C42+的几何构型和Jahn Teller效应

用从头计算法QCISD/6-311G得到了C₄²⁺分子的10种不同的几何构型,其中包括C_s,C_∞v,C_2v,D_2h,D_∞h,D_4h,D_2d,C_3v等不同的构型.计算表明C₄²⁺的T_d构型不能稳定存在,详细讨论了T_{d 关键词： 几何构型 4}²⁺')" href="#">C₄²⁺ Jahn Teller效应     

Stretch-Bender Calculations of the Rovibronic Energies in the Excited, ÃA1, Electronic State of NH2 and of the Near-Resonant High-Lying Levels of the X?B1 State

The extended stretch-bender Hamiltonian, incorporating spin-orbit coupling and overall rotation, has been used to calculate the spin-vibronic structure of the rovibronic energies in the region where the vibronic states of the excited òA₁ electronic state of NH₂ interact with near-resonant high-lying levels of the X?²B₁ state of NH₂. A detailed comparison has been made with the experimental measurements which were made of these rovibronic states, the majority of which are due to Ramsay, Vervloet, and their collaborators. We have shown that, as in our study of the vibronic levels of the X?²B₁ state below the barrier to linearity, in order to fit the variation of the effective vibronic spin-orbit coupling constant over the whole of this energy regime, the effective linear molecule spin-orbit coupling constant, A_SO must be increased from the earlier value of 50 cm⁻¹ of Ch. Jungen, K.-E. J. Hallin, and A. Merer (Mol. Phys.40, 65-94 (1980)) to 61.6 cm⁻¹. The impact of Fermi resonance, in both the òA₁ and X?²B₁ states, on the observed rovibronic structure has been assessed. The pattern of calculated spin-rovibronic levels, including the effects of spin uncoupling, is in good agreement with that measured experimentally.     

Two-photon vibronic spectroscopy of allene at 7.0–10.5 eV: experiment and theory

2?+?1 resonance-enhanced multiphoton ionization (REMPI) spectra of allene at 7.0–10.5?eV have been observed. The excited vibronic symmetry has been determined from polarization-ratio measurements. Based on the vibronic energies and peak intensities calculated using ab initio MO and time-dependent density functional theory, the very congested REMPI spectra have been assigned as due to π*?←?π, 3p?←?π, 4s?←?π, 4p?←?π, and 4d?←?π transitions. Vibrational progressions related to the CH₂ twisting (ν₄ ～770?cm^?1) have been observed for several excited electronic states. Calculated Franck–Condon factors also confirm that CH₂ twisting is the most active mode in the vibronic spectra of allene. In this study, theoretical calculations of two-photon intensities and polarization ratios have been made through the ab initio computed one-photon transition dipole moments to various electronic states as intermediates. As a starting point to interpret the complicated vibronic spectrum of allene, the theoretical approach, without vibronic couplings, has been applied to predict the peak positions, spectral intensities, and polarization ratios of Rydberg states, and qualitatively shows a considerable agreement with experimental observations.     

Vibronic Transitions of Trivalent Er and Ce in BaY2F8 Single Crystals

High resolution (0.02 cm^?1) Fourier transform spectroscopy was applied in the 9–300 K and 100–24,000cm^?1 ranges, respectively, to detect in Er^3? and Ce^3? doped BaY₂F₈ single crystals (1) the narrow line spectra due to the intraconfigurational 4f→4f transitions of the rare earths (RE) and (2) the possible vibronic tails accompanying the zero-phonon lines. The ²F_5/2→²F_7/2 transition was monitored for the Ce^3?-doping and the crystal field splitting of the initial and final manifold was determined. Weak vibronic spectra accompanying six among the nine investigated 4f→4f transitions of Er^3? and the ²F_5/2→²F_7/2 transition of Ce^3? were detected. The vibronic spectra amplitude was found to scale with the RE contents. On the basis of the IR- and Raman-active vibrational modes, either measured or quoted in the literature, most of the vibronic lines could be successfully assigned to the lattice modes. Violations of the selection rules were envisaged and discussed.     

