## What is Quantum Chemistry?

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

## History

The study of electromagnetic field, electromagnetic interactions and the attempts to quantize it are the root causes for the emergence of quantum chemistry. Quantum chemistry emerged in 1926 with the discovery of Schrödinger equation for the application towards hydrogen atom. Based on this application, the phenomenon of chemical bond was introduced. Further much progress was achieved by few scientists namely Mulliken, Max Born, Oppenheimer, Linus Pauling, Huckel, Hartree, Fock etc. Further discovery of cathode rays by Faraday, black body radiation by Kirchoff, Boltzmann’s suggestion on physical state of energy, Max Plank’s quantum hypothesis, photoelectric effect by Albert Einstein etc., are few more progresses achieved in quantum mechanics. The major contribution towards quantum chemistry is made by Linus Pauling. The rapid development of computer knowledge in the recent years further developed quantum mechanics methods, specifically in density functional theory methods, which help to understand, design the molecular properties and reactions occurring even in the biological systems.

In late 1920’s another stepping stone in the field of quantum chemistry has been made. It is the quantum field theory. Paul Dirac was the one who clarified the quantum field theory primarily. In later 1940’s and 1950’s the quantum field theory has been made more advanced. Quantum field theory can be considered as the combination of classical field theory, quantum mechanics and special relativity. Quantum electrodynamics (QED) is one of the most important theories among different aspects of quantum mechanics.

## Quantum Electrodynamics (QED)

The theory of quantum electrodynamics (QED) has been formulated by Richard Feynman. Feynman is the one who has developed Feynman perturbation series and Feynman diagram. Quantum electrodynamics (QED) can be considered as the quantum field theory of electromagnetic force. Quantum electrodynamics (QED) deals with the interaction between light and matter. More precisely it deals with the interaction of charged particles with an electromagnetic field. QED can be considered as the first theory which is in line with quantum mechanics and special relativity. The anomalous magnetic moment of electron and the Lamb shift can be effectively explained using quantum electrodynamics. In total, Feynman has developed the first successful quantum field theory.

In the perspective of quantum field theory, the exchange of virtual photons will lead to the exchange force between electrons. Feynman has used diagrams to describe this.

The physical chemistry book on quantum chemistry and spectroscopy which has been authored by Thomas Engel deals which all the concepts in quantum chemistry including Schrödinger equation, Born-Oppenheimer approximation, statistical mechanics, computational chemistry, quantum mechanics, quantum electrodynamics and so on.

## What is Electromagnetic Spectrum?

It is a group of spectrums or frequencies present in electromagnetic radiation along with their respective photon energies and wavelengths. They contain electromagnetic waves whose frequencies ranges from less than 1 hertz to greater than 10^{25} hertz. The frequency range is further divide into spectral bands and the electromagnetic waves present in each spectral band are given different names, beginning from low frequency or high wavelength radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays at short wavelength or high frequency.

## De-Broglie Hypothesis

In 19^{th} century end, it was thought that light is a wave of electromagnetic radiation while matter are of localized particles. In 1924, based on the Einstein’s equation of wavelength (λ) related to momentum (*p*), De Broglie postulated a formula that could relate and determine the wavelength of any material. De-Broglie was the first scientist to propose that matter behaves as a wave and thus named them as ‘De Broglie waves’. Thus the De Broglie equation is given as

$$\text{\lambda =h/p=h/mv}$$

where, h is Planck constant, *p* is momentum. This relationship holds good for various types of matter which exhibit both particle and wave nature. This concept is known as wave-particle duality.

**Wavefunction**: In quantum chemistry, the wavefunction describes the wave characteristics of a particle mathematically. Wavefunction is a variable quantity.

## Heisenberg’s Uncertainty Principle

The uncertainty principle is only the fundamental principle in quantum chemistry which reveals the limit of an extent to know about the behaviour of the atomic and subatomic particles. In general, the position and the velocity of a moving object such as an engine or an automobile can be measured as the uncertainty of these objects are too small to be considered. But in the case of atomic and subatomic particles such as electrons, the position and the velocity cannot be measured at a time. Thus, the uncertainty principle by Werner Heisenberg states that, if the position of a subatomic particle is determined more precisely, then the possibility to determine the momentum of the particles is very less; as these variable pairs are termed as canonically conjugate variables (for example, momentum (p) /position (x) or energy (E) /time (t) etc.) among which the uncertainty plays a major role.

$$\begin{array}{l}\text{\Delta p\Delta xh/4\pi}\\ \text{\Delta t\Delta Eh/4\pi}\end{array}$$

where, Δ indicates the uncertainty and h is Planck's constant.

## Black Body Radiation

It is a type of thermal electromagnetic radiation emitted by a black body present in thermodynamic equilibrium. A black body is a substance which absorbs completely various frequencies of light. As it is expected to be in thermodynamic equilibrium, it should re-emit the same quantity of light it has absorbed and thus acts as a perfect ideal emitter. A black body radiation concept is completely a theoretical and imaginary concept. Naturally, no material acts as a black body but in few cases, graphite acts as a black body to 96%. A spontaneously emitted thermal radiation from a perfectly insulated container present in thermal equilibrium contains black body radiation internally, which is emitted through a minute hole whose effect on equilibrium is negligible. Best example for black body radiation emitters is sun and a hot stove.

Wien showed that the spectrum radiation emitted by a black body at any temperature is related to any spectrum at any other temperature, that is, the shape of a spectrum at any temperature can be calculated with the shape of a spectrum at a particular temperature. Thus, Wien’s displacement law of a black body states that the spectral intensity of an emitted radiation is expressed with respect to the wavelength or frequency.

## Photoelectric Effect

When electromagnetic radiations hit a metal or material, electrons are emitted. This type of effect is called as photoelectric effect and the electrons emitted are called as photoelectrons. Photoelectrons are similar to normal electrons in their properties and behavior. The process together is termed as photoemission. This phenomenon in quantum chemistry helps to understand the properties of atoms, molecules, ions etc. Thus from this phenomenon it is showed that as the frequency of light increases, kinetic energy of the photoelectrons also increases and an increase in light amplitude increases the current. Thus, Einstein proposed that light travels with particles called photons with energy given as

$$\text{E=hv}$$

## Practice Problems

Calculate the de Broglie wavelength of a moving electron with a velocity of 3.5 x 10^{5} m/s?

Solution: Given velocity/speed = 3.5 x 10^{5} m/s

Mass of electron = 9.1 x 10^{–31} Kg (Standard value obtained)

h – planck’s constant = 6.63 x 10^{–34} Js (Standard value obtained)

λ = h/p = h/mv

= 0.23 × 10^{–9} m

Thus the calculated de Broglie wavelength is 0.23 × 10^{–9} m.

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for Bachelors and Masters in Chemistry.

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