UNIT-2. �Chemical Bonding

Prepared by Dr.J.A.Chaudhari

SARDAR PATEL UNIVERSITY�Programme: B.Sc �Semester: 2�Syllabus with effect from: 2022

Paper Code: US02CCHE51

Total Credit: 4

Title of Paper: GENERAL CHEMISTRY- II �

• Chemical Bonding : The Lewis Theory, Sidgwick-Powell Theory, Valence Shell Electron Pair Repulsion (VSEPR) Theory, effect of Lone Paris, Effect of Eletronegativity, Isoelectronic Principle, Some Example using VSEPR Theory, like BF₃ and the [BF₄]^- ion, Ammonia NH₃, Water H₂O, Phosphorus pentachloride PCl₅, Chloride trifluoride ClF₃, Sulphur hexafluoride SF6, The triiodode ion I₃^-, Sulphur tetrafluoride SF₄, Iodine heptafluoride IF₇.

• LCAO Mehtod, s-s Combination of Orbital, s-p Combination of Orbitals, p-p Combination of Orbitals, Rules for Linear Combination of Atomic Orbitals, Examples of Molecular Orbital Treatment for Homo Nuclear Diatomic Molecules H₂⁺,H₂, He₂⁺, He₂, C₂ , O₂, B₂, F₂.

• Selected Topics in Inorganic Chemistry, Concise Inorganic Chemistry, 5th Edition, J D Lee. (UNIT - 2)

The Periodic Table

10-Ne: 1s² 2s² 2p⁶

20-Ca: [Ar] 4s²

1-H: 1s¹

2-He: 1s²

3-Li: 1s² 2s¹

4-Be: 1s² 2s²

5-B: 1s² 2s² 2p¹

6-C: 1s² 2s² 2p²

7-N: 1s² 2s² 2p³

8-O: 1s² 2s² 2p⁴

9-F: 1s² 2s² 2p⁵

11-Na: [Ne] 3s¹

12-Mg: [Ne] 3s²

13-Al: [Ne] 3s² 3p¹

14-Si: [Ne] 3s² 3p²

15-P: [Ne] 3s² 3p³

16-S: [Ne] 3s² 3p⁴

17-Cl: [Ne] 3s² 3p⁵

18-Ar: [Ne] 3s² 3p⁶

19-K: [Ar] 4s¹

21-Sc: [Ar] 3d¹4s²

22-Ti: [Ar] 3d²4s²

23-V: [Ar] 3d³4s²

24-Cr: [Ar] 3d⁵4s¹

25-Mn: [Ar] 3d⁵4s²

26-Fe: [Ar] 3d⁶4s²

27-Co: [Ar] 3d⁷4s²

28-Ni: [Ar] 3d⁸4s²

29-Cu: [Ar] 3d¹⁰4s¹

30-Zn: [Ar] 3d¹⁰4s²

2.1 Introduction:

There are several different theories which explain the electronic structure and shapes of known molecules. The value of a theory lies more in its usefulness than in truth. Being able to predict the shape of a molecule is important. In many cases all theories give the correct answer.

The octet rule :

This was first theory to explain a covalent bond in terms of electrons. If two electrons are shared between two atoms, this constitutes a bond and binds the atoms together. For many light atoms a stable arrangement is attained when atom is surrounded by eight electrons. This ‘octet’ can be made up from ‘totally owned’ and some electrons which are ‘shared’.

(2.2) The Lewis Theory :

• Octet : “When two or more electrons are shared between two atoms, which constitutes bond(s) and if atom is surrounded by stable electronic configuration of eight electrons, such arrangement of electrons is called octet”.

• જ્યારે બે પરમાણુ વચ્ચે બે અથવા વધુ ઇલેક્ટ્રોન વહેંચવામાં આવે છે, જે બોન્ડ બનાવે છે અને જો આઠ ઇલેક્ટ્રોનની સ્થિર ઇલેક્ટ્રોનિક ગોઠવણી દ્વારા અણુ ઘેરાયેલો હોય, તો ઇલેક્ટ્રોનની આ પ્રકારની વ્યવસ્થા ઓક્ટેટ કહેવામાં આવે છે.

• Octet rule : “Atoms continue to form bonds until they have made up an octet of electrons”. This rule explains the observed valences in large number of cases.(આ નિયમ મોટી સંખ્યામાં અવલોકન મૂલ્યોને સમજાવે છે.)

