A simple truth hidden in plain sight: All molecules are entangled according to chemical common sense

An equation that determines the numbers of electrons for molecules is proposed based on chemical common sense. It shows that all molecules are entangled in number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. It also leads to the concept of fractional numbers of electrons for molecules in a statistical sense. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. Wavefunction interpretation of this equation of nature shows that an individual molecule with noninteger number of electrons is locally physical albeit locally unreal. The complete theoretical proof of the equation is still to be had.Comment: Added acknowledgemen

Density functional theory for molecular size consistency and fractional charge

We show that the exact universal functional can be accurately approximated as a sum of local parts F(rho_x)+(rho_y) for a system made of distantly separated densities rho_x and rho_y of fractional charge. The derived F has the same form as the one from the grand-canonical-ensemble treatment. For a molecule that is made of an external potential that has two distantly separated locales, F can be applied with an accurate, external-potential-based constraint and achieve the size consistency. The outer loop in the two-step constrained search formalism is modified to include a search over the number of electrons in each locale of the external potential. Components of F can be extracted based on the Kohn-Sham assumption and with an aid of a model external potential where a molecule with fractional charge (referred to as fractional molecule) can be defined as part of a single non-fractional molecule of two-fold degeneracy with a nondegeneracy condition. We show that the ensemble density of a fractional molecule is non-degenerate noninteracting wavefunction v-representable. The noninteracting kinetic energy and the exact exchange energy functionals of such a density are well defined and have the same forms as those for nonfractional systems. A correlation functional is defined that pertains to the fractionally occupied highest occupied molecular orbital only. The exact exchange energy is discontinuous as the number of electrons passing through an odd integer but its sum with the new correlation energy is continuous. This sum remains an upper-bound to the formal Kohn-Sham exchange-correlation energy of the fractional molecule. It yields the correct result for a well-designed example of effective fractional occupancies in literature

IL12. Density Functional Theory Method for Nondynamic/Strong Correlation

Nondynamic and strong correlation imposes the major challenge to the current density functional theory (DFT), and counts for the majority of the failures of DFT in a variety of areas such as catalysis, organic open-shell molecules and materials. The problem is often characterized as multireference in nature. In this talk, we will present a density functional model based on single-determinant Kohn-Sham density functional theory [1]. It combines Becke’13 method with a new model for kinetic correlation via adiabatic connection based on physical arguments and some exact conditions for both the weak and strong correlations. The result is a single-term functional for correlation of all strength, and is named as KP16/B13 (Kong-Proynov’16/Becke’13). KP16/B13 is the first model of its kind implemented with self-consistent field. The preliminary results show that the model, with only three empirical parameters, recovers the majority of left-right nondynamic/strong correlation upon bond dissociation and performs well for near equilibrium properties such as heats of formation, singlet−triplet energy splittings of diradicals. It also describes well a linear chain of H atoms with many strongly correlated electrons. The new development offers the hope for efficient computation of systems with multireference in nature. Jing Kong, Middle Tennessee State University Emil Proynov, Middle Tennessee State Universit

Quenching depends on morphologies: implications from the ultraviolet-optical radial color distributions in Green Valley Galaxies

In this Letter, we analyse the radial UV-optical color distributions in a sample of low redshift green valley (GV) galaxies, with the Galaxy Evolution Explorer (GALEX)+Sloan Digital Sky Survey (SDSS) images, to investigate how the residual recent star formation distribute in these galaxies. We find that the dust-corrected $u-r$ colors of early-type galaxies (ETGs) are flat out to $R_{90}$, while the colors turn blue monotonously when $r>0.5R_{50}$ for late-type galaxies (LTGs). More than a half of the ETGs are blue-cored and have remarkable positive NUV$-r$ color gradients, suggesting that their star formation are centrally concentrated; the rest have flat color distributions out to $R_{90}$. The centrally concentrated star formation activity in a large portion of ETGs is confirmed by the SDSS spectroscopy, showing that $\sim$50 % ETGs have EW(H$\rm \alpha$)$>6.0$ \AA. For the LTGs, 95% of them show uniform radial color profiles, which can be interpreted as a red bulge plus an extended blue disk. The links between the two kinds of ETGs, e.g., those objects having remarkable "blue-cored" and those having flat color gradients, are less known and require future investigations. It is suggested that the LTGs follow a general picture that quenching first occur in the core regions, and then finally extend to the rest of the galaxy. Our results can be re-examined and have important implications for the IFU surveys, such as MaNGA and SAMI.Comment: ApJ Letter, accepted. Five figure

Multilabel Consensus Classification

In the era of big data, a large amount of noisy and incomplete data can be collected from multiple sources for prediction tasks. Combining multiple models or data sources helps to counteract the effects of low data quality and the bias of any single model or data source, and thus can improve the robustness and the performance of predictive models. Out of privacy, storage and bandwidth considerations, in certain circumstances one has to combine the predictions from multiple models or data sources to obtain the final predictions without accessing the raw data. Consensus-based prediction combination algorithms are effective for such situations. However, current research on prediction combination focuses on the single label setting, where an instance can have one and only one label. Nonetheless, data nowadays are usually multilabeled, such that more than one label have to be predicted at the same time. Direct applications of existing prediction combination methods to multilabel settings can lead to degenerated performance. In this paper, we address the challenges of combining predictions from multiple multilabel classifiers and propose two novel algorithms, MLCM-r (MultiLabel Consensus Maximization for ranking) and MLCM-a (MLCM for microAUC). These algorithms can capture label correlations that are common in multilabel classifications, and optimize corresponding performance metrics. Experimental results on popular multilabel classification tasks verify the theoretical analysis and effectiveness of the proposed methods

Density Functional Model for Nondynamic and Strong Correlation

A single-term density functional model for nondynamic and strong correlation is presented, based on single-determinant Kohn-Sham density functional theory. It is derived from modeling the adiabatic connection and contains only two nonlinear empirical parameters. Preliminary tests show that the model recovers majority of nondynamic correlation during a molecular dissociation and at the same time performs reasonably for atomization energies. It demonstrates the feasibility of developing DFT functionals for nondynamic and strong correlation within the single-determinant KS scheme.Comment: Journal of Chemical Theory and Computation, 201