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

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

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

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

Estimation of protein coding density in a corpus of DNA sequence data

A number of experimental methods have been reported for estimating the number of genes in a genome, or the closely related coding density of a genome, defined as the fraction of base pairs in codons. Recently, DNA sequence data representative of the genome as a whole have become available for several organisms, making the problem of estimating coding density amenable to sequence analytic methods. Estimates of coding density for a single genome vary widely, so that methods with characterized error bounds have become increasingly desirable. We present a method to estimate the protein coding density in a corpus of DNA sequence data, in which a ‘coding statistic’ is calculated for a large number of windows of the sequence under study, and the distribution of the statistic is decomposed into two normal distributions, assumed to be the distributions of the coding statistic in the coding and noncoding fractions of the sequence windows. The accuracy of the method is evaluated using known data and application is made to the yeast chromosome III sequence and to C.elegans cosmid sequences. It can also be applied to fragmentary data, for example a collection of short sequences determined in the course of STS mapping.

Assessment of volumetric bone mineral density of the femoral neck in postmenopausal women with and without vertebral fractures using quantitative multi-slice CT.

OBJECTIVE: To demonstrate the validity and reliability of volumetric quantitative computed tomography (vQCT) with multi-slice computed tomography (MSCT) and dual energy X-ray absorptiometry (DXA) for hip bone mineral density (BMD) measurements, and to compare the differences between the two techniques in discriminating postmenopausal women with osteoporosis-related vertebral fractures from those without. METHODS: Ninety subjects were enrolled and divided into three groups based on the BMD values of the lumbar spine and/or the femoral neck by DXA. Groups 1 and 2 consisted of postmenopausal women with BMD changes <-2SD, with and without radiographically confirmed vertebral fracture (n=11 and 33, respectively). Group 3 comprised normal controls with BMD changes > or =-1SD (n=46). Post-MSCT (GE, LightSpeed16) scan reconstructed images of the abdominal-pelvic region, 1.25 mm thick per slice, were processed by OsteoCAD software to calculate the following parameters: volumetric BMD values of trabecular bone (TRAB), cortical bone (CORT), and integral bone (INTGL) of the left femoral neck, femoral neck axis length (NAL), and minimum cross-section area (mCSA). DXA BMD measurements of the lumbar spine (AP-SPINE) and the left femoral neck (NECK) also were performed for each subject. RESULTS: The values of all seven parameters were significantly lower in subjects of Groups 1 and 2 than in normal postmenopausal women (P<0.05, respectively). Comparing Groups 1 and 2, 3D-TRAB and 3D-INTGL were significantly lower in postmenopausal women with vertebral fracture(s) [(109.8+/-9.61) and (243.3+/-33.0) mg/cm3, respectively] than in those without [(148.9+/-7.47) and (285.4+/-17.8) mg/cm(3), respectively] (P<0.05, respectively), but no significant differences were evident in AP-SPINE or NECK BMD. CONCLUSION: the femoral neck-derived volumetric BMD parameters using vQCT appeared better than the DXA-derived ones in discriminating osteoporotic postmenopausal women with vertebral fractures from those without. vQCT might be useful to evaluate the effect of osteoporotic vertebral fracture status on changes in bone mass in the femoral neck.

Trabecular bone score is associated with volumetric bone density and microarchitecture as assessed by central QCT and HRpQCT in Chinese American and white women.

Although high-resolution peripheral quantitative computed tomography (HRpQCT) and central quantitative computed tomography (QCT) studies have shown bone structural differences between Chinese American (CH) and white (WH) women, these techniques are not readily available in the clinical setting. The trabecular bone score (TBS) estimates trabecular microarchitecture from dual-energy X-ray absorptiometry spine images. We assessed TBS in CH and WH women and investigated whether TBS is associated with QCT and HRpQCT indices. Areal bone mineral density (aBMD) by dual-energy X-ray absorptiometry, lumbar spine (LS) TBS, QCT of the LS and hip, and HRpQCT of the radius and tibia were performed in 71 pre- (37 WH and 34 CH) and 44 postmenopausal (21 WH and 23 CH) women. TBS did not differ by race in either pre- or postmenopausal women. In the entire cohort, TBS positively correlated with LS trabecular volumetric bone mineral density (vBMD) (r = 0.664), femoral neck integral (r = 0.651), trabecular (r = 0.641) and cortical vBMD (r = 0.346), and cortical thickness (C/I; r = 0.540) by QCT (p < 0.001 for all). TBS also correlated with integral (r = 0.643), trabecular (r = 0.574) and cortical vBMD (r = 0.491), and C/I (r = 0.541) at the total hip (p < 0.001 for all). The combination of TBS and LS aBMD predicted more of the variance in QCT measures than aBMD alone. TBS was associated with all HRpQCT indices (r = 0.20-0.52) except radial cortical thickness and tibial trabecular thickness. Significant associations between TBS and measures of HRpQCT and QCT in WH and CH pre- and postmenopausal women demonstrated here suggest that TBS may be a useful adjunct to aBMD for assessing bone quality.