(Que-Discuss the Lewis theory to explain covalent bond with suitable example)

(i) Covalent bond in chlorine molecule:

A chlorine atom has seven electrons in its outer shell, so by sharing one electron with another Cl-atom both atoms attain an octet and form a chlorine molecule-Cl₂

Defination of Covalent Bond: The chemical bond formed between two atoms due to the sharing of electron pair(s) is called covalent bond. 

(ii) Covalent bond in carbon tetrachloride

(CCl₄) : A carbon atom has four electrons in its outer shell and by sharing all four electrons and forming four bonds it attains octet status in CCl₄.

(iii) Covalent bond in ammonia (NH₃) : A nitrogen atom has five valence electrons and in ammonia it shares three of five outer electrons forming three bonds and thus attaining a stable arrangement of eight electrons.

(iv) Covalent bond in H₂O and HF:

In a similar way oxygen atom attain an octet by sharing two electrons in H₂O and fluorine atom completes octet by sharing one electron in HF molecule.

(v) Covalent bond in CO₂ :

Double bonds in CO₂ are explained by sharing four electrons between two atoms carbon and oxygen.

Exceptions to the octet rule :

Beryllium and boron have less than four outer electrons. Even if all the outer electrons are used to form bonds an octet cannot be attained.

The octet rule is also not obeyed where atoms have an extra energy level which is close in energy to the p-level, may accept electrons and used for bonding purpose. As for example PF₃ obeys octet rule but that of PF₅ does not. Any compound with more than four covalent bonds may break the octet rule i.e. compounds of elements after the first two period in the periodic table.

PF₅-molecule

PF₃ molecule

The octet rule does not obeyed by molecule which have odd number of electrons e.g. NO (15-electrons), ClO₂ (33-electrons).

(2.3) SidgwickPowell Theory :

In 1940 Sidgwick and Powell suggested that molecules or ions which contain only single bonds, the approximate shape can be predicted from the number of electron pairs in the outer or valence shell of central atom.

These electron pairs may be one or more bonding pairs and also lone pairs. Both these type of electron pairs were taken as equivalent, since all electron pairs take up equal space. They repeal each other. Repulsion is minimized if the electron pairs are oriented in space as far apart as possible.

Postulates :

1. If there are two electron pairs in the valence shell of the central atom the orbital containing them will be oriented at 180° to each other. If these orbitals overlap with orbitals from other atom to form bonds, then shape of molecule will be linear.

2. If there are three electron pairs in the v.s. of the central atom the orbital containing them will be oriented at 120° to each other. If these orbitals overlap with orbitals from other atom to form bonds, gives triangular structure.

4. For five electron pairs, the shape is triangular bipyramidal.

3. If there are four electron pairs on the central atom, they will be oriented at 109° 28’, and the shape is tetrahedral.

5. For six electron pairs, the bond angles are 90° and the shape is octahedral.

Table-2. 1 Molecular shape predicated by Sidgwick-Powell Theory

Table-2. 1 Molecular shape predicated by Sidgwick-Powell Theory

Table-2. 1 Molecular shape predicated by Sidgwick-Powell Theory

2.4 Valence Shell Electron Pair Repulsion

Theory (VSEPR-Thcory) :

To predict and explain the molecular shapes and bond angles more exactly, Gillespie and Nyholm in 1957 extended Sidgwick-Powell theory as the ‘Valence Shell Electron Pair Repulsion’ Theory (VSEPR-Theory) may be summarized:

• The shape of molecule is determined by repulsion between the entire(all) electron pairs present in the v. s. of central atom.

• Repulsion between two lone pairs is greater than repulsion between lone pair and a bond pair, since a lone pair of electrons take up more space round the central atom than bond pair, which is also greater than repulsion between two bond pairs. Thus the presence of lone pairs on the central atom causes distortion in shape.

The repulsions are such that:

Lone-pair ↔ lone-pair > lone-pair ↔ bond-pair > bond-pair ↔ bond-pair;(↔ means repulsion)

• The magnitude(Intenticity) of repulsions between bonding pairs of electrons depends on the electro negativity difference between central atom and other atoms.

• Double bond causes more repulsion than single bond and triple bond causes more repulsion than a double bond.

