**Inoragnic chemistry**

Inorganic chemistry is concerned with the properties and behavior of inorganic compounds, which include metals, minerals, and organometallic compounds. While organic chemistry is defined as the study of carbon-containing compounds and inorganic chemistry is the study of the remaining subset of compounds other than organic compounds, there is overlap between the two fields (such as organometallic compounds, which usually contain a metal or metalloid bonded directly to carbon).Alfred Werner is considered to be father of inorganic chemistry.

The blog has tried to describe minimum chemical facts and concepts that are necessary to understand modern inorganic chemistry. All the elements except superheavy ones have been discovered and theoretical frameworks for the bonding, structure and reaction constructed. The main purposes of inorganic chemistry in near future will be the syntheses of the compounds with unexpected bonding modes and structures, and discoveries of novel reactions and physical properties of new compounds.

More than ten million organic compounds are known at present and infinite number of inorganic compounds are likely to be synthesized by the combination of all the elements. Recently, really epoch making compounds such as complex copper oxides with high-temperature superconductivity and a new carbon allotrope C60 have been discovered and it is widely recognized that very active research efforts are being devoted to the study of these compounds. By the discoveries of new compounds, new empirical laws are proposed and new theories are established to explain the bondings, structures, reactions, and physical properties. However, classical chemical knowledge is essential before studying new chemistry. Learning synthetic methods, structures, bondings, and main reactions of basic compounds is a process requisite to students.

This blog describes important compounds systematically along the periodic table, and readers are expected to learn typical ones both in the molecular and solid states. The necessary theories to explain these properties of compounds come from physical chemistry.

Inorganic chemistry is of fundamental importance not only as a basic science but also as one of the most useful sources for modern technologies. Elementary substances and solid-state inorganic compounds are widely used in the core of information, communication, automotive, aviation and space industries as well as in traditional ones. Inorganic compounds are also indispensable in the frontier chemistry of organic synthesis using metal complexes, homogeneous catalysis, bioinorganic functions, etc. One of the reasons for the rapid progress of inorganic chemistry is the development of the structural determination of compounds by X-ray and other analytical instruments. It has now become possible to account for the structure-function relationships to a considerable extent by the accumulation of structural data on inorganic compounds. It is no exaggeration to say that a revolution of inorganic chemistry is occurring. We look forward to the further development of inorganic chemistry in near future.

The experimental chemist in his daily work and thought is concerned with observing and, to as great an extent as possible, understanding and interpreting his observations on the nature of chemical compounds. Today, chemistry is a vast subject. In order to do thorough and productive experimental work, one must know so much descriptive chemistry and so much about experimental techniques that there is not time to be also a master of chemical theory. Theoretical work of profound and creative nature, which requires a vast training in mathematics and physics, is now the particular province of specialists.

And yet, if one is to do more than merely perform experiments, one must have some theoretical framework for thought. In order to formulate experiments imaginatively and interpret them correctly, an understanding of the ideas provided by theory as to the behavior of molecules and other arrays of atoms is essential. The problem in educating student chemists-and in educating ourselves is to decide what kind of theory and how much of it is desirable. In other words, to what extent can the experimentalist afford to spend time on theoretical studies and at what point should he say, "Beyond this I have not the time or the inclination to go?" The, answer to this question must of course vary with the special field of experimental work and with the individual. In some areas fairly advanced theory is indispensable. In others relatively little is useful.

For the most part, however, it seems fair to say that molecular quantum mechanics, that is, the theory of chemical bonding and molecular dynamics, is of general importance. The number and kinds of energy levels that an atom or molecule may have are rigorously and precisely determined by the symmetry of the molecule or the environment of the atom. Thus, from symmetry considerations alone, we can always tell what the qualitative features of a problem must be. We shall know, without any quantitative calculations whatever, how many energy states there are and what interactions and transitions between them may be occur.

In other words, symmetry considerations alone can give us a complete and rigorous answer to the question “What is possible and what is completely impossible?" Symmetry consideration alone can not , however, tell us how likely it is that the possible things will actually take place. Symmetry can tell us that in principle two Stats of the system must differ in their energy, but only by computation or measurement can we determine how great the difference will be again symmetry can tell us that only certain absorption bands in the electronic or vibration spectrum of a molecule may occur. By using symmetry considerations alone we may predict the number of vibrational fundamentals, their activities in the infrared and Raman spectra, and the way in which the various bonds and inter bond angles contribute to them for any molecule possessing some symmetry. The actual magnitudes of the frequencies depend on the interatomic forces in the molecule, and these cannot be predicted from symmetry properties.

In recent years, the use of X-ray crystallography by chemists has improved enormously. No chemist is fully equipped to do research (or read the literature critically) in any field dealing with crystalline compounds, without a general idea of the symmetry conditions that govern the formation of crystalline solids. An understanding of this approach requires only a superficial knowledge of quantum mechanics.

In a number of applications of symmetry methods, however, it would be artificial and foolishness to exclude religiously all quantitative considerations. Thus, it is natural to go a few steps beyond the procedure for determining the symmetries of the possible molecular orbitals and explain how the requisite linear combinations of atomic orbitals may be written down and how their energies may be estimated. It has also appeared desirable to introduce some quantitative ideas into the treatment of ligand field theory.

**Where Is Inorganic Chemistry Used?**

Inorganic compounds are used as catalysts, pigments, coatings, surfactants, medicines, fuels, and more. They often have high melting points and specific high or low electrical conductivity properties, which make them useful for specific purposes. For example:

Ammonia is a nitrogen source in fertilizer, and it is one of the major inorganic chemicals used in the production of nylons, fibers, plastics, polyurethanes (used in tough chemical-resistant coatings, adhesives, and foams), hydrazine (used in jet and rocket fuels), and explosives.

