Simple Bonding Theories of Molecules PDF

# Simple Bonding Theories of Molecules ## Atomic Orbitals: - **The region in three-dimensional space around the nucleus, where there is a maximum probability of finding an electron is called an orbital.** | Orbital | No. of Orbitals | Notation | |---|---|---| | 1 | 1 | 1s | | 2 | 2 | 2s, 2p | | 3...

# Simple Bonding Theories of Molecules ## Atomic Orbitals: - **The region in three-dimensional space around the nucleus, where there is a maximum probability of finding an electron is called an orbital.** | Orbital | No. of Orbitals | Notation | |---|---|---| | 1 | 1 | 1s | | 2 | 2 | 2s, 2p | | 3 | 3 | 3s, 3p, 3d | | 4 | 4 | 4s, 4p, 4d, 4f | | 5 | 4 | 5s, 5p, 5d, 5f | | Orbital | Value of l | |---|---| | s | 0 | | p | 1 | | d | 2 | | f | 3 | | Orbital | l | Max no. of e- in an orbital 2(2l+1)= 4l+2 |
|---|---|---|
| s | 0 | 4x0+2=2 |
| p | 1 | 4x1+2=6 |
| d | 2 | 4x2+2=10 |
| f | 3 | 4x3+2=14 | - **The order of energy of orbitals in an orbit is as follows:** $s < p < d < f$. - **For n=4, there are 4s, 4p, 4d, 4f** - **Energy of Orbitals of different Orbits:** *Fig* - **Shape of Atomic Orbitals:**
 - **Angular probability distribution curve gives the probability of finding an electron in a given direction. Hence it gives the shape of the orbitals. The size, shape and orientation of the different types of orbitals can be obtained by wave mechanics. Shape of orbitals depend on the wave function Ψ.** - $$s-Orbital: l=0,m=0$$ *Fig*
 - $$p-Orbital: l=1, m=-1, 0, +1$$ *Fig*
 - $$d-Orbital: l=2, m=-2, -1, 0, 1, 2.$$ *Fig*
 - $$f-orbital: l=3, m=-3, -2, -1, 0, 1, 2, 3.$$ ## Aufbau's Principle: - **'Aufbau' is a German word which means 'to build up.' The gradual addition of electrons in sub-shells on the basis of increasing energy gives rise to new elements. This principle is known as Aufbau Principle.** - **According to this principle:** "**The orbitals are filled up in the order of increasing energy.**" *Fig* $1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<6d<7p.$ ## (n+l) Rule: - **(n+l) rule, where (n) is principal quantum no. and (l) is azimuthal quantum number. It states that:** - i) **The new electron will enter in that orbital where (n+l) has a minimum value, ie orbital having the lowest value of (n+l) has the lowest energy.** - ii) **For the same value of (n+l) for two orbitals, the orbital with lower value of n will be lower in energy.** ## Limitations (Exceptions) of Aufbau Principle: - **Aufbau principle does not agree with some of the transition elements.**
eg. Cr(24), Cu(29), Ag(47), Pd(46) & Au(79) etc. | Element | Aufbau Order | Actual Order
|
|---|---|---| | Cr(24) | 1s²,2s², 2p⁶, 3s², 3p⁶, 4s², 3d⁴ | 1s²,2s², 2p⁶, 3s², 3p⁶, 4s¹, 3d⁵ | | Cu(29) | 1s²,2s², 2p⁶, 3s², 3p⁶, 4s², 3d⁹ | 1s²,2s², 2p⁶, 3s², 3p⁶, 4s¹, 3d¹⁰ | - **It is due to the fact that half filled (d⁵) and completely filled (d¹⁰) electronic configuration have extra stability.** ## Valence Bond Theory (VBT) - **This theory was developed by Heitler & London in 1927 and later on extended by Pauling & Slater in 1931.** - **According to VBT:** - i) **The covalent bond is formed by overlapping of atomic orbitals. The atomic orbitals must contain unpaired electrons of opposite spin, which are neutralised due to overlapping.** - ii) **Atomic orbitals containing parallel spinning electrons will not overlap, as they will repel each other. Hence, the spin of both the electrons must be opposite.** - iii) **The bounded pair of electrons is localised between the combining atoms.** - iv) **The no. of covalent bond will be equal to the no. of unpaired electron present in the atomic orbitals. eg. N-atom has three unpaired electron in 2p3 orbit, so two N atoms combine to form 3 bonds.
