DFT in a nutshell

The purpose of this short essay is to introduce students and other newcomers to the basic ideas and uses of modern electronic density functional theory, including what kinds of approximations are in current use, and how well they work (or not). The complete newcomer should find it orients them well, while even longtime users and aficionados might find something new outside their area. Important questions varying in difficulty and effort are posed in the text, and are answered in the Supporting Information. © 2012 Wiley Periodicals, Inc.     

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.     

Free‐energy differences between states with different conformational ensembles

Multiple conformations separated by high‐energy barriers represent a challenging problem in free‐energy calculations due to the difficulties in achieving adequate sampling. We present an application of thermodynamic integration (TI) in conjunction with the local elevation umbrella sampling (LE/US) method to improve convergence in alchemical free‐energy calculations. TI‐LE/US was applied to the guanosine triphosphate (GTP) to 8‐Br‐GTP perturbation, molecules that present high‐energy barriers between the anti and syn states and that have inverted preferences for those states. The convergence and reliability of TI‐LE/US was assessed by comparing with previous results using the enhanced‐sampling one‐step perturbation (OSP) method. A linear interpolation of the end‐state biasing potentials was sufficient to dramatically improve sampling along the chosen reaction coordinate. Conformational free‐energy differences were also computed for the syn and anti states and compared to experimental and theoretical results. Additionally, a coupled OSP with LE/US was carried out, allowing the calculation of conformational and alchemical free energies of GTP and 8‐substituted GTP analogs. © 2013 Wiley Periodicals, Inc.     

解P_0非线性互补问题的光滑Levenberg-Marquardt方法

本文研究了一个P0非线性互补问题.利用信赖域技术获得了求解该问题的光滑Levenberg-Marquardt算法,该算法在一定条件下具有全局性.利用局部误差界还获得了该算法的超线性和二次收敛.数值结果表明该算法是有效的.     

可加稳定过程的自相交局部时

本文研究了可加稳定过程的自相交局部时的问题.利用Borel–Canteil引理等方法,得到可加稳定过程的自相交局部时的Hlder上界,推广了文献[5]中的结果.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Twisted Phenanthro[9,10-d]imidazole Derivatives as Non-doped Emitters for Efficient Electroluminescent Devices with Ultra-Deep Blue Emission and High Exciton Utilization Efficiency

Herein, two deep-blue emissive molecules ( SAF-PI and SAF-DPI ) are designed and synthesized using spiro[acridine-9,9’-fluorene] as a donor (D) substituted with 2-(3-methylphenyl)-1-phenyl-phenanthro[9,10-d]imidazole as an acceptor (A), forming twisted D−A and A−D−A structures, respectively. The photophysical studies and density functional theory (DFT) calculations reveal that both molecules exhibit hybridized local excited and charge transfer (HLCT) characteristics with deep blue emission color. They are effectively applied as non-doped emitters in OLEDs. Particularly, SAF-PI -based device achieves the high-definition television (HDTV) standard blue color emission peaked at 428 nm with CIE coordinate of (0.156, 0.053), a narrow full width at half maximum of 55 nm, a maximum external quantum efficiency (EQE_max) of 4.57% and an exciton utilization efficiency of 65%.