4f-5d Transitions of Tb3+ in Cs2NaYF6: the effect of distortion of the excited-state configuration

The low-temperature absorption and excitation spectra of interconfigurational 4f-5d transitions of Tb(3+) in a cubic fluoride host demonstrate the appearance of a first-order linear Jahn-Teller effect for the high-spin excited states of the excited electronic configuration 4f(7)5d involving 5d t(2g) orbitals. The τ(2g) mode is observed to be responsible for the splitting of the otherwise degenerate 5d t(2g) orbitals.     

Cluster expansion of the wavefunction. Ionization potentilals of benzene

The vertical and adiabatic ionization potentiais of benzene are studied by the cluster expansion of the wavefunction theory. The calculation confirms the assignment of the photoelectron spectrum experimentally proposed by Jonsson and Lindholm. The nature of the Jahn-Teller effect in states arising from ionization of doubly degenerate π and σ orbitals is also discussed.     

B(OCH3)3电子结构的Hel紫外光电子能谱研究

人们知道，Hel紫外光电子能借（PES）提供研究分子轨道能量、能级次序、成键类型以及由光电子峰强度所反映的电离轨道特性等信息是其他手段没有的，因而PES技术已广泛地用于众多化合物分子电子结构的研究中．有机础化合物由于它们高的反应活性作为合成试剂而信受人们重视［‘－     

Excited states of porphyrin macrocycles

S1 --> S(n) spectra of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication have been measured in the energy range 2-3 eV above S1 at room temperature in solution by means of transient absorption spectroscopy exciting with femtosecond pulses. Highly excited pi pi* states not active in the conventional S0 --> S(n) spectrum have been observed. The experimental data are discussed on the basis of the time dependent density functional theory taking advantage of large scale calculations of configuration interaction between singly excited configurations (DF/SCI). The DF/SCI calculation on porphyrin has allowed to assign g states active in the S1 --> S(n) spectrum. Applying the same calculation method to tetraoxaporphyrin dication the S0 --> S(n) spectrum is reproduced relatively to the Q and B (Soret) bands as well as to the weaker E(u) bands at higher energy. According to our calculation the S1 --> S(n) transient spectrum is related to states of g symmetry mainly arising from excitations between doubly degenerate pi and pi* orbitals such as 2e(g) --> 4e(g). In the case of diprotonated porphyrin it is shown that the complex of the macrocycle with two trifluoroacetate anions plays a significant role for absorption. Charge transfer excitations from the anions to the macrocycle contribute to absorption above the Soret band, justifying the intensity enhancement of the S0 --> S(n) spectrum with respect to the other two macrocyclic systems.     

Spatial imaging of individual vibronic states in the interior of single molecules

Selective excitations of specific vibronic modes in position space are realized in single naphthalocyanine molecules adsorbed on an ultrathin alumina film by a scanning tunneling microscope at low temperature. Distinct spatial distributions are imaged for the different vibronic modes, which are in accordance with spectra recorded over different points of the molecule and its orbital structure. These distinct vibronic images, together with the differential conductance images and calculated molecular orbitals, lead to vibrational excitations that are associated with the doubly degenerate lowest unoccupied molecular orbitals (LUMO)--LUMO-α and LUMO-β. These results reveal the presence of different molecular conformations on the surface and the nature of the electron-vibrational coupling.     

Jahn-Teller effect for short-lived states: study of the complex potential energy surfaces

The Jahn-Teller effect for bound electronic states has been investigated for many decades. In contrast, nothing is known regarding its occurrence for short-lived electronic states. Here we investigate the linear and the quadratic E multiply x e Jahn-Teller effect for degenerate resonance states with special regard to the complex potential energy surfaces. We find many new phenomena for both the real and imaginary parts of the potential energy surfaces including additional minima and intersections. Possible simplifications of the equations describing the adiabatic potential energy surfaces are discussed. We also briefly investigate other Jahn-Teller effects in linear approximation. The theoretical concepts are exemplified by calculating ab initio data for the degenerate Pi(*)-type resonance states of the tris(boramethyl)amin anion along two different doubly degenerate vibrational modes.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

