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 investigation of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 11Δg state of B2H2

A variational approach for the ab initio handling of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules is presented. The model Hamiltonian involves four nuclear degrees of freedom which correlate for a linear nuclear arrangement with two doubly degenerate bending modes. The bond lengths are assumed to be kept fixed at their equilibrium values and the effect of end-over-end rotations is neglected. The kinetic energy operator and the general form of the potential surfaces employed allow in principle for a treatment of large amplitude bending vibrations. However, because of restrictions implied, such as neglect of coupling between bending and stretching vibrations and interactions with other electronic states, the approach is aimed primarily at molecules bending with relatively small amplitudes around their linear equilibrium geometries. Two algorithms are developed, one for symmetric acetylene-like (A-B-B-A) molecules, the other for asymmetric (A-B-C-D) species. The approach is applied to calculate the vibronic spectrum of the lowest lying excited state, ¹Δ_g, of B₂H₂, employing ab initio computed potential energy surfaces.     

Optical properties of low-dimensional organic conductors with differently oriented conducting layers: (EDT-TTF)3Hg2Br6 and (EDT-TTF)3Hg(SCN)3I0.5(PhCl)0.5

Spectral optical investigations of two low-dimensional organic molecular conductors with differently oriented conducting layers of ethylenedithiotetrathiafulvalene (EDT-TTF) molecules, namely, the (EDT-TTF)₃Hg₂Br₆ and (EDT-TTF)₃Hg(SCN)₃I_0.5(PhCl)_0.5 single crystals, have been carried out. The polarized reflectance spectra of the single crystals have been measured in the frequency range 700–6500 cm⁻¹ (0.087–0.810 eV) at temperatures from 300 to 15 K. The optical conductivity spectra have been obtained using the Kramers-Kronig relations, and their quantitative analysis has been performed in terms of a theoretical model that takes into account electron-electron correlations in the approximation of the Hubbard Hamiltonian for trimerized stacks, the vibronic coupling, and the influence of the counterion on the electronic states in the trimer. A satisfactory agreement between the theoretical and experimental spectra for both crystals made it possible to estimate the parameters of the electronic structure of the crystals in the conducting plane: the integral t of the electron transfer between the EDT-TTF molecules in the trimer, the energy U of the Coulomb repulsion between two electrons (holes) in one EDT-TTF molecule, the electron transfer damping constant γ _e , the energy shift Δ of the molecular orbital under the influence of the anions and vibronic coupling, the vibronic coupling constant g _n , and the binding energy E _p of the molecular polaron. It has been found that there are large differences in the anisotropies of the optical properties and the obtained Hubbard parameters of the electronic structure for the studied crystals.

     

Feshbach resonances of the C3H− anion: laser autodetachment spectroscopy and ab initio calculations

The electronic spectra of the C₃H^? and C₃D^? anions have been studied above the lowest electron detachment threshold. On the basis of the vibrational, rotational analysis and ab initio calculations, the photodetachment spectrum is assigned to the d³ A″←a³ A″ Feshbach resonance in the bent chain C₃H(D)^? anion. The vibronic system is characterized by a long vibrational progression involving the CCH in plane bending mode ν₄. The potential curves along this coordinate obtained from the spectral analysis and theoretical calculations reveal the importance of vibronic coupling in the electronic excited states. A strong Renner–Teller effect is thought to be the reason for the existence of the Feshbach resonance because the ⁴Σ^? neutral parent and the ³Π anion excited states are close in energy. As for the neutral, ν₄ appears to be the active mode and drives the interaction between the Feshbach and the dipole bound states.     

Electron resonance studies of the renner effect

The gas phase electron resonance spectra of NCO in its ground ²Π_3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the ¹⁴N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.     

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.     

The effective Hamiltonian for the Renner-Teller effect

A derivation of the effective vibronic Hamiltonian for a linear triatomic molecule in a Π electronic state within the harmonic approximation is presented. In addition to the well-established vibrational and Renner-Teller coupling terms, there is a small term which has been overlooked before. The form of this term is derived and the parameter involved, g_K, is related to other observable quantities. Several experimental examples are presented which demonstrate that the extra term is needed to reproduce the vibronic levels in Π electronic states, the contribution being of the order of a few cm^?1.     