 :N≡N:**
 - v) **The paired electrons present in the outermost shell don't take part in chemical bond formation. Such e - form bonds only when they can be unpaired.
eg:
7N → 1s², 2s², 2p³
 1 1 1 
It combines with 3 (F) atoms to form.
 But N can’t form pentafluoride (NF₅) because there is no orbital available in n=2.
 15P → 1s², 2s², 2p⁶, 3s², 3p³, 3d⁰
 1 1 1
 Phosphorus form both PCl₃ as well as PCl₅-
The three unpaired electrons in 3p orbital of phosphorus combine with 3 Cl atom and PCl₃ formed. In addition to this one electron of 3s² of phosphorus is unpaired and enters into vacant 3d orbital. 
3s¹, 3p₁, 3p₂, 3d₁, 3d⁰ll
 from PCl₅-** ## Overlap of Atomic Orbital:
 - **In formation of covalent bonds, overlap of atomic orbitals are of three types:**
 - **i) s-s overlap**
 - **ii) s-p overlap**
 - **iii) p-p overlap** - **i) s-s Overlap:**
 - **s-orbital is spherically symmetrical. Hence s-orbital can overlap in all directions. This the bond formed due to overlap of s- orbitals is non-directional. The bond is called (σ) bond. It is symmetrical about the nuclear axis.**
 - **eg. formation of He Molecules…
** - **ii) s-p Overlap:** - **Overlap of s-orbital of one of the combining atoms with the p-orbital of the other is called s-p overlap.**
 - **In this type of overlap, s-orbital overlaps with any of the three p-orbitals. It is directional. Here the bond formed is known as σ-bond.
 eg: H-F, H₂O, NH₃ etc.** - **iii) p-p overlap:** - **In this type of overlap, the p- orbital of one atom overlaps with the p- orbital of another atom. This type of overlap can take place in two ways:**
 - **Co-axial or Head-on overlapping.
Sidewise or Collateral overlapping.
** - **Co-axial / Head on / End on overlapping:** *Fig*
 - **p-orbital is directional. This type of overlap results by the combination of two such atoms whose p- orbitals are available for covalent bond formation. In this, overlapping takes place on one axis.**
 - **eg. F₂, Cl₂, Br₂ etc.
Fg → 1s², 2s², 2pₓ², 2pᵧ², 2p₂²
** - **Side wise / Collateral Overlapping:
** - **In this type of overlapping. both p-orbitals (by or b₂) combine side wise. The bond is formed σ-Bond.
eg. formation of O₂, N₂ etc.
