The Dihydrogen Molecule

Here the integration J dr is over the coordinates of both electrons. Such integrals are therefore eight-dimensional (three spatial variables and one spin variable per electron). Integration over the spin variables is straightforward, but the spatial variables are far from easy a particular source of trouble arises from the electron repulsion term. 

In the case of the hydrogen molecule-ion H2 , we defined certain integrals Saa, Taa, Tab, Labra- The electronic part of the energy appropriate to the Heitler-London (singlet) ground-state wavefunction, after doing the integrations 

Single hydrogenic Is valence bond Heitler and London f = 1 3.156 86.8 

We often refer to Heitler and London s method as the valence bond (VB) model. A comparison between the experimental and the valence bond potential energy curves shows excellent agreement at large 7 ab but poor quantitative agreement in the valence region (Table 4.3). The cause of this lies in the method itself the VB model starts from atomic wavefunctions and adds as a perturbation the fact that the electron clouds of the atoms are polarized when the molecule is formed. 

A slight improvement in the predicted dissociation energy occurs if the Is orbital exponent is treated as a variational parameter. 

27 aa + 2Sab ab 2Vaara 2Vaarb 4SabVabra + aabb + abab 

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The two preceding applications showed that our hydrogenic model fits well with the helium atom and the dihydrogen molecule for the determination of the polarization functions except that their exponent ( is different from Co which is the exponent of the genuine basis set It is obvious that the hydrogenic model will fit less and... 

The third major mechanism is based on homolytic cleavage of the dihydrogen molecule by metal-metal (Co) bonded species or by a paramagnetic complex (equations 3 and 4)15. 

The dihydrogen molecule assumes a side-on terminal coordination. The W-H2 distance is 1.95 A (X-ray diffraction) or 1.89 A (neutron diffraction). The H-H distance is 0.75 A (X-ray diffraction) or 0.82 A (neutron diffraction), with respect to 0.74 A for molecular hydrogen in the gaseous state. 

Woelk and coworkers [252, 270] have provided a detailed view into the activation and transfer of the dihydrogen molecule during hydrogenations in SCCO2, using PHIP and their toroid cavity NMR autoclave. For the asymmetric hydrogenation... 

The dihydrogen molecule is the smallest molecule in existence. It has a strong covalent bond with a dissociation energy of 103 kcal mol [1], In a hydrogenation reaction, this bond has to be broken and two new C-H bonds are formed, one of the simplest forms of chemical reaction. 

This process does not necessarily have to be simultaneous, but the two atoms of the dihydrogen molecule must retain a spin-spin coupling throughout the whole process. Conversely, if they are not transferred pair-wise (i. e., if the transferred hydrogen atoms stem from different dihydrogen molecules or if they lose their coupling in the course of the process), no polarization can be detected. 

Covalent Bonding I the Dihydrogen Molecule-ion, H2+, and the Dihydrogen Molecule... 

This chapter consists of the application of the symmetry concepts of Chapter 2 to the construction of molecular orbitals for a range of diatomic molecules. The principles of molecular orbital theory are developed in the discussion of the bonding of the simplest molecular species, the one-electron dihydrogen molecule-ion, H2+, and the simplest molecule, the two-electron dihydrogen molecule. Valence bond theory is introduced and compared with molecular orbital theory. The photo-electron spectrum of the dihydrogen molecule is described and interpreted. 

The application of group theory to define the orbitals of the dihydrogen molecule... 

The molecular orbital theory of the dihydrogen molecule is dealt with in detail above, and describes how the two electrons occupy a bonding molecular orbital so that they are equally shared between the two nuclei. This state of affairs can be written symbolically in the form ... 

To obtain an accurate assessment of the interelectronic repulsion energy of the H2 molecule it is essential to carry out calculations in which the hydrogen nuclei are a constant distance apart. The following calculations are for an internuclear distance of 74 pm for both molecules, which is the equilibrium internuclear distance in the dihydrogen molecule. 

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