Valence shell electron pair repulsion (VSEPR) theory Valence shell electron pair repulsion (VSEPR) theory (1957) is a model in chemistry, which is used for predicting the shapes of individual molecules, based upon their extent of electron-pair electrostatic repulsion, determined using steric numbers. The theory is also called the Gillespie- Nyholm theory after the two main developers. The premise of VSEPR is that a constructed Lewis structure is expanded to show all lone pairs of electrons alongside protruding and projecting bonds, for predicting the geometric shape and lone-pair behavior of a compound through consideration of the total coordination number. VSEPR theory is based on the idea that the geometry of a molecule or polyatomic ion is determined primarily by repulsion among the pairs of electrons associated with a central atom. The pairs of electrons may be bonding or nonbonding (also called lone pairs). Only valence electrons of the central atom influence the molecular shape in a meaningful way. Basic assumptions 1. Pairs of electrons in the valence shell of a central atom repel each other. 2. These pairs of electrons tend to occupy positions in space that minimize repulsions and maximize the distance of separation between them. 3. The valence shell is taken as a sphere with electron pairs localizing on the spherical surface at maximum distance from one another. 4. A multiple bond is treated as if it is a single electron pair and the two or three electron pairs of a multiple bond are treated as a single super pair. 1
5. Where two or more resonance structures can depict a molecule the VSEPR model is applicable to any such structure. Three types of repulsion take place between the electrons of a molecule: The lone pair-lone pair repulsion The lone pair-bonding pair repulsion The bonding pair-bonding pair repulsion. A molecule must avoid these repulsions to remain stable. When repulsion cannot be avoided, the weaker repulsion (i.e. the one that causes the smallest deviation from the ideal shape) is preferred. The lone pair-lone pair (lp-lp) repulsion is considered to be stronger than the lone pair-bonding pair (lp-bp) repulsion, which in turn is stronger than the bonding pair-bonding pair (bp-bp) repulsion. Hence, the weaker bp-bp repulsion is preferred over the lp-lp or lp-bp repulsion. Note: In order to assignment hybridization for covalent molecules according to VSEPR you must draw the Lewis dot diagram for the molecule, determine the number of bonding and non-bonding as well as calculation formal charge for central atom and then calculate of electron pairs as fellow: # of valence electrons for central atom(valence state)=? e # of electrons for terminal atoms(one electron for atom) =?e # of pi bonds = -?e (-1 for one π-bond) Linear Atoms are arranged in a straight line. 2
Bond angle: 180 Ex: CO 2 O=C=O C=4e 2O=2e 2π=-2e # of electron =4e/2=2 pairs of electron i.e. type of hybridization is sp(linear structure) Trigonal Planar Triangular and flat molecule Three atoms are attached to the central atom. No lone pairs on the central atom Bond angle: 120 Ex: HCHO O H H C= 4e 2H=2e O=1e 1π=-1e # of electron =6e/2=3 pairs of electron i.e. type of hybridization is sp 2 (trigonal structure) Tetrahedral Four atoms are attached to the central atom. Bond angle: 109.5 Ex: CH 4, CCl 4 H H 3 H H
C= 4e 4H=4e # of electron =8e/2=4 pairs of electron i.e. type of hybridization is sp 3 (tetrahedral structure) Pyramidal Three atoms attached to the central atom. One lone pair on the central atom Bond angle: 107 Ex: NH 3 N= 5e 3H=3e # of electron =8e/2=4 pairs of electron i.e. type of hybridization is sp 3 (tetrahedral structure) but general shape is pyramidal Bent Usually two atoms attached to the central atom. Two lone pairs on the central atom Bond angle: 105 Ex: H 2 O O= 6e 2H=2e # of electron =8e/2=4 pairs of electron i.e. type of hybridization is sp 3 (tetrahedral structure) but general shape is bent or angular. 4
Other examples; NO 3 -, NH 4 + O - N + O O - H N + H H H N + = 4e 3O=3e 1π=-1e # electron =6e/2=3 pairs of electron i.e. type of hybridization is sp 2 (trigonal structure) N + = 4e 4H=4e # of electron =8e/2=4 pairs of electron i.e. type of hybridization is sp 3 (tetrahedral structure) 5
(Molecular Shapes) A = the central atom, X = an atom bonded to A, E = a lone pair on A Note: There are lone pairs on X or other atoms, but we don't care. We are interested in only the electron densities or domains around atom A. 6