** ## Sigma (σ) & Pi (π) Bonds: ### Sigma Bonds: - **Covalent bonds are formed by the overlap of atomic orbitals. Sigma bonds ane formed by the axial / head on / end on overlap of orbitals.** *Fig* - **This σ - bond is formed when:**
 - **s-s overlapping occurs
** - **s-p overlapping occurs
** - **p-p coaxial overlapping occurs
** ### Pi (π) Bonds: - **π - Bonds are formed by the sidewise or lateral overlap of atomic orbitals. π-Bonds are comparatively weaker than σ-bonds.** *Fig* - **Single bond has σ - bond, double bond contains 1 σ & 1 π bonds. Whereas triple bond contains 1 σ & 2 π bonds.** ## Characteristics of π - bond :- - **i) This is weaker than σ - bond.** - **ii) π - bond is formed only after the formation of σ -bond.** - **iii) It is not possible to rotate π - bond along internuclear axis.** ## Strength of Covalent Bond : - **The strength of covalent bond depends upon the types of overlap.** $p-p (coaxial) bond > s-p bond > s-s bond > π - bond $ ## Comparison b/w Sigma & Pi Bond | Sr.No. | σ - Bond | π - Bond | |---|---|---| | 1 | It is formed by overlapping of orbitals along the molecular axis. | It is formed by the sidewise or lateral overlap of two p-orbitals. | | 2 | It is stronger bond | It is weaker than σ - bond. |- | 3 | In σ-bond, the atom can be rotated along the bond axis freely. | Free rotation is not possible around the π- bond, because the e- clouds overlap above & below the plane of the atoms. Hence it will destroy the sidewise overlap of orbitals. | 
 | 4 | The bond direction is determined from σ-bond. It also determines the extent of bond length. | It has no effect on bond attraction, when π - bond is formed. The bond length shortens. | ## Bond Length:- - **Distance b/w nuclei of two bounded atoms is called the Bond length. It is a small distance which is measured by X - Ray Spectroscopy, in (Å) unit. Bond length is actually a sum of two covalent radii.** *Fig*
 $$Bond Length = rA+rB$$ - **The bond length decreases in the order:** *Single Bond > Double Bond > Triple Bond.* | Bond | Bond length(Å) | Bond | Band length (Å) |
|---|---|---|---| | C=C | 1.34 | C-H | 1.08 |
| C=O | 1.22 | C-O | 1.43 |
| C=N | 1.29 | C-N | 1.47 |
| C≡N | 1.20 | C≡C | 1.54 |
| N=N | 1.22 | O-H | 0.97 |
| N=0 | 1.20 | H-C | 1.09 |
| C≡O | 1.13 | H-H | 1.74 |
| N≡N | 1.10 | N-H | 1.01 |
| N≡O | 1.06 | N-N | 1.47 |
| | | N-P | 1.77 |
| | | O-O | 1.48 | ## Factors Affecting Bond Length: - **i) Size of Atom:**
 - **The bond length increases with increase in size of atoms.** - **Size of atom ↑ Bond length ↑** - **eg. H-I> H-Br > H-Cl > H-F** - **ii) Multiplicity of Bond:** - **Bond length decreases with the multiplicity of the Bond.** - **eg. C=C < C=C < C-C** - **iii) Percentage s-character:** - **With the rise in the percentage of s- character in a hybrid orbital, Bond length decreases.
 eg.** | Hybrid Orbital | Hybridization | % s-character | Bond length |
|---|---|---|---| | CH₃-CH₃ | sp³ | $ \frac{100}{4} = 25%$ | 1.54 Å |
| CH₂ = CH₂ | sp² | $ \frac{100}{3} = 33.3$ | 1.34 Å |
| C≡C | sp | $ \frac{100}{2} = 50$ | 1.20 Å | ## Hybridisation: - **Linus Pauling developed the concept of Hybridisation.** - **"Hybdisation is a process of intermixing of atomic orbitals of an atom, to form new hybrid orbitals of equivalent shape & energy."** eg. s+p+p+p = 4sp³ Hybrid orbitals *Fig* ### Why Hybridisation? - **VBT fails to explain the structure of some Polyatomic molecules.
eg. CH₄- C= 1s²,2s², 2p²** *Fig* **According to VBT, CH₄ should have 3 equivalent - Bonds and 1 different - Bond.** - **But experimentally, CH₄ has all 4 Bonds are equivalent.** ## After Hybridisation: - **Hybrid orbitals always form sigma (σ) bond & unhybridised orbitals form π-bond.** - **Total hybrid orbitals = Sum of orbitals combining.** - **All hybrid orbitals always have equal energy & shape.** - **Hybrid orbitals form better bonds than atomic orbitals.** *Lion (M) + Tiger (F) → Liger (more powerful)* ## Types of Hybridisation - **sp, sp², sp³ & sp³d, sp³d², sp³d³** ### sp Hybridization:
 *Fig* - **When one s and one p orbital of an atom mix together, they give rise to two sp hybrid orbitals.** - **Structure : Linear** - **Bond Angle : 180°
** - **% s- character : $ \frac{100}{2} = 50%$** - **eg: BeCl₂
 Be → 1s²,2s², 2p⁰** *Fig*
 - **Be → 1s²,2s², 2p⁰** *Fig* ### sp² Hybridization: - **When 1 s and 2 p orbital of an atom mix together, they give rise to three sp² hybrid orbitals of same energy and same structure.** - **Structure : Trigonal Planar
** - **Bond Angle : 120°
** - **% s - character : $ \frac{100}{3} = 33.3%$** - **eg. BCl₃**
 ### sp³ Hybridization: - **When 1 s and 3p orbital of an atom mix together, they give rise to four sp³ hybrid orbitals of same energy and same structure.** - **Structure : Tetrahedral
