The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory

A new all-round density functional based on spin states and SN2 barriers

We report here a new empirical density functional that is constructed based on the performance of OPBE and PBE for spin states and SN 2 reaction barriers and how these are affected by different regions of the reduced gradient expansion. In a previous study [Swart, Sol̀, and Bickelhaupt, J. Comput. Methods Sci. Eng. 9, 69 (2009)] we already reported how, by switching between OPBE and PBE, one could obtain both the good performance of OPBE for spin states and reaction barriers and that of PBE for weak interactions within one and the same (SSB-sw) functional. Here we fine tuned this functional and include a portion of the KT functional and Grimme's dispersion correction to account for π- π stacking. Our new SSB-D functional is found to be a clear improvement and functions very well for biological applications (hydrogen bonding, π -π stacking, spin-state splittings, accuracy of geometries, reaction barriers)

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

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

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

Formulació matricial de la teoria de pertorbacions de Rayleigh-Schrödringer: monodimensional

Es repassa la formulació de la Teoria de Pertorbacions en notació matricial i s'exposa una aplicació senzilla com és la solució del problema de la partícula sotmesa a un potencial d'atracció dins la caixa quàntica monodimensional

Estructura i dinàmica del sistema bentònic en llacunes costaneres dels aiguamolls de l'Empordà

S'ha estudiat l'estructura i dinàmica del sistema bentònic de llacunes costaneres de la maresma dels aiguamolls de l'Empordà (NE de la península Ibèrica) i els factors que les determinen. Amb aquesta finalitat es van prendre mostres d'organismes del bentos (mensualment), nutrients i pigments de l'aigua (setmanalment) i el sediment (mensualment), així com paràmetres físics de l'aigua (setmanalment), durant dos cicles d'inundació (1997-1998 i 1998-1999). En aquesta maresma els factors determinants per als organismes bentònics i el contingut en nutrients del sediment són principalment físics: el grau de permanència de l'aigua, el confinament i la granulometria. De manera que els factors tròfics tenen menys pes que els físics tal com es posa de manifest amb les associacions de nematodes. El règim hídric de les llacunes integra des del grau de permanència de l'aigua fins a la salinitat i el confinament, per la qual cosa a partir de la caracterització dels diferents tipus de règim hídric es poden discriminar les tres tipologies d'ambients amb comunitats bentòniques diferenciades en l'estructura, la composició i la dinàmica temporal. Així, les tres comunitats diferenciades són: (1) la d'aigües permanents caracteritzada per una riquesa i diversitat elevades i constants en el temps, i per un nombre més elevat de tàxons sense adaptacions per passar situacions adverses; (2) la d'aigües semipermanents i temporànies d'inundació pulsativa, caracteritzada per una menor riquesa i diversitat, i per la dominància d'organismes amb estructures de resistència per passar la fase seca i aguantar condicions desfavorables, i (3) la d'aigües temporànies d'inundació continuada, caracteritzada per una major variabilitat de la riquesa i diversitat al llarg del cicle i per una singularitat taxonòmica més elevada, ja que s'observen cladòcers i una major representació taxonòmica dels insectes. Durant la realització d'aquest estudi els dos cicles d'inundació van suposar entrades d'aigua en el sistema diferents, per això es va diferenciar un cicle humit (1997-1998) i un de sec (1998-1999). En relació amb la major importància de les entrades d'aigua en el sistema, es va observar un contingut en nutrients de l'aigua significativament superior durant el cicle humit. Pel que fa al sediment, la seva major inèrcia explicaria la manca de diferències significatives en el contingut en nutrients del sediment del cicle humit i del sec. Ara bé, sí que s'observa diferència en la composició d'organismes. Així, la variabilitat interanual en l'estructura de la comunitat bentònica de la maresma es pot atribuir a una situació d'estrès provocada pel cicle sec. Aquesta situació va comportar un augment de la diversitat per disminució de la dominància a totes les llacunes estudiades, determinada, en gran manera, per la disminució de l'abundància original de poblacions dominants i característiques d'ambients permanents, Corophium orientale, o temporànies, Gammarus aequicauda. No existeix un patró estacional en les comunitats estudiades, sinó que els principals canvis en el plàncton i el bentos són deguts a pertorbacions hídriques. Aquestes pertorbacions provoquen que s'estableixi una situació en què dominen uns tàxons característics en el plàncton (Synchaeta i Eutintinnus) i, en canvi, que en el bentos es perdi l'estructura pròpia de les comunitats característiques dels diferents ambients (comunitats dominades per Corophium orinetale en aigües permanents i per Chironomus salinarius en temporànies). La severitat és diferent en funció del grau de permanència de l'aigua, i és més alta en ambients permanents i més baixa en els temporanis. La major severitat en ambients permanents ve determinada per la menor adaptació del bentos d'aigües permanents a les fluctuacions ambientals i a l'efecte de la predació sobre el plàncton. A més, tant en el bentos com en el plàncton es donen fenòmens d'histèresi, segons els quals l'efecte de la pertorbació no solament depèn de la causa pertorbadora sinó també de l'estat en què es troba la comunitat en el moment de la pertorbació.

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.