Competition between Jahn-Teller effect and spin-orbit coupling in Td Au20 ±γ, γ = 1,2,3

In this work we explored the competition between spin-orbit and Jahn-Teller effects as decisive influences in the ground states of the T_d Au₂₀ ^±γ (γ=1,2,3). All our electronic calculations were based in the relativistic density functional theory in the zeroth-order regular approximation (ZORA) to the Dirac equation. Calculations were done in both versions of ZORA: scalar relativistic and full-relativistic including the spin-orbit interaction. We concluded that for the Au₂₀ ^-3 ion is necessary to use a full-relativistic theory in order to predict a symmetry-lowering from tetrahedral. We predict a trigonal C_3v isomeric form for this trianion due to a Jahn-Teller distortion of its parent T_d. For the rest of ions we found a tendency to conserve their pristine tetrahedral configurations. In these cases we found one of both possibilities: a quenching of the vibronic interaction by spin-orbit coupling or simply a weak Jahn-Teller effect which is not enough to distort appreciably the cluster.     

具有D4h对称性构型的C2+4分子的Jahn-Teller效应与能级分裂

依据量子理论与配位场理论,利用群论和对称性分析的方法探讨了C²⁺₄分子在具有D_4h对称性构型时,E×(b_1g+b_2g)系统的Jahn-Teller效应中的相关问题.研究了C²⁺₄分子的电子态与声子态的对称性及其活跃声子态,讨论了系统声子间的耦合与CG系数,构建了E×(b_1g+b_{2g 关键词： 2+4分子')" href="#">C²⁺4分子 对称性 能级分裂 Jahn-Teller畸变}     

Theoretical study of the electron paramagnetic resonance parameters and local structure for the tetragonal Ir<Superscript>2+</Superscript> centre in NaCl

The electron paramagnetic resonance (EPR) parameters (the g factors, hyperfine structure constants and the superhyperfine parameters) for the tetragonal Ir²⁺ centre in NaCl are theoretically investigated from the perturbation formulas of these parameters for a 5d⁷ ion in tetragonally elongated octahedra. This impurity centre is attributed to the substitutional [IrCl₆]⁴⁻ cluster on host Na⁺ site, associated with the 4% relative elongation along the C ₄-axis due to the Jahn-Teller effect. Despite the ionicity of host NaCl, the [IrCl₆]⁴⁻ cluster still exhibits moderate covalency and then the ligand orbital and spin-orbit coupling contributions should be taken into account. In addition, the theoretical EPR parameters based on the Jahn-Teller elongation show good agreement with the observed values.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

Theoretical study of the electronic structure of a tetragonal chromium(III) complex

The low-temperature single-crystal polarized absorption and the luminescence spectra of Cs₂[CrCl₂(H₂O)₄]Cl₃ are theoretically analyzed in order to determine the electronic structure of the trans-[CrCl₂(H₂O)₄]⁺ complex. This study, based on the Racah theory, leads to a good agreement between the theoretical and experimental energy levels. The electronic-exited state ⁴T_2g(O_h) is split into ⁴E_g and ⁴B_2g components due to the lowering of the symmetry from O_h to D_4h. The polarized absorption spectrum and the theoretical energies show that the ⁴E_g(D_4h) state is lower in energy than the ⁴B_2g(D_4h) state. The resolved vibronic structure in the luminescence spectrum reveals a progression in a non-totally symmetric b_1g mode, a manifestation of a Jahn-Teller effect in the emitting state ⁴T_2g(O_h). Both Jahn-Teller and spin-orbit coupling in the orbitally degenerated ⁴E_g(D_4h) state are necessary to account for the spectroscopic observations.     

Models of solid-state influences in systems with Jahn-Teller distortions

A system with the Jahn-Teller distortion, namely the complex CuCl ₆ ^4– , has been investigated in various surroundings represented by [CuCl ₆ ^4– ...n Na⁺] ^q clusters. The degree of the tetragonal distortion has been calculated using the quantum-chemical CNDO method and compared with values produced by the point-charge model.Presented at the International Symposium on Solid State Chemistry, October 28–31, 1986, Karlovy Vary, Czechoslovakia.     

