Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

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

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+ 1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values

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

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

Double Concentric Autofluorescence Ring in NR2E3-p.G56R-linked Autosomal Dominant Retinitis Pigmentosa.

Purpose: We report an unusual appearance of fundus autofluorescence (FAF) associated with NR2E3-p.G56R-linked autosomal dominant retinitis pigmentosa (ADRP).Methods: Patients were enrolled among three generations in a Swiss family. Molecular diagnosis identified a c.166G>A (p.G56R) mutation. Ophthalmic examination included fundus photography, FAF, near-infrared autofluorescence (NIA), optical coherence tomography (OCT) and visual fields (VF).Results: Fundus examination revealed a wide range of features from unremarkable to attenuated arterial caliber, clumped and spicular pigment deposits in the mid-periphery and optic nerve pallor. FAF showed a double concentric hyperautofluorescent ring: an inner perimacular ring which tended to be smaller in older patients, and an outer ring located along the vascular arcades, which appeared to extend over time towards the periphery and eventually became hypoautofluorescent. The inner and outer hyperautofluorescent rings were seen both on NIA and FAF at a similar localization. There was also a spatial correspondence between the loss of photoreceptor inner segment and outer segment junction on OCT and the area delimited by both double FAF and NIA rings. VF showed either midperipheral annular scotoma or constricted visual field loss in advanced cases, correlating with dystrophic non-functional retinal regions demarcated by the hyperautofluorescent annuli. A double ring of hyperautofluorescence was observed in all but one patient of two additional families, but not in patients harboring mutations in other ADRP genes, including PRPF3, RHO, RP1, PRPH2, PROM1 and CTRP5.Conclusions: The presence of a double concentric hyperautofluorescent ring of FAF may represent a highly penetrant early phenotypic marker of NR2E3-p.G56R-linked ADRP.

EU cohesion aid to Spain: a data set. Part II: 1994-99 planning period

In this paper we construct a data set on EU cohesion aid to Spain during the planning period 1994-99. The data are disaggregated by region, year and function and attempt to approximate the timing of actual executed expenditure on assisted projects.

Image quality assessment in digital mammography: part I. Technical characterization of the systems.

In many European countries, image quality for digital x-ray systems used in screening mammography is currently specified using a threshold-detail detectability method. This is a two-part study that proposes an alternative method based on calculated detectability for a model observer: the first part of the work presents a characterization of the systems. Eleven digital mammography systems were included in the study; four computed radiography (CR) systems, and a group of seven digital radiography (DR) detectors, composed of three amorphous selenium-based detectors, three caesium iodide scintillator systems and a silicon wafer-based photon counting system. The technical parameters assessed included the system response curve, detector uniformity error, pre-sampling modulation transfer function (MTF), normalized noise power spectrum (NNPS) and detective quantum efficiency (DQE). Approximate quantum noise limited exposure range was examined using a separation of noise sources based upon standard deviation. Noise separation showed that electronic noise was the dominant noise at low detector air kerma for three systems; the remaining systems showed quantum noise limited behaviour between 12.5 and 380 µGy. Greater variation in detector MTF was found for the DR group compared to the CR systems; MTF at 5 mm(-1) varied from 0.08 to 0.23 for the CR detectors against a range of 0.16-0.64 for the DR units. The needle CR detector had a higher MTF, lower NNPS and higher DQE at 5 mm(-1) than the powder CR phosphors. DQE at 5 mm(-1) ranged from 0.02 to 0.20 for the CR systems, while DQE at 5 mm(-1) for the DR group ranged from 0.04 to 0.41, indicating higher DQE for the DR detectors and needle CR system than for the powder CR phosphor systems. The technical evaluation section of the study showed that the digital mammography systems were well set up and exhibiting typical performance for the detector technology employed in the respective systems.

Comparative gene finding in chicken indicates that we are closing in on the set of multi-exonic widely-expressed human genes

The recent availability of the chicken genome sequence poses the question of whether there are human protein-coding genes conserved in chicken that are currently not included in the human gene catalog. Here, we show, using comparative gene finding followed by experimental verification of exon pairs by RT–PCR, that the addition to the multi-exonic subset of this catalog could be as little as 0.2%, suggesting that we may be closing in on the human gene set. Our protocol, however, has two shortcomings: (i) the bioinformatic screening of the predicted genes, applied to filter out false positives, cannot handle intronless genes; and (ii) the experimental verification could fail to identify expression at a specific developmental time. This highlights the importance of developing methods that could provide a reliable estimate of the number of these two types of genes.

A set of primers for plastid indels and nuclear microsatellites in the invasive plant Heracleum mantegazzianum (Apiaceae) and their transferability to Heracleum sphondylium

This study reports the isolation and polymorphism characterization of four plastid indels and six nuclear microsatellite loci in the invasive plant Heracleum mantegazzianum. These markers were tested in 27 individuals from two distant H. mantegazzianum populations. Plastid indels revealed the presence of five chlorotypes while five nuclear microsatellite loci rendered polymorphism. Applications of these markers include population genetics and phylogeography of H. mantegazzianum. A very good transferability of markers to Heracleum sphondylium was demonstrated.