** - **Bond Angle : 109.5⁰
** - **% s - character : $ \frac{100}{4} = 25%$** - **eg. CH₄
** ### sp³d Hybridization: - **s + p + p + p + d = 5sp³d
** - **Structure : Trigonal Bipyramidal
** - **Bond Angle : (90°,120°,180°) 120° at equatorial position, 90° b/w equatorial & axial.
** - **% s - character : $ \frac{100}{5} = 20%$** - **eg. PCl₅**
 ### sp³d² Hybridization: - **s + p + p + p + d + d = 6sp³d²
** - **Structure : Octahedral
** - **Bond Angle : 90°
** - **% s - character : $ \frac{100}{6} = 16.66%$**
 - **eg. SF₆
** ### sp³d³ Hybridization: - **s + p + p + p + d + d +d = 7sp³d³
** - **Structure : Pentagonal Bipyramidal
** - **Bond Angle : 72°, 180°, 90.
** - **% s - character : 19.28 % 
** - **eg. IF₇
** ## Note: | | | | | |---|---|---|---| | C-C | sp³ | C₂H₆ | | C=C | sp² | C₂H₄ | | C≡C | sp | C₂H₂ | ## Short Trick to find Hybridisation: **Hybridisation (CA) = Atom Attached + Lone Pair** ### Find Hybridisation of following central atom of following molecules: - **i) CH₄** *Fig*
 **Hybridisation = 4 + 0 = sp³**
 - **ii) NH₃** *Fig* **Hybridisation = 3 + 1 = sp³** - **iii) H₂O** *Fig* **Hybridisation = 2 + 2 = sp³** ## Note: Point: - **i) Only valence orbitals are hybridised.** - **ii) Orbitals undergoing hybridisation must be comparable energy.** - **iii) Filled orbitals also undergo hybridisation.**
 - **iv) Vacant orbitals do not undergo hybridisation but pi- bonds are always unhybridised.** - **v) Total (sigma bond + lone pairs) = type of hybridisation** - **vi) Only central atom in one atom system is hybridised.** ## Bent's Rule: - **This rule was stated by "Henry A. Bent" in 1961. According to this rule:** - **"Atomic s-character concentrates in orbitals directed towards electropositive substituent."** - **Bent's Rule explains the relationship b/w the orbital hybridisation of central atom in molecules and the electronegativity of substituents.** - **s-orbitals closer to the nucleus so as the % s-character in hybrid orbital increase, its electronegativity increase too. Hence directed towards more electro-positive group.** - **sp³d² < dp³d < sp³ < sp² < sp
** - **Order of % s-character increase
Order of electronegativity.** - **Eg. PCl₃F₂** *Fig* - **F → more electronegative → axial position 
Cl → less electronegative
 → equatorial position.** ## VSEPR Theory: **: Valence Shell Electron Pair Repulsion Theory:** ### Why VSEPR couldn't explain shapes of the molecules. - **eg why NH₃ is pyramidal
 why H₂O is Bent structure.**
 - **This theory was developed by Sidgwick & Powell in 1990. VSEPR theory is a model used to predict 3D molecular geometry based on the no. of valence shell electron bond pairs among the atoms in a molecule or ion. This model assumes that electron pairs will arrange themselves to minimize repulsion effect from one another.** ## VSEPR Theory Postulates : - **i) "Shape of molecule depends on total valence electrons around central atom."**
 eg CH₄, NH₃, H₂O etc.
 - **ii) Valence electrons repel one another due to same charge.** eg. BF₃, CH₄, etc.
