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

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

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 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

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Relations among several nuclear and electronic density functional reactivity indexes

A set of connections among several nuclear and electronic indexes of reactivity in the framework of the conceptual Density Functional Theory by using an expansion ofthe energy functional in terms of the total number of electrons and the normal coordinates within a canonical ensemble was derived. The relations obtained provided explicit links between important quantities related to the chemical reactivity of a system. This paper particularly demonstrates that the derivative of the electronic energy with respect to the external potential of a system in its equilibrium geometry was equal to the negative of the nuclear repulsion derivative with respect to the external potential

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

One- and two-center physical space partitioning of the energy in the density functional theory

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (Hartree-Fock) exchange for the same Kohn-Sham orbitals

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor–acceptorsubstituted azobenzene. It is observed that both electronic and vibrational contributions to the electricdipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected densityfunctional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange correlation potentials amend the drawbacks of their conventional counterparts

Recollida selectiva porta a porta

Sap la gent quin és el model de recollida selectiva porta a porta? Ajuda aquest sistema a la preservació del medi ambient o es tracta simplement d’un mite? Això és el que ens vam preguntar nosaltres a l’inici del treball. Aquest model s’aplica des del mes de novembre del 2008 a Palau-solità i Plegamans, un municipi del Vallès Occidental. A partir de l’estudi d’aquest cas pràctic hem volgut analitzar la viabilitat d’aquest sistema i la seva acceptació social. Comprovarem que aquest sistema és deficitari i que els impostos juguen un paper molt important en el finançament del sistema actual.Un altre objectiu és comparar el sistema porta a porta que hi ha actualment amb el que es va proposar en l’anterior legislatura, basat en la divisió del poble en dues zones amb models de recollida diferents. Concretament, ens interessa saber si va ser una bona idea canviar de sistema i, tal com veurem més endavant, la resposta és afirmativa.També volem saber si aquest model es podria aplicar a altres municipis amb densitat i poblacions diferents. A través d’aquest treball, veurem que la densitat de la població és un dels factors més importants, malgrat que influeixen altres elements (per exemple, l’acceptació social).

Oferta educativa i desenvolupament econòmic a la comarca del Berguedà

Tard o d’hora, en algun moment de la nostra vida, hem de prendre decisions respecte allò que volem estudiar per tal de poder desenvolupar el capital humà que portem a dins. En algun moment deixarem de ser individus inactius, simples estudiants, per passar a ocupar un lloc en el món laboral. Però, és sempre tant senzilla aquesta decisió? Trobem sempre el que busquem allà on volem i en el moment adequat?Qüestions com aquestes no només sorgeixen a persones com vostè, lector, sinó també potser, a la persona que es troba asseguda al seu costat, al seu company de cafè,... en definitiva, a tota una societat amb diferents inquietuds i preocupacions. I és en aquest moment, en el qual la decisió personal es transforma en global, quan els requeriments d’una societat esdevenen unaprioritat.La necessitat d’especialitzar-se en aquells estudis que cadascú desitja i la importància de saber amb certesa que allà on estudiem disposarem de l’oferta laboral adequada, semblen qüestions insignificants per aquells qui viuen en grans ciutats, però, passa el mateix en les zones amb poca densitat de població? Què passa amb aquell capital humà que abandona la seva llar per buscar la formació o el treball que més desitja i manca allà on viu?Amb el treball que presentem a continuació pretenem mostrar la rellevància que pot tenir la manca d’una oferta educativa adequada, sobre el desenvolupament econòmic d’una societat. Tractem d’explicar fins a quin punt la connexió entre el món educatiu i laboral d’una població, poden condicionar al desenvolupament socioeconòmic, tot basant-nos en el cas específic de la comarca del Berguedà.

Residus reciclables o deixalles terminals?

El nostre projecte consisteix en l’anàlisi econòmic de les polítiques públiques de gestió de residus exclusivament municipals. Pretenem, mitjançant l’anàlisi d’un municipi representatiu com és Sant Cugat, dissenyar un sistema de reciclatge -adaptat a aquesta localitat en concret- que sigui el més eficaç possible, incrementant les quantitats recollides i controlant els costos tot i tenint en compte les preferències dels propis usuaris.Amb això, pretenem cercar la fórmula més exacta possible, adaptable a cada tipus de municipi (edificació vertical o horitzontal, extensió, densitat de població, etc.), per tal que els nivells de reciclatge del nostre país arribin a ser equiparables als europeus, avui encara molt llunyans.Tot i que valorem molts sistemes de reciclatge ja existents, ens centrem prioritàriament en l’estudi del Porta A Porta (PAP), el qual creiem el més adequat per a Sant Cugat després d’haver analitzat estadísticament el que opinen els ciutadans mitjançant unes enquestes, així com dades oficials de poblacions on ja hi està implementat.No obstant això, després d’haver comprovat que la satisfacció real dels usuaris del PAP a Vilassar de Mar, on hi funciona des de 2003, no és la que seria d’esperar, hem reflexionat sobre les causes i les solucions possibles a aquests problemes, de manera que ho puguem evitar de cara a crear el sistema per a la població objecte del nostre treball.