The document provides an introduction to computational chemistry methods, including ab initio, semi-empirical, and density functional theory approaches. It outlines the central theme of relating molecular structure, dynamics, and function through computational modeling. Example applications include modeling small molecules, proteins, crystals and surfaces across various scales from quantum to molecular mechanical methods. Hands-on exercises are included to provide experience with computational chemistry techniques.
This document discusses computational methods for theoretical chemistry. It describes how quantum chemical calculations can be used to simulate molecular structures, vibrational frequencies, and spectra. The main computational methods covered are molecular mechanics, semi-empirical quantum chemistry, and ab initio quantum chemistry. Molecular mechanics uses classical physics approximations while quantum chemistry methods solve the Schrodinger equation using different levels of approximation.
Computational chemistry uses computers to simulate chemical systems and solve equations that model their properties. It is considered a third pillar of scientific investigation, along with theory and experiment. There are several computational methodologies including quantum mechanics, molecular mechanics, and molecular dynamics. Computational chemistry software can be used to optimize molecular geometries, map potential energy surfaces, perform conformational analyses, and calculate many other molecular properties and reaction kinetics. These methods have improved significantly with increasing computer power over the past few decades.
Computational chemistry uses numerical simulations based on the laws of physics to model chemical structures and reactions. There are different types of computational models of varying accuracy and computational cost, including molecular mechanics, semi-empirical, ab initio, and density functional theory methods. The accuracy of calculations also depends on the basis set used to describe molecular orbitals. Computational chemistry has become an important tool for characterizing nanomaterials.
In computational physics and Quantum chemistry, the Hartree–Fock (HF) method also known as self consistent method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system or many electron system in a stationary state
Computational chemistry uses theoretical chemistry calculations incorporated into computer programs to calculate molecular structures and properties. It can calculate properties such as structure, energy, charge distribution, and spectroscopic quantities using methods that range from highly accurate ab initio methods to less accurate semi-empirical and molecular mechanics methods. Computational chemistry allows medicinal chemists to use computer power to measure molecular geometry, electron density, energies, and more for applications such as conformational analysis, docking ligands in receptor sites, and comparing ligands.
1. Hartree-Fock theory describes molecules using a linear combination of atomic orbitals to approximate molecular orbitals. It treats electrons as independent particles moving in the average field of other electrons.
2. The Hartree-Fock method involves iteratively solving the Fock equations until self-consistency is reached between the input and output orbitals. This approximates electron correlation by including an average electron-electron repulsion term.
3. The Hartree-Fock method satisfies the Pauli exclusion principle through the use of Slater determinants, which are antisymmetric wavefunctions that go to zero when the spatial or spin coordinates of any two electrons are identical.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
This document discusses computational methods for theoretical chemistry. It describes how quantum chemical calculations can be used to simulate molecular structures, vibrational frequencies, and spectra. The main computational methods covered are molecular mechanics, semi-empirical quantum chemistry, and ab initio quantum chemistry. Molecular mechanics uses classical physics approximations while quantum chemistry methods solve the Schrodinger equation using different levels of approximation.
Computational chemistry uses computers to simulate chemical systems and solve equations that model their properties. It is considered a third pillar of scientific investigation, along with theory and experiment. There are several computational methodologies including quantum mechanics, molecular mechanics, and molecular dynamics. Computational chemistry software can be used to optimize molecular geometries, map potential energy surfaces, perform conformational analyses, and calculate many other molecular properties and reaction kinetics. These methods have improved significantly with increasing computer power over the past few decades.
Computational chemistry uses numerical simulations based on the laws of physics to model chemical structures and reactions. There are different types of computational models of varying accuracy and computational cost, including molecular mechanics, semi-empirical, ab initio, and density functional theory methods. The accuracy of calculations also depends on the basis set used to describe molecular orbitals. Computational chemistry has become an important tool for characterizing nanomaterials.
In computational physics and Quantum chemistry, the Hartree–Fock (HF) method also known as self consistent method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system or many electron system in a stationary state
Computational chemistry uses theoretical chemistry calculations incorporated into computer programs to calculate molecular structures and properties. It can calculate properties such as structure, energy, charge distribution, and spectroscopic quantities using methods that range from highly accurate ab initio methods to less accurate semi-empirical and molecular mechanics methods. Computational chemistry allows medicinal chemists to use computer power to measure molecular geometry, electron density, energies, and more for applications such as conformational analysis, docking ligands in receptor sites, and comparing ligands.