Molecular Orbital Theory(MOT) When two atoms approach each other, according to the molecular orbital concept, their atomic orbitals overlap. The electrons no longer belong to one atom but to the molecule as a whole. To represent this process, we can combine the two atomic wave functions to give two molecular orbitals. This realistic representation of the bonding in covalent compounds involves the linear combination of atomic orbitals and is thus called the LCAO method. If it is s orbitals that mix, then the molecular orbitals formed are given the representation of σ and σ* (pronounced sigma and sigma-star). Figure below shows simplified electron density plots for the atomic orbitals and the resulting molecular orbitals. For the s orbital, the electron density between the two nuclei is increased relative to that between two independent atoms. There is an electrostatic attraction between the positive nuclei and this area of higher electron density, and the σ orbital is called a bonding orbital. Conversely, for the σ* orbital, the electron density between the nuclei is decreased, and the partially exposed nuclei cause an electrostatic repulsion between the two atoms. Thus, the σ* orbital is an antibonding orbital. Figure below 7
illustrates the variation in the energies of these two molecular orbitals as the atoms are brought together. When the atoms are an infinite distance apart, there is no attraction or repulsion, and so under those conditions they can be considered as having a zero energy state. As a result of electrostatic attraction between the electrons of one atom and the nuclear protons of the other, bringing together two atoms results in a decrease in energy. Figure above shows that the energy of the bonding orbital reaches a minimum at a certain internuclear separation. This point represents the normal bond length in the molecule. At that separation, the attractive force between the electron of one atom and the protons of the other atom is just balanced by the repulsions between the two nuclei. When the atoms are brought closer together, the repulsive force between the nuclei becomes greater, and the energy of the bonding orbital starts to rise. For electrons in the antibonding orbital, there is no energy minimum. Electrostatic repulsion increases continuously as the partially exposed nuclei come closer and closer. Another way to picture the two types of molecular orbitals is to consider them as wave combinations. The overlap of electron wave functions of the constituent atoms in constructive interference corresponds to a bonding 8
orbital. Destructive interference, however, corresponds to an antibonding orbital. Several general statements can be made about molecular orbitals: 1. writing of electron configuration for two atoms or ions 2.For orbitals to overlap, the signs on the overlapping lobes must be the same. 3. Whenever two atomic orbitals mix, two molecular orbitals are formed, one of which is bonding and the other antibonding. The bonding orbital is always lower in energy than the antibonding orbital. 4. For significant mixing to occur, the atomic orbitals must be of similar energy. 5. Each molecular orbital can hold a maximum of two electrons, one with spin +1/2, the other -1/2. 6. The electron configuration of a molecule can be constructed by using the Aufbau principle by filling the lowest energy molecular orbitals in sequence. 7. When electrons are placed in different molecular orbitals of equal energy, the parallel arrangement (Hund s rule) will have the lowest energy. 8. The bond order in a diatomic molecule is defined as the summation of bonding electron minus the summation of antibonding electron divided two. 9
Molecular Orbitals for Period 1 Diatomic Molecules 1-H 2 + molecular ion 1H 1s 1 1H + 1s 0 Figure below is an energy-level diagram that depicts the occupancy of the atomic orbitals and the resulting molecular orbitals. Hence, the σ orbital arising from the mixing of two 1s atomic orbitals is labeled as σ 1s. Notice that the energy of the electron is lower in the σ 1s molecular orbital than it is in the 1s atomic orbital. This is a result of the simultaneous attraction of the electron to two hydrogen nuclei. It is the net reduction in total electron energy that is the driving force in covalent bond formation. In addition to the energy of the electron is higher in the σ* 1s molecular orbital than it is in the 1s atomic orbital Molecular orbital diagram for the H 2 + molecular ion. The electron configuration of the dihydrogen cation is written as (σ 1s ) 1. Experimental studies of this ion show that it has a bond length of 106 pm and a bond strength of 255 kj.mol -1. 10
2- H 2 hydrogen molecule 1H 1s 1 1H 1s 1 The energy-level diagram for the hydrogen molecule, H 2, is shown in Figure below. Molecular orbital diagram for the H 2 molecule. The electron configuration of the dihydrogen molecule is written as (σ 1s ) 2. The greater the bond order, the greater the strength of the bond and the shorter the bond length. This correlation matches our experimental findings of a shorter bond length (74 pm) and a much stronger bond (436 kj.mol -1 ) than that in the dihydrogen cation. 11
3- He 2 + molecular ion 2He 1s 2 2He + 1s 1 Molecular orbital diagram for the He 2 + molecular ion. The electron configuration of the dihelium cation is written as (σ 1s ) 2 (σ* 1s ) 1 The existence of a weaker bond is confirmed by the bond length (108 pm) and bond energy (251 kj.mol -1 ) values about the same as those of the dihydrogen ion. 4-He 2 molecule 2He 1s 2 2He + 1s 2 12