Motional averaging in an excited state of ZnS: Cu2+

The single isotropic g factor found in the ²E excited state of ZnS:Cu²⁺ is hard to reconcile with the properties of this state, in particular with the moderate strength of the E ? ? vibronic coupling. A vibronic coupling between this state and the vibronic levels of the ground ²T₂ state due to τ₂ modes can bring about motional averaging between strain split states of ²E through a two phonon non-resonant process. In general, excited state mechanisms will be effective between states of the same spin multiplicity and which have large Stoke shifts.     

Magnetic field effect on the H2CS fluorescence from the first excited singlet state Ã1A2

Fluorescence intensity in thioformaldehide vapours (H₂CS), excited to the ÃA₂ different vibronic levels of the ùA₂ ? [Xtilde]¹A₁ transition, were measured as a function of an external magnetic field. On excitation to these levels, dynamics in zero and non-zero field may be described in the small-molecule limit, with fluorescence exhibiting an almost exponential decay. A magnetic field changes the integrated intensity and decay lifetime of the thioformal-dehide fluorescence induced from different vibronic levels of the ù A₂ state. We found that the magnetic field effect grows at lower gas pressures. The measured field dependences of the magnetic field effect can be fitted using field-saturated functions. The measured data were explained by the indirect mechanism theory (nuclear-spin and electron-spin decoupling mechnism).     

First-principles band-structure calculations as a tool for the quantitative interpretation of Raman spectra of high temperature superconductors

We have performed first-principles band structure calculations in order to investigate vibronic and optical properties of YBa₂Cu₃O₇. A formalism describing temperature dependent Raman spectra from such ab-initio results has been applied to the 500 cm^?1 apex oxygen mode and its overtone in good agreement with experimental results. The dynamical matrix of the five A_1g modes established by atomic-force calculations is studied in detail showing rather good agreement with experimental eigen-frequencies and normal coordinates. The effect of isotope substitutions on the phonon frequencies is investigated. We demonstrate that the calculated vibronic properties of high T_c materials are improved by applying a generalized gradient correction scheme for the treatment of exchange and correlation effects instead of the local-density approximation.     

Stretch-Bender Calculations of the Rovibronic Energies in the X?B1 Electronic Ground State of NH2

The extended stretch-bender Hamiltonian, incorporating spin-orbit coupling and overall rotation, has been used to calculate the spin-vibronic structure of the X?²B₁ state of NH₂ up to the barrier to linearity of this state. A detailed comparison has been made with experimental measurements of these rovibronic states, the majority of which are due to Vervloet and his collaborators. We have shown that, in order to fit the variation of the vibronic spin-orbit coupling constant over the whole of this energy regime, the effective linear molecule spin-orbit coupling constant, A_SO, must be increased from the earlier value of 50 cm⁻¹ of Ch. Jungen, K.-E. J. Hallin, and A. Merer (Mol. Phys.40, 65-94 (1980)) to 61.6 cm⁻¹. Evidence has also been provided for the large quenching of the spin-orbit coupling as the molecule bends, reflected in the large valuee of g_K=6 cm⁻¹. The pattern of calculated spinrovibronic levels, including the effects of spin uncoupling, is in good agreement with that measured experimentally.     

Magnetic circularly polarized emission and magnetic circular dichroism of resolved vibronic lines in Cs2GeF6: Mn4+

Magnetic circularly polarized emission (M.C.P.E.) and magnetic circular dichroism (M.C.D.) techniques have been used to study at low temperatures resolved vibronic lines of the ⁴ A _2g ?² E_g transition in octahedral Mn⁴⁺(3d³) in the cubic host Cs₂GeF₆. Measurements have been made with applied magnetic field (and light propagation) along the [001] (F-Mn-F bond) and [111] directions. Though the Zeeman energy patterns are isotropic, the intensity patterns are not, and U′(Γ₈) eigenvectors for arbitrary field orientation have been derived. These have been used to calculate Zeeman intensity patterns for the [001] and [111] crystallographic directions, and the observed intensity variations with orientation are found to provide useful information about intensity mechanisms. In the case of the magnetic dipole origin, the intensity patterns as a function of orientation can be well accounted for by a first-order mechanism which, however, does not predict the small positive M.C.D. observed at the zero-field energy in the [111] orientation. A detailed analysis of this feature and previously measured energy spacings suggest that ζ_3d(Mn⁴⁺) should have a value of ～360 cm^-1 rather than the value 240 cm^-1 usually assumed. Electric dipole vibronic sidebands have been observed corresponding to v ₆(t _2u ), v ₄(t _1u ), v ₃(t _1u ), v ₄(t _1u ) + v ₅(t _2g ) and v ₂(e_g ) + v ₆(t _2u ). Using a U′→U′ vibronic intensity mechanism with spin-orbit mixing (Appendix A), the M.C.P.E. and total emission patterns for the first two of these regions can be quite well accounted for quantitatively. The corresponding M.C.D. in both cases, while in qualitative agreement with the M.C.P.E., shows much more complicated splitting patterns which are not explicable in terms of a simple k = 0 model. The other three vibronic regions can be accounted for qualitatively. In Appendix B a formula is derived which explicitly relates the M.C.P.E. of a vibronic emission line to its M.C.D. absorption counterpart.     