1. Hartree-Fock theory describes molecules using a linear combination of atomic orbitals to approximate molecular orbitals. It treats electrons as independent particles moving in the average field of other electrons.
2. The Hartree-Fock method involves iteratively solving the Fock equations until self-consistency is reached between the input and output orbitals. This approximates electron correlation by including an average electron-electron repulsion term.
3. The Hartree-Fock method satisfies the Pauli exclusion principle through the use of Slater determinants, which are antisymmetric wavefunctions that go to zero when the spatial or spin coordinates of any two electrons are identical.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
Gaussian is a computational chemistry software package used to calculate the structures and properties of molecules. It uses quantum mechanics and density functional theory to solve chemical problems without experiments. Gaussian can optimize molecular geometries, calculate vibrational frequencies, and determine properties like infrared spectra. It provides information on molecular energies, structures, reaction pathways and more through simulation.
(This presentation is in .pptx format, and will display well when embedded improperly, such as on the SlideShare site. Please download at your discretion, and be sure to cite your source)
Review of the Hartree-Fock algorithm for the Self-Consistent Field solution of the electronic Schroedinger equation. This talk also serves to highlight some basic points in Quantum Mechanics and Computational Chemistry.
March 21st, 2012
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Gaussian is capable of performing several quantum chemical calculations including molecular energies, geometry optimization, vibrational frequencies, NMR properties, potential energy surfaces, and reaction pathways. It takes a Gaussian input file specifying the calculation type, theory, basis set, coordinates, etc. Common calculation types include single point energy, geometry optimization, and vibrational frequency. The output file provides optimized geometry, frequencies, energies, and other molecular properties.
Quantum calculations and calculational chemistrynazanin25
This document discusses computational chemistry and different methods for calculating molecular structure and properties using computers. It describes two main approaches: molecular mechanics, which views molecules as collections of atoms and calculates potential energy based on bonding parameters; and quantum mechanics, which uses the Schrodinger equation and approximations like Born-Oppenheimer and molecular orbital theory. Specific quantum methods discussed include semi-empirical, ab initio, and density functional theory. Popular computational programs and visualization software are also listed.
This document summarizes several quantum mechanics methods for calculating molecular properties, including semi-empirical, density functional theory (DFT), and correlation methods. It discusses how semi-empirical methods approximate integrals to speed up calculations compared to Hartree-Fock. DFT is described as an alternative to wavefunction methods that uses the electron density. Popular DFT functionals and how they include exchange and correlation are outlined. Geometry optimization and vibrational frequency calculations are also summarized.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
This document provides an overview of a molecular modeling course schedule and topics. The course will cover molecular properties, surfaces, electrostatics, electron microscopy, crystallography, NMR, molecular mechanics, sequence to structure relationships, visualization, molecular dynamics, ligand parameterization, and drug design. Key dates include a homework deadline of January 15th and a final exam on January 22nd. The instructor will discuss topics like classical forcefields, molecular dynamics simulations, solvation models, and hands-on exercises.
Key concepts of Geometrical Isomerism useful for the Undergraduate and Postgraduate students of Pharmacy , Chemistry and Post graduates of Pharmaceutical and Medicinal Chemistry
Basics of Quantum and Computational ChemistryGirinath Pillai
Basic fundamentals of theoretical, quantum and computational chemistry. The methods and approaches helps in predicting the electronic structure properties as well as other spectral data.
The document discusses quantum mechanics and ab initio methods. It explains that the Schrodinger equation is the basic wave equation used in quantum mechanics to describe particle behavior. Ab initio methods refer to solving the Schrodinger equation without approximations, which is the highest level of quantum mechanics. There are two approaches to ab initio - calibrated uses a fixed basis set and calibrates calculations, while converged uses improving basis sets until results converge. Ab initio is based on the self-consistent field method and Hartree-Fock approximation to calculate energies and new orbitals iteratively until self-consistency is achieved.