Because of more repulsion of lone pair with bond pair, the H-N-H bond reduced from 109°28' to 107°48'. In H₂O the O-atom has two lone pairs and two bond pairs of electrons in its outer shell.

Effect of Lone Pairs :

In CH₄ there are four bonding pairs of electrons in the outer shell of central C-atom and the structure is regular tetrahedron with H-C-H bond angle of 109° 28'. In NH₃ the N-atom is surrounded by three bonding pairs and one lone pair of electrons in it’s the outer shell.

In a similar way SF₆ has six bond pairs in the outer shell of central S-atom and is a regular octahedron molecule with bond angles of 90°. In BrF₅ the Br-atom is surrounded by six electron pairs, made of five bond pairs and one lone pair, which reduces the bond angle from 90⁰ to 84°30'.

The shape of H₂O molecule is based on a tetrahedron with two corners occupied by bond pairs and other corner by lone pairs. Hence bond angle reduces from 109°28' to 105°27'.

In XeF₄ it might be expected that two lone pairs would distort bond angles in an octahedron, but it remain 90°, this is because of lone pairs are occupying two trans positions and the molecule is square planar.

The shape of molecules having five electrons pairs are all based on trigonal bipyramidal, lone pairs distort the structures. The lone pairs always occupy the equatorial position.

In I₃^- (tri iodide ion) the central I-atom surrounded by five electron pairs, made up of two bond pairs and three lone pairs. The lone pairs occupy all three equatorial positions, thus giving a linear arrangement with bond angle of exactly 180°.

The structures of NF₃ and NH₃ are based on a tetrahedron with one corner occupied by a lone pair. Now χ_F>χ_H, hence high electro- -negativity of F-atom of NF₃ molecule pulls away bonding electrons further away from the N-atom than in NH₃ molecule.

Effect of electronegativity:

Thus the repulsion between bond pairs is less in NF₃ causes a greater distortion from tetrahedral and gives a F-N-F bond angle of 102°30', compared to 107°48' in NH₃. The same effect is found in H₂O (bond angle 104°27‘) and F₂O (bond angle 102°).

2.5 Isoelcctronic Principle :

“The species having same number of valence electrons are called isoelectronic species which have same structure”. Thus BF₄^-, CH₄ and NH₄⁺ are all tetrahedral; CO₃^-2, NO₃^- and SO₃ are all planar triangle and CO₂,N₃^- and NO₂⁺ are all linear.

Que: show the covalent bond formation in Cl₂ and H₂O by Lewis theory.

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Que: Draw the structure of PCl₅ and ClF₃

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Que: Defination of hybridization. Discuss the sp² hybridization in BF₃

Que- O₂ molecule is paramagnetic where as O₂^-2 ion(peroxide ion) is diamagnetic. Explain giving diagram on the basis of molecular orbital theory.

2.6 Some Examples Using the VSEPR

Theory:

(1) BF₃ and [BF₄]^- ion :

In both cases central atom is boron with electronic configuration : 1s²2s²2p¹, indicates three electrons in its outer shell. If all these electrons are used to form bonds with three fluorine atoms, then central boron will be surrounded by three electrons pairs.

The structure of BF₃ is triangular planar. The bonds are actually shorter (1.30 A⁰) than would be expected for single bonds (1.52 A⁰), due to p_π-p_π interaction, that is bonds possess some double bond character.

The [BF₄^-] ion may be regarded as being formed by adding F^- ion to BF₃ molecule by means of co-ordinate bond. Thus B-atom has four electron pairs in its outer shell; hence BF₄^- is tetrahedral.

Fig. BF₃ and BF₄^-

Ammonia molecule (NH₃) :

N-atom is central atom and has five electrons in its outer shell [N(Z=7)= 1s² 2s² 2p³]. Three of these electrons are used to form bonds with three H-atoms and two electrons do not take part in bonding and constitute a ‘lone pair’. N-atom in NH₃ surrounded by four electron pairs (3-bond pairs and 1-lone pair) gives rise to a tetrahedral structure.

Three position occupied by H-atoms and fourth position by lone pair. The structure of NH₃ either described as tetrahedral with one corner occupied by a lone pair, or as pyramidal. The presence of the lone pair causes distortion of bond angle from 109°28' to 107°48'.

