Laser spectroscopic studies of several Rydberg states of MgO

We report extensive spectroscopic measurements of rovibronic transitions from the MgO X 1Sigma+ ground state to the high-energy E 1Sigma+, F 1Pi1, and G 1Pi1 Rydberg states. Perturbations in the E 1Sigma+ and G 1Pi1 states were observed. The Rydberg molecular orbital character of the three states is examined, given ab initio calculations by Thummel et al. [Chem. Phys. 129, 417 (1989)]. It is concluded that the E 1Sigma+ and G 1Pi1 states consist primarily of the MgO+ X 2Pi ionic core, surrounded by 3ppi and 3psigma Rydberg electron clouds, respectively, and that the F 1Pi1 state consists primarily of the MgO+ A 2Sigma+ ionic core surrounded by a 3ppi Rydberg electron cloud. Spectroscopic characterizations of some unassigned vibrational levels of analogous MgO 3Pi2 states in this energy region are also reported.     

Cluster size effects in core excitons of 1s-excited nitrogen

Cluster size effects in core excitons below the N 1s ionization energy of nitrogen clusters are reported in the energy regime 405-410 eV. These results are compared to the molecular Rydberg states as well as the corresponding bulk excitons of condensed nitrogen. The experimental results are assigned using ab initio calculations. It is found that the lowest excitons (N 1s-->3ssigma and N 1s-->3ppi) are blueshifted relative to the molecular Rydberg transitions, whereas others (N 1s-->3dpi and N 1s-->4ppi) show a redshift. Results from ab initio calculations on (N(2))(13) clearly indicate that the molecular orientation within a cluster is critical to the spectral shift, where bulk sites as well as inner- and outer-surface sites are characterized by different inner-shell absorption energies. These results are compared to the experimental spectra as well as previous work on site-selectively excited atomic van der Waals clusters, providing an improved spectral assignment of core exciton states in weakly bound molecular clusters and the corresponding condensed phase.     

Ground and excited states of NH4: Electron propagator and quantum defect analysis

Vertical excitation energies of the Rydberg radical NH4 are inferred from ab initio electron propagator calculations on the electron affinities of NH4+. The adiabatic ionization energy of NH4 is evaluated with coupled-cluster calculations. These predictions provide optimal parameters for the molecular-adapted quantum defect orbital method, which is used to determine Einstein emission coefficients and radiative lifetimes. Comparisons with spectroscopic data and previous calculations are discussed.     

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.     

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.     

Hartree-fock calculations for excited rydberg states

A method is introduced which allows to compute self-consistent restricted Hartree-Fock wave functions for excited Rydberg configurations. The concepts of reorganization and electron correlation of Rydberg states are discussed. As an illustration Hartree-Fock calculations for the (ls)(nl) Rydberg series of He are presented.     

Applications of effective core potentials and density functional theory to the spin states of iron porphyrin

We investigated the performance of the B3LYP density functional in combination with ab initio effective core potentials (ECPs) that are derived from either Hartree-Fock or Dirac-Fock calculations. The transferability of ab initio ECPs is assessed on the basis of comparison with all-electron density functional calculations. For iron(II) porphyrin in particular, our assessment focused on the relative energetic ordering of five low-lying spin states, 1A1G, 3A1G, 3B2G, 5A2G, and 5B1G, and their properties, including optimized structures, charge distribution, spin density, and vibrational frequencies. Our results show that core electron correlation and core-valence electron correlation do not have significant effects on the relative energetics of the spin states of iron porphyrin. Our calculations suggest that effects of replacing the core electrons with ECPs are less significant than the choice of basis functions. We conclude that ab initio ECPs such as LANL2, RCEP, and MEFIT-R may be combined with the B3LYP density functional theory to provide consistent and accurate results.     

Rydberg-valence mixing in the carbon 1s near-edge X-ray absorption fine structure spectra of gaseous alkanes

We have acquired high-resolution carbon 1s near-edge X-ray absorption fine structure (NEXAFS) spectra of methane, ethane, propane, isobutane, and neopentane. These experimental measurements are complemented by high-quality ab initio calculations, performed with the improved virtual orbital approximation. The degree and character of Rydberg-valence mixing in the preedge of the NEXAFS spectra of these species is explored. Significant Rydberg-valence mixing only occurs when there are excited states of valence sigma(C-H) character that have the appropriate symmetry to interact with excited states of Rydberg character. Our results show that this mixing is only present when there are C-H bonds to the core excited carbon atom.     

Geometry optimizations of open-shell systems with the fragment molecular orbital method

The ability to perform geometry optimizations on large molecular systems is desirable for both closed- and open-shell species. In this work, the restricted open-shell Hartree-Fock (ROHF) gradients for the fragment molecular orbital (FMO) method are presented. The accuracy of the gradients is tested, and the ability of the method to reproduce adiabatic excitation energies is also investigated. Timing comparisons between the FMO method and full ab initio calculations are also performed, demonstrating the efficiency of the FMO method in modeling large open-shell systems.     

