The electronic states of buta-1,3-diene studied by ab initio configuration interaction and DFT methods,and electron energy loss spectroscopy

The electronic vertical excitation energies for singlet and triplet valence, and Rydberg states of trans-buta-1,3-diene have been computed using ab initio multi-reference multi-root CI procedures with a [4s3p3d3f] set of Rydberg functions. Close numerical agreement between theory and experiment was found for a number of low-lying electronic states.     

Multireference configuration interaction studies on higher valence and Rydberg states of OClO, ionization potentials, and electron detachment energies

MRCI results are reported for the vertical excitation energies (VEE) and oscillator strengths f of doublet states of OClO up to 11 eV, including 3b(1) → 4s, 4p, 3d, 5s, 5p, 4d, and most 1a(2), 8a(1), 5b(2) → 4s and 4p Rydberg states. The lowest Rydberg states 3b(1) → 4s and 3b(1) → 4p(x) have mixed valence-Rydberg character. The observed spectral bands were reassigned to include valence states which have generally higher oscillator strengths. The well-known valence state 1(2)A(2) has a VEE of 3.63 eV, and a relatively high f of 0.042. Overall, the calculated oscillator strengths are in good agreement with measured values. The lowest quartet state, 1(4)B(2), lies at 6.95 eV. Quartet Rydberg states start with 1a(2) → 4s at 9.28 eV. According to calculated vertical ionization potentials (VIP) of OClO, the second VIP at 12.59 eV is reassigned from 1(3)B(1) to 1(3)B(2) (ionization from 1a(2), rather than 8a(1)), and the third VIP at 12.63 eV from 1(1)B(1) to 1(3)B(1) (ionization from 8a(1)). Vertical electron detachment energies of OClO(-) have been calculated up to 8.9 eV. There is good agreement with experimental values.     

Femtosecond photoelectron imaging of transient electronic states and Rydberg atom emission from electronically excited he droplets

Ultrafast relaxation of electronically excited pure He droplets is investigated by femtosecond time-resolved photoelectron imaging. Droplets are excited by extreme ultraviolet (EUV) pulses with photon energies below 24 eV. Excited states and relaxation products are probed by ionization with an infrared (IR) pulse with 1.6 eV photon energy. An initially excited droplet state decays on a time scale of 220 fs, leading predominantly to the emission of unaligned 1s3d Rydberg atoms. In a second relaxation channel, electronically aligned 1s4p Rydberg atoms are emitted from the droplet within less than 120 fs. The experimental results are described within a model that approximates electronically excited droplet states by localized, atomic Rydberg states perturbed by the local droplet environment in which the atom is embedded. The model suggests that, below 24 eV, EUV excitation preferentially leads to states that are localized in the surface region of the droplet. Electronically aligned 1s4p Rydberg atoms are expected to originate from excitations in the outermost surface regions, while nonaligned 1s3d Rydberg atoms emerge from a deeper surface region with higher local densities. The model is used to simulate the He droplet EUV absorption spectrum in good agreement with previously reported fluorescence excitation measurements.     

Electronic spectroscopy and ultrafast energy relaxation pathways in the lowest Rydberg States of trimethylamine

Resonance-enhanced multiphoton ionization photoelectron spectroscopy has been applied to study the electronic spectroscopy and relaxation pathways among the 3p and 3s Rydberg states of trimethylamine. The experiments used femtosecond and picosecond duration laser pulses at wavelengths of 416, 266, and 208 nm and employed two-photon and three-photon ionization schemes. The binding energy of the 3s Rydberg state was found to be 3.087 +/- 0.005 eV. The degenerate 3p x, y states have binding energies of 2.251 +/- 0.005 eV, and 3p z is at 2.204 +/- 0.005 eV. Using picosecond and femtosecond time-resolved experiments we spectrally and temporally resolved an intricate sequence of energy relaxation pathways leading from the 3p states to the 3s state. With excitation at 5.96 eV, trimethylamine is found to decay from the 3p z state to 3p x, y in 539 fs. The decay to 3s from all the 3p states takes place with a 2.9 ps time constant. On these time scales, trimethylamine does not fragment at the given internal energies, which range from 0.42 to 1.54 eV depending on the excitation wavelength and electronic state.     

