## Table of contents

An effective substitute to work out the Schrodinger equation was provided by the Honhenberg and Kohn in form of a theorem some thirty years ago. After the approval of the Schrodinger’s equation in 1926, the main concern was the solution to obtain the end result of the equation through the proper way. After two years, Dirac stated, in his publication on the topic of the quantum mechanics of multi-electron scenario; The physical laws governing and mandatory for the theories based on mathematics that are applicable to major portion of physics and almost the complete chemistry are now established even then there is a difficulty in their implementations as when these are applied to the system, these lead towards complex solution which is not easy to resolve. Considering these deject assertion, the problems while elucidating the Schrodinger equation to real-world situations has lead the chemistry to a new chapter that is ab initio theory; this included all the important non- experimental procedures. With the advancements in science and technology, the use of computer-based and software based method has proven to be a more accurate method and allowed the chemists for the application of theories to the molecular combinations with more precision. The constant and defined aim of quantum chemistry is to get results that are more precise and accurate in the well-suited laboratory ambience and assessment. With veracity calculations about one kcal/mole of energy can be accomplished when the operating systems are miniature for example bimolecular system, even till now we are looking for the accuracy in case of an intermediate and extensive organization. Considering ab initio procedure, the study will begin with a probationary atomic system and this system may or may not be established before. After the utilization of the geometry examination with energy depreciation method, a balanced system (normally a smaller conversion states) has achieved.

In order to get energy-related terms like atomization energy, enthalpy, bond energies, entropies or any other parameter either the expected value or calculable parameter that can be obtained from the wave function of the atomic framework or any of its part can be calculated directly in a simple way. In order to check the durability of the given system, second derivatives are derived in correspondence with spatial coordinates (the Hessian matrix). Other aims might include checking the systems interact with each other and at last to predict the formation and degradation mechanisms. All of these desired aims will be achieved with the passage of time. Ab initio method, when used combined with minute experimental improvements is providing good results and hence these are the more obvious systems to be used for theoretical chemist organizations. Here we will deal with the study of static atomic frameworks, for these systems the relativistic holdings are not appropriate; the use of non- relativistic time-independent Schrodinger mathematical statements can be explained. The wave functions are part of the molecular schemes and these are adiabatically divided into electronic and nuclear parts; hence both the entities are considered separately and not merged into each other while solving the problems. This approach is considered as the Born-Oppenheimer Approximation. Apart from the above three methodologies, the mathematical statement for non-relativistic time independent situation by the Schrodinger is termed as the Schrodinger equation, has not been solved in many cases till now. In this study, we will present the effectiveness of Density Functional Theory (DFT) to elucidate the Schrodinger equation by following the more accurate methodology which has circumvent the procedure for wave function calculations. Ab initio procedures are counted in numbers of density functional procedures; we will consider the ab initio procedure only for those procedures which include the wave function way for the energy eigenvalue from the Schrodinger equation, as against to density functional (DF) process which utilizes the electronic density to get the same parameter values. In order to avoid the ambiguity that was already created in the naming system, it is necessary to discriminate among the semiempirical and ab initio approaches, the bases of functions that are either fitted or not to the experimental statistics.

## Density Functional Theory’s Function

Generally, the density functional theory has been utilized progressively in the number of areas of chemistry and materials sciences to account for and indicating the attributes for complicated scenarios at an atomic level. More calculatedly, DFT in form of data processing approach has been studied by checking the formulations and progression entities. These systems have the laboratory results that are overburdened with inappropriate outcomes and unsteady ambience. The current Density functional theory application includes the working on the interpretation of the impact of dopants on state conversion features in case of oxides; in case of dilute magnetic semiconductor materials the study of magnetic behaviour and also the magnetic and electronic attitudes study of dilute magnetic semiconductors and ferroelectrics. One more application recently found for the DFT methodology has accuracy in indicating the reactiveness of few Nano frameworks to the air contaminations like Sulphur dioxide and acrolein and also the indication of mechanical parameters.

On the basis of utilization purpose, the Kohn-sham theory has been improvised in vast applications practically. While taking in account the solid state estimations, the normal density approaches are routinely used together with plane wave basis sets, just as an electron gas approach suits best to the delocalized electrons in a boundless solid system. In the case of molecular counting, we need more practical operatives and there has been developed a great collection of exchange-correlation operatives to be utilized in more chemical exercises. Not every function is appropriate works for the electron gas likeness, even then they must minimize to LDA in the ranges of the electron gas. Revised Perdew-Burke-Ernzerhof exchange model is now the most commonly improvised operation which is a straight forward observed gradient parametrization of the electronic gas exclusive of any free constants yet it can be precisely used calorimetrically for the gas phase molecular estimations. In the world of Chemistry one famous operation established under the name of BLYP (derived from the Becke used for exchange portion whereas Lee, Yang and Parr used for the coordination portion). More generally used is B3LYP term which is a mixed operation where the transferable energy is mixed with the original energy extracted from the Hartee-Fock theory and the exchange energy is derived from the Becke’s exchange operation. Together with the transferable and other parallel operations, three major criterions regulate the hybrid or mixed operations, particularly defining the accurate amount of energy that has been fused in the system. Those constants that can be altered in these operations are set to a “training set” of the particles. Even though the result provided by these functions are appropriate for many of the systems but till now no pathway has caved for the betterment of these results ( contrary to some of the common method available based on the wave function methodology including configuration interaction method or coupled-cluster theory). So considering the current situation it seems difficult to handle the DFT procedure with error and its comparison with other experimental findings.