Water molecule (H₂O) :

(Question :Discuss the structure of H₂O and PCl₅ molecule)

The central atom is oxygen and has six outer electrons [Electronic configuration : 1s² 2s² 2p⁴]. O-atom shares two electrons with two H-atoms form bonds, thus completing octet. The other four electrons on O-atom are non bonding. That is O-atom is surrounded by four electron pairs hence the structure of H₂O is based on a tetrahedron. Out of four electron pairs two are bonding and two are lone pairs.

Thus structure of H₂O described as tetrahedral with two positions occupied by lone pairs. The presence of two lone of electrons distort the bond angle from 109°28' to 104°27'. Any triatomic molecule must be either linear of else angular. H₂O is bent molecule since the molecule is based on tetrahedron.

Phosphorus pentachloride (PCl₅) :�

Gaseous PCl₅ is covalent. In PCl₅, P-atom is central atom and has five outer electrons in its valence shell. All the five outer electrons are used to form bonds with the five Cl-atoms. Thus in PCl₅ molecule the valence shell of P-atom contains five electron pairs.

Hence the structure of PCl₅ is trigonal bipyramid All the electron pairs are bonding type, that is there are no lone pairs, so the structure do not undergo distortion. However a trigonal bipyramid is not completely regular structure, since some bond angles are of 90° and others are of 120°. Thus PCl₅ is highly reactive. In solid state it splits into [PCI₄]⁺ and [PCl₆] ions as follow.

Fig. Structure of PCl₅

Chorine trifluoride (ClF₃) :

Here chorine is central atom with seven outer electrons [Cl (Z =17)= [Ne] 3s² 3p⁵]. Cl-atom shares 3-electrons with three F-atom, hence Cl-atom is surrounded by five electron pairs in its v.s. out of five pairs, three are bond pairs and two are lone pairs, hence the structure should be trigonal bipyramid.

Tbp structure is not regular shape, since all the positions are not equivalent. Lone pairs occupy two out of three comers and F-atoms occupy the other three corners. Three different arrangements are possible as shown in figure

The most stable structure will be one of lowest energy that is with the minimum repulsion between five orbitals. The strongest repulsion occurs between two lone pairs. Lone pair-bond pair repulsions are next strongest and bond pair-bond pair repulsion is the weakest one. Repulsion between two groups at 90° > Repulsion between two groups at 120°.

Structure-l has six 90° repulsion between lone pair and atoms. Structure-2 has one 90⁰ pepulsion between two lone pairs plus three 90° repulsion between lone pairs and atoms. Structure-3 has four 90⁰ repulsion between lone pairs and atoms. Hence Structure-3 is most probable. The observed bond angles are 87⁰ 48’ is close to theoretical 90⁰. The distortion in angle is caused by the presence of the two lone pairs.

Sulphur tetrailuoride (SF₄) :

In SF₄ molecule sulphur is central atom and has six outer electrons {S (Z =16)=[Ne] 3S² 3P⁴) Four electrons are used to form bonds with four F-atoms and two electrons are non bonding. Central S-atom is surrounded by five electron pairs hence structure of SF₄ is based on a trigonal bipyramid. Out of five electron pairs one is lone pair. To minimize the repulsive force lone pair occupies an equitorial position.

Fig. SF₄ molecule

Tri iodide ion (I₃^-): � When iodine (I₂) is dissolved in aqueous potassiun iodide, the tri iodide ion I₃^- is formed. It is an example of poly halide ion, which has similar structure to that of BrICl^-. The shape of I₃^- ion must be linear. I₃^- ion is regarded as being formed by co-ordinate bond between I₂ and I^- ion.

[I₂ + I^- ] → [I – I - I]^-

In I₃^- ion central I-atom has seven outer electrons {I(Z= 53) = [Kr] 4d¹⁰5S² 5P⁵}. One of outer electron is used to form bond with another I-atom, thus forming I₂ –molecule. The I–atom now have a share in eight electrons. One of the I-atom accept a lone pair of electron from I^- ion.

Now central I-atom contains ten outer electrons (five pairs). Thus shape of I₃^- ion is based on a trigonal bipymmid. There are two bond pairs and three lone pairs.

In order to minimize repulsion, three lone pairs occupy the equatorial positions, and I-atoms are located at the centre and in the two apical positions. The ion is therefore linear, with bond angle exactly 180° and hybridisation is sp³d.