A ppt compiled by Yaseen Aziz Wani pursuing M.Sc Chemistry at University of Kashmir, J&K, India and Naveed Bashir Dar, a student of electrical engg. at NIT Srinagar.
Warm regards to Munnazir Bashir also for providing us with refreshing tea while we were compiling ppt.
This document discusses the Shapiro reaction, which was discovered by Robert H. Shapiro in 1967. The reaction involves converting aryl sulfonyl hydrazones of aldehydes and ketones into olefins using alkyl lithium reagents, grignard reagents, or alkali metal amides at -78°C. The reaction mechanism proceeds through deprotonation, elimination, and loss of nitrogen to form alkenyl intermediates. The Shapiro reaction has been used in the total synthesis of natural products like phytocassane D and in the formation of ring B in the Nicolaou Taxol total synthesis.
This document outlines classical molecular dynamics simulations. It discusses using force fields to model molecular interactions and integrating equations of motion to simulate molecular motion. Molecular dynamics simulations allow studying processes such as protein folding but are limited by timescale. Ensembles, thermostats, and barostats control temperature, pressure and allow sampling different conditions. The document highlights challenges in achieving longer timescales and higher accuracy simulations.
This document provides an overview of density functional theory (DFT). It discusses the history and development of DFT, including the Hohenberg-Kohn and Kohn-Sham theorems. The document outlines the fundamentals of DFT, including how it uses functionals of electron density rather than wavefunctions to simplify solving the many-body Schrodinger equation. It also describes the self-consistent approach in DFT calculations and provides examples of popular DFT software packages.
This document provides an introduction to statistical mechanics and different types of statistics. It discusses classical statistics, which includes Maxwell-Boltzmann statistics, and quantum statistics, which includes Bose-Einstein (B-E) and Fermi-Dirac (F-D) statistics. Maxwell-Boltzmann statistics treats particles as distinguishable and applies to ideal gases, while B-E and F-D statistics treat particles as indistinguishable and apply to photons/bosons and electrons/fermions, respectively. The key differences between the statistics are whether particles can occupy the same state (B-E allows multiple occupancy, F-D allows only single occupancy) and the formulas that describe the most probable distribution of particles
The Born-Oppenheimer approximation, proposed in 1927 by physicists Max Born and J. Robert Oppenheimer, treats the motions of nuclei and electrons in molecules separately. It approximates that the nuclei in a molecule are stationary relative to the rapidly moving electrons. This allows molecular structure and properties to be determined by first solving the electronic Schrodinger equation at fixed nuclear positions, and then adding the internuclear repulsion energy to obtain the total internal energy of the molecule. As a result of this approximation, molecules have well-defined shapes determined by the equilibrium positions of their nuclei.
Density functional theory (DFT) provides an alternative approach to calculate properties of molecules by working with electron density rather than wave functions. DFT relies on two theorems linking the ground state energy and electron density. Approximations must be made for the exchange-correlation functional, with popular approximations including LDA, GGA, and hybrid functionals. DFT calculations can determine properties like molecular geometries, energies, vibrational frequencies, and more using software packages. While computationally efficient, DFT has limitations such as its reliance on approximate exchange-correlation functionals.
Molecular modelling for M.Pharm according to PCI syllabusShikha Popali
THE MOLECULAR MODELLING IS THE MOST IMPORTANT TOPIC FOR CHEMISTRY STUDENTS , HENCE THE THEORY OF MOLECULAR MODELLING IS COVER IN THIS PRESNTATION . HOPE THIS MATTER SAISFY ALL AS WE HAVE TRIED TO ATTEMPT ALL TH TOPICS OF IT.
Gaussian is a computational chemistry software package used to calculate the structures and properties of molecules. It uses quantum mechanics and density functional theory to solve chemical problems without experiments. Gaussian can optimize molecular geometries, calculate vibrational frequencies, and determine properties like infrared spectra. It provides information on molecular energies, structures, reaction pathways and more through simulation.
(This presentation is in .pptx format, and will display well when embedded improperly, such as on the SlideShare site. Please download at your discretion, and be sure to cite your source)
Review of the Hartree-Fock algorithm for the Self-Consistent Field solution of the electronic Schroedinger equation. This talk also serves to highlight some basic points in Quantum Mechanics and Computational Chemistry.