Chlorine is used in the manufacture of polyvinyl chloride (used for pipes, clothing, furniture etc.), agrochemicals (e.g., fertilizer, insecticide, or soil treatment), and pharmaceuticals, as well as chemicals for water treatment and sterilization.

Titanium dioxide is the naturally occurring oxide of titanium, which is used as a white powder pigment in paints, coatings, plastics, paper, inks, fibers, food, and cosmetics. Titanium dioxide also has good ultraviolet light resistance properties, and there is a growing demand for its use in photocatalysts.

Inorganic chemistry is a highly practical science—traditionally, a nation’s economy was evaluated by their production of sulfuric acid because it is one of the more important elements used as an industrial raw material.

**Industries that Hire Inorganic Chemists**

**Environmental Science**

Environmental chemistry uses inorganic chemistry to understand how the uncontaminated environment works, which chemicals in what concentrations are present naturally, and with what effects. They also identify the effects of additives, such as fertilizers, on natural processes. The U.S. Environmental Protection Agency and other agencies detect and identify the nature and source of pollutants.

Companies that focus in environmental science include CH2M Hill, Bechtel, Veolia, URS Corporation, Black & Veatch, Tetra Tech, Energy Solutions, and government agencies as the U.S. Environmental Protection Agency (EPA). These companies study the chemical and biochemical phenomena that occur in natural places. They use atmospheric, aquatic, and soil chemistry, as well as analytical chemistry.

**Fibers and Plastics**

Fibers are materials that are continuous filaments or discrete elongated pieces, similar to lengths of thread. They are important for a variety of applications, including holding tissues together in both plants and animals. There are many different kinds of fibers including textile fiber, natural fibers, and synthetic or human-made fibers such as cellulose, mineral, polymer, and microfibers. Fibers can be spun into filaments, string, or rope; used as a component of composite material; or matted into sheets to make products such as paper. Fibers are often used in the manufacture of other materials. The strongest engineering materials are generally made as fibers, for example, carbon fiber and ultra-high-molecular-weight polyethylene. Synthetic fibers can often be produced cheaply and in large amounts as compared to natural fibers, but natural fibers have benefits some applications, especially for clothing.

Plastic material is any of a wide range of synthetic or semisynthetic organic solids used in the manufacture of industrial products. Plastics are typically polymers of high molecular mass and may contain other substances to improve performance and/or reduce production costs. Monomers of plastic are either natural or synthetic organic compounds.

Thermoplastics are plastics that do not undergo chemical change in their composition when heated and therefore can be molded again and again; examples are polyethylene, polypropylene, polystyrene, polyvinyl chloride, and polytetrafluoroethylene. The raw materials needed to make most of these plastics come from petroleum and natural gas.

Because of their relatively low cost, ease of manufacture, versatility, and imperviousness to water, plastics are used in a wide range of products, from paper clips to spaceships. However, these same properties make them persist beyond their usefulness, so much current work is focused on making photodegradable or other more environmentally friendly versions.

Examples of companies that focus in fibers and plastics are Albemarle, Bayer, Celanese, The Dow Chemical Company, Eastman Chemical Company and DuPont,

**Microchip**

Chemistry and material science allows the production of inorganic electronics with highly ordered layers and interfaces that organic and polymer materials cannot provide. Precise control of surface composition results in microchips with specific, desired properties.

An integrated circuit or monolithic integrated circuit (also referred to as IC, chip, or microchip) is an electronic circuit manufactured by the patterned deposition (or diffusion) of trace elements into the surface of a thin substrate of semiconductor material. Additional materials are deposited and patterned to form interconnections between semiconductor devices.

Integrated circuits are used in virtually all electronic equipment today and have revolutionized society. Computers, cell phones, and other digital appliances are now inextricable parts of the structure of modern societies, made possible by the low cost of production of integrated circuits.

Integrated circuits are also being developed for sensoric applications in medical implants and other bioelectronic devices. These environments require special sealing strategies to avoid corrosion or biodegradation of the exposed semiconductor materials.

Examples of companies that focus in microchips are Intel, Hitachi, AMD, Agilent, Alcatel-Lucent, STMicroelectronics, IBM, Texas Instruments, Rohm Semiconductor, and Samsung Semiconductor,

**Mining, Ore, and Metals**

Mining involves the extraction of valuable minerals or other geological materials from the earth or from an ore body, vein, or seam. Materials recovered by mining can include base metals, precious metals, iron, uranium, coal, diamonds, limestone, oil shale, rock salt, and potash. Any material that cannot be grown through agricultural processes or created in a laboratory or factory comes from mining. In the wider sense, mining comprises extraction of any nonrenewable resource (e.g., petroleum, natural gas, or even water) for human use.

Examples of companies that focus in mining, ore, and metals are BHP Billiton, Vale, RioTinto, Shenhua Group, Suncor, Glencore, and Barrick.

**Paint, Pigment, and Coatings**

A pigment is a material that changes the color of reflected or transmitted light as the result of wavelength-selective absorption. Pigments are classified as either organic (derived from plant or animal sources) or inorganic (derived from salts or metallic oxides).

Pigments are used for coloring paint, ink, plastic, fabric, cosmetics, food, and other materials. Most pigments used in manufacturing and the visual arts are dry inorganic colorants, usually ground into a fine powder. This powder is added to a vehicle (or binder), which is a relatively neutral or colorless material that suspends the pigment and gives the paint its adhesion.