 - **iii) Electrons occupy at certain distance to minimize repulsion.** - **iv) Multiple bond is treated as Single super pair.** -**Note: (i) Repulsion Order
 Lp-Lp > Lp-Bp > Bp-Bp**
 - **v) Geometry consider : Lone pair + Bond Pair.**
 - **vi) Shape consider : Only Bond pair.
** - **vii) When molecule doesn't have lone pair Shape = Geometry** ### Example: - **No lone pair
** - **CH₄** *Fig* - **Shape : Tetrahedral
 Geometry : Tetrahedral.** ## Structure Prediction : No lone Pair | Type | Structure | Angle | Exp. | |---|---|---|---| | AB₂ | Linear | 180º | BeCl₂ |
| AB₃ | Trigonal Planar | 120º | BF₃ |
| AB₄ | Tetrahedral 
 | 109°28' | CH₄ |
| AB₅ | Trigonal Bipyramidal
 | 90, 120, 180
 | PCl₅ |
| AB₆ | Octahedral
 | 90° | SF₆ | ## Structure Prediction : Lone Pair: | AB_E Type | Geometry | | | |---|---|---|---| | AB₂E | Uncomplay | B.P + L.P = 2+1 = 3 = Trigonal Planar | | | | Shape | B.P = 2 | Bent | | | | *Fig* | | | eg | SO₂ | | | | | | | | AB₃E | | | | | | Geometry | B.P + L.P = 3+1 = 4 | Tetrahedral | | | Shape | B.P = 3 | Trigonal Pyramidal | | | | *Fig* | | | | eg | NH₃ | | | | | | | | AB₂E₂ | | | | | | Geometry | B.P + L.P = 2+2 = 4 | Tetrahedral | | | Shape | B.P = 2 | Bent | | | | *Fig* | | | | eg | H₂O | | | | | | | | AB₄E | | | | | | Geometry | B.P + L.P = 4+1 = 5 | Trigonal Bipyramidal | | | Shape | B.P = 4 | See-saw |
 | | | *Fig* | | | | eg | SF₄ | | | | | | | | AB₃E₂ | | | | | | Geometry | B.P + L.P = 3+2 = 5 | Trigonal Bipyramidal | | | Shape | B.P = 3 | T-shape | | | | *Fig* | | | | eg | ClF₃ | | | | | | | | AB₅E | | | | | | Geometry | B.P + L.P = 5+1 = 6| Octahedral | | | Shape | B.P = 5 | Square Pyramidal | | | | *Fig* | | | | eg | BrF₅ | | | | | | | | AB₄E₂ | | | | | | Geometry | B.P + L.P = 4+2 = 6 | Octahedral | | | Shape | B.P = 4 | Square Planar | | | *Fig* | | | | | eg | XeF₄ | | ## The shape of SO₄^2- is: - (i) Square Planar - (ii) Tetrahedral - (iii) Trigonal Bipyramidal - (iv) Hexagonal *Fig* ## How many pairs of valence electrons are required for square pyramidal geometry? - (i) 4 - (ii) 5 - (iii) 6 - (iv) 8 - **For square pyramidal (AB₅E)** *Fig*
 **6 valence electron pairs.** ## Limitation of VSEPR Theory: - **i) VSEPR is not able to predict the geometry of certain transition metal complexes.** - **ii) This theory is not useful for predicting the shape molecules containing inert pair of electrons.** - **iii) This theory is unable to explain the shape of molecules having highly localized π-e.** - **iv) This theory cannot explain the shape of highly polar molecules.
 eg. Li₂O & H₂O should have similar structure but Li₂O → linear while H₂O → Bent.** - **v) Thus shape and geometry of both covalent molecules are determined by VSEPR Theory and hybridisation. Both are complementary to each other.** ## Molecular Orbital theory: - **MOT was developed in the year after VBT had been established in 1927 by, Fridrich Hund & Rober S. Mulliken.** ### Reason for M.O.T : - **i) According to VBT, molecule with even no. of electrons are Diamagnetic. But experimentally O₂ is paramagnetic.** ### Postulates : - **i) Electrons ane filled in molecular orbitals like it is filled in various atomic orbitals.** *Fig* - **Combining Atomic Orbitals** - **Bonding πs
 Molecular Orbitals** - **ii) Only atomic orbitals of proper symmetry & comparable energy forms molecular orbitals.
