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We present herein the first comprehensive study of the one‐ and two‐photon absorption of Fe(CO)5 utilising a hierarchy of linear‐ and quadratic‐response coupled cluster (LR‐ and QR‐CC) methodologies to provide an in‐depth characterisation, as well as potential energy curves for axial and equatorial bond dissociations, highlighting the state crossings leading from the bright 1A2′′ state through to the dissociative 1E′ state. We have characterised a range of metal‐to‐ligand charge transfer (MLCT) and ligand field (LF) states that are in agreement with both previous studies and experiment, including the identification of a series of E′ states that present Rydberg character in the 5.9–7.2 eV region. Due to the rapid excited state dissociation of Fe(CO)5 through the low lying 1E′ and 2E′′ ligand‐field states, we have also included an LR‐CCSD analysis of the major dissociative product, Fe(CO)4. Analysis of the C2v geometry of Fe(CO)4 reveals four accessible ligand field states at 1.085, 1.684, 1.958, and 2.504 eV respectively, reinforcing the highly unstable nature of Fe(CO)4 along with a strong MLCT band between 4.300 and 5.573 eV. This band overlaps with one in the spectra of Fe(CO)5 suggesting that full fragmentation could proceed by two paths: two‐photon excitation leading to dissociation, or through sequential one‐photon absorption events, the first causing dissociation to and the second initiating further fragmentation of the complex.

Concerning the leading factors in the context of excited states analyses, namely charge centroids of the orbitals involved in the excitations, distance between orbital centroids, and overlap integrals a new metric denominated as index is proposed to assign the characters and optical properties of electronically excited states. Using several molecules from different categories and also a well-studied standard database regarding time-dependent density functional theory (TD-DFT) studies as benchmark criteria, accountability of the developed index has numerically been assessed for local, charge transfer, and Rydberg excitations. It is shown that the nature of excited states can be discriminated using the index where its superior performance for those situations in which the previous descriptors were not helpful is also unveiled. We have also examined relationships between the index and optical properties of some molecules under study in the framework of sum-over-state (SOS) approach. It is observed that there are correlations between the proposed index and computed hyperpolarizabilities based on SOS scheme. These findings offer the possibility of estimating excited states properties of large systems from simple descriptors of excited states without performing calculations of high-order response functions explicitly.

Studies of ion-molecule reactions at low temperatures are difficult because stray electric fields in the reaction volume affect the kinetic energy of charged reaction partners. We describe a new experimental approach to study ion-molecule reactions at low temperatures and present, as example, a measurement of the ${\rm H}_2^+ + {\rm H}_2\rightarrow {\rm H}_3^+ + {\rm H}$ reaction with the ${\rm H}_2^+$ ion prepared in a single rovibrational state at collision energies in the range $E_{\rm col}/k_{\rm B} = 5$-60 K. To reach such low collision energies, we use a merged-beam approach and observe the reaction within the orbit of a Rydberg electron, which shields the ions from stray fields. The first beam is a supersonic beam of pure ground-state H$_2$ molecules and the second is a supersonic beam of H$_2$ molecules excited to Rydberg-Stark states of principal quantum number $n$ selected in the range 20-40. Initially, the two beams propagate along axes separated by an angle of 10$^\circ$. To merge the two beams, the Rydberg molecules in the latter beam are deflected using a surface-electrode Rydberg-Stark deflector. The collision energies of the merged beams are determined by measuring the velocity distributions of the two beams and they are adjusted by changing the temperature of the pulsed valve used to generate the ground-state ${\rm H}_2$ beam and by adapting the electric-potential functions to the electrodes of the deflector. The collision energy is varied down to below $E_{\rm col}/k_{\rm B}= 10$ K, i.e., below $E_{\rm col}\approx 1$ meV, with an energy resolution of 100 $\mu$eV. We demonstrate that the Rydberg electron acts as a spectator and does not affect the cross sections, which are found to closely follow a classical-Langevin-capture model in the collision-energy range investigated. Because all neutral atoms and molecules can be excited to Rydberg states, this method of studying

The Shannon entropy, the desequilibrium and their generalizations (Renyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically symmetric potential V(r) can be decomposed into angular and radial parts. The radial part depends on the analytical form of the potential, but the angular part does not. In this article, we first calculate the angular entropy of any central potential by means of two analytical procedures. Then, we explicitly find the dominant term of the radial entropy for the highly energetic (i.e., Rydberg) stationary states of the oscillator-like systems. The angular and radial contributions to these entropic measures are analytically expressed in terms of the quantum numbers which characterize the corresponding quantum states and, for the radial part, the oscillator strength. In the latter case, we use some recent powerful results of the information theory of the Laguerre polynomials and spherical harmonics which control the oscillator-like wavefunctions.

