A molecular orbital

Ultraviolet photoelectron spectroscopy (UPS) results have provided detailed infomiation about CO adsorption on many surfaces. Figure A3.10.24 shows UPS results for CO adsorption on Pd(l 10) [58] that are representative of molecular CO adsorption on platinum surfaces. The difference result in (c) between the clean surface and the CO-covered surface shows a strong negative feature just below the Femii level ( p), and two positive features at 8 and 11 eV below E. The negative feature is due to suppression of emission from the metal d states as a result of an anti-resonance phenomenon. The positive features can be attributed to the 4a molecular orbital of CO and the overlap of tire 5a and 1 k molecular orbitals. The observation of features due to CO molecular orbitals clearly indicates that CO molecularly adsorbs. The overlap of the 5a and 1 ti levels is caused by a stabilization of the 5 a molecular orbital as a consequence of fomiing the surface-CO chemisorption bond. 

Shephard M J and Paddon-Row M N 1996 Conformational analysis of Cgg ball and chain molecules a molecular orbital study Aust. J. Chem. 49 395-403... 

Figure 2.8. The iwo orbitals overlap giving a covalent bond and ihe tvvv electrons are (>ir in a molecular orbital. (If the t o nuclei could be pushed together completely, the...

Ferrocene (Figure 2-61a) has already been mentioned as a prime example of multi-haptic bonds, i.c, the electrons tlrat coordinate tire cyclopcntadicnyl rings with the iron atom are contained in a molecular orbital delocalized over all 11 atom centers [811, for w hich representation by a connection table having bonds between the iron atom and the five carbon atoms of cither cyclopcntadicnyl ring is totally inadequate. 

ITyperChem uses the Linear Combination of Atomic Orhilals-Molecular Orbital (LCAO-MO) approximation for all of itsah initio sem i-empirical melh ods. If rg, represen is a molecular orbital and... 

To this pom t, th e basic approxmi alien is th at th e total wave I lnic-tion IS a single Slater determinant and the resultant expression of the molecular orbitals is a linear combination of atomic orbital basis functions (MO-LCAO). In other words, an ah miiio calculation can be initiated once a basis for the LCAO is chosen. Mathematically, any set of functions can be a basis for an ah mitio calculation. However, there are two main things to be considered m the choice of the basis. First one desires to use the most efficient and accurate functions possible, so that the expansion (equation (49) on page 222). will require the few esl possible term s for an accurate representation of a molecular orbital. The second one is the speed of tW O-electron integral calculation. 

Tie first consideration is that the total wavefunction and the molecular properties calculated rom it should be the same when a transformed basis set is used. We have already encoun-ered this requirement in our discussion of the transformation of the Roothaan-Hall quations to an orthogonal set. To reiterate suppose a molecular orbital is written as a inear combination of atomic orbitals ... 

A molecular orbital is a linear combination of basis functions. Normalization requires that the integral of a molecular orbital squared is equal to 1. The square of a molecular orbital gives many terms, some of which are the square of a basis function and others are products of basis functions, which yield the overlap when integrated. Thus, the orbital integral is actually a sum of integrals over one or two center basis functions. 

FIGURE 2 5 Genera tion of (T and a molecular orbitals of H2 by combining Is orbitals of two hydrogen atoms... 

The mechanism of the Diels-Alder reaction is best understood on the basis of a molecular orbital approach To understand this approach we need to take a more detailed look at the rr orbitals of alkenes and dienes... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

A molecular orbital description of benzene has three tt orbitals that are bonding and three that are antibonding Each of the bonding orbitals is fully occupied (two electrons each) and the antibonding orbitals are vacant... 

When a molecular orbital method was used to calculate the charge distribution in cyclohexadienyl cation it gave the results indicated How does the charge at each carbon compare with that deduced by examining the res onance structures for cyclohexadienyl cation ... 

Configuration Interaction (or electron correlation) adds to the single determinant of the Hartree-Fock wave function a linear combination of determinants that play the role of atomic orbitals. This is similar to constructing a molecular orbital as a linear combination of atomic orbitals. Like the LCAO approximation. Cl calculations determine the weighting of each determinant to produce the lowest energy ground state (see SCFTechnique on page 43). 

To derive the states arising from a molecular orbital configuration in a diatomic molecule see Sections 7.2.2 and 7.2.4. There are two states, and 11 /2, arising from this configuration and is the lower in energy and, therefore, the ground state. 

A MOLECULAR ORBITAL ANALYSIS OF THE DIELS-ALDER REACTION... 

The picture of benzene as a planar- framework of a bonds with six electrons in a delocalized TT orbital is a useful, but superficial, one. Six electrons cannot simultaneously occupy any one orbital, be it an atomic orbital or a molecular- orbital. We can fix this with the more accurate molecular- orbital picture shown in Figure 11.4. We learned in Section 2.4 that when atomic orbitals (AOs) combine to give molecular- orbitals (MOs), the final number of MOs must equal the original number of AOs. Thus, the six 2p AOs of six 5/r -hybridized carbons combine to give six tt MOs of benzene. 

Figure 11.14 shows a molecular orbital diagrfflTt for cycloheptatrienyl cation. There are seven tt MOs, three of which are bonding and contain the six tt electrons of the cation. Cycloheptatrienyl cation is a Hiickel (4n + 2) system and is an aromatic ion. 

When a molecular orbital method was used to calculate the... 

The anomeric effect is best explained by a molecular orbital analysis that is beyond the scope of this text. 

Thus, Segura replaced ct with a scaled energy change, obtained by a molecular orbital calculation, for this proton transfer ... 

Multiplying a molecular orbital function by a or P will include electron spin as part of the overall electronic wavefunction i /. The product of the molecular orbital and a spin function is defined as a spin orbital, a function of both the electron s location and its spin. Note that these spin orbitals are also orthonormal when the component molecular orbitals are. 

Fig. A. Molecular-orbital representation of the 1-centrc F-Xe-F bond, (a) The possible combinations of colinear p, atomic orbitals, and (b) the energies of the resulting MOs (schematic).

A convenient orbital method for describing eleetron motion in moleeules is the method of molecular orbitals. Molecular orbitals are defined and calculated in the same way as atomic orbitals and they display similar wave-like properties. The main difference between molecular and atomic orbitals is that molecular orbitals are not confined to a single atom. The crests and troughs in an atomic orbital are confined to a region close to the atomic nucleus (typieally within 1-2 A). The electrons in a molecule, on the other hand, do not stick to a single atom, and are free to move all around the molecule. Consequendy, the crests and troughs in a molecular orbital are usually spread over several atoms. 

The first step in constructing a molecular orbital picture of a chemical reaction is to decide which orbitals are most likely to serve as the electron donor and electron acceptor orbitals. It should be obvious that the electron donor orbital must be drawn from the set of occupied orbitals, and the electron acceptor orbital must be an unoccupied orbital, but there are many orbitals in each set to choose from. 

Antibonding Molecular Orbital. A Molecular Orbital that is andbonding between particular atomic centers. The opposite is a Bonding Molecular Orbital. 

Nonbonded Molecular Orbital. A molecular orbital that does not show any significant bonding or antibonding characteristics. Nonbonded molecular orbitals often correspond to Lone Pairs. 

Don t confuse the state wavefunction with a molecular orbital we might well want to build the state wavefunction, which describes all the 16 electrons, from molecular orbitals each of which describe a single electron. But the two are not the same. We would have to find some suitable one-electron wavefunctions and then combine them into a slater determinant in order to take account of the Pauli principle. 

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