2Σ States Research Articles

Quantum Equation-of-Motion Method with Single, Double, and Triple Excitations.

The quantum equation-of-motion (qEOM) method with single and double excitations (qEOM-SD) has been proposed to study electronically excited states, but it fails to handle states dominated by double excitations. In this work, we reformulate the qEOM method within the effective Hamiltonian framework that satisfies the killer condition, and then present an efficient implementation incorporating single, double, and triple excitations. To reduce computational complexity, we employ point-group symmetry and perturbation theory to screen triple excitations, effectively reducing the scaling from No6Nv6 to No5Nv5, where No and Nv are the numbers of occupied and virtual spin orbitals, respectively. Furthermore, we account for the effect of neglected triple excitations by introducing a perturbative correction to the excitation energy. We apply this method to challenging cases where the qEOM-SD method exhibits significant errors, such as the 2 1Δ state of CH+ and the 2 1Σ state of HF. Our new method achieves energy errors below 0.18 eV while incorporating less than 8.2% of triple excitations. Additionally, we extend the operator screening technique to the quantum subspace expansion method for the efficient inclusion of selected triple excitations.

Reactive collisions between electrons and BeH+ above dissociation threshold.

Our previous studies of dissociative recombination and vibrational excitation/de-excitation of the BeH+ ion, based on the multichannel quantum defect theory, are extended to collision energies above the dissociation threshold, taking into account the vibrational continua of the BeH+ ion and, consequently, its dissociative excitation. We have also significantly increased the number of dissociative states of 2Π, 2Σ+ and 2Δ symmetry included in our cross section calculations, generating the most excited ones by using appropriate scaling laws. Our results are suitable for modeling the kinetics of BeH+ in edge fusion plasmas for collision energies up to 12 eV.

Accurate Ab Initio Investigation of Electronic and Radiative Properties, and Cross Sections for Charged Diatomic Systems FrLi+ and FrNa.

This paper presents an extensive ab initio investigation of the electronic properties and elastic collisions of charged diatomic systems FrLi+ and FrNa+. We employ an accurate ab initio approach using nonempirical pseudopotentials for Li+, Na+, and Fr+ cores. We calculate the potential energy curves of the ground state and low-lying excited states of 2Σ+, 2Π, and 2Δ symmetries, identifying and interpreting avoided crossings between higher 2Σ+ and 2Π states. The spectroscopic parameters, transition dipole moments, and vibrational energies associated with 1-32Σ+ states are calculated, along with the radiative lifetimes of the vibrational states trapped in the 22Σ+ state. Using accurate potential energy data, we evaluate partial and total cross sections across a wide range of energies. At low energies (<1 mK), the elastic cross section follows the Wigner law threshold comportment, while at high energies, it scales as E-1/3. To the best of our knowledge, no theoretical or experimental data have been collected on these charged diatomic systems until now. Hence, we proceeded to analyze our findings by comparing them with data acquired from comparable systems. The information pertaining to electronic structures, spectroscopic parameters, transition properties, and collision data provided in this work is expected to serve as a valuable guideline for future theoretical and experimental research on each considered system.

N–H collision integrals with study of repulsive interactions

Abstract Collision integrals are calculated and analyzed for the ground state nitrogen N ( S 4 ) and hydrogen H ( S 2 ) atoms involving the 3Σ and 5Σ electronic states in the temperature range of 1000–30 000 K. Influence of the quality of different known potential energy functions on the collision integrals was also studied and compared with the available data. Based on our analysis, the repulsive potential and its description beyond simple exponential also at small interatomic distances is necessary to obtain reliable collision integrals. Besides the ground state atoms, for the first time the collision integrals for excited nitrogen atoms (N ( D 2 ) and N ( P 2 ) ) with ground state hydrogen H ( S 2 ) were also calculated. The corresponding potential energy curves are also computed by using multireference configuration interaction (MRCI) method of electronic structure theory with aug-cc-pV6Z basis set. The resulting collision integrals were fitted to simple functional forms.

Low collision energy mutual neutralization reaction of He+ and H−

A Semi-classical Landau-Zener model is employed to theoretically study mutual neutralization in the collisions of 4He+ and H−/D−. The model includes ten covalent states and an ion-pair state of 2Σ+ symmetry for the HeH molecular system. Here the assumption is that only two states are interacting at a given internuclear position. In the diabatic representation, the nuclear dynamics relevant for mutual neutralization is modelled for collision energies below 100 eV. The mutual neutralization reaction cross section and final states distribution are computed and compared with previous theoretical and experimental results.

