• Over the past two decades, quantum chemistry and molecular simulation has emerged as an insightful and accurate design tool in academic and industrial research.
• The availability of powerful computers and the development of very precise theoretical frameworks have enabled chemists, chemical engineers, and materials scientists to evaluate properties of molecules and materials accurately, map out prominent chemical phenomena, and design chemical operations based on atomic-level knowledge pertinent to the system under investigation.

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Introduction

• Quantum chemistry is now widely deployed in research and development departments of major chemical industries around the world to study the course of chemical reactions, to design catalysts with potent active sites, and to fine-tune properties of materials toward the desired optical and electronic attributes.

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Introduction

• Major applications of quantum chemistry in chemical industries include the following:

• Optimizing the performance of reactors,

• Interpreting the experimental results at the laboratory scale before proceeding to mass production.

• Shortlisting chemicals and catalysts that warrant further experimental scrutiny.

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Introduction

• While the governing equations and approaches in quantum chemistry are of a purely theoretical and physicochemical nature, the questions that quantum chemistry attempts to answer are truly practical.
• Quantum chemical calculations are carried out via various computer codes; most notably, Gaussian09, ADF, VASP, Crystal, DMol3, and CASTEP.

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Introduction

• Electronic structure calculations serve an important role in the understanding of chemical structure and reactivity.
• The release of user-friendly, commercial electronic structure programs has led to increased access to the techniques of computational chemistry.
• Density functional theory (DFT) is a type of electronic structure calculation that continues to gain popularity.

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Introduction

Some important types of modern electronic structure calculations are:

• Hartree−Fock (HF),
• Møller−Plesset perturbation theory (MP),
• configuration interaction (CI), and
• density functional theory (DFT).

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Introduction

• HF, MP, and CI calculations rely on the computation of the atomic or molecular wave function, whereas DFT requires computation of the total electron density and technically does not require a wave function.
• HF theory has a number of well-established shortcomings and this method alone is generally not accurate enough to study most chemical reactions.

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Introduction

• MP and CI, which build upon the HF calculation, provide very accurate electronic energies for small atoms and molecules when using very large basis sets, but the methods are too computationally expensive to apply to larger atoms and molecules.
• Modern implementations of DFT can provide much higher accuracy than HF calculations at a lower computational cost. The low computational cost of DFT has led to a steady increase in the use of density functional theory for the study of larger molecules.

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Introduction

• Researchers in many areas of chemistry routinely use electronic structure methods to predict molecular structures as well as physicochemical properties and even to predict the outcome of a chemical reaction.
• Solution of the Schrödinger wave equation provides the wavefunctions, Ψ, which describe the behavior of electrons in atoms and molecules, as well as the eigenvalues, viz their associated energies, E.
• It is well-known, however, that exact analytical solutions can only be found for simple cases such as the hydrogen atom or hydrogen-like ions.

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Introduction

10

Introduction

• Density functional theory, DFT, is based not on the wavefunction, but rather on the electron probability density function or electron density function, commonly called simply the electron density or the charge density, designated by ρ (x, y, z).

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• Unlike the wavefunction, it is measurable, e.g. by X-ray diffraction or electron diffraction.

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• It is a function of position only, that is, of just three variables (x, y, z), while the wavefunction of an n-electron molecule is a function of 4n variables, three spatial coordinates and one spin coordinate, for each electron.

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Density functional theory

• A wavefunction for a ten electron molecule will have 40 variables. In contrast, no matter how big the molecule may be, the electron density remains a function of three variables.

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• The electron density function, then, trumps the wavefunction in three ways:

it is measurable,

it is intuitively comprehensible, and

it is mathematically more tractable.

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Density functional theory

13

The Nobel Prize in chemistry 1998 was divided equally between Walter Kohn “for his development of the density-functional theory” and John A. People “for his development of computational methods in quantum chemistry”.

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• The first Hohenberg-Kohn theorem says that “all the properties of a molecule in a ground electronic state are determined by the ground state electron density function ρ_o(x, y, z) ”.

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• In other words, given ρ_o(x, y, z) we can in principle calculate any ground state property, e.g. the energy, E_0.

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• The significance of this theorem is that it assures us that there is in principle a way to calculate molecular properties from the electron density.

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The Hohenberg–Kohn Theorem

• The second theorem defines an energy functional for the system and proves that the correct ground state electron density minimizes this energy functional.

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• The ground state energy may be obtained variationally: the density that minimises the total energy is the exact ground state density.

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• The second Hohenberg–Kohn theorem says that any trial electron density function will give an energy higher than (or equal to, if it were exactly the true electron density function) the true ground state energy.

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The Kohn-Sham Theorem

• A generalized DFT expression is

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where T_S is the kinetic energy functional, E_ne is the electron-nuclear attraction functional, J is the Coulomb part of the electron-electron repulsion functional, and E_xc represents the exchange correlation functional.

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Density Functional Theory