Ch2_Methodology_11-18-04

Ch2_Methodology_11-18-04 - CHAPTER 2 METHODOLOGY 2.1...

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35 CHAPTER 2 METHODOLOGY 2.1 Message for the reader Readers with a strong computational background can skip section 2.2 and move onto section 2.3. Section 2.2 is intended for individuals, who are not familiar with or have no computational chemistry exposure so as to gain the basic fundamentals about computational terminologies, methodologies and techniques. 2.2 A basic understanding of computational chemistry Basic fundamentals are now introduced to show how the power of computational programming has allowed us to study important physical properties in simple and complex systems that may be hard to do experimentally. Understanding the definitions and acronyms of numerous methodologies that have been developed by programmers and used in this project will be explained in detail throughout this section. The first thing to keep in mind is any computational program will evaluate the energy of a configuration of atoms. But most importantly, is it our job to find the most stable configurations, i.e. the one with the lowest energy. There are numerous computational methods that have been created and each method does different calculations for properties of interest. However, the problem is that different programs use different definitions of energy which can be
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36 different than the experimental energetics defined thermodynamically. Properties as the change in enthalpy, free energy, and entropy are important in thermochemistry; whereas chemical quantum mechanics describes the behavior of electrons and obtains electronic equilibrium energies (see figures 1.1a and 1.1b). Finally, statistical mechanics provides the means to go between the thermodynamic properties and electronic equilibrium energies. Thus, as Young states “there is a difference between the energy of the system, composed of all molecules, and the energy of the individual molecule and this amount of energy in the entire system that is measurable as the temperature of the system” [1]. 2.2.1 Ab Initio methodology, HF and MP2 The first computational methodology discussed is ab initio , which is Latin for “from the beginning” [2]. Such calculations may use mathematical approximations, but do not utilize any experimental chemical data. These methods often use a linear combination of atomic orbitals to make molecular orbitals. Hartree-Fock (HF) theory is the most basic of ab initio methods. HF does not account for the instantaneous electrostatic interaction between electrons. Each electron interaction is considered in the average field of the nuclei and all the other electrons. Thus, the HF wavefunction can be written as a product (only of the occupied orbitals) with the electron-electron repulsion and the total energy of the electron calculated as a sum in the average field of all the other electrons, where Ψ total is (2.1) Determinants, det, are a form of wavefunctions which express the indistinguishability of electrons (all permutations of electrons) in the orbitals. The procedure for solving the Φ = Ψ a a total det
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Ch2_Methodology_11-18-04 - CHAPTER 2 METHODOLOGY 2.1...

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