Theoretical Characterisation of Phosphinyl Radicals and Their Magnetic Properties: g Matrix

The g matrices (g tensors) of various phosphinyl radicals (R₂P^.) were calculated using the DFT and multireference configuration interaction (MRCI) methods. The g matrices were distinctly dependent on the molecular structure of the radical. To thoroughly examine this dependence, the contributions from individual atoms and excited states were calculated. The former revealed the gain from the phosphorus atom to be preeminent unless P?O or P?S bonds are present in the radical molecule. The contributions owing to excited states arising from electronic transitions between doubly occupied molecular orbitals and the SOMO were clearly positive, as in the case of semiquinone and niroxide radicals. The transitions from the phosphorus lone pair were of paramount importance. Surprisingly, unlike for semiquinones and nitroxides, a significant negative contribution was observed from excitations from the SOMO to unoccupied molecular orbitals. For radicals with P?O bonds, this contribution to the g₂ component was dominant.     

Orbital disproportionation and spin crossover as a pseudo Jahn-Teller effect

It is shown that in systems with electronic half-closed-shell configurations of degenerate orbitals, e(2) and t(3) (which have totally symmetric charge distribution), ground state distortions from high-symmetry geometries may occur due to a strong pseudo Jahn-Teller effect (PJTE) in the excited states, resulting also in a novel phenomenon of PJT-induced spin crossover. There is no JTE neither in the ground state term nor in the excited terms (including degenerate terms) of these configurations but a strong PJT mixing between two excited states [((1)E+(1)A) [cross-filled circle] e and ((2)T(1)+(2)T(2)) [cross-filled circle] e in the e(2) and t(3) cases, respectively] pushes down the lower term to cross the ground state of the undistorted system and to form the global minimum with a distorted geometry. The analysis of the electronic structure of this distorted configuration shows that it is accompanied by orbital disproportionation: instead of proportional population of all degenerate orbitals by one electron each (as in the ground state of the undistorted system that follows Hund's rule), two electrons with opposite spins occupy one orbital, resulting in transformations of the type (e(theta);e(epsilon))-->(e(theta)e(theta)) for e(2) and (t(x);t(y);t(z))-->(t(x);t(x);t(z)) for t(3) systems. Since the two geometry configurations, undistorted and distorted, appertain to different electronic terms that have different spin states, the formation of the global minimum with the distorted configuration is accompanied by a spin crossover. Distinguished from the known spin-crossover phenomenon in some transition metal compounds, the two states with different spin in the PJT-induced spin crossover have also different nuclear configurations, undistorted and distorted, that coexist with a relatively small energy difference. The change of configuration reduces significantly the rate of relaxation between the two states; the relaxation is further reduced by the lower spin-orbital coupling in the light-atom systems as compared with transition metal compounds. This means that there may be systems for which the switch between the two states (in both directions) under perturbations may be observed as a single-molecule phenomenon. Systems with half-closed-shell electronic configurations e(2) and t(3) are available in a variety of molecules from different classes, organic and inorganic; the theory is illustrated here by ab initio calculations for a series of molecular systems, including Si(3), Si(3)C, CuF(3), Na(3), Si(4), Na(4), Na(4) (-), and C(60) (3-), which are in agreement with the experimental data available.     

Electronic structure, spectra, and magnetic circular dichroism of cyclohexa-, cyclohepta-, and cyclooctapyrrole

Three recently obtained expanded porphyrins represent nice examples of compounds for which the electronic and spectral properties can be predicted from symmetry considerations alone. Perimeter-model-based theoretical analysis of the electronic structure of doubly protonated cyclo[6], cyclo[7], and cyclo[8]pyrrole leads to the anticipation of qualitatively the same electronic absorption and magnetic circular dichroism patterns for all three compounds. These predictions are fully confirmed by experiments, as well as DFT and INDO/S calculations. Due to a characteristic pattern of frontier molecular orbitals, a degenerate HOMO and a strongly split LUMO pair, the three cyclopyrroles show comparable absorption intensity in the Q and Soret regions. Magnetic circular dichroism spectra reveal both A and B Faraday terms, of which the signs and magnitudes are in remarkably good agreement with theoretical expectations. The values of the magnetic moments of the two lowest degenerate excited states have also been obtained.     