March 21st, 2012
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Gaussian is capable of performing several quantum chemical calculations including molecular energies, geometry optimization, vibrational frequencies, NMR properties, potential energy surfaces, and reaction pathways. It takes a Gaussian input file specifying the calculation type, theory, basis set, coordinates, etc. Common calculation types include single point energy, geometry optimization, and vibrational frequency. The output file provides optimized geometry, frequencies, energies, and other molecular properties.
Quantum calculations and calculational chemistrynazanin25
This document discusses computational chemistry and different methods for calculating molecular structure and properties using computers. It describes two main approaches: molecular mechanics, which views molecules as collections of atoms and calculates potential energy based on bonding parameters; and quantum mechanics, which uses the Schrodinger equation and approximations like Born-Oppenheimer and molecular orbital theory. Specific quantum methods discussed include semi-empirical, ab initio, and density functional theory. Popular computational programs and visualization software are also listed.
This document summarizes several quantum mechanics methods for calculating molecular properties, including semi-empirical, density functional theory (DFT), and correlation methods. It discusses how semi-empirical methods approximate integrals to speed up calculations compared to Hartree-Fock. DFT is described as an alternative to wavefunction methods that uses the electron density. Popular DFT functionals and how they include exchange and correlation are outlined. Geometry optimization and vibrational frequency calculations are also summarized.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
This document provides an overview of a molecular modeling course schedule and topics. The course will cover molecular properties, surfaces, electrostatics, electron microscopy, crystallography, NMR, molecular mechanics, sequence to structure relationships, visualization, molecular dynamics, ligand parameterization, and drug design. Key dates include a homework deadline of January 15th and a final exam on January 22nd. The instructor will discuss topics like classical forcefields, molecular dynamics simulations, solvation models, and hands-on exercises.
Key concepts of Geometrical Isomerism useful for the Undergraduate and Postgraduate students of Pharmacy , Chemistry and Post graduates of Pharmaceutical and Medicinal Chemistry
Basics of Quantum and Computational ChemistryGirinath Pillai
Basic fundamentals of theoretical, quantum and computational chemistry. The methods and approaches helps in predicting the electronic structure properties as well as other spectral data.
The document discusses quantum mechanics and ab initio methods. It explains that the Schrodinger equation is the basic wave equation used in quantum mechanics to describe particle behavior. Ab initio methods refer to solving the Schrodinger equation without approximations, which is the highest level of quantum mechanics. There are two approaches to ab initio - calibrated uses a fixed basis set and calibrates calculations, while converged uses improving basis sets until results converge. Ab initio is based on the self-consistent field method and Hartree-Fock approximation to calculate energies and new orbitals iteratively until self-consistency is achieved.
A ppt compiled by Yaseen Aziz Wani pursuing M.Sc Chemistry at University of Kashmir, J&K, India and Naveed Bashir Dar, a student of electrical engg. at NIT Srinagar.
Warm regards to Munnazir Bashir also for providing us with refreshing tea while we were compiling ppt.
This document discusses the Shapiro reaction, which was discovered by Robert H. Shapiro in 1967. The reaction involves converting aryl sulfonyl hydrazones of aldehydes and ketones into olefins using alkyl lithium reagents, grignard reagents, or alkali metal amides at -78°C. The reaction mechanism proceeds through deprotonation, elimination, and loss of nitrogen to form alkenyl intermediates. The Shapiro reaction has been used in the total synthesis of natural products like phytocassane D and in the formation of ring B in the Nicolaou Taxol total synthesis.
This document outlines classical molecular dynamics simulations. It discusses using force fields to model molecular interactions and integrating equations of motion to simulate molecular motion. Molecular dynamics simulations allow studying processes such as protein folding but are limited by timescale. Ensembles, thermostats, and barostats control temperature, pressure and allow sampling different conditions. The document highlights challenges in achieving longer timescales and higher accuracy simulations.
This document provides an overview of density functional theory (DFT). It discusses the history and development of DFT, including the Hohenberg-Kohn and Kohn-Sham theorems. The document outlines the fundamentals of DFT, including how it uses functionals of electron density rather than wavefunctions to simplify solving the many-body Schrodinger equation. It also describes the self-consistent approach in DFT calculations and provides examples of popular DFT software packages.
