Photocatalysis and it's mechanism

The term can be generally used to describe a process where light is  used to activate a substance.The photocatalyst that modifies the rate of a chemical reaction without itself being involved in the chemical transformation. Thus, the main difference between a conventional thermal catalyst and photocatalyst is that  the former is activated by heat whereas the latter is activated by photons of appropriate energy. The principle of photocatalysis is based on the activation of a semiconductor particulate material by the action of radiation with an appropriate wavelength.  Photocatalysis is used for the elimination of several pollutants ( alkanes, alkenes, phenols, aromatics, pesticides) and complete mineralization of the organic compounds.

When a photocatalyst is irradiated with a light of suitable wavelength, an electron is excited to the conduction band (CB), leaving behind a positive hole in the valence band (VB). The electron in the CB can be utilized to reduce any substrate, whereas the hole in the VB can be used for oxidizing some compounds.

Reference: Photocatalysis principles and applications by Rakshit ametha

Page number 9-11

TiO2 photocatalysis is widely used in a variety of applications and products in the environmental and energy fields, including self-cleaning surfaces, air and water purification systems, sterilization, hydro- gen evolution, and photoelectrochemical conversion. The development of new materials, however, is strongly required to provide enhanced performances with respect to the photocatalytic properties and to find new uses for TiO2 photocatalysis. In this review, recent developments in the area of TiO2 photo- catalysis research, in terms of new materials from a structural design perspective, have been summarized. The dimensionality associated with the structure of a TiO2 material can affect its properties and func-
tions, including its photocatalytic performance, and also more specifically its surface area, adsorption, reflectance, adhesion, and carrier transportation properties.


https://www.sciencedirect.com/science/article/pii/S1389556712000421

Operators in quantum mechanics

The principal
mathematical difference between classical mechanics and quantum mechan-
ics is that whereas in the former physical observables are represented by
functions , in quantum mechanics they
are represented by mathematical operators.

 An operator is a symbol for an
instruction to carry out some action, an operation, on a function. In most of
the examples we shall meet, the action will be nothing more complicated than
multiplication or differentiation.

Linear operator:

Schrödinger equation

The Schrödinger equation, sometimes called the Schrödinger wave equation, is a partial differential equation. It uses the concept of energy conservation (Kinetic Energy + Potential Energy = Total Energy) to obtain information about the behavior of an electron bound to a nucleus. It does this by allowing an electron's wave function, Ψ, to be calculated.
Solving the Schrödinger equation gives us Ψ and Ψ2. With these we get the quantum numbers and the shapes and orientations of orbitals that characterize electrons in an atom or molecule.

The Schrödinger equation gives exact solutions only for nuclei with one electron: H, He+, Li2+, Be3+, B4+, C5+, etc. In mathematical language, we say that analytic solutions for Ψ are possible only for one-electron systems. One-electron systems are often described as hydrogenic - meaning "like hydrogen.For all other atoms, ions, and molecules, no analytic solutions for Ψ are possible;


There is a time-dependent Schrödinger equation and a time-independent Schrödinger equation.

The time-independent equation considers the electron's quantum state to be unchanging, hence it considers the electron as a standing wave. The time-independent equation allows electron densities (i.e. the sizes and shapes of atomic and molecular orbitals) to be found using Ψ2, the square of the wave function.

The p orbitals below are examples of Ψ2:px,py,pz.



https://www.chemicool.com/definition/schrodinger_equation.html

Electronic structure

Electrons are the “glue” that holds the nuclei together in the chemical bonds of
molecules and ions. It  is the nuclei’s positive charges that bind the electrons to
the nuclei. Electronic structure theory deals with the quantum states of the electrons, usually within the Born- Oppenheimer approximation .It also addresses the forces that the electrons’ presence creates on the nuclei; it is these forces that determine the geometries and energies of various stable structures of the molecule as well as transition states connecting these stable structures. Because there are ground and excited
electronic states, each of which has different electronic properties, there are different
stable-structure and transition-state geometries for each such electronic state. Electronic
structure theory deals with all of these states, their nuclear structures, and the
spectroscopies.

Reference
http://simons.hec.utah.edu/NewUndergradBook/Chapter6

Effect of Li Adsorption on the Electronic and Hydrogen Storage Properties of Acenes

Due to the presence of strong static correlation effects and noncovalent interactions, accurate prediction of the electronic and hydrogen storage properties of Li-adsorbed acenes with n linearly fused benzene rings (n = 3-8) has been very challenging for conventional electronic structure methods.To meet this challenge using developed thermally-assisted-occupation density functional theory (TAO-DFT) with dispersion corrections.

Woodward's rules

Woodward's rules, named after Robert Burns Woodward and also known as Woodward–Fieser rules are several sets of empirically derived rules which attempt to predict the wavelength of the absorption  maximum (λmax) in an ultraviolet visible spectrum of a given compound. Inputs used in the calculation are the type of chromophores present, the substituents on the chromophores, and shifts due to the solvent. Examples are conjugated carbonyl compounds,conjugated dienes, and polyenes.

Example

Reference 

https://en.m.wikipedia.org/wiki/Woodward's_rules

Infrared spectroscopy

Infrared spectroscopy or vibrational spectroscopy involves the interaction of infrared radiation with matter. It covers a range of techniques, mostly based on absorption spectroscopy. As with all spectroscopic techniques, it can be used to identify and study chemical substances. Samples may be solid, liquid, or gas. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer.