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.     

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.     

Multiple groups in the symmetry classification of adiabatic electronic wavefunctions

It was originally shown by Longuet-Higgins and colleagues that when the electronic Schrödinger equation is solved as a function of the nuclear coordinates the adiabatic electronic wavefunction can undergo a change of sign after completing a closed circuit. This geometric phase occurs for a circuit around a conical intersection, and in particular around a conical intersection corresponding to a linear Jahn—Teller effect. The adiabatic wavefunctions are classified here under a group called the adiabatic multiple group, which is a generalization of the ‘vibronic double group’ of C _3v introduced by Hougen, and is distinct from the familiar electron-spin double group. Although the real electronic wavefunctions can be only double-valued, the groups can have higher multiplicity because of the possibility of different circuits. For a number of symmetric- and spherical-top point groups, the adiabatic multiple group is shown to be the direct product of the point group with a phase group. The adiabatic multiple group can be applied to individual adiabatic orbitals, and so to configurations built from these orbitals. This leads to the rule that the linear Jahn—Teller effect vanishes in the single-configuration approximation for configurations containing non-degenerate electrons plus an even number of e electrons. There does not appear to be any cancellation effect for electron configurations of cubic molecules containing f electrons.     

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.     

Adiabatic-diabatic transformations for molecular systems: a model study of two interacting conical intersections

A model is presented for studying the interaction between two conical intersections (e.g. a dimer of two bound molecules each characterized by a conical intersection). The model is an extension of a previous model for a single conical intersection formed by an electron housed in a vibrating molecule (Baer, M. and Englman, R., 1992, Molec. Phys., 75, 293). We distinguish between two situations: when the coupling is weak (for instance when it takes place in the asymptotic region) and when it is strong. The study is accomplished by calculating the adiabatic—diabatic transformation (ADT) matrix. Whereas the features of the ADT matrix for weak coupling seem reasonable (and to a certain extent expected), we find some unexpected features in the case of strong coupling. In particular, the two characteristic ADT angles of the uncoupled systems namely (?_1/2) and (?_2/2) are replaced by two new ADT angles, namely, (?₁ + ?₂)/2 and (?₁—?₂)/2. This implies that the corresponding nuclear wavefunctions, which originally were multi-valued, become single-valued in cases of strong interaction.     

Electronic interaction between valence and dipole-bound states of the cyanoacetylene anion

The electron attachment properties of cyanoacetylene HCCCN are investigated with particular emphasis on the coupling between dipole-bound and valence states. As an initial step both the dipole-bound and the valence state of HCCCN^- are studied separately using high level ab initio methods. Predictions for the geometry of the valence anion, the electron binding energy of the dipole-bound state, the energy of the temporary anion associated with vertical attachment into the valence state, the vertical detachment energy of the valence anion, and the adiabatic electron affinity of HCCCN are given. Our results indicate that the electron affinity found in the NIST web-book is not that of HCCCN but of some other C₃HN species. The two anionic states interact with each other, and we study their electronic coupling by computing the two electron binding energies along one- and two-dimensional cuts through the potential energy surfaces, and fitting a diabatic model potential to the ab initio data. In particular, the two-dimensional cuts allow us to examine the geometry dependence of the electronic coupling, and to ask the question whether the coupling elements inferred from one-dimensional cuts represent typical values. Moreover, the influence of the theoretical method on the computed coupling elements is investigated, and the possibility of employing the diabatic model potential as a mean to extrapolate bound state binding energies into the metastable domain is pointed out.     

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}     

Coriolis coupling in degenerate vibronic states of spherical top molecules

The first-order contribution of coriolis coupling to the rotational energies of degenerate vibronic states of spherical top molecules is considered for both even and odd numbers of electrons in octahedral or tetrahedral molecules. For E vibronic states the contribution vanishes, while for F ₁, F ₂, E _1/2 and E _5/2 states simple formulae are given. For G _3/2 states the energies are in general complicated, but simple formulae are given for two limiting cases.     

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.