A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

The Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electron-electron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electron correlation. We show how to evaluate the parameters of the model from high-level ab initio calculations on two-atom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MS-RASPT2 method is used to generate accurate potential energy curves for ethene as a function of carbon-carbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MS-RASPT2 method.     

Empirical correlation methods for temporary anions

A temporary anion is a short-lived radical anion that decays through electron autodetachment into a neutral molecule and a free electron. The energies of these metastable species are often predicted using empirical correlation methods because ab initio predictions are computationally very expensive. Empirical correlation methods can be justified in the framework of Weisskopf-Fano-Feshbach theory but tend to work well only within closely related families of molecules or within a restricted energy range. The reason for this behavior can be understood using an alternative theoretical justification in the framework of the Hazi-Taylor stabilization method, which suggests that the empirical parameters do not so much correct for the coupling of the computed state to the continuum but for electron correlation effects and that therefore empirical correlation methods can be improved by using more accurate electronic structure methods to compute the energy of the confined electron. This idea is tested by choosing a heterogeneous reference set of temporary states and comparing empirical correlation schemes based on Hartree-Fock orbital energies, Kohn-Sham orbital energies, and attachment energies computed with the equation-of-motion coupled-cluster method. The results show that using more reliable energies for the confined electron indeed enhances the predictive power of empirical correlation schemes and that useful correlations can be established beyond closely related families of molecules. Certain types of σ* states are still problematic, and the reasons for this behavior are analyzed. On the other hand, preliminary results suggest that the new scheme can even be useful for predicting energies of bound anions at a fraction of the computational cost of reliable ab initio calculations. It is then used to make predictions for bound and temporary states of the furantrione and croconic acid radical anions.     

Comparison of the transfer and green matrix methods for the surface problem in periodic chains

For the first time, ab initio Hartree- Fock calculations for the end states of periodic chains are performed with the transfer matrix formalism. The applicability of the method is tested on semi-infinite Li-, LiH-, HF- and H₂O-chains. It is found that the numerical applications of the transfer matrix method in its applied form on the ab initio level have some drawbacks due to the limited number of perturbed end cells which can be taken into account. The comparison with Green matrix (Koster-Slater) calculations shows that the transfer matrix method in its Hartree-Fock version is not faster; this is contrary to the results reported for tight binding model Hamiltonians.     

On the Additivity of Molecular Fragment Dipole Moments of 5‐Substituted Indole Derivatives

The estimate of the magnitude and the orientation of molecular electric dipole moments from the vector sum of bond or fragment dipole moments is a widely used approach in chemistry. However, the limitations of this intuitive model have rarely been tested experimentally, particularly for electronically excited states. Herein, we find rules for a number of indole derivatives by using rotationally resolved electronic Stark spectroscopy and ab initio calculations. Based on a natural‐bond‐orbital analysis, we discuss whether the vector additivity rule can be applied in a given electronic state. From a comparison of the experimental data with ab initio calculations, we deduced that the additivity model does not apply when the flow of electron density from the substituent is opposed to that inside the chromophore.     

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)(+).     

Collision-energy-resolved Penning ionization electron spectroscopy of thiazole and benzothiazole: study of ionic states and anisotropic interactions between a metastable He(23S) atom and hetero cyclic compounds

Anisotropic interactions between a metastable He(2(3)S) atom and aromatic heterocyclic compounds (thiazole and benzothiazole) as well as their electronic structures were studied by means of collision-energy/electron-energy resolved two-dimensional Penning ionization electron spectroscopy combined with ab initio molecular orbital calculations. Different collision-energy dependence of partial ionization cross sections (CEDPICS) were clearly observed for different ionic states depending on anisotropic extents of molecular orbitals from which an electron is removed. It was found that thiazole and benzothiazole most strongly attract a He(2(3)S) atom around the region where the nitrogen lone pair orbital extends. For another heteroatom, sulfur, it is relatively weak, but a certain attractive interaction was found for the directions perpendicular to the molecular plane. Benzothiazole was shown to widely attract a He(2(3)S) atom in the out-of-plane directions, since the benzene moiety showed a deeper potential well than the five-membered ring. Assignments of the ionic states including shake-up states were also discussed from observed CEDPICS and ab initio molecular orbital calculations. In particular, for the satellite bands, a negative collision energy dependence of the band intensity was well supported by a configuration-interaction calculation that assigns the satellite bands to be the ionization from pi orbitals accompanying pi-pi or n-pi excitations.     

