Basis set superposition error-counterpoise corrected potential energy surfaces : application to hydrogen peroxide ... X (X=F-, Cl-, Br-, Li+, Na+) complexes

Møller-Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X- and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1-5), using the full counterpoise method, yielding small BSSE values for the 6-311 + G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1-3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

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

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

Splitting statistical potentials into meaningful scoring functions: testing the prediction of near-native structures from decoy conformations

Background: Recent advances on high-throughput technologies have produced a vast amount of protein sequences, while the number of high-resolution structures has seen a limited increase. This has impelled the production of many strategies to built protein structures from its sequence, generating a considerable amount of alternative models. The selection of the closest model to the native conformation has thus become crucial for structure prediction. Several methods have been developed to score protein models by energies, knowledge-based potentials and combination of both.Results: Here, we present and demonstrate a theory to split the knowledge-based potentials in scoring terms biologically meaningful and to combine them in new scores to predict near-native structures. Our strategy allows circumventing the problem of defining the reference state. In this approach we give the proof for a simple and linear application that can be further improved by optimizing the combination of Zscores. Using the simplest composite score () we obtained predictions similar to state-of-the-art methods. Besides, our approach has the advantage of identifying the most relevant terms involved in the stability of the protein structure. Finally, we also use the composite Zscores to assess the conformation of models and to detect local errors.Conclusion: We have introduced a method to split knowledge-based potentials and to solve the problem of defining a reference state. The new scores have detected near-native structures as accurately as state-of-art methods and have been successful to identify wrongly modeled regions of many near-native conformations.

X-chromosome tiling path array detection of copy number variants in patients with chromosome X-linked mental retardation

Background: Aproximately 5–10% of cases of mental retardation in males are due to copy number variations (CNV) on the X chromosome. Novel technologies, such as array comparative genomic hybridization (aCGH), may help to uncover cryptic rearrangements in X-linked mental retardation (XLMR) patients. We have constructed an X-chromosome tiling path array using bacterial artificial chromosomes (BACs) and validated it using samples with cytogenetically defined copy number changes. We have studied 54 patients with idiopathic mental retardation and 20 controls subjects. Results: Known genomic aberrations were reliably detected on the array and eight novel submicroscopic imbalances, likely causative for the mental retardation (MR) phenotype, were detected. Putatively pathogenic rearrangements included three deletions and five duplications (ranging between 82 kb to one Mb), all but two affecting genes previously known to be responsible for XLMR. Additionally, we describe different CNV regions with significant different frequencies in XLMR and control subjects (44% vs. 20%). Conclusion:This tiling path array of the human X chromosome has proven successful for the detection and characterization of known rearrangements and novel CNVs in XLMR patients.

The neuronal basis of attention: rate versus synchronization modulation

Extensive theoretical and experimental work on the neuronal correlates of visual attention raises two hypotheses about the underlying mechanisms. The first hypothesis, named biased competition, originates from experimental single-cell recordings that have shown that attention upmodulates the firing rates of the neurons encoding the attended features and downregulates the firing rates of the neurons encoding the unattended features. Furthermore, attentional modulation of firing rates increases along the visual pathway. The other, newer hypothesis assigns synchronization a crucial role in the attentional process. It stems from experiments that have shown that attention modulates gamma-frequency synchronization. In this paper, we study the coexistence of the two phenomena using a theoretical framework. We find that the two effects can vary independently of each other and across layers. Therefore, the two phenomena are not concomitant. However, we show that there is an advantage in the processing of information if rate modulation is accompanied by gamma modulation, namely that reaction times are shorter, implying behavioral relevance for gamma synchronization.

Testing I(1) against I(d) alternatives in the presence of deteministic components

This paper discusses the role of deterministic components in the DGP and in the auxiliary regression model which underlies the implementation of the Fractional Dickey-Fuller (FDF) test for I(1) against I(d) processes with d ∈ [0, 1). This is an important test in many economic applications because I(d) processess with d & 1 are mean-reverting although, when 0.5 ≤ d & 1,, like I(1) processes, they are nonstationary. We show how simple is the implementation of the FDF in these situations, and argue that it has better properties than LM tests. A simple testing strategy entailing only asymptotically normally distributed tests is also proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OECD countries, an issue that has important consequences to discriminate between growth theories, and on which there is some controversy.

Panel index VAR models: Specification, Estimation, Testing and Leading Indicators

This paper proposes a method to conduct inference in panel VAR models with cross unit interdependencies and time variations in the coefficients. The approach can be used to obtain multi-unit forecasts and leading indicators and to conduct policy analysis in a multiunit setups. The framework of analysis is Bayesian and MCMC methods are used to estimate the posterior distribution of the features of interest. The model is reparametrized to resemble an observable index model and specification searches are discussed. As an example, we construct leading indicators for inflation and GDP growth in the Euro area using G-7 information.

Stepwise multiple testing as formalized data snooping

It is common in econometric applications that several hypothesis tests arecarried out at the same time. The problem then becomes how to decide whichhypotheses to reject, accounting for the multitude of tests. In this paper,we suggest a stepwise multiple testing procedure which asymptoticallycontrols the familywise error rate at a desired level. Compared to relatedsingle-step methods, our procedure is more powerful in the sense that itoften will reject more false hypotheses. In addition, we advocate the useof studentization when it is feasible. Unlike some stepwise methods, ourmethod implicitly captures the joint dependence structure of the teststatistics, which results in increased ability to detect alternativehypotheses. We prove our method asymptotically controls the familywise errorrate under minimal assumptions. We present our methodology in the context ofcomparing several strategies to a common benchmark and deciding whichstrategies actually beat the benchmark. However, our ideas can easily beextended and/or modied to other contexts, such as making inference for theindividual regression coecients in a multiple regression framework. Somesimulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.