Molecular orbital theory.

Molecular orbital theoryviews a molecule as a set of positive nuclei with electrons moving in the field of these nuclei. Electrons in a molecule do not necessary belong to any individual atom. The electrons occupy orbitalsthat extend the entire molecule called molecular orbitals (MOs).Quantity of MOs is equal to quantity ofatomic orbitals they are formed from. The ground state electronic structure of a molecule is derived by placing the appropriate number of electrons into the set of MOs. The MOs are filled according to the same principles, as atomic orbitals: (1) each electron is placed into the lowest energy orbital available, (2) no more than two electrons populate a single orbital, and (3) electrons with unpaired spins are spread out as much as possible, over orbitals of the same energy.

The simplest way to visualize shapes of molecular orbitals is to consider various combinations of atomic orbitals that reside on the nuclei composing the molecule, taking into account the signs of the wave functions. Energies of molecular orbitals can be calculated from energies of atomic orbitals they are formed from.

Bonding molecular orbital. When portions of orbitals with the same sign overlap, the amplitudes of orbitals are added. The resulting molecular orbital has a shape that concentrates electron density between the two nuclei. Electrons placed in such a molecular orbital tend to hold the nuclei together and stabilize a molecule. For that reason, this orbital is called a bonding molecular orbital.

Antibonding molecular orbital. When portions of orbitals of opposite signs overlap, a molecular orbital produced has the maximum electron density outside the region between the two nuclei. If the electrons of a molecule are placed into this molecular orbital, they destabilize the molecule, therefore the orbital is said to be antibonding. Antibonding character of an orbital is denoted by an asterisk superscript (*).

Nonbonding molecular orbital. In some cases interaction of two orbitals result in appearance of two overlaps zones: one with the same signs of portions of orbitals and the second with the opposite ones. The increase of the electron density in one zone is completely compensated by the decrease of the electron density in the second one. The electrons of a molecule placed into this molecular orbital, neither stabilize, nor destabilize the molecule, therefore the orbital is said to be nonbonding.

The net bond order can be defined as:

Electrons, placed into the bonding molecular orbital lead to stable bond formation and, therefore, energy of this orbital is lower than that of the two initial atomic orbitals. On the other hand, electrons, placed into the antibonding orbital lead to destabilization of the molecule and thus to state higher in energy than that of the two initial atomic orbitals. This can be represented schematically, as shown in Fig. 3.5, where the energies of the atomic orbitals of the separate appear on both sides of the energy-level diagram and the energies of the molecular orbitals are placed in the center. Using this simplest diagram we can examine the bonding in the H₂ molecule (Fig. 3.5). There are two electrons in H₂ that we place in the lowest-energy molecular orbital, the s_1s. Using the same diagram, we can see why the molecule He₂ does not exist. The species would have four electrons, two of which would be placed into the s_1s orbital and. The other two would be forced to occupy the s*_1s orbital. As a result, the net bond order has a value of zero for He₂. Since the bond order is zero in He₂, the molecule doesn’t exist. Thus, the net bond order in molecular ion He₂⁺ is equal to 0.5, this particle may exists in appropriate external conditions.

For diatomic molecules of second period elements, only molecular orbitals derived from the interaction of the valent shell 2s and 2p orbitals should be considered. The 1s orbitals are not involved to any appreciable extent in the bonding in these molecules.

The real mark of success for the molecular orbital theory is an adequate description of the O₂ molecule. This molecule is found experimentally to be paramagnetic with two unpaired electrons. In addition, its bond length and bond energy suggest, that there is a double bond between the two oxygen atoms. Paramagnetic properties of the O₂ molecule can’t be explained by a valence bond theory; an attempt gives us (1) a molecule with a double bond and all the electrons paired, (2) a molecule containing two unpaired electrons, but oxygen are bonded by single O-O bond only. The molecular orbital description of O₂ is shown in Fig 3.6. The first 10 of 12 valence electrons populate all the same molecular orbitals, as in N₂. The final 2 electrons must then be placed in the p*_2px and p*_2py antibonding orbitals. As these orbitals are of the same energy, electrons spread themselves out with their spins in the same directions. These two antibonding electrons cancel the effect of the two of the p-bonding electrons, so the net bond order in O₂ has a value of two. So, for O₂ molecule predictions of the MO theory are in precise agreement with experimental evidence (both bond order and quantity of unpaired electrons is predicted correctly).

