Exchange and correlation near the nucleus in density functional theory

The near nucleus behavior of the exchange-correlation potential $v_{xc}({\bf r})$ in Hohenberg-Kohn-Sham density functional theory is investigated. It is shown that near the nucleus the linear term of $O(r)$ of the spherically averaged exchange-correlation potential ${\bar v}_{xc}(r)$ is nonzero, and that it arises purely from the difference between the kinetic energy density at the nucleus of the interacting system and the noninteracting Kohn-Sham system. An analytical expression for the linear term is derived. Similar results for the exchange $v_{x}({\bf r})$ and correlation $v_{c}({\bf r})$ potentials are also obtained separately. It is further pointed out that the linear term in $v_{xc}({\bf r})$ arising mainly from $v_{c}({\bf r})$ is rather small, and $v_{xc}({\bf r})$ therefore has a nearly quadratic structure near the nucleus. Implications of the results for the construction of the Kohn-Sham system are discussed with examples.Comment: 10 page

The on-top pair-correlation density in the homogeneous electron liquid

The ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation density $g(0)$, in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density $g(r)$ at zero distance $r=0$.Comment: 8 pages, 4 figure

Constraint-based, Single-point Approximate Kinetic Energy Functionals

We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be relatively simple. We therefore require that the functionals be based on DFT constraints, local, dependent upon a small number of parameters fitted to a training set of limited size, and applicable beyond the scope of the training set. Our previous "modified conjoint" generalized-gradient-type functionals were constrained to producing a positive-definite Pauli potential. Though distinctly better than several published GGA-type functionals in that they gave semi-quantitative agreement with Born-Oppenheimer forces from full Kohn-Sham results, those modified conjoint functionals suffer from unphysical singularities at the nuclei. Here we show how to remove such singularities by introducing higher-order density derivatives. We give a simple illustration of such a functional used for the dissociation energy as a function of bond length for selected molecules.Comment: 16 pages, 9 figures, 2 tables, submitted to Phys. Rev.

Meta-analysis of neural systems underlying placebo analgesia from individual participant fMRI data

The brain systems underlying placebo analgesia are insufficiently understood. Here we performed a systematic, participant-level meta-analysis of experimental functional neuroimaging studies of evoked pain under stimulus-intensity-matched placebo and control conditions, encompassing 603 healthy participants from 20 (out of 28 eligible) studies. We find that placebo vs. control treatments induce small, widespread reductions in pain-related activity, particularly in regions belonging to ventral attention (including mid-insula) and somatomotor networks (including posterior insula). Behavioral placebo analgesia correlates with reduced pain-related activity in these networks and the thalamus, habenula, mid-cingulate, and supplementary motor area. Placebo-associated activity increases occur mainly in frontoparietal regions, with high between-study heterogeneity. We conclude that placebo treatments affect pain-related activity in multiple brain areas, which may reflect changes in nociception and/or other affective and decision-making processes surrounding pain. Between-study heterogeneity suggests that placebo analgesia is a multi-faceted phenomenon involving multiple cerebral mechanisms that differ across studies

Meta-analysis of neural systems underlying placebo analgesia from individual participant fMRI data

The brain systems underlying placebo analgesia are insufficiently understood. Here we performed a systematic, participant-level meta-analysis of experimental functional neuroimaging studies of evoked pain under stimulus-intensity-matched placebo and control conditions, encompassing 603 healthy participants from 20 (out of 28 eligible) studies. We find that placebo vs. control treatments induce small, widespread reductions in pain-related activity, particularly in regions belonging to ventral attention (including mid-insula) and somatomotor networks (including posterior insula). Behavioral placebo analgesia correlates with reduced pain-related activity in these networks and the thalamus, habenula, mid-cingulate, and supplementary motor area. Placebo-associated activity increases occur mainly in frontoparietal regions, with high between-study heterogeneity. We conclude that placebo treatments affect pain-related activity in multiple brain areas, which may reflect changes in nociception and/or other affective and decision-making processes surrounding pain. Between-study heterogeneity suggests that placebo analgesia is a multi-faceted phenomenon involving multiple cerebral mechanisms that differ across studies

