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}     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ^? could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ? (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)?(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ? (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ^? radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ^n? fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

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.     

Intramolecular electron transfer in mixed-valence complexes [(NH3)5Ru-L-Ru(NH3)5]5+ (L = N2, pyz, pym, 4,4’-bipy, bpa)

The dynamics of the intramolecular electron transfer from Ru(II) to Ru(III) in binuclear mixed-valence complexes [NH₃)₅Ru -L-Ru(NH₃)₅]⁵⁺ (L = N₂, pyz, bipy, pym, bpa) is analyzed by the semiempirical CINDO + CI method. Translated from ZhurnalStruktumoi Khimii, Vol. 39, No. 4, pp. 579–590, July–August, 1998.     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ⁻ could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ⊗ (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)⊗(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ⊗ (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ⁻ radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ⁿ⁻ fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

Temperature-dependent photoluminescence in La2/3Ca1/3MnO3

Visible photoluminescence and its temperature dependence of La_2/3Ca_1/3MnO₃ in the temperature range 138-293 K were measured. It was observed that the main broad band centered at ∼1.77 eV with the shoulders at ∼1.57 and ∼1.90 eV existed in the entire temperature range. It can be well fitted by three Gaussian curves B₁, B₂ and B₃ centered at ∼1.52, ∼1.75 and ∼1.92 eV, respectively. The intensities of the peak B₁ and B₂ vary as temperature increases. In the entire temperature range, the intensity of B₁ increases with increasing temperature, whereas that of B₂ decreases. The photoluminescence mechanisms for La_2/3Ca_1/3MnO₃ are presented based on the electronic structures formed by the interactions among spin, charge and lattice, in which B₁ was identified with the charge transfer excitation of an electron from the lower Jahn-Teller split e_g level of a Mn³⁺ ion to the e_g level of an adjacent Mn⁴⁺ ion, B₂ is assigned to the transition between the spin up and spin down e_g bands separated by Hund's coupling energy E_J and B₃ is attributed to the transition, determined by the crystal field energy E_C, between a t_2g core electron of Mn³⁺ to the spin up e_g bands of Mn⁴⁺ by a dipole allowed charge transfer process.     

Molecular Force Fields of XY6 Type Molecules

Octahedral molecules of XY₆ type belonging to O_h symmetry have six normal modes of vibrations. On group theoretical considerations, Λ_vib, = a^1g + e_g + 2t_1u + t_2g + t_2u     

The Raman Spectrum and Full Vibrational Assignment of Ethylenediamne Dihydrochloride

A full vibrational analysis was recently made for the H³N⁺CH₂CH₂N⁺H₃ ion, on the basis of infrared measurements, and a partial vibrational assignment proposed¹. The observed fundamentals were interpreted In terms of a C_2h, symmetry for the ion. There are thirty-six fundamentals (r - lla_g + 8A_u + 7B_g + 10B_u; A_g and B_g Raman-active only; A_u and B_u infrared-active only). In addition to the eighteen infrared-active vibrations, a number of bands was observed which were assigned as formally forbidden Raman-active modes, excited by strong hydrogen bonding causing departure from the exact site symmetry of the species.     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

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.     

Electronic states of C2H6 +

The complete photoelectron spectrum of ethane has been measured in the valence region using Ne, He I, and He II resonance radiation. The resolution of these spectra is sufficient to partially resolve vibronic structure accompanying the transition to the ground ionic state. The similarity of this structure with that obtained from model calculations using the Jahn-Teller theorem strongly suggests that the active vibration in this transition is a doubly degenerate CH₃ deformation mode and that the ground ionic state is a Jahn-Teller split ² E _g state. These experiments suggest a ² A _1g term for the first excited ionic state. The transition to the ² A _2u state of the ion contains evidence for two active vibrations v ₁ (C–H stretch) and v ₃ (C-C stretch).     

Indirect measurements of the Jahn-Teller quenched spin-orbit splitting in the 5T2g-state of KMgF3:Fe2+

The energy separation of the first excited spin-orbit States Γ_3g, Γ_4g from the Γ_5g ground state, in the orbital ⁵T_2g triplet state of Fe²⁺ in KMgF₃, has been estimated from temperature dependence measurements on the 7860 cm^-1 zero-phonon-line (ZPL) transition from Γ_5g to the orbital ⁵E_g doublet state. Using a simplified crystal field energy level model, we find the Γ_5g Γ_3g, Γ_4g separation to be ～30 cm^-1, indicating that the vibronic Jahn-Teller coupling is considerably stronger in KMgF₃:Fe²⁺ than in MgO:Fe²⁺. Far infrared absorption data on KMgF₃:Fe²⁺ in magnetic fields up to 6T, are found to be consistent with this interpretation.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.     

