Theoretical Study of Triatomic Systems Involving Helium Atoms

The triatomic ⁴He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: ⁴He + ⁴He + ⁴He → ⁴ He₂ + ⁴He and ⁴He + ⁴He + ³He → ⁴He₂ + ³He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is ⁴He₂ X with X = ⁷Li, ²³Na, ³⁹K, ⁸⁵ Rb, and ¹³³Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as ⁴He + ⁴He + ⁷Li → ⁴ He₂ + ⁷Li and ⁴He + ⁴He + ⁷Li → ⁴ He⁷Li + ⁴He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.     

Calculation of diatomic molecules with the lctoc method. Excited states of some homonuclear molecules and ions

Calculations are performed, using a basis of two-center functions described previously, for excited states of the following three-and four-electron compounds: H₂ ^–, He₂ ⁺, He₂, Li₂ ⁺². High efficiency is demonstrated for the frozen ionic core approximation and the nonorthogonal orbital method in such calculations. For four-electron systems the practical feasibility of the frozen hybrid core approximation is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 53–56, August, 1987.     

Structure and dynamics of cationic van-der-Waals clusters

Ar_nHCl⁺ van-der-Waals clusters for n = 1–13 are investigated with the “minimal diatomics-in-molecules (DIM) model” using ab-initio input data obtained from multi-reference configuration-interaction calculations plus subsequent projection onto valence-bond wavefunctions. The results for the complexes with n = 1–3 are checked against ab-initio calculations at the coupled-cluster (CCSD) level with the same one-electron atomic basis set as for the input data generation (aug-cc-pVTZ from Dunning). In addition to the electronic ground state, the first excited ²A^￠^2\!A^{\prime} state for the triatomic complex (n = 1) is also studied. The results from the DIM model are shown to be in fair agreement with those from advanced conventional ab-initio calculations, although there are differences in detail. The comparison justifies the extension of the DIM approach to n > 3. Systematic analysis of the local minima of the multi-dimensional potential-energy surfaces (PESs), carried out with the combined method described in part I (Monte-Carlo sampling plus subsequent steepest-descent optimization), reveals simple building-up regularities for the most stable structures (i.e. those corresponding to the global PES minimum) at each n: apart from always having a nearly linear (Ar–H–Cl)⁺ fragment as core, the aggregates show little or no symmetry. Secondary local minima are also determined and their structures interpreted. The PESs for the low-lying excited states reveal a much more complicated topography compared to the Ar_nH⁺ clusters allowing a variety of photo-processes. The energy level sequence of the first five excited electronic states and the stability of the clusters in these states is studied as a function of the cluster size n.     

Structure and dynamics of cationic van-der-Waals clusters

Ar_nHCl⁺ van-der-Waals clusters for n = 1–13 are investigated with the “minimal diatomics-in-molecules (DIM) model” using ab-initio input data obtained from multi-reference configuration-interaction calculations plus subsequent projection onto valence-bond wavefunctions. The results for the complexes with n = 1–3 are checked against ab-initio calculations at the coupled-cluster (CCSD) level with the same one-electron atomic basis set as for the input data generation (aug-cc-pVTZ from Dunning). In addition to the electronic ground state, the first excited state for the triatomic complex (n = 1) is also studied. The results from the DIM model are shown to be in fair agreement with those from advanced conventional ab-initio calculations, although there are differences in detail. The comparison justifies the extension of the DIM approach to n > 3. Systematic analysis of the local minima of the multi-dimensional potential-energy surfaces (PESs), carried out with the combined method described in part I (Monte-Carlo sampling plus subsequent steepest-descent optimization), reveals simple building-up regularities for the most stable structures (i.e. those corresponding to the global PES minimum) at each n: apart from always having a nearly linear (Ar–H–Cl)⁺ fragment as core, the aggregates show little or no symmetry. Secondary local minima are also determined and their structures interpreted. The PESs for the low-lying excited states reveal a much more complicated topography compared to the Ar_nH⁺ clusters allowing a variety of photo-processes. The energy level sequence of the first five excited electronic states and the stability of the clusters in these states is studied as a function of the cluster size n.     

