How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

Basis set superposition error effects, excited-state potential energy surface and photodynamics of thymine

En aquesta tesi he estudiat l'efecte de l'error de superposició de base (BSSE) en la planaritat d'algunes molècules. He observat que l'ús d'alguns mètodes de càlcul amb determinades funcions de base descriuen mínims d'energia no planars per les bases nitrogenades de l'ADN. He demostrat que aquests problemes es poden arreglar utilitzant el mètode Counterpoise per corregir el BSSE en els càlculs. En aquesta tesi també he estudiat la fotofísica de la timina i els resultats mostren que existeixen dos camins de relaxació des de l'estat excitat que permeten la regeneració de l'estructura inicial de forma ultraràpida.

Implementation and application of basis set superposition error-correction schemes to the theoretical modeling of weak intermolecular interactions

This thesis deals with the so-called Basis Set Superposition Error (BSSE) from both a methodological and a practical point of view. The purpose of the present thesis is twofold: (a) to contribute step ahead in the correct characterization of weakly bound complexes and, (b) to shed light the understanding of the actual implications of the basis set extension effects in the ab intio calculations and contribute to the BSSE debate. The existing BSSE-correction procedures are deeply analyzed, compared, validated and, if necessary, improved. A new interpretation of the counterpoise (CP) method is used in order to define counterpoise-corrected descriptions of the molecular complexes. This novel point of view allows for a study of the BSSE-effects not only in the interaction energy but also on the potential energy surface and, in general, in any property derived from the molecular energy and its derivatives A program has been developed for the calculation of CP-corrected geometry optimizations and vibrational frequencies, also using several counterpoise schemes for the case of molecular clusters. The method has also been implemented in Gaussian98 revA10 package. The Chemical Hamiltonian Approach (CHA) methodology has been also implemented at the RHF and UHF levels of theory for an arbitrary number interacting systems using an algorithm based on block-diagonal matrices. Along with the methodological development, the effects of the BSSE on the properties of molecular complexes have been discussed in detail. The CP and CHA methodologies are used for the determination of BSSE-corrected molecular complexes properties related to the Potential Energy Surfaces and molecular wavefunction, respectively. First, the behaviour of both BSSE-correction schemes are systematically compared at different levels of theory and basis sets for a number of hydrogen-bonded complexes. The Complete Basis Set (CBS) limit of both uncorrected and CP-corrected molecular properties like stabilization energies and intermolecular distances has also been determined, showing the capital importance of the BSSE correction. Several controversial topics of the BSSE correction are addressed as well. The application of the counterpoise method is applied to internal rotational barriers. The importance of the nuclear relaxation term is also pointed out. The viability of the CP method for dealing with charged complexes and the BSSE effects on the double-well PES blue-shifted hydrogen bonds is also studied in detail. In the case of the molecular clusters the effect of high-order BSSE effects introduced with the hierarchical counterpoise scheme is also determined. The effect of the BSSE on the electron density-related properties is also addressed. The first-order electron density obtained with the CHA/F and CHA/DFT methodologies was used to assess, both graphically and numerically, the redistribution of the charge density upon BSSE-correction. Several tools like the Atoms in Molecules topologycal analysis, density difference maps, Quantum Molecular Similarity, and Chemical Energy Component Analysis were used to deeply analyze, for the first time, the BSSE effects on the electron density of several hydrogen bonded complexes of increasing size. The indirect effect of the BSSE on intermolecular perturbation theory results is also pointed out It is shown that for a BSSE-free SAPT study of hydrogen fluoride clusters, the use of a counterpoise-corrected PES is essential in order to determine the proper molecular geometry to perform the SAPT analysis.

Interaccions moleculars: correcció de l'error de superposició de base i propietat de les funcions flotants

A primary interest of this thesis is to obtain a powerful tool for determining structural properties, electrical and reactivity of molecules. A second interest is the study of fundamental error based on complex overlay of bridge hydrogen. One way to correct this error, using Counterpoise correction proposed by Boys and Bernardi. Usually the Counterpoise correction is applied promptly on the geometries previously optimized. Our goal was to find areas of potential which had all the points fixed with CP. These surfaces have a minimum corresponding to a surface other than corrected, ie, the geometric parameters will be different. The curvature of this minimum will also be different, therefore the vibrational frequency will also change when they are corrected with BSSE. Once constructed these surfaces have been studied various complex. It has also been investigated as the method for calculating the error influenced on the basis superposition.