     

Predissociation and photodissociation of IBr

The observed predominance of excited Br(² P _1/2) atoms in the nearultra-violet photodissociation products of IBr is shown to be quantitatively consistent with an intermediate coupling regime in the visible absorption region, which invalidates the traditional interpretation of the B′(O ⁺) state as a new Born-Oppenheimer state arising from a strongly avoided potential curve crossing. A general theory of predissociation at intermediate coupling, covering the positions, intensities and widths of the spectral lines, shows that both diabatic and adiabatic characteristics must be taken into account. The presence of a sharp level is predicted at any coincidence between an adiabatic and a diabatic term value with the same J value, and the spacing between neighbouring lines is shown to depend on an average between the diabatic and adiabatic rotational constants. The theory is successfully applied to the B(³Π _{o ⁺} ) and B′(O ⁺) states of IBr, and potential curves for the two states are reported. The analysis is consistent with the following curve crossing parameters r_x = 3·220 Å, E_x = 16 915 cm^-1, V ₁₂ = 170 cm^-1, and ΔF = 9178 cm^-1 Å^-1, and with the following spectroscopic constants for the B′(O ⁺) state of IBr⁷⁹:

     

Domino mechanisms in photoinduced phase transitions

Photoinduced structural phase transitions via excited electronic states are discussed theoretically using a one-dimensional model composed of localized electrons and lattices under the adiabatic or diabatic approximation. We show that the global structural change by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such phenomena. Spatiotemporal dynamics of nonequilibrium first-order phase transitions is also investigated in detail in terms of photoinduced nucleations and domino processes of the domain boundaries (domain walls), which are in striking contrast to the mean-field dynamics. In the adiabatic regime, after the spontaneous emission of a photon, an initial local structural change (i) remains locally, (ii) induces cooperatively a global structural change, or (iii) disappears and returns to the initial phase. Dynamical features of the case (ii) are characterized by the deterministic (semichaotic) domino process; domain walls between the two phases move determinis-tically at a constant velocity (with changing speed) without further spontaneous emissions in the case of strong (weak) dissipation. In the diabatic regime, similar three types of structural change exist. The domain-wall dynamics is described as the stochastic domino process, which is accompanied by the successive radiative transitions. A new theoretical treatment is also proposed to study crossover between the adiabatic and diabatic regimes.     

Non-adiabatic coupling and conical intersection(s) between potential energy surfaces for HeH2 +

By computing the non-adiabatic coupling terms and the adiabatic-to-diabatic transformation angle along closed contours in nuclear configuration space using the CASSCF method and the aug-cc-pVTZ basis set for the lowest three electronic states of HeH₂ ⁺, we explore the conical intersection between states in near collinear and noncollinear geometries, particularly in the C _2v geometry.     

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.     

用Sin-DVR方法求解在绝热表象下锥形交叉分子振动本征态

在波恩-奥本海默近似中,分子中原子核的运动通常采用绝热表象的基态势能面来描述,一般情况下这样是比较好的近似. 然而当势能面上存在锥形交叉时,即使体系的能量远远低于锥形交叉点,绝热基态势能面近似将不再有效. 锥形交叉的出现,使得绝热表象下描述核运动的哈密顿中出现了两个额外的附加项：对角波恩－奥本海默近似校正(DBOC)项和几何相位(GP)项. 尤其GP项,使得基态绝热势能面近似失效. 这两项在锥形交叉点处的数值是发散的,因此在绝热表象中来严格描述核运动,会使量子动力学的计算存在数值收敛的困难. 在量子分子动力学计算中,最常用的数值方法是分离变量表象方法(DVR). 本文通过在绝热表象和透热表象下求解涉及两个电子态且包含锥形交叉的二维的薛定谔方程来验证Sinc-DVR的数值收敛性. 计算结果显示,在绝热表象中采用通常格点密度分布的Sinc-DVR方法,即使在没有特别的处理DBOC和GP项时,也可以得到比较可靠的结果. 此时的数值不确定性并没有比引入任意的向量势来纠正GP效应的不确定性更差. 需要特别注意的是,纠正GP效应的任意向量势的精确形式,通常是不易得到其精确形式的.     

Diabatization of the reactive F + H<Subscript>2</Subscript> system employing rigorous Berry phases

In this article are presented the first ever derived single-valued diabatic potentials for the reactive H₂ +  F system based on a rigorous study of the conical intersection (ci) and Born-Oppenheimer non-adiabatic coupling terms (BO NACTs). This study revealed the existence of a Jahn-Teller (1, 2) ci located at a point on the collinear axis and a Renner-Teller (2, 3) ci along this axis. The diabatic potentials were calculated employing the rigorous adiabatic-to-diabatic transformation (ADT) angles (also known as mixing angles) which possess integer Berry phases along any closed contour at the region of interest in configuration space. The ADT angles were calculated employing BO NACTs and line integrals.     