Photoionisation of the CH radical using the B-spline R-matrix method

Aims. The primary motivation for this paper is to provide accurate data for the photoionisation of the CH radical, including the absolute total photoionisation cross-section, partial cross-sections, and photoelectron angular distribution. In addition, the near threshold features in the photoionisation curve (which are absent in previous studies) are produced with high precision. Methods. A multichannel wavefunction based on the R-matrix approach, which uses the configuration interaction (CI) method to describe electronic correlation, is carried out in the present calculations. A set of B-spline orbitals is employed to represent the accurate continuum. The distinctive feature of the present calculations allows us to generate a more accurate description of the bound and continuum states than those employed before. Results. Total photoionisation cross-sections from the ground state of CH radicals and partial cross-sections corresponding to 1π, 3σ, and 2σ states of CH+ ions are presented for photon energies ranging from threshold to 80 eV. Extensive resonance structures, which are absent in previous studies, are observed for the first time near the ionisation threshold. The cross-section dataset obtained from the present calculations is expected to be sufficiently accurate and comprehensive for most current modelling applications involving the photon and CH radical scattering system.

Charge-Transfer-Induced Predissociation in Rydberg States of Molecular Cations: MgAr.

Very little is known about the Rydberg states of molecular cations, i.e., Rydberg states having a doubly charged ion core. With the example of MgAr+, we present general features of the structure and dynamics of the Rydberg states of molecular cations, which we find are subject to the process of charge-transfer-induced predissociation. Our study focuses on the spectrum of low-n Rydberg states with potential-energy functions associated with the Mg+(3d and 4s) + Ar(1S0) dissociation asymptotes. In particular, we have recorded spectra of the 3dπΩ′ (Ω′ = 1/2, 3/2) Rydberg states, extending from the lowest (v′ = 0) vibrational levels to their dissociation limits. This spectral range encompasses the region where the onset of predissociation by interaction with the mostly repulsive 2Σ and 2Π charge-transfer states associated with the Mg(3s2) + Ar+(2P1/2,3/2) dissociation asymptotes is observed. This interaction leads to very strong perturbations of the 3dπ Rydberg states of MgAr+, revealed by vibrational progressions exhibiting large and rapid variations of the vibrational intervals, line widths, and spin–orbit splittings. We attribute the anomalous sign and magnitude of the spin–orbit coupling constant of the 3dπ state to the interaction with a 2Π Rydberg state correlating to the Mg+(4p) + Ar(1S0) dissociation limit. To analyze our spectra and elucidate the underlying process of charge-transfer-induced predissociation, we implemented a model that allowed us to derive the potential-energy functions of the charge-transfer states and to quantitatively reproduce the experimental results. This analysis characterizes the main features of the dynamics of the Rydberg series converging to the ground state of MgAr2+. We expect that the results and analysis reported here are qualitatively valid for a broader range of singly charged molecular cations, which are inherently prone to charge-transfer interactions.

Positions and intensities of hyperfine components of all rovibrational dipole lines in the HD molecule

We report results of a theoretical analysis of hyperfine interactions in the HD molecule. We present the calculated coupling constants: spin-rotation, spin-spin and electric quadrupole coupling constants for all bound states of HD in its ground electronic 1Σ state. We provide a list of positions and intensities of 108 320 hyperfine components of 5 129 dipole transitions from the P and R branches. The positions and intensities of the hyperfine components are necessary for a proper interpretation of accurate measurements of rovibrational transition frequencies in HD which are used for tests of quantum electrodynamics of molecules and searches for new physics beyond the Standard Model.

Photodetachment in cold ion traps

We present a computational investigation of the photodetachment (PD) dynamics of C2H− in its ground, electronic 1Σ state, cooled in an ion trap with He as a buffer gas. Our analysis employs a range of PD rates from quantum dynamics, selective choices of the anion’s initial rotational state populations as the laser is switched on, and different operational trap conditions. Our results show that a variety of outcomes for the initial state-dependent PD process is possible by selecting different initial conditions in the cold trap, the latter generating a dynamical interplay between the anion’s populations of rotational states, induced by the buffer gas, and the chosen laser frequency and laser power. Specific parameter selections during the PD process will be shown to cause different abundances of the rotational states of the anion in the trap.Graphical abstract

Ab initio complex potential energy curves of the He*(1s2p1P)-Li dimer.