We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules which form in an ultra-cold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the Cs perturber atoms by including the full set of spin-resolved 1,3 S_J and 1,3 P_J scattering phase shifts, and allow for the mixing of singlet (S = 0) and triplet (S = 1) spin states through Rydberg electron spinorbit and ground state electron hyperfine interactions. Excellent agreement with observed data in Sasmannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line positions and profiles is obtained. We also determine the spin- dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules for which all of the relativisticcontributions are accounted.

Ensemble density functional theory (DFT) is a theory potentially able to describe electronic states inaccessible to traditional time-dependent DFT approaches, e.g. Rydberg and double excitations. When combined with ensemble wavefunction approaches through a range-separation scheme of Stoll and Savin (Density Functional Methods in Physics, 1985, 177-207), a resulting multiconfiguration ensemble DFT is able to address also such challenging phenomena as bond breaking in the electronically excited molecules. Ensemble DFT is, however, crippled by the so-called “ghost interaction” error, analogous to the self-interaction error in the ground-state DFT. We are exploring ways to alleviate this effect. We also study the importance of spin polarization in the density functional, the self-consistency effects and the impact of tunable parameters on the quality of shapes of potential energy surfaces. © 2016 Wiley Periodicals, Inc.

This topical review addresses how semiconductor systems may reveal scalable properties similar to those known from Rydberg atoms and in which ways they may be utilized for precision sensing and to realize huge long-range interactions in semiconductor systems. Due to the interdisciplinary nature of the field, it has a twofold purpose: First, it may serve as an introduction to Rydberg physics for semiconductor physicists unfamiliar with the topic. Second, it may also serve as an overview of the specific opportunities and challenges arising in semiconductor physics for researchers who are familiar with Rydberg physics of cold atom gases, but new to the field of semiconductor physics. The review starts with an introduction on the general properties of excitons in semiconductors. Then, the material system Cu2O, which is the best developed platform for semiconductor Rydberg physics at the moment, is discussed in detail., Advanced quantum technologies;Vol. 3. 2020, issue 11, article 1900134

We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge–resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed. © 2015 Wiley Periodicals, Inc.

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 C(60) 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.

