Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Static and dynamic structure of liquid metals: Role of the different parts of the interaction potential

The influence of different parts of the interaction potential on the microscopic behavior of simple liquid metals is investigated by molecular dynamics simulation. The role of the soft-core repulsive, short-range attractive, and long-range oscillatory forces on the properties of liquid lithium close to the triple point is analyzed by comparing the results from simulations of identical systems but truncating the potential at different distances. Special attention is paid to dynamic collective properties such as the dynamic structure factors, transverse current correlation functions, and transport coefficients. It is observed that, in general, the effects of the short-range attractive forces are important. On the contrary, the influence of the oscillatory long-range interactions is considerably less, being the most pronounced for the dynamic structure factor at long wavelengths. The results of this work suggest that the influence of the attractive forces becomes less significant when temperature and density increase.

Quasi-Potency and Cyclic subgroup separability

We study the profinite topology on discrete groups and in particular the property of cyclic subgroup separability. We investigate the class of quasi-potent, cyclic subgroup separable groups, producing many examples and showing how it behaves with respect to certain group constructions.

Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞

"Vegeu el resum a l'inici del document del fitxer adjunt."

A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules

An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry (nuclear relaxation contribution) and vibrational motion (vibrational contribution) of a molecular system. Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required. To show the useful efficiency of the analytical evaluation of electrical properties (the so-called AEEP method), results for calculations on water and pyridine at the SCF/TZ2P and the MP2/TZ2P levels of theory are reported. The results obtained are compared with previous theoretical calculations and with experimental values

Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0={T0egy, T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates KS with attributes above T1≤T0. An eigenproblem of dimension d0+d1 for S0+S 1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j≥2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0, 1, 2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S 0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24 × 106, involving 1.2 × 1012 nonzero matrix elements, and 8.4×109 Slater determinants

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Non-Quasi-Competitiveness and Stability in Cournot's Model

This paper retakes previous work of the authors, about the relationship between non-quasi-competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in the literature that the loss of quasi-competitiveness is linked, in the long run as new firms entered the market, to instability of the model, the authors in their previous work put forward a model in which a situation of monopoly changed to duopoly losing quasi-competitiveness but maintaining the stability of the equilibrium. That model could not, at the time, be extended to any number of oligopolists. The present paper exhibits such an extension. An oligopoly model is shown in which the loss of quasi-competitiveness resists the presence in the market of as many firms as one wishes and where the successive Cournot's equilibrium points are unique and asymptotically stable. In this way, for the first time, the conjecture that non-quasi- competitiveness and instability were equivalent in the long run, is proved false.

Aggregation of liposomes induced by calcium: A structural and kinetic study

In this work, the calcium-induced aggregation of phosphatidylserine liposomes is probed by means of the analysis of the kinetics of such process as well as the aggregate morphology. This novel characterization of liposome aggregation involves the use of static and dynamic light-scattering techniques to obtain kinetic exponents and fractal dimensions. For salt concentrations larger than 5 mM, a diffusion-limited aggregation regime is observed and the Brownian kernel properly describes the time evolution of the diffusion coefficient. For slow kinetics, a slightly modified multiple contact kernel is required. In any case, a time evolution model based on the numerical resolution of Smoluchowski's equation is proposed in order to establish a theoretical description for the aggregating system. Such a model provides an alternative procedure to determine the dimerization constant, which might supply valuable information about interaction mechanisms between phospholipid vesicles.

Rapid Biodiversity Assessment and Monitoring Method for Highly Diverse Benthic Communities: A Case Study of Mediterranean Coralligenous Outcrops

Increasing anthropogenic pressures urge enhanced knowledge and understanding of the current state of marine biodiversity. This baseline information is pivotal to explore present trends, detect future modifications and propose adequate management actions for marine ecosystems. Coralligenous outcrops are a highly diverse and structurally complex deep-water habitat faced with major threats in the Mediterranean Sea. Despite its ecological, aesthetic and economic value, coralligenous biodiversity patterns are still poorly understood. There is currently no single sampling method that has been demonstrated to be sufficiently representative to ensure adequate community assessment and monitoring in this habitat. Therefore, we propose a rapid non-destructive protocol for biodiversity assessment and monitoring of coralligenous outcrops providing good estimates of its structure and species composition, based on photographic sampling and the determination of presence/absence of macrobenthic species. We used an extensive photographic survey, covering several spatial scales (100s of m to 100s of km) within the NW Mediterranean and including 2 different coralligenous assemblages: Paramuricea clavata (PCA) and Corallium rubrum assemblage (CRA). This approach allowed us to determine the minimal sampling area for each assemblage (5000 cm² for PCA and 2500 cm²for CRA). In addition, we conclude that 3 replicates provide an optimal sampling effort in order to maximize the species number and to assess the main biodiversity patterns of studied assemblages in variability studies requiring replicates. We contend that the proposed sampling approach provides a valuable tool for management and conservation planning, monitoring and research programs focused on coralligenous outcrops, potentially also applicable in other benthic ecosystems

Cenozoic evolution of eastern Iberia: structural data and dynamic model.

Iberia underwent intraplate deformation during the Mesozoic and Cenozoic. In eastem Ibena, compression took place during the Palaeogene and early Miocene, giving rise to the Iberian Chain, and extension started during the early Miocene in the coastal areas and the Valencia trough; during early Miocene compression continued in the western Iberian Chain whereas extension had started in the eastern Iberian Chain. From the kinematic data obtained from the major compressional and extensional structures formed dunng the Cenozoic, a simple dynamic model using Bott's (1959) formula is presented. The results show that both extension and compression may have been produced assuming a main horizontal stress-axis approximately N-S, in a similar direction that the convergence between Europe, Ibena and Afnca dunng the Cenozoic.

Setting priorities in clinical and health services research: Properties of an adapted and updated method

Objectives: The objectives of this study is to review the set of criteria of the Institute of Medicine (IOM) for priority-setting in research with addition of new criteria if necessary, and to develop and evaluate the reliability and validity of the final priority score. Methods: Based on the evaluation of 199 research topics, forty-five experts identified additional criteria for priority-setting, rated their relevance, and ranked and weighted them in a three-round modified Delphi technique. A final priority score was developed and evaluated. Internal consistency, test–retest and inter-rater reliability were assessed. Correlation with experts’ overall qualitative topic ratings were assessed as an approximation to validity. Results: All seven original IOM criteria were considered relevant and two new criteria were added (“potential for translation into practice”, and “need for knowledge”). Final ranks and relative weights differed from those of the original IOM criteria: “research impact on health outcomes” was considered the most important criterion (4.23), as opposed to “burden of disease” (3.92). Cronbach’s alpha (0.75) and test–retest stability (interclass correlation coefficient = 0.66) for the final set of criteria were acceptable. The area under the receiver operating characteristic curve for overall assessment of priority was 0.66. Conclusions: A reliable instrument for prioritizing topics in clinical and health services research has been developed. Further evaluation of its validity and impact on selecting research topics is required