Fig. 3.5 Bonding in the H₂ molecule.

Fig. 3.6 Bonding in the O₂ molecule

Polar covalent bond. If the two atoms joined by the covalent bond differ in electronegativity, the electron pair will be pulled more towards the atom with the higher electronegativity. For example, consider the HCl molecule. Chlorine is more electronegative, than hydrogen; therefore, more than half of the electron density of the bond pair is concentrated around the chlorine atom. As a result, the chlorine atom is negatively charged and the hydrogen atom is positively charged in the HCl molecule. However, electron transfer from H to Cl is not complete, and HCl is far from being ionic compound. The measurement suggest, that these charges are only about +0.17 on the hydrogen atom and –0.17 on the chlorine one. (The partial charges on atoms are usually indicated by lowercase Greek letter delta: d+ and d-). Equal negative and positive charges separated by a distance constitute a dipole. Thus, the HCl molecule is a dipole and is said to be polar. A dipole is defined quantitatively by its dipole moment, the product of the charge on either end of the dipole and the distance between the charges. A bond with a large dipole moment is said to be very polar, while nonpolar bond will have no dipole moment at all.

There is no sharp dividing between covalent and ionic substances. Even in compounds that we think of being ionic, such as NaCl, there is some degree of covalent character of the bonds between atoms. As a very rough guide, bonds become more than 50% ionic when the electronegativity difference between the atoms is lager than about 1.7 and we normally consider substances with these bonds as being ionic compounds.

3.3 Ionic Bond

Ionic bond in binary compound is formed by attraction of oppositely charged ions. Electronegativities of atoms forming ionic bond should differ significantly (see previous paragraph). Representative elements (s- and p-) often have ns²np⁶ (n³2) electron configuration in ionic compounds. For d- and f-elements the octet rule doesn’t work well, instead, particular stable electron configurations (for example, nd⁵ or nd¹⁰) are formed.

For most of nonmetallic elements, addition of an electron to the atom is energetically favorable; therefore these elements readily form anions. Thus, formation of an anion with a charge of 2- or larger is always endothermic. When a valent shell is completed, any additional electron must enter the next higher shell. This also requires a very large amount of energy. As successive ionization energies increase in magnitude, formation of highly charged cations is energetically favorable.

Attractions between opposite charged ions, which occur when the ionic compound is formed, produce a large decrease in the potential energy (greater, then total energy required to form the ions). This is the principle reason of the stability of ionic compounds. A crystalline lattice of ionic compound is composed of ions of opposite charges, regularly arranged to achieve a minimum of potential energy. The arrangement of ions in the lattice depends on the charges of the ions and their radii, but is practically unaffected by electronic structures of the ions. The energy delivered when a crystalline lattice is formed from gaseous ions is called the lattice energy. Ionic bond is nonsaturable and nondirectional, in contrast to covalent bond.

Polarization of an anion by the cationisaconcept used to explain ionic-covalent character of the bonds in metal - nonmetal compounds. Cations of metallic elements are almost always smaller than anions of nonmetallic elements. The positive charge of the cation is therefore concentrated in a rather small volume, while the negative charge of the anion is spread over a much larger volume. When a cation is located near an anion it pulls part of the electron density into the region between the two nuclei. The electron cloud of the anion becomes distorted (non-spherical) and the anion is said to be polarizedby the cation. Since polarization increases the electron density between nuclei, the greater the degree of polarization, the greater the degree of covalent character of the bonds.

There are two major factors that contribute to cation’s ability to polarize a given anion. All other things being equal, a cation with a 2+ charge will distort the electron cloud of an anion more, that one with 1+ charge. The second factor is the size of the cation. In a small cation the positive charge is highly concentrated and has a strong effect on the anion. The same positive charge on a larger cation will be more spread out, so it won’t distort the anion’s electron cloud as well. A cation effect on the anion is therefore directly proportional to its positive charge and inversely proportional to its radii. This ratio is called the ionic potential (f):

f = q/r

The ionic potentialsof Be²⁺ and Li⁺ are high because of their radii are small (e.g., LiI is ionic but has some covalent bonding present).

Going down the periodic table group, the charge on the cations stays the same (for example, Be²⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺). The sizes of the cations increase, so their ionic potential decrease. Therefore, going down the group, compounds with the same anion should become more and more ionic (for example, MgCl₂ should be more ionic, than BeCl₂).