Absorption and resonance Raman spectroscopy of the 1Bu state of trans‐1,3,5‐hexatriene including vibronic coupling

The vibronic coupling between the first excited S₁ (2¹A_g) and the second excited S₂ (1¹B_u) singlet electronic states in spectroscopy of trans‐1,3,5‐hexatriene molecule is investigated on the basis of a model consisting of two electronic states coupled by two vibrational modes. Employing a perturbation theory that treats the intramolecular couplings in a perturbative manner, the absorption and resonance Raman cross sections and excitation profiles of this molecule are calculated using the time‐correlation function formalism. The non‐Condon corrections are included in evaluation of cross sections. The multidimensional time‐domain integrals that arise in these calculations have been evaluated for the case in which S₀ (1¹A_g) S₂ (1¹B_u) electronic transition takes place between displaced and distorted harmonic potential energy surfaces. The calculated spectra are in good agreement with the experimental ones. Copyright © 2011 John Wiley & Sons, Ltd.     

Ab initio investigation of the vibronic structure of the C2H spectrum

A purely ab initio study of the vibronic structure of the X ²Σ⁺, A ²Π system of C₂H is presented. An approach is developed for a simultaneous treatment of three electronic states coupled via the bending and C-C stretching vibrations. On the basis of the results of the present calculations, it is possible to reliably interpret previous experimental findings.     

Coupled ab initio potential energy surfaces for the two lowest 2A′ electronic states of the C2H molecule

Realistic two-valued potential energy surfaces for the reaction C(³P) + CH(X²Π) → C₂ + H have been constructed from a set of high level ab initio data describing the first two ²A′ electronic states of the C₂H system. These states have linear equilibrium configurations, known as the X ²Σ⁺ and A²Π states, and are coupled by a conical intersection. They lead to the formation of C₂(X¹Σ⁺ _g) and C₂(a³Π_u) considering an adiabatic dissociation process. The ab initio calculations are of the multireference configuration interaction variety and were carried out using a polarized triple-zeta basis set. Using the ab initio adiabatic energies and the matrix elements of the dipole moment, a 2 × 2 diabatic representation of the electronic Hamiltonian was built. Each element of this Hamiltonian matrix was expressed within the double many-body expansion (DMBE) scheme which is based, in this case, on the extended Hartree-Fock approximate correlation energy model (EHFACE). The analytical adiabatic potential energy surfaces are then obtained as the eigenvalues of this matrix, and display correctly the Σ/Π conical intersection. Moreover, the non-adiabatic couplings given by our analytical model are compared with the ab initio ones, and good qualitative agreement is observed.     

Spectroscopic characterization of structural isomers of naphthalene: 1-Phenyl-1-butyn-3-ene

Laser induced fluorescence (LIF), single vibronic level dispersed fluorescence (DFL) spectra, and high resolution rotationally resolved scans of the S₀–S₁ transition of the C₁₀H₈ isomer 1-phenyl-1-butyn-3-ene have been recorded under jet-cooled conditions. The S₀–S₁ origin of PAV at 34 922 cm⁻¹ is very weak. A vibronic band located 464.0 above the origin, assigned as 30¹₀, dominates the LIF excitation spectrum, with intensity arising from vibronic coupling with the S₂ state. High resolution scans of the S₀–S₁ origin and 30¹₀ vibronic bands determine that the former is a 65:35 a:b hybrid band, while 30¹₀ is a pure a-type band, confirming the role for vibronic coupling and identifying the coupled state as the S₂ state. DFL spectra of all vibronic bands in the first 800 cm⁻¹ of the spectrum were recorded. A near-complete assignment of the vibronic structure in both S₀ and S₁ states is obtained. Herzberg–Teller vibronic coupling is carried by two vibrations, ν₂₈ and ν₃₀, involving in-plane deformations of the vinylacetylene side chain, leading to Duschinsky mixing evident in the intensities of transitions in excitation and DFL spectra. Extensive Duschinsky mixing is also present among the lowest five out-of-plane vibrational modes, involving motion of the side chain. Comparison with the results of DFT B3LYP and TDDFT calculations with a 6-311+G(d,p) basis set confirm and strengthen the assignments.     