Vibronic coupling in the first four electronic states of CH2F+2

Vibronic coupling in the energetically lowest first four electronic states of CH₂F⁺₂ is studied in this paper. A model 4×4 Hamiltonian is constructed in a diabatic electronic representation employing normal coordinates of vibrational modes and standard vibronic coupling theory. Extensive ab initio quantum chemistry calculations are carried out to determine the parameters of the Hamiltonian and energetic ordering of the electronic states. The topographical features of the latter are examined at length and several conical intersections are established. Nuclear dynamics calculations on coupled electronic states are carried out from first principles by propagating wave packet. Theoretically calculated broad band vibronic structure of the four states are found to be in good accord with the experimental results.     

Electrochemical determination of the lithium ion diffusion coefficient in TiS2

Long-time chronoamperometry of TiS₂ electrodes immersed in saturated LiClO₄/DMF solution was employed to investigate the charge transport processes which govern the rate of Li⁺ intercalation in TiS₂. The intercalation rate and hence, the current, appears to be controlled by the rate of Li⁺ diffusion within the TiS₂. A model has been developed which predicts the current-time behavior under the control of Li⁺ solid state diffusion. The close agreement of this model with the experimental data allows the solid state diffusion coefficient and other transport parameters (such as effective electrode area) to be evaluated from the measured average grain boundary distance. Typical TiS₂ grain boundary distances in the 3–10 μm range yield a geometric mean value of 1.3 × 10^?9 cm²/s for the solid state diffusion coefficient; this is in close agreement with previously reported diffusivities as measured by NMR spin-lattice relaxation techniques.     

Isotopic effects of the N(2D) + H2 → NH + H reaction: a quantum time-dependent wave packet investigation

Based on the potential energy surface reported by Li and co-workers (J. Comput. Chem. 34 1686–1696 (2013)), the dynamics calculations of N(²D)?+?H₂(v ₀?=?0, j ₀?=?0) reaction and its isotopic variants HD and D₂ are studied using time-dependent wave packet method in the collision energy range of 0.01–1.0?eV. Dynamics properties such as reaction probability, differential cross section, and integral cross section are studied at state-to-state level of theory. Present values are compared with available theoretical and experimental results. The results indicate that the integral cross sections of N(²D)?+?D₂ reaction are in general good agreement with the experimental data at collision energy below 0.15?eV. The rotational state-resolved integral cross sections of N(²D)?+?H₂/HD/D₂ reactions are compared with experimental values for the first time, with the obtained values being in good agreement with the experimental data.     

First principles theory of hyperfine interactions in spinels: ZnAl2O4

The nuclear quadrupole interactions of²⁷Al and⁶⁷Zn, both at the B-site in the spinel ZnAl₂O₄ have been studied using the Hartree-Fock cluster procedure including the influence of the ions outside the cluster. The theoretical value –3.85 MHz ofe ² qQ for²⁷Al is in very good a agreement with the experimental value of 3.68 MHz (sign undetermined). For⁶⁷Zn at the Al site the theoretical value is –8.26 MHz in reasonable agreement with the experimental value of –11.34 MHz indicating that lattice distortion effects associated with Zn as an impurity at the Al site are relatively small.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Quantum efficiency of Nd-doped lasers measured by pump-induced crystal heating: application to the Nd3+:Gd2(MoO4)3 crystal

