The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations

The vertical electronic spectrum of formaldehyde has been studied by means of (SC)²-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchán, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the ²B₂ state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)² dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is satisfactory, in spite of the remarkable reduction in the CI space dimension. The consistency of the (SC)²-MR-SDCI results was tested also against the CCLR and CASPT2 results using the same basis sets and against the CCLR results using Dunning's aug- and daug-cc-pVQZ basis sets. The ³A₁(π → π *) state is correctly placed as the second excited triplet while the highly multi-configurational nature of the ¹A₁(π → π *) state is confirmed as well as its greatly mixed valence-Rydberg nature. This state is predicted as lying under the 10 eV level, on top of the (n_y → 3d) Rydberg states that are predicted in the 8.9–9.5eV region. The 5 ¹B₂(n^y → 4s) Rydberg state and the ¹B₂(σ_y → π*) also are predicted in this region. The triplet states also were calculated with the (SC)²-MR-SDCI method. The vertical ordering of the 2 ¹A₁(n_y → 3p_y) and 2 ¹B₂(n_y → 3p_z) states is discussed, as well as that of the ¹B₁(σ → π*) and the Rydberg ¹B₁(n_y → 3d_xy) states. This work shows the highly reliable values that may be reached applying the dressing method along with a large basis set. Such a procedure is made possible using an MR-SDCI selection of spaces instead of the CAS-SDCI that was used up to now in most (SC)² dressing applications.     

Virial coefficients and equations of state for mixtures of hard discs,hard spheres and hard hyperspheres

The composition-independent virial coefficients of a d-dimensional binary mixture of (additive) hard hyperspheres following from a recent proposal for the equation of state of the mixture (Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1) are examined. Good agreement between theoretical estimates and available exact or numerical results is found for d = 2, 3, 4 and 5, except for mixtures whose components are very disparate in size. A slight modification that remedies this deficiency is introduced and the resummation of the associated virial series is carried out, leading to a new proposal for the equation of state. The case of binary hard sphere mixtures (d = 3) is analysed in some detail.     

Ferrimagnetic coupling in oxamido-bridged Mn(II)Cu(II) compounds: a combined CASPT2 and DDCI study

Multiconfigurational perturbation theory (CASPT2) and difference dedicated configuration interaction (DDCI) are applied to study the ferrimagnetic coupling in an oxamido-bridged Mn(II)Cu(II) molecular species. CASPT2 reproduces the experimental coupling very well. From the partition of the CASPT2 energy, the most important contributions to the coupling are established. Spin populations are calculated with DDCI. The successive improvement of the N-electron wave function allows us to analyse the contributions to the spin delocalization.     

A Popov-theory-based survey on digital control of infinite-dimensional systems with unboundedness

This paper represents a Popov-theory-based assessment of thecurrent status of the digital control of infinite–dimensionalsystems with certain unboundedness in control and/or observation,summarizing some results and indicating which, in the authors'opinion, would be the promising directions for future research.     

An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

Hadron structure in the ladder model (II)

The (flavor non-singlet) probability Φ(k) to find a far-off-shell quark in a hadron is obtained in the renormalization group improved ladder model for QCD in the space-like axial gauge in the region k_T²??2k·P, extending an earlier result for the region k_T²≈?2k·P. The resulting Drell-Yan cross section at measured Q_T agrees in the appropriate limit with that given by Parisi and Petronzio (and disagrees with the DDT form). By using a soft photon method in an abelian gauge theory, I argue that ladder diagrams with strong ordering of gluon q· P's in fact dominate Φ(k) in the high-energy limit considered.     

Factorization for one-loop corrections in the Drell-Yan process

We study all the one-loop corrections to the Drell-Yan process in QCD, including gluon exchanges involving spectator partons. Our method demonstrates weak factorization at measured dimuon Q^T, and is suitable for generalization to higher orders.     

Liquid structure of the ionic liquid 1,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]amide

Neutron diffraction has been used to determine the liquid structure of 1,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]amide ([dmim][NTf2]). Significantly smaller charge ordering is found in this liquid compared with analogous chloride and hexafluorophosphate salts due to the diffuse charge density and size of the [NTf2]- anion. This is manifested in a much larger cation-cation and cation-anion separation and an overlap of the cation-cation and cation-anion shells. Comparison of the liquid structure with the crystal structure reported by Holbrey et al. (Dalton Trans. 2004, 2267) indicates little correlation, for example, the [NTf2]- anion adopts a trans orientation predominantly in the liquid whereas a cis orientation is found in the solid phase.     

A correlation between the order parameters of rigid solutes dissolved in two nematic solvents and in a mixture of them

The orientational data of four rigid solutes dissolved in the nematic solvents ZLI1132, EBBA and in a 55wt% ZLI1132 + EBBA mixture have been obtained from proton NMR spectra at different temperatures and used to find a relationship between the solute order in the two nematics and in their mixture. A crossed comparison of the data shows that a simple linear relation, where the normalized weights of the combination are coincident with the molar fractions of ZLI1132 and EBBA in the mixture, gives excellent agreement independently of the solutes and temperatures. Consideration is given to the possibility of a generalization of the results to any mixture of two nematics.