Examples of companies that focus in paint, pigment, and coatings are Continental Chemical, Lintech International, Shepherd Chemical Company, DuPont, The Valspar Corporation, and Glidden Paints (A division of PPG Industries).

**Chemistry: a Science for the twenty-first century:**

- Chemistry has ancient roots, but is now a modern and active, evolving science
- Chemistry is often called the central science, because a basic knowledge of chemistry is essential for students in biology, physics, geology and many other subjects.
- Chemical research and development has provided us with new substances with specific properties. These substances have improved the quality of our lives.

**Elements and Periodicity**

The elements are found in various states of matter and define the independent constituents of atoms, ions, simple substances, and compounds. Isotopes with the same atomic number belong to the same element. When the elements are classified into groups according to the similarity of their properties as atoms or compounds, the periodic table of the elements emerges. Chemistry has accomplished rapid progress in understanding the properties of all of the elements. The periodic table has played a major role in the discovery of new substances, as well as in the classification and arrangement of our accumulated chemical knowledge. The periodic table of the elements is the greatest table in chemistry and holds the key to the development of material science. Inorganic compounds are classified into molecular compounds and solid-state compounds according to the types of atomic arrangements.

**The origin of elements and their distribution **

All substances in the universe are made of elements. According to the current generally accepted theory, hydrogen and helium were generated first immediately after the Big Bang, some 15 billion years ago. Subsequently, after the elements below iron (Z = 26) were formed by nuclear fusion in the incipient stars, heavier elements were produced by the complicated nuclear reactions that accompanied stellar generation and decay. In the universe, hydrogen (77 wt%) and helium (21 wt%) are overwhelmingly abundant and the other elements combined amount to only 2%.

**Discovery of elements**

The long-held belief that all materials consist of atoms was only proven recently, although elements, such as carbon, sulfur, iron, copper, silver, gold, mercury, lead, and tin, had long been regarded as being atom-like. Precisely what constituted an element was recognized as modern chemistry grew through the time of alchemy, and about 25 elements were known by the end of the 18th century. About 60 elements had been identified by the middle of the 19th century, and the periodicity of their properties had been observed.

The element technetium (Z = 43), which was missing in the periodic table, was synthesized by nuclear reaction of Mo in 1937, and the last undiscovered element promethium (Z = 61) was found in the fission products of uranium in 1947. Neptunium (Z = 93), an element of atomic number larger than uranium (Z = 92), was synthesized for the first time in 1940. There are 103 named elements. Although the existence of elements Z = 104-111 has been confirmed, they are not significant in inorganic chemistry as they are produced in insufficient quantity.

All trans-uranium elements are radioactive, and among the elements with atomic number smaller than Z = 92, technetium, prometium, and the elements after polonium are also radioactive. The half-lives (refer to Section 7.2) of polonium, astatine, radon, actinium, and protoactinium are very short. Considerable amounts of technetium 99Tc are obtained from fission products. Since it is a radioactive element, handling 99Tc is problematic, as it is for other radioactive isotopes, and their general chemistry is much less developed than those of manganese and rhenium in the same group.

Atoms are equivalent to alphabets in languages, and all materials are made of a combination of elements, just as sentences are written using only 26 letters.

**Electronic structure of elements **

Wave functions of electrons in an atom are called atomic orbitals. An atomic orbital is expressed using three quantum numbers; the principal quantum number, n; the azimuthal quantum number, l; and the magnetic quantum number, ml. For a principal quantum number n, there are n azimuthal quantum numbers l ranging from 0 to n-1, and each corresponds to the following orbitals

l : 0, 1, 2, 3, 4, …

s, p, d, f, g, …

**Definition of group**

A group C is a collection of elements which satisfy the following conditions.

1. For any two elements a and b in the group the product a x b is also an element of the group.

In order for this condition to have meaning, we must, of course, have agreed on what we mean by the terms "multiply " and "product. Perhaps we might say combination instead of product in order to avoid pointless incorrect connotations. Let us not yet force ourselves to any particular law of combination but merely say that, if A and B are two elements of a group, we point out that we are combining them by simply writing AB or BA. Now instantaneously the question arises if it makes any difference whether we write AB or BA. In ordinary algebra it does not, and we say that multiplication is commutative, that is xy = yx, or 3 x 6 = 6 x 3. In group

2. There exists an unit element 1 in the group such that 1 x a = a x 1 = a for every element a or in other words one element in a group must commute with all others and leave them unchanged. It is customary to designate this element with the letter E and it is usually called the identity element.

3. There must be an inverse (or reciprocal) element a-1 of each element a such that

a x a-1 = a -1 x a = 1.

or every element must have a reciprocal,which is also an element of the group. The element R is the reciprocal the element S if RS = SR =E where E is the identity. Obviously, if R is the reciprocal of S, then S is the reciprocal of R. Also, E is its own reciprocal.

At this point we shall prove a small theorem concerning reciprocals which The associative law of multiplication must hold. This is expressed in the following way

A (BC) = (AB)C

In simple words, we may combine B with C in the order BC and then combine this product, S, with A in the order AS, or we may combine A with B in the order AB, obtaining a product, say R, which we then combine with C in the order RC and get the same final product either way. In general, of course, the associative property must hold for the continued product of any number of elements.

