Spectroscopic constants

Hyperfine Interaction Constants. In the doublet states X 11 and A A, where the unpaired electron occupies the 2n or the 5o MO, respectively, hyperfine Interaction occurs between the electron spin (S=1/2) and the nuclear spin of P (1=1/2) or (1=1/2). This results in a splitting of the rotational levels into four sublevels. Hf splitting of the rotational lines have been observed in the v=1 -2 band of the A A -X rir system applying high-resolutlon laser photofragment spectroscopy [12, 13]. The following Frosch-Foley hf interaction constants a, bp (=b + c/3), c, d (see [36, pp. 34/8]) for the ip and nuclei have been derived (constants In MHz three standard deviation in parentheses) [13]  

Estimates using experimental a( H) and c( H) values for the SH(2rij) radical. - Assumed to be negligibly small. 

Some conclusions concerning the electronic structure of PH+ in the X and A states have been drawn by considering the magnitudes and signs of the hf constants For the ground state, the experimental dipole-dipole Interaction constants a( P) and c( P) are close to the calculated (ab initio SCF) values for the free P atom or P+ ion, and the Fermi contact term bp( P) is 

MCSCF calculation and choosing two different approximations for the effective nuclear charges Zeff of P and H [28]. 

Rotational and Vibrational Constants. Internuclear Distance. Experimental results are available for the ground state X 211 and the excited state A 2A, which have been obtained from rotational analyses of the UV-visible A-X system. Rotational constants Be or Bq, ae, Ye, Dq, vibrational constants cOe, cOgXe, or AG1/2, and internuclear distances re or ro are given in Table 4. 

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Cheung A S C, Yoshino K, Freeman D E, Friedman R S, Dalgarno A and Parkinson W H 1989 The Schumann-Runge absorption-bands of 0 0 in the wavelength region 175-205 nm and spectroscopic constants of isotopic oxygen molecules J. Mol. Speotroso. 134 362-89... 

More often than not, the following spectroscopic constants are available for a diatomic molecule ... 

The study of molecular systems containing metal atoms, particularly transition metal atoms, is more challenging than first-row chemistry from both an experimental and theoretical point of view. Therefore, we have systematically studied (3-5) the computational requirements for obtaining accurate spectroscopic constants for diatomic and triatomic systems containing the first- and second-row transition metals. Our goal has been to understand the diversity of mechanisms by which transition metals bond and to aid in the interpretation of experimental observations. 

The CPF approach gives quantitative reement with the experimental spectroscopic constants (24-25) for the ground state of Cu2 when large one-particle basis sets are used, provided that relativistic effects are included and the 3d electrons are correlated. In addition, CPF calculations have given (26) a potential surface for Cus that confirms the Jahn-Teller stabilization energy and pseudorotational barrier deduced (27-28) from the Cus fluorescence spectra (29). The CPF method has been used (9) to study clusters of up to six aluminum atoms. 

Many of these points are well illustrated by Cu2, which has become a benchmark for theoretical calculations owing to its relative simplicity and the availability of accurate experimental data. The theoretical spectroscopic constants are quite poor unless the 3d electrons are correlated, even though both Cu atoms nominally have a 3d °4s occupation. In fact, quantitative agreement with experiment is achieved only if both the 3d and 4s electrons are correlated, both higher excitations and relativistic effects are included, and large one-particle basis sets, including several sets of polarization functions, are used (24,25). This level of treatment is difficult to apply even to Cua, let alone larger Cu clusters. 

Table II. Spectroscopic constants for selected CuxBey systems...

Potential energy curve one-electron properties spectroscopic constants... 

Table 2.Values of some spectroscopic constants for the PN X state...

Potential energy curvesfor the K U.and Astates. Selected one-electron properties. Spectroscopic constants... 

The third column of table 1 contains the spectroscopic constants of the four E states, based on the corrected adiabatic potentials. Apart from the Dc, Tg and energies, which are bound to coincide with the experimental values, we observe a remarkable improvement in the computed vibrational levels of the state. The... 

Schwerdtfeger, P., Fischer, T Dolg, M Igel-Mann, G., Nicklass, A., Stoll, H. and Haaland, A. (1995) The Accuracy of the Pseudopotential Approximation. 1. An Analysis of the Spectroscopic Constants for the Electronic Ground States of InCl and InCh. Journal of Chemical Physics, 102, 2050-2062. 

This chapter is restricted to a discussion of halogen-bonded complexes B XY that involve a homo- or hetero-dihalogen molecule XY as the electron acceptor and one of a series of simple Lewis bases B, which are chosen for their simplicity and to provide a range of electron-donating abilities. Moreover, we shall restrict attention to the gas phase so that the experimental properties determined refer to the isolated complex. Comparisons with the results of electronic structure calculations are then appropriate. All of the experimental properties of isolated complexes B- XY considered here result from interpreting spectroscopic constants obtained by analysis of rotational spectra. 

Evidence for a significant contribution from the ionic form [BX] + - -Y in a gas-phase complex B- XY was first deduced from the spectroscopic constants of H3N- -ClF, as obtained by analysis of its rotational spectrum [63]. In particular, the value ka = 34.3 N m 1 of the intermolecular stretching force constant (obtained from the centrifugal distortion constant Dj in the man-... 

An analysis of the Fourier Transform i.r. spectrum of PF around 946 cm-1 gave rise to nine spectroscopic constants for the Vg band and five for the Vg + v -v band which allowed calculation of the wavenumbers of the Vg band with a precision of 1 x 10-3 cm-1.11... 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

Bartell and coworkers investigated the structures of a series of noncyclic alkanes by means of gas electron diffraction (14, 44, 45) and invoked for the interpretation of their results a simple force field which contained to a high extent vibrational spectroscopic constants of Snyder and Schachtschneider. This force field reproduces bond lengths and bond angles of acyclic hydrocarbons well, energies of isomerisation satisfactorily. As an example, Fig. 8 shows geometry parameters of tri-t-butylmethane as observed by electron diffraction and calculated with this force field (14). 

Many other useful forms have been proposed (Steele and Lippincott, 1962) and their parameters were related to spectroscopic constants as will be given for the Morse potential by Eq. (1.14). Quite often, the potential V(r) is expanded as a power series in the displacement from equilibrium (force field method)... 

The low-lying excited states of the hydrogen molecule conhned in the harmonic potential were studied using the configuration interaction method and large basis sets. Axially symmetric harmonic oscillator potentials were used. The effect of the confinement on the geometry and spectroscopic constants was analyzed. Detailed analysis of the effect of confinement on the composition of the wavefunction was performed. 

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