H atomic orbital

B The H-atom orbitals 3s, 3p and 3d are degenerate. Therefore, the 9 quantum number combinations are ... 

Each H-atom orbital is labeled with the reflection plane it resides oa... 

A full quantum mechanical calculation of the simplest dimer ion is a formidible task (—e.g., [F—H... H—F] with 21 electrons). We are forced to examine the matter using various approximations. Using a molecular orbital approach we can view the problem as one of five electrons associated with the several atomic cores. For [F—H... H—F], the amplest MO could be built from 2 P orbitals on F and Is orbitals on H, as in Table I. By symmetry, the orbital coefficients for the two F atomic orbitals will be identical in magnitude as will those of the two H atomic orbitals. The orbital coefficients, cit, can thus be chosen to be positive definite if the sign convention in Table I is used. The MO s should be... 

When the 1 s orbital is used in the place of the actual H-atom orbital, one has a as a variation parameter to adjust the wave function. The energy expression becomes... 

Table 1 Numbers of states under various constraints for methane and four tetrahedral hybrids and four H-atom orbitals.

M—H bonds in the heavier hydrides are made of mostly np (M) and Is (H) atomic orbitals. The 6s population on the Bi atom in BiH3 is 0.14 larger than the 5s population on SbHj, while the 5s and 4s populations on SbHj and AsHj differ by only 0.07. This is mainly due to the relativistic mass-velocity stabilization of the 6s shell of Bi, also known as the inert-pair effect. As a result, the lightest NH3 and the heaviest BiHj exhibit considerable deviation from the trends given by other members in this group. 

Cusachs, L G, Corrington, J. H. Atomic orbitals for semiempirical molecular orbital calculations, in Sigma molecular orbital theory, by Sinanoglu, O., Wiberg, K. B., New Haven Yale University Press 1970, pp. 256- 272 Cusachs, L. G, Reynolds, J, W. J. Chem. Phys. 43, S160 (1965)... 

Multiplying one of the two H atom orbitals by —1 is required for constructive interference combination with two + signs leads to destruction interference. 

The physical picture on the Z -dependence of IAPbI can be qualitatively explained as follows. As described in eq. (4), the bond overlap population Pb is obtained from the sum of all overlap populations between the X and F or H atomic orbitals. Accordingly, APb depends on the relativistic variation of the radial wavefunctions of the atomic orbitals for each molecule. Because the relativistic effects on the atomic orbitals of fluorine or hydrogen atom are negligibly small, the relativistic effects on atomic orbitals of the atom X play a... 

In the H atom, orbitals in a given shell are degenerate (have the same energy). 

Now let us consider the arrangement of the electrons in Li (Z = 3). In the ground state, the H atomic orbital is fully occupied and the third electron could occupy either a 2s or 2p orbital. Which arrangement will possess the lower energy An electron in a 2s or 2p atomic orbital experiences the effective charge, of a nucleus partly shieldedhy the ly... 

Two electrons (spin-paired) are accommodated in the lowest energy H atomic orbital. 

If an atomic orbital contains two electrons, they must have opposite spins so that the sets of quantum numbers for the two electrons are different e.g. in the H atomic orbital ... 

Molecular orbital theory can be applied to any homonudear diatomic molecule, but as more valence atomic orbitals become available, the MO diagram becomes more complex. Treatments of the bonding in He2, Li2 and Be2 are similar to that for H2. In practice. He does not form He2, and the construction of an MO diagram for He2 is a useful exercise because it rationalizes this observation. Figure 1.19a shows that when the two H atomic orbitals of two He atoms interact, a and a MOs are formed as in H2. However, each He atom contributes two electrons, meaning that in He2, both the bonding and antibonding MOs are fully occupied. The bond order (equation 1.31) is zero and so the MO picture of He2 is consistent with its non-existence. 

The ground state configurations of H and F are and [He]2 2p respectively. Since Zgff(F) > Zgff(H), the F 2s and 2p atomic orbital energies are significantly lowered with respect to the H H atomic orbital (Figure 1.27). 

Fig. 4.20 The ligand group orbital approach to the bonding in CH4. (a) The 2, 2p, 2py and 2p atomic orbitals of carbon, (b) The four hydrogen H atomic orbitals combine to generate four ligand group orbitals (LGOs).

Fig. 23.3 Overlap of the H H atomic orbital with (a) two or (b) three appropriate metal hybrid orbitals to form p-H and P3-H bridges, (c) For an interstitial H atom within an octahedral Mg-cage, a delocalized description involves the overlap of the H H atomic orbital with six appropriate metal orbitals to give a 7c-2e interaction.

Notice that the number of AOs combined always equals the number of MOs formed two H atomic orbitals combine to form two H2 molecular orbitals. 

This geometry possesses three important elements of symmetry, the molecular plane and two planes that bisect the molecule. All MOs must be either symmetric or antisymmetric with respect to each of these symmetry planes. With the axes defined as in the diagram above, the orbitals arising from carbon 2p have a node in the molecular plane. These are the rr and rr orbitals. Because the two atomic orbitals are perpendicular (orthogonal) to all the other atomic orbitals and the other orbitals lie in the nodal plane of the p orbitals, there is no interaction of the p with the other C and H atomic orbitals. The rr orbital is symmetric with respect to both the x-z plane and the y-z plane. It is antisymmetric with respect to the molecular (x-y) plane. On the other hand, rr is antisymmetric with respect to the y-z plane. 

Figure 2.8 (a) The F atomic orbitals, (b) The HF molecular orbitals, (c) The H atomic orbital, (d) Interaction of H I5 orbital with one of the fluorine p orbitals. The overlap of these two orbitals results in a lowering of the energy of the system. The dotted lines joining (6) to (d) emphasize that it is only the fluorine p orbital which overlaps with the H orbital that has a lower energy. The two pairs of unpaired electrons (unshaded lobes) have the same energy in the molecule that they did on the F atom, since these so-called lone pairs are unperturbed by the presence of the hydrogen atom. 

The SCF LCAO ab initio representation of the molecular electronic density p(r) is a function of the 3D position variable r, and is defined in terms of a set of h atomic orbitals (p,(r), i= 1,2,..., n. The n x n dimensional density matrix P can be computed from the set of self-consistent coefficients of atomic orbitals in the occupied molecular orbitals. In terms of this density matrix P, the electronic density p(r) of the molecule can be written as... 

Because of the similarity in symmetry the quantum-chemical behavior of the H-atomic orbital and the 5important difference as far as the bond strength is concerned. Before bonding with the metal surface, the 5anti bonding orbital fragments with the surface metal orbitals, 5ir electron density is transferred to the metal. Overall donation of electrons from the 5a orbital to the metal surface occurs. The smaller the difference in energy between the unoccupied surface orbitals and the CO 5a orbital, the larger this electron donation and the stronger the 5a CO metal bond. 

The 3a and l r molecular orbitals are composed primarily of carbon 2pa and Ipn atomic orbitals respectively, but the 3 a molecular orbital will have a small but significant admixture of the hydrogen H atomic orbital. The lowest excited electronic states arise from a 3a l r electronic excitation, and four different electronic states are possible ... 

H-H distances are equal then, by symmetry the atomic orbital (AO) coefficients of the left and right H atom orbitals in the resultant i/// must be equal. 

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