Vacuum ultraviolet-infrared photo-induced Rydberg ionization spectroscopy: C-H stretching frequencies for trans-2-butene and trichloroethene cations

We have demonstrated the two-color vacuum ultraviolet (VUV)-infrared (IR) photoinduced Rydberg ionization (PIRI) experiment. Trichloroethene (ClCH=CCl2) and trans-2-butene (trans-CH3CH=CHCH3) were prepared in Rydberg states in the range of effective principal quantum number n* approximately 7-93 by VUV excitation prior to IR-induced autoionization. The observed VUV-IR-PIRI spectra are found to be independent of n*, suggesting that the electron Rydberg orbital is conserved, i.e., the Rydberg electron is behaving as a spectator during the excitation process. The observed IR active C-H stretching vibrational frequencies nu12+ = 3072+/-5 cm(-1) for ClCH=CCl2+ and nu23+ =2908+/-3 cm(-1), nu25+ =2990+/-10 cm(-1) and nu30+ =3022+/-10 cm(-1) for trans-CH3CH=CHCH3+ are compared with predictions based on ab initio quantum-chemical procedures and density functional calculations.     

The generalized valence bond π orbitals of ethylene and allyl cation

Using a fixed sigma core obtained from full electron ab initio Hartree-Fock calculations, the spatially projected GVB orbitals for the pi electron systems of ethylene and allyl cation are reported. The GVB(SP) method generates wavefunctions possessing the correct spatial and spin symmetry without restricting the nature of the individual orbitals. The GVB(SP) wavefunction provides a simple interpretation of the molecule in terms of orbitals each containing a single electron. The resulting total energies and excitation energies agree very well with full configuration interaction calculations.     

Electronic states and nature of bonding of the molecule NiSi by all electron ab initio HF-CI and CASSCF calculations

All electron ab initio Hartree-Fock (HF), configuration interaction (CI) and multiconfiguration self-consistent field (CASSCF) calculations have been applied to investigate the low-lying electronic states of the NiSi molecule. The ground state of the NiSi molecule is predicted to be¹Σ⁺. The chemical bond in the¹Σ⁺ ground state is a double bond composed of one σ and one π bond. The σ bond is due to a delocalized molecular orbital formed by combining the Ni 4s and the Si 3pσ orbitals. The π bond is a partly delocalized valence bond, originating from the coupling of the 3dπ hole on Ni with the 3pπ electron on Si. Withing the energy range 1 eV 18 electronic states have been identified. The lowest lying electronic states have been characterized as having a hole in either the 3dπ or the 3dδ orbital of Ni, and the respective final states are formed when either of these holes are coupled to the 3pπ valence electron of Si.     

Ab initio and quantum-defect calculations for the Rydberg states of ArH

Potential energy curves were evaluated for the ground and thirteen low-lying excited electronic states of the ArH molecule over a wide range of internuclear distances by the multi-reference averaged quadratic coupled cluster method. The ab initio energy differences and transition dipole moments were used to estimate Einstein emission coefficients, absorption oscillator strengths and radiative lifetimes. Diagonal and off-diagonal quantum defects, as functions of internuclear distance, were extracted from ab initio potentials of the lowest Rydberg states of the neutral ArH molecule by taking account of configuration interaction between Rydberg series converging to the ground and two electronic excited states of the ArH(+) cation. The derived quantum-defect functions were used to generate manifolds of higher excited Rydberg states. The agreement between experimental and calculated energies and radiative transition probabilities was found to be as good as or better than that obtained by earlier calculations.     

Properties of nearly one-electron molecules. I. An iterative Green function approach to calculating the reaction matrix

An ab initio R-matrix method for determining the molecular reaction matrix of scattering theory is introduced. The method makes use of a principal-value Green function to compute the collision channel wave functions for the scattered electron, in combination with the Kohn variational scheme for the evaluation of R-matrix eigenvalues on a spherical boundary surface at short range. This technique permits the size of the bounded volume in the variational calculation to be reduced, making the computations fast and efficient. The reaction matrix is determined in a form that minimizes its energy dependence. Thus the procedure does not require modification or an increase in the computational effort to study the electronic structure and dynamics in Rydberg molecules with extremely polar ion cores. The analysis is specialized to examine the bound-state and free-electron scattering properties of nearly one-electron molecular systems, which are characterized by a Rydberg/scattering electron incident on a closed-shell ion core. However, it is shown that the treatment is compatible with all-electron/ab initio representations of open-shell and nonlinear polyatomic ion cores, emphasizing its generality. The introduced approach is used to calculate the electronic spectrum of the calcium monofluoride molecule, which has the extremely polar (Ca+2F-)+e- closed-shell ion-core configuration. The calculation utilizes an effective single-electron potential determined by M. Arif, C. Jungen, and A. L. Roche [J. Chem. Phys. 106, 4102 (1997)] previously. Close agreement with experimental data is obtained. The results demonstrate the practical utility of this method as a viable alternative to the standard variational approaches.