**Some Examples of Groups**

The significance of the above defining rules, we may consider an infinite group and then some finite groups. As an infinite group we may take all of the integers, both positive, negative, and zero. If we take as our law of combination the ordinary algebraic process of addition, then rule 1 is satisfied. Clearly, any integer may be obtained by adding two others. Note that we have an Abelian group since the order of addition is immaterial. The identity of the group is 0, since 0 + n = n + 0 = n. Also, the associative law of combination holds, since, i.e., [(+3) + (-7)] + (+1043) = (+3) + [(-7) + (+1043)]

The reciprocal of any element, n, is ( -n), since ( + n) + ( -n) = 0

**Group Multiplication Tables**

If we have a absolute and non redundant list of the elements of a finite group and we know what all of the possible products (there are h2 ) are, then the group is absolutely and uniquely defined at least in an abstract sense. The foregoing information can be presented most conveniently in the form of the group multiplication table. This consists of h rows and h columns. Each column is labeled with a group element, and so is each row. The entry in the table under a given column and along a given row is the product of the elements which head that column and that row. Because multiplication is in general not commutative, we must have an agreed upon and consistent rule for the order of multiplication. Arbitrarily, we shall take factors in the order - (column element) x (row element) thus at the intersection of the column labeled by X and the row labeled by Y we find the element, which is the product XY. We now prove an important theorem about group multiplication tables, called the rearrangement theorem

**Dihedral group**

The symmetry of a square is the 4-fold dihedral D4 symmetry. To understand a discrete group, we first identify how many elements are in the group which is called the order of the group h. It is obvious that any integer multiples of π/2 rotations would leave the square invariant. There are four in equivalent rotations of this kind. A mirror inversion of the square is also an invariant transformation.

Applying inversion to the previous rotations, we get another four rotations Thus, the elements of D4 group are

D4={I,R,R2 ,R3 ,P,PR,PR2 ,PR3 } (1)

That is to say the order of the group h = 8.

General not commutative, we must have an agreed upon and consistent rule for the order of multiplication. Thus at the intersection of the column labeled by X and the row labeled by Y we find the element, which is the product XY. We now prove an important theorem about group multiplication tables, called the rearrangement theorem. Each row and each column in the group multiplication table lists each of the group elements once. Form this it follows that no two rows may be identical nor may any two columns be identical. This each row and each column is a rearranged list of the group elements. PROOF. Consider the group consist of the h elements E, A2 , A3 , ... , Ah. The elements in a given row, say the nth row, are EAn ,A2An ,…………….AnAn…………..,AhAn

Since no two group elements, Ai and Aj for instance are the same, no two, products, AiAn and AjAn , can be the same. The h entries in the nth row are all diverse. Since there are only h group elements, each of them must be there once and only once. The argument can obviously be adapted to the columns.

**Groups of orders 1, 2, and 3**

Consider now systematically examine the possible abstract groups of low order, using their multiplication tables to define them. There is, of course, formally a group of order 1, which consists of the identity element alone.

**Molecular Symmetry and Symmetry Groups**

At the end of the unit learner will be able to

- Understand the symmetry elements and symmetry operations generated by them
- Understand that how symmetry elements co-related with optical isomerism
- Determination of point groups

**Introduction**

In a nonmathematical sense the concept of symmetry is associated with regularity or proportionality. In short it is associated with beauty. Consider an example of sign of exclamation. Now we rotate this sign seven times, through an angle of 45o about an axis passing through the centre of the dot and perpendicular to the plane of the paper. The symmetry operation (rotation) about the symmetry element (axis) gives a beautiful flower in which each petal of flower is related to one another by rotation through 45o about the symmetry axis.

In dealing with molecules, which are present in various conformations, we try to identify the symmetry elements and symmetry operations that will tell us that how the atoms in the molecules are related to one another in space. To do this we should know the kinds of symmetry elements and operations generated by them.

**Symmetry Elements and Symmetry Operations**

Although symmetry operations and symmetry elements are related to each other but are two different things. Symmetry element is a geometrical entity such as line plane or a point with respect to which one or more symmetry operations may be carried out.

A symmetry operation is the actual movement of atoms in a molecule such that after the operation has been carried out every atom is coincident with an equivalent atom. In other words after the operation has been carried out on a molecule we get an equivalent or identical configuration. In other words if we note the position and orientation of the body before and after a movement is carried out, that movement is a symmetry operation, if these two orientations are indistinguishable.

Types of Symmetry Element: There are our types of symmetry elementsa)

a) Proper axis of symmetry (C)

b) Plane of symmetry (σ)

c) Improper axis of symmetry (S)

d) Centre of inversion (i)

One or more symmetry operations are associated with one symmetry element. Some authors have included identity as a symmetry element, but it is a symmetry operation.

**a) Proper axis of symmetry:**

It is an imaginary axis around which the rotation carried out on the molecule, which takes the molecule from one orientation to the other equivalent indistinguishable orientation. The proper axis of symmetry is represented by Cn

And the operations generated by this are represented by Cn m

Where n= order of the axis and m = no. of times the operation is carried out

The order of axis is defined as the number of times an operation is to be carried out so as to get an identical configuration

n=2π/θ

θ = angle by which rotation is carried out

**b) Plane of Symmetry**

It is an imaginary plane within the molecule which bisects it into two equal half which are mirror image s of each other. A plane of symmetry exists when a reflection through the plane gives an equivalent configuration. Plane of symmetry is represented by σ.

**Types of plane of symmetry: the plane of symmetry can be divided into three types**

1) Vertical plane of symmetry (σv) - The plane passing through the principal axis and one of the subsidiary axis (If present) is called vertical plane of symmetry.