Profiling the binding motif between Be and Mg in the ground state via a single-reference coupled cluster method

We present a study on the performance of our iterative triples correction for the coupled cluster singles and doubles excitations (CCSDT-1a+d) method for computation of potential energy surface (PES), spectroscopic constants, and vibrational spectrum for the ground state (X¹Σ⁺) BeMg, where the ostensible inadequacy of the CCSD and CCSD(T) methods is quite expected. We compare our results with those obtained using state-of-the-art multireference configuration interaction (MRCI) investigations reported earlier by Kerkines and Nicolaides. Our estimated dissociation energy (417.37 cm^?1), equilibrium distance (3.285 Å), and vibrational frequency (82.32 cm^?1) are in good agreement with recent results of advanced MRCI calculations for X¹Σ⁺ BeMg PES, which exhibits a shallow well of 469.4 cm^?1 with a minimum at 3.241 Å and a harmonic vibrational frequency of 85.7 cm^?1. Very weakly bound nature of X¹Σ⁺ BeMg is clearly reflected from these values. In accord with MRCI studies, a comparison of BeMg with iso-valence weakly bound ground-state species, Be₂ and Mg₂, suggests that its characteristics do not exhibit any resemblance to Be₂ rather, it shows a close kinship to Mg₂. The agreement of our derived vibrational levels with those obtained via the high-level MRCI calculations is very encouraging reflecting the potential of the suitably modified single-reference coupled cluster (SRCC) method, CCSDT-1a+d as a tool for the study of multireference van der Waals systems.     

Theory of Isotope Effects on He+ Trapping in Solid Hydrogen

We are currently investigating the influence of vibrational effects on the strength of trapping of He⁺ in solid hydrogen. Such effects can lead to an isotope dependence of the trapping energy associated with the hydrogen molecules and He⁺ ion. At the present time, our focus is on the isotope effect for ³He⁺ and ⁴He⁺, which we are studying through the vibrational motions of the trapped He⁺ ions in the potential they experience as they move about their equilibrium positions. The potential governing the vibrations has been obtained from Hartree–Fock cluster calculations of the total energy of the cluster composed of the He⁺ ion and up to the third nearest neighbor hydrogen molecules as a function of the displacement of the He⁺ ion from its trapped position. The energy eigenvalues for the ground vibrational states of ³He⁺ and ⁴He⁺ in this potential come out as 1.29 and 0.96 meV, respectively, leading to corresponding reductions by these amounts in the binding energy of 8.6 eV for both ions without vibrational effects. The difference of these reductions can be considered as an isotope shift, its value for this case being 0.33 meV. From the analysis for these results, it is suggested that isotope shift effects for deuteron and triton in solid D–T would have the same order of magnitude. A procedure for more accurate investigations of the isotope shifts is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Does the Helium Trimer Have Bound Rotational States?

For the ⁴He₃ trimer, calculations predict two bound states with total angular momentum J = 0. This result gave rise to speculations that also bound states with J ≠ 0 might exist. Using the symmetry-adapted version of the adiabatic hyperradial approach (SAHA) we search for such bound states. Our conclusion is that ⁴He₃ has no bound rotationally excited states. This revised version was published online in August 2006 with corrections to the Cover Date.     

A variational method for the calculation of spin-rovibronic energy levels of triatomic molecules with three interacting electronic states

A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C₂H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 1²A'(X²Σ⁺), 2²A'(A²Π), 1²A''(A²Π) electronic states of C₂H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm¹.     

Quartet states of He+ 2

The low lying quartet spectrum of the molecular helium cation is investigated by configuration interaction calculations. Using large Gaussian basis sets, potential energy curves for n ⁴Σ⁺ _u,g and n ⁴Π_u,g are computed for the states n = 1,…, 5. Several of these states lead to equilibrium configurations having rather extended bond lengths and some of them also a relatively large dissociation energy. The spectroscopic properties of these equilibrium configurations are studied. Quartet He⁺ ₂ is most strongly bound in its lowest state 1 ⁴Σ_u with R _e = 3.424 Å and D _e = 1.348 eV.     

