Rydberg or Valence? The Long‐Standing Question in the UV Absorption Spectrum of 1,1′‐Bicyclohexylidene

The electronic excited states of the olefin 1,1′‐bicylohexylidene (BCH) are investigated using multiconfigurational complete active space self‐consistent‐field second order perturbation theory in its multi‐state version (MS‐CASPT2). Our calculations undoubtedly show that the bulk of the intensity of the two unusually intense bands of the UV absorption of BCH measured with maxima at 5.95 eV and 6.82 eV in the vapor phase are due to a single ππ* valence excitation. Sharp peaks reported in the vicinity of the low‐energy feature in the gas phase correspond to the beginning of the π3s_R Rydberg series. By locating the origin of the ππ* band at 5.63 eV, the intensity and broadening of the observed bands and their presence in solid phase is explained as the vibrational structure of the valence ππ* transition, which underlies the Rydberg manifold as a quasi‐continuum.     

Experimental and theoretical studies of the valence-shell dipole excitation spectrum of molecular fluorine

Electron energy loss measurements and concommitant RPAE calculations are reported of the valence-shell dipole excitation spectrum of molecular fluorine. The measured spectrum is dominated by a series of strong features in the 12–16 eV interval which are in accord with X¹Σ_g⁺→¹Σ_u⁺ bands assigned in a previously reported high-resolution optical study. These features are attributed on basis of the present RPAE calculations to configuration mixing between 1π_g→npπ_u Rydberg and 3σ_g→3σ_u intravalence excitations. A depleted X→V_σ charge-transfer excitation is correspondingly observed at ≈17 eV, in good accord with the calculated values. The appearance of the σ→σ* transition in F₂ below the 3σ_g^?1 threshold is in marked contrast to the situation in other light diatomic molecules, in which cases σ→σ* transitions appear as intravalence shape resonances in photoionization continua. Assignments are also provided of weak, irregularly spaced X¹Σ_g⁺→¹Π_u excitations the origins of which are attributed to configuration mixing between 1π_g→npσ_u and 1π_u→nsσ_g Rydberg series.     

Electronic band structure of solid CO2 as determined from the hv-dependence of photoelectron emission

Photoelectron energy distribution curves from solid CO₂ have been determined for excitation energies from hv = 14 up to 40 eV using synchrotron radiation. A 1:1 correspondence to the gas-phase photoelectron spectrum is observed for the occupied molecular orbitals. The vertical binding energies E_B^v (E_VAC = 0) and widths (fwhm) of the valence bands of solid CO₂ are determined to be 13.0 and 0.95 eV (1π_g); 16.7 and 1.1 eV (1π_u); 17.6 and 0.85 eV (3σ_u) and 18.8 and 0.8 eV (4σ_g) for the individual bands respectively. The partial photoemission cross sections differ importantly from those of the gas phase in exhibiting pronounced maxima at 5.2 eV (1π_g), 4.4–5.3 eV (1π_u + 3σ_u) and 4.2 eV (4σ_g) above the vacuum level, which is attributed to effects of high density of final (conduction-band) states. Further weaker maxima are observed at higher photon energies. Contrary to the case for the gas phase, the resonances are unperturbed in the solid by degenerate autoionizing molecular Rydberg states. The molecular origin of the resonances in the continuum is discussed and related to X-ray absorption spectra, electron-scattering data and to theoretical cross-section calculations. It is shown that the same set of resonances is observed in the different experiments. The resonances occur however at different energies due to different Coulomb interactions. The photoemission results presented provide also a key to the hitherto unexplained optical spectrum of solid CO₂ in the VUV range, making possible an assignment of the structures observed to Frenkel-type excitons (hv ≤ 15 eV) and interband transitions (hv ? 15 eV).     

