Introduction to Quantum Chemistry

Introduction to Quantum Chemistry

• Quantum chemistry is a crucial component of chemical engineering.
• Without quantum mechanics, many chemical properties cannot be explained.

Explaining Chemical Phenomena Without Quantum Mechanics

• Periodic trends in element properties
• Structure of compounds (e.g., tetrahedral carbon in ethane, planar ethylene)
• Bond lengths and strengths
• Discrete spectral lines (IR, NMR, Atomic Absorption)
• Electron microscopy and surface science

Quantum Chemical Calculations in Chemical Processes

• The calculations are essential in chemical process industries.
• Computing ideal gas thermodynamic and spectroscopic properties
• Predicting molecular structures
• Analyzing reaction pathways
• Calculating heats of formation and related properties
• Predicting thermodynamic properties of non-ideal systems through interaction energies and molecular simulations

Thermodynamic and Spectroscopic Properties

• Ideal gas law (PV = nRT)
• Internal energy (U = nCvT)
• Enthalpy (H = U + PV = nCvT)
• Work done and heat transfer (Isothermal, Adiabatic, Isobaric)
• Spectroscopic properties
  • Rotational energy levels
  • Vibrational energy levels
  • Spectra (spectrum, electronic transitions, absorption and emission)

Computational Methods and Quantum Chemistry in Chemical Processes

• Computational methods/quantum chemistry are used to determine spectroscopic properties and energy levels using quantum methods (Gaussin, VASP, etc).
• Molecular simulations (Molecular Dynamics or Monte Carlo) help determine the thermodynamic properties of gases under various conditions.

Molecular Structure Prediction

• Potential energy surfaces (PES) represent the energy of a system.
• Molecular mechanics describes bond lengths, angles, torsion angles, van der Waals interactions, and electrostatics.
• Quantum mechanics (Hartree-Fock, Density Functional Theory (DFT)) provides a more precise way to predict structures.
• Geometry optimization minimizes molecular system energy (locating most stable conformation).

Analyzing Reaction Pathways

• Reaction coordinate on the potential energy surface represents the reaction coordinate where the highest energy point is the transition state.
• Transition state search
• Computed using quantum chemical methods (DFT or HF).

Electromagnetic Spectrum

• The electromagnetic spectrum displays the range of wavelengths and frequencies of electromagnetic radiation.
• Wavelength decreases as frequency increases.
• Different types of electromagnetic radiation interact with matter and can excite atoms or molecules, resulting in measurable changes.

Energy of a Photon

• Energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.
• E = hν = hc/λ (where h is Planck's constant, v is frequency, c is the speed of light, and λ is wavelength).

Light Absorption and Emission

• Electrons absorb light to transition from a lower energy level to a higher energy level.
• As electrons transition from higher to lower energy levels, they emit light.

Electron Transition in Hydrogen Atom

• Energy difference (ΔE) is determined using the Rydberg formula ΔE = -Rhc(1/n_final² - 1/n_initial²)
• The value of ΔE is positive during absorption.

Photoelectric Effect

• Light striking a metal surface can eject electrons (photoelectric effect).
• The current produced is proportional to the intensity of the light.
• There is a threshold frequency below which no electrons are ejected.

Wave-like Nature of Particles

• Particles can exhibit wave-like properties.
• De Broglie wavelength relates particle momentum and wavelength (λ = h/p).

Compton Effect

• X-rays scattering by electrons lead to a change in wavelength.
• Photons lose energy during the interaction and momentum is exchanged.