Microwave electronic spectrum of the Ne⋯Ne+ long-range complex: The interaction potential

Imaging Recoil Ions from Optical Collisions between Ultracold, Metastable Neon Isotopes

We present an experimental scheme that combines the well-established method of velocity-map imaging with a cold trapped metastable neon target. The device is used for obtaining the branching ratios and recoil-ion energy distributions for the penning ionization process in optical collisions of ultracold metastable neon. The potential depth of the highly excited dimer potential is extracted and compared with theoretical calculations. The simplicity to construct, characterize, and apply such a device makes it a unique tool for the low-energy nuclear physics community, enabling opportunities for precision measurements in nuclear decays of cold, trapped, short-lived radioactive isotopes.

Theoretical study on low-lying electronic states of Kr2(+), Xe2(+), and Rn2(+)

In this work, the equation-of-motion coupled-cluster approach with spin-orbit coupling (SOC) for ionization potentials (IP) at the singles and doubles level (EOMIP-CCSD) is employed to calculate spectroscopic constants of low-lying states of rare gas dimer ions Kr2(+), Xe2(+), and Rn2(+). Two approaches are proposed to include contributions of triples: (1) energies of these states are calculated by adding the IPs from EOMIP-CCSD and the CCSD(T) energy of the rare gas dimers and (2) CCSD(T) energies without SOC for Rg2(+) are first calculated and energies of these states with SOC are determined subsequently using the SOC matrix between these states. The first approach can provide accurate results for the three most stable states, while overestimates bond lengths for the other states. The second approach has been adopted previously and the SOC matrix element between (2)Σ1∕2 (+) and (2)Π1∕2 states was set to be 1/2 times that of the SOC constant. In our work, the SOC matrix elements are determined from the calculated IPs and reasonable results for these states can be achieved with this approach, which could be useful for experimental works.

On the R-dependence of the spin-orbit coupling constant: Potential energy functions of Xe(2) (+) by high-resolution photoelectron spectroscopy and ab initio quantum chemistry

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of Xe(2) has been measured between 97 350 and 108 200 cm(-1), following resonant two-photon excitation via selected vibrational levels of the C 0(u) (+) Rydberg state of Xe(2). Transitions to three of the six low-lying electronic states of Xe(2) (+) could be observed. Whereas extensive vibrational progressions were observed for the transitions to the I(32g) and I(32u) states, only the lowest vibrational levels of the II(12u) state could be detected. Assignments of the vibrational quantum numbers were derived from the analysis of the isotopic shifts and from the modeling of the potential energy curves. Adiabatic ionization energies, dissociation energies, and vibrational constants are reported for the I(32g) and the I(32u) states. Multireference configurational interaction and complete active space self-consistent field calculations have been performed to investigate the dependence of the spin-orbit coupling constant on the internuclear distance. The energies of vibrational levels, measured presently and in a previous investigation (Rupper et al., J. Chem. Phys. 121, 8279 (2004)), were used to determine the potential energy functions of the six low-lying electronic states of Xe(2) (+) using a global model that includes the long-range interaction and treats, for the first time, the spin-orbit interaction as dependent on the internuclear separation.

Pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy of metastable He2: Ionization potential and rovibrational structure of He2+

A supersonic beam of metastable He(*) atoms and He(2) (*) a (3)Sigma(u) (+) molecules has been generated using a pulsed discharge at the exit of a pulsed valve prior to the gas expansion into vacuum. Pulsed-field-ionization zero-kinetic-energy photoelectron spectra of the He(2) (+) X(+) (2)Sigma(u) (+) (v(+)=0-2)<--He(2) (*) a (3)Sigma(u) (+) (v(")=0-2) transitions and photoionization spectra of He(2) (*) in the vicinity of the lowest ionization thresholds have been recorded. The energy level structures of (4)He(2) (+) X(+) (2)Sigma(u) (+) (v(+)< or =2,N(+)< or =23) and (3)He(2) (+) X(+) (2)Sigma(u) (+) (v(+)=0,N(+)< or =11) have been determined, and an accurate set of molecular constants for all isotopomers of He(2) (+) has been derived in a global analysis of all spectroscopic data reported to date on the low vibrational levels of He(2) (+). The analysis of the photoionization spectrum by multichannel quantum defect theory has provided a set of parameters describing the threshold photoionization dynamics.

Tests of functionals for systems with fractional electron number

In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest many-electron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in Hartree-Fock theory the energy curves downward. Perdew-Zunger self-interaction correction [Phys. Rev. B 23, 5048 (1981)] significantly reduces the many-electron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a long-range corrected hybrid functional can be nearly many-electron SIE-free in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties.

Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An "M-electron self-interaction-free" functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1<N<or=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC's produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.

Assessment of a long-range corrected hybrid functional

Common approximate exchange-correlation functionals suffer from self-interaction error, and as a result, their corresponding potentials have incorrect asymptotic behavior. The exact asymptote can be imposed by introducing range separation into the exchange component and replacing the long-range portion of the approximate exchange by the Hartree-Fock counterpart. The authors show that this long-range correction works particularly well in combination with the short-range variant of the Perdew-Burke-Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, here denoted LC-omegaPBE, is remarkably accurate for a broad range of molecular properties, such as thermochemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer.

