Molecular spectroscopic constants

It is neither intended nor possible to give a comprehensive review of relativistic density functional calculations on small molecules. To be able to compare the methods described in Sec. 2, we will primarily discuss molecules for which computational results from a variety of different methods are aveulable. Molecules containing heavy elements from the left half of the periodic table (including lanthanides and actinides) will not be discussed, as most of this is covered in the eirti-cle by V. Pershina in this volume. Likewise, only calculations of molecular spectroscopic constants such as bond lengths (r ), (harmonic) vibrational frequencies ((0 ) and binding energies (D ) are... 

Although quite good for atoms, the HFKS method does not seem to be much of an improvement over the HF method for molecular spectroscopic constants such as equilibrium distances or vibrational frequencies The reason is, as we have said, the poor behavior of the HF method for bond dissociation. One would expect that the use of MD wave functions instead of the HF determinant would yield better results. 

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. 

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.). 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

Our spectroscopic study of the (ErxYi.x)2BaNiOs system (0.1wave functions, and g-factors of the Er3+ ion practically do not depend on x. It is physically reasonable to assume that the molecular-field constant X of the Er-Ni interaction also does not depend on x. In this case, Eqs. (2) and (3) are valid for an arbitrary x and the ordered magnetic moments of the Er and Ni magnetic subsystems can be extracted from the experimentally measured ground-state splittings. 

The polarizability a is an important second-order molecular property. Its variation with internuclear separation has been investigated for H2 and Hs by Zeroka,58 using the method of Das and Bersohn. Spectroscopic constants calculated from the BO and adiabatic KW functions for H2 were also studied by Wu and Beckel.59... 

The answer to the question why calculate spectroscopic constants is not merely to find the value . There are in fact two possible reasons why one should use theoretical methods to compute spectroscopic constants. Firstly, there are cases where an experimental value has been measured for some constant, but the observed magnitude or even sign is not comprehensible in terms of the idea of electronic structure which the spectroscopist has in mind. In such cases a relatively crude calculation which only reproduces the observation to an order of magnitude may offer explanations in terms of perturbations by unobserved states or the atomic constitution of molecular orbitals. 

Heijser, W., A. Th. van Kessel, and E. J. Baerends (1976). Self-consistent molecular Hartree-Fock-Slater calculations. IV. On electron densities, spectroscopic constants and proton affinities of some small molecules. Chem. Phys. 16, 371-79. 

Another problem of a rigorous comparison of ab initio results with experiment is encountered with any observable which Is determined by a polynomial fit to calculated points. Some molecular properties (mainly spectroscopic constants) depend on the fitting procedure rather strongly and if an inappropriate fit is used the discrepancies with experiment which are found may be erroneously assigned to basis set or correlation effects. 

Molecular and spectroscopic constants are based on the analysis of electronic spectra published by Martin and Barrow (5). The constants are in excellent agreement with those from earlier studies (6, 7). The electronic states are taken from Rosen (2) with the exception of the upper ir state and the b z" state. The upper state is estimated to be approximately In a linear relationship with the two lower states. The b r state is assigned by analogy with AIF, AlCl and AlBr (8). 

Q t r v Molecular and spectroscopic constants for the ground state and the 2 state are taken from a... 

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