Publications

A Novel Image Retrieval Approach with Bag-of-Word Model and Gabor Feature

In the past few years, image retrieval has been one of the hot spots in computer vision field. Among many image retrieval techniques, Bag-of, Word (BoW) model is one of the effective and efficient methods that can search images with visual vocabularies and it is insensitive to massive data and various geometric attacks. But the classical BoW algorithm used some descriptors as its visual words, such as SIFT, which are also used to build visual vocabulary. The main problem with traditional BoW algorithm is that the visual vocabulary could not reflect the spatial information of visual words. And most BoW algorithms utilize one single feature as their feature vector, some other important features are ignored. All these factors have influenced the accuracy of final result in traditional BoW model. In order to solve the problem, we propose a novel image retrieval method with BoW and Gabor feature. The paper first proposes a new saliency map extraction method, and then the saliency score is used to build visual vocabulary. At last, Gabor feature is combined with visual vocabulary together to compute similarity. In order to test the effectiveness of the algorithm, we evaluate our method on the SIMPLICITY dataset and Stanford dataset. Experiments results demonstrate the effectiveness and accuracy of the proposed method.

Indirect-path methods for atomic and molecular energies, and new Koopmans theorems

Staircase and ladder methods are proposed for atomic and molecular total and dissociation energies. In both methods, the energies are generated by employing indirect paths via information obtained from effective potentials. In the staircase method, the energies are determined in steps by successive alternations of electron and proton removals. Within the Hartree-Fock (HF) staircase formulation, the energy for electron removal is taken as the negative of the highest-occupied orbital energy, and the energy for proton removal is obtained as the difference of conventional HF total-energy expectation values. The HF staircase total and dissociation energies are significantly superior to the traditional HF values. In the ladder method, total energies are obtained by summing successive highest-occupied orbital energies for fixed nuclei. Both methods are useful within more advanced many-body theories and are exact within exact Kohn-Sham density-functional theory where the magnitude of the highest-occupied orbital energy equals the experimental ionization energy. Self-interaction-corrected density-functional results are presented. We assert two new Koopmans theorems: (1) the energy $\mathcal{E}$ of the highest-occupied HF orbital would give the experimental ionization energy $I$ if the exact ground-state wave function were free of single excitations out of this orbital, and (2) $\mathcal{E}=\ensuremath{-}I$ when the exact correlation potential, ${v}_{c}([n];\mathrm{r})$, is added to the Fock potential and self-consistency is achieved in both the HF orbitals and in the density $n$.

EXPLORING THE ADIABATIC CONNECTION BETWEEN WEAK- AND STRONG-INTERACTION LIMITS IN DENSITY FUNCTIONAL THEORY

Symmetry breaking and self-interaction correction in the chromium atom and dimer

Density functional approximations to the exchange-correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew-Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ∼4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. These results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.

Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]

For the molecules Be 2 , F 2 , and P 2 of Table For these broken-symmetry solutions, the UHF atomization energies become 17, 220, and 141 kcalmol, respectively, and the mean absolute error of all the UHF atomization energies becomes 69.8 kcalmol.

First beyond-LSDA density functional satisfying a tight lower bound for exchange

<i>α</i>‐Helix‐Driven Regulation of Aqueous Circularly Polarized Luminescence in Homopolypeptide Self‐Assembly

ABSTRACT Biopolymer‐driven supramolecular chirality in aqueous media has gained significant advancements in hierarchical chiral nanostructures. However, researches on the aqueous circularly polarized luminescence (CPL) induced by supramolecular self‐assembly and its mechanism have been rarely reported. Herein, we explore the hierarchical chirality transfer in self‐assembled fluorescent homopolypeptide systems showing aqueous CPL, and unveil an α ‐helix‐dominated CPL regulation mechanism. A relationship is established between molecular structure (degree of polymerization, DP), supramolecular assembly (self‐assembly temperature, T SA ), and resulting CPL properties. The stabilization for the homopolypeptide α ‐helix by increasing DP and decreasing T SA enables efficient chirality transfer from the polypeptide backbone to its terminal chromophore, thereby improving CPL properties. Our work elucidates the critical role of α ‐helix control in aqueous CPL systems, providing insights for designing biocompatible and tunable CPL‐active nanomaterials.

Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.

Improved Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme

Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is non-multiplicative, which prevents systematic comparison of meta-GGA bandstructures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the gaps in the exact KS band structure. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.

Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional

Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H₂ molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

Accurate Density Functional for the Energy: Real-Space Cutoff of the Gradient Expansion for the Exchange Hole

The density-gradient expansion of the fermion exchange hole is analyzed in real space. Unlike the local-density approximation, the second-order gradient-expansion approximation is found to violate two important properties of the exact hole: The exact hole is negative everywhere, and represents a deficit of one electron. Imposition of these exact constraints leads to an accurate new density functional for the exchange energy. Residual errors in the exchange energy for atoms are about 1% of this quantity. The new functional approximation may be generalized to include correlation.

Comparative first-principles study of elastic constants of covalent and ionic materials with LDA, GGA, and meta-GGA functionals and the prediction of mechanical hardness

Can desorption be described by the local density formalism?

Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction

We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a ``normal'' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to $\ensuremath{-}1$. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly varying density or because of error cancellation between exchange and correlation. ``Abnormal'' regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high density, and rapidly varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than $\ensuremath{-}1$. Regions between these extremes are described by a hybrid functional mixing exact and semilocal exchange energy densities locally, i.e., with a mixing fraction that is a function of position $\mathbf{r}$ and a functional of the density. Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters, corresponding roughly to the four kinds of abnormal regions. Our local hybrid functional is perhaps the first accurate fourth-rung density functional or hyper-generalized gradient approximation, with full exact exchange, that is size-consistent in the way that simpler functionals are. It satisfies other known exact constraints, including exactness for all one-electron densities, and provides an excellent fit to the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact constraints, physical insights, and paradigm examples hopefully suppress ``overfitting.''

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to the leading order (-0.221Z^5/3 and -0.021Z ln Z, respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E_x(N, Z) ≈ -0.354N^2/3Z (as known before only for Z ≫ N ≫ 1) and E_c ≈ -0.02N ln N. These asymptotic estimates are most correct for atomic ions with large N and Z ≫ N, but we find that they are qualitatively and semi-quantitatively correct even for small N and N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely predictive approximate density functionals should be designed to recover the correct asymptotics. It is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

First beyond-LSDA density functional satisfying a tight lower bound for exchange

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic couplings and spin polarization energy with quantitative accuracy is beyond the predictive power of today’s density-functional theory (DFT) due to their intrinsic multi-reference character. Herein, we create a benchmark dataset of 25 magnetic systems with non-local spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (ΔEspin) of these systems using complete active space self-consistent field (CASSCF) and coupled cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here, and also have the lowest mean absolute error for predicting both ΔEspin (0.34 eV, 0.32 eV and 0.31 eV) and J (11.74 meV, 12.66 meV and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.