Water-Soluble Fullerene (C60) Derivatives as Nonviral Gene-Delivery Vectors

A new class of water-soluble C60 transfecting agents has been prepared using Hirsch-Bingel chemistry and assessed for their ability to act as gene-delivery vectors in vitro. In an effort to elucidate the relationship between the hydrophobicity of the fullerene core, the hydrophilicity of the water-solubilizing groups, and the overall charge state of the C60 vectors in gene delivery and expression, several different C60 derivatives were synthesized to yield either positively charged, negatively charged, or neutral chemical functionalities under physiological conditions. These fullerene derivatives were then tested for their ability to transfect cells grown in culture with DNA carrying the green fluorescent protein (GFP) reporter gene. Statistically significant expression of GFP was observed for all forms of the C60 derivatives when used as DNA vectors and compared to the ability of naked DNA alone to transfect cells. However, efficient in vitro transfection was only achieved with the two positively charged C60 derivatives, namely, an octa-amino derivatized C60 and a dodeca-amino derivatized C60 vector. All C60 vectors showed an increase in toxicity in a dose-dependent manner. Increased levels of cellular toxicity were observed for positively charged C60 vectors relative to the negatively charged and neutral vectors. Structural analyses using dynamic light scattering and optical microscopy offered further insights into possible correlations between the various derivatized C60 compounds, the C60 vector/DNA complexes, their physical attributes (aggregation, charge) and their transfection efficiencies. Recently, similar Gd@C60-based compounds have demonstrated potential as advanced contrast agents for magnetic resonance imaging (MRI). Thus, the successful demonstration of intracellular DNA uptake, intracellular transport, and gene expression from DNA using C60 vectors suggests the possibility of developing analogous Gd@C60-based vectors to serve simultaneously as both therapeutic and diagnostic agents

Are All Placebo Effects Equal? Placebo Pills, Sham Acupuncture, Cue Conditioning and Their Association

Placebo treatments and healing rituals have been used to treat pain throughout history. The present within-subject crossover study examines the variability in individual responses to placebo treatment with verbal suggestion and visual cue conditioning by investigating whether responses to different types of placebo treatment, as well as conditioning responses, correlate with one another. Secondarily, this study also examines whether responses to sham acupuncture correlate with responses to genuine acupuncture. Healthy subjects were recruited to participate in two sequential experiments. Experiment one is a five-session crossover study. In each session, subjects received one of four treatments: placebo pills (described as Tylenol), sham acupuncture, genuine acupuncture, or no treatment rest control condition. Before and after each treatment, paired with a verbal suggestion of positive effect, each subject's pain threshold, pain tolerance, and pain ratings to calibrated heat pain were measured. At least 14 days after completing experiment one, all subjects were invited to participate in experiment two, during which their analgesic responses to conditioned visual cues were tested. Forty-eight healthy subjects completed experiment one, and 45 completed experiment two. The results showed significantly different effects of genuine acupuncture, placebo pill and rest control on pain threshold. There was no significant association between placebo pills, sham acupuncture and cue conditioning effects, indicating that individuals may respond to unique healing rituals in different ways. This outcome suggests that placebo response may be a complex behavioral phenomenon that has properties that comprise a state, rather than a trait characteristic. This could explain the difficulty of detecting a signature for “placebo responders.” However, a significant association was found between the genuine and sham acupuncture treatments, implying that the non-specific effects of acupuncture may contribute to the analgesic effect observed in genuine acupuncture analgesia.National Center for Complementary and Alternative Medicine (U.S.) (R01AT005280

Searching for New Physics beyond the Standard Model in Electric Dipole Moment

This is a theoretical review of exploration of new physics beyond the Standard Model (SM) in electric dipole moment (EDM) in elementary particles, atoms, and molecule. EDM is a very important CP violating phenomenon and sensitive to new physics. Starting with the estimations of EDM of quarks-leptons in the SM, we explore the new signals beyond the SM. However, these works drive us to more wide fronteers where we serach fundamental physics using atoms and molecules and vice versa. Paramagnetic atoms and molecules have great enhancement factor on electron EDM. Diamagnetic atoms and molecules are very sensitive to nuclear P and T odd processes. Thus the EDM becomes the key word not only of New Physics but also of unprecedented fruitful collaboration among particle, atomic. molecular physics. This review intends to help such collaboration over the wide range of physicists.Comment: 95pages. References are added. Appendix K is revise