Molecules with sufficiently large dipole moments were predicted to form weakly bound negative ions in the dipolar field and such dipole-bound anions have been observed and characterized experimentally. Negative ions with dipolar molecular cores can have excited dipole-bound states (DBSs) near the detachment threshold, analogous to Rydberg states in neutral molecules. DBSs in excited anions were first observed as resonances in photodetachment crosssections. Ultrahigh resolution spectroscopy has been reported on excited DBSs of a number of anions near their detachment threshold by autodetachment. The theory for autoionization from Rydberg states was first developed by Berry, who predicted a Dv= 1 vibrational propensity rule, that is, the Rydberg state undergoes a vibrational relaxation by one vibrational quantum in the molecular core during autoionization, in which the vibrational energy is transferred to the Rydberg electron. The Dv= 1 propensity rule has been observed in autoionization of numerous molecules and mode-specific autoionization has been observed by photoelectron spectroscopy, in which the kinetic energies of the outgoing electrons are measured. The same Dv= 1 propensity rule should apply in autodetachment from DBSs of excited anions and has been inferred in previous studies. However, the electron kinetic energies of the outgoing autodetached electrons from the excited DBSs have not been measured by electron spectroscopy. All prior studies of DBSs in excited anions are dominated by rotational effects and pure vibrational autodetachment from DBSs has not been reported, even though vibrational autodetachment has been observed in weakly bound anions and has been used effectively as a spectroscopic tool for anions. Here we report the direct observation of pure vibrational autodetachment from DBSs of cryogenically cooled phenoxide anions using high-resolution photoelectron imaging. Autodetachment from eight vibrational levels of the DBS in optically exited phenoxide anions are observed and the Dv= 1 propensity rule is found to be strictly obeyed. Three vibrational modes, which have weak Franck–Condon factors in the nonresonant photodetachment, are observed to be dramatically enhanced. Excitation to the bound ground vibrational level of the DBSs of phenoxide is observed using resonant two-photon detachment, allowing the binding energy of the DBSs to be directly measured. The phenoxy radical (C6H5OC) is an important transient specie involved in numerous environmental and biological processes. Its vibrational spectroscopy has been studied in solution and in argon matrices. Photoelectron spectroscopy (PES) of the phenoxide anion (C6H5O ) consists of an extensive vibrational progression in the v11 mode. [30] A recent high-resolution PE imaging study of phenoxide yielded an accurate electron affinity (18178 7 cm ) and a v11 vibrational frequency (519 cm ) for the phenoxy radical. The current experiments are carried out using a PES apparatus equippedwith an electrospray ionization source, a cryogenically controlled ion trap, and a high-resolution PE imaging system. The phenoxide anions were produced by electrospray of a mixed phenol/sodium hydroxide solution. Anions from the electrospray source were transported into a temperature-controlled ion trap, where they were accumulated and cooled for 0.1 s before being ejected into the extraction zone of a time-of-flight mass spectrometer. A dye laser was used in the current study and the imaging system was calibrated using the known spectra of Au . The resolution of the imaging system has been described recently and can reach about 2 cm 1 for low-energy electrons. The PE images and spectra at 20 K are shown in Figure 1 at four photon energies. These data are similar to those reported recently, with two important differences. First, the cryogenically cooled ions completely eliminate the vibrational hot bands and result in narrower line widths. The 0 !0 transition (00 ) in Figure 1a reveals rotational contours (see inset) and defines a more accurate electron affinity of 18173 3 cm 1 for the phenoxy radical. More importantly, in addition to the dominating v11 vibrational progression, vibrational transitions with weak Franck–Condon factors are observed, that is, modes v9, v10, and v18 and their combination bands with mode v11. The modes v9 and v10 are both totally symmetric with a1 symmetry, [29,35] similar to mode v11, and are allowed transitions. However, mode v18 has b1 symmetry and its activity must be due to vibronic couplings, as observed recently in high-resolution PE imaging of other small polyatomic anions. The angular distributions of all the vibrational peaks because of the a1 modes display splus dorbital characters, consistent with the p-type orbital from which the electron is detached. The angular distributions of the vibrational peaks because of the v18 mode are different, displaying distinct p-orbital character (Figure 1). The different angular distributions for the different vibrational modes are interesting and can be used in vibrational assignments in [*] Dr. H. T. Liu, D. L. Huang, P. D. Dau, Prof. Dr. L. S. Wang Department of Chemistry, Brown University Providence, RI 02912 (USA) E-mail: Lai-Sheng_Wang@brown.edu

The first high level ab initio quantum-chemical calculations of potential energy surfaces (PESs) for low-lying singlet excited states of norbornadiene in the gas phase are presented. The optimization of the stationary points (minima and conical intersections) and the recalculation of the energies were performed using the multireference configuration interaction with singles (MR-CIS) and the multiconfigurational second-order perturbation (CASPT2) methods, respectively. It was shown that the crossing between valence V2 and Rydberg R1 states close to the Franck–Condon (FC) point permits an easy population switch between these states. Also, a new deactivation path in which the doubly excited state with (π3)2 configuration (DE) has a prominent role in photodeactivation from the R1 state due to the R1/DE and the DE/V1 conical intersections very close to the R1 and DE minima, respectively, was proposed. Subsequent deactivation from the V1 to the ground state goes through an Olivucci–Robb-type conical intersection that adopts a rhombic distorted geometry. The deactivation path has negligible barriers, thereby making ultrafast radiationless decay to the ground state possible. © 2013 Wiley Periodicals, Inc.

The intensity patterns of some Rydberg line series in the X-ray spectra of foil-excited fast ion beams bear a resemblance to patterns seen with SN remnants or after charge exchange (CX). Closer scrutiny of the ion-foil interaction process reveals why this is no more than a chance resemblance, because the underlying processes are very different. However, electron beam ion traps are suitable for CX observations (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.