All-valence-electron Cl calculations on the electronic spectrum of diborane

All-valence-electron Cl calculations have been carried out for diborane B₂H₆ and its positive ion employing a rather large double-zeta AO basis including polarization functions in order to study the electronic spectrum of this system. Transitions from four different valence MOs are found to lead to low-lying electronic transitions of both Rydberg and valence type in each case. Ad mixture of valence character in the otherwise Rydberg-like (nx, 3s), (ny, 3s) and (σ, 3pz) transitions calculated to lie between 11.0 and 11.6 eV is indicated as being primarily responsible for the highly intense shoulder found in this region of the B₂H₆ spectrum. The other strong feature with essentially continuous absorption peaking at 9.3 eV is suggested to result from superposition of several Rydberg-type transitions in the generally broad absorption pattern expected for the ¹(π,π^*) species at significantly higher vertical excitation energy. Quite good agreement is obtained between calculation and experiment for all of the six lowest IPs of diborane and also for the locations of the ¹(n, π^*) and ¹(σ, π^*) transitions previously assigned to the two weak features observed at 6.8 and 8.3 eV in this spectrum.     

Multiconfigurational perturbation theory (CASPT2) applied to the study of the low-lying singlet and triplet excited states of cyclopropene

The electronic spectrum of cyclopropene has been studied using multiconfigurational second-order perturbation theory (CASPT2) with extended ANO-type basis sets. The calculation comprises two valence states and the 3s, 3p, 3d members of the Rydberg series converging to the π and σ ionization limits. A total of twenty singlet and twenty triplet excited states have been analyzed. The results confirm the valence nature of the lowest energy singlet-singlet band and yield a conclusive assignment: the first dipole-allowed transition in cyclcopropene is due to absorption to a (σ → π*) state. The (π → π*) (V) state is interleaved among a number of Rydberg states in the most intense band of the system. The remaining spectral bands are due to Rydberg transitions of higher energy. The two lowest singlet-triplet transitions involve the same valence states. The results are in agreement with available experimental data and provide a number of new assignments of the experimental spectra.     

A MS-CASPT2 study of the low-lying electronic excited states of CH2BrCl

The low-lying singlet excited states of CH₂BrCl have been calculated using multiconfigurational CASSCF, second-order perturbation theory CASPT2 and its multistate extension MS-CASPT2. The CASSCF method shows spurious valence–Rydberg mixing and a wrong order of states. Inclusion of dynamical correlation by single root CASPT2 lowers dramatically the energy of the valences states but does not lead to a complete separation between valence and Rydberg states. This situation is improved by the MS-CASPT2 calculations, which gives two valence states for both A^′ and A″ symmetries below the lowest Rydberg state, corresponding to n(Br)→σ^*(C–Br) and n(Cl)→σ^*(C–Cl) transitions at 6.1 eV (203 nm) and 7.2 eV (173 nm), and being repulsive along C–Br and C–Cl coordinates.     

All-valence-electron CI treatment of the electronic spectrum of trans-butadiene

An all-valence-electron CI treatment is reported for the low-lying valence and Rydberg states of butadiene. All singly- and doubly-excited configurations relative to a series of the leading terms in a given CI expansion are taken into account, with resulting secular equation orders of as high as 150 000. The agreement between calculated and experimental transition energies is invariably better than 0.2 eV where comparison is possible, with all low-lying valence triplet and Rydberg singlet excited states being unambiguously assigned. The valence-shell excitation to the 2 ¹A_g species is concluded to correspond to the 7.06 eV band system, while the forbidden singlet—singlet transition reported by McDiarmid is assigned as x₂ → 3s. The possibility of an avoided crossing between Rydberg valence ¹B_u excited states having a determining influence on the appearance of the broad intense V₁—N absorption is also discussed.     

Ab initio calculations on the ground-state symmetry of the 1-imidazolyl and 1-pyrazolyl radical

Geometry optimization by ab initio methods with a STO→3G basis set and a subsequent calculation with the 4—31G basis set indicates that 1-imidazolyl and 1-pyrazolyl radical both have B₁(π)-symmetry. The former has an A₂(π)-state of 0.50 eV, and a σ-state at 0.54-eV. The latter has an A₂-state at 0.23 eV and a metastable σ-state at 0.45 eV. If formed in the σ-state, 1-pyrazolyl may live long enough to react as a σ-radical. A limited CI has little effect, except that the A₂-states are coming down relatively to the other states. For both radicals the σ-state has a double minimum potential, even though in pyrazolyl the nitrogen atoms possessing the electron-deficient lone pair orbitals are neighbours.     

