Molecular orbital atomic orbitals

Atomic orbitals Molecular orbitals Atomic orbitals... 

In thissection we cons de [ homonuclear diatomic molecules (those composed of two identical atoms) of elements in Period 2 of the periodic table. Since the lithium atom has a 15 25 electron configuration, it would seem that we should use the Li I5 and 2s orbitals to form the molecular orbitals of the Ll2 molecule. However, the I5 orbitals on the lithium atoms are much smaller than the 2s orbitals and therefore do not overlap in space to any appreciable extent (see Fig. 9.31). Thus the two electrons in each I5 orbital can be assumed to be localized and not to participate in the bonding. To participate in molecular orbitals, atomic orbitals must overlap in space. This means that only the valence orbitals of the atoms contribute significantly to the molecular orbitals of a particular molecule. 

Molecules. The electronic configurations of molecules can be built up by direct addition of atomic orbitals (LCAO method) or by considering molecular orbitals which occupy all of the space around the atoms of the molecule (molecular orbital method). 

LCAO method A method of calculation of molecular orbitals based upon the concept that the molecular orbital can be expressed as a linear combination of the atomic orbitals. 

The carbon atom has a share in eight electrons (Ne structure) whilst each hydrogen atom has a share in two electrons (He structure). This is a gross simplification of covalent bonding, since the actual electrons are present in molecular orbitals which occupy the whole space around the five atoms of the molecule. 

B3.1.5.2 THE LINEAR COMBINATIONS OF ATOMIC ORBITALS TO FORM MOLECULAR ORBITALS EXPANSION OF THE SPIN ORBITALS... 

Hence we have two molecular orbitals, one along the line of centres, the other as two sausage-like clouds, called the n orbital or n bond (and the two electrons in it, the n electrons). The double bond is shorter than a single C—C bond because of the double overlap but the n electron cloud is easily attacked by other atoms, hence the reactivity of ethene compared with methane or ethane. 

Ferrocene Figure 2-47) provides a prime ex.ample of multi-haptic bonds, i.e, a situation where the electrons that coordinate the cyclopentadienyl rings with the iron atom arc contained in molecular orbitals delocalised over the iron atom and the 10 carbon atoms of the cyclopentadienyl rings [82. ... 

Boranes are typical species with electron-deficient bonds, where a chemical bond has more centers than electrons. The smallest molecule showing this property is diborane. Each of the two B-H-B bonds (shown in Figure 2-60a) contains only two electrons, while the molecular orbital extends over three atoms. A correct representation has to represent the delocalization of the two electrons over three atom centers as shown in Figure 2-60b. Figure 2-60c shows another type of electron-deficient bond. In boron cage compounds, boron-boron bonds share their electron pair with the unoccupied atom orbital of a third boron atom [86]. These types of bonds cannot be accommodated in a single VB model of two-electron/ two-centered bonds. 

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. 

Drawing-, text-, and structure-input tools are provided that enable easy generation of flow charts, textual annotations or labels, structures, or reaction schemes. It is also possible to select different representation styles for bond types, ring sizes, molecular orbitals, and reaction arrows. The structure diagrams can be verified according to free valences or atom labels. Properties such as molecular... 

The next step towards increasing the accuracy in estimating molecular properties is to use different contributions for atoms in different hybridi2ation states. This simple extension is sufficient to reproduce mean molecular polarizabilities to within 1-3 % of the experimental value. The estimation of mean molecular polarizabilities from atomic refractions has a long history, dating back to around 1911 [7], Miller and Sav-chik were the first to propose a method that considered atom hybridization in which each atom is characterized by its state of atomic hybridization [8]. They derived a formula for calculating these contributions on the basis of a theoretical interpretation of variational perturbation results and on the basis of molecular orbital theory. 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

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... 

Ch em uses Slater atom ic orbitals to con struct sent i-em pirical molecular orbitals. I he complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and arc not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

All m oleciilar orbitals are com biiiations of the same set of atom ic orbitals they differ only by their LCAO expansion coefficients. HyperC hem computes these coefficients, C p. and the molecular orbital energies by requiring that the ground-state electronic energy beat a minimum. That is, any change in the computed coefficients can only increase the energy. 

Even with the minimal basis set of atomic orbitals used m most sem i-empirical calculatitm s. the n urn ber of molecii lar orbitals resulting from an SCFcalciilation exceeds the num ber of occupied molecular orbitals by a factor of about two. The n um ber of virtual orbitals in an ah initio calculation depends on the basis set used in this calculation. 

MP2 correlation energy calculations may increase the computational lime because a tw o-electron integral Iran sfonnalion from atomic orbitals (.40 s) to molecular orbitals (MO s) is ret]uired. HyperClicrn rnayalso need additional main memory arul/orcxtra disk space to store the two-eleetron integrals of the MO s. 

The first term in eludes the electrostatic attraction s and repulsions between the net charges on pairs of atoms, one from each molecule. The second in volves in teraction s between occupied and vacant molecular orbitals on the two molecules. The hypothesis is that the reaction proceeds in a way to produce the most favorable... 

---