Derivatives of the thiolate-protected gold cluster Au25(SR)18-1

Loss of small fragments (like AuL, Au₂L₃, Au₄L₄) have been found systematically in several MALDI and FAB experiments on thiolate-protected gold clusters of different sizes. When using the cluster Au₂₅L₁₈ ^-1 as parent cluster, the fragmented cluster Au₂₁L₁₄ ^-1 has been reported to be obtained in high proportion (L = SCH₂CH₂Ph). Here we analyse a few possible fragmentation patterns of the well-known parent cluster Au₂₅L₁₈ ^-1 (L = SCH₃). Using DFT calculations we study the different atomic configurations obtained after a AuL fragment is lost from Au₂₅L₁₈ ^-1. We found energetically favourable configurations that can be written as Au₁₃ [Au₂L₃]_6-z [AuL₂] _z ^-1, where the modification can be described as a replacement of the long protecting unit by a short one (Au₂L₃  →  AuL₂). A full replacement (z = 6) gives rise to a protected Au₁₉L₁₂ ^-1 cluster. This mechanism does not modify the super-atomic electronic structure of the gold core, i.e., all these fragments remain an 8 electron super-atom clusters exactly like the parent Au₂₅L₁₈ ^-1. We suggest that the Au₁₉L₁₂ ^-1 cluster could be realized by using a bulky thiolate, such as the tert-butyl thiolate SC(CH₃)₃ .     

Singlet-triplet pseudo Jahn-Teller centers in copper oxides

One of the most interesting attributes of a hole CuO ₄ ⁵ center in doped cuprates is the complexity of the ground state as a result of electronic pseudodegeneracy. An extra hole injected into the initial CuO ₄ ⁶ cluster with a b _1g hole can occupy not only the very same hybrid Cu 3d-O 2p orbital state, producing a Zhang-Rice A _1g singlet, but also the pure oxygen e _u state, generating a singlet or triplet ^1,3 E _u term, with close energies. The pseudo Jahn-Teller effect induced by pseudodegeneracy of the singlet ¹ A _1g and ¹ E _u terms is analyzed in detail. Fiz. Tverd. Tela (St. Petersburg) 40, 1795–1804 (October 1998)     

A Sharp Condition for Scattering of the Radial 3D Cubic Nonlinear Schrödinger Equation

We consider the problem of identifying sharp criteria under which radial H ¹ (finite energy) solutions to the focusing 3d cubic nonlinear Schrödinger equation (NLS) i? _t u + Δu + |u|² u = 0 scatter, i.e., approach the solution to a linear Schrödinger equation as t → ±∞. The criteria is expressed in terms of the scale-invariant quantities ${\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}}We consider the problem of identifying sharp criteria under which radial H ¹ (finite energy) solutions to the focusing 3d cubic nonlinear Schr?dinger equation (NLS) i∂ _t u + Δu + |u|² u = 0 scatter, i.e., approach the solution to a linear Schr?dinger equation as t → ±∞. The criteria is expressed in terms of the scale-invariant quantities and M[u]E[u], where u ₀ denotes the initial data, and M[u] and E[u] denote the (conserved in time) mass and energy of the corresponding solution u(t). The focusing NLS possesses a soliton solution e ^it Q(x), where Q is the ground-state solution to a nonlinear elliptic equation, and we prove that if M[u]E[u] < M[Q]E[Q] and , then the solution u(t) is globally well-posed and scatters. This condition is sharp in the sense that the soliton solution e ^it Q(x), for which equality in these conditions is obtained, is global but does not scatter. We further show that if M[u]E[u] < M[Q]E[Q] and , then the solution blows-up in finite time. The technique employed is parallel to that employed by Kenig-Merle [17] in their study of the energy-critical NLS.     

Calculation of potential energy curves for Rb2 including relativistic effects

All-electron relativistic calculations have been performed on the Rb₂ molecule. The molecular orbitals are optimized within a spin-free no-pair Hamiltonian formalism and spin-orbit coupling is treated using quasi-degenerate perturbation theory. Potential curves of the ground state and several excited states are calculated, and the spectroscopic constants T _e, D _e, R _e and ω_e are in good agreement with experimental values. The spin-orbit splittings at the 5p and 6p asymptotic limits are found to be underestimated by about 30%. Large perturbations in the spectra from the 1¹Σ⁺ _u(A) state are predicted due to an avoided crossing with a 1 ³Π_ub state caused by spin-orbit interaction. The predissociation dynamics of the 2 ¹Π_uC and 3 ¹Π_uD states is discussed. The calculations support the observation that a (1) ³ Δ_u state causes the fast predissociation of the ^{3 1}Π_uD state but rule out the (2)³Σ⁺ _u state as causing the slow predissociation at the lower part of the 3 ¹Π_uD potential energy curve.     