The absorption spectrum of the anthracene molecule in the vacuum ultraviolet

The optical absorption of anthracene vapour for photon energies from 5 to 8.5 eV was found to differ in finer structure from the spectra reported earlier for parts of this range. Above the strong ¹B_2u long axis polarized πlπ^* transition at 5.24 eV three short axis polarized ¹B_1u ππ^* transitions are assigned on the basis of the oriented gas model in comparison to spectra from anthracene single crystals. A tentative new assignment for most of the additionally observed sharp Rydberg bands leading to the first ionization potential at 7.47 eV is given.     

Valence-shell momentum distributions and ionization energies of carbon disulfide

Valence-shell binding energy spectra and momentum distributions of CS₂ have been measured using non-coplanar symmetric binary (e,2e) spectroscopy. The present measurements are compared with previously published binding energy spectra calculated using the many body 2ph-TDA Green's function (GF) method and the symmetry-adapted cluster configuration-interaction (SAC CI) method. The measured and the calculated binding energy spectra both show extensive population splittings particularly above 20 eV, confirming a significant breakdown of independent particle ionization picture. A relatively strong-outer valence many-body state at 17.0 eV is shown to be satellite of the (2π₀)^?1 state, in accord with earlier conclusions of photoelectron studies. Momentum distributions measured at several carefully chosen binding energies are compared with the corresponding molecular orbital momentum distributions calculated using small and extended gaussian basis sets. The good qualitative agreement between momentum distributions measured in the inner-valence region wth theoretical 4σ_m and 5σ_g orbital momentum distributions confirms the qualitative predictions of satellite parentages by GF and SAC CI calculations. Momentum and position density contour maps of individual orbitals are used to interpret the shapes and atomic characters of the experimental momentum distributions. Momentum densities of the valence orbitals of CS₂ are compared with those of the respective valence isoelectronic species CO₂     

Application of electronic and ir spectroscopy to the determination of σp-, σ+p- and σoR-constants of some organosilicon and organogermanium substituents

The σ_p- and σ⁺_p- constants of some silicon- and germanium-containing substituents have been determined from electronic absorption spectroscopy data of charge-transfer (CT) complexes of phenylgermanes, benzylsilanes and benzylgermanes with tetracyanoethylene (TCNE). Resonance constants of corresponding substituents have been determined from the integrated intensity values of aromatic ring stretching modes (IR spectroscope data) of benzylsilanes and benzylgermanes. It is shown that the effect of dπpπ interaction in phenylgermanes remains practically unchanged in the course of the transition from the ground state to the CT state. The high negative values of σ⁺_p-constants for benzylorganosilicon and benzylorganogermanium substituents indicate the presence of considerable σ, π-conjugation in the CT state of benzylsilanes and benzylgermanes. This effect is also established for the ground state of the above mentioned compounds from their σ^o_R-values. The effect of σ,π-conjugation is displayed in greater degree in the ground state as well as in the CT state in benzylgermanes as compared with benzylsilanes.     

Non-empirical SCF and Cl Study of the ground and excited states of thioformaldehyde