Impact of physical activity on energy balance, food intake and choice in normal weight and obese children in the setting of acute social stress: a randomized controlled trial.

BACKGROUND: Psychological stress negatively influences food intake and food choices, thereby contributing to the development of childhood obesity. Physical activity can also moderate eating behavior and influence calorie intake. However, it is unknown if acute physical activity influences food intake and overall energy balance after acute stress exposure in children. We therefore investigated the impact of acute physical activity on overall energy balance (food intake minus energy expenditure), food intake, and choice in the setting of acute social stress in normal weight (NW) and overweight/obese (OW/OB) children as well as the impact of psychological risk factors. METHOD: After receiving written consent from their parents, 26 NW (BMI < 90(th) percentile) and 24 7-to 11-year-old OW (n = 5)/OB (n = 19, BMI ≥ 90(th) percentile) children were randomly allocated using computer-generated numbers (1:1, after stratification for weight status) to acute moderate physical or to sedentary activity for 30 min. Afterwards, all children were exposed to an acute social stressor. Children and their parents completed self-report questionnaires. At the end of the stressor, children were allowed to eat freely from a range of 12 different foods (6 sweet/6 salty; each of low/high caloric density). Energy balance, food intake/choice and obesity-related psychological risk factors were assessed. RESULTS: Lower overall energy balance (p = 0.019) and a decreased choice of low density salty foods (p < 0.001) in NW children compared with OW/OB children was found after acute moderate physical activity but not sedentary activity. Independent of their allocation, OW/OB children ate more high density salty foods (104 kcal (34 to 173), p = 0.004) following stress. They scored higher on impulsive behavior (p = 0.005), restrained eating (p < 0.001) and parental corporal punishment (p = 0.03), but these psychological factors were not related to stress-induced food intake/choice. Positive parenting tended to be related to lower intake of sweet high density food (-132 kcal, -277 to 2, p = 0.054). CONCLUSIONS: In the setting of stress, acute moderate physical activity can address energy balance in children, a benefit which is especially pronounced in the OW/OB. Positive parenting may act as a protective factor preventing stress-induced eating of comfort food. TRIAL REGISTRATION: clinicaltrials.gov NCT01693926 The study was a pilot study of a project funded by the Swiss National Science Foundation (CRSII3_147673).

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

Effects of zoledronate versus placebo on spine bone mineral density and microarchitecture assessed by the trabecular bone score in postmenopausal women with osteoporosis: A three-year study.

The trabecular bone score (TBS) is an index of bone microarchitectural texture calculated from anteroposterior dual-energy X-ray absorptiometry (DXA) scans of the lumbar spine (LS) that predicts fracture risk, independent of bone mineral density (BMD). The aim of this study was to compare the effects of yearly intravenous zoledronate (ZOL) versus placebo (PLB) on LS BMD and TBS in postmenopausal women with osteoporosis. Changes in TBS were assessed in the subset of 107 patients recruited at the Department of Osteoporosis of the University Hospital of Berne, Switzerland, who were included in the HORIZON trial. All subjects received adequate calcium and vitamin D3. In these patients randomly assigned to either ZOL (n = 54) or PLB (n = 53) for 3 years, BMD was measured by DXA and TBS assessed by TBS iNsight (v1.9) at baseline and 6, 12, 24, and 36 months after treatment initiation. Baseline characteristics (mean ± SD) were similar between groups in terms of age, 76.8 ± 5.0 years; body mass index (BMI), 24.5 ± 3.6 kg/m(2) ; TBS, 1.178 ± 0.1 but for LS T-score (ZOL-2.9 ± 1.5 versus PLB-2.1 ± 1.5). Changes in LS BMD were significantly greater with ZOL than with PLB at all time points (p < 0.0001 for all), reaching +9.58% versus +1.38% at month 36. Change in TBS was significantly greater with ZOL than with PLB as of month 24, reaching +1.41 versus-0.49% at month 36; p = 0.031, respectively. LS BMD and TBS were weakly correlated (r = 0.20) and there were no correlations between changes in BMD and TBS from baseline at any visit. In postmenopausal women with osteoporosis, once-yearly intravenous ZOL therapy significantly increased LS BMD relative to PLB over 3 years and TBS as of 2 years. © 2013 American Society for Bone and Mineral Research.

Evaluation of the potential use of trabecular bone score to complement bone mineral density in the diagnosis of osteoporosis: a preliminary spine BMD-matched, case-control study.