LiHe is an intriguing open-shell dimer. It is an extremely weakly bound system, and its vibrational bound-state radius extends far into the classically forbidden regions. Exciting helium into 1s2p leads to a 2Σ and a 2Π state, in which lithium is in its ground state. These states are located above the ionization threshold of the Li atom, which makes them metastable, i.e., resonance states. Under these conditions, energy transfer between the atoms over large distances is feasible within the framework of interatomic Coulombic decay (ICD). These states are investigated theoretically; herein, we present and analyze the complex potential energy curves of the 2Σ and 2Π states, where their imaginary parts describe the decay rate of these resonance states. We employ the resonance via Padé approach to calculate these potentials. Thereby, we use the equation-of-motion coupled-cluster method to compute stabilization graphs as input data for the analytical dilation (via Padé) into the complex energy plane. The procedure is suitable for studying Feshbach resonances and ICD states such as the LiHe 2Σ and 2Π states. The resulting ab initio complex potential energy curves will be used in future work to describe the dynamics of the process HeLi + hν → He*Li → HeLi+ + eICD, which is amenable to experiment.

Ultracold polar molecules as qudits

We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of 40Ca19F and 87Rb133Cs, which are examples of molecules with 2Σ and 1Σ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a four-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension d = 4 to perform the Deutsch algorithm.

Effect of isotropic collisions with neutral hydrogen on the polarization of the CN solar molecule

ABSTRACT In this work, we study the solar molecule CN, which presents conspicuous profiles of scattering polarization. We start by calculating accurate potential energy surfaces for the singlet and triplet electronic ground states in order to characterize the collisions between the CN molecule in its X 2Σ state and the hydrogen in its ground state 2S. The potential energy surfaces are included in the Schrödinger equation to obtain the scattering matrix and the probabilities of collisions. Depolarizing collisional rate coefficients are computed in the framework of the infinite order sudden approximation for temperatures ranging from T = 2000 K to T= 15 000 K. We give an interpretation of the results and compare the singlet and triplet collisional rate coefficients. We show that, for typical photospheric hydrogen density (nH = 1015−1016 cm−3), the X 2Σ state of CN is partially or completely depolarized by isotropic collisions.

MAVEN‐IUVS Observations of the CO2+ UV Doublet and CO Cameron Bands in the Martian Thermosphere: Aeronomy, Seasonal, and Latitudinal Distribution

AbstractWe analyze two Martian years of dayglow measurements of the CO Cameron bands and the CO2+ ultraviolet doublet (UVD) at 298–299 nm with the Imaging UltraViolet Spectrograph on board the Mars Atmosphere and Volatile EvolutioN (MAVEN) orbiter. We show that the altitude and the brightness of the two emissions peaks are strongly correlated, although data were collected over a wide range of latitudes and seasons. Averaged limb profiles are presented and compared with numerical simulations based on updated calculations of the production of the CO (a3Π) and the CO2+ (B 2Σ) states. The model simulations use the solar flux directly measured on board MAVEN with the Extreme Ultraviolet Monitor and the neutral densities provided by the Mars Climate Database version 5.3, adapted to the conditions of the observations. We show that the altitude and the shape of the sample limb profiles are well reproduced using the Mars Climate Database neutral atmosphere. The simulated peak intensities of the CO2+ UVD and Cameron bands are in good agreement considering the uncertainties on the excitation cross sections and the calibration of the Imaging Ultraviolet Spectrograph (IUVS) and Extreme Ultraviolet Monitor instruments. No significant adjustment of the electron impact cross section on CO2 to produce the a3Π state is needed. Seasonal‐latitudinal maps of the Cameron and UVD peak altitude observed during two Martian years show variations as large as 23 km. Model simulations of the amplitude of these changes are in fair agreement with the observations except during the southern summer dust period (Ls = 270–320°) when the calculated rise of the dayglow layer is underestimated.

A matrix isolation ESR investigation of Mg+-N2.

