A quantum defect model for the s, p, d, and f Rydberg series of CaF

We present an improved quantum defect theory model for the "s," "p," "d," and "f" Rydberg series of CaF. The model, which is the result of an exhaustive fit of high-resolution spectroscopic data, parameterizes the electronic structure of the ten ("s"Σ, "p"Σ, "p"Π, "d"Σ, "d"Π, "d"Δ, "f"Σ, "f"Π, "f"Δ, and "f"Φ) Rydberg series of CaF in terms of a set of twenty μ(ll('))(Λ) quantum defect matrix elements and their dependence on both internuclear separation and on the binding energy of the outer electron. Over 1000 rovibronic Rydberg levels belonging to 131 observed electronic states of CaF with n? ≥ 5 are included in the fit. The correctness and physical validity of the fit model are assured both by our intuition-guided combinatorial fit strategy and by comparison with R-matrix calculations based on a one-electron effective potential. The power of this quantum defect model lies in its ability to account for the rovibronic energy level structure and nearly all dynamical processes, including structure and dynamics outside of the range of the current observations. Its completeness places CaF at a level of spectroscopic characterization similar to NO and H(2).     

Bias effects on the electronic spectrum of a molecular bridge

In this paper the effect of bias and geometric symmetry breaking on the electronic spectrum of a model molecular system is studied. Geometric symmetry breaking can either enhance the dissipative effect of the bias, where spectral peaks are disabled, or enable new excitations that are absent under zero bias conditions. The spectral analysis is performed on a simple model system by solving for the electronic response to an instantaneously impulsive perturbation in the dipole approximation. The dynamical response is extracted from the electronic equations of motion as expressed by the Keldysh formalism. This expression provides for the accurate treatment of the electronic structure of a bulk-coupled system at the chosen model Hamiltonian electronic structure level.     

Multi‐state multi‐reference Møller–Plesset second‐order perturbation theory for molecular calculations

This work presents multi‐state multi‐reference Møller–Plesset second‐order perturbation theory as a variant of multi‐reference perturbation theory to treat electron correlation in molecules. An effective Hamiltonian is constructed from the first‐order wave operator to treat several strongly interacting electronic states simultaneously. The wave operator is obtained by solving the generalized Bloch equation within the first‐order interaction space using a multi‐partitioning of the Hamiltonian based on multi‐reference Møller–Plesset second‐order perturbation theory. The corresponding zeroth‐order Hamiltonians are nondiagonal. To reduce the computational effort that arises from the nondiagonal generalized Fock operator, a selection procedure is used that divides the configurations of the first‐order interaction space into two sets based on the strength of the interaction with the reference space. In the weaker interacting set, only the projected diagonal part of the zeroth‐order Hamiltonian is taken into account. The justification of the approach is demonstrated in two examples: the mixing of valence Rydberg states in ethylene, and the avoided crossing of neutral and ionic potential curves in LiF. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Ab initio study of the VUV-induced multistate photodynamics of formaldehyde

Although formaldehyde, H?CO, has been extensively studied there are still several issues not-well understood, specially regarding its dynamics in the VUV energy range, mainly due to the amount of nonadiabatic effects governing its dynamics. Most of the theoretical work on this molecule has focused on vertical excitation energies of Rydberg and valence states. In contrast to photodissociation processes involving the lowest-lying electronic states below 4.0 eV, there is little known about the photodynamics of the high-lying electronic states of formaldehyde (7-10 eV). One question of particular interest is why the (π, π*) electronic state is invisible experimentally even though it corresponds to a strongly dipole-allowed transition. In this work we present a coupled multisurface 2D photodynamics study of formaldehyde along the CO stretching and the symmetric HCH bending motion, using a quantum time-dependent approach. Potential energy curves along all the vibrational normal modes of formaldehyde have been computed using equation-of-motion coupled cluster including single and double excitations with a quadruply augmented basis set. In the case of the CO stretching coordinate, state-averaged complete active space self-consistent field followed by multireference configuration interaction was used for large values of this coordinate. 2D (for the CO stretching coordinate and the HCH angle) and 3D (including the out-of-plane distortion) potential energy surfaces have been computed for several Rydberg and valence states. Several conical intersections (crossings between potential energy surfaces of the same multiplicity) have been characterized and analyzed and a 2D 5 × 5 diabatic model Hamiltonian has been constructed. Based on this Hamiltonian, electronic absorption spectra, adiabatic and diabatic electronic populations and vibrational densities have been obtained and analyzed. The experimental VUV absorption spectrum in the 7-10 eV energy range is well reproduced, including the vibrational structure and the high irregularity in the regime of strong interaction between the (π, π*) electronic state and neighboring Rydberg states.     