2) Horizontal plane of symmetry (σh ) - The plane perpendicular to the axis is called horizontal plane of symmetry.

3) Dihedral plane of symmetry (σd ) – The plane passing through principal axis but passing in between two subsidiary axes is called dihedral plane.

**c) Improper Axis of Symmetry**

An improper axis of rotation is said o exist when rotation about an axis followed by a reflection in a plane perpendicular to the axis of rotation results in an equivalent or identical configuration or in other words we can say that it is an imaginary axis on which the molecule has to be rotated and then reflected on a plane perpendicular to the rotation axis to get an equivalent or identical configuration.

The improper axis of rotation is represented by Sn. The operations generated by it are represented by Sn m, where

n = order of axis and

m= no. of times the operation is being performed.

**d) Centre of inversion**

A molecule is said to possess a centre of symmetry if reflection of each atom through centre of the molecule results in its coincidence with an equivalent atom. We define it as for every atom at x, y z here exist an identical atom at -x,-y,-z. It means that if any atom in the molecule is connected with the centre of symmetry, equivalent atom lies on the opposite side.

This is best illustrated by the following example The centre of inversion is represented by i and the operations generated by this is expressed by i n . It can be seen that i n =E {if n=even}i n =i { if n= odd}

Unlike plane of symmetry, the centre of inversion generates only one operation.

The configuration generated by S2 axis is equivalent to that generated by a centre of inversion and hence an S2 axis is always represented by i. Other examples of molecule having centre of inversion are CO2, C2H4, N2O2, [Co(NH3)6]3+ etc.

**Identity**

This is an operation which brings back the molecule to the original orientation. It is represented by E. There are several different types of operations which bring back the molecule to its original orientation, they are not considered separately but are put together as identity. For example an axis of four folds symmetry C4 1 , C4 2 and C4 3 are considered as rotation operations. But C4 4 that is rotation by 360o is not considered as a rotational operation because it is an identity operation. Over a plane of symmetry only one reflection operation is considered. If the reflection is repeated, the original orientation is obtained and hence the second reflection is an identity operation. Thus the identity operation in effect means doing nothing on the molecule and hence does not seem to be of much importance lies in considering the molecules as a group and to apply the group theory to molecules.

**Product of Symmetry Operations**

When we say that we are multiplying 2 symmetry operations we mean that we are combining the two operations and the resulting combination of the two operations is the product of the multiplication. When we write he multiplication and the product in the following wayyx=z we mean that operation x is carried out first and then operation y, giving the same net effect as would the carrying out of the single operation z. Here it should be noted that the order in which the operations are applied is the order in which they written from right to left. When the results of the sequence xy is the same as the result of the sequence yx, the two operations x and y are said to commute.

**Equivalent Symmetry Elements and Atoms**

Any set of symmetry element chosen so that any member can be transformed into each and every other member of the set by some operation is said to be a set of equivalent symmetry elements.

**Symmetry Elements and Optical Isomerism**

As we have discussed all the symmetry elements in previous section. Now in this section we will see that how symmetry elements are correlated with optical isomerism. Optical isomers or enantiomers are the molecules which cannot be superimposed on its mirror image and such molecules are said to be chiral and are optically active. The word chiral is a Greek word which means “hand”. So the property of handedness is known as chirality. Human hands are chiral because both the hands are mirror image of each other but are non superimposible. So the enantiomers occur only with those compounds whose molecules are chiral.

Consider the example of 2-butanol, which is a chiral molecule. The enantiomers of 2-butanol are drawn in the three dimensional projection formula. The mirror image of 2-butanol isomer is non-superimposableupon the original molecule.

Thus the compounds of the type Cabcd exist in enantiomeric form and are described as chiral and the carbon with different atoms or groups as substituents is called a stereogenic centre or simple stereocentre. Molecules which are superimposible on its mirror image are known as achiral molecules. An imaginary plane that bisects a molecule in such a way that the two halves of the molecule are mirror images of each other then plane of symmetry exists. A molecule with a plane of symmetry cannot be chiral. Such molecules are achiral.

An alternative approach to decide if or not a structure is chiral that is in enantiomeric form (optically active) is to determine the symmetry of a molecule. When the molecule has a centre of symmetry (Ci) or a plane of symmetry (σ) or n-fold alternating axis of symmetry (Sn), the mirror images of the molecules are superimposible and the molecule is achiral (optically inactive).

**Classes of Symmetry Operations**

Before studying classes of symmetry operations we must read about the groups. A set of elements is said to form a group when the elements of the set are related to one another by some rules. For any set of elements to form a group the following four conditions must be satisfied:

1) The product of any two elements and the square of each element must be a member of the set. For example if A an B are two elements of a set and we are multiplying them by simply writing A X B or B X A. The products of the elements are C and D respectively. These C and D must be a member of set. In group theory the cumulative law does not hold generally, since both the products are different. So order of multiplications is important. However there are certain groups for which the products are cumulative, such groups are known as Abeliangroup.

2) One element in the set must commute with all other elements and leave them unchanged. In the group of A, B and C, if C is such element, then

AC=CA=A

BC=CB=B

This element is called identity E.

3) The associative law of multiplication must hold, this is expressed in the following equation:

A(BC)=(AB)C

In general the associative property must be hold for any number of elements-

(AB)(CD)(EF)(GH)=A(BC)(DE)(FG)H=(AB)C(DE)(FG)H

4) Every element must have a reciprocal which is also an element of the group. The element R is the reciprocal of the element S if RS=SR=E, where E= identity obviously. If R is reciprocal of S then S is the reciprocal of R and also E is its own reciprocal.

