On the Zeeman effect of 2Π states in diatomic molecules

The theory of the Zeeman effect in ²Π states of diatomic molecules is reconsidered. Second order terms due to the interaction with ²Δ states, which were left out in a previous investigation, are now included. The total correlation between the spin-rotation coupling constant and the centrifugal distortion in the spin-orbit coupling renders the fitted molecular g factors somewhat ambiguous. This problem is handled by a transformation of the basis for the Hamiltonian matrix. The theoretical results are exemplified for the ²Π ground state of OH for which EPR data are available for both the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ substates. A combination of ab initio predictions and fitted values of the g factors finally yields new information concerning the separate contributions from ²Σ⁺, ²Σ^?, and ²Δ states to the contamination of the ²Π ground state in OH.     

A periodic table of free diatomic molecules—II predicted internuclear separations from curve-fitted data

Recent theory substantiates the stacking order of the areas in the recently proposed periodic table of the free diatomic molecules. The periodic table suggests curve-fitting algorithms for r_e which, after semi-empirical perturbations yield ground-state values for r_e which agree with literature values and with those from an alternate algorithm to from 5 to 8%. 800 predicted r_e extend to superheavy quasimolecules and to molecules with superheavy atoms, and many pertain to molecules of laser interest.     

Finite size scaling for critical parameters of simple diatomic molecules

We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres, Z ⁺ e ^?Z⁺. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Z_c = 1.228279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.     

Accurate relations for the isotopically invariant spectroscopic parameters of diatomic molecules

Equations are obtained relating the isotopically invariant spectroscopic parameters U_mj, which must be considered as conditions in the least-squares method in spectral analysis. Expressions are given for the first seven Dankhem potential parameters in terms of U_m0 and U_m1. The contribution to the spectroscopic coefficients Y_mj due to violation of the Born-Oppenheimer approximation is calculated for¹²C¹⁶O.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 18–21, November, 1984.It remains to thank Yu. S. Makushkin, V. Ya. Galin, andV. F. Golovko for valuable discussions of the work.     

A determination of fundamental Zeeman parameters for the OH radical

Measurements of the gas-phase E.P.R. spectra of OH in the J = 9/2 and 11/2 levels of the X²II state at 26 GHz and 35 GHz respectively are reported. Confocal and semi-confocal optical resonators have been used in place of the more conventional microwave cavities for these experiments. The data are analysed, together with previous measurements by Radford on other rotational levels in the determination of six independent g factors:

These parameters are interpreted in terms of the electronic structure of the OH radical. In agreement with previous workers, it is found that the major contaminant of the X²II state is the A²Σ⁺ state and that this pair of states is a good example of Van Vleck's pure precession hypothesis.     

An investigation of the interaction between close-lying 2σ and 2II states of diatomic molecules

A perturbation calculation of the interaction between close-lying ²σ and ²II states of diatomic molecules has been carried out to the fourth order. The formula for the spin-splitting of the ²σ states thus obtained has been found to yield a proper explanation for the large anomalies encountered in the spinsplitting of the B ²σ states of the hydrides and deuterides of Ca, Sr and Ba. Especially for CaH, CaD, SrH and SrD good agreement between theoretical and fitted values has been found for the higher-order correction terms to the spin-splitting.     

Gas temperature determination from the unresolved rotational structure of vibronic bands of diatomic molecules

Journal of Applied Spectroscopy -     

First‐principles calculations of Mössbauer hyperfine parameters for solids and large molecules

Electronic structure calculations based on density functional theory were performed for solids and large molecules. The solids were represented by clusters of 60–100 atoms embedded in the potential of the external crystal. Magnetic moments and Mössbauer hyperfine parameters were derived.     

Calculation of centrifugal distortion constants for diatomic molecules from RKR potentials

Expressions are developed for computing the centrifugal distortion constants D_v, H_v, and L_v directly from the Rydberg-Klein-Rees rotationless potential of a diatomic molecule. These expressions involve summations over integrals of the wavefunctions of all neighboring vibrational levels. Application is made to the X¹Σ⁺ state of CO and the $\text{X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂. In these applications, we have neglected the contributions of the continuum wavefunctions. For higher vibrational levels, particularly those near the dissociation limit, this approximation would be expected to fail. For the lowest vibrational levels of an electronic state, this method gives the same results for D_v, H_v, and L_v as the Dunham relations. However, for intermediate vibrational levels the present method is an improvement since expressions for only a few coefficients of the Dunham expansion are available. The use of D_v and H_v values calculated from Rydberg-Klein-Rees potentials in an iterative improvement of the reduction of spectroscopic data is described.     