El error como causa de inculpabilidad en el ilícito tributario

El artículo 342 del Código Tributario, al hablar de los elementos constitutivos de los ilícitos tributarios, establece que es necesaria la presencia de dolo o culpa rechazando la responsabilidad objetiva, que si acepta para contravenciones o faltas reglamentarias, es decir la culpabilidad como elemento del delito tributario es reconocida, lo cual lleva a que el artículo 338 del Código Tributario, reconozca al error como una circunstancia que excluye la responsabilidad penal tributaria, pero no existe desarrollo sobre el contenido del precepto. Esta falta de explicación obliga a recurrir al desarrollo que se ha dado sobre el tema por otras ramas del derecho, así se analizan las explicaciones realizadas por el Derecho Constitucional y el Derecho Penal, siendo este último donde más desarrollo se ha dado sobre el tema, sin poder olvidar la importancia de los derechos fundamentales de la persona. La presente tesis busca aportar criterios que sean útiles y aplicables en el campo tributario, para lo cual se tratará los siguientes temas: Derecho Penal Administrativo, naturaleza de las infracciones tributarias: Derecho Penal aplicable al campo tributario, la culpabilidad en Tratados Internacionales sobre derechos humanos, principio de culpabilidad y sus elementos, error como eximente de responsabilidad, límites de la presencia del error y elusión tributaria.

El error judicial inexcusable en el Estado constitucional de derechos y justicia

Esta investigación estudia el rol del juez en el Estado constitucional de derechos y justicia en el Ecuador, el error inexcusable y el procesamiento disciplinario por error judicial inexcusable desde sus principios de legalidad y taxatividad, la etiología del error, el órgano competente y la independencia judicial. Presenta conclusiones y recomendaciones.

Land Cover Sampling Biases Associated with Roadside Bird Surveys

Roadside surveys such as the Breeding Bird Survey (BBS) are widely used to assess the relative abundance of bird populations. The accuracy of roadside surveys depends on the extent to which surveys from roads represent the entire region under study. We quantified roadside land cover sampling bias in Tennessee, USA, by comparing land cover proportions near roads to proportions of the surrounding region. Roadside surveys gave a biased estimate of patterns across the region because some land cover types were over- or underrepresented near roads. These biases changed over time, introducing varying levels of distortion into the data. We constructed simulated population trends for five bird species of management interest based on these measured roadside sampling biases and on field data on bird abundance. These simulations indicated that roadside surveys may give overly negative assessments of the population trends of early successional birds and of synanthropic birds, but not of late-successional birds. Because roadside surveys are the primary source of avian population trend information in North America, we conclude that these surveys should be corrected for roadside land cover sampling bias. In addition, current recommendations about the need to create more early successional habitat for birds may need reassessment in the light of the undersampling of this habitat by roads.

Off-road sampling reveals a different grassland bird community than roadside sampling: implications for survey design and estimates to guide conservation