Variational calculations on the hydrogen molecular ion

We present high-precision non-relativistic variational calculations of bound vibrational—rotational state energies for the H⁺ ₂ and D⁺ ₂ molecular ions in each of the lowest electronic states of Σ _g , Σ _u , and Π _u symmetry. The calculations are carried out including coupling between Σ and Π states but without using the Born—Oppenheimer or any adiabatic approximation. Convergence studies are presented which indicate that the resulting energies for low-lying levels are accurate to about 10^?13. Our procedure accounts naturally for the lambda-doubling of the Π _u state.     

Theoretical study of vibronic perturbations in magnesium carbide

ABSTRACT

Understanding molecular systems with complex multi-configurational bonding has been of interest to both experimentalists and theoreticians for many years. High level dynamically weighted MRCI calculations were used to generate accurate potential energy curves for the triplet ground state ³Σ^?, and triplet excited states up to (4 ³Σ^?, 4 ³Π and 1 ³Δ) and quintet (1 ⁵Σ^? and 1 ⁵Π) states up to 50,000 cm^?1 above the ground state minimum. The lowest four ³Π states of magnesium mono-carbide (MgC) are strongly coupled leading to lifetimes that are shortened by pre-dissociation for most of the vibronic states. Non-adiabatic derivative couplings between the ³Π states were used to determine diabatic potential energy curves. The state mixing role of spin–orbit coupling, which is much weaker than the non-adiabatic interactions, is discussed. A coupled vibronic Hamiltonian was solved to compute and assign strongly mixed vibronic states. The results are compared and contrasted with the valence iso-electronic beryllium carbide (BeC) system whose results were published earlier [B.J. Barker, I.O. Antonov, J.M. Merritt, V.E. Bondybey, M.C. Heaven, and R. Dawes, J. Chem. Phys. 137, 214313 (2012)]. Transitions, spectroscopic constants and band origins are expected to aid experimental detection of MgC in the future.     

The ion-molecule reaction O+ (4S) + N2(X1Σ+) → NO+ (X1Σ +, v′) + N(4S) and the predissociation of the A2Σ+ and B2Π states of N2O+

The potential energy surfaces (PESs) for several electronic states involved in the reaction O⁺ (⁴S) + N₂(X¹Σ⁺) → NO⁺ (X¹Σ ⁺, v′) + N(⁴S) and the role of the ionic N₂O⁺ intermediate have been investigated by ab initio calculations. The ⁴A″ PES, which correlates with the ground state educts, has a barrier of about 1 eV, and therefore at low collision energies the reaction cannot take place adiabatically on this surface. However, the spin-orbit coupling in the entrance channel allows the system to pass into the Renner-Teller system of the X² Π electronic ground state of the N₂O⁺ intermediate. The reaction then proceeds on these surfaces up to the region in the exit channel where a similar coupling allows it to reach the product quartet asymptote. At collision energies higher than about 1 eV, the reaction proceeds mainly on the adiabatic PES of the ⁴A″ state. The A²Σ⁺ state of N₂O⁺ predissociates via a vibronic coupling with the B²Π state, and in bent structures via a spin-orbit coupling with the ⁴A″ component of the ⁴II state. The electronic structure of the B²Π state is found to be of crucial importance for the understanding of the reactive processes in low lying electronic states of N₂O⁺.     

