Molecular orbitals construction

These compounds are often referred to as hypervalent. The apical bonds in a trigonal bipyramid are described by molecular orbitals constructed from a p-orbital on the central atom and o-bonding orbitals (p- or sp hybrid) on the apical ligands. The molecular orbitals can be drawn as ... 

Figure A.14 Energy diagram for the adsorption of an atom on a d-metal. Chemisorption is described with molecular orbitals constructed from the d-band of the metal and atomic orbitals of the adatom. The chemisorption bond in b) is weaker, because the antibonding chemisorption orbital is partially filled (compare Fig. A.5).

Evaluation of these integrals and expansion of the above determinant leads to a polynomial of degree N in , the roots of which give the energies of the molecular orbitals constructed in the above manner. The coefficients Cfj may be determined by substitution of the particular E into the simultaneous linear equations covered by the above determinant together with the normalization equation... 

Symbols A and B cepresem otoms j, y, anti z represent orkntaoori ef lhe p crtilals. Note that the "atomic orbital labels (e.g.. Is) can apply only to molecular orbitals constructed by mi King two orbitals of lhe same type. We shall see later (page (64) that this is an overamplificaiion. 

Another array of orbitals with lhe same sort of linear combinations is that of the rr system of cydopolyencs (benzene, naphthalene) with which you are probably already Familiar The molecular Orbitals constructed from sets of parallel p orbitals are both bonding and antibonding at various energies. The system b particularly stable if Huckd s rule 2m + 2 electrons, see also Chapter 15) e obeyed In the case of an mb rate array of hythogen atoms (Is1), the situation is unstable (as you should have questioned immcdiniclvl it reverts to an array of H2 mdeoics ... 

Ground state 02 and the chosen 3drr Rydberg level have the same 3Zg" symmetry but differ in their molecular orbital construction ... 

It is evident from a comparison of 5 and 4 that the reflection transforms >pi into i/j2. The reader should verify that the a reflection and the C2 rotation also transform symmetry correct. The result we have found will generally hold when molecular orbitals constructed by the LCAO method from hybrid atomic orbitals are subjected to symmetry operations. Each of those orbitals in the set of MO s that is not already symmetry correct will be transformed by a symmetry operation into another orbital of the set. 

Many of the principles and techniques for calculations on atoms, described in section 6.2 of this chapter, can be applied to molecules. In atoms the electronic wave function was written as a determinant of one-electron atomic orbitals which contain the electrons these atomic orbitals could be represented by a range of different analytical expressions. We showed how the Hartree-Fock self-consistent-field methods could be applied to calculate the single determinantal best energy, and how configuration interaction calculations of the mixing of different determinantal wave functions could be performed to calculate the correlation energy. We will now see that these technques can be applied to the calculation of molecular wave functions, the atomic orbitals of section 6.2 being replaced by one-electron molecular orbitals, constructed as linear combinations of atomic orbitals (l.c.a.o. method). 

Figure 7-27. Molecular orbital construction in an ideal octahedral complex formation. Reproduced by permission [109], copyright (1982) The Nobel Foundation.

Construction of molecular orbitals Construction of hybrid orbitals Predicting the decrease of degeneracies of d orbitals under a ligand field Predicting the allowedness of chemical reactions... 

To explain this type of structure we have chosen sodiiam chloride. The sodium atom has one valence electron and the chlorine atom, seven electrons. Each atom is surrounded by six neighbors of the other element. Consequently, in classical theory, it is impossible, with the eight available electrons, to build two electron bonds between the sodium and chlorine atoms and still respect the equivalence between the neighboring atoms. The situation is the same for localized molecular orbitals, doubly utilized. In return, it is possible to describe the system by means of four delocalized molecular orbitals, constructed on the s and p orbitals of each chlorine atom, as well as on the sp d2 hybrid orbitals of the neighboring sodium atoms pointing toward the chlorine atom. The delocalized system is constructed from ten atomic orbitals (hybrid or not). This structure is a generalization of the case of where each of two molecular... 

There are molecular orbitals constructed from atomic orbitals, hybrid in general, belonging to certain atoms of a tridimensional rigid framework, and from orbitals of one or many metallic atoms. 

The T-molecular orbitals constructed from the 2pi orbitals on each carbon atom of butadiene provide an example for this case. The symmetry is Cih and the reducible representation r(0) has the characters... 

For a molecule with a total of m atomic basis functions (xi, X2 , Xm will be a total of m resultant molecular orbitals constructed from them. For most purposes these atomic orbitals can be assumed to be real functions and normaUzed (equation 1.7) such that the probability of finding an electron in Xju when integrated over all space is unity. Here Xpi is the complex conjugate of equation 1.8 we show an alternative, useful, way of writing such integrals. The molecular orbitals of... 

Molecular Orbital Construction from Fragment Orbitals... 

MOLECULAR ORBITAL CONSTRUCTION FROM FRAGMENT ORBITALS... 

LCAO). A molecular orbital constructed as a linear combination of atomic orbitals. (3.5)... 

Figure 24.1 shows the molecular orbitals (MOs) for both ethene and 1,3-butadiene and identifies the highest occupied molecular orbitals (the HOMOs) and the lowest unoccupied molecular orbitals (the LUMOs) for both compounds. The MOs shown include the p-orbitals on each carbon atom. How are these molecular orbitals constructed First, only the p-orbitals of the diene and the alkene are used because these orbitals are involved in the Diels-Alder reaction. An alkene has two jt-electrons, so it will have two n-molecrdar orbitals. The two orbitals cannot be of the same energy, and the two electrons will reside, spin paired (see Chapter 3, Section 3.1.2), in the lowest energy orbital. 

---