The trabecular bone score (TBS) is a new parameter that is determined from gray-level analysis of dual-energy X-ray absorptiometry (DXA) images. It relies on the mean thickness and volume fraction of trabecular bone microarchitecture. This was a preliminary case-control study to evaluate the potential diagnostic value of TBS as a complement to bone mineral density (BMD), by comparing postmenopausal women with and without fractures. The sample consisted of 45 women with osteoporotic fractures (5 hip fractures, 20 vertebral fractures, and 20 other types of fracture) and 155 women without a fracture. Stratification was performed, taking into account each type of fracture (except hip), and women with and without fractures were matched for age and spine BMD. BMD and TBS were measured at the total spine. TBS measured at the total spine revealed a significant difference between the fracture and age- and spine BMD-matched nonfracture group, when considering all types of fractures and vertebral fractures. In these cases, the diagnostic value of the combination of BMD and TBS likely will be higher compared with that of BMD alone. TBS, as evaluated from standard DXA scans directly, potentially complements BMD in the detection of osteoporotic fractures. Prospective studies are necessary to fully evaluate the potential role of TBS as a complementary risk factor for fracture.

Correlations between trabecular bone score, measured using anteroposterior dual-energy x-ray absorptiometry acquisition, and 3-dimensional parameters of bone microarchitecture: an experimental study on human cadaver vertebrae.

Developing a novel technique for the efficient, noninvasive clinical evaluation of bone microarchitecture remains both crucial and challenging. The trabecular bone score (TBS) is a new gray-level texture measurement that is applicable to dual-energy X-ray absorptiometry (DXA) images. Significant correlations between TBS and standard 3-dimensional (3D) parameters of bone microarchitecture have been obtained using a numerical simulation approach. The main objective of this study was to empirically evaluate such correlations in anteroposterior spine DXA images. Thirty dried human cadaver vertebrae were evaluated. Micro-computed tomography acquisitions of the bone pieces were obtained at an isotropic resolution of 93μm. Standard parameters of bone microarchitecture were evaluated in a defined region within the vertebral body, excluding cortical bone. The bone pieces were measured on a Prodigy DXA system (GE Medical-Lunar, Madison, WI), using a custom-made positioning device and experimental setup. Significant correlations were detected between TBS and 3D parameters of bone microarchitecture, mostly independent of any correlation between TBS and bone mineral density (BMD). The greatest correlation was between TBS and connectivity density, with TBS explaining roughly 67.2% of the variance. Based on multivariate linear regression modeling, we have established a model to allow for the interpretation of the relationship between TBS and 3D bone microarchitecture parameters. This model indicates that TBS adds greater value and power of differentiation between samples with similar BMDs but different bone microarchitectures. It has been shown that it is possible to estimate bone microarchitecture status derived from DXA imaging using TBS.

Effects of Exemestane and Tamoxifen Treatment on Bone Texture Analysis Assessed by TBS in Comparison With Bone Mineral Density Assessed by DXA in Women With Breast Cancer.

We performed an analysis of a substudy of the randomized Tamoxifen Exemestane Adjuvant Multinational trial to determine the effects of exemestane (EXE) and tamoxifen (TAM) adjuvant treatment on bone mineral density (BMD) measured by dual-energy X-ray absorptiometry compared with the trabecular bone score, a novel grey-level texture measurement that correlates with 3-dimensional parameters of bone texture in postmenopausal women with hormone receptor-positive breast cancer for the first time. In total, 36 women were randomized to receive TAM (n = 17) or EXE (n = 19). Patients receiving TAM showed a mean increase of BMD in lumbar spine from baseline of 1.0%, 1.5%, and 1.9% and in trabecular bone score of 2.2%, 3.5%, and 3.3% at 6-, 12-, and 24-mo treatment, respectively. Conversely, patients receiving EXE showed a mean decrease from baseline in lumbar spine BMD of -2.3%, -3.6%, and -5.3% and in trabecular bone score of -0.9%, -1.7%, and -2.3% at 6-, 12-, and 24-mo treatment, respectively. Changes in trabecular bone score from baseline at spine were also significantly different between EXE and TAM: p = 0.05, 0.007, and 0.006 at 6, 12, and 24mo, respectively. TAM induced an increase in BMD and bone texture analysis, whereas EXE resulted in decreases. The results were independent from each other.

Current-density-functional approach to large quantum dots in intense magnetic fields

Within current-density-functional theory, we have studied a quantum dot made of 210 electrons confined in a disk geometry. The ground state of this large dot exhibits some features as a function of the magnetic field (Beta) that can be attributed in a clear way to the formation of compressible and incompressible states of the system. The orbital and spin angular momenta, the total energy, ionization and electron chemical potentials of the ground state, as well as the frequencies of far-infrared edge modes are calculated as a function of Beta, and compared with available experimental and theoretical results.