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

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

Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

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

Enteral versus parenteral nutrition: comparison of energy metabolism in lean and moderately obese women.

Continuous respiratory-exchange measurements were performed on ten moderately obese and ten lean young women for 1 h before, 3 h during, and 3 h after either parenteral (IV) or intragastric (IG) administration of a nutrient mixture infused at twice the postabsorptive, resting energy expenditure (REE). REE rose significantly from 0.98 +/- 0.02 to 1.13 +/- 0.03 kcal/min (IV) and from 0.99 +/- 0.02 to 1.13 +/- 0.02 kcal/min (IG) in the lean group; from 1.10 +/- 0.02 to 1.27 +/- 0.03 kcal/min (IV) and from 1.11 +/- 0.02 to 1.29 +/- 0.03 (IG) in the obese group. These increases resulted in similar nutrient-induced thermogenesis of 10.0 +/- 0.7% (IV) and 9.3 +/- 0.9% (IG) in the lean group; of 9.2 +/- 0.7% (IV) and 10.1 +/- 0.8% (IG) in the obese. Nutrient utilization was comparable in both groups and in both routes of administration, although the response time to IG feeding was delayed. These results showed no significant difference in both the thermogenic response and nutrient utilization between moderately obese and control groups using acute IV or IG feeding.

Energy requirements during reproduction and reproductive effort in shrews (Soricidae)

The energy requirements of reproducing and non-reproducing females of three species of Crocidura (C. russula, C. viaria, C. olivieri), and two species of Sorex (S. coronatus, S. minutus) were measured. Members of these two genera show different rates of metabolism and reproductive strategies (extreme altriciality and larger litter size in Sorex). During pregnancy, the daily energy intake (on either an absolute or a mass-specific basis) remained close to the non-reproductive value in all species. The absolute energy intake increased strongly after parturition and was influenced by the litter size. Peak energy intake of lactating females was extremely high, typically between 100% and 200% above the non-reproductive requirements in the Crocidura and about 300% above the non-reproductive intake in the Sorex. The mass-specific daily energy intake was reduced during lactation in the three smaller species but not in C. viaria and C. olivieri. This decrease probably involves the different thermoregulatory abilities and/or basal rate of metabolism of the pups. Average reproductive effort was about 50%, in the Crocidura species and above 150% in the Sorex species. The higher effort in the latter is partly due to a larger litter size. But in addition, extreme altriciality in the Sorex leads to an earlier increase in the energy requirements and thus is an energetically more expensive reproductive mode. The present results support the hypothesis that a higher basal rate of metabolism is associated with a higher reproductive effort in shrews.

[Archives de la Parole]. , [Parable of the prodigal son] : récit en dravidien, telugu, Province de Madras / [Sir George Grierson], éd. ; Linguistic survey of India ; Voix parlée, homme

[Traditions. Asie. Inde. Présidence de Madras [i.e. Chennai]. Ceded Districts]

[Archives de la Parole]. , [Parable of the prodigal son] : récit en télougou / [Sir George Grierson], éd. ; Linguistic survey of India ; Voix parlée, homme

[Traditions. Asie. Inde. Province de Madras [i.e. Chennai]]

[Archives de la Parole]. , [Parable of the prodigal son] : récit en télougou [sic] / [Sir George Grierson], éd. ; Linguistic survey of India ; [Ranga], voix

[Traditions. Asie. Inde. Province de Madras [i.e. Chennai]. Etat du Tamil Nadu]

[Archives de la Parole]. , Pombada Songs / [Sir George Grierson], éd. ; Linguistic survey of India ; [Tyampa Pombada et Venku], voix

[Traditions. Asie. Inde. Province de Madras [i.e. Chennai]. Région de Kanara]

[Archives de la Parole]. , [Cowardice of the Bania class] : récit shindi [i.e. sindhi] / [Sir George Grierson], éd. ; Linguistic survey of India ; [Mulshankar Somjimal], voix

[Traditions. Asie. Inde. Présidence de Bombay. Pakistan. Province du Sind. Tharparkar]

[Archives de la Parole]. , [Parable of the prodigal son] : récit en hindoustani [mēwātī] / [Sir George Grierson], éd. ; Linguistic survey of India ; [Jainti Pershad], voix

[Traditions. Asie. Inde. Province de Delhi]