Ab initio SCF and Cl calculations are reported for ground and various low-lying Rydberg and valence excited states of thioformaldehyde H₂CS. A double-zeta basis of near Hartree-Fock quality is employed in this work and the importance of polarization functions is also assessed. The calculations indicate uniformly larger CX bond lengths in this system than for H₂CO in the corresponding electronic states; they also lind potential minima for H₂CS non-planar nuclear conformations in the (n,π^*) and (π,π^*) excited states but in each case the calculated inversion barriers are seen to be smaller than those encountered in formaldehyde. The vertical transition energies to the various excited states studied are also found to be significantly smaller in H₂CS than in H₂CO but the order of electronic states is concluded to be virtually identical for the two systems. The lowest-lying excited states are the ^3,1(n,π^*) species calculated at 1.84 and 2.17 eV respectively; the first two allowed transitions are indicated to be the Rydberg species (n,s_R) and (n,px_R) at 5.83 and 6.62 eV. These are followed by the two allowed transitions σ → π^* and π → π^* at 7.51 and 7.92 eV respectively, both well below the first ionization limit in H₂CS. The much smaller splitting between the ^3,1(π,π^*) species in H₂CS than in H₂CO is attributed to the relatively diffuse charge distribution of the sulfur atom compared to that of oxygen.     

Theoretical study on the vertical electronic spectrum of carbonyl fluoride,F2CO

Ab initio self-consistent-field (SCF ) and configuration interaction (CI ) calculations on the ground and excited states of carbonyl fluoride (F₂CO) were carried out at its experimental ground-state equilibrium geometry. Vertical transition energies deduced from the CI results provide assignments for the electronic systems I–IV, experimentally observed by Workman and Duncan. The singlet excited state, ¹A₁ (π→π*), is found to be a mixed valence–Rydberg state and to he 1 to 1.2 eV above the suggested experimental value, irrespective of the choice of the basis used for the CI calculations.     

Ab initio MRD-CI study of the rydberg states of methylene

Potential curves have been calculated for the low-lying Rydberg states of CH₂ as well as for a number of its valence-shell species by employing the ab initio MRD-CI method. The first Rydberg transition is found to occur with a vertical energy of 6.38 eV (1b₁ → 3s), but the corresponding upper state is believed to be strongly predissociated since it correlates directly with the CH(²II) + H(²S_g) ground state fragments at lower energy. The assignment of the first observed Rydberg transition at 8.757 eV by Herzberg as 1b₁ → 3dπ is confirmed almost quantitatively in the calculations, while the corresponding minimum 1P value is computed to be 10.21 eV compared to the experimental result of 10.3 ± 0.1 eV. The dissociation energy of methylene in its ground state is calculated to be 4.47 eV, and this result also fits in well with experimental evidence, which determines a lower limit for this quantity of D₀ > 4.23 eV. Finally, it is found that none of the Rydberg states nor any of the higher-lying valence-shell species of methylene are of sufficiently low energy to play a significant role in the experimental determination of the ¹A₁-³B₁ splitting of this system.     

Vibrational and electronic excitation in p-benzoquinone by electron impact

Vibrational and electronic excitation by electron impact in p-benzoquinone was studied using a trochoidal electron spectrometer. Two distinct patterns of vibrational excitation were observed. First, low quanta of a few selected vibrations are specifically excited at incident electron energies corresponding to shape resonances. Some resonances excite mainly the CO stretch, others the CH stretch vibration, and this selectivity is used in the discussion of the assignment of the resonances. A second pattern is an unspecific excitation of a quasi-continuum where no structure due to individual vibrational levels can be discerned. This feature peaks at threshold, large amounts of vibrational energy can be deposited in the molecule, and the excitation also proceeds via shape resonances. Electronic excitation spectra in the valence and Rydberg regions are also presented and discussed. A band observed at 4.37 eV with low residual energies has been tentatively assigned to the second π — π* triplet state ³B_3g.     

A CI non-empirical pseudopotential calculation of the vertical valence excited states of the iodine molecule

The non-empirical atomic pseudopotential proposed by Durand and Barthelat has been used, together with the CIPSI algorithm for large scale CI, to calculate the vertical transition energies of the iodine molecule, in a valence extended (double-zeta + d) basis set. All the valence excited states were considered. The mixing of configurations is very important especially for the Σ⁺_g, Π_g and Π_u symmetries. The experimentally known transition energies are calculated within a 1 eV error, despite the lack of diffuse orbitals and spin-orbit interaction. Some qualitative Mulliken's estimates are discussed. A new ³Σ⁺_g state from the 10 σ_u → 11 σ_u single excitation is predicted in the 9 eV region.     

