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

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

The hardness profile as a tool to detect spurious stationary points in the potential energy surface

The energy and hardness profile for a series of inter and intramolecular conformational changes at several levels of calculation were computed. The hardness profiles were found to be calculated as the difference between the vertical ionization potential and electron affinity. The hardness profile shows the correct number of stationary points independently of the basis set and methodology used. It was found that the hardness profiles can be used to check the reliability of the energy profiles for those chemical system

Model-independent bounds for the potential and kinetic energy of liquid 4He at zero temperature

Using the experimental values of the chemical potentials of liquid 4He and of a 3He impurity in liquid 4He, we derive a model-independent lower (upper) bound to the kinetic (potential) energy per particle at zero temperature. The values of the bounds at the experimental saturation density are 13.42 K for the kinetic energy and -20.59 K for the potential energy. All the theoretical calculations based on the Lennard-Jones potential violate the upper-bound condition for the potential energy.

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

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Basis set effects on the energy and hardness profiles of the hydrogen fluoride dimer

In earlier work, the present authors have shown that hardness profiles are less dependent on the level of calculation than energy profiles for potential energy surfaces (PESs) having pathological behaviors. At variance with energy profiles, hardness profiles always show the correct number of stationary points. This characteristic has been used to indicate the existence of spurious stationary points on the PESs. In the present work, we apply this methodology to the hydrogen fluoride dimer, a classical difficult case for the density functional theory methods

An approach to costs and energy consumption in private urban Spanish Mediterranean landscapes from a simplified model in sprinkle irrigation

The number of private gardens has increased in recent years, creating a more pleasant urban model, but not without having an environmental impact, including increased energy consumption, which is the focus of this study. The estimation of costs and energy consumption for the generic typology of private urban gardens is based on two simplifying assumptions: square geometry with surface areas from 25 to 500 m2 and hydraulic design with a single pipe. In total, eight sprinkler models have been considered, along with their possible working pressures, and 31 pumping units grouped into 5 series that adequately cover the range of required flow rates and pressures, resultin in 495 hydraulic designs repeated for two climatically different locations in the Spanish Mediterranean area (Girona and Elche). Mean total irrigation costs for the locality with lower water needs (Girona) and greater needs (Elche) were € 2,974 ha-¹ yr-¹ and € 3,383 ha-¹ yr-¹, respectively. Energy costs accounted for 11.4% of the total cost for the first location, and 23.0% for the second. While a suitable choice of the hydraulic elements of the setup is essential, as it may provide average energy savings of 77%, due to the low energy cost in relation to the cost of installation, the potential energy savings do not constitute a significant incentive for the irrigation system design. The low efficiency of the pumping units used in this type of garden is the biggest obstacle and constraint to achieving a high quality energy solution

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Rethinking economy-wide rebound measures: an unbiased proposal

In spite of having been first introduced in the last half of the ninetieth century, the debate about the possible rebound effects from energy efficiency improvements is still an open question in the economic literature. This paper contributes to the existing research on this issue proposing an unbiased measure for economy-wide rebound effects. The novelty of this economy-wide rebound measure stems from the fact that not only actual energy savings but also potential energy savings are quantified under general equilibrium conditions. Our findings indicate that the use of engineering savings instead of general equilibrium potential savings downward biases economy-wide rebound effects and upward-biases backfire effects. The discrepancies between the traditional indicator and our proposed measure are analysed in the context of the Spanish economy.

Theoretical study of the second-order vibrational Stark effect

The behaviour of the harmonic infrared frequency of diatomic molecules subjected to moderate static uniform electric fields is analysed. The potential energy expression has been developed as a function of a static uniform electric field, which brings about a formulation describing the frequency versus field strength curve. With the help of the first and second derivatives of the expressions obtained, which correspond to the first- and second-order Stark effects, it was possible to find the maxima of the frequency versus field strength curves for a series of molecules using a Newton-Raphson search. A method is proposed which requires only the calculation of a few energy derivatives at a particular value of the field strength. At the same time, the expression for the dependence of the interatomic distance on the electric field strength is derived and the minimum of this curve is found for the same species. Derived expressions and numerical results are discussed and compared with other studi

An alternative approach to fundamental general physics concepts

An alternative approach to the fundamental general physics concepts has been proposed. We demonstrate that the electrostatic potential energy of a discrete or a continuous system of charges should be stored by the charges and not the field. It is found that there is a possibility that any electric field has no energy density, as well as magnetic field. It is found that there is no direct relation between the electric or magnetic energy and photons. An alternative derivation of the blackbody radiation formula is proposed. It is also found that the zero-point of energy of electromagnetic radiation may not exist.

A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules

An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry (nuclear relaxation contribution) and vibrational motion (vibrational contribution) of a molecular system. Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required. To show the useful efficiency of the analytical evaluation of electrical properties (the so-called AEEP method), results for calculations on water and pyridine at the SCF/TZ2P and the MP2/TZ2P levels of theory are reported. The results obtained are compared with previous theoretical calculations and with experimental values

Autosuficiència energètica. Estudi pilot a Alinyà (Alt Urgell)

A aquest estudi s'ha analitzat si és viable l'autosuficiència energètica en base a un estudi pilot al nucli rural d'Alinyà aprofitant els recursos naturals de la zona. S'ha realitzat un estudi del consum energètic de la població i s'ha comparat amb el potencial de producció energètica dels recursos renovables locals incloent energia provinent de la biomassa i aprofitada en calderes individuals per a cada habitatge, energia solar en teulades i energia hidroelèctrica a partir de centrals minihidràuliques restaurades ja existents. També s’ha realitzat un anàlisi per detectar possibles factors d’ineficiència energètica i a partir d’aquí, proposar una sèrie de mesures per corregir aquesta. S'han comptabilitzat les emissions de CO2 derivades del consum energètic i les proporcions que representa cada tipus de font energètica sobre el total del nucli. També s'ha establert una comparativa del consum mitjà per habitant i any entre la població i Catalunya; el consum a Alinyà és d'1,46 Tep's, mentre que el de Catalunya és d'1,7 Tep's, el nostre estudi no contempla la mobilitat, si se li resta aquest vector a la mitjana de Catalunya veiem que és de 0,9 Tep's, per tant, hi observem un major consum energètic. El 76% del consum d'Alinyà prové dels combustibles fòssils, concretament del gasoil, el nucli té una forta dependència respecte a aquesta energia, que a més a més representa el 86% (56T CO2 eq.) de les emissions totals de CO2. Per finalitzar, s'ha demostrat que és possible assolir l'autosuficiència energètica mitjançant l'implantació d'una combinació d'estratègies, viables en tots els aspectes; tant tècnics com socioeconòmics. Abastint el poble d'energia a un menor cost econòmic i amb un estil de vida més respectuós amb el medi ambient.

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes