Emissive or Nonemissive? A Theoretical Analysis of the Phosphorescence Efficiencies of Cyclometalated Platinum(II) Complexes

We herein report a theoretical analysis based on a density functional theory/time‐dependent density functional theory (DFT/TDDFT) approach to understand the different phosphorescence efficiencies of a family of cyclometalated platinum(II) complexes: [Pt(NCN)Cl] ( 1 ; NCN=1,3‐bis(2‐pyridyl)phenyl^?), [Pt(CNN)Cl] ( 2 ; CNN=6‐phenyl‐2,2′‐bipyridyl^?), [Pt(CNC)(CNPh)] ( 3 ; CNC=2,6‐diphenylpyridyl^2?), [Pt(R‐CNN)Cl] ( 4 ; R‐CNN=3‐(6′‐(2′′‐naphthyl)‐2′‐pyridyl)isoquinolinyl^?), and [Pt(R‐CNC)(CNPh)] ( 5 ; R‐CNC=2,6‐bis(2′‐naphthyl)pyridyl^2?). By considering both the spin–orbit coupling (SOC) and the electronic structures of these complexes at their respective optimized singlet ground (S₀) and first triplet ( ) excited states, we were able to rationalize the experimental findings that 1) 1 is a strong emitter while its isomer 2 is only weakly emissive in CH₂Cl₂ solution at room temperature; 2) although the cyclometalated ligand of 3 has a higher ligand‐field strength than that of 1 , 3 is nonemissive in CH₂Cl₂ solution at 298 K; and 3) extension of π conjugation at the lateral aryl rings of the cyclometalated ligands of 2 and 3 to give 4 and 5 , respectively, leads to increased emission quantum yields under the same conditions. We found that Jahn–Teller and pseudo‐Jahn–Teller effects are operative in complexes 2 and 3 , respectively, on going from the optimized S₀ ground state to the optimized excited state, and thus lead to large excited‐state structural distortions and hence fast nonradiative decay. Furthermore, a strong‐field ligand may push the two different occupied d orbitals so far apart that the SOC effect is small and the radiative decay rate is slow. This work is an example of electronic‐structure‐driven tuning of the phosphorescence efficiency, and the DFT/TDDFT approach is demonstrated to be a versatile tool for the design of phosphorescent materials with target characteristics.     

Quantum‐chemical study of the singlet oxygen emission

Intensity distribution in rotational lines of the 0–0 band of the a¹Δ_g → X³Σ transition in the oxygen molecule at λ = 1270 nm is studied by quadratic response (QR) method in a framework of multiconfiguration self‐consisted field (MCSCF) theory. The distance dependence of the transition magnetic moment and the (0–0)/(0–1) bands intensity ratio are calculated. A short review of previous theory of the red and infrared atmospheric oxygen bands and of their enhancement by collisions is presented to analyze and compare the new results. Enhancement of these bands in O₂ collisions with Li₂ and N₂ molecules is calculated by QR method. Diamagnetic species simulate solvent molecules of different optical polarizability. Specific influence of collisions on vibronic bands is stressed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-singular dichotomy for orbital measures of classical simple Lie algebras

We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie group satisfy a smoothness dichotomy: Either μ ^k is singular to Lebesgue measure or μ ^k ∈ L ². The minimum k for which μ ^k ∈ L ² is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure. S. K. Gupta appreciates the hospitality of the Department of Pure Mathematics at the University of Waterloo where some of this research was done. K. E. Hare was supported in part by NSERC.     

On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems

The determination of the basin of attraction of a periodic orbit can be achieved using a Lyapunov function. A Lyapunov function can be constructed by approximation of a first-order linear PDE for the orbital derivative via meshless collocation. However, if the periodic orbit is only accessible numerically, a different method has to be used near the periodic orbit. Borg's criterion provides a method to obtain information about the basin of attraction by measuring whether adjacent solutions approach each other with respect to a Riemannian metric. Using a numerical approximation of the periodic orbit and its first variation equation, a suitable Riemannian metric is constructed.     

符号动力系统与费马小定理

费马小定理是数论中的一个重要定理.利用符号动力系统计算周期轨的方法给出了费马小定理一个新的证明,讨论了数的整除性,并解释了费马小定理的几何意义.     

A computational investigation of topological insulator Bi2Se3 film

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.     

The global dynamics of a class of vector fields in ℝ<Superscript>3</Superscript>

In this paper, we find a bridge connecting a class of vector fields in ℝ³ with the planar vector fields and give a criterion of the existence of closed orbits, heteroclinic orbits and homoclinic orbits of a class of vector fields in ℝ³. All the possible nonwandering sets of this class of vector fields fall into three classes: (i) singularities; (ii) closed orbits; (iii) graphs of unions of singularities and the trajectories connecting them. The necessary and sufficient conditions for the boundedness of the vector fields are also obtained.     

Spin–orbit coupling effects on the in-plane optical anisotropy of semiconductor quantum wells

We theoretically study the influence of the spin–orbit coupling(SOC) on the in-plane optical anisotropy(IPOA) induced by in-plane uniaxial strain and interface asymmetry in(001) GaAs/AlGaAs quantum wells(QWs) with different well width. It is found that the SOC has more significant impact on the IPOA for the transition of the first valence subband of heavy hole to the first conduction band(1H1E) than that of 1L1E. The reason has been discussed. The IPOA of(001) InGaAs/InP QWs has been measured by reflectance difference spectroscopy, whose amplitude is about one order larger than that of GaAs/AlGaAs QWs. The anisotropic interface potential parameters of InGaAs/InP QWs are also determined. The influence of the SOC effect on the IPOA of InGaAs/InP QWs when the QWs are under tensile, compressive or zero biaxial strain are also investigated in theory. Our results demonstrate that the SOC has significant effect on the IPOA especially for semiconductor QWs with small well width, and therefore cannot be ignored.     

Effect of normalized plasma frequency on electron phase-space orbits in a free-electron laser

Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.