If we have a set of elements and we know all the possible products then the group is completely and uniquely defined. This information can be presented in the form of a table called the multiplication table.

**Symmetry Point Groups and their Classification**

We have seen that a complete set of operations do constitute a group. In this section we shall see that different kinds of groups will be obtained by collecting various symmetry operations. These symmetry groups are called point groups.

When symmetry operations are performed on a molecule the physical properties do not change. The centre of symmetry of the molecule remains unshifted during symmetry operations. This is because all symmetry operations pass through centre of symmetry, hence the molecular group is known as point groups. The symbols that are used for symmetry groups are called Schoenflies symbols after their inventor.

**Classification of point groups**

Point groups are classified as follows:

1) **Non-axial point groups: **A point group which does not have any proper axis of rotation is known as non-axial point groups. A molecule which has only identity (E) and no other operation is possible belongs to C1 point group. When a plane of symmetry is present it generates a group of order two means only two symmetry operations are possible that is, σ and E. Such molecules belong to Cs point group. Similarly another group of order two is formed when a molecule has inversion centre, (i and E) this group is represented by Ci . it should be remembered that molecule having i is equal to S2 , hence a molecule with only S2 belongs to point group Ci.

2) **Axial point groups:** when the molecules have proper or improper axis of rotation. Let us consider molecules where the proper axis is the only symmetry element present. It belongs to the point group Cn. When a molecule has a Cn axis with a vertical plane as the elements of symmetry then the molecule is said to belong the point group Cnv. If the molecule has a Cn axis with σh instead of σv then the point group is Cnh. If one or more C2 axis is present perpendicular to Cn axis (principal axis) then such molecule belongs to Dn point group. If in a molecule a σh or σd is present in addition to C2 perpendicular to Cn then it belongs to Dnh or Dnd respectively. Molecule with Sn axis form a group called Sn.

3) **Special point groups:**

**a) Linear molecules: **linear molecules have axis of infinite fold of symmetry C∞. It can be of two types. One is symmetrical linear molecule in which C2 axis perpendicular to C∞ is present so it is classified as D∞h point group.

**b) Cubic molecules: **Molecules with cubic symmetry have two types of point groups. One is tetrahedral point group (Td). The structure has four trigonal faces, four corners and six edges. The most common example of molecule having tetrahedral geometry is CH4 . The molecule has 24 symmetry operations. Molecules having tetrahedral geometry but do not possess all the 24 operations do not belong to Td point group (CH3Cl, CHCl3 ). Other is octahedral point group (Oh). The structure has eight trigonal faces, six corners and twelve edges.

**c) The following steps will lead to a correct classification:**

- Identify whether the molecule belongs to any special class that is if the molecule is linear it can be assigned either D∞h (symmetrical) or C∞V (unsymmetrical) point group. If the molecule is cubic it belongs Oh or Td point group.
- If the molecule does not belong to special class then look for proper axis of rotation. If molecule has no proper axis of rotation then see whether it has centre of symmetry or plane of symmetry. If element i is present then it belongs to Ci and if σ is present then it belongs to Cs. If none of them is present then C1 point group is assigned to the molecule.
- If an even order improper axis is present and no plane and proper axis of rotation is found. Except it is collinear with principal axis. Then the point group is Sn.
- If the molecule has only Cn axis it belongs to point group Cn, otherwise go to step1

**Representations of Groups**

Some object are ”more symmetrical” than others. A sphere is more symmetrical than a cube because it looks the same after rotation through any angle about the diameter. A cube looks the same only if it is rotated through certain angels about specific axes, such as 90o , 180o , or 270o about an axis passing through the centers of any of its opposite faces, or by 120o or 240o about an axis passing through any of the opposite corners. Here are also examples of different molecules which remain the same after certain symmetry operations: NH3 , H2O, C6H6 , CBrClF. In general, an action which leaves the object looking the same after a transformation is called a symmetry operation. Typical symmetry operations include rotations, reflections, and inversions. There is a corresponding symmetry element for each symmetry operation, which is the point, line, or plane with respect to which the symmetry operation is performed. For instance, a rotation is carried out around an axis, a reflection is carried out in a plane, while an inversion is carried out in a point.

**Symmetry operations**

The classification of objects according to symmetry elements corresponding to operations that leave at leastone common pointunchanged gives rise to the pointgroups. These are five kinds of symmetry operations and five kinds of symmetry elements of this kind. These symmetry operations are as follows.

- The identity, E, consists of doing nothing: the corresponding symmetry element is an entire object. In general, any object undergo this symmetry operation. The example of the molecule which has only the identity symmetry operation is C3H6 O3, DNA, and CHClBrF.
- The n-fold rotation about an n-fold axis of symmetry, Cn is a rotation through the angle 360o/n. Particularly, the operation C1 is a rotation through 360o which is equivalent to the identity E. H2 O molecule has one twofold axis, C2 . N H3 molecule has one threefold axis, C3 which is associated with two symmetry operations: 120o rotation C3 and 240o (or −120o) rotation C2 . C6 H6 molecule has one sixfold axis C6 and six twofold axes C2. If a molecule possess several rotational axes, then the one of them with the greatest value of n is called the principal axis. All linear molecules including all diatomics has C∞ axis because rotation on any angle remains the molecule the same.
- The reflection in a mirror plane, σ may contain the principal axis of a molecule, or be perpendicular to it. If the plane contains the principal axis, it is called vertical and denoted σv. For instance, H2O molecule has two vertical planes of symmetry and N H3 molecule has tree. A vertical mirror plane which bisects the angle between two C2 axes is called a dihedral plane and is denoted by σd. If the plane of symmetry is perpendicular to the principal axis, it is called horizontaland denoted σh. For instance, C6H6 molecule has a C6 principal axis and a horizontal mirror plane.
- The inversion through the center of symmetry is the operation which transforms all coordinates of the object according to the rule: (x, y,z) → (−x, −y, −z). For instance, a sphere, or a cube has a center of inversion, but H2O, and NH3 have not. C6H6 molecule has a center of inversion.
- The n-fold improper rotation about an n-fold axis of symmetry, Sn is a com- bination of two successive transformations. The first transformation is a rotation through 360o/n and the second transformation is a reflection through a plane perpen- dicular to the axis of the rotation. Note that neither operation alone needs to be a symmetry operation. For instance, CH4 molecule has three S4 axes.