We applied an improved long-range correction scheme including a short-range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau-B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long-range portion of Hartree-Fock (HF) exchange to excitation energies of large molecules (Chai and Head-Gordon, J Chem Phys 2008, 128, 084106) and additional short-range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short-range to mid-range (0.5–3 A) to ground state properties achieved high performances of LCgau-B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x-family. We also found that while a small μ value (∼0.2) in LC-DFT is appropriate to the local excitation and intramolecular charge-transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation-energy calculations. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011

Starting with the Hamilton-Jacobi equation, Campos et al. have applied Hylleraas' method along with the series obtained by Wind-Jaffe to several molecular ions, among which the H2+ system, to determine their electronic energies in different states. In this work, we have fitted the potential energy curves for the 2pπ, 3dσ, 4dσ, 4fπ, 4fσ, 5gσ, and 6iσ electronic states of the H2+ ion employing the Rydberg generalized function. From these fittings, the spectroscopic constants and the rovibrational energies have been determined by two distinct methods: Dunham's and the discrete variable representation. The theoretically obtained results are in a satisfactory agreement and are expected to provide a comparison source to future works in the experimental field. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Flash Photolysis of ditropyl and ditropyl sulphide in excess inert gas yields the transient spectrum of the tropyl radical. This spectrum consists of a Rydberg series in the ordinary U.V. converging to an ionisation limit at 6.237 eV. Under the same conditions, flash photolysis of cycloheptatriene or of 7-cyanocycloheptatriene yields toluene or toluonitriles respectively. In the former case, the benzyl radical is observed; this is formed from an energy-rich, quenchable precursor.

Large-scale multi-reference configuration interaction calculations are carried out for the prediction of potential energy curves of several small radicals in their ground and excited valence-shell and Rydberg states. The Gaussian AO basis employed therein is of double-zeta plus polarization quality and includes up to f functions and semi-diffuse p and d functions for proper description of charge-transfer and correlation effects. Special emphasis is placed on AH and AH2 systems and their positive and negative ions with A=Si, P and S from the second-row and on the distinctions relative to their first-row analogues. Various properties such as spin-orbit splittings and radiative lifetimes are also calculated. The importance of configuration interaction treatments for the correct prediction of the ordering of states in the transition metal hydrides ScH, ScH+, TiH and TiH+ is also pointed out. The relative stability of states in a large number of AB systems with A and B from the first and/or second-row is discussed in light of their importance for larger systems with an AB center and with respect to their photoelectron spectrum which oftentimes does not allow the direct intercombination between ground states of neutral systems and their corresponding ions. The work should demonstrate the capability of today's theoretical ab initio methods for obtaining reliable information for small systems parallel or complementary to experimental studies.

A modified regional self-interaction correction (mRSIC) method is proposed for obtaining accurate core-excitation energies in time-dependent density functional theory (TDDFT) calculations. The mRSIC method is an improvement of the RSIC method (Tsuneda et al. J Comput Chem 2003, 24, 1592). It takes into account the energy contributions from 2s and higher atomic orbitals that the RSIC method neglects. Furthermore, mRSIC improves the poor description for the nuclear-electron cusp of Gaussian basis functions. The mRSIC method was combined with a long-range correction (LC) scheme, which has been proved to give accurate valence-, Rydberg-, and charge transfer (CT)-excitation energies. In so doing, it dramatically improved the accuracy of the calculated core-excitation energies and did not affect the already accurate values of valence-, Rydberg-, and CT-excitation energies produced by the LC functionals. These results mean that the combined scheme is accurate for all excitation energy forms. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009

The analytic information theory of quantum systems includes the exact determination of their spatial extension or multidimensional spreading in both position and momentum spaces by means of the familiar variance and its generalization, the power and logarithmic moments, and, more appropriately, the Shannon entropy and the Fisher information. These complementary uncertainty measures have a global or local character, respectively, because they are power-like (variance, moments), logarithmic (Shannon) and gradient (Fisher) functionals of the corresponding probability distribution. Here we explicitly discuss all these spreading measures (and their associated uncertainty relations) in both position and momentum for the main prototype in D-dimensional physics, the hydrogenic system, directly in terms of the dimensionality and the hyperquantum numbers which characterize the involved states. Then, we analyze in detail such measures for s-states, circular states (i.e., single-electron states of highest angular momenta allowed within an electronic manifold characterized by a given principal hyperquantum number), and Rydberg states (i.e., states with large radial hyperquantum numbers n). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

The frame transformation for an s-wave electron in the field of a degenerate symmetric top molecular ion core is used to interpret the results of a series of rotational bandshape fittings of one- and two-photon absorption spectra of methyl iodide in the region of the lowest Rydberg transitions. The frame transformation is defined between alternative representations of the total wavefunction in which the spin of the Rydberg electron is successively decoupled from the molecular frame to the laboratory frame. It is shown that uncoupling of the spin from the molecular axis is essentially complete in the 6s states of CH3I. Calculations are also presented which indicate that the dynamic Jahn-Teller interaction leds to substantial angular momentum quenching in some vibronic levels of this molecule.

