Ro-vibrating energy states of a diatomic molecule in an empirical potential

An approximate analytical solution of the Schrödinger equation is obtained to represent the rotational–vibrational (ro-vibrating) motion of a diatomic molecule. The ro-vibrating energy states arise from a systematical solution of the Schrödinger equation for an empirical potential (EP) V _±(r) = D _e {1 ? (?/δ)[coth (ηr)]^±1/1 ? (?/δ)}² are determined by means of a mathematical method so-called the Nikiforov–Uvarov (NU). The effect of the potential parameters on the ro-vibrating energy states is discussed in several values of the vibrational and rotational quantum numbers. Moreover, the validity of the method is tested with previous models called the semiclassical (SC) procedure and the quantum mechanical (QM) method. The obtained results are applied to the molecules H₂ and Ar₂.     

Exact solutions and spectrum analysis of a noncentral potential in the presence of vector potential

We studied exact solutions and spectrum analysis of the pseudoharmonic oscillator in the presence of θ-dependent scalar potential and the sum of two vector potentials Dirac magnetic monopole and Aharonov-Bohm field. The effect of the Dirac magnetic monopole (g), Aharonov-Bohm field (ℱ) , the dissociation energy of diatomic molecules (D _e), equilibrium intermolecular separation (r _e), and the reduced mass (μ) on the energy spectrum for some diatomic molecules (CO, NO, N₂, CH, H₂, and ScH) are analyzed. We compared our results with theoretical experiments of pseudoharmonic oscillator potential in a molecular system.     

Calculation of bond dissociation energies of diatomic molecules using bond function basis sets with counterpoise corrections

Bond function basis sets combined with the counterpoise procedure are used to calculate the molecular dissociation energies D_e of 24 diatomic molecules and ions. The calculated values of D_e are compared to those without bond functions and/or counterpoise corrections. The equilibrium bond lengths r_e and harmonic frequencies o_e are also calculated for a few selected molecules. The calculations at the fourth-order Møller-Plesset approximation (MP 4) have consistently recovered about 95–99% of the experimental values for D_e; compared to as low as 75% without use of bond functions. The calculated values of r_e are typically 0.01 Å larger than the experimental values, and the calculated values of o_e are over 95% of the experimental values. © 1996 John Wiley & Sons, Inc.     

Autoionizing rydberg states of. The Li2 molecule: Molecular constants for Li2+

Autoionizing Rydberg series of Li₂ have been observed in the two-step optical cxcitation of a supersonic lithium beam. The series limits are vibrational states of Li₂⁺. In the most probable assignment IP(Li₂) = 41236.4 ± 2.5 cm^?1 and for Li₂⁺ω_e = 263.45 ± 1.3 cm^?1; ω_eχ_e = 1.35 ± O.2 cm^?1; r_e = 3.032 ± 0.01 Å; D_e = 10807 ± 150 cm^?1.     

Electronic structure and bonding of Be2

Laser-induced fluorescence of Be₂ produced by laser vaporization of the metal is observed and analyzed. The X¹Σ_g⁺ ground state is characterized by r_e = 2.45 A and D_e = 790 ± 30 cm^?1. The spectroscopic constants and lifetimes of the much more strongly bound A ¹Πu and B ¹Σ_g⁺ states are also obtained. The Be₂ molecular properties and bonding are discussed and compared with related species.     

Exact solutions of the Schr?dinger equation for the pseudoharmonic potential: an application to some diatomic molecules

For arbitrary values n and ? quantum numbers, we present the solutions of the 3-dimensional Schr?dinger wave equation with the pseudoharmonic potential via the SU(1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r ² and ${r\frac{d}{dr}}$ are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the Hellmann–Feynman theorem, the expectation values of r ² and p ² are obtained. The energy states, the expectation values of r ² and p ² and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O₂, N₂, CH, H₂, ScH) for arbitrary values of n and ? quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.     

Molecular structure of SmBr<Subscript>3</Subscript> and DyBr<Subscript>3</Subscript> according to the data of simultaneous electron diffraction and mass spectrometric experiment

The saturated vapors of samarium and dysprosium tribromides were investigated for the first time by electron diffraction with mass spectrometric monitoring at temperatures of 1151(10) K and 1141(10) K. Dimer molecules (up to 2 mole %) were found in vapors along with monomer molecules. The SmBr₃ and DyBr₃ molecules have a pyramidal effective configuration with bond angles ∠_gBr-Sm-Br=115.1(9)° and ∠_gBr-Dy-Br=115.3(7)°. The difference between the internuclear distances of SmBr₃ and DyBr₃ (r _g(Sm-Br) = 2.653(6) Å and r _g(Dy-Br) = 2.609(5) Å) coincides with the difference between the ionic radii of Sm³⁺ and Dy³⁺. The insignificant pyramidality of the r _g configuration and the low deformation vibration frequencies of SmBr₃ and DyBr₃ may be indicative of a planar equilibrium geometry of D _3h symmetry. The equilibrium distances r _e(Sm-Br) and r _e(Dy-Br) have been evaluated and compared with the values obtained by quantum chemical calculations.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Binding Matter with Antimatter: The Covalent Positron Bond