Jahn-Teller effect in Rydberg series: a multi-state vibronic coupling problem

Two simple limiting cases of Jahn-Teller (JT) coupling in Rydberg states of polyatomic molecules are considered, namely(i) JT coupling in Rydberg orbitals as well as in the ionization continuum (nondegenerate ion core, degenerate Rydberg series) and(ii) JT coupling in the ion core (degenerate ion core, nondegenerate Rydberg series). For both models simple and efficient algorithms for the computation of spectra (dynamical JT effect) are developed. The orbital JT effect is shown to represent a novel type of multi-state vibronic coupling, giving rise to interesting spectroscopic phenomena, among them resonant inter-Rydberg perturbations and JT induced autoionization. Particular attention is paid to the demonstration of the characteristic spectroscopic signatures of the two types of JT coupling in Rydberg states.     

Electron-phonon interactions in photoinduced excited electronic states in fluoroacenes

The electron-phonon coupling constants [l(B1u(HOMO-->LUMO))] in the photoinduced excited electronic states in fluoroacenes are estimated and compared with those in the monoanions (l(LUMO)) and cations (l(HOMO)). The l(B1u(HOMO-->LUMO)) values are much larger than the l(LUMO) and l(HOMO) values in fluoroacenes. Furthermore, the Coulomb pseudopotential mu* values for the excited electronic states are estimated to be smaller than those for the monoanions and cations. The complete phase patterns difference between the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) is the main reason why the electron-phonon coupling constants and the mu* values are larger and smaller, respectively, in the photoinduced excited electronic states than in the monoanions and cations. The possible electron pairing and Bose-Einstein condensation in the excited electronic states of fluoroacenes are discussed. Because of larger electron-phonon coupling constants and smaller mu* values in the excited electronic states than in the charged states, the conditions under which the electron-electron interactions become attractive can be more easily realized, in principle, in the excited electronic states than in the charged states in fluoroacenes. The l(B1u(HOMO-->LUMO)) values hardly change by H-F substitution, even though the l(LUMO) and l(HOMO) values significantly increase by H-F substitution in acenes. Antibonding interactions between carbon and fluorine atoms in the HOMO and LUMO are the main reason why the l(B1u(HOMO-->LUMO)) values hardly change by H-F substitution in acenes.     

Ground- and excited-state electronic structure of an iron-containing molecular spin photoswitch

The electronic structure of the cation of [Fe(ptz)(6)](BF(4))(2), a prototype of a class of complexes that display light-induced excited-state spin trapping (LIESST), has been investigated by time-independent and time-dependent density-functional theories. The density of states of the singlet ground state reveals that the highest occupied orbitals are metal centered and give rise to a low spin configuration Fe(2+)(3d(xy) ( upward arrow downward arrow)3d(xz) ( upward arrow downward arrow)3d(yz) ( upward arrow downward arrow)) in agreement with experiment. Upon excitation with light in the 2.3-3.3 eV range, metal-centered spin-allowed but parity-forbidden ligand field (LF) antibonding states are populated which, in conjunction with electron-phonon coupling, explain the experimental absorption intensities. The computed excitation energies are in excellent agreement with experiment. Contrary to simpler models we show that the LF absorption bands, which are important for LIESST, do not originate in transitions from the ground to a single excited state but from transitions to manifolds of nearly degenerate excited singlets. Consistent with crystallography, population of the LF states promotes a drastic dilation of the ligand cage surrounding the iron.     