In this paper we show how the quantum efficiency of Nd³⁺-doped laser crystals can be measured by means of a very simple method. This method is based on a multiwavelength study of pump-induced crystal heating, and its major advantage is the simplicity of the required experimental set-up. It has been used to determine the quantum efficiency of the main infrared laser channel (⁴ F _3/2?⁴ I _11/2) of the Nd³⁺:Gd₂(MoO₄)₃ non-linear laser crystal. The value obtained for the quantum efficiency (φ=0.97) is in good agreement with that obtained from the Judd–Ofelt formalism (φ=0.95). Received: 25 October 2000 / Revised version: 2 January 2001 / Published online: 27 April 2001     

Analysis of the sideband fluorescence of Eu2+:CaF2

The vibronic fluorescence of Eu²⁺:CaF₂ at 4130 Å is calculated be treating the associated Jahn-Teller problem in the classical static limit and extracting the usual oscillator shifts in a cluster calculation. A_1g and E_g contributions are separated via the pronounced one-phonon structure. The J-T stabilization energy and the 10Dq value for the 5d electron are estimated to be 600 cm^?1 and 16,000 cm^?1 respectively.     

Simulation of structured 4T1→6A1 emission bands of Mn2+ impurity in Zn2SiO4: A first-principle methodology

A sequential, fully first-principle theoretical study of the Mn²⁺ green emission bands in the Zn₂SiO₄:Mn²⁺ phosphor is presented for the first time. A combined approach is developed based on the modern periodic density-functional theory and cluster ab initio wave-function-based electronic structure methods, the linear response theory for lattice phonons, and generating function formalism of vibronic spectra within the displaced multi-mode harmonic oscillator model. We obtain fairly good agreement between the calculated low- and high-temperature emission band positions, widths, zero-phonon lines and phonon wings and the available experimental emission studies, with special emphasis on Mn²⁺ distribution over two non-equivalent Zn²⁺ sites in the Zn₂SiO₄ material. An interpretation for vibronic structure observed in the low-temperature emission spectrum of this phosphor is suggested based on the present first-principle study.     

Calculation of the hyperfine structure of the 42 S 1/2, 42 P 1/2, 42 P 3/2 states in the 3d 10 nl configuration of Cu

The hyperfine structure of the 4² S _1/2, 4² P _1/2, 4² P _3/2 states in the 3d ¹⁰ nl configuration of Cu has been evaluated using many-body perturbation theory. Polarisation effects were included in all orders and correlation to third-order. By the use of iteration methods, a large number of higher order diagrams were also included. The correlation effects between the valence electron and the 3d shell were found to be very important. The results forA(² S _1/2) andA(² P _1/2) 5827MHz and 440 MHz, respectively, are in good agreement with the experimental results, whereas the result forA(² P _3/2)=83 MHz is far from the experimental value. No explanation was found for the discrepancy. The quadrupole values were found to be ?206 mb for⁶³Cu and ?185 mb for⁶⁵Cu.     

The magnetic circular dichroism spectrum of the 1 B 2u ←1 A 1g transition of benzene in the vapour phase

The magnetic circular dichroism (MCD) spectrum of the ¹ B _2u ←¹ A _1g transition of benzene has been measured in the vapour phase. Many of the bands due to transitions between single vibronic levels display A terms. It has been shown that the angular momentum arises by vibronic mixing both of the ¹ E _1u state with the ¹ B _1u state and of the ¹ E _2g states with the ¹ A _1g ground state by e _2g vibrations. The magnitudes and signs of the experimental and calculated ratios, A/D, for the A ₀ ⁰ vibronic origin are in excellent agreement. Two strong MCD progressions of opposite sign with B-term dispersion have been observed in regions of low absorption. These are identified with vibronic origins due to the v ₈ and v ₉ e _2g modes. By contrast the MCD spectrum of hexadeuterobenzene vapour has a much lower magneto-rotational strength and displays none of the striking features of the benzene MCD spectrum.     

Optoelectronic properties of rutile (TiO2)

We present here a study of the electronic and optical properties of rutile (TiO₂). An investigation into the energy, pressure and temperature dependence of n_eff and ε_{∞ eff} is presented. Using the calculated values of n_eff and ε_{∞ effs}, we evaluate the Penn gap. The Penn gap thus obtained is shown to be in good agreement with the reflectivity data and also with the value obtained from band structure. In addition, we also show that essentially the Varshni formula explains the temperature dependence of the energy gap for rutile fairly well.