The adducts formed between 25Mg+ with 14N2 and 25Mg+ with 15N2 have been trapped in a solid neon matrix and studied with electron spin resonance (ESR) spectroscopy. These radical species were formed through the interaction of laser ablated magnesium and nitrogen gas. The Mg+-N2 radical species was found to have a ground electronic state of 2Σ+ in a linear configuration with discrete coupling to the proximate nitrogen resolved in the spectra. Fitting the ESR spectra allowed magnetic parameters to be determined as follows: g⊥ = 2.0012(5), g∥ = 2.0015(8), A⊥(1-14N) = 32(3) MHz, A∥(1-14N) = 34(5) MHz, A⊥(1-15N) = 45(4) MHz, A∥(1-15N) = 47(6) MHz, A⊥(25Mg) = -581(5) MHz, and A∥(25Mg) = -582(5) MHz, and estimates derived for A⊥(2-14N) = 1(2) MHz, A∥(2-14N) = 2(5) MHz, A⊥(2-15N) = 2(2) MHz, and A∥(2-15N) = 4(6) MHz. Ab initio calculations using the coupled-cluster single double triple methodology showed that the linear form was 59.7 kcal mol-1 more stable than the T-shaped form. The potential energy curve around the equilibrium geometry was explored using the complete active space self-consistent field approach, and Hartree-Fock singles and double configuration interaction and multireference singles and double configuration interaction calculations of the hyperfine coupling constants were undertaken, and reasonable agreement with the experiment was observed.

High resolution laser spectroscopy of the [13.8]0.5 – X2Δ3/2 and [14.2]1.5 – X2Δ3/2 transitions of hafnium monofluoride (HfF)

Laser-induced fluorescence (LIF) spectra of the (0, 0) and (1, 0) bands of the [13.8]0.5 – X2Δ3/2 and [14.2]1.5 – X2Δ3/2 transitions of HfF have been obtained at high resolution (∼120 MHz) using a laser ablation source. Spectra of all five isotopologues, from 180HfF to 176HfF have been clearly resolved and the two most abundant, 180HfF and 178HfF, were chosen for analysis. The rotational levels of the [13.8]0.5 state showed clear Ω – doubling closely resembling that of a 2Σ state in the v = 0 level. Irregularity in the doubling in the v = 1 level and in the isotope shift indicated a strong perturbation affecting this level. The final fit included all the previously analysed bands in the visible region and the doubling of all the Ω = 0.5 states and the isotope effect are examined and discussed.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 52S through 72S.

The excited state interatomic potential energy surfaces for Rb + He are computed at the spin-orbit multi-reference configuration interaction level of theory using all-electron basis sets of triple and quadruple-zeta quality that have been contracted for Douglas-Kroll-Hess (DKH) Hamiltonian and includes core-valence correlation. Davidson-Silver corrections (MRCI+Q) are employed to ameliorate size consistency error. An extrapolation of CASSCF energies is performed using the procedure of Karton and Martin whereas extrapolation of correlation energy is performed using an expression involving the inverse powers of (lmax + 1/2), the highest angular momentum value present in the basis set. The spin-orbit energies in the limit of complete basis set are obtained by replacing the energy eigenvalues in the spin-orbit matrix by the relativistic-corrected MRCI+Q energies extrapolated to the complete basis set limit. MRCI diabatic potential energy surfaces for a few selected 2Σ states are calculated to study the general topology and avoided crossings and repulsive form of the 6s 2Σ+ state. Important features of the potential energy surfaces are discussed with implications for alkali laser spectroscopy.

Radiative association of He(23P) with lithium cations: [formula omitted] processes

The radiative association processes originating in the 13Π continuum of the He (23P)+Li+ collisional system are investigated in this study. The calculations of the dynamic collision processes are based on highly accurate state-of-the-art ab initio calculations of the potential energy functions for the 13Π and the three lowest 3Σ states of HeLi+ and the associated transition dipole-moment functions. Cross-sections for the spontaneous and stimulated radiative association processes are calculated as functions of collision energy. The corresponding rate coefficients characterizing the efficiency of the formation of the molecular ion in its a3Σ+, b3Σ+, and c3Σ+ states from the initial 13Π state are obtained over a wide range of temperatures. At very low temperatures the 1→b process has a maximum rate-coefficient value of about 7.9×10−13cm3s−1, whereas process 1→a reaches its maximum value of 2.0×10−13cm3s−1 at a temperature of about 500K. Altogether the three radiative association processes investigated here can be considered as the continuum-to-bound state radiative transition part of the total quenching of the initial collision channel.