Configuration interaction study of the ground and excited states of TiO2 ring structures

Theoretical studies of the ground and lowest excited singlet and triplet states of a series of titanium dioxide ring structures, (TiO(2))(2n), n = 3-9, are reported. Calculations are based on many-electron configuration theory, where energies of states and geometrical structures are determined by variational energy minimization. The lowest energy excited states correspond to excitations from oxygen 2p levels to unoccupied 3d orbitals on titanium. For each ring system, two types of excited state solutions are investigated: those that maintain periodic symmetry for individual orbitals and solutions that allow the symmetry to be broken. The latter solutions which correspond to localized states or excitons are found to be significantly lower in energy than the symmetric solutions. We compare the vertical excitation energy of these well-defined geometrical structures with size effects reported in experimental studies.     

Hydrogen dissociation on small aluminum clusters

Transition states and reaction paths for a hydrogen molecule dissociating on small aluminum clusters have been calculated using density functional theory. The two lowest spin states have been taken into account for all the Al(n) clusters considered, with n=2-6. The aluminum dimer, which shows a (3)Π(u) electronic ground state, has also been studied at the coupled cluster and configuration interaction level for comparison and to check the accuracy of single determinant calculations in this special case, where two degenerate configurations should be taken into account. The calculated reaction barriers give an explanation of the experimentally observed reactivity of hydrogen on Al clusters of different size [Cox et al., J. Chem. Phys. 84, 4651 (1986)] and reproduce the high observed reactivity of the Al(6) cluster. The electronic structure of the Al(n)-H(2) systems was also systematically investigated in order to determine the role played by interactions of specific molecular orbitals for different nuclear arrangements. Singlet Al(n) clusters (with n even) exhibit the lowest barriers to H(2) dissociation because their highest doubly occupied molecular orbitals allow for a more favorable interaction with the antibonding σ(u) molecular orbital of H(2).     

Efficient formulation and computer implementation of the active-space electron-attached and ionized equation-of-motion coupled-cluster methods

The efficient, general-purpose implementations of the active-space electron-attached (EA) and ionized (IP) equation-of-motion coupled-cluster (EOMCC) methods including up to 3p-2h and 3h-2p excitations, called EA-EOMCCSDt and IP-EOMCCSDt, respectively, are discussed. The details of the algorithm that enables one to achieve a high degree of code vectorization for the active-space methods and the factorized forms of the EA- and IP-EOMCCSDt equations that maximize the benefits of using active orbitals in the process of selecting the dominant 3p-2h and 3h-2p excitations are presented. The results of benchmark calculations for the low-lying doublet and quartet states of the CH and SH radicals reveal that the active-space EA-EOMCCSDt and IP-EOMCCSDt methods are capable of producing results for the electronic excitations in open-shell systems that match the high accuracy of EA- and IP-EOMCC calculations with a full treatment of 3p-2h and 3h-2p excitations, even when the excited states of interest display a manifestly multideterminantal nature, with the costs that can be on the same order of those characterizing the basic EOMCC singles and doubles approach.     

Complex dynamics at conical intersections: vibronic spectra and ultrafast decay of electronically excited trifluoroacetonitrile radical cation

An ab initio quantum dynamical study is performed here to examine the complex nuclear motion underlying the first two photoelectron bands of trifluoroacetonitrile. The highly overlapping structures of the latter are found to originate from transitions to the five lowest electronic states (viz., X(2)E, A(2)A1, B(2)A2, C(2)A1, and D(2)E) of the trifluoroacetonitrile radical cation. The Jahn-Teller (JT) instability of the doubly degenerate X and, D and their pseudo-Jahn-Teller (PJT) interactions with the nondegenerate A, B, and C electronic states along the degenerate vibrational modes lead to multiple multidimensional conical intersections and complex nuclear trajectories through them. It is found that the JT splitting is very weak in the X and relatively stronger in the D state. However, the PJT couplings play the pivotal role in the detailed shape of the vibronic bands of the radical cation. Ultrafast nonradiative decay of electronically excited radical cation has been examined. The findings of this paper are compared with the experimental data and are also discussed in relation to those observed for the methyl cyanide radical cation.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.