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.     

Homogeneous interaction of ion-pair states of ClF

The energies, rotational constants, and isotope shifts of vibrational levels of the homogeneously perturbed ion-pair states E, f, β, and Gof the ClF molecule are calculated by the methods of diabatic and adiabatic potentials. The spectroscopic constants of initial diabatic potentials and the parameters of interaction for which the best agreement between theory and experiment is achieved are presented.     

Inter-state coupling and definitions of bright and dark states

Contrary to a standard definition of diabatic states (i.e., those without momentum-dependent coupling), based on the construction from adiabatic ones, we defined diabatic states as bright and dark states of a given experiment. Namely, they are defined as states providing maximum, respectively, zero value of electronic transition dipole moments projected to a given polarization vector. Second, the state from (or to) which the optical transition is performed is not from the space of investigated electronic excited state manifold, but it is chosen by the observer. It is shown, for this case, that the inter-state coupling is a general function of vibrational coordinates. The explicit dependence of the inter-state coupling on vibrational coordinates is particularly important for system with strong Stokes shift. The role of exact definitions of bright and dark states as well as the inter-state coupling is discussed with respect to the coherent structure of electronic population observed in optical spectroscopy.     

Vibronic Sidebands of Coherent Phonon States

Recently experiments have been reported about phonon sidebands in doped crystals, which may originate from coherent phonon states. The corresponding modes are either confined phonon modes in nanocrystals or localized phonon modes in bulk materials, both showing small damping due to phonon-phonon interaction. We present a theory of the lineshape of vibronic sideband spectra due to coherent phonon states using the conventional model of linear electron-phonon coupling and displaced equilibrium positions of the oscillators in the initial and final electronic states. Unlike in the conventional theory, the initial state of the oscillator is taken as a coherent phonon state and not as a thermalized one. Under these conditions we got an exact analytical solution for the lineshape of the vibronic sideband. The lineshape is determined by two parameters, the Huang-Rhys parameter S and the coherence parameter α of the phonon state. For α = 0 the lineshape converts into the standard Pekarian form for T = 0.     

Theoretical exploration of ultrafast spectroscopy of small clusters

We present the ultrafast multistate nuclear dynamics involving adiabatic and nonadiabatic excited states of non-stoichiometric halide deficient clusters (Na_nF_n-1) characterized by strong ionic bonding and one-excess electron for which the “frozen ionic bonds” approximation has been justified allowing to consider the optical response of the single excess electron in the effective field of the other electrons. We combined the Wigner-Moyal representation of the vibronic density matrix with the ab initio multi state molecular dynamics in the ground and excited electronic states including the nonadiabatic couplings calculated “on the fly” at low computational demand. This method allows the simulation of femtosecond pump-probe and pump-dump signals based on an analytical formulation, which utilizes temperature dependent ground state initial conditions, an ensemble of trajectories carried out on the electronic excited state as well as on the ground state after the passage through the conical intersection in the case of nonadiabatic dynamics and for probing either in the cationic state or in the ground state. The choice of the systems we presented has been made in order to determine the timescales of the fast geometric relaxation leaving the bonding frame intact as during the dynamics in the first excited state of Na₄F₃, and of the bond breaking processes leading to conical intersection between the first excited state and the ground state as in Na₃F₂. The former is the smallest finite system prototype for an surface F-center of bulk color centers. The latter allows to study the photo isomerization in full complexity taking into account all degrees of freedom. In the case of Na₄F₃ after the fast geometric relaxation in the excited state leading to deformed cuboidal structure without breaking of bonds, different types of internal vibrational redistribution (IVR) processes have been identified in pump-dump signals by tuning the dump laser. In contrast, from the analysis of the pump-probe signals of Na₃F₂ cluster, the timescales for the metallic and the ionic bond breaking, as well as for the passage through conical intersection have been determined. Finally the conditions under which these processes can be experimentally observed have been identified. Received 22 December 2000