The atomic radii decrease going from left to right across the period, while the charges of the cations increase (Na⁺ — Mg²⁺ — Al³⁺). This causes a rapid increase of the ionic potential and corresponding increase of the covalent character of the bonds. Simple ions with large positive charges like C⁴⁺, N⁵⁺, S⁶⁺, Cl⁷⁺, Ti⁴⁺, V⁵⁺, Cr⁶⁺, Mn⁷⁺, couldn’t exist. If the oxidation state of an atom is high, polar covalent bond is formed.

3.4 Metallic bond.

A metal is composed of regularly arranged positive ions (nuclei and core electrons) with the valence electrons belonging to the crystal as a whole instead to any single atom. This is sometimes described as an array of positive ions in a "sea of electrons" or in the electron gas. An electrostatic attraction occurs between the lattice of positive ions and delocalized electrons. Metallic bond is nonsaturable and nondirectional, similar to ionic bond.

Electronic band structure model. When atoms of metallic element come together, their outermost atomic orbitals overlap to form bonding and antibondingmolecular orbitals - in much the same sort of way that a covalent bond is formed. The difference, however, is that all identical outermost orbitals of all of the atoms overlap to give a vast number of molecular orbitals which extend over the whole piece of metal[3].

A large number of molecular orbitals formed from identical atomic orbitals have very close energies; this range of energies is called an energy band.An energy band, occupied by electrons iscalled a valence band; an unoccupied one is called conduction band.A forbidden band (or a band gap) is a forbidden energy range which separates bands that may contain electrons. In a metal valence band is partially filled and not separated from conduction band. In a semiconductor or an insulator a valence band contains many orbitals, most of which are occupied, whereas conduction band (separated by a band gap) contains many orbitals most of which are empty.

The valence electrons in metals, unlike those in covalently bonded substances, are capable of wandering relatively freely from one atom to another throughout the entire crystal. Many of the characteristic properties of metals, such as metallic luster, high thermal and electrical conductivity are attributable to the delocalization of the valence electrons. The valence electrons are always free to move when an electrical field is applied.

Malleability and ductility of metals are related to the presence of the mobile valence electrons and nondirectional character of the metallic bond. When a metal is shaped or drawn, it does not fracture, because the ions in its crystal are quite easily displaced with respect to one another. The delocalized valence electrons prevent the ions from coming too close, therefore strong repulsive forces that can cause fracture of the crystal are not generated.

Until less then half of valent orbitals of an atom are filled, the more electrons can be involved in bonding, the stronger the attractions tend to be. So, melting points of metals differ significantly: mercury is a liquid at ambient conditions, while tungsten melts at 3410°C.

3.5 Polarity of molecules and molecular structure.

Molecule polarity is an important property because many of the physical properties of substances depend on it.When a molecule consist only two atoms, it must be polar, if the bond is polar (the two atoms joined by the bond differ in electronegativity). However, if there are three or more atoms in a molecule, this molecule may be nonpolar, even when the bonds are polar. The overall polarity of a molecule (overall dipole moment) can be considered as to result from the sum of the individual bond dipoles, which add together like vectors. For example, the C-O bonds in carbon dioxide molecule are polar, because oxygen is more electronegative, than carbon (3.5 and 2.5, respectively). The individual bond dipoles can be represented by arrows, directed from positively charged atom to the negatively charged one (the arrow shows shift of the electron density). The bond dipoles in CO₂ molecule are oriented in opposite directions and they exactly cancel each other:

= = ®

Similarly, bond dipoles of flat triangle molecules AX₃, tetrahedral AX₄, trigonal bipyramidal AX₅ and octahedral AX₆, cancel each other. Thus, if the atoms bonded to the central atom A are not the same, the individual bonds will differ in polarities and cancelation of the bond dipoles usually can’t occur.

In most cases, when there are lone pairs in the valence shell of the central atom, the bond dipoles do not completely cancel. For example, in bent molecules (Н₂О, OF₂ or SO₂) two bond dipoles do not cancel each other entirely. As a result, these molecules have a net dipole moment are polar. Another example is ammonia molecule. It has a trygonal pyramidal shape and the three bond dipoles do not cancel each other entirely. Therefore, the NH₃ molecule is polar. Thus, there are two types of nonpolar molecules that have lone pairs on the central atom: one is the linear AX₂E₃ structure and the other is the square planar AX₄E₂ structure.