Although much work has been done concerning the absolute ordering of the occupied π molecular orbitals of 1,4-cyclohexadiene, this ordering has not yet been directly proven. Consequently, the ordering of the vacant π* orbitals cannot be said to be directly proven. Most recently, an electron impact spectroscopic investigation of the electronic transitions of 1,4-cyclohexadiene revealed that only two clear Rydberg transitions are present. Both are to p-Rydberg orbitals and each is from a different occupied π orbital. However, since only indirect assignments of those transitions were possible, the absolute ordering of the occupied π molecular orbitals is still unproven. The application of multiphoton ionization spectroscopy can directly answer this problem. For molecules like 1,4-cyclohexadiene, that have a center of symmetry, transitions which involve an even number of photons have selection rules gg or uu, while transitions with an odd number of photons have selection rules gu or ug. In the two-photon spectrum of this molecule only one strong signal, at 6.42 eV, has been observed. (The second transition at 7.30 eV is not accessible with two-photon excitation.) In the three-photon spectrum only one signal, at 7.30 eV, has been observed. From these results the signal at 6.42 eV can be unambiguously assigned as a uu transition, while the signal at 7.30 eV is assigned as a gu transition. Since all p-Rydbergs are of “u” symmetry, these assignments thus confirm the predicted ordering of the occupied π molecular orbitals: πu (SS) above πg(SA).

Digital computer calculations in SCF MO approximation on the two lowest excited states of BH, 1σ22σ23σ4σ, 3Σ+ and 1Σ+, from 2.0 a.u. out to dissociation are reported. As shown previously by Grimaldi and coworkers [1], these are stable Rydberg states, but it is now shown that the 3Σ+ potential curve on increasing the interatomic distance R goes over a maximum and then becomes a repulsion curve dissociating to normal atoms. The changing characteristics of the 2σ, 3σ and 4σ orbitals as a function of R are described and discussed.

Estimates of the relative free energies of O H—O bonding in 2,6-dialkyl hindered phenol-water interactions have been made based on CNDO/2 potentials. To compute the free energies it was found necessary to examine a number of phenolic conformers for each interaction since conformers of small populations in the unbonded species became dominant in the bonded forms. An empiric potential was developed from the CNDO/2 results for a linear O H—O bond based on the Rydberg potential. The limitations of using electrostatic terms in the potential were examined. The steric effects of neighboring atoms were accurately incorporated into the potential by the use of repulsive exponential terms. Charge directionality from the proton acceptor was not observed. Reproducibility in hydrogen bonding was achieved to ±0.13 kcal over a 3–7 kcal range of hydrogen-bond interaction. The statistics of the interaction were computed for 2,6-dimethyl, 2,6-diisopropyl, and 2,6-di-t-butyl phenol conformer-water interactions. The average energies of interaction were very similar, being 5.5, 5.4, and 5.4 kcal, respectively, compared to the minimum energies of interaction of 7.4, 7.4, and 6.9 kcal observed for each compound. While the differences between the free energies of interaction of the phenolic proton acceptors were entropy dominated, the estimate of the difference between the 2,6-dimethyl and 2,6-diisopropyl phenol-water interactions was small (0.3 kcal). A similar difference comparison for the less entropy favored 2,6-di-t-butyl phenol-water interaction gave an estimate of 1.5 kcal.

Using photoelectron and optical spectroscopy, the ionization potentials of a large number of organic molecules in their Rydberg excited states were determined. In the limit of large alkyl substituents surrounding a central chromophoric group, it was found that the ionization potential of 3s, 3p, and 3d MO's are independent of the central group in direct contrast to the situation in the ground state. This is interpreted as showing that in the excited states of the limiting molecules, the Rydberg orbitals are completely n = 3 orbitals on the alkyl groups rather than on the central atoms as in the corresponding hydrides.