This document provides an introduction to statistical mechanics and different types of statistics. It discusses classical statistics, which includes Maxwell-Boltzmann statistics, and quantum statistics, which includes Bose-Einstein (B-E) and Fermi-Dirac (F-D) statistics. Maxwell-Boltzmann statistics treats particles as distinguishable and applies to ideal gases, while B-E and F-D statistics treat particles as indistinguishable and apply to photons/bosons and electrons/fermions, respectively. The key differences between the statistics are whether particles can occupy the same state (B-E allows multiple occupancy, F-D allows only single occupancy) and the formulas that describe the most probable distribution of particles
The Born-Oppenheimer approximation, proposed in 1927 by physicists Max Born and J. Robert Oppenheimer, treats the motions of nuclei and electrons in molecules separately. It approximates that the nuclei in a molecule are stationary relative to the rapidly moving electrons. This allows molecular structure and properties to be determined by first solving the electronic Schrodinger equation at fixed nuclear positions, and then adding the internuclear repulsion energy to obtain the total internal energy of the molecule. As a result of this approximation, molecules have well-defined shapes determined by the equilibrium positions of their nuclei.
Density functional theory (DFT) provides an alternative approach to calculate properties of molecules by working with electron density rather than wave functions. DFT relies on two theorems linking the ground state energy and electron density. Approximations must be made for the exchange-correlation functional, with popular approximations including LDA, GGA, and hybrid functionals. DFT calculations can determine properties like molecular geometries, energies, vibrational frequencies, and more using software packages. While computationally efficient, DFT has limitations such as its reliance on approximate exchange-correlation functionals.
Molecular modelling for M.Pharm according to PCI syllabusShikha Popali
THE MOLECULAR MODELLING IS THE MOST IMPORTANT TOPIC FOR CHEMISTRY STUDENTS , HENCE THE THEORY OF MOLECULAR MODELLING IS COVER IN THIS PRESNTATION . HOPE THIS MATTER SAISFY ALL AS WE HAVE TRIED TO ATTEMPT ALL TH TOPICS OF IT.
The document discusses the electronic structure of atoms. It begins by explaining waves and electromagnetic radiation, and how Max Planck and Albert Einstein showed that energy is quantized and proportional to frequency. Niels Bohr then used this idea to explain atomic spectra and proposed that electrons can only occupy certain orbits corresponding to discrete energy levels. Later, developments in quantum mechanics by de Broglie, Heisenberg, Schrodinger and others led to the current quantum mechanical model of the atom. Electrons are described by four quantum numbers and occupy distinct electron configurations according to Hund's rule and the Pauli exclusion principle.
The document discusses the electronic structure of atoms. It begins by explaining waves and electromagnetic radiation, and how Max Planck and Albert Einstein showed that energy is quantized and proportional to frequency. Niels Bohr then used this idea to explain atomic spectra and proposed that electrons can only occupy certain orbits within atoms. Later, developments in quantum mechanics by scientists such as Louis de Broglie, Werner Heisenberg, and Erwin Schrodinger established that electrons behave as waves and have discrete energy levels defined by quantum numbers. Electron configurations describe the distribution of electrons in orbitals according to these quantum numbers.
1. The document discusses the electronic structure of atoms, describing how quantum mechanics explains the discrete energy levels and emission spectra of electrons in atoms.
2. It introduces the key concepts of quantum mechanics including quantization of energy, wave-particle duality of matter, and Schrodinger's wave equation.
3. The four quantum numbers (n, l, ml, ms) are described which specify the possible states of electrons in atoms, such as their orbital type and orientation.
General Theory of electronic configuration of atomsIOSR Journals
The “General Theory of electronic configuration of atoms” is an original study introduced by the author in chemistry in 2004. In this paper, the author developed a new method to write the electronic configuration for any atom, regardless of whether it actually exists or not in nature. This new method is based on Quantum theory and on three new and original formulae introduced and developed by the author. This method can be used to gather information about any atom’s properties: its period, its group, its peripheral number of electrons and its theoretical electronic peripheral configuration. The main advantage of this method is that one can immediately knows the information about an atom, by a simple hand calculation without the need of software. Even if the atomic number is huge (as Z=123453). This method can be used in general chemistry courses and it is an extremely efficient method used for teaching and in the exam.
