All posts by shankharajsarkar

About shankharajsarkar

See the Universe with my eyes.

[Explanation]: Concept of Photoelectron Spectroscopy (PES)

Photoelectron Spectroscopy (PES) is an excellent technique for determining atomic and molecular electronic energy levels. When an atom or molecule is subjected to high energy radiation, electrons are ejected due to collision with photon. (This experiment proves particle nature of electrons.)
Instrumentation:

Monochromatic X-ray or UV-rays fall on the sample and ejected electrons pass between a pair of electrically charged hemispherical plates which acts as a filter of kinetic energy.

Figure: UVPES and XPES

Types of PES:

Generally PES are of two types-

 1.  UVPES

In UVPES, UV radiation (a He lamp of wavelength 58.4nm and energy 21.2 eV) falls on the atoms and eject electrons. Since, UV has a very low energy, it can eject only the valence electrons.
 2. XPES

X-rays (K line of Aluminium and Magnesium of energy 1486.6 eV and 1536.2 eV) fall on the metal or atom and eject electrons. Since, X-rays are highly energetic, it can eject core electrons also.
Both these techniques are used to study different properties of catalytic surfaces. That is why both these techniques are known as Electronic Spectroscopy for Chemical Analysis, ESCA.
Thanks for reading 🙂

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​Density Functional Theory: A Philosophical Explanation

Density Functional Theory was proposed in 1970s. The idea behind the Density Functional Theory (DFT) can be understood from a well known and widely popular story of Archimedes. It was 200 B.C. when Archimedes proposed his theory on ‘Density’, which is proportional to the displacement of water of a particular mass by that substance. Knowing density, we can find various other properties of that substance, like volume, mass depending on its value we can predict whether a substance will float or sink in a particular liquid, whether an aeroplane will fly or not etc. Not only macroscopic substance, but also we can predict the properties of the molecules depending on its electron densities. This is the basis of this theory.

DFT is different from the Hartree-Fock theory in the sense that the later completely depends on the total molecular wave function of the molecule on the other hand, the former depends on the density of electron cloud. So we need to call it- Density ‘Function’ Theory (cause it calculates energy and all related things as a function of density), but why the term ‘Functional’ is used in place of ‘Function’. The suffix ‘-al’ is related more to the mathematics than the philosophy.

According to mathematics,

if y= f(x) (Read: y is a function of x)

and z= f(y),

then z= [x] (Read: z is a functional of x)

In mathematics, function of a function is known as functional. This is how the term ‘Functional’ came in Density Functional Theory.

Let me explain it technically,

E.g, E = f(density) = f(radius),

Therefore, energy and radius are in functional relationship.

We know,

Total Energy of a molecule,

E = E(ke)+E (n,n)+E (e,n)+E(xc)

Where,

E(ke)= Kinetic energy of electrons

E (n,n)= Nuclear-Nuclear repulsion energy

E (e,n)= Electron-Nucleus attraction energy

E(xc)= Exchange correlation energy

The value of exchange correlation energy, E(xc), is very less in the order of large values of negative power of 10. But it produces a huge impact on the total energy of the molecule. If we don’t consider the value of E(xc), and calculate the ionisation energy with the remaining equation the value will come out in negative, that’s an error, as we know the ionisation energy can not have negative values.
DFT is named that way because the theory is contributed by tens of scientist. So we can’t give it a name unlike Schrödinger theory or Hartree-Fock theory. But we can not ignore the pioneering work of Kohn and Sham, who gave the fundamental equation of DFT, that is known as Kohn-Sham equation.

For calculating energy from the Kohn-Sham equation, we need to find density, rho.
Density can be calculated as follows.

The above calculation is done computationally using Gaussian software. For this, we need to feed it with different basis set followed by the name of method (can be selected by keeping in mind what percentage of accuracy we want in our result as compared to experimental result). Basis set is almost similar to atomic orbitals.
Example of basis set: 6-31+G* (Six minus three one plus G star)

Where, 6 gives 6Gaussians for the core electrons, 3 gives 3Gaussians, 1 gives 1Gaussians respectively for the valence electrons- which gives a total of 10Gaussians for a single electron system, i.e, H atom. Higher the number of Gaussian, higher is the accuracy of the result with experimental values for a particular atom or molecule. For higher accuracy in result, we can use the term CBS (means: complete basis set). In other words, ‘Gaussian’ is the unit of accuracy.
For Hydrogen atom (1s1), if we use 6-31G basis set, we will get 10G. For Lithium (1s2 2s1), we will get 30G.

For DFT, the total number of integration is given by, N^3, for Hartree-Fock Theory, the number of integration is N^4 and for MP2 theory the number of calculation is N^5 (where N is the number of Gaussians). Higher the value of integration, higher is the accuracy and higher is the time it consumes. Here is a latest theory that gives the theoretical result with so accuracy that even let us doubt the value of experimental result. This is called CCSD(T), i.e, Couple Cluster Singlet Doublet with perturbation Triplet. Now imagine the calculation of energy with the help of CCSD(T)/CBS. This takes a total of N^7 integration. It may take 2 years approximately to calculate the energy of Hydrogen molecule with our laptops.