**Representation of group**

representation of a group of the type we shall be interested in may be defined as a set of matrices, each corresponding to a single operation in the group, that can be combined among themselves in a manner parallel to the way in which the group elements-in this case, the symmetry operations combine. Thus, if two symmetry operations in a symmetry group, say C2 and σ, combine to give a product C2 ', then the matrices corresponding to C2 and a must multiply together to give the matrix corresponding to C. But we have already seen that, if the matrices corresponding to all of the operations have been correctly written down, they will naturally have this property.

**The Great Orthogonality Theorem**

All of the properties of group representations and their characters, which are important in dealing with problems in valence theory and molecular dynamics, can be derived from one basic theorem concerning the elements of the matrices which constitute the irreducible representations of a group. In order to state this theorem, which we shall do without proof, some notation must be introduced. The order of a group will, as before, be denoted by h. The dimension of the ith representation, which is the order of each of the matrices which constitute it, will be denoted by l i .

The various operations in the group will be given the generic symbol R. The element in the mth row and the nth column of the matrix corresponding to an operation R in the ith irreducible representation will be denoted Γ(R)mn. Finally, it is necessary to take the complex conjugate (denoted by *) of one factor on the lefthand side whenever imaginary or complex numbers are involved.

**Group Theory and Quantum Mechanics**

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other wellknown algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, can be modelled by symmetry groups. Thus group theory and the closely related representationtheory have many important applications in physics and chemistry.

Quantum mechanics is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the Planck constant. It departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. Quantum mechanics provides a substantially useful framework for many features of the modern periodic table of elements including the behavior of atoms during chemical bonding and has played a significant role in the development of many modern technologies.

In advanced topics of quantum mechanics, some of these behaviors are macroscopic and emerge at only extreme energies or temperatures. For example, the angular momentum of an electron bound to an atom or molecule is quantized. In contrast, the angular momentum of an unbound electron is not quantized. In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects.

The mathematical formulations of quantum mechanics are abstract. A mathematical function, the wavefunction, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. Mathematical manipulations of the wavefunction usually involve bra–ket notation which requires an understanding of complex numbers and linear functionals. The wavefunction formulation treats the particle as a quantum harmonic oscillator, and the mathematics is akin to that describing acoustic resonance. Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics. For instance, in a quantum mechanical model the lowest energy state of a system, the ground state, is non-zero as opposed to a more "traditional" ground state with zero kinetic energy (all particles at rest). Instead of a traditional static, unchanging zero energy state, quantum mechanics allows for far more dynamic, chaotic possibilities.

**Wave function as basis for irreducible representations**

The wave equation for any physical system is

Hψ = Eψ (1)

Here H is the Hamiltonian operator, which indicates that certain operations are to be carried out on a function written to its right. The wave equation states that, if the function is an eigenfunction, the result of performing the operations indicated by H will yield the function itself multiplied by a constant that is called an eigenvalue.

Eigenfunctions are conventionally denoted ‘ψ’, and the eigenvalue, which is the energy of the system, is denoted E. The Hamiltonian operator is obtained by writing down the expression for the classical energy of the system, which is simply the sum of the potential and kinetic energies for systems of interest to us, and then replacing the momentum terms by differential operators according to the postulates of wave mechanics. We need not concern ourselves with this construction of the Hamiltonian operator in any detail.

The only property of it which we shall have to use explicitly concerns its symmetry with respect to the interchange of like particles in the system to which it applies. The particles in the system will be electrons and atomic nuclei. If any two or more particles are interchanged by carrying out a symmetry operation on the system, the Hamiltonian must be unchanged. A symmetry operation carries the system into an equivalent configuration, which is, by definition, physically indistinguishable from the original configuration. Clearly then, the energy of the system must be the same before and after carrying out the symmetry operation. Thus we say that any symmetry operator, R, commutes with the Hamiltonian operator, and we can write

RH = HR (2)

The Hamiltonian operator also commutes with any constant factor c. Thus

Hcψ = c Hψ = c Eψ (3)

**Chemical bond**

Is the attractive force interaction of atoms assemble into molecules. There are significant changes of bonding particles in energies of the valence shell electrones and orbitals. The System wants to minimize the energy content – isolated atoms have got higher energies than molecules. Bond energy dissipate into surrounding in order to minimalise the Energy of the System.

**Why elements reacts together?**

„The Stable Octet Rule“ – all other elements than Noble gases want to mimic their extremely stable („fullfilled“) electronic configuration by the reaction with other elements - „octet“ generally means valence orbitals filled with all electrones.

__Exceptions from the Octet Rule: __

**HYPOvalency – less than octet **

3 valence e- - only 6 shared e-!

