Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. I. General formalism

A general formalism will be outlined, which uses steady-state wave functions for the study of nonlinear phenomena occurring in molecular systems interacting with intense electromagnetic fields. The steady-state approach has the advantage of being free from the secular divergencies and normalization terms which appear in a perturbation expansion of the time-dependent wave function. A physical interpretation of the steady states will be given by considering the interaction between the molecule and the quantized electromagnetic field. The steady states appear as states of the combined system molecule plus electromagnetic field, with eigenvalues corresponding to the energy levels of the combined system in a semiclassical approximation. Evolution operators will be introduced and used to derive formulas for n-photon transition probabilities between molecular states both in the ordinary configuration Hilbert space and in the composite Hilbert space spanned by the steadystate wave functions.     

SCF-CI studies of the equilibrium structure and the proton transfer barrier H3O 2 −

Large-scale configuration interaction (CI) calculations have been performed in order to study the effect of the correlation energy on the equilibrium geometrical structure, the stability, and on the energy barrier of the proton transfer reaction in the hydrogen bonded system HO^– · HOH. An extended Gaussian basis set including polarization functions on each nuclear centre has been employed to approximate the molecular Orbitals. All possible single and double replacements resulting from a single determinant Hartree-Fock reference state have been taken into account in the CI wavefunction. Compared to the SCF results the equilibrium oxygen/oxygen distance has been obtained from the CI calculations to be smaller by about 0.08 Å and the correlation energy has been found to stabilize the composed system by 3.6 kcal/mole. An almost symmetric equilibrium structure with the hydrogen bonding H-atom midway between the two oxygen centres has been obtained in the CI treatment, whereas SCF calculations yield an asymmetric geometrical configuration with a small energy barrier of 1.4 kcal/mole for the proton transfer process.     

Thin-layer chromatography and multivariate data analysis of willow bark extracts

In most cases the pharmacological activity of plant extracts is not assigned to single components and often not all active ingredients are known. Approaches other than those considering single compounds only to analyze plant material have proven helpful for a better characterization of extracts in their entirety. In this study extracts of willow bark are analyzed by high-performance thin-layer chromatography (HPTLC) and two different pharmacological tests [the 2,2'-azobis (2-amidinopropane) dihydrochloride reaction and the xanthine/xanthine oxidase reaction] with the help of multivariate data analysis. Described are two models using the results of the chromatographic study of 22 various extracts of willow bark and their pharmacological properties. The chromatographic data are obtained by a special TLC scanner that enables measurement of HPTLC tracks simultaneously in the range of lambda = 200-400 nm. Additionally, the developed models are used to predict the activity of another three extracts of willow bark demonstrating the quality of the model.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

MOLCAS 7: The Next Generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two‐electron integrals and in the generation of so‐called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self‐consistent field, density functional theory, 2nd order perturbation theory, complete‐active space self‐consistent field multiconfigurational reference 2nd order perturbation theory, and coupled‐cluster methods. The report further elaborates on the implementation of a restricted‐active space self‐consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas‐Kroll‐Hess transformation for one‐component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so‐called picture‐change‐free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Solution and latex properties of model alkali‐soluble rheology modifiers,synthesized via the reversible addition–fragmentation chain transfer process,and the effects of the ethylene oxide chain length on the rheological properties

Model alkali‐soluble rheology modifiers were synthesized through the reversible addition–fragmentation chain transfer polymerization of methyl methacrylate, methacrylic acid, and three different associative macromonomers containing 20, 50, and 100 ethylene oxide spacer units, respectively. The synthesized polymers showed well‐controlled molar masses and narrow molar mass distributions. The rheological properties of the model alkali‐soluble rheology modifiers were measured in alkali solutions and in the presence of a well‐characterized core–shell emulsion. The steady‐shear viscosity data for the emulsion solutions, thickened with the associative rheology modifiers, were described by the Carreau model. The rheology modifiers containing the macromonomers with the longest ethylene oxide spacer units produced the highest viscosity in the latex systems but the lowest viscosity in alkali solutions. The highest viscosities in alkali solutions were obtained for the rheology modifiers containing macromonomers with 50 ethylene oxide spacer units. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2502–2512, 2004     

Theory of cross phase modulation for the vibrational modes of trapped ions

We analyze nonlinear coupling between individual vibrational quanta for trapped ions. The nonlinear Coulomb interaction causes a Kerr-type Hamiltonian, for which we derive an analytical expression for the coupling constant χ. In contrast to a previously published formula [C.F. Roos, T. Monz, K. Kim, M. Riebe, H. Häffner, D.F.V. James, R. Blatt, Phys. Rev. A 77 (2008) 040302(R)], our result is in close agreement with experimental data.     

A new full-Newton step <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) infeasible interior-point algorithm for semidefinite optimization

Interior-point methods for semidefinite optimization have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, the second author designed a primal-dual infeasible interior-point algorithm with the currently best iteration bound for linear optimization problems. Since the algorithm uses only full Newton steps, it has the advantage that no line-searches are needed. In this paper we extend the algorithm to semidefinite optimization. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem, close to their central paths. Two types of full-Newton steps are used, feasibility steps and (ordinary) centering steps, respectively. The algorithm starts from strictly feasible iterates of a perturbed pair, on its central path, and feasibility steps find strictly feasible iterates for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterates close enough to the central path of the new perturbed pair. The starting point depends on a positive number ζ. The algorithm terminates either by finding an ε-solution or by detecting that the primal-dual problem pair has no optimal solution (X ^*,y ^*,S ^*) with vanishing duality gap such that the eigenvalues of X ^* and S ^* do not exceed ζ. The iteration bound coincides with the currently best iteration bound for semidefinite optimization problems.