Now the fact is that, DFT gives a poor value of exchange energy but a good value of correlation energy. On the other hand, Hartree Fock theory gives a good value of exchange energy and poor value of correlation energy. The human nature is to experiment with things that they do not understand and Scientists are no different. So they made the hybrid of HF and DFT to get a better result of exchange and correlation energy. In the language of Gaussian software, it is called B3LYP (Becke’s 3 parameter hybrid functional with correlation from Lee, Yang and Parr).

B3LYP: DFT+HF

To get a pure result based on DFT, one can use BP86 (Becke and Perdew exchange correlation functional invented in the year 1986).

BP86: DFT

NASA Confirms Seven Earth-Like Planets Orbiting A Nearby Star: Three of Them Has The Chance To Have Alien Life

NASA finally found 7 habitable planets orbiting a common star, which is 39 light years away from us. 

Photo Credit: NASA

NASA’s Spitzer Space Telescope revealed the system of 7 exoplanets orbiting a star TRAPPIST-1, named after the Transiting Planets and Planetesimals Small Telescope (TRAPPIST) in Chile. In May 2016, researchers using TRAPPIST reported three exoplanets of the system, finally after groundbreaking research and using sophisticated Spitzer telescope, four more planets are found orbiting the star.
According to the scientists, 3 out of these 7 planets are in the Goldilocks zone, means their distance from their star is such that it is neither too hot, nor too cold to support liquid water on their surface. The mass and densities of these planets are calculated. Based on the data, all the planets are likely to be rocky. Though the mass of the 7th planet are not yet calculated, but it is thought to be “icy-snowball” like planet. 
The star that the seven planets are orbiting is called a red dwarf– it’s small, dim, and cool compared to our own sun, but it can burn for a very, very long time– somewhere on the order of a trillion years, or even longer.
The discovery sets a record of largest number of habitable planets orbiting a common star.
Carl Sagan once quoted, “The universe is a pretty big place. If it’s just us, seems like an awful waste of space.”

Thanks For Reading 🙂
Reference:

1. Michaël Gillon, Amaury H. M. J. Triaud, Brice-Olivier Demory, Emmanuël Jehin, Eric Agol, Katherine M. Deck, Susan M. Lederer, Julien de Wit, Artem Burdanov, James G. Ingalls, Emeline Bolmont, Jeremy Leconte, Sean N. Raymond, Franck Selsis, Martin Turbet, Khalid Barkaoui, Adam Burgasser, Matthew R. Burleigh, Sean J. Carey, Aleksander Chaushev, Chris M. Copperwheat, Laetitia Delrez, Catarina S. Fernandes, Daniel L. Holdsworth, Enrico J. Kotze, Valérie Van Grootel, Yaseen Almleaky, Zouhair Benkhaldoun, Pierre Magain, Didier Queloz. Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 . Nature, 2017; 542 (7642): 456 DOI: 10.1038/nature21360

The Hidden Member Of Periodic Table: The “Element Zero”

Chemistry has a total of 118 known elements in the periodic table. Most of the elements after atomic number 90 is artificial or man-made elements. The numbering of elements in periodic table is done by the number of protons present in the nucleus of a particular atom. For example, Hydrogen has one proton in the nucleus so its atomic number is 1, Helium has two protons in the nucleus thus its atomic number is 2 and so on.

The interesting thing is that the nucleus of an element not only contains protons but also neutrons. But according to the convention, the atomic number is measured as the number of protons present in a particular nucleus. So what will be the atomic number of an element which contain no proton but neutron?

The element zero is called ‘neutronium’ or ‘Neutrium’. The word neutronium is first suggested by Scientist Andreas von Antropoff in 1926, before the discovery of Neutron. Neutronium is found in the dense core of the Neutron Stars. The ‘element zero’ is a hot topic of research for the astrophysicist to solve the mysteries of many astronomical phenomenons. 

Thanks For Reading. 🙂

[In Short] Carbon: Different Allotropes

Allotrope of an element means ‘different structural arrangement of that element’.

The popular allotropes of carbon are- Diamond, Graphene, Fullerene

There are many other forms of carbon also available like Lonsdaleite.

a) Diamond. b) Graphene. c) Lonsdaleite. d) C60. e) C540. f) C70. g) Amorphous Carbon. h) Single walled carbon nanotube.

(a) represents the structure of diamond, where each carbon is linked with four other carbon atoms forming a tetrahedron.

In diamond, each Carbon atom is sp3 hybridised.

(b) represents the structure of graphene. (There are four graphene units in the above picture) Graphene units piles up on one another to form graphite. That means graphite is a polymer of graphene.

