On Λ-type doubling in multiplet states of diatomic molecules

Explicit expressions valid in the neighborhood of Hund's case (a) and (b) are obtained for the width of Λ-type doubling of multiplet Π terms up to septet multiplicity. Moreover, a relation between the constants occurring in the expressions of Hund's cases (a) and (b) is given.     

On the Zeeman effect in electronic transitions of diatomic molecules

The Zeeman effect for diatomic molecules is calculated in a representation with Hund's case (a) wave functions as a basis set. The resulting expressions are simpler and easier to handle than those obtained from previous calculations on the basis of cace (b) wave functions. The calculations of intensities and polarization of Zeeman patterns is presented for transitions between doublet states with arbitrary spin-orbit (if Λ≠ 0) or spin-rotation (if Λ = 0) interaction, and for case (a)-case (a) transitions of any multiplicity. These calculations are in good agreement with observations.     

Approximate spectral absorption coefficients of electronic transitions in diatomic molecules

Spectral absorption coefficients for electronic transitions in diatomic molecules have been calculated for a total of 50 transitions in 23 different molecules. The calculation is based on a “smeared” line model of individual vibrational bands and an anharmonic-oscillator semi-rigid rotator model for the vibrational-rotational energies. Improvements over similar calculations include the use of explicit band head positions and the effect of reversed bands. Comparison of the results of the smeared line model calculations based on (1) a perturbed harmonic oscillator potential for the NO-γ band system and (2) a Rydberg-Klein-Rees potential for the CN-Red band system have been made and show excellent agreement.     

Vibration-rotational matrix elements for infrared transitions of diatomic molecules

Theoretical expressions for the vibro-rotational matrix elements corresponding to i.r. transitions vJ→v′J′ with v ⩽ v ′ ⩽ v + 6 are obtained in terms of quadratic polynomials in m, including contributions from the Dunham potential energy parameters a₁ to a₅ and from dipole-moment expansion coefficients M₀ to M₇. The formalism has been applied to vibrational transitions in the ground electronic state of CO and HCl. The Herman-Wallis coefficients have been derived for the bands 0-0 to 0-4 of CO and 0-0 to 0-6 of HCl and are compared with experimental data.     

Approximate spectral absorption coefficients for pure rotational transitions in diatomic molecules

Approximate spectral absorption coefficients for the pure rotational spectra of diatomic molecules have been computed by using (a) the “just-overlapping line” model, and (b) a model involving smearing of the rotational structure. As has been shown previously for the infrared vibration-rotation spectra and for the electronic band spectra, the two models yield effectively identical results. Numerical data are presented for OH, CO, NO, HCl, HBr, and HF.     

Systematics of vibrational intensities for “diatomic” molecules: Approximate formulas

Several approximations are discussed which enable one to estimate electric dipole moment transition matrix elements for diatomic molecules based on a very limited amount of experimental data. For strongly polar molecules, a simplistic point-charge dipole model in which there is no vibrational charge flux predicts a simple relation between the permanent moment, M₀, and its derivative with respect to internuclear separation, M₁. This is found to be approximately valid for a surprisingly large number of polar molecules. Next, approximate matrix elements for the fundamental and overtone bands are presented for a linear dipole moment function. Finally, systematic trends for molecules having similar electronic structures are investigated and combined with the approximations discussed above in order to estimate the transition moments for several molecules of astrophysical interest. An extension to the ν₃ fundamental and overtone bands of CH₄ is suggestive that some of these ideas may be applicable to certain polyatomic molecules as well.     

Induced radiative transitions of intermediate molecules in heavy ion collisions

Three types of transitions exists in intermediate molecules occuring in heavy ion scattering: spontaneous radiative, induced non-radiative, and induced radiative decay. The latter ones yield an asymmetric angular distribution for molecular X-rays with respect to the ion-beam axis. The experimental verification of this effect would furnish an experimentum crucis for both, the existence of molecular X-rays and the induced radiative transitions.     

Forbidden transitions in homopolar isotopically unsymmetric diatomic molecules and the dipole moment of HD

The theoretical expressions for the intensities of forbidden rotational and rotation-vibration spectra of homopolar isotopically unsymmetric diatomic molecules, made allowed by the breakdown of the Born-Oppenheimer approximation, are derived. The results are applied to HD and it is shown that among the previously overlooked contributions to the dipole moment of the molecule there is one with a very significant value in the direction H^?D⁺. A rotationally dependent contribution arising from centrifugal distortion is extremely small. The intensities of the fundamental and overtone bands of HD are also considered.     