We report sufficient theoretical evidence of the energy stability of the e⁺?H₂^2? molecule, formed by two H^? anions and one positron. Analysis of the electronic and positronic densities of the latter compound undoubtedly points out the formation of a positronic covalent bond between the otherwise repelling hydride anions. The lower limit for the bonding energy of the e⁺?H₂^2? molecule is 74 kJ mol^?1 (0.77 eV), accounting for the zero‐point vibrational correction. The formation of a non electronic covalent bond is fundamentally distinct from positron attachment to stable molecules, as the latter process is characterized by a positron affinity, analogous to the electron affinity.     

Negative ion photoelectron spectroscopy of teo−

We have recorded the photoelectron spectrum of Te0⁻ using a hot-cathode discharge ion source and a negative ion photoelectron spectrometer. The adiabatic electron affinity of TeO is determined to be 1.697±0.022 eV. The negative ion parameters determined in this work are: (w_e″(TeO⁻) = 690 ± 80 cm⁻¹, r_e″(TeO⁻) = 1.884 ± 0.028 Å. and D_o     

A new method of calculation of the melting temperatures of crystals of Group 1A metal halides and francium metal

A new method of calculation of melting temperatures of binary ionic crystals has been suggested. The method is based on finding a matrix relation between the ionic radii (the lattice energy U) and melting temperature of ionic crystals of the MX type, where M is a Group 1A metal, and X is a halogen. From the equation for the lattice energy U, a new equation has been derived for calculation of the melting temperature of ionic crystals with the use of only the ionic radii and the degree of bond ionicity ?: T _m = f(U, ?). The average error of determination of T _m for alkali-metal halides is 2.80%. The melting temperatures of francium halides and alkali-metal astatides (including FrAt) have been calculated. It has been shown that the accuracy of calculation of the melting temperature of ionic crystals depends on the degree of bond ionicity: the error increases with an increase in the covalent contribution. On the basis of the melting temperatures of metal halide crystals, a method has been developed for the calculation of the melting temperatures of corresponding metals. The melting temperature of francium has been calculated to be 24.861 ± 0.517°C.     

Nature of closed‐ and open‐shell interactions between noble metals and rare gas atoms

Interactions between noble metals and rare gases have become an interesting topic over the last few years. In this work, a computational study of the open‐shell (d¹⁰s¹) and closed‐shell (d¹⁰s and d¹⁰s²) noble metals (M = Cu, Ag, and Au) with three heaviest rare gas atoms (Rg = Kr, Xe, and Rn) has been performed. Potential energy curves based on ab initio [MP2, MP4, QCISD, and CCSD(T)] and DFT functionals (M06‐2X and CAM‐B3LYP) were obtained for ionic and neutral AuXe complexes. Dissociation energies indicate that neutral metals have the lowest and cationic metals have the highest affinities for interaction with rare gas atoms. For the same metals, there is a continuous increase in dissociation energies (D_e) from Kr to Rn. The nature of bonding and the trend of D_e and equilibrium bond lengths (R_e) have been interpreted by means of quantum theory of atoms in molecules, natural bond orbital, and energy decomposition analysis. © 2013 Wiley Periodicals, Inc.     

Self-consistent molecular hartree—fock—slater calculations. IV. On electron densities,spectroscopic constants and proton affinities of some small molecules

The use of the Xα exchange approximation in calculations on small molecules is studied. Electron densities are very similar to Hartree—Fock densities, as judged from density difference maps. The statistical total energy, E_Xα, is used in order to calculate R_eB_e, ω₃ and D_e of a series of diatomic molecules. The agreement with experiment is again similar to that in Hartree—Fock calculations. Proton affinities can also be calculated very well. The Hartree—Fock—Slater and Hartree—Fock models show on the whole very analogous behaviour. These results are obtained by using accurate, unapproximated, potentials and densities.     

Gas phase high temperature photoelectron spectroscopy: The tin monoxide molecule

The HeI photoelectron spectrum of SnO (X¹Σ⁺) has been recorded. Two bands have been observed corresponding to ionization from the 6π and 13 ionization energies of 9.98 and 10.12 eV respectively. Vibrational structure associated with the first band has been analysed to give

and D_e = 3.23 ± 0.10 eV in the SnO⁺ (X²Π) state. An assessment has been made of the ability of Hartree-Fock-Slater calculations, multiple-scattering SCF-Xα calculations and ab ini energies for the group IV diatomic monoxide molecules.     