Metastable helium cluster He<Stack><Subscript>4</Subscript><Superscript>*</Superscript></Stack>

The existence of a metastable cluster He ₄ ^* with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He ₂ ^* molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He ₄ ^* system on the distance between the He ₂ ^* triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He ₂ ^* molecules is in the ³Σ _u ⁺ state, while the other is in the ³Π_g state. The radiation lifetime τ of the metastable cluster He ₄ ^* is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He ₂ ^* (³Σ _u ⁺ ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy E_acc ≈ 9 eV/atom accumulated in the He ₄ ^* cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He ₄ ^* cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).     

X-ray absorption near edge structure (XANES) for KCl

The cluster calculations of K and L_2,3 edge XANES of K and Cl in KCl within the multiple scattering theory formalism using nonlocal HF potentials with abd without consideration of core hole field were performed. For K spectra the influence of the core hole potential is rather weak and the results are similar to those obtained with Xα potentials. For L_2,3 spectra, particularly for that of K⁺, core hole field leads to a radical redistribution of oscillator strength caused mainly by the spatial rearrangement of d like states. Calculated XANES curves show good over-all agreement with the experimental spectra (the L_2,3 absorption of K⁺ in KCl was measured using the synchrotron radiation of the USSR Academy of Sciences storage ring VEPP-2M in Novosibirsk).     

Theoretical study of charge-exchange and excitation processes in collisions of He<Superscript>+</Superscript> ions with C<Superscript>5+</Superscript>, N<Superscript>6+</Superscript>, and O<Superscript>7+</Superscript> hydrogen-like ions

Data on the cross sections for single-electron charge exchange and excitation in collisions of He⁺ ions with C⁵⁺, N⁶⁺, and O⁷⁺ ions in the He⁺ ion energy range of 0.2–3.0 MeV are obtained for the first time. The cross sections for the single-electron charge transfer into the singlet and triplet 1snl states of C⁴⁺, N⁵⁺, and O⁶⁺ (2≤n≤5) ions and for the 1s → 2p _{0, ±1} electronic excitation of He⁺(1s) ions are calculated. The calculations were performed by solving close-coupling equations on the basis of ten two-electron quasi-molecular states.     

The reactions of Cl+ (3P) and Cl+ (1D) with hydrogen sulphide. A G2 molecular orbital study

G2 ab initio molecular orbital calculations have been performed to study the potential energy surfaces (PESs) associated with the reactions of Cl⁺ in its ³P ground state and in its ¹D first excited state with hydrogen sulphide. [H₂, Cl, S]⁺ singlet and triplet state cations present very different bonding characteristics. The latter are systematically ion-dipole or hydrogen-bonded weakly bound species, while the former are covalent molecular ions. As a consequence, although the Cl⁺(³P) is 34.5 kcal mol^?1 more stable than Cl⁺(¹D), the global minimum of the singlet PES lies 37.3 kcal mol^?1 below the global minimum of the triplet PES. Both singlet and triplet potential energy surfaces show significant differences with respect to those associated with Cl⁺ + H₂O reactions as well as with SH₂ reactions with F⁺. In both cases, the major product should be SH⁺ ₂; SH⁺ and HCl⁺ being the minor products, in agreement with the experimental evidence. The estimated heat of formation for the most stable H₂SCl⁺ singlet state species is 198 ± 1 kcal mol^?1.     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.     

Exit angle dependence of charge-state distribution of backscattered He ions

Exit angle and energy dependences of the charge-state distribution of backscattered He ions were investigated when 500 keV He⁺ ions were incident on SiO₂. The energy dependence of the He⁺ fraction was estimated by comparing the measured He⁺ spectra with the simulated spectra of He ions in all charge states at the exit angles of 5-25° with respect to the SiO₂ surface. We found that the He⁺ fraction is almost independent of the exit angle at energies higher than 250 keV and the observed energy dependence of the He⁺ fraction is in good agreement with that for the carbon-foil-transmission experiment. In the low energy region (<250 keV), however, the He⁺ fraction decreases as the exit angle decreases.     

Multi-reference coupled-cluster study of the ionic-neutral curve crossing LiF

The recently developed exponential multi-reference wavefunction ansatz [J. Chem. Phys. 123 (2005) 84102] and the single-reference formalism multi-reference coupled cluster ansatz [J. Chem. Phys. 94 (1991) 1229] are applied to calculate the potential energy surface of LiF. The avoided crossing region for the ionic and the covalent ¹Σ⁺ states are analysed using plain self-consistent field and state averaged complete active space orbitals. Additionally, dipole moments are reported. All results are discussed and compared with full and multi-reference configuration interaction calculations.     

