Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

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

A new, automated, four-colour interphase FISH approach for the simultaneous detection of specific aneuploidies of diagnostic and prognostic significance in high hyperdiploid ALL

In hyperdiploid acute lymphoblastic leukaemia (ALL), the simultaneous occurrence of specific aneuploidies confers a more favourable outcome than hyperdiploidy alone. Interphase (I) FISH complements conventional cytogenetics (CC) through its sensitivity and ability to detect chromosome aberrations in non-dividing cells. To overcome the limits of manual I-FISH, we developed an automated four-colour I-FISH approach and assessed its ability to detect concurrent aneuploidies in ALL. I-FISH was performed using centromeric probes for chromosomes 4, 6, 10 and 17. Parameters established for automatic nucleus selection and signal detection were evaluated (3 controls). Cut-off values were determined (10 controls, 1000 nuclei/case). Combinations of aneuploidies were considered relevant when each aneuploidy was individually significant. Results obtained in 10 ALL patients (1500 nuclei/patient) were compared with those by CC. Various combinations of aneuploidies were identified. All clones detected by CC were observed by I-FISH. I-FISH revealed numerous additional abnormal clones, ranging between 0.1% and 31.6%, based on the large number of nuclei evaluated. Four-colour automated I-FISH permits the identification of concurrent aneuploidies of prognostic significance in hyperdiploid ALL. Large numbers of cells can be analysed rapidly by this method. Owing to its high sensitivity, the method provides a powerful tool for the detection of small abnormal clones at diagnosis and during follow up. Compared to CC, it generates a more detailed cytogenetic picture, the biological and clinical significance of which merits further evaluation. Once optimised for a given set of probes, the system can be easily adapted for other probe combinations.

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.

Genometric analyses of the organization of circular chromosomes: a universal pressure determines the direction of ribosomal RNA genes transcription relative to chromosome replication.

Selective pressures related to gene function and chromosomal architecture are acting on genome sequences and can be revealed, for instance, by appropriate genometric methods. Cumulative nucleotide skew analyses, i.e., GC, TA, and ORF orientation skews, predict the location of the origin of DNA replication for 88 out of 100 completely sequenced bacterial chromosomes. These methods appear fully reliable for proteobacteria, Gram-positives, and spirochetes as well as for euryarchaeotes. Based on this genome architecture information, coorientation analyses reveal that in prokaryotes, ribosomal RNA (rRNA) genes encoding the small and large ribosomal subunits are all transcribed in the same direction as DNA replication; that is, they are located along the leading strand. This result offers a simple and reliable method for circumscribing the region containing the origin of the DNA replication and reveals a strong selective pressure acting on the orientation of rRNA genes similar to the weaker one acting on the orientation of ORFs. Rate of coorientation of transfer RNA (tRNA) genes with DNA replication appears to be taxon-specific. Analyzing nucleotide biases such as GC and TA skews of genes and plotting one against the other reveals a taxonomic clusterization of species. All ribosomal RNA genes are enriched in Gs and depleted in Cs, the only so far known exception being the rRNA genes of deuterostomian mitochondria. However, this exception can be explained by the fact that in the chromosome of the human mitochondrion, the model of the deuterostomian organelle genome, DNA replication, and rRNA transcription proceed in opposite directions. A general rule is deduced from prokaryotic and mitochondrial genomes: ribosomal RNA genes that are transcribed in the same direction as the DNA replication are enriched in Gs, and those transcribed in the opposite direction are depleted in Gs.

Genome-wide analysis of cancer/testis gene expression.

Cancer/Testis (CT) genes, normally expressed in germ line cells but also activated in a wide range of cancer types, often encode antigens that are immunogenic in cancer patients, and present potential for use as biomarkers and targets for immunotherapy. Using multiple in silico gene expression analysis technologies, including twice the number of expressed sequence tags used in previous studies, we have performed a comprehensive genome-wide survey of expression for a set of 153 previously described CT genes in normal and cancer expression libraries. We find that although they are generally highly expressed in testis, these genes exhibit heterogeneous gene expression profiles, allowing their classification into testis-restricted (39), testis/brain-restricted (14), and a testis-selective (85) group of genes that show additional expression in somatic tissues. The chromosomal distribution of these genes confirmed the previously observed dominance of X chromosome location, with CT-X genes being significantly more testis-restricted than non-X CT. Applying this core classification in a genome-wide survey we identified >30 CT candidate genes; 3 of them, PEPP-2, OTOA, and AKAP4, were confirmed as testis-restricted or testis-selective using RT-PCR, with variable expression frequencies observed in a panel of cancer cell lines. Our classification provides an objective ranking for potential CT genes, which is useful in guiding further identification and characterization of these potentially important diagnostic and therapeutic targets.