Theoretical study of low-lying electronic states and emission spectra of the excimer ions NaHe and NaNe

Ab initio CASSCF calculations using the Gaussian basis set aug_cc_pVTZ developed by Dunning et al. specifically for calculations at the post-HF level was carried out for excimer NaHe⁺ and NaNe⁺ ions in order to determine spectroscopic characteristics and radiation lifetimes of their low-lying excited electronic states. The computed emission spectra of these were shown to be in good agreement with the experimental ones observed recently by Hammer et al. (Hyperfine Interactions 88 (1994) 151). Contrary to the earlier popular opinion, all excited electronic states of these ions, correlating with the limit Rg⁺+Na, and not just the radiating singlet states turn out to be bound. It was shown that under the conditions of an experiment similar to the one performed by Hammer et al., the excited triplet NaHe⁺(1³Σ⁺) states can decay as a result of their interactions with a high-energy Ar⁺ beam. This decay has to be accompanied with the formation of the ions He⁺, which in turn can interact with sodium atoms to yield the radiating NaHe⁺(2¹Σ⁺) states again and, thus to maintain the emission observed in the experiment.     

Regio- and stereoselectivity in the Diels–Alder reaction of vinylallenes with acrolein: an ab initio study

To explore the regio- and stereoselectivity in Diels–Alder reactions of vinylallenes with acrolein, a parent vinylallene/acrolein system and a methyl-substituted vinylallene/acrolein system were studied. Ab initio calculations were used to identify eight transition state structures for each of the two Diels–Alder reactions at various computational levels (RHF/6-31G(d), RHF/6-311G(2d), B3LYP/6-311G(2d), and MP2/6-311G(2d)). The relative energies of the endo and exo transition states along with the regioselectivity have been determined from these calculations. In the parent vinylallene/acrolein system, the endo s-cis transition structure is the preferred stereoselectivity at all levels of theory, however, there is no regioselectivity. In the methyl substituted vinylallene/acrolein system, the endo s-trans transition state tends to compete with the endo s-cis transition state at the RHF levels of theory and is 1 kcal/mol more stable at the B3LYP/6-311G(2d) level of theory. Also, in the methyl-substituted system, there is now a definite preference for one regioisomer over the other. Both Diels–Alder reaction systems are asynchronous with the methyl-substituted system being more pronounced.     

All electron ab initio investigations of the electronic states of the MoN molecule

The low lying electronic states of the molecule MoN were investigated by performing all electron ab initio multi-configuration self-consistent-field (CASSCF) calculations. The relativistic corrections for the one electron Darwin contact term and the relativistic mass-velocity correction were determined in perturbation calculations. The electronic ground state is confirmed as being ⁴∑⁻. The chemical bond of MoN has a triple bond character because of the approximately fully occupied delocalized bonding π and σ orbitals. The spectroscopic constants for the ground state and ten excited states were derived. The excited doublet states ²∑⁻, ²Γ, ²Δ, and ²∑⁺ are found to be lower lying than the ⁴Π state that was investigated experimentally. Elaborate multi-configuration configuration-interaction (MRCI) calculations were carried out for the states ⁴∑⁻ and ⁴∏ using various basis sets. The spectroscopic constants for the ⁴∑⁻ ground state were determined as r_e=1.636 Å and ω_e=1109 cm⁻¹, and for the ⁴∏ state as r_e=1.662 Å and ω_e=941 cm⁻¹. The values for the ground state are in excellent agreement with available experimental data. The MoN molecule is polar with a charge transfer from Mo to N. The dipole moment was determined as 2.11 D in the ⁴∑⁻ state and as 4.60 D in the ⁴∏ state. These values agree well with the revised experimental values determined from molecular Stark spectroscopic measurements. The dissociation energy, D_e, is determined as 5.17 eV, and D₀ as 5.10 eV.     