Profiles of (υ′;υ″ = 0) bands recorded in excitation spectra using b30+u ← X10g+ transitions in Cd2 and B31 ← X10+ transitions in CdAr

Profiles of the (υ′;υ ^″ = 0) vibrational bands recorded using the b³0⁺ _u ← X¹0_g ⁺ and B³1?←?X¹0⁺ transitions in Cd₂ and CdAr complexes, respectively, are presented and analysed. Specifically, CdAr and Cd₂ complexes are simultaneously propagating in a supersonic beam. Transitions in these complexes can be used to provide the conditions for selective detection of one of the complexes in the expansion. Extended analysis of the B³1- and b³0⁺ _u -state vibrational progressions provided improved values for ω′ _e x′ _e and ω′ _e vibrational characteristics, as well as D′ _e well depths and R _e ′ bond lengths of the B³1- and b³0⁺ _u-state potentials. Several of the CdAr bands were recorded with partly resolved rotational structure. The new characterisation of the B³1 state, along with results of the rotational and isotopic analyses of the band profiles, agrees with the most recent results of ab initio calculations, while results obtained for the b³0⁺ _u state call for improvement in the ab initio calculations for Cd₂.     

Probable location of a 1E2g state of the benzene molecule

Photoexcitation spectra of benzene in rare gas matrices show a previously unreported transition near 46000 cm^?1. The observed bands are not explicable in terms of site splittings, impurity states, aggregation effects, intermediate radius states of the matrix, triplet states, excimer states, exciplex states or $\text{σ-π}{}^1$ transitions. The vibronic spacings in these spectra could be those expected for a ¹E_2g ← ¹A_1g transition and on this and other evidence we argue that the ordering of origins of the first four spin allowed intravalence states of benzene is ¹B_2u (38086 cm^?1), ¹E_2g (near 46400 cm^?1), ¹B_1u (48450 cm^?1) and ¹E_1u (55430 cm^?1). Our data also show that the transition ¹B_1u ← ¹A_1g accounts for most of the intensity of the 210 nm absorption band system. Our ordering of the spin allowed states permits interpretation of experimental data of others, confirms certain semi-empirical and ab initio SCF MO CI calculations in which account is taken of higher excitations and illustrates the necessity of including such higher excitations. The intensity of the ¹E_2g ← ¹A_1g transition is at least an order of magnitude less than previously calculated indicative of the difficulty of choosing suitable wavefunctions for the ¹E_2g state and of calculating “forbidden” transition probabilities.     

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 spectra and vibronic coupling of pyrazine

The absorption and fluorescence spectra of pyrazine have been observed in vapor, solution and crystal, and the vibrational structures have been analyzed in detail. The fluorescence spectrum consists of long progressions of the nontotally symmetric vibration ν₅(b_2g), and the absorption spectrum contains also the progression of the corresponding excited state vibration ν′₅(b_2g. However, the pattern of the latter progression is unusual because of the highly anharmonic nature of the potential of the ¹B^3u state, which may be expressed by a functional form containing a quadratic term in the normal coordinate. All the experimental results suggest that the known vibronic interaction between the ${}^1\text{B}{}_{\mathrm{3u}}\text{(n,π}{}^1\text{)}$ state and the ${}^1\text{B}{}_{\mathrm{1u}}\text{(π, π}{}^1\text{)}$ state through the vibration ν₂(b_2g) is strong. The vibronic coupling and the potential of the ¹B_3u state were found to be very sensitive to solvent.     

Fluorescence spectra of matrix-isolated Se2

Laser induced fluorescence spectra are reported for samples of natural selenium and of the separated ⁷⁸Se and ⁸⁰Se isotopes in Ar and Kr matrices. The B(0_u⁺) → X(0_g⁺) and B(1_u) → X(1_g) systems of Se₂, already known in the gas, are observed by both single photon and biphotonic excitation considerably red-shifted in the matrices. The A(0_u⁺) → X(0_g⁺) emission of Se₂, not observed in the vapor, appears in the matrices with its origin near 15 100 cm^?1. Another system with ν₀₀ = 24 429 cm^?1 and ω″_e = 538 cm^?1 is thought to belong most probably to some polyatomic Se_n molecule.     

Applications of photoelectron spectroscopy to molecular propertles: XVIII. The vertlcal ionization potentials of diphosphene as calculated by perturbation corrections to koopmans' theorem

The vertlcal ionization potentials (VIP's) of dimethyl diphosphene have been computed using perturbation corrections to Koopmans' theorem. These corrections allow an estimate of the effects of polarization and correlation, and show for this molecule an important contribution of the specific correlation of the ion for the ²A_g and ²B_u states. The results predict for the first three VIP's the ordering ²A_g, ²A_u, ²B_u, in agreement with our previous assignment.