Charged cores in ionized $\mathsf{{^{4}He}}$ clusters III: A quantum modeling for the collisional relaxation dynamics

When a pure ⁴He droplet is ionized by electron impact, the most abundant fragment detected in mass spectra after ionization is He₂ ⁺ . All the models that have been proposed thus far to explain the experimental evidence therefore involve the formation of the He₂ ⁺ molecular ion. The understanding of the interactions between this ion and the surrounding He atoms in the cluster and of their dynamical behavior during cluster break-up is an important element for the modeling of the cluster evolution after the ionization event. In previous works [1,2] we have computed and described the Potential Energy Surface (PES) of the electronic ground state for the He₃ ⁺ system that provides the required forces between He₂ ⁺ and He. After ionization He₂ ⁺ is presumably formed by association of an He ⁺ and any of the neutral atoms in the cluster via a 3-body collision process. The ensuing vibrational quenching of the hot molecular ion may release the energy necessary to evaporate the entire droplet, or most of it, and give the fragmentation patterns detected by experiments. We present here a model quantum dynamics that generates vibrational deexcitation cross-sections and the corresponding rate coefficients for the collision of He₂ ⁺ with He. A timescale of the cluster evaporation due to vibrational relaxation is estimated and the present findings are compared with earlier studies on the same system.Received: 15 June 2004, Published online: 24 August 2004PACS: 31.15.Qg Molecular dynamics and other numerical methods - 34.50.Ez Rotational and vibrational energy transfer - 36.40.Wa Charged clusters     

Electronic and vibrational spectroscopy of the low-lying states of potassium mono-sulphide KS,and comparison in the series of MS (M = Li,Na, K,Rb, Cs)

ABSTRACT

Potential energy curves (PECs) of the lowest electronic states of the potassium mono-sulphide KS have been determined with highly correlated ab initio calculations, using internally contracted multi reference interaction configuration methods including Davidson correction (MRCI?+?Q) with and without considering spin-orbit effects. For the three low-lying bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. An analysis of the properties of the three bound states, X²Π, 1²Σ⁺ and 2²Π, illustrates the common characteristics of the whole series of compounds in the MS family (M?=?Li, Na, K, Rb, Cs). Indeed, the shapes of the PECs of these bound states are strongly affected by the interactions between the two ionic states, ²Σ⁺ and ²Π, correlating at large internuclear separations (R_MS) to the first ionic dissociation limit [M⁺?+?S^?] and the electronic states correlating to the three/four lowest dissociation limits. The spectroscopy of these low-lying electronic states and the lifetime of their vibrational levels are thus affected by the spin-orbit interactions which are mainly related to the S atom and consequently common to all alkali-metal mono-sulphides.     

The ion-molecule reaction O+ (4S) + N2(X1Σ+) → NO+ (X1Σ +, v′) + N(4S) and the predissociation of the A2Σ+ and B2Π states of N2O+

The potential energy surfaces (PESs) for several electronic states involved in the reaction O⁺ (⁴S) + N₂(X¹Σ⁺) → NO⁺ (X¹Σ ⁺, v′) + N(⁴S) and the role of the ionic N₂O⁺ intermediate have been investigated by ab initio calculations. The ⁴A″ PES, which correlates with the ground state educts, has a barrier of about 1 eV, and therefore at low collision energies the reaction cannot take place adiabatically on this surface. However, the spin-orbit coupling in the entrance channel allows the system to pass into the Renner-Teller system of the X² Π electronic ground state of the N₂O⁺ intermediate. The reaction then proceeds on these surfaces up to the region in the exit channel where a similar coupling allows it to reach the product quartet asymptote. At collision energies higher than about 1 eV, the reaction proceeds mainly on the adiabatic PES of the ⁴A″ state. The A²Σ⁺ state of N₂O⁺ predissociates via a vibronic coupling with the B²Π state, and in bent structures via a spin-orbit coupling with the ⁴A″ component of the ⁴II state. The electronic structure of the B²Π state is found to be of crucial importance for the understanding of the reactive processes in low lying electronic states of N₂O⁺.