An effective Hamiltonian for diatomic molecules: Ab initio calculations of parameters of HCl+

The form of the effective Hamiltonian for a diatomic molecule in an electronic state intermediate between Hund's cases (a) and (b) is reexamined. The derivation is performed in three stages: (i) an electronic contact transformation removes the effects of matrix elements which couple different electronic states; (ii) a vibrational contact transformation removes matrix elements coupling different vibrational states; and (iii) a spin-rotational contact transformation removes indeterminacies in the final Hamiltonian. Expressions for the effective parameters resulting from these transformations are presented. The Hamiltonian is in a convenient form for fitting to experimental data, and the formulas for the parameters assist in the comparison with ab initio calculations. The relations between the present parameters and those employed in the computer program of Zare, Schmeltekopf, Harrop, and Albritton [J. Mol. Spectrosc.46, 37–66 (1973)] are given, and make it possible to correct a previous misunderstanding regarding the value of the spin-rotation parameter γ_e in the X²Π state of HCl⁺. The parameters obtained for this state are compared with ab initio calculations which take account of first-order perturbations within the state and second-order perturbations from the A²Σ⁺ state and from the four states of the configuration … $\text{σ}{}^2\text{π}{}^2\text{σ}{}^1$. The A²Σ⁺ state is the dominant perturber, but the contributions from the other states are not negligible. For example, their contribution to γ_e is larger than the first-order contribution.     

Properties of diatomic molecules from dynamical models for alkali halide crystals

Recently reported central interionic potentials for alkali halide crystals, which have been derived from dynamical models including polarisation and shell deformations, are used in calculations of the internuclear distances, vibrational frequencies and binding energies of the corresponding alkali halide molecules. The results are in good agreement with experimentally determined values.     

Tables for direct determination of spectral line parameters,from spectrometric data—II. Intermediate Voigt broadening

Tables and curves are presented for the calculation of spectral-line parameters from observed spectra for combined Doppler and Lorentz Broadening (Voigt profile), using a spectrometer of known instrument response function.     

A semi-empirical formula for total cross sections of electron scattering from diatomic molecules

A fitting formula based on the Born approximation is used to fit the total cross sections for electron scattering by diatomic molecules (CO, N₂, NO, O₂ and HCl) in the intermediate- and high-energy range. By analyzing the fitted parameters and the total cross sections, we found that the internuclear distance of the constituent atoms plays an important role in the e-diatomic molecule collision process. Thus a new semi-empirical formula has been obtained. There is no free parameter in the formula, and the dependence of the total cross sections on the internuclear distance has been reflected clearly. The total cross sections for electron scattering by CO, N₂, NO, O₂ and HCl have been calculated over an incident energy range of 10–4000 eV. The results agree well with other available experimental and calculation data.     

Independence of magnetic texture and hyperfine data from Mössbauer spectra of a ferromagnetic metallic glass

We analysed the Mössbauer spectra of ferromagnetic 2605 S2 metglas submitted to various external stresses; it is concluded that the hyperfine parameters and their correlations do not depend on the state of the magnetic texture. Thus the amorphous alloy can be considered as an isotropic material submitted to a small field of stresses; also, methods based on linear combination of spectra can be used.     

The hyperfine structure of diatomic molecules: Hund's case (cα)

The hyperfine splitting in diatomic molecules is treated according to an unperturbed model that is denoted Hund's coupling case (c_α). The advantages of this model are: (i) Rapid convergence of the perturbation expansion (spin-orbit interaction is included in the unperturbed Hamiltonian), (ii) hyperfine interactions of the type ΔJ ≠ 0 are automatically included, (iii) simple rotational-independent matrix elements result for the hyperfine Hamiltonian, and (iv) it is rather easy to judge whether the various hyperfine parameters are correlated or not. Numberical diagonalization of a secular matrix of dimension (2S + 1)(2I + 1) (or less for singular levels) yields the hyperfine splittings. The interaction with remote electronic states is included through a Van Vleck transformation. The coupling case (c) matrix elements are readily specialized to coupling case (a), and the present method is applied to the a³Π₁ substate of InH (optical), the X³Σ^? state of ³³SO and ¹⁷O¹⁶O (microwave) and to the X²Π state of ⁷LiO (radio frequency).     

Dynamics of diatomic molecules confined in a chemical trap II. Nuclear magnetic resonance experiments on CO in solid C60

A detailed nuclear magnetic resonance (NMR) study of CO isolated in a matrix of C₆₀ is reported. CO in C₆₀ shows both quantum and classical behaviour on the NMR timescale. Below 10 K orientational quantum tunnelling for part of the CO molecules is inferred from an analysis of the line shapes. Above 30 K, however, the system can be treated classically due to the dense rovibronic level structure at energies above 30 cm^?1.     

On the determination of the Debye temperature from experimental data

It is shown that the Debye temperature as a function of temperature must satisfy certain equations in order for the thermodynamic functions calculated in terms of the Debye temperature to satisfy both the third law of thermodynamics and the law of equipartition of energy. A general expression for the Θ(T) function satisfying these thermodynamic laws is found.