11: Computational Quantum Chemistry
- Page ID
- 11788
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Computational chemistry is the field of chemistry that uses mathematical approximations and computer programs to solve problems of chemical interest. Quantum chemistry is a subfield that addresses the equations and approximations derived from the postulates of quantum mechanics; specifically involving solving the Schrödinger equation for molecular systems. Quantum chemistry is typically separated into ab initio, which uses methods that do not include any empirical parameters or experimental data and semi-empirical which do.
- 11.1: Overview of Quantum Calculations
- This page explores multielectron electronic wavefunctions, focusing on antisymmetric wavefunctions for identical particles like helium under the Pauli Exclusion Principle. It introduces Slater determinants for constructing these wavefunctions in multielectron systems. Additionally, it covers the creation of a single determinant wavefunction using molecular orbitals from Gaussian basis functions and discusses energy calculation methods such as the Self Consistent Field Method.
- 11.2: Gaussian Basis Sets
- This page discusses basis sets in theoretical chemistry, which are crucial for creating molecular orbitals and describing electronic states using wavefunctions from the Schrödinger equation. It highlights the variational method for optimizing ground state energy and contrasts Slater-type orbitals (STOs) with Gaussian-type orbitals (GTOs). While STOs provide accurate electron density descriptions, they are computationally complex.
- 11.3: Extended Basis Sets
- This page discusses Gaussian Type Orbitals (GTOs) and various basis sets used in quantum chemistry. It defines minimal basis sets, particularly the STO-nG type, and contrasts them with more complex double, triple, and quadruple-zeta basis sets, which enhance accuracy in electron density representation. The trade-off between accuracy and computational cost is highlighted, along with a list of extended basis set types utilized in practice.
- 11.4: Orbital Polarization Terms in Basis Sets
- This page explains Pople's basis sets that utilize polarization functions (marked by *) to enhance minimal basis sets with additional p and d functions for improved molecular charge representation. It also highlights the importance of diffuse functions (indicated by +), which accurately capture the tail of atomic orbitals, especially in anions and large molecules.
- 11.E: Computational Quantum Chemistry (Exercises)
- This page provides exercises and discussions related to Chapter 11 of "Physical Chemistry: A Molecular Approach" by McQuarrie and Simon. It covers topics such as ab initio calculations, molecular Hamiltonians, and Gaussian integrals, including detailed exercises on molecular geometry, vibrational frequencies, and atomic orbitals.