Each carbon atom in graphene is sp2 hybridized. As a result of which there is one electron in nonbonding orbital. That is why it can conduct electricity (due to availability of free nonbonding electron).

Graphite consist of layers of graphene units. The distance between any two layer is 0.335 nano meter.

(c) represents Lonsdaleite. It is also called ‘Hexagonal Diamond’ because of its hexagonal close packing of arrangement. It forms when meteorites containing graphite strike the Earth. The great heat and stress of the impact transforms the graphite into diamond, but retains graphite’s hexagonal crystal lattice.

(g) represents amorphous form of carbon. Its property depends on the ratio of sp2 and sp3 hybridised carbon present in the material.

It lacks ordered arrangement of carbon.

d, e, f, h ——> fullerene

Fullerenes (also called buckyballs) are molecules of varying sizes composed entirely of carbon that take on the form of hollow spheres, ellipsoids, or tubes.

(h) can also be called as ‘carbon nanotubes’…

Remember: 

1. The surface of diamond is lipophillic (oil loving) and hydrophobic (water hating), which means it cannot get wet by water but can be in oil.

2. Graphite has a thermal conductivity upto 3500 °C

Thanks For Reading 🙂

[The Northeast India] Natural Resources: What Should Universities and Institutes Do?

​The North-Eastern region of India is rich in many useful natural resources. We have acres of tea gardens, dozens of oilfields and thousands of miraculous species of herbs in our vast landmass. We can study those resources and make available the reports to various industries, e.g., pharmaceutical, rubber, petroleum and energy.

We can set some new or modify our old laboratories of our universities and institutes to test the chemical samples. We need to know the chemistry involved in there to modify and enrich our products that are already available to the consumers. For example, the tea tree oil has magical antiseptic property. It can heal wounds and kill germs of many infamous viruses.

If each Universities and Institutions can transform themself into research and development centre for that particular region, then the students will be encouraged to take part in such research activities automatically.

[Explanation] What is Viscosity? 

Viscosity of a liquid implies the viscous force that tends to prevent the relative motion of a liquid layer compared to another layer in its contact.

The coefficient of viscosity ‘n’ is the numerical measure of viscosity, and it is defined as the frictional force, F per unit area per unit velocity gradient i.e., 

n= F/{A(dv/dx)}

Where, 

A is the surface area and

dv/dx is the velocity gradient.
On addition of a solute having larger molecular size and increased intermolecular forces, the coefficient of viscosity of water increases. Thus, addition of a solute increases the viscosity of water. With increase in its concentration, the viscosity of the solution is increased further.


Thanks for reading 🙂

বিশ্বাসঘাতিকা

​যাহার শক্তি শুশিয়া জয়িলা ভুবন,

সে আজ নিজ হাতে করিল তর্পণ।

তোমার সদৃশ স্বর্ণলতিকার আর নাই ঠাঁই,

যাইতে পারো আর কোনো বাঁধাধরা নাই।

সময় থাকিতে করিলা যারে হেলা;

নিজ চোখে দেখে নিও বিধাতার খেলা।।

[Explanation] Boiling Point Elevation: Cause & Effect

Introduction:

Boiling point elevation describes the phenomenon that the boiling point of liquid (a solvent) will be higher when a non volatile solute is dissolved in it than when it is pure.

Cause and Effect :

Boiling point elevation is the reduction of chemical potential of the liquid solvent as a result of the presence of a non-volatile solute. The physical basis of lowering of chemical potential is entropic.
In the absence of solute, the pure liquid solvent has an entropy that reflects its disorder. Its vapour pressure reflects the tendency of the liquid to change towards greater entropy, which can be achieved if the liquid is vaporized to form a more chaotic gas. When a solute is present, there is an additional contributions to the entropy of the liquid. Since there is already an additional randomness in the liquid, the system reaches its maximum entropy. When less liquid evaporates then the solute, and the randomness it causes is absent. The effect of the solute is a lower vapour pressure and hence a higher boiling point.
Thanks for reading 🙂

O- Substituted benzene derivative and aliphatic derivative do not obey the Hammett equation. Why?

When a reaction occurs at a position ortho to the substituent inside polar effect, steric effect also operates owing to the close position of the reaction centre and the substituent, the steric interaction takes place. m- and p- position being far away from reaction centre, the m- and p- substituent doesn’t have any steric effect on it. They have polar influence on it. Owing to the steric effect, o-substituted benzene derivative do not show the linear relationship i.e., Hammett equation.
The aliphatic derivative do not obey the Hammett equation because C- chains are very flexible and have zigzag structure. The substituents experience steric interaction to the reaction centre even it is far away from the substituent. Thus, like o- substituted benzene derivative, aliphatic derivative also do not obey the Hammett equation.

Note: 

The logarithm of the equilibrium constant of different reaction have a straight line, i.e., linear relationship. This implies that the substituent except their polar effect through changes of Potential Energy and no steric and entropies changes occur. Hence, Hammett equation is referred to have a Linear Free Energy Relationship (LFER).