On electronic structure of H2 in palladium

Using quasi-relativistic CNDO method the electronic structure of¹[Pd₁₄ ...n H]^q clusters (n=0 or 2) with various total charges, q, is investigated for various H-H configurations. All systems are more stable for q=–2 than for q=0. Lower unit cell dimensions cause the energy stabilization of the H-H subsystem, the dihydrogen charge is more positive and the H-H bond is stronger. The results on electronic structure calculations indicate the existence of higher electron states with significant shifts of energy minima.     

从头计算研究BCl+基态和激发态的势能曲线和光谱性质

基于相关一致极化4zeta(aug-cc-pVQZ)基组, 应用量子化学从头计算中高水平的多参考组态相互作用方法计算了BCl⁺ 两个离解极限B⁺(¹S_g)+Cl(²P_u)和B (²P_u)+Cl⁺ (³P_g)的14个Λ-S态势能曲线. 在计算中考虑了Davidson修正(+Q)和标量相对论效应, 并首次在计算中考虑了BCl⁺ 的旋轨耦合效应, 获得了由能量最低的4个Λ-S态分裂出的7个Ω 态. 计算结果表明相同对称性的Ω 态的势能曲线存在着非常明显的避免交叉. 通过分析Λ-S态的电子结构, 得到了各态的电子跃迁特性, 并确认了电子态的多组态性质. 使用LEVEL程序通过求解径向的Schrödinger方程得到了束缚Λ-S 和Ω态的光谱参数D_e, R_e, T_e, ω_e, ω_eχ_e和B_e. 通过和已有的Λ-S态X²∑⁺ 的实验数据进行对比发现, 本文所得的计算结果与实验结果非常一致. 而文中其他电子态的光谱参数均为首次报道. 关键词： 势能曲线 光谱参数 多参考组态相互作用方法 旋轨耦合     

boldmath B3Σu-–X3Σg- transition in selenium dimer: ab initio multireference configuration interaction calculations

Theoretical investigation of low-lying electronic states and B³Σ_u^-–X³Σ_g^- transition properties of selenium dimer using size-extensivity singly and doubly excitation multireference configuration interaction theory with nonrelativistic all-electron basis set and relativistic effective core potential plus its split valence basis set is presented in this paper. The spectroscopic constants of ten low-lying Λ-S bound states have been obtained and compared with experiments. Spin-orbit calculations for coupling between B³Σ_u^- sates and repulsive ¹Π_u, ⁵Π_u states have been made to interpret the predissociation mechanisms of the B³Σ_u^- state. The lifetimes of B³Σ_u^- (v=0～6) have been calculated with scalar relativistic effects included or excluded, respectively, and reasonably agree with experimental values.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field

A rigorous path integral representation of the solution of the Cauchy problem for the pure-imaginary-time Schrödinger equation _t (t, x)=–[H–mc ²](t,x) is established.H is the quantum Hamiltonian associated, via the Weyl correspondence, with the classical Hamiltonian [(cp–eA(x))²+m ² c ⁴]^1/2+e(x) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Lévy process.     

Spectroscopic and molecular properties of 14 selected electronic states of Si2 molecule

The potential energy curves (PECs) of the X³Σ_g⁻, D³Π_u, a¹Δ_g, b¹Π_u, H′³Σ_u⁻, K³Σ_u⁻, 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states of the Si₂ molecule are investigated using the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach with the correlation-consistent basis sets of Dunning and co-workers. The effects on the PECs by the core-valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction is made with the aug-cc-pCV5Z basis set. And the relativistic correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The PECs of all these electronic states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. Using the PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs determined by the MRCI+Q/CV+DK+56 calculations, the vibrational levels and inertial rotation constants of the first 20 vibrational states are evaluated and compared with the RKR data for these electronic states when the rotational quantum number J equals zero. On the whole, as expected, the most accurate spectroscopic parameters and molecular constants of the Si₂ molecule are determined by the MRCI+Q/CV+DK+56 calculations. And the spectroscopic parameters of the 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states obtained by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment.     