Bonding in heteronuclear transition-metal diatomics: NbIr

Bonding in transition-metal molecules presents novel features: (i) s electron bonding is overcome by multiple d electron bonding, (ii) intraatomic exchange favoring atomic magnetization competes with bonding that tends to pair the electrons, and (iii) in the heteronuclear dimers, the ionic terms may be important due to strong charge-transfer effects. The NbIr heteronuclear diatomic molecule shows all these features clearly. The cellular multiple scattering-x_αβ calculation presented in this paper shows the ground state to correspond to antiferromagnetic coupling between the highly magnetic Nb atom and the Ir atom. A one-electron charge transfer from Nb to Ir was found; the result is an ionic structure, Nb⁺Ir^?, for the dimer. The computed equilibrium distance, 4.100 a.u., corresponds to a region where d bonding strongly overcomes the s bonding, which alone would have stabilized the molecule at 5.950 a.u. At intermediate interatomic separations, 5.35 a.u., the NbIr system has a state in which all molecular orbitals are bonding with a high hybridization between the ns and (n ? 1)d electrons of each atom, resulting in a (almost entirely) covalent high multiple-bond formation for this meta-stable state of the dimer.     

A comparison of variational and non-variational internally contracted multiconfiguration-reference configuration interaction calculations

Summary The internally contracted multiconfiguration-reference configuration interaction (CMRCI) method and several non-variational variants of this method (averaged coupled pair approximation (ACPF), quasidegenerate variational perturbation theory (QD-VPT), linearized coupled pair many electron theory (LCPMET)) have been employed to compute potential energy functions and other properties for a number of diatomic molecules (F₂, O₂, N₂, CN, CO) using large basis sets and full valence CASSCF reference wavefunctions. In most cases the variational CMRCI wavefunctions yield more accurate spectroscopic constants than any of the employed non-variational methods. Several basis sets are compared for the N₂ molecule. It is found that atomic natural orbital (ANO) contractions led to significant errors in the computedr _e , _e , andD _e values.     

Large electron correlation effect leading to BeBe bond

The bonding of the beryllium diatomic molecule (Be₂) in the ground state is exclusively made from the electron correlation effect. Unlike the ordinary van der Waals bond, where the electron correlation of the dispersion type makes weak bond energy (D_e) at large bond distance (R_e), the BeBe bond is surprisingly strong with D_e = 830 cm^?1 and R_e = 245 pm. This paper presents in an analytical way the different electron correlation effects with the corresponding spectroscopic data.     

The structure of bis(1,1,1,5.5,5-hexafluoro-2,4. pentadionato) copper(II) as determined by gas phase electron diffraction

The r_g structure of bis(1,1,1,5,5,5-hexafluoroacetylacetonato) copper(II) has been determined by gas phase electron diffraction. The experimental data were found to be consistent with a D_2h model in which the oxygens from the two ligands are arranged in an essentially square planar configuration about the copper atom (∠OCuO = 90.6° ± 1.2°). It was possible to obtain a precise value for the copper oxygen bond length, r_g = 1.919 ± 0.008 Å, since this distance appeared as an isolated peak in the radial distribution curve. Structural parameters for the ligand (r_g(C-O) = 1.276 ± 0.009 Å, r_g(C-C_ring) = 1.392 ± 0.015 Å, r_g(C-CF₃)= 1.558 ± 0.009 Å and r_g(C-F) = 1.339 ± 0.003 Å), while less precisely determined are, nevertheless, consistent with reported values for related molecules. A model for the rotational isomerism of the four CF₃ groups was invoked in order to explain various features in the radial distribution curve in a region from 2.5 to 5.5 Å.     

The nature of the bonding of Li+ to H2O and NH3; A3 initio studies

Ab initio wavefunctions have been calculated for the complex of Li⁺ with NH₃ and H₂O in order to better characterize the nature of the bonding. Hartree—Fock and generalized valence bond calculations were performed using a double zeta basis plus polarization functions. The binding energies obtained at the GVB level are D_e (Li⁺ — NH₃) = 40.4 kcal/mol and D_e (Li⁺ ? H₂O) = 37.6 kcal/mol, in reasonable agreement with experimental values. Model calculations indicate that the Li⁺ ? base bond is basically electrostatic. Small basis sets were found to lead to D_e as large as 75 kcal/mol for Li⁺ — NH₃, a significant overestimation. Repulsions due to the Li⁺ core are responsible for keeping the Li⁺ too far away for significant relaxation effects.