Differential cross sections for the atomic transitions 2p)ns) and 2p)np) are studied within the First Born Approximation by using a one-electron model based on hydrogen-like orbitals with appropriate effective nuclear charges. For single electron excitations, the related dimensionless quantity, the generalized oscillator strength, can be scaled to yield f(k) which depends upon the ratio of effective nuclear charges and reduced momentum transfer k. Calculations of f(k) versus k show that Rydberg series exhibit in f(k) extrema which are nearly the same for all members of the series, whereas excitations to different series exhibit a different number and positioning of the extrema. These trends suggest that patterns in generalized oscillator strengths can be used as an experimental tool to probe various types of transitions and to unravel Rydberg series. Comparison of theoretical values with available experimental results indicates close agreement.

For a fixed-angle potential energy surface (PES), W(Q), following the zero virial path (ZVP), on which ..sigma../sub ..mu..//sup N/Q/sub ..mu../ . del /sub ..mu../W(Q) = 0, provides an efficient way for locating the transition state and generating a good approximation to the minimum-energy reaction path; vector Q = (Q/sub 1/, ..., Q/sub N/ stands for nuclear coordinates. An algorithm which employs the ZVP following is proposed for exploring PESs when starting from the reactant (or product) region. It seems that this approach allows one to avoid some discontinuities in the reaction coordinate, which often result from the bottom-following procedures. The implications of the integral forms of the virial theorem are examined and a new way of constructing potential energy functions W(R) for diatomic molecules is proposed. It starts with the normalization of the kinetic component T(R) of the potential: integral/sub 0//sup infinity/(T(R) - T(infinity))dR = Z/sub A/Z/sub B/, where Z/sub A/ and Z/sub B/ are the nuclear charges and R is the internuclear distance. The modified potentials are derived for four different analytical representations of T(R), T/sub X(R)(X = M, R, RM, and HH) by the Morse, Rydberg, Rosen--Morse, and Hulbert--Hirschfelder functions, respectively. The three-parameter modified potentials (X = M,more » R, and RM) are tested against known spectroscopic data for H/sub 2//sup +/ and H/sub 2/.The modified potentials require one less experimental constant to fit the potential parameters than do their original analogs. It follows that the Morse and Rydberg functions constitute satisfactory representations of the kinetic component T(R), and that enforcing its normalization improves predictions of spectroscopic constants and relations between them. 46 references.« less

The electronic structure of the HeH+2 system consists of an intricate mixture of bound and repulsive states. As an initial step in a multidisciplinary study of this electronic structure a careful examination has been made of the effects of correlation on the ground-state potential energy surface. A first treatment of the triatomic excited states is also reported in terms of the vertical excitation spectrum near the equilibrium geometry found for the ground state. The latter treatment concentrates on the valence and first few Rydberg states; a more extensive treatment of the Rydberg states is left to a later article.

The vacuum ultraviolet absorption spectrum of 1,1-C2H2D2 has been reexamined. Using the symmetric top approximation and the Merer-Schoonveld (A. J. Merer and L. Schoonveld, Can. J. Phys. 47, 1731 (1969)) potential for the lowest-energy s Rydberg (R1s) state of ethylene, the energies and relative intensities of the first few torsional vibrations (v4′) in the R1s state of 1,1-C2H2D2 have been computed. The agreement with experiment is excellent. This result negates the recent proposal (F. H. Watson, Jr. and M. N. Nycum, Spectrosc. Lett. 8, 223 (1975)) that the N → R1s transition obtains allowedness only through vibronic coupling. The energies and relative intensities of v4′ have also been computed for CH3D, 1,2-C2H2D2 (cis and trans) and C2HD3. The Merer-Schoonveld potential is in excellent agreement with experiment in all instances. Some discussion of the photoelectron spectra is also provided.

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.

Using the recently introduced maximum overlap method and Hartree-Fock Perturbation Theory (HFPT), we compute Hartree-Fock (HF) wavefunctions for triplet 1 sn sstates of the helium atom. Comparison with near-exact results from Nakatsuji's free ICI method reveals that HF theory provides a simple route to accurate energies of these Rydberg states, especially for large n. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 1915-1919, 2009

Infrared transient absorption (IRTA) spectra for excitons and biexcitons in CuCl bulk crystal have been measured by pump-probe spectroscopy. The IRTA peak energy of the exciton agrees with the transition energy between Rydberg 1s to 2p states reported in one- and two-photon absorption measurement. On the other hand, the IRTA peak energy of the biexcitons locates in energy higher than that of the excitons, which is reasonable by taking hydrogen molecule model into account. In addition, our results support the enhancement of the transition energy between 1s and 2p states in quantum dots compared to the bulk case. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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 pi pi* valence excitation. Sharp peaks reported in the vicinity of the low-energy feature in the gas phase correspond to the beginning of the pi 3s(R) Rydberg series. By locating the origin of the pi pi* 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 pi pi* transition, which underlies the Rydberg manifold as a quasi-continuum.

