Atomic structure, bonding and spectroscopic techniques notes — Unit 1

The classical Bohr model of the atom failed to explain the spectra of multi-electron atoms and the splitting of spectral lines. This led to the development of the Quantum Mechanical Model, based on dual nature of matter and the uncertainty principle.

⇒de Broglie's Hypothesis

Louis de Broglie proposed that matter, like light, possesses a dual nature: behaving both as a particle and as a wave. The wavelength of a moving particle is inversely proportional to its momentum.

λ = h / p
λ = h / (mv)

Where:
λ = Wavelength
h = Planck's constant (6.626 x 10^-34 J·s)
m = mass of the particle
v = velocity

⇒Heisenberg's Uncertainty Principle

It is impossible to determine simultaneously and with absolute precision both the exact position and the exact momentum (or velocity) of a microscopic particle like an electron.

Δx · Δp ≥ h / (4π)
Δx · (mΔv) ≥ h / (4π)

Where:
Δx = Uncertainty in position
Δp = Uncertainty in momentum

The foundation of quantum mechanics is the Schrödinger wave equation. It describes the wave-like behavior of an electron in an atom mathematically.

⇒Time-Independent Equation

∇²ψ + (8π²m / h²)(E - V)ψ = 0

Where:
∇² = Laplacian operator (∂²/∂x² + ∂²/∂y² + ∂²/∂z²)
ψ (psi) = Wave function
m = mass of electron
h = Planck's constant
E = Total energy
V = Potential energy

⇒Physical Significance of ψ and ψ²

• ψ (Wave Function): It is a mathematical amplitude function. By itself, it has no direct physical meaning. It can be positive or negative.
• ψ² (Probability Density): The square of the wave function represents the probability of finding an electron in a specific tiny volume of space around the nucleus. A higher ψ² means a higher probability of finding the electron (an orbital).

Valence Bond Theory (VBT) failed to explain the paramagnetic nature of O2 and the existence of fractional bond orders. Molecular Orbital Theory (MOT) was proposed by Hund and Mulliken to address these flaws.

⇒Postulates of MOT

• When atoms combine to form a molecule, their atomic orbitals merge and lose their individual identity to form new orbitals called Molecular Orbitals (MOs).
• The number of molecular orbitals formed is exactly equal to the number of atomic orbitals combining.
• MOs are polycentric (influenced by multiple nuclei), whereas atomic orbitals are monocentric.
• Electrons in the molecule are filled in these MOs according to the Aufbau principle, Pauli's exclusion principle, and Hund's rule.

⇒LCAO Method

Linear Combination of Atomic Orbitals (LCAO) is the mathematical process of combining atomic wave functions.

The stability and properties of a molecule can be directly calculated from its Molecular Orbital configuration.

⇒Bond Order Calculation

Bond order indicates the number of chemical bonds between two atoms.

Bond Order (B.O.) = 1/2 [ Nb - Na ]

Nb = Number of electrons in Bonding MOs
Na = Number of electrons in Anti-Bonding MOs

• If B.O. > 0: The molecule is stable and exists.
• If B.O. ≤ 0: The molecule is unstable and does not exist (e.g., He2).
• A higher B.O. means a shorter bond length and a stronger bond.

⇒Magnetic Properties

MOT perfectly predicts the magnetic behavior of molecules based on their electron pairing.

Metals conduct electricity, are malleable, and have high melting points. To explain these properties, we use the Band Theory, which is an extension of Molecular Orbital Theory applied to macroscopic solids.

⇒Formation of Bands

In a metal crystal, billions of atoms are packed together. Their atomic orbitals combine to form billions of molecular orbitals. Because these MOs are so close in energy, they merge into a continuous 'energy band'.

• Valence Band (VB): The band containing the valence electrons. It can be fully or partially filled.
• Conduction Band (CB): The next higher energy band, which is completely empty at absolute zero.
• Forbidden Gap (Band Gap): The energy difference between the top of the VB and the bottom of the CB. Electrons cannot exist here.

⇒Classification of Materials

Spectroscopy is the study of the interaction between electromagnetic radiation (light) and matter. It is the most powerful tool in chemistry for determining the structure of unknown compounds.

⇒Electromagnetic Spectrum

Electromagnetic radiation travels in waves. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.

E = hν = hc / λ

E = Energy
ν = Frequency
c = Speed of light
λ = Wavelength

⇒Types of Transitions

Different regions of the spectrum trigger different types of transitions inside molecules:

UV-Visible spectroscopy involves the absorption of ultraviolet (200-400 nm) or visible (400-800 nm) light, causing the excitation of valence electrons from lower to higher energy molecular orbitals.

⇒Electronic Transitions

When a molecule absorbs UV light, electrons jump from bonding (or non-bonding) orbitals to anti-bonding orbitals. The possible transitions, in order of decreasing energy requirement, are:

• σ → σ* (Sigma to Sigma star): Requires very high energy (Vacuum UV). Seen in alkanes.
• n → σ* (Non-bonding to Sigma star): Requires less energy. Seen in molecules with lone pairs like H2O, CH3OH.
• π → π* (Pi to Pi star): Seen in compounds with double/triple bonds (alkenes, alkynes).
• n → π* (Non-bonding to Pi star): Requires the lowest energy. Seen in compounds with double bonds and lone pairs (e.g., carbonyl group C=O).