Grassland bird species continue to decline steeply across North America. Road-based surveys such as the North American Breeding Bird Survey (BBS) are often used to estimate trends and population sizes and to build species distribution models for grassland birds, although roadside survey counts may introduce bias in estimates because of differences in habitats along roadsides and in off-road surveys. We tested for differences in land cover composition and in the avian community on 21 roadside-based survey routes and in an equal number of adjacent off-road walking routes in the grasslands of southern Alberta, Canada. Off-road routes (n = 225 point counts) had more native grassland and short shrubs and less fallow land and road area than the roadside routes (n = 225 point counts). Consequently, 17 of the 39 bird species differed between the two route types in frequency of occurrence and relative abundance, measured using an indicator species analysis. Six species, including five obligate grassland species, were more prevalent at off-road sites; they included four species listed under the Canadian federal Species At Risk Act or listed by the Committee on the Status of Endangered Wildlife in Canada: Sprague’s Pipit (Anthus spragueii), Baird’s Sparrow (Ammodramus bairdii), the Chestnut-collared Longspur (Calcarius ornatus), and McCown’s Longspur (Rhynchophanes mccownii). The six species were as much as four times more abundant on off-road sites. Species more prevalent along roadside routes included common species and those typical of farmland and other human-modified habitats, e.g., the European Starling (Sturnus vulgaris), the Black-billed Magpie (Pica hudsonia), and the House Sparrow (Passer domesticus). Differences in avian community composition between roadside and off-road surveys suggest that the use of BBS data when generating population estimates or distribution models may overestimate certain common species and underestimate others of conservation concern. Our results highlight the need to develop appropriate corrections for bias in estimates derived from roadside sampling, and the need to design surveys that sample bird communities across a more representative cross-section of the landscape, both near and far from roads. 

Biased representation of disturbance rates in the roadside sampling frame in boreal forests: implications for monitoring design

The North American Breeding Bird Survey (BBS) is the principal source of data to inform researchers about the status of and trend for boreal forest birds. Unfortunately, little BBS coverage is available in the boreal forest, where increasing concern over the status of species breeding there has increased interest in northward expansion of the BBS. However, high disturbance rates in the boreal forest may complicate roadside monitoring. If the roadside sampling frame does not capture variation in disturbance rates because of either road placement or the use of roads for resource extraction, biased trend estimates might result. In this study, we examined roadside bias in the proportional representation of habitat disturbance via spatial data on forest “loss,” forest fires, and anthropogenic disturbance. In each of 455 BBS routes, the area disturbed within multiple buffers away from the road was calculated and compared against the area disturbed in degree blocks and BBS strata. We found a nonlinear relationship between bias and distance from the road, suggesting forest loss and forest fires were underrepresented below 75 and 100 m, respectively. In contrast, anthropogenic disturbance was overrepresented at distances below 500 m and underrepresented thereafter. After accounting for distance from road, BBS routes were reasonably representative of the degree blocks they were within, with only a few strata showing biased representation. In general, anthropogenic disturbance is overrepresented in southern strata, and forest fires are underrepresented in almost all strata. Similar biases exist when comparing the entire road network and the subset sampled by BBS routes against the amount of disturbance within BBS strata; however, the magnitude of biases differed. Based on our results, we recommend that spatial stratification and rotating panel designs be used to spread limited BBS and off-road sampling effort in an unbiased fashion and that new BBS routes be established where sufficient road coverage exists.

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

Spatial variability of flow statistics within regular building arrays

Turbulence statistics obtained by direct numerical simulations are analysed to investigate spatial heterogeneity within regular arrays of building-like cubical obstacles. Two different array layouts are studied, staggered and square, both at a packing density of λp=0.25 . The flow statistics analysed are mean streamwise velocity ( u− ), shear stress ( u′w′−−−− ), turbulent kinetic energy (k) and dispersive stress fraction ( u˜w˜ ). The spatial flow patterns and spatial distribution of these statistics in the two arrays are found to be very different. Local regions of high spatial variability are identified. The overall spatial variances of the statistics are shown to be generally very significant in comparison with their spatial averages within the arrays. Above the arrays the spatial variances as well as dispersive stresses decay rapidly to zero. The heterogeneity is explored further by separately considering six different flow regimes identified within the arrays, described here as: channelling region, constricted region, intersection region, building wake region, canyon region and front-recirculation region. It is found that the flow in the first three regions is relatively homogeneous, but that spatial variances in the latter three regions are large, especially in the building wake and canyon regions. The implication is that, in general, the flow immediately behind (and, to a lesser extent, in front of) a building is much more heterogeneous than elsewhere, even in the relatively dense arrays considered here. Most of the dispersive stress is concentrated in these regions. Considering the experimental difficulties of obtaining enough point measurements to form a representative spatial average, the error incurred by degrading the sampling resolution is investigated. It is found that a good estimate for both area and line averages can be obtained using a relatively small number of strategically located sampling points.