We have observed remarkable changes in the magnetic properties of excitons as they acquire kinetic energy. In particular, the Zeeman splittings and diamagnetic shifts of excitonic transitions when magnetic fields are applied along the growth direction of (001) wide quantum wells of CdTe, ZnSe, ZnTe and GaAs are found to to have a strong dependence on the translational wavevector Kz. The behaviour of the Zee-man splittings corresponds to enhancement of the magnetic moments of the excitons. This enhancement is particularly marked when their translational kinetic energy becomes comparable with the exciton Rydberg and can be described by what appears to be a universal function of Kz. A model for the behaviour is outlined which involves motionally-induced mixing between the 1S hydrogenic exciton ground state and excited nP states. The observations imply that there are significant changes in the structure of the exciton as its translational kinetic energy increases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, we present the rovibrational energies and spectroscopic constants of the molecular ion H in the electronic states 1sσ, 7iσ, 5fπ, 5gπ, 6iπ, and 6iϕ. The H electronic energies were obtained from the solution of Hamilton–Jacobi equations in association with the series established by Wind–Jaffe. The calculated energies were fitted using the extended Rydberg functions and polynomials in bond order coordinates. From these analytical forms, we evaluated the H rovibrational spectroscopic constants for each state using two different procedures. The first was obtained combining the rovibrational energies, determined through the nuclear Schrodinger equation solution, and a diatomic rovibrational energy equation. The second was determined using the Dunham method. The results obtained are in a good agreement with both experimental and theoretical data available in the literature. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

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. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

We present our experiments on the applicability of ultracold Rydberg gases for quantum information processing. As quantum computing relies on entanglement mediated through interparticle interactions, we have experimentally implemented three approaches to induce ultralong-range interactions between Rydberg atoms: van-der-Waals interactions, interactions of permanent dipoles induced by an electric field, and resonant dipole-dipole interactions (Forster resonances). Advantages and limitations of the approaches are discussed.

Quite different meanings are attached by chemists to the words element, atom, orbital, order of orbitals or configurations. This causes conceptual inconsistencies, in particular with respect to the transition-metal elements and their atoms or ions. The different meanings will here be distinguished carefully. They are analyzed on the basis of empirical atomic spectral data and quasi-relativistic density functional calculations. The latter are quite reliable for different average configuration energies of transition-metal atoms. The so-called "configurations of the chemical elements", traditionally displayed in periodic tables, are the dominant configurations of the lowest spin-orbit levels of the free atoms. They are chemically rather irrelevant. In many-electron systems the ns and np AOs are significantly below the more hydrogen-like nd ones. Even (n+1)s is below nd for all light neutral atoms from C onwards, but only up to the first elements of the respective long rows! The most common orbital order in transition-metal atoms is 3p << 3d < 4s etc. The chemically relevant configuration in group g is always d(g) instead of d(g-2) s(2). Conceptually clear reasoning eliminates apparent textbook inconsistencies between simple quantum-chemical models and the empirical facts. The empirically and theoretically well-founded Rydberg (n-deltal) rule is to be preferred instead of the historical Madelung (n+l) rule with its large number of exceptions.

Using the complete active space self-consistent field method with a large atomic natural orbital basis set, 10, 13, and 9 electronic states of the OClO radical, OClO+ cation, and OClO− anion were calculated, respectively. Taking the further correlation effects into account, the second-order perturbation (CASPT2) calculations were carried out for the energetic calibration. The photoelectron spectroscopy of the OClO radical and OClO− anion were extensively studied in the both case of the adiabatic and vertical ionization energies. The calculated results presented the relatively complete assignment of the photoelectron bands of the experiments for OClO and its anion. Furthermore, the Rydberg states of the OClO radical were investigated by using multiconfigurational CASPT2 (MS-CASPT2) theory under the basis set of large atomic natural orbital functions augmented with an adapted 1s1p1d Rydberg functions that have specially been built for this study. Sixteen Rydberg states were obtained and the results were consistent with the experimental results. © 2006 Wiley Periodicals, Inc. J Comput Chem 28: 467–477, 2007