Cationic Rydberg states observed in resonantly enhanced electron spectra of CS2

The inner valence electron spectrum of the CS₂ molecule has been investigated in the binding energy range between 18.6 and 26.3 eV using synchrotron radiation for ionisation. Photon energies in the range from 67 to about 167 eV have been used, with particular focus on 166.70, 166.89 and 167.09 eV for which S2p electrons are resonantly transferred into Rydberg orbitals close to the ionisation threshold. From there, autoionisation takes the molecule into various cationic states characterized by two valence holes and a Rydberg spectator electron. Many new bands are observed which contain vibrational progressions with spacings around 120 meV in most cases. These are assigned as excitations of the totally symmetric stretching ν₁ mode in the cationic state. The new bands reflect states in the cation that are close to the electronic states of the dication and assignments are made by comparison to double ionisation electron spectra.     

Theoretical study of the electronic spectra ofcis-1,3,5-hexatriene andcis-1,3-butadiene

Summary The electronic spectra forcis-1,3-butadiene andcis-1,3,5-hexatriene have been studied using multiconfiguration second-order perturbation theory (CASPT2) and extended ANO basis sets. The calculations comprise all singlet valence excited states below 8.0 eV, the first 3s, 3p, 3d Rydberg states, and the second 3s state. The four lowest triplet states were also studied. The resulting excitation energies forcis-hexatriene have been used in an assignment of the experimental spectrum, leading to a maximum deviation of 0.13 eV for the vertical transition energies. The calculations place the 1¹ B ₂ state 0.04 eV below the 2¹ A ₁ state. 16 excited states were studied incis-butadiene, using a CASPT2 optimized ground state geometry. The 1¹ B ₂ state was located at 5.58 eV, 0.46 eV below the 2¹ A ₁ state and 0.09 eV above the experimental value. No experimental assignments are available for the 15 other transitions. On leave from: Departmento de Quimica Física, Universidad de Valencia, Dr. Moliner 50, Burjassot, E-46100-Valencia, Spain     

The valence and Rydberg excited states of CH2: A theoretical exploration

Using the completed active space second‐order perturbation (CASPT2) method, valence and Rydberg excited states of CH₂ molecule are probed with the large atomic natural orbital (ANO‐L) basis set. Five states are optimized and the geometric parameters are in good agreement with the available data in literatures, furthermore, the state of 2¹B₁ is obtained for the first time. Valence and Rydberg excited states of CH₂ are also calculated for the vertical transitions with the ANO‐L+ basis set that is constructed by adding a set of 1s1p1d Rydberg orbitals into the ANO‐L basis set. Two Rydberg states of the p?³A₂ and r?³B₁ at 9.88 and 10.50 eV are obtained for the first time, and the 3a₁ → 3d_yz nature of the state p?³A₂ and the 3a₁ → d_x2?y2 nature of the state r?³B₁ are confirmed. © 2012 Wiley Periodicals, Inc.     

Chlorine K shell photoabsorption spectra of gas phase HCl and Cl2 molecules

High resolution photoabsorption spectra of HCl and Cl₂ have been measured near the chlorineK edge in the 2810–2850 eV photon energy range. Below the ClK edge, the strongest resonance is interpreted as a simple core excitation into the unoccupied σ* valence orbital for both molecules, leading to a markedly repulsive state. Higher resonances due to low lying Rydberg states, are observed in both systems, but with a larger oscillator strength for HCl as compared to Cl₂. In Cl₂, the σ* orbital is deep enough to avoid any mixing with Rydberg orbitals. In HCl, we observe the dipole forbidden Cl 1s → 4s transition which denotes a strong 4s–4p hybridization. Above the ClK edge, the multiplet features seen for HCl are analysed in terms of double-core-valence excited vacancy states. In Cl₂, their counterpart are found very close to the ionization threshold because of the deep σ* orbital and possibly because the excited core and valence electrons originates either from the same atomic site or from different ones.