Diatomic molecules coupling calculations

Vaara and Pyykko presented a theory for the magnetic-field-dependent quadrupole splitting in the Xe NMR spectra in isotropic media and tested it by ab initio electronic structure calculations. Evidence exists only for even-power magnetic field dependence. The dominant mechanism is verified to be the electric field gradient caused by the diamagnetic distortion of the atomic electron cloud, quadratic in the magnetic field. NQCC for diatomic molecules were calculated by Bryce and Wasylishen. Turner et al performed a systematic computational study of the geometrical dependence of the deuteron quadrupole interaction parameters (DQCC and asymmetry parameter) for the water-formaldehyde model system. Bematowicz and Szymanski studied NMR spectra of a spin nucleus scalar coupled to two equivalent spin-1 nuclei... 

As mentioned earlier, heavy polar diatomic molecules, such as BaF, YbF, T1F, and PbO, are the prime experimental probes for the search of the violation of space inversion symmetry (P) and time reversal invariance (T). The experimental detection of these effects has important consequences [37, 38] for the theory of fundamental interactions or for physics beyond the standard model [39, 40]. For instance, a series of experiments on T1F [41] have already been reported, which provide the tightest limit available on the tensor coupling constant Cj, proton electric dipole moment (EDM) dp, and so on. Experiments on the YbF and BaF molecules are also of fundamental significance for the study of symmetry violation in nature, as these experiments have the potential to detect effects due to the electron EDM de. Accurate theoretical calculations are also absolutely necessary to interpret these ongoing (and perhaps forthcoming) experimental outcomes. For example, knowledge of the effective electric field E (characterized by Wd) on the unpaired electron is required to link the experimentally determined P,T-odd frequency shift with the electron s EDM de in the ground (X2X /2) state of YbF and BaF. 

Most diatomic molecules have a force constant in the range 10 to 10 N m h A common tool for the calculation of Kp in diatomic molecules (often extended to couples of atoms in polyatomic molecules) is Badger s rule ... 

In the following, we will discuss a number of different adsorption systems that have been studied in particular using X-ray emission spectroscopy and valence band photoelectron spectroscopy coupled with DFT calculations. The systems are presented with a goal to obtain an overview of different interactions of adsorbates on surfaces. The main focus will be on bonding to transition metal surfaces, which is of relevance in many different applications in catalysis and electrochemistry. We have classified the interactions into five different groups with decreasing adsorption bond strength (1) radical chemisorption with a broken electron pair that is directly accessible for bond formation (2) interactions with unsaturated it electrons in diatomic molecules (3) interactions with unsaturated it electrons in hydrocarbons ... 

To summarize, therefore, it is reasonable to say that ab initio calculations of spin-orbit coupling constants may be successfully performed on atoms (although relativistic wavefunctions will be necessary for the heavier ones) and diatomic molecules (especially hydrides). For larger molecules, such methods may be too time-consuming and resort to semi-empirical techniques will be necessary. The atoms-in-molecules approach has proved extremely successful, but it should be possible to use semi-empirical wavefunctions with the full hamiltonian before long. This will be probably more useful with very large molecules. 

An alternative approach widely used in polyatomic molecule studies is based on the Golden Rule and a perturbative treatment of the anharmonic coupling (57,62). This approach is not much used for diatomic molecules. In the liquid O2 example cited above, the Hamiltonian must be expanded to 30th order or so to calculate the multiphonon emission rate. But for vibrations of polyatomic molecules, which can always find relatively low-order VER pathways for each VER step, perturbation theory is very useful. In the perturbation approach, the molecule s entire ladder of vibrational excitations is the system and the phonons are the bath. Only lower-order processes are ordinarily needed (57) because polyatomic molecules have many vibrations ranging from higher to lower frequencies and only a small number of phonons, usually one or two, are excited in each VER step. The usual practice is to expand the interaction Hamiltonian (qn, Q) in Equation (2) in powers of normal coordinates (57,62) ... 

Hansen and Pearson [27] have recently employed a linear superposition of exponential repulsive interaction potentials between an inert atom and the atoms of a homonuclear diatomic molecule. They then performed a three-dimensional semiclassical calculation of the vibrational-transition probability including simultaneous rotational transitions. They conclude that the effect of coupled rotational transitions leading predominantly to AJ = 2 affect the vibrational-transition rate by 50% or more. 

As mentioned, the quadrupolar and magnetic shielding interactions are frequently the most important contributors to the total SSNMR spectrum of the quadrupolar halogens. Some calculations of indirect nuclear spin-spin coupling tensors involving chlorine, bromine, and iodine have been performed, particularly for gaseous diatomic molecules.However, we focus here on the parameters of current importance to the analysis of solid powdered samples (i.e. the EFG and a tensors). 

---