Electronic structure of high-temperature superconductors I. Y-Ba-Cu-O systems

The electronic structure of high-T _c copper based superconductors has been studied using the quasirelativistic INDO molecular orbital method. Model clusters of YBa₂Cu₃O _y systems have been investigated fory ranging between 6·0 and 7·0. Monomeric units [Ba₈Cu₃O _x ] ^q and [Y₄Ba₈Cu₄O _x ] ^q , dimeric units [Ba₁₂Cu₆O _x ] ^q and [Y₆Ba₁₂Cu₈O _x ] ^q as well as tetrameric units [Ba₁₈Cu₁₂O _x ] ^q over 300 valence orbitals have been studied. From the set of occupied molecular orbitals the density of states (DOS) function has been calculated along with its d-orbital projection. The highest occupied molecular orbitals cover the oxygen p-band whereas the copper d-band lies at lower energies. Superconducting phase models (y=6·75 to 7·0) have a higher d-DOS function at higher energies with respect to the non-superconducting phase (y=6·0).     

Assignments of the nπ singlet states of p-benzoquinone

The vapor phase fluorescence spectra of p-benzoquinone-h₄ and d₄ are reported and discussed in relation to the assignment of the low lying singlet states. The low temperature, polarized single crystal electronic absorption spectra of p-benzoquinone and several of its isotopic derivatives are reported. From the isotope shifts and band polarizations of the various vibronic origins, a detailed vibronic analysis is offered of the electronic absorption spectrum of p-benzoquinone which indicates a near degeneracy of the ¹A_u and ¹B_1g electronic states.     

Thepin structure employed as current amplifier

Injection of excess carriers into thei region of a forward biasedpin diode diminishes proportionally its resistivity (primary circuit). Resistivity variations in thei region are used to control higher currents and powers in the secondary circuit. This basic idea is developed quantitatively for a simplified symmetrical model of thepin structure in a stationary regime and then generalized for the asymmetrical case. The frequency characteristics of the electronic device are studied. For demonstration of the theoretical results thepin structure in silicon with known parameters is used.Notation 2d [m] length ofi region - D [m² s^–1] ambipolar diffusion constant - e [C] electron charge - E ₂ [Vm^–1] electric field strength iny direction - i ₁ [Am^–2] current density inx direction - i ₂ [Am^–2] current density iny direction - i _m [Am^–2] current density due to recombination of carriers ini region - i _1ef ,i _2ef [Am^–2] effective values of currentsi ₁,i ₂ - i _ns ,i _ps [Am^–2] saturated current densities from the heavily dopedn, p regions - i intrinsic region - I [A] total current throughp-n junction - I ₁ [A] total current in pin diode - I ₂ [A] current in secondary circuit - k[J grad^–1] Boltzmann's constant - L=(D) [m] ambipolar diffusion length of carriers in middle region - n(x) [m^–3] excess electron concentration in middle region - ¯n [m^–3] average value of electron concentration in middle region - n _i [m^–3] intrinsic electron concentration - n _A [m^–3] acceptor concentration inp region - n _D [m^–3] donor concentration inn region - p(x) [m^–3] excess hole concentration in middle region - q [m²] area of electrodes 3 and 4 - Q [C] charge stored ini region - R [m^–3 s^–1] recombination rate - s [m] width of diode - t [m] thickness of diode - T [K] absolute temperature - U [V] voltage acrossp-n junction - U ₁ [V] voltage acrosspin diode - U ₂ [V] voltage across terminals of secondary circuit - U _m [V] voltage drop acrossi region - V _D [V] voltage drop acrossn — i andp — i junctions at zero load - W ₁ [W] power inpin diode circuit - W ₂ [W] power in secondary circuit - x [m] distance from center of diode - coefficient in current amplification factor - [rad] phase shift of diode current with respect to applied voltage - [s] life time of excess carriers ini region - [m² V^–1 s^–1] carrier mobility ini region in the symmetrical model - _n [m² V^–1 s^–1] electron mobility ini region - _p [m² V^–1 s^–1] hole mobility ini region - [^–1 m^–1] conductivity