Quantum defect analysis is applied to time-dependent density functional theory (TDDFT) calculations of the Rydberg series of the He and Be atoms. The focus of the present study is on excitation energies obtained with different exchange-correlation potentials and kernels. Excitation energies are reobtained from the quantum defect values, and it is shown that these energies can be very accurately obtained from knowledge of the quantum defect alone. TDDFT results are compared within the adiabatic local density approximation for the case in which all virtual states are included in the calculation with results obtained when the number of states is truncated. Quantum defect analysis is used to demonstrate that truncation leads to serious errors. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

We study the dynamics of structural relaxation, induced by excitation of an NO molecule, to its A 2 Σ + Rydberg state in rare gas (RG) solids. Classical molecular dynamics simulations were carried out to describe the dynamics of the cage, formed by RG atoms surrounding the NO molecule. The results show a behaviour characterized by an impulsive expansion of the cage radius at short times, followed by a complex oscillatory pattern around the average NO-RG distance of -3.9 A for NO(A 2 Σ + )-Ne, ∼4 A for NO(A 2 Σ + )-Ar, -4.24 A for NO(A 2 Σ + )-Kr, and ∼4.55 A for NO(A 2 Σ + )-Xe. The size of the cage radius in the Rydberg state increases from -5% (Xe) to ∼25% (Ne) when compared with the initial cage radius. The experimental work showed a recurrence time of ∼ 1.4 ps (Ne) and ∼0.8 ps (Ar), while in our theoretical results we obtained ∼2 ps (Ne) and 0.8 ps (Ar), which is in good agreement with experimental results. The molecular dynamics simulations of the higher shells reveal a high degree of directionality of the propagation of the deformation in the solids, except in the NO-Ne solid system. We explained the dependences of the different behaviour in each system.

This work presents multi-state multi-reference Moller–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 Moller–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

A short summary of the n-electron valence state perturbation theory (NEVPT) is provided, and the defects inherent in cases of quasi-degeneration are underscored. A new version of the theory, called QD-NEVPT, based on quasi-degenerate perturbation theory, is presented. The new theory introduces an effective interaction among the zero-order wave functions and overcomes the difficulties of state-specific NEVPT. An application concerning the interaction among the π π* and Rydberg singlets of formaldehyde is presented. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

The photoionization of carbon monoxide from its ground state was studied theoretically. Partial photoionization cross sections were calculated up to a photon energy of 50 eV for the different Rydberg series that constitute the ionization channels of CO from its ground state. These values conform fairly well to the experimental ones found in the literature, in particular near the threshold region and at large photon energies. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Photoionization cross sections of CF3Br and CF3I were calculated with the molecular-adapted quantum defect orbital (MQDO) approach. The partial cross sections corresponding to the different Rydberg series that constitute the ionization channels of both molecules from their ground states are reported. Good agreement with experiment was found. An analysis of the results reveals that the cross section profiles are largely independent of the nature of the ligands. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

A basis set of quantum defect orbitals (QDOs) has been adopted for the diagonalization of the Hamiltonian matrix of nonhydrogenic atoms in the presence of an external electric field, so that the Stark structure of the Rydberg states has been possible to determine. The presently obtained Stark maps are in excellent agreement with those resulting from theory and experiment, as reported in the literature for a few representative atoms. The adequacy of the Stark quantum defect orbital (SQDO) procedure for accurately dealing with properties related to the Stark effect in atoms is suggested. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

The excited states of ethylene are systematically analyzed and characterized according to the natural orbitals (NOs) resulting from multireference configuration interaction singles and doubles (MRCISD) calculations. By comparing the shapes and nodal structures of the NOs with those of hydrogen atomic orbitals, the Rydberg series can be classified. Two or three different types of Rydberg series appear within five excited states for each symmetry of D2h. For example, in the 1Ag symmetry there are three series having np and two nf hydrogen-like atomic orbitals. Electronic correlation effects for the (π→π*) V state are also discussed on the basis of a complete active space self-consistent field (CASSCF) calculation, showing that electron correlation effects merely within the valence space cannot explain contraction of the V state. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005