⇒Chromophores and Auxochromes

The absorption maximum (λmax) of a compound can shift due to substituents or solvent effects. These shifts are critical for structural diagnosis.

⇒Types of Shifts

⇒The Beer-Lambert Law

The foundational law for quantitative analysis using UV-Vis. It states that the absorbance of a solution is directly proportional to the concentration of the absorbing species and the path length of the light.

A = ε · c · l

A = Absorbance (No units)
ε = Molar absorption coefficient (L·mol^-1·cm^-1)
c = Concentration (mol/L)
l = Path length of the cuvette (usually 1 cm)

IR Spectroscopy deals with the infrared region of the spectrum (usually 4000 to 400 cm^-1). Absorption of IR radiation causes changes in the vibrational energy levels of molecules.

⇒Principle of IR

Bonds in a molecule are not rigid; they act like springs. They constantly vibrate. When the frequency of the incoming IR radiation exactly matches the natural vibrational frequency of a bond, the radiation is absorbed, and the amplitude of vibration increases.

⇒Types of Molecular Vibrations

• Stretching: The distance between two atoms increases or decreases along the bond axis. (Requires higher energy).
• - Symmetric Stretching: Both bonds stretch together.
• - Asymmetric Stretching: One bond stretches while the other compresses.
• Bending: The angle between two bonds changes. (Requires lower energy).
• - In-plane: Scissoring, Rocking.
• - Out-of-plane: Wagging, Twisting.

An IR spectrum is plotted as % Transmittance vs Wavenumber (cm^-1). The spectrum is heavily utilized to identify functional groups present in an unknown organic compound.

⇒The Two Main Regions

⇒Key IR Absorption Peaks to Memorize

Nuclear Magnetic Resonance (NMR) is arguably the most powerful tool for determining the exact carbon-hydrogen framework of an organic molecule. It relies on the interaction of atomic nuclei with radio waves in a strong magnetic field.

⇒The Principle of NMR

Nuclei with an odd mass number (like ^1H, ^13C) possess a property called 'nuclear spin', making them act like tiny bar magnets.

• Normally, these tiny magnets spin in random directions.
• When placed in a massive external magnetic field (B0), they align either WITH the field (Alpha state, lower energy) or AGAINST the field (Beta state, higher energy).
• When irradiated with Radio Frequency (RF) waves, the nuclei in the lower energy state absorb energy and flip to the higher energy state. This is called Resonance.

⇒Equivalent and Non-Equivalent Protons

In a molecule, protons (Hydrogen atoms) experience different electronic environments based on what atoms they are near. Protons in the exact same chemical environment are 'Equivalent' and will absorb at the exact same frequency, producing ONE single signal in the NMR spectrum.

Example: In CH3-CH2-OH (Ethanol), there are three distinct electronic environments: the CH3 group, the CH2 group, and the OH group. Therefore, Ethanol will show 3 separate signals on an NMR spectrum.

Protons in different environments absorb radio waves at slightly different frequencies. This difference in absorption position is called the Chemical Shift.

⇒Shielding and Deshielding

The exact magnetic field felt by a proton is affected by the electrons circulating around it.

⇒The TMS Reference

Chemical shifts are measured in parts per million (ppm) relative to a standard reference compound: Tetramethylsilane (TMS). TMS is highly shielded, so its signal is defined as exactly δ = 0.0 ppm.

An NMR spectrum doesn't just show single spikes. The signals are often split into multiple smaller peaks. This is caused by Spin-Spin Coupling (or Splitting).

⇒The n+1 Rule

The magnetic field of a proton is affected by the spin states of the protons on immediately adjacent carbon atoms. This causes its signal to split.

Number of peaks in a signal = n + 1

Where 'n' is the number of equivalent protons on adjacent carbon atoms.

⇒Interpreting Ethanol (CH3-CH2-OH)

• The CH3 group: The adjacent carbon (CH2) has 2 protons. So n=2. Splitting = 2+1 = 3 peaks (a Triplet).
• The CH2 group: The adjacent carbon (CH3) has 3 protons. So n=3. Splitting = 3+1 = 4 peaks (a Quartet).
• The OH group: Hydroxyl protons usually don't couple due to rapid chemical exchange. It appears as a broad Singlet.

Therefore, the NMR spectrum of ethanol consists of a triplet (for CH3), a quartet (for CH2), and a singlet (for OH). By looking at the splitting, you can map exactly which carbon is connected to which!

⇒End-of-Unit Verification

• Write the mathematical equations for de Broglie's hypothesis and Heisenberg's uncertainty principle.
• Explain the physical significance of ψ and ψ² in the Schrödinger wave equation.
• List the main postulates of Molecular Orbital Theory and explain how BMOs and ABMOs are formed using LCAO.
• Draw the MO energy level diagrams for N2 and O2, calculate their bond orders, and predict their magnetic properties.
• Use Band Theory to explain the difference between conductors, insulators, and semiconductors based on band gap (Eg).
• Define the terms Chromophore and Auxochrome, and explain Bathochromic and Hypsochromic shifts in UV-Vis spectroscopy.
• State the selection rule for IR spectroscopy and identify which molecules (e.g., HCl vs N2) are IR active.
• Explain the difference between the Functional Group region and the Fingerprint region in an IR spectrum.
• Define Chemical Shift in NMR, explain the role of TMS, and distinguish between shielded and deshielded protons.
• Apply the n+1 rule to predict the spin-spin splitting pattern for molecules like ethanol or ethyl bromide.