**HYPERvalency – more than octet**

5 valence e- means 10 shared e-!

**Examples of inorganic compounds include:**

- Sodium chloride (NaCl): used as table salt.
- Silicon dioxide (SiO2): used in computer chips and solar cells.
- Sapphire (Al2O3): a well-known gemstone.
- Sulfuric acid (H2SO4): a chemical widely used in the production of fertilizers and some household products such as drain cleaners.

**Why is inorganic chemistry important?**

Inorganic chemistry is used to study and develop catalysts, coatings, fuels, surfactants, materials, superconductors, and drugs. Important chemical reactions in inorganic chemistry include double displacement reactions, acid-base reactions, and redox reactions.

**Inorganic chemists: Salary, career path, job outlook, education and more**

Inorganic chemists study the structure, properties, and reactions of molecules that do not contain carbon, such as metals. They work to understand the behavior and the characteristics of inorganic substances. Inorganic chemists figure out how these materials, such as ceramics and superconductors, can be modified, separated, or used in products.

**Education Required**

A bachelor’s degree in chemistry or a related field is needed for entry-level chemist or materials scientist jobs. Research jobs require a master’s degree or a Ph.D. and also may require significant levels of work experience. Chemists and materials scientists with a Ph.D. and postdoctoral experience typically lead basic- or applied-research teams. Combined programs, which offer an accelerated bachelor’s and master’s degree in chemistry, also are available.

**Job Outlook**

The projected percent change in employment from 2016 to 2026: 7% (As fast as average) (The average growth rate for all occupations is 7 percent.)

**Advancement**

Chemists typically receive greater responsibility and independence in their work as they gain experience. Greater responsibility also is gained through further education. Ph.D. chemists usually lead research teams and have control over the direction and content of projects, but even Ph.D. holders have room to advance as they gain experience. As chemists become more proficient in managing research projects, they may take on larger, more complicated, and more expensive projects.

Median pay: How much do Chemists and Materials Scientists make?

$75,420 Annual Salary

$36.26 per hour

**Why Is Chemistry So Hard?**

Chemistry has a reputation as a hard class and difficult science to master. Here's a look at what makes chemistry so hard.

**Chemistry Uses Math**

You have to be comfortable with math up through algebra to understand and work chemistry problems. Geometry comes in handy, plus you'll want calculus is you take your study of chemistry far enough.

Part of the reason many people find chemistry so daunting is because they are learning (or re-learning) math at the same time they are learning chemistry concepts. If you get stuck on unit conversions, for example, it's easy to get behind.

**Chemistry Isn't Just in the Classroom**

One common complaint about chemistry is that it counts for the same credit hours as any other class, but requires a lot more from you both in class and outside it.

You've got a full lecture schedule, plus a lab, problems, and a lab write-up to do outside of class, and maybe a pre-lab or study session to attend. That's a big time commitment.

While that may not make chemistry more difficult, it leads to burn-out a lot earlier than with some studies. You've got less free time to wrap your head around the material on your own terms.

**Its Own Language**

You can't understand chemistry until you understand the vocabulary. There are 118 elements to learn, a lot of new words, and the entire system of writing chemical equations, which is its own special language.

There is more to chemistry than learning the concepts. You have to learn how to interpret and communicate the way chemistry is described.

**It's Hard Because of the Scale**

Chemistry is a vast discipline. You don't just learn basics and build on them, but switch gears into new territory fairly often.

Some concepts you learn and build on, but there is always something new to throw into the mix. Simply put, there is a lot to learn and only a limited time to get it into your brain.

Some memorization is required, but mostly you need to think. If you're not used to working through how something works, flexing your mind can take effort.

**It's Hard Because You Think It's Hard**

Another reason chemistry is hard is that you've been told it's hard. If you think something is difficult, you're setting yourself up to fulfill that expectation.

The solution to this is to truly believe you can learn chemistry. Achieve this by breaking up study time into manageable sessions, don't fall behind, and take notes during lectures, lab, and during your reading. Don't psych yourself out and don't give up as soon as the going gets tough.

**Easy Isn't Always Better**

Even though it is challenging, chemistry is worthwhile, useful, and possible to master. What other science explains so much of the everyday world around you?

You may need to learn new study skills and change the way you organize your time, but anyone with the will to learn chemistry can do so. As you succeed, you'll gain a deep sense of accomplishment.

**Advantages and Disadvantages of Inorganic Fertilizers**

**Advantages**

Organic fertilizers generally do not contain high levels of nutrients and might not be suitable to sustain high intensity crop production. Large scale agricultural facilities prefer inorganic fertilizers as they provide a more accurate control over their nutrient supply. Inorganic fertilizers are supplied in a water-soluble form which ensures that they are easily absorbed by plants. Much less inorganic fertilizer can therefore be applied to have the same result as organic fertilizers.

**Disadvantages**

The two major disadvantages of inorganic fertilizers are that:

Inorganic fertilizers must be manufactured industrially. This involves cost in terms of both chemicals and the energy involved in the production. Air pollution is also a result of these industrial processes.

Nutrients which are not taken up by plants, will either accumulate in the soil therefore poisoning the soil, or leach into the ground water where they will be washed away and accumulate in water sources like dams or underground rivers.

**Optional Video: Challenges of fertilizer production**

You might watch the video below to get a sense of the complex process of fertilizer production in an industrial plant. Fertilizer production is a very energy-intensive process. An optimal plant operation and the efficient use of resources are decisive factors for economic success. Siemens products and in particular the SIMATIC PCS 7 process control system help dealing with the requirements.