Fig. The tri Iodide Ion

Important Points To Remember:� I₃^- is formed by the bonding of I₂ with I⁻ ion.� During the combination of Iodine atoms, the central atom gains a negative charge whose value will be 1.� I⁻ ion is the donor and I₂ molecule is the acceptor. Electrons are mostly accommodated in the empty d-orbitals.

Sulphur hexafluoride (SF₆) : Here sulphur is central atom with six outer electrons. All these electrons are use to form bonds with F-atoms. Thus in SF₆, the S-atom has six electron pairs in its v.s., hence structure is octahedral. There are no lone pairs, so structure is regular octahedral with bond angle of 90°.

Fig. SF₆ Molecule

Iodine hepta fluoride (IF₇) : This is only common example of non transition element (I) using seven orbitals for bonding giving pentagonal bipyramid shape. Central I-atom is surrounded by seven bond pairs of electrons. There is no lone pair.

Fig. IF₇ Molecule

MOLECULAR ORBITAL METHOD:

According to the valence bond (electron pair) theory, a molecule is considered to be made up of atoms and electrons occupy atomic orbitals. Atomic orbitals from the same atom combine to produce hybrid orbitals which can overlap more effectively with orbitals from other atoms, thus producing stronger bonds.(જે અન્ય પરમાણુથી કક્ષકો સાથે વધુ અસરકારક રીતે ઓવરલેપ કરી શકે છે, આમ મજબૂત બંધનું નિર્માણ કરે છે)

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In MOT, the valency electrons are considered to be associated with all the nuclei in the molecule. Thus the atomic orbitals from different atoms must be combined to produce molecular orbitals.

આમ, અણુ કક્ષકોનું નિર્માણ કરવા માટે વિવિધ પરમાણુની પરમાણુ કક્ષકોનું મિશ્રણ કરવું જોઇએ

Electrons may be considered either as particles or waves, therefore in an atom it may be described as occupying an atomic orbital or by a wave function ψ which is a solution of Schrodinger wave equation. Electrons in a molecule are said to occupy molecular orbitals

ઇલેક્ટ્રોન કાં તો કણો અથવા તરંગ હોવાનું માનવામાં આવે છે, તેથી અણુમાં તે પરમાણુ ભ્રમણ કક્ષા પર અથવા તરંગનું કાર્ય ψ તરીકે વર્ણવવામાં આવી શકે છે, જે શ્રોડિન્જર તરંગ સમીકરણનો ઉકેલ છે.

The wave function describing a molecular orbital may be obtained by one of two procedures

LCAO METHOD :

Que-Give an account of LCAO method.

1.Linear combination of atomic orbitals (LCAO) method. 2. United atom method.

Consider wave function ψ_(A) and ψ_(B) for atomic orbitals of two atoms A and B respectively. When these two atoms overlap then the wave function for the molecule ψ_(AB) (molecular orbital) can be obtained by a linear combination of the atomic orbitals.

ψ_(AB) = N{C₁ψ_(A) + C₂ψ_(B)}

where N is a normalizing constant chosen to ensure that the probability of finding an electron in the whole of the space is unity and C_l and C₂ are constants chosen to give a minimum energy for ψ_(AB). If atoms A and B are similar then C₁ = C₂.

The probability of finding electron in a volume dv is ψ²dv, so the probability density ψ²dv for the combination of two atoms as above is related to the wave function squared:

ψ²_(AB) = N[C₁²ψ²_(A) + 2C_lC₂ ψ_(A)ψ_(B) +C₂²ψ²_(B)]

On the right of the equation, the first term C₁²ψ²_(A) is related to the probability of finding an electron on isolated(અલગ) atom A. The third term C₂²ψ²_(B) is related to the probability of finding an electron on isolated atom B. The middle term is related to overlap between the two atomic orbitals which is called the overlap integral. This term represents the difference between the electron clouds in individual atoms and in the molecule. The larger this term the stronger is the bond.

s-s combinations of orbitals:

Que-Discuss s-s combinations of orbitals:

Suppose the atom A and B are hydrogen atoms; then the wave functions for 1s atomic orbitals of both atoms are ψ_(A) and ψ_(B)) respectively.