Quantum state-resolved molecular scattering of NO (2Π1/2) at the gas-[Cnmim][Tf2N] room temperature ionic liquid interface: Dependence on alkyl chain length, collision energy, and temperature

Room temperature ionic liquids (RTILs) represent a promising class of chemically tunable, low vapor pressure solvents with myriad kinetic applications that depend sensitively on the nature of gas-molecule interactions at the liquid surface. This paper reports on rovibronically inelastic dynamics at the gas-RTIL interface, colliding supersonically cooled hyperthermal molecular beams of NO (Π1/22, N = 0) from 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (or [Cnmim][Tf2N]) and probing the scattered NO molecules via laser induced fluorescence (LIF) from the A(2Σ) state. Specifically, inelastic energy transfer into NO rovibrational and electronic degrees of freedom is explored as a function of RTIL alkyl chain length (n), incident collision energy (Einc) and surface temperature (Ts). At low collision energies (Einc = 2.7(9) kcal/mol), the scattered NO molecules exhibit a rotational temperature (Trot) systematically colder than Ts for all chain lengths, which signals the presence of non-equilibrium dynamics in the desorption channel. At high collision energies (Einc = 20(2) kcal/mol), microscopic branching into trapping/desorption (TD) and impulsive scattering (IS) pathways is clearly evident, with the TD fraction (α) exhibiting a step-like increase between short (n = 2, 4) and long (n = 8, 12, 16) alkyl chains consistent with theoretical predictions. For all hydrocarbon chain lengths and RTIL temperature conditions, NO rotational excitation in the IS channel yields hyperthermal albeit Boltzmann-like distributions well described by a “temperature” (TIS = 900 -1200 K) that decreases systematically with increasing n. Non-adiabatic, collision induced hopping between ground and excited spin-orbit states is found to be independent of RTIL alkyl chain length and yet increase with collision energy. The scattering data confirm previous experimental reports of an enhanced presence of the alkyl tail at the gas-RTIL interface with increasing n, as well as provide support for theoretical predictions of an alkyl length dependent shift between chains oriented parallel vs. perpendicular to the surface normal.

Structure and electronic properties of the doubly charged diatomic dications BeX2+ (X = Na, K)

The structural and electronic properties of the doubly charged diatomic dications BeX2+ (X = Na, K) have been systematically investigated. The ab initio calculations method is based on the use of non-empirical pseudopotentials for the Be2+, Na+, and K+ cores, Gaussian basis sets, and parameterized l-dependent polarization potentials. The potential energy curves and their spectroscopic properties for the low-lying electronic states of 2Σ+, 2Π, and 2Δ symmetries have been determined for the species BeNa2+ and BeK2+ for the first time. Results show, for each diatomic dication, that the ground and the first excited electronic states are repulsive. For both systems, for which no experimental and theoretical data are available, we discuss our results by comparing their potential energies with similar systems. Numerous avoided crossings between electronic states of 2Σ+ and 2Π symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic structures Be(2+)X and Be(+)X(+). Furthermore, the transition dipole functions from the ground state to the 2-102Σ+ and between neighbor electronic states of 2Σ+ symmetry, revealed many abrupt changes, which are localized at particular distances corresponding to the positions of the avoided crossings.

A LABORATORY STUDY OF C 3 H + AND THE C 3 H RADICAL IN THREE NEW VIBRATIONALLY EXCITED 2 Σ STATES USING A PIN-HOLE NOZZLE DISCHARGE SOURCE

Rotational lines of the positive molecular ion C3H+ and of the neutral C3H radical in three new vibrationally excited states with 2Σ symmetry have been detected in a supersonic molecular beam in the centimeter-wave band. The fundamental rotational line of the ion is quite weak, but is observed with similar intensity in a dc discharge through several different hydrocarbon gases when helium is the buffer gas. Under these conditions, the fractional abundance of C3H+ relative to C3H is estimated to be of order 10−4, i.e., toward the lower end of the ratio (10−3–10−4) found for protonated ions using the same discharge nozzle. For each new 2Σ state of the C3H radical, spectroscopic constants, including those describing hydrogen hyperfine structure, have been determined to high precision. Lines of one 2Σ state (B = 11271 MHz) are particularly intense in our molecular beam; for this state and a second one (B = 11306 MHz), millimeter-wave transitions have also been observed between 180 and 340 GHz using a long path dc glow absorption spectrometer. On the basis of intensity measurements with this spectrometer, the inferred rotation–vibration constant α, and theoretical calculations, the state with B = 11271 MHz is tentatively assigned to the ν5 bending mode, predicted to lie ∼300 cm−1 above ground.