Full configuration interaction calculation of the low lying valence and Rydberg states of BeH

The all-electron full configuration interaction (FCI) vertical excitation energies for some low lying valence and Rydberg excited states of BeH are presented in this article. A basis set of valence atomic natural orbitals has been augmented with a series of Rydberg orbitals that have been generated as centered onto the Be atom. The resulting basis set can be described as 4s2p1d/2s1p (Be/H) + 4s4p3d. It allows to calculate Rydberg states up to n= {3,4,5} of the s, p, and d series of Rydberg states. The FCI vertical ionization potential for the same basis set and geometry amounts to 8.298 eV. Other properties such as FCI electric dipole and quadrupole moments and FCI transition dipole and quadrupole moments have also been calculated. The results provide a set of benchmark values for energies, wave functions, properties, and transition properties for the five electron BeH molecule. Most of the states have large multiconfigurational character in spite of their essentially single excited nature and a number of them present an important Rydberg-valence mixing that is achieved through the mixed nature of the particle MO of the single excitations.     

Singly and doubly excited states of butadiene, acrolein, and glyoxal: Geometries and electronic spectra

Excited-state geometries and electronic spectra of butadiene, acrolein, and glyoxal have been investigated by the symmetry adapted cluster configuration interaction (SAC-CI) method in their s-trans conformation. Valence and Rydberg states below the ionization threshold have been precisely calculated with sufficiently flexible basis sets. Vertical and adiabatic excitation energies were well reproduced and the detailed assignments were given taking account of the second moments. The deviations of the vertical excitation energies from the experiment were less than 0.3 eV for all cases. The SAC-CI geometry optimization has been applied to some valence and Rydberg excited states of these molecules in the planar structure. The optimized ground- and excited-state geometries agree well with the available experimental values; deviations lie within 0.03 A and 0.7 degrees for the bond lengths and angles, respectively. The force acting on the nuclei caused by the excitations has been discussed in detail by calculating the SAC-CI electron density difference between the ground and excited states; the geometry relaxation was well interpreted with the electrostatic force theory. In Rydberg excitations, geometry changes were also noticed. Doubly excited states (so-called 2 (1)A(g) states) were investigated by the SAC-CI general-R method considering up to quadruple excitations. The characteristic geometrical changes and large energetic relaxations were predicted for these states.     

Resolved: electronic states underneath broad absorptions

The far UV absorption spectra of many polyatomic molecules show featureless, broad bands, even though the lifetimes of the underlying electronic states can be long enough to render the states observable. Using photoionization from Rydberg states we measure electron binding energies, thereby referencing the electronic spectra to the adiabatic ionization energy. In trimethylamine, we find that the 3s, the 3p(x,y), and the 3p(z) Rydberg states have binding energies of 3.087, 2.251, and 2.204 eV, respectively. Vibrational motions excited while preparing the Rydberg states do not interfere with the spectra.     

Energy flow and fragmentation dynamics of n,n-dimethylisopropylamine

The energy flow and fragmentation dynamics of N,N-dimethylisopropylamine (DMIPA) upon excitation to the 3p Rydberg states has been investigated with use of time-resolved photoelectron and mass spectrometry. The 3p states are short-lived, with a lifetime of 701 +/- 45 fs. From the time dependence of the photoelectron spectra, we infer that the primary reaction channel leads to the 3s level, which itself decays to the ground state with a decay time of 87.9 +/- 10.2 ps. The mass spectrum reveals fragmentation with cleavage at the alpha C-C bond, indicating that the energy deposited in vibrations during the internal conversion from 3p to 3s exceeds the bond energy. A thorough examination of the binding energies and temporal dynamics of the Rydberg states, as well as a comparison to the related fragmentation of N,N-dimethyl-2-butanamine (DM2BA), suggests that the fragments are formed on the ion surfaces, i.e., after ionization and on a time scale much slower than the fluorescence decay from 3s to the ground state.     

The electronic states of 1,2,4-triazoles: a study of 1H- and 1-methyl-1,2,4-triazole by vacuum ultraviolet photoabsorption and ultraviolet photoelectron spectroscopy and a comparison with ab initio configuration interaction computations

The first vacuum ultraviolet absorption spectrum of a 1,2,4-triazole has been obtained and analyzed in detail, with assistance from both an enhanced UV photoelectron spectroscopic study and ab initio multi-reference multi-root configuration interaction procedures. For both 1H- and 1-methyl-1,2,4-triazoles, the first ionization energy bands show complex vibrational structure on the low-energy edges of otherwise unstructured bands. Detailed analysis of these bands confirms the presence of three ionized states. The 6-7 eV VUV spectral region shows an unusual absorption plateau, which is interpreted in terms of the near degeneracy of the first two ionization energies, leading to a pseudo Jahn-Teller effect. The "fingerprint" of the ionization spectrum yields band origins for several Rydberg states. The configuration interaction study shows that although the equilibrium structure for the first cation is effectively planar, the second cation shows significant twisting of the ring system. Some calculated singlet electronic states also show skeletal twisting in which the ring C-H is substantially out of plane.     