BF自由基X1∑+和a3∏态光谱常数和分子常数研究

采用内收缩多参考组态相互作用方法和相关一致基aug-cc-pV6Z, 对BF自由基X¹∑⁺和a³∏ 态的势能曲线进行了研究. 计算是在0.095---1.33 nm的核间距内进行的. 为获得更准确的结果, 计算中还考虑了Davidson修正、相对论修正及核价相关修正对势能曲线的影响. 相对论修正采用的方法是二阶DouglasKroll哈密顿近似, 修正计算是在cc-pV5Z基组水平上进行的. 核价相关修正使用的是cc-pCV5Z基组. 利用得到的势能曲线, 拟合出了各种修正下BF自由基X¹∑⁺和a³∏ 态的光谱常数D_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e和α_e、并与实验结果进行了比较. 结果表明: 考虑Davidson修正、相对论修正和核价相关修正后得到的光谱常数最接近实验结果. 利用修正后的势能曲线, 通过求解径向振转Schrödinger方程, 找到了转动量子数J = 0时这两个电子态的全部振动态, 并计算了每一电子态前20个振动态的振动能级、惯性转动常数和离心畸变常数, 其值与已有的实验结果较为一致. 本文得到的光谱常数和分子常数达到了很高的精度, 能为进一步的光谱实验提供可靠的参考.     

Isotope effects on vibronic coupling of pyrazine

The vibronic couplings of pyrazine-d₀ and pyrazine-d₄ between the lowest electronic excited states ¹B_3u(n, π^*) and ¹B_2u(π, π^*) through the out-of-plane CH bending vibration ν_10a(b_1g) have been studied from the Raman, electronic absorption and fluorescence spectra. The isotope effects on the scattering cross section of the ν_10a Raman line, the vibrational potential in the ¹B_3u(n, π^*) state and on the frequency change of the ν_10a vibration between the ground and the lowest electronic excited states are well explained by conventional Herzberg-Teller coupling mechanism. However, the intensities of the vibronic bands in the electronic absorption and fluorescence spectra are hardly explained with this coupling mechanism.     

The lowest electronic states of Ne2 +, Ar2 + and Kr2 +: comparison of theory and experiment

Non-relativistic configuration interaction (CI) ab initio calculations using large basis sets have been carried out to determine the potential curves of the first electronic states of Ne₂ ⁺, Ar₂ ⁺ and Kr₂ ⁺. The spin—orbit interaction was treated assuming that the spin—orbit coupling constant is independent of the internuclear separation (R). For Ar₂ ⁺, calculated dissociation energies and equilibrium separations are in good agreement with experimental results. The calculations for Ne₂ ⁺ suggest that the lowest vibrational level of the I(1/2u) ground state observed by threshold photoelectron spectroscopy by Hall et al. [1995, J. Phys. B: At. molec. opt. Phys., 28, 2435] and assigned to either ν = 0 or ν = 2 actually corresponds to ν = 4. The calculations also predict the I(1/2g) state of Ne₂ ⁺ and Ar₂ ⁺ to possess a double-well potential and that of Kr₂ ⁺ to be repulsive at short range and to only possess a single shallow well at large internuclear separation. The ab initio calculations provide an explanation for the observation made by Yoshii et al. [2002, J. chem. Phys., 117, 1517] that Kr₂ ⁺ and Xe₂ ⁺ dissociate after photoemission from the II(1/2u) state to the I(1/2g) state whereas Ar₂ ⁺ does not.     

Vibronic state and optical spectrum of the N i2+ impurity ion in CaO

The relative intensities of vibronic splitting components of the³A_2g→¹T_2g optical electronic dipole transition induced by odd local vibrations and spin-orbit interaction are calculated for an impurity center with O _h point-group symmetry. The polarization dependences and magnetic circular dichroism (MCD) are found for the vibronic components in an external magnetic field. In contrast with the previous works, the calculation is not confined to the nearest-term approximation. It is shown that measurements of the polarization dependences and MCD allow one to identify unambiguously the vibronic components. A comparison with the experiment is carried out for theNi ²⁺ ion in CaO. A. M. Gor'kii Ural State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 19–23, June, 1999.     

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.     

cis Acrolein: Mixing of the S0 and S1 electronic states by the (a″) skeletal torsional vibration

Large effects of vibronic coupling upon vibrational levels of the ground (¹A′) and first excited (¹A″) singlet electronic states of cis acrolein (2-propenal) are successfully modeled. Some implications for CH₂CHCHO spectroscopy and photophysics are discussed briefly.