Ground and excited states of the Rydberg radical H3O: electron propagator and quantum defect analysis

Vertical excitation energies of the Rydberg radical H(3)O are inferred from ab initio electron propagator calculations on the electron affinities of H(3)O(+). The adiabatic ionization energy of H(3)O is evaluated with coupled-cluster calculations. These predictions provide optimal parameters for the molecular-adapted quantum defect orbital method, which is used to determine oscillator strengths. Given that the experimental spectrum of H(3)O does not seem to be available, comparisons with previous calculations are discussed. A simple model Hamiltonian, suitable for the study of bound states with arbitrarily high energies is generated by these means.     

Electronic and cationic states of 2-methylpropene (isobutene) studied by VUV absorption,scattered electron spectroscopy and AB initio multireference configuration interaction calculations

VUV (6.2–9 eV) and electron scattering spectra (1–9 eV) have been recorded for 2-methylpropene (isobutene). Also, electronic states of the molecule, including the ground state and cationic states, have been investigated using ab initio multi-reference configuration interaction calculations. Some Koopmans-type in the UV photoelectron spectrum are reassigned and a number of shake-up states computed. In the electronic spectrum, Rydberg excited have been assigned and a second valence excited state (σ π*) located within about 1 eV of the V(ππ*) state. The experiments show, and theory confirms, that the Rydberg R(π3s) state has a positive electron affinity. Some interesting correlations between ionisation energies, energies of shake-up state electronic excitation energies are identified.     

Valence and dipole-bound anions of the most stable tautomers of guanine

Anionic states of guanine, which is the only nucleic acid base of which the anions have not yet been studied in either photoelectron spectroscopic (PES) or Rydberg electron transfer (RET) experiments, have been characterized for the four most stable tautomers of neutral guanine using a broad spectrum of electronic structure methods from the density functional theory, with the B3LYP exchange-correlation functional, to the coupled-cluster method, with single, double, and perturbative triple excitations. Both valence and dipole-bound anionic states were addressed. We identified some of the difficulties facing future PES or RET experiments on the anion of guanine. Even if guanine is successfully transferred to the gas phase without thermal decomposition, it is critical to have the canonical amino-oxo (G) and both amino-hydroxy (GH and GHN7H) tautomers in the beam, not only the most stable, a noncanonical, amino-oxo tautomer (GN7H), as the latter does not support an adiabatically bound anionic state. We also suggested a scheme for enrichment of gas-phase guanine with the canonical tautomer, which is not the most stable in the gas phase, but which is of main interest due to its biological relevance. The tautomers G, GN7H, and GHN7H support vertically bound valence anionic states with the CCSD(T) value of vertical detachment energy of +0.58, +0.21, and +0.39 eV, respectively. These anionic states are, however, adiabatically unbound and thus metastable. The vertical electronic stability of these valence anionic states is accompanied by serious "buckling" of the molecular skeleton. The G and GHN7H tautomers support dipole-bound states with the CCSD(T) values of adiabatic electron affinity of 65 and 36 meV, respectively. A contribution from higher-than-second-order correlation terms represents, respectively, 48 and 68% of the total vertical electron detachment energy determined at the CCSD(T) level.     

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.     

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.     

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.     

High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2

Experimental and theoretical methodologies have been developed to determine the hyperfine structure of molecular ions from detailed studies of the Rydberg spectrum and have been tested on molecular hydrogen. The hyperfine structure in l=0-3 Rydberg states of H2 located below the X 2Sigmag+(v+=0,N+=1) ground state of ortho H2+ has been measured in the range of principal quantum number n=50-65 at sub-MHz resolution by millimeter wave spectroscopy following laser excitation to np and nd Rydberg states using a variety of single-photon and multiphoton excitation sequences. The np1(1), nd1(1), and the nf1(0-3) Rydberg states were found to be metastable and to have lifetimes of more than 5 micros beyond n=50. Members of other series, such as the nd1(2), nd1(3), and the np1(0) series, were found to have lifetimes of more than 1 mus. Local perturbations induced by low-n Rydberg states belonging to series converging on rovibrationally excited levels of H2+ reduce the lifetimes in narrow ranges of n values. The hyperfine structure is strongly dependent on the value of the orbital angular momentum l. In the penetrating s and p states at n approximately 50 the exchange interaction dominates over the hyperfine interaction and the levels can be labeled by the total electron spin angular momentum quantum number S (S=0 or 1). In the less penetrating d and f Rydberg states, the hyperfine interaction between the core nuclear and electron spins is larger than the exchange interaction and the Rydberg states are of mixed singlet and triplet character. A procedure based on the Stark effect and on the systematic analysis of selection rules and combination differences was developed to determine the orbital and the total angular momentum quantum numbers l and F and to construct an energy map of p and f Rydberg levels between n=54 and 64 with relative positions of an accuracy of better than 1 MHz. Multichannel quantum defect theory (MQDT) was extended to treat the hyperfine structure in molecular Rydberg states and was used to analyze the observed hyperfine structure of the p and f Rydberg states of H2. The frame transformation between the Born-Oppenheimer channels described by the angular momentum coupling scheme (abetaJ) and the asymptotic channels described by the (e[bbetaS+]) coupling scheme was derived and enables an elegant treatment of all intermediate coupling cases. Purely ab initio quantum defect theory reproduced the experimentally determined positions to within 40 MHz for the p levels and 13 MHz for the f levels. By slight adjustments of the quantum defect functions and their energy dependences and by consideration of the p-f interaction, of the singlet-triplet splittings of the f levels, and of the departure of the ionic levels from pure coupling case (bbetaS+), the agreement between theory and experiment could be improved to 600 kHz. By comparing the results of MQDT calculations of the hyperfine structure of f Rydberg levels with those of coupled equations calculations, the frame transformation approximation of MQDT was shown to be accurate to within 300 kHz. The extrapolated ionic hyperfine structure of the X 2Sigmag+(v+=0,N+=1) ionic level corresponds to the ab initio prediciton of Babb and Dalgarno [Phys. Rev. A 46, R5317 (1992)] within the experimental error.     