Multilevel rotational transitions in the intermediate stage of three-photon ionization of molecules

Ionization and dissociation of diatomic molecules induced by a weak field (after preliminarily populating an intermediate level) and by intense, linearly polarized monochromatic radiation have been studied. Field-induced mixing of rotational components of various electronic-vibrational states of molecules (such as CO, NO, etc.) at field strength f∼10⁻⁴–10⁻⁵ atomic units can lead to migration among states with different angular momenta J. Therefore, ions with rotational momenta J ⁺ much higher than those prescribed by selection rules for three-photon absorption can be formed from molecules in the ground state. The possibility of selective formation of ions with J ⁺≫1 and zero projection of the angular momentum on the polarization vector of the external electromagnetic radiation has been investigated. Zh. éksp. Teor. Fiz. 111, 1624–1632 (May 1997)     

Asymptotic neutrality of diatomic molecules

We use the no-binding theorem of Thomas-Fermi theory to prove that a large diatomic molecule is almost neutral. That is to say, that if the total nuclear charge isZ then the numberN of electrons required for the diatomic molecule to be stable satisfies . In contrast to the atomic case the emphasis here is on the lower bound onN. Our analysis will imply a new bound on the size of the molecule. These results are proved in the Born-Oppenheimer approximation. We also give bounds onN which hold for allZ by a very elementary method, not assuming the Born-Oppenheimer approximation.Work supported by a Danish Research Academy fellowship and U.S. National Science Foundation grant PHY-85-15288-A03Adress from September 1989: Department of Mathematics, The University of Michigan, Ann Arbor, Michigan 48109 USA     

Dissociation energy of diatomic molecules

The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D _e[[1−exp{−b(r−r _e)}]/ [1−Cexp{−b(r−r _e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD _e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω _ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.     

Critical binding of diatomic molecules

The behaviour of two bodies that are just bound or nearly bound is discussed. A class of potentials is given for which Schrödinger's equation has exact solutions at critical binding (zero binding energy). This class includes the known solution for the 6–10 potential. For a general potential characterized by a coupling parameter α, it is shown that the bound state energy tends to zero as -(α - α₀)², where α₀ is the critical value of the coupling parameter. Small energy scattering of atoms which are near critical binding (e.g. helium atoms) is examined. It is shown that determination of the total cross-section up to terms of order k ² is in principle sufficient to distinguish between bound and virtual states of the diatomic molecule.     

Sticking probability of diatomic molecules

The problem of destruction of a negative ion in a slow collision with a metallic surface is considered. It is shown that the electron exchange between the atomic and metallic potential wells is the most important destruction mechanism for the negative ions. The electron transition probability of this process is calculated by a method which provides asymptotically exact result.     

Dissociation energy of diatomic molecules

We propose a modified potential energy function that is as easily used as the Hulburt-Hirschfelder (H-H) function. Dissociation energies have been estimated for MgO, CaO, and SrO and other molecules.     

Nuclear spin conversion in diatomic molecules

A mechanism of the internal interaction in dimers that mixes different nuclear spin modifications has been proposed. It has been shown that the intramolecular current associated with transitions between electronic terms of different parities can generate different magnetic fields on nuclei, leading to transitions between spin modifications and to the corresponding changes in rotational states. In the framework of the known quantum relaxation process, this interaction initiates irreversible conversion of nuclear spin modifications. The estimated conversion rate for nitrogen at atmospheric pressure is quite high (10^?3–10^?5 s^?1).     

Matrix elements for the vibrational transitions 0 → 0 to 0 → 7 of diatomic molecules

The vibrational matrix elements, including sixth-order contributions, are given for the transitions 0 → υ′ (υ′ ? 7), using an eighth-power internuclear Dunham potential and an eight-term power series expansion of the dipole moment.     

Contraction of diatomic molecules upon chemisorption

On the basis of self-consistent model calculations for H₂ standing upright on a jellium surface it is shown that contraction of a molecular bond is possible upon chemisorption in spite of a weakened intramolecular interaction. This leads us to point out the possibility of a reduced bond length for CO on Ni (100). A large enough reduction would make the recent conflicting LEED and angular resolved UPS data for this system compatible.