Molecular orbital diagram for the 1s atomic orbitals of the (theoretical) He 2 molecule. The electron configuration of the He 2 molecule is written as (σ 1s ) 2 (σ* 1s ) 2 Molecular Orbitals for Period 2 Diatomic Molecules Li 2 molecule 3Li 1s 2 2s 1 3Li 1s 2 2s 1 In Li 2 molecule the 1s atomic orbital is filled, and so there will be no net bonding contribution from these orbitals. Hence, we need only consider the filling of the molecular orbitals derived from the 2s atomic orbitals Molecular orbital diagram for the 2s atomic orbitals of the Li 2 (gasphase) molecule. The electron configuration of the Li 2 molecule is written as (σ 2s ) 2 Both the measured bond length and the bond energy are consistent with this value for the bond order. 13
At the beginning of the period 2 (B 2,C 2 and N 2 ), the levels differ in energy by only about 0.2 MJ.mol -1. In these circumstances, the wave functions for the 2s and 2p orbitals become mixed. One result of the mixing is an increase in energy of the σ 2p molecular orbital to the point where it has greater energy than the π 2p orbital. This ordering of orbitals applies to (B 2, C 2, and N 2 ) the σ-π crossover occurring between dinitrogen and dioxygen. N 2 molecule 7N 1s 2 2s 2 2p 3 7N 1s 2 2s 2 2p 3 Molecular orbital diagram for the 2p atomic orbitals of the N 2 molecule. The electron configuration of the N 2 molecule is written as (π 2p ) 4 (σ 2p ) 2. 14
For all three of these diatomic molecules, B 2, C 2, N 2, O 2, and F 2, the bonding and antibonding orbitals formed from both 1s and 2s atomic orbitals are filled, and so there will be no net bonding contribution from these orbitals. Hence, we need only consider the filling of the molecular orbitals derived from the 2p atomic orbitals. For the Period 2 elements beyond dinitrogen, the σ 2p orbital is the lowest in energy, followed in order of increasing energy by π 2p, π* 2p, and σ* 2p. O 2 molecule 8O 1s 2 2s 2 2p 4 8O 1s 2 2s 2 2p 4 According to Hund s rule, there are indeed two unpaired electrons; this diagram conforms with experimental measurements. Molecular orbital diagram for the 2p atomic orbitals of the O 2 molecule. 15
The electron configuration of the O 2 molecule is written as (σ 2p ) 2 (π 2p ) 4( π* 2p ) 2 The bond order of O 2 is consistent with bond length and bond energy measurements. Thus, the molecular orbital model explains our experimental observations perfectly. F 2 molecule 9F 1s 2 2s 2 2p 5 9F 1s 2 2s 2 2p 5 Molecular orbital diagram for the 2p atomic orbitals of the F2 molecule. The electron configuration of the F 2 molecule is written as (σ 2p ) 2 (π 2p ) 4( π* 2p ) 4 16
Molecular Orbitals for Heteronuclear Diatomic Molecules When we combine atomic orbitals from different elements, we have to consider that the atomic orbitals will have different energies. For elements from the same period, we find that the higher the atomic number, the higher the Z eff and hence the lower the orbital energies. Examples CO molecule 6C 1s 2 2s 2 2p 2 8O 1s 2 2s 2 2p 4 The oxygen atomic orbitals are lower in energy than those of carbon as a result of the greater Z eff, but they are close enough in energy that we can construct a molecular orbital diagram similar to that of the homonuclear diatomic molecules. 17
Simplified molecular orbital diagram for the 2s and 2p atomic orbitals of the CO molecule. The electron configuration of the CO molecule is written as (π 2p ) 4 (σ 2p ) 2. The very high bond energy of 1072 kj.mol -1 supports this prediction(triple bond). The molecular orbital diagram also indicates that the triple bond is not made up of three equivalent bonds, as the electron-dot diagram suggests, but of a combination of one σ and two π bonds. HCl molecule 1H 1s 1 17Cl 1s 2 2s 2 2p 6 3s 2 3p 5 The molecular orbital approach can be applied to diatomic molecules containing atoms of different periods. For example the hydrogen chloride molecule (Figure below). Calculations show that the 3p orbitals of chlorine have a slightly lower energy than that of the 1s orbital of hydrogen. The 1s orbital can only form a σ bond, which must be with the 3p orbital that is aligned along the bonding axis (traditionally chosen as the p z orbital). Hence, we conclude that a σ bonding and σ antibonding pair of orbitals will 18
be formed between the 1s (H) and 3p (Cl) orbitals. With each atom contributing one electron, the bonding molecular orbital will be filled. This configuration yields a single bond. The two other 3p orbitals are oriented in such a way that no net overlap (hence, no mixing) with the 1s orbital of hydrogen can occur. As a result, the electron pairs in these orbitals are considered to be nonbonding. That is, they have the same energy in the molecule as they did in the independent chlorine atom. Molecular orbital diagram for the 1s atomic orbital of hydrogen and the 3p atomic orbitals of chlorine in the HCl molecule. 19