CASSCF and multireference CI with singles and doubles study of low-lying valence and Rydberg states of 2H-tetrazole

Complete active space self-consistent field (CASSCF) and multireference CI with singles and doubles (MR-CISD) calculations [including extensivity corrections, at MR-CISD+Q and multireference averaged quadratic coupled cluster (MR-AQCC) levels] have been performed to characterize the low-lying valence and the Rydberg states of 2H-tetrazole. The highest level results (MR-AQCC/d'-aug'-cc-pVDZ) indicate the following ordering of the valence singlet excited states: S(1) (n-pi*), 6.06 eV; S(2) (n-pi*), 6.55 eV; S(3) (pi-pi*), 6.55 eV. The MR-CISD+Q/d'-aug'-cc-pVDZ results indicate the same ordering, but at slight higher energies: 6.16, 6.68, and 6.69 eV, respectively. According to our MR-CISD+Q/d'-aug'-cc-pVDZ results, the next two states are Rydberg states, at 7.69 eV (pi-3s) and 7.89 eV (n-3s). The calculated energies of these two states, as well as their proximity, are consistent with the conclusion reached by Palmer and Beveridge (Chem Phys 1987, 111, 249) that the first band of the photoelectron spectrum of 2H-tetrazole is likely to be associated to the first two ionizations processes (of pi and N lone pair electrons), at energies close to 11.3 eV.     

Femtosecond multiphoton ionization of pyrrole

The photoionization dynamics of pyrrole are investigated by using a photoelectron imaging method and a tunable femtosecond laser. Two-photon nonresonant ionization experiments in the wavelength range from 261 to 298 nm indicate that the cation and neutral ground states have similar structures. The main vibrational excitation in the cation ground state is the v(8) mode. Two-photon absorption at 406 nm projects neutral pyrrole into a mixed state comprising the 1B(2) valence and 3p Rydberg states. Ionization from this mixed state mainly results in the overtone excitation of vibrational mode v(8) and v(9) of the cation state. In the wavelength range from 336 to 364 nm, a mixed state comprising the 3d/4s Rydberg and the 4A(1) valence states are populated by the absorption of two photons through vibronic coupling. The partition ratio among these states varies with the excitation wavelength, resulting in dramatic changes in both kinetic energy distributions and angular distributions. As the laser wavelength becomes shorter, from 336 to 314 nm, higher excited states, 3B(2), 5A(1), 6A(1), 7B(1) and 4B(2), can be populated. Photoelectron angular distributions provide supplementary verification of assignments. Our experiments indicate that femtosecond multiphoton ionization and photoelectron imaging methods are powerful tools for investigating short-lived intermediated excited states, which cannot be detected in nanosecond experiments.     

Carbon 1s excitation spectroscopy of propyne, trifluoropropyne, and propargyl alcohol

The C 1s excitation spectra of propyne (HC2CH3), 3,3,3-trifluoropropyne (HC2CF3), and propargyl alcohol (HC3CH3OH) have been studied using synchrotron radiation and ion time-of-flight mass spectrometry. Discrete peaks below the carbon 1s ionization thresholds are compared and assigned, aided in part by ab-initio calculations incorporating an explicit C 1s hole. Calculated C 1s ionization potentials are in good agreement with previously reported experimental values. Calculated absolute excitation energies consistently underestimate the transition term values, but calculated relative excitation energies and intensities are in good agreement with the experimental results. The spectra are dominated by intense C 1s --> pi transitions. In the case of propyne, C 1s excitations from each of the three chemically inequivalent carbon atoms are observed. The effect of electronegative substitution is found to be different for the C 1s --> Rydberg transitions than for transitions to unoccupied valence levels, with Rydberg transition energies shifting with changes in the C 1s ionization potentials but valence transition energies showing only small changes with electronegative substitution. The C 1s (3a1,4a1) --> pi (6e) transitions of trifluoropropyne are shifted to lower energy relative to propyne even though the electronegative fluorine atoms cause a significant shift to higher energy in the corresponding C 1s IPs.     

Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Structural dynamics and energy flow in Rydberg-excited clusters of N,N-dimethylisopropylamine

In molecular beams, the tertiary amine N,N-dimethylisopropyl amine can form molecular clusters that are evident in photoelectron and mass spectra obtained upon resonant multiphoton ionization via the 3p and 3s Rydberg states. By delaying the ionization pulse from the excitation pulse we follow, in time, the ultrafast energy relaxation dynamics of the 3p to 3s internal conversion and the ensuing cluster evaporation, proton transfer, and structural dynamics. While evaporation of the cluster occurs in the 3s Rydberg state, proton transfer dominates on the ion surface. The mass-spectrum shows protonated species that arise from a proton transfer from the alpha-carbon of the neutral parent molecule to the N-atom of its ionized partner in the dimer. DFT calculations support the proton transfer mechanism between tightly bonded cluster components. The photoelectron spectrum shows broad peaks, ascribed to molecular clusters, which have an instantaneous shift of about 0.5 eV toward lower binding energies. That shift is attributed to the charge redistribution associated with the induced dipoles in surrounding cluster molecules. A time-dependent shift that decreases the Rydberg electron binding energy by a further 0.4 eV arises from the structural reorganization of the cluster solvent molecules as they react to the sudden creation of a charge.     

Beyond vinyl: electronic structure of unsaturated propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl hydrocarbon radicals

Vertical excitation energies and oscillator strengths for several valence and Rydberg electronic states of vinyl, propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl radicals are calculated using the equation-of-motion coupled cluster methods with single and double substitutions (EOM-CCSD). The ground and the lowest excited state (n <-- pi) equilibrium geometries are calculated using the CCSD(T) and EOM-SF-CCSD methods, respectively, and adiabatic excitation energies for the n <-- pi state are reported. Systematic changes in the geometries, excitation energies, and Rydberg state quantum defects within this group of radicals are discussed.     

3s Rydberg and cationic States of pyrazine studied by photoelectron spectroscopy

We have studied 3s(n-1 and pi-1) Rydberg states and D0(n-1) and D1(pi-1) cationic states of pyrazine [1,4-diazabenzene] by picosecond (2 + 1) resonance-enhanced multiphoton ionization (REMPI), (2 + 1) REMPI photoelectron imaging, He(I) ultraviolet photoelectron spectroscopy (UPS), and vacuum ultraviolet pulsed field ionization photoelectron spectroscopy (VUV-PFI-PE). The new He(I) photoelectron spectrum of pyrazine in a supersonic jet revealed a considerably finer vibrational structure than a previous photoelectron spectrum of pyrazine vapor. We performed Franck-Condon analysis on the observed photoelectron and REMPI spectra in combination with ab initio density functional theory and molecular orbital calculations to determine the equilibrium geometries in the D0 and 3s(n-1) states. The equilibrium geometries were found to differ slightly between the D0 and 3s states, indicating the influence of a Rydberg electron on the molecular structure. The locations of the D1-D0 and 3s(pi-1)-3s(n-1) conical intersections were estimated. From the line width in the D1 <-- S0 spectrum, we estimated the lifetime of D1 to be 12 fs for pyrazine and 15 fs for fully deuterated pyrazine. A similar lifetime was estimated for the 3s(pi-1) state of pyrazine by REMPI spectroscopy. The vibrational feature of D1 observed in the VUV-PFI-PE measurement differed dramatically from that in the UPS spectrum, which suggests that the high-n Rydberg (ZEKE) states converging to the D1 vibronic state are short-lived due to electronic autoionization to the D0 continuum.     

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.     

Probing Rapidly‐Ionizing Super‐Atom Molecular Orbitals in C60: A Computational and Femtosecond Photoelectron Spectroscopy Study

Super‐atom molecular orbitals (SAMOs) are diffuse hydrogen‐like orbitals defined by the shallow potential at the centre of hollow molecules such as fullerenes. The SAMO excited states differ from the Rydberg states by the significant electronic density present inside the carbon cage. We provide a detailed computational study of SAMO and Rydberg states and an experimental characterization of SAMO excited electronic states for gas‐phase C₆₀ molecules by photoelectron spectroscopy. A large band of 500 excited states was computed using time‐dependent density functional theory. We show that due to their diffuse character, the photoionization widths of the SAMO and Rydberg states are orders of magnitude larger than those of the isoenergetic non‐SAMO excited states. Moreover, in the range of kinetic energies experimentally measured, only the SAMO states photoionize significantly on the timescale of the femtosecond laser experiments. Single photon ionization of the SAMO states dominates the photoelectron spectrum for relatively low laser intensities. The computed photoelectron spectra and photoelectron angular distributions are in good agreement with the experimental results.