When these two atoms overlap, two combinations of the wave functions ψ_(A) and ψ_(B) are possible :

1. Where the signs of the two wave functions are the same: These wave functions regarded as waves that are in phase, which when combined add up to give a larger resultant wave.

ψ_(g) = N[C₁ψ_(A) + C₂ψ_(B)]

2. Where the signs of the two wave functions are different: These wave functions correspond to waves that are completely out of phase and which cancel each other by destructive(દૂર કરવું) interference.

ψ_(u) = N[C₁ψ_(A) + (-C₂ψ_(B))] = N[C₁ψ_(A) -C₂ψ_(B))]

From above discussion, following point are noted.

When a pair of atomic orbitals (i.e. ψ_(A) and ψ_(B)) combine, they give rise to a pair of molecular orbitals (i.e. ψ_(g) and ψ_(u)). Therefore the number of molecular orbitals produced must be equal to the number of atomic orbitals combined.

The function ψ_(g) leads to increased electron density in between the nuclei (see figure), and is therefore called bonding molecular orbital (BMO) which has lower energy than the atomic orbitals.

The function ψ_(u) results in two lobes of opposite sign cancelling and hence giving zero electron density in between the nuclei (see figure). This is an antibonding molecular orbital (ABMO) which has higher energy than the atomic orbitals.

The wave functions (molecular orbitals) are designated ψ_(g) and ψ_(u), where ‘g’ stands for gerade (even) and ‘u’ for ungerade (odd). g and u refer to the symmetry of the orbital about its centre. If the sign of the lobes remain the same, the orbital is gerade, and if the sign changes, the orbital is ungerade, when the orbital is roted along axis joining nuclei and the axis perpendicular to nuclei.

Figure: Energy of ψ_(g) and ψ_(u) molecular orbitals

Above figure show that the energy of the bonding molecular orbital passes through a minimum, and the distance between the atoms at this point corresponds to the internuclear distance between the atoms when they form a bond.

Consider the energy levels of the two 1s atomic orbitals and of the bonding ψ_(g) and antibonding orbitals.

The energy of the bonding molecular orbital is lower than that of the atomic orbital by an amount Δ. This is known as the stabilization energy. Similarly the energy of the antibonding molecular orbital is increased by Δ. Molecular orbitals accommodate two electrons with opposite spins same as atomic orbitals.

In the case of two hydrogen atoms combining, there are two electrons to be considered: ls-orbital of both H-atom combined, hence two electrons occupy the BMO i.e. ψ_(g).

When the overlapping lobes have same sign this results in a bonding MO with an increased electron density between the nuclei.

s-p combinations of orbitals

An s-orbital may combine with a p-orbital provided that the lobes of the p orbital are pointing along the axis joining the nuclei.

When the overlapping lobes have opposite signs this gives an antibonding MO with a reduced electron density in between the nuclei as shown in the below figure.

Figure: s-p combination of atomic orbitals

p-p combinations of orbitals

(Que:p-p combination of orbitals yields two different type of molecular orbitals. Explain.)

Consider the combination of two p-orbitals which both have lobes pointing along the axis joining the nuclei. Both a bonding MO and an antibonding MO are produced (below figure).

Figure: p-p combination of

atomic orbitals giving σ-bonding

When the overlapping lobes have same sign this results in a bonding MO with an increased electron density between the nuclei. When the overlapping lobes have opposite signs this gives an antibonding MO with a reduced electron density in between the nuclei as shown in the above figure.

Next consider the combination of two p orbitals which both have lobes perpendicular to the axis joining the nuclei. Lateral overlap of orbitals will occur, resulting in π-bonding and π^*-antibonding MOs being produced (see below figure).

Figure: p-p combination of

atomic orbitals giving π-bonding

Difference between σ- and π- Molecular Orbitals

π-bonding :

π-bonding is important in many organic compounds such as ethane, ethylene and benzene and also in a number of inorganic compounds such as CO₂ and CN^-.

The remaining p-orbital on each C atom is at right angles to the π-bonds so far formed which overlap sideways to give a π-bond. C=C though stronger than a C-C bond, is not twice as strong.