Isomerism in OBe3F3 + cation: anab initio study

Ab initio MP2/6-31G^*//HF/6-31G^*+ZPE(HF/6-31G^*) calculations of the potential energy surface in the vicinity of stationary points and the pathways of intramolecular rearrangements between low-lying structures of the OBe₃F₃ ⁺ cation detected in the mass spectra of μ₄-Be₄O(CF₃COO)₆ were carried out. Ten stable isomers with di- and tricoordinate oxygen atoms were localized. The relative energies of six structures lie in the range 0–8 kcal mol⁻¹ and those of the remaining four structures lie in the range 20–40 kcal mol⁻¹. Two most favorable isomers, aC _2v isomer with a dicoordinate oxygen atom, planar six-membered cycle, and one terminal fluorine atom and a pyramidalC _3v isomer with a tricoordinate oxygen atom and three bridging fluorine atoms, are almost degenerate in energy. The barriers to rearrangements with the breaking of one fluorine bridge are no higher than 4 kcal mol⁻¹, except for the pyramidalC _3v isomer (∼16 kcal mol⁻¹). On the contrary, rearrangements with the breaking of the O−Be bond occur with overcoming of a high energy barrier (∼24 kcal mol⁻¹). A planarD _3h isomer with a tricoordinate oxygen atom and linear O−Be−H fragments was found to be the most favorable for the OBe₃H₃ ⁺ cation, a hydride analog of the OBe₃F₃ ⁺ ion; the energies of the remaining five isomers are more than 25 kcal mol⁻¹ higher. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 420–430, March, 1999.     

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

Problems of the electronic structure of nonmetals in a wide energy region of fundamental absorption (review)

The article surveys the main unsolved problems of the electronic structure of nonmetals in a wide energy region of fundamental absorption. Udmurtia State University, 71, Krasnogeroiskaya Str., Izhevsk, 426034, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 3, pp. 299–315, May–June, 1999.     

Classical Lattice-Gas Models of Quasicrystals

One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.     

Completeness Relation of Squeezed States in Squeezing Parametric Space Gained by Virtue of IWOP Technique

Using the newly developed technique of integration within an ordered product of operators, we prove that single-mode (or two-mode) squeezed states span a complete space in squeezing parametric space. The proof is concise and direct, and no further knowledge of SU(1,l) general coherent state theory is needed in our discussion.     

A three body approach to study the structural properties of 2-n halo nuclei and the search for Efimov states

The discovery of neutron rich isotopes of the lightest elements on the neutron drip line exhibiting a halo structure has opened up new vistas in research activities. The novel structural features associated with the halo phenomena have been the subject for extensive theoretical and experimental investigations in recent times. In this talk, I propose to present a broad overview of the recent developments in this field, bringing out the striking features which show that a large number oflight nuclei near the neutron drip line are characterized by a clear separation between a ‘normal’ core nucleus and a loosely bound low density veil of neutrons. Specifically, the two neutron halos offer a natural premises, from a theoretical standpoint, to employ three body techniques for studying their detailed structural properties. A considerable part of the talk will be devoted to report and highlight the results on a number of light halo nuclei such as ¹¹Li, ¹¹Be, ¹⁹B and ²²C on which we have been carrying out investigations employing a simple but realistic three body model. These three body systems which have been termed as ‘Borromean’ (i.e while three body systems are bound, the corresponding binary subsystems on the other hand are unbound) are characterized by large spacial extension and very low separation energy of the neutron. They are, therefore, ideally suited for exploring the possibility of the existence of Efimov states in two neutron halo nuclei. We have recently carried out the three body analyses to predict the possibility of the occurrence of such states on which experimental work at various laboratories is underway.     

量子态的概率克隆和认证

随机地选自一组非正交的量子态不可能通过幺正过程精确克隆。但是如果 幺正演化和选择性测量过程结合起来,则可以以一定的概率精确地克隆上述输入态,文章简述了概率克隆研究的最新进展,并同它和量子态认证之间的密切联系。