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** Molecular orbitals symmetry adapted **

** Orbital interactions symmetry-adapted **

** Symmetry adapted orbitals group **

** Symmetry-Adapted Linear Combinations of Hydrogen Orbitals in Ammonia **

To generate the above Ai and E symmetry-adapted orbitals, we make use of so-ealled symmetry projeetion operators Pe and Pa These operators are given in terms of [Pg.592]

Finally, it must be mentioned that localized orbitals are not always simply related to symmetry. There are cases where the localized orbitals form neither a set of symmetry adapted orbitals, belonging to irreducible representations, nor a set of equivalent orbitals, permuting under symmetry operations, but a set of orbitals with little or no apparent relationship to the molecular symmetry group. This can occur, for example, when the symmetry is such that sev- [Pg.47]

The original set of 19 orbitals would have led to a 1 x 19 determinant in eqn (12-2.1), but now instead, by using the equally valid set of symmetry adapted orbitals, we have [Pg.254]

The convention is to use lowercase letters for the symmetry species of one-electron functions.) Since each irreducible representation occurs only once in (9.72), these symmetry-adapted orbitals are also the (unnormalized) MOs. As a check, using (9.73), (9.74), and (9.65), we find for the matrix A of the similarity transformation that reduces the matrices of TAO to block-diagonal form [Pg.216]

These equations state that the three Ish orbitals can be combined to give one Ai orbital and, since E is degenerate, one pair of E orbitals, as established above. With knowledge of the ni, the symmetry-adapted orbitals can be formed by allowing the projectors [Pg.594]

In order to solve the Kohn-Sham equations (Eqn. (2)) we used the molecular orbital-linear combination of atomic orbitals (MO-LCAO) approach. The molecular wave functions 0j are expanded the symmetry adapted orbitals Xj) which are also expanded in terms of the atomic orbitals [Pg.358]

The z axis is the internuclear axis, and the z axes on atoms a and b point toward each other. Without using the full group-theory formalism, we can write down by inspection the following symmetry-adapted orbitals, which [Pg.216]

An example will help illustrate these ideas. Consider the formaldehyde molecule H2CO in C2V symmetry. The configuration which dominates the ground-state wavefunction has doubly occupied O and C Is orbitals, two CH bonds, a CO o bond, a CO 7t bond, and two O-centered lone pairs this configuration is described in terms of symmetry adapted orbitals as follows (lai22aj23ai2lb22 [Pg.197]

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.9. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 610. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals tr, t72. < i> and are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon [Pg.639]

When the basis set was enlarged, almost linearly dependent basis functions appeared. They were akin to some orbitals generated on different atoms in the moleeule beeause the linear eombination of many basis functions at multi-centers spanned the space repeatedly. The linear dependence among the symmetry-adapted orbitals was removed before the orthogonalization. [Pg.114]

See also in sourсe #XX -- [ Pg.150 , Pg.206 , Pg.250 ]

** Molecular orbitals symmetry adapted **

** Orbital interactions symmetry-adapted **

** Symmetry adapted orbitals group **

** Symmetry-Adapted Linear Combinations of Hydrogen Orbitals in Ammonia **

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