplitude reveal the existence of a two-fold degenerate spectrum. The results are interpreted in terms of solutions of two coupled effective Schr\"{o}dinger equations for a finite square well with additional $\delta$-functions situated at the borders.Comment: arXiv admin note: substantial text overlap with arXiv:1203.119

Towards standard methods for benchmark quality ab initio thermochemistry --- W1 and W2 theory

Two new schemes for computing molecular total atomization energies (TAEs) and/or heats of formation ($\Delta H^\circ_f$) of first-and second-row compounds to very high accuracy are presented. The more affordable scheme, W1 (Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter. It requires CCSD (coupled cluster with all single and double substitutions) calculations in $spdf$ and $spdfg$ basis sets, while CCSD(T) [i.e. CCSD with a quasiperturbative treatment of connected triple excitations] calculations are only required in $spd$ and $spdf$ basis sets. On workstation computers and using conventional coupled cluster algorithms, systems as large as benzene can be treated, while larger systems are feasible using direct coupled cluster methods. The more rigorous scheme, W2 (Weizmann-2) theory, contains no empirical parameters at all and yields a mean absolute error of 0.23 kcal/mol, which is lowered to 0.18 kcal/mol for molecules dominated by dynamical correlation. It involves CCSD calculations in $spdfg$ and $spdfgh$ basis sets and CCSD(T) calculations in $spdf$ and $spdfg$ basis sets. On workstation computers, molecules with up to three heavy atoms can be treated using conventional coupled cluster algorithms, while larger systems can still be treated using a direct CCSD code. Both schemes include corrections for scalar relativistic effects, which are found to be vital for accurate results on second-row compounds.Comment: J. Chem. Phys., in press; text 30 pages RevTeX; tables 10 pages, HTML and PostScript versions both included Reason for replacement: fixed typos in Table II in proo