** *Fig* - **iii) Electrons in atomic orbitals ane monocentric but in molecular orbitals, they are polycentric.** *Fig* - **iv) Total atomic orbitals combining = Total molecular orbitals formed.** *Fig* - **v) Bonding Molecular Orbital & High stability
 Low energy
** - **Antibonding Molecular Orbital & Low stability, High energy
** - **vi) Electrons are filled by following Aufbau’s & Pauli's principle & Hund’s rule
** ## Types of Molecular Orbitals: - **1. s-s molecular Orbital (σ)** *Fig* - **2. p-p molecular Orbital (σ)** *Fig* - **3. p-p molecular Orbital (π)** *Fig* ## Molecular Orbital Diagram: ### Electrons ≤14 : - **eg. Ne, Be etc.** *Fig* ### Electrons > 14: - **eg. O₂, Mg, etc.** *Fig* ## Applications of M.O.T. - **Bond Order
** - **Stability
** - **Nature of Bond
** - **Bond Length
** - **Magnetic Nature
** ### Bond order: - **Total bonds present b/w two atoms.** - **Bond Order = No - Na
/ 2** - **Nb -> no. of bonding e-
 Na -> no. of antibonding e-** - **Trick to Remember:** | No. of Electrons | Bond Order |
|---|---| | 10 | 1.0 |
| 11 | 1.5 |
| 12 | 2.0 |
| 13 | 2.5 |
| 14 | 3.0 |
| 15 | 2.5 |
| 16 | 2.0 |
| 17 | 1.5 |
| 18 | 1.0 | ### Stability : - **Stability ∝ Bond Order.
Nb > Na → Stable
Nb < Na → Unstable
 Nb = Na → Unstable
** - **eg.** *Fig* - **H-atom
 H-atom
He molecule
Bond order = 2-0/2 = 1
Stable
** *Fig* - **He atom
 He atom
 He₂ Molecule
Bond order = 2-2/2 = 0
 Unstable
** ### Nature of Bond: | Molecule | Bond Nature | Bond order | |---|---|---| | H-H | Single | 1 | | O=O | Double | 2 | | N≡N | Triple | 3 | ### Bond Length: - **Bond length ∝ 1 / Multiplicity of Bond
 
** ### Magnetic Behavior: - **Diamagnetic:** Molecular orbitals have all electrons paired up. *Fig* - **Paramagnetic:** Molecular orbitals have all electrons unpaired electrons.*Fig* - **Short trick:
Total no. of electrons : odd / 10/16 → paramagnetic
Total no. of electrons : Even → Diamagnetic**
 ## Comparison of V.B.T. & M.O.T. ### Similarities: - **i) Accosiding to both theories, the basic principles involved in the distribution of electrons are similar. Hence in each orbital (A.O. or M.O.) max. two electrons are present.** - **ii) Both theories explain covalency and formation of (σ) & (π) bonds.
** - **iii) According to both theories, the electron density is maximum b/w the nuclei.**
 - **iv) In both theories, the atomic & molecular orbitals are filled up accariding to Aufbay’s principle, Pauli’s exclusion principle and Hund’s Rule.
** - **v) Both explain the directional nature of covalent bonds.** - **vi) The symmetry of overlapping orbital remains the same and has approximately the same energy.** - **vii) Both explain the non-existence of He₂ molecule.** ### Differences: | Sr.no | V.B.T. | M.O.T. | |---|---|---| | 1 | The two atoms participating in covalent bond do not lose their individual identities. | The two atoms participating in covalent bond lose their individual identities. | | 2 | Atomic orbitals are monocentric. | Molecular orbitals are polycentric. | | 3 | Resonance is an integral part of V.B.T. | Resonance has no role in M.O.T. | | 4 | It doesn't explain paramagnetism of O₂ molecules | It explain para-magnetism of O₂ molecules. |