Communication: Heavy Rydberg states: the H+H- system

Heavy Rydberg states are analogs of electronic Rydberg states, but with the electron replaced by a much heavier ion. We calculate ab initio the extremely long-range vibrational H(+)H(-) heavy Rydberg states in H(2), and compare these to recent experiments. The calculated resonance positions and widths agree well with experiment, but we predict additional sharp interloper resonances corresponding to vibrational states trapped inside the barrier on potential energy curve 7 (1)Σ(g)(+).     

The far-ultraviolet spectra of transition metal complexes

The intense bands which are found beyond the d-d bands in the electronic absorption spectra of transition metal complexes are usually assigned to intra-ligand or charge transfer transitions. However, Rydberg transitions originating with either the mainly 3d or ligand orbitals are also expected to contribute in this part of the spectrum. To explore this the vapor phase electronic absorption spectra of the tri-hexafluoroacetyl-acetonate complexes of Al, Sc, V, Cr, Fe and Mn have been recorded up to about 80000 cm^-1. In order to locate the Rydberg bands, quantum chemical calculations were carried out using the multiple scattering Xα MO method. Among the 4p and 4f type Rydberg bands there are several which are spin, Laporte, symmetry and angular momentum allowed and are expected to contribute strongly to the intensity observed in the ultraviolet and far-ultraviolet parts of the spectrum. The corresponding Rydberg states can mix, however, with valence-shell states of the same symmetry.The far-ultraviolet spectra of three sandwich compounds: bicyclopentadienyl Fe, Co and Ni were also determined. Due to the very low ionization potentials of these compunds, Rydberg transitions can contribute to the observed bands at rather low frequencies.     

Insight into the Rydberg states of CH

Ab initio electronic structure calculations of a relatively large number of Rydberg states of the CH radical were carried out employing the multireference single and double excitation configuration interaction (MRD-CI) method. A Gaussian basis set of cc-pV5Z quality augmented with 12 diffuse functions was used together with an extensive treatment of electron correlation. The main focus of this contribution is to investigate the 3d Rydberg complex assigned by Watson [Astrophys. J. 555, 472 (2001)] to three unidentified interstellar bands. The authors' calculations reproduce quite well the absolute excitation energies of the three components of the 3d complex, i.e., 2Sigma+(3dsigma), 2Pi(3dpi), and 2Delta(3ddelta), but not the energy ordering inferred from a rotational assignment of the 3d<--X 2Pi laboratory spectrum. The computation of the 4d complex is reported for the first time along with a number of other higher lying Rydberg species with an X 1Sigma+ core. The lowest Rydberg states belonging to series converging to the a 3Pi and A 1Pi excited states of CH+ are also calculated.     

Photoinduced Rydberg ionization spectroscopy of phenylacetylene: vibrational assignments of the C state of the cation

The photoinduced Rydberg ionization spectrum of the third excited electronic state of phenylacetylene cation was recorded via the origin of the cation ground electronic state. The origin of this state is 17 834 cm(-1) above the ground state of the cation, and the spectrum shows well-resolved vibrational features to the energy of 2200 cm(-1) above this. An assignment of the vibrational structure was made by comparison to calculated frequencies and Franck-Condon factors. From the assignments, and electronic structure considerations, the electronic symmetry of the C state is established to be (2)B(1).     

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.