## Philosophical Perspective of Density Functional Theory for Chemical Reaction

The main focus now a day is on the application of Density Functional theory for the determination of electronic arrangements of atoms, molecules and more precisely for solids. Density Functional theory serves as the principle foundation for the forecasting of an electronic network of matter. The density functional accession for the cause and effect studies during a reaction certainly providing the active motion to the nuclei should excel this theory more in future. Related with this theory we also have postulated a theory under the name of “theory of intrinsic reaction coordinates (IRC)” to make its connection as an exclusive pathway for the reaction. Energetically, the IRC can be viewed as the main point for the reaction flow via the transition state (changeover point) of the reaction.

IRC constructs a curve that is connecting two points which are reacting species and the product formed through the intermediate formation confined in the Riemannian outline space for the participant nuclei. Vibrational motion that is very smooth is representative of the nuclear movement of the transition mode in the IRC and is characterized by the negative force constant. According to the established fact of Stable Limit Theorem, the flexibility feature of IRC is confined for the stability at the balanced point. The assembling to the flexible vibrational motion in the IRC curves is given for the stability point. When such IRC curves are obtained, it is stable evidence suggesting that the flow of electron during a chemical pathway is responsible for the softness character which is related with the nuclear repulsion; in turn, it suggests the flexibility of the vibrations during a chemical reaction. Here we will elaborate the density functional side of the chemical pathway to bring about the reaction together with IRC perspective. This is very crucial to check for the path of electron density movement that brings about the chemical reaction to a product formation and to check for the features that are responsible for the flexible vibrational mode. N is the number of electrons is an ordered parameter, whereas the electron density flow is a mixture of two processes i.e. variable N process and the equi-N process. To check the kinetics of the electron density flow, a unique division of the reaction index is examined to perform the studies on the given topic. This will be an application for the innovative “apparatus “density functional theory as presented by the writer. When studied in detail, the Thermo-dynamical approach will be helpful to examine the route for a reaction. Born-Oppenheimer approach is utilized for the nonrelativistic electrons system.

In order to check the measurements of molecular and electronic setups at the ground state, density functional techniques are adopted. Since many operations are competing for utilization, these will contest with the finest result yielding ab initio procedures. This review will deal only with the theoretical elaboration of the Kohn sham density functional scheme. This scheme (Kohn Sham exchange-correlation operation has many scopes for improvement even then it can be used for the theoretical proceeding excluding the demand for considering the uniform electron gas estimation. With these theoretical gaining in the field, more advancement with precision can be attained for work in functional methodology.

## Chemical Reactions and Their Pathways in View of Density Functional Theory

The robust division of system of reactivity has been suggested to check for the electron density progression with the reaction correspondents. One on one relation is examined among the parameter like density matrix and the electron density and this is the universal developed structure for density functional. Density functional is considered as a thermodynamic parameter that is supposed to follow the phenomenon of largest entropy and this cannot be restraint by the N or v representability. The operative parameter for the density functional in regards to electron density will be presented as the response operator. The mechanism of any of chemical reaction is not so simple, it consists of a number of variables like the extensible electron density processes, the related response operator as well as newly derived heat related factors and their effects, these variables are clearly pointed and presented to make useful data for the calculations. The reaction correspondent with clearly defined attributes will be discussed as the fresh thermodynamic entities. The flexible vibrational manner worth in the chemical reactivity index is explained in detail relating it with the density functional theory.

Density Functional Theory (DFT) is another way for determining the actual energy surfaces for the systems; it is a substitute for the old wave function established approaches like Hartree-Fock, configuration interaction and multi-body perturbation theory. This methodology is useful in settling the issues of the electron-electron coordination by a set of quasi one particle Schrodinger equation, and the Kohn-Sham equation. On reality ground, some approximations are suggested for the exchange and the correlation energy and this approximation is local density approximation (LDA). This approximation is very effective when dealing with multi-electron systems like molecules. Historically, Gunnarsson, Rarris, Jones, Baerends and Ellis were the pioneer in the solid state physics for investigating the molecules in 1970, from there DFT-LDA got the attention for the chemical setups and the chemistry behind the reactions. It is because of the successful attempts to make corrections to LDA by gradient corrections. DFT is advantageous since it requires very little computational work to generate data for larger molecules in comparison with the “post-Hartree-Fock methods, configuration interaction and multi-body perturbation theory. Although the computational method for DFT has been utilized for the molecular calculations even then more experience has been gained with the old traditional methods than with DFT method. This study is focusing on the present efforts along with the result of using DFT for the computational method as this is the latest approach. DFT is leading towards the ways for direct feigning of the chemical procedure through the mixture of DFT and molecular dynamics and the DFT with the practical quantum dynamics. Here only the procedure for the chemical reaction mechanisms will be discussed. All the previously reported problems of defining and estimating the reaction path will not be described. Only the energy for transition framework will be considered at the saddle point in between the two minimum energy spots. For understanding term transition state (TS) will be used for these frameworks although it is not true according to Eyring concept of the transition state.

## Salvation of C60 Fullerene by Ionic Liquids II, Speculative Insight:

Fullerene C60 contains a total of 60 carbon atom that are spherically arranged. It was found by Smalley et al, in 1985 and its discovery has led to the opening of many fields for research like medicine, material chemistry, technology, solar cell, cosmetics etc. How Fullerene behaves in solution, it will decide their use in technology. It is not completely miscible with water and has finer solubility in an aromatic and organic solvent so non-polar solvents are preferable. Numbers of studies have been performed to improve C60 solubility along with lowering of its ability of self-agglomerating keeping in view the variables like solubility data, thermodynamics of solution and other physicochemical dimensions in solution form.

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