Dissociative ionization of neon clusters Nen, n=3 to 14: A realistic multisurface dynamical study

The molecular dynamics with quantum transitions (MDQT) method is applied to study the fragmentation dynamics of neon clusters following vertical ionization of neutral clusters with 3 to 14 atoms. The motion of the neon atoms is treated classically, while transitions between the adiabatic electronic states of the ionic clusters are treated quantum mechanically. The potential energy surfaces are described by the diatomics-in-molecules model in a minimal basis set consisting of the effective 2p orbitals on each neon atom for the missing electron. The fragmentation mechanism is found to be rather explosive, with a large number of events where several atoms simultaneously dissociate. This is in contrast with evaporative atom by atom fragmentation. The dynamics are highly nonadiabatic, especially at shorter times and for the larger clusters. Initial excitation of the neutral clusters does not affect the fragmentation pattern. The influence of spin-orbit coupling is also examined and found to be small, except for the smaller size systems for which the proportion of the Ne+ fragment is increased up to 43%. From the methodological point of view, most of the usual momentum adjustment methods at hopping events are shown to induce nonconservation of the total nuclear angular momentum because of the nonzero electronic to rotation coupling in these systems. A new method for separating out this coupling and enforcing the conservation of the total nuclear momentum is proposed. It is applied here to the MDQT method of Tully but it is very general and can be applied to other surface hopping methods.

Rydberg states of the rare gas dimers

This work is dedicated to Gerhard Herzberg and his prodigious contributions to molecular spectroscopy. Of particular relevance here is Herzberg's seminal 1987 article (Annu. Rev. Phys. Chem. 38, 27 (1987)) in which he discussed the electronic structures of several groups of molecules he termed "Rydberg molecules". Among these are the rare gas dimers (Rg2), a group whose study has benefited significantly from recent advances in laser excitation and synchrotron-based spectroscopies, as well as in theory. Following the spirit of Herzberg's 1987 article, this paper reviews some of the more prominent features of Rydberg states in the Rg2 family as viewed from the current perspective.Key words: rare gas dimers, rare gas dimer excited states, Rg2 electronic structures, Rydberg states of He2, Ne2, Ar2, Kr2, and Xe2, electronic states of He2, Ne2, Ar2, Kr2, and Xe2.

Potential energy curves of diatomic molecular ions from high-resolution photoelectron spectroscopy. I. The first six electronic states of Ar2+

High-resolution photoelectron spectroscopic data have been used to determine the potential energy curves of the first six electronic states of Ar2+. The potential energy functions properly include the effects of the long-range interactions and of the spin-orbit interaction and are of spectroscopic accuracy (1-2 cm(-1)) over a wide range of internuclear distances. The total number of adjustable parameters could be reduced to only 12 by truncating the long-range interaction series after the R(-6) term and assuming an R-independent spin-orbit coupling constant. This assumption was verified to be valid to an accuracy of +/-2 cm(-1) over the range of internuclear distances between 3.0 and 4.6 A. The interaction potential proposed by Siska [P. E. Siska, J. Chem. Phys. 85, 7497 (1986)] was generalized to a form that is expected to be sufficiently flexible to describe chemical bonding in other diatomic molecular ions. The potential energy curves are more accurate than the best available ab initio curves by two orders of magnitude and provide quantitative information on dissociation energies and equilibrium internuclear distances. The local maximum between the two potential wells of the I(1/2g) state was determined to lie 62 cm(-1) below the Ar(1S0)+Ar(+)(2P(3/2)) dissociation limit, and the II(1/2g) state is found to be significantly more bound (De=177 cm(-1)) than previously assumed.

Potential energy curves of diatomic molecular ions from high-resolution photoelectron spectra. II. The first six electronic states of Xe[sub 2][sup +]

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of Xe(2) has been measured between 90 000 and 109 000 cm(-1) following single-photon excitation from the ground neutral state. Transitions to five of the six low-lying electronic states of Xe(2) (+) could be observed. Whereas extensive vibrational progressions were observed for the X0(g) (+)-->I(1/2u), I(3/2g), and II(1/2u) photoelectron transitions, only the lowest vibrational levels of the I(3/2u) and II(1/2g) states could be detected. Unambiguous assignments of the vibrational quantum numbers were derived from the analysis of the isotopic shifts of the vibrational bands and of the intensity distribution and from the modeling of the potential energy curves. Analytical potential energy curves of spectroscopic accuracy (i.e., approximately 1 meV) were determined for all six low-lying electronic states using a global model, which includes the first (charge-induced dipole, proportional to 1/R(4)) member of the long-range interaction series and treats the spin-orbit interaction explicitly. The assumption of an R-independent spin-orbit coupling constant was tested and found to be an excellent approximation.

Probing electronic states of Ne2+ and Ar2+ by measuring kinetic-energy-release distributions

Dissociative decay of metastable, electronically excited neon and argon dimer ions produces fragment ions with strikingly dissimilar kinetic-energy-release distributions. The distributions have been modeled based on ab initio calculations of potential energy curves. The unusual bimodal distribution observed for dissociation of Ne2+ arises from competition between radiative and nonradiative decay of the long-lived II(1/2)(u) state. For Ar2+, however, electronic predissociation is insignificant.