In the molecular orbital theory the explanation of the π-bonding is slightly different. The two p-orbitals involved in π-bonding combine to form two π-MO, one bonding and one antibonding. Since there are only two electrons involved, these occupy the π-bonding MO. The molecular orbital explanation becomes more important in non-localized π-bonding in which π-bonding covers several atoms as in benzene, NO₃^- and CO₃^-2.

In ethylene each C-atom uses sp-hybrid orbitals to form π-bonds to the other C-atom and H-atom. These four atoms form a linear molecule. Each C-atom has two p-orbitals at right angles to one another and these overlap sideways with the equivalent p-orbitals on the other C-atom, thus forming two π-bonds.

Thus a C≡C triple bond is formed, which is stronger than a C=C double bond. The majority of strong π-bonds occur between elements of the first short period in the periodic table, for example C≡C , C≡N, C≡O, C=C and C=O.

RULES FOR LINEAR COMBINATION OF ATOMIC ORBITALS

To decide which atomic orbitals may be combined to form molecular orbitals, three rules must be considered:

1. The atomic orbitals must be roughly of the same energy. This is important when two different types of atoms are overlap.

પરમાણુ કક્ષકો લગભગ સમાન ઉર્જાની હોવી જોઈએ. મહત્વપૂર્ણ એ છે કે જ્યારે બે અલગ પ્રકારના પરમાણુ ઓવરલેપ થાય છે.

2. The orbitals must overlap one another as much as possible. This implies that the atoms must be close enough for effective overlap.

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કક્ષાઓ એકબીજાને શક્ય એટલું એકબીજા પર ઓવરલેપ થવી જોઈએ. આનો અર્થ એ છે કે અણુઓ અસરકારક ઓવરલેપ માટે પૂરતી નજીક હોવી આવશ્યક છે.

3. In order to produce bonding and antibonding MOs, either the symmetry of the two atomic orbitals must remain unchanged when rotated about the internuclear line, or both atomic orbitals must change symmetry in an identical manner.

QUE-Molecular orbitals (How molecular orbitals defined ?)

In the same way that each atomic orbital has a particular energy, and may be defined by four quantum numbers, each molecular orbital has a definite energy, and is also defined by four quantum numbers.

1. The principal quantum number ‘n’ has the same significance as in atomic orbitals.

2. The subsidiary quantum number ‘l’ also has the same significance as in atomic orbitals.

3. The magnetic quantum number of atomic orbitals is replaced by a new quantum number λ

4. The spin quantum number

The Pauli Exclusion Principle :

The Pauli principle also applies to molecular orbitals:

Note: The order of energy of molecular orbitals has been determined mainly from spectroscopic data.

In simple homo nuclear diatomic molecules (for oxygen and heavier elements) the order of energy of molecular orbitals in increasing order is :

σ_1s< σ*_1s< σ_2s< σ*_2s< σ_2px< π2p_y = π2p_z <π*2p_y =π*2p_z<σ*_2px

Note that the 2p_y and 2p_z atomic orbital gives both π- bonding and π* anti-bonding MOs. The bonding π2p_y and π2p_z MOs have exactly the same energy and are said to be double degenerate. In a similar way the anti-bonding π*2p_y and π*2p_z MOs have the same energy and are also doubly degenerate.

The energies of the σ_2p and π2p MOs are very close together. The order of MOs shown above is correct for oxygen and heavier elements, but for the lighter elements like boron, carbon and nitrogen the π2p_y and π2p_z are probably lower than σ_2px and order of energy is: σ_1s< σ*_1s< σ_2s< σ*_2s< π2p_y = π2p_z < σ_2px <σ*_2px<π*2p_y =π*2p_z

• Examples of molecular orbital treatment for homo nuclear diatomic molecules:

Homo nuclear means that there is only one type of nucleus that is one element present and diatomic means that the molecule is composed of two atoms.

H₂ molecule: H₂ molecule is form by two H-atoms. Each H-atom has one electron and hence there are two electrons in the H₂ molecule. These occupy the lowest energy MO i.e. σ1s². This is shown in below figure

Figure : Atomic and Molecular orbital of H-atom

The electron configuration of H₂ molecule is σ1s².This results in a saving of energy of 2Δ, which corresponds to the bond energy. The system is stabilized and bond is formed. Hence H₂ molecule is exist. where, n_B is total electron in BMO and n_A is total electron in ABMO

• Bond order = (n_B - n_A)/2

H₂⁺molecule ion: This may be considered as a combination of H-atom with H⁺ ion. This gives one electron in the molecular ion which occupies the lowest energy MO i.e. σ1s¹. The energy of H₂⁺ ion is lower than that of the constituent atom and ion by an amount Δ, so there is some stabilization.

H₂⁺ species exists but is not common since H₂ is much more stable. However, H₂⁺ can be detected spectroscopically when H₂ gas under reduced pressure is subjected to an electric discharge.

• Bond order = (n_B - n_A)/2 =1-0/2 =0.5

He₂ molecule

There are two electrons in each He atom, hence four electrons in He₂ molecule. The electron configuration of He₂ is σ1s², σ*1s².

The 2Δ stabilization energy from filling the σ1s MO is cancelled by the 2Δ destabilization energy from filling the σ*1s MO. Thus a bond is not formed and the molecule does not exist.

Bond order = (n_B - n_A)/2 =2-2/2 =0

He₂⁺ molecule ion: This may be considered as a combination of a He atom and a He⁺ ion. There are three electrons in the molecular ion which are arranged in MOS : σ1s², σ*1s¹.

• Bond order = (n_B - n_A)/2 =2-1/2 =0.5

The filled σ1s BMO gives 2Δ stabilization, while the half-filled σ*1s gives Δ destabilization. Overall there is Δ stabilization. Thus the helium molecule ion can exist. It is not very stable, but it has been observed spectroscopically.

Li₂ molecule:

Each Li atom has two electrons in inner shell and one in outer shell, giving three electrons. Thus total six electrons in the Li₂ molecule. The diagram of this is show in below figure.

Figure: Atomic and Molecular orbital of Li-atom

The electron configuration of Li₂ is

σ1s², σ*1s² , σ2s².

Bond order = (n_B - n_A)/2 =4-2/2 = 2/2 = 1

This is shown that inner shell of filled σ1s² and σ*1s² MOs do not contribute to the bonding. They are essentially the same as the atomic orbitals from which they were formed and are sometimes written as K.K, σ2s²

• Be₂ molecule
• A beryllium atom has two electrons in the first shell and two electrons in the second Shell. Thus in the Be₂ molecule there are eight electrons.
• The electron configuration of Be₂ is σ1s², σ*1s² , σ2s², σ*2s² or K K, σ2s², σ*2s²

• Ignoring the inner shell, it is seen that the effects of the bonding σ2s and antibonding σ*2s levels cancel, so there is no stabilization and Be₂ molecule does not exrst.
• Bond order = (n_B - n_A)/2 =4-4/2 = 0

• B₂ molecule
• Each boron atom has 2 + 3 electrons. The B₂ molecule thus contains ten electrons. The diagram of this is show in below figure.

Figure: Atomic and Molecular orbital of B-atom

Figure: Atomic and Molecular orbital of B-atom

• The electron configuration of B₂ molecule is σ1s², σ*1s² , σ2s², σ*2s² ,π2p_y¹ ,π2p_z¹.

• Boron is a light atom and the order of energies of MOS is different from the usual arrangement. Thus the π2p_y and π2p_z orbitals are lower in energy than the ,σ2p_x.. The inner shell does not participate in bonding. The effects of bonding and antibonding σ2s orbitals cancel but stabilization occurs from the filling of the π2p_y and π2p_z orbitals and hence a bond is formed and B₂ molecule exists.

Bond order = (n_B - n_A)/2 =6-4/2 = 2/2 = 1

• C₂ molecule

Figure: Atomic and Molecular orbital of C-atom

• C₂ molecule

Figure: Atomic and Molecular orbital of C-atom

• The electron configuration of C₂ molecule is is σ1s², σ*1s² , σ2s², σ*2s² ,π2p_y² ,π2p_z².

The molecule should be stable, since the two π2p_y., and π2p_z BMOS provide 4Δ of stabilization energy, giving two bonds. In fact carbon exists as a macro molecule in graphite and diamond.

Bond order = (n_B - n_A)/2 =8-4/2 = 4/2 = 2

Que- O₂ molecule is paramagnetic where as O₂^-2 ion(peroxide ion) is diamagnetic. Explain giving diagram on the basis of molecular orbital theory.

Que: F₂ molecule is diamagnetic and there is a single bond between F-atom. Explain on basis of MOT.