So any atomic number can be developed and we can find its electronic configuration regardless of whether it actually exists or not in nature.
-The traditional method of writing an electronic configuration is like this
⏞ ⏞ ⏞ ⏞ ⏞ ⏞ Until finding the peripheral electronic configuration.
So the new method developed in this paper is mainly works on the peripheral electronic configuration without passing through the traditional method. It gives us directly the peripheral electronic configuration, for example ⏞ .
In this way we have eliminated a very long process of calculation. This is a big advantage for the proposed method ahead the traditional one.
The main goal of introducing this paper is to reduce the calculation of obtaining the main information about an atom for example its period, group, number of electrons in the peripheral configuration and finding its peripheral electronic configuration as fast as possible even if the atom doesn’t exist in reality. This paper doesn’t explain the relativistic effects, because it is not the main goal of the proposed theory. We can still obtain the information about any atom without considering the relativistic effects.
Transmission electron microscopy (TEM) is a technique that uses electrons to image ultrastructures of cells. TEM provides higher resolution than light microscopes due to electrons having much shorter wavelengths than visible light. In TEM, electrons are accelerated through an electromagnetic lens system and interact with a thin sample. Elastic scattering of electrons forms the image, which is magnified and detected on a screen. TEM allows visualization of sub-cellular structures down to single atom columns and is widely used in materials science and cell biology.
This document provides an introduction to computational quantum chemistry. It defines computational chemistry as using mathematical approximations and computer programs to solve chemical problems based on quantum mechanics. Specifically, computational quantum chemistry focuses on solving the Schrödinger equation for molecular systems using approximations like the Born-Oppenheimer approximation. It discusses how computational methods can be used to calculate various molecular properties and motivates the need for approximations due to the inability to exactly solve the Schrödinger equation for complex molecules. The document then provides an overview of common computational methods like Hartree-Fock, configuration interaction, Møller-Plesset perturbation theory, and coupled cluster theory.
This document provides an introduction to computational quantum chemistry. It defines computational chemistry as using mathematical approximations and computer programs to solve chemical problems based on quantum mechanics. Specifically, computational quantum chemistry focuses on solving the Schrödinger equation for molecular systems using approximations like the Born-Oppenheimer approximation. It also discusses methods for approximating the wavefunction like Hartree-Fock, configuration interaction, and density functional theory as well as expanding the molecular orbitals in a basis set of atomic orbitals.
Computational Chemistry aspects of Molecular Mechanics and Dynamics have been discussed in this presentation. Useful for the Undergraduate and Postgraduate students of Pharmacy, Drug Design and Computational Chemistry
Advantages and applications of computational chemistrymanikanthaTumarada
The document discusses computational chemistry methods for calculating various thermodynamic and electronic properties of molecules. It provides an overview of computational chemistry and the properties that can be calculated, such as structure, energy, dipole moment, polarizability, ionization potential, HOMO/LUMO energies, chemical hardness and softness. It also describes different computational methods like classical molecular mechanics and molecular dynamics, as well as quantum chemistry methods including semi-empirical, ab initio and density functional theory approaches. Specific examples are given of calculating properties like dipole moment, polarizability, ionization potential using computational methods.
The document provides an overview of the Network Theory syllabus for the 2020-21 academic year. It discusses the course details including credits, contact hours, assessments, pre-requisites and outcomes. The syllabus covers topics such as basic circuit concepts, network theorems, resonant circuits, transient behavior, Laplace transforms, and two-port networks. It also introduces some basic concepts of network theory including different electrical elements, circuit analysis techniques, and passive elements like resistors, capacitors, and inductors.
This document describes simulations of the Raman-Brillouin electronic density (RBED) for semiconductor thin films and superlattices. It introduces the RBED as an effective electronic density that describes resonant light scattering, even when many electronic states are involved. For isolated silicon layers, it uses the envelope function approximation to calculate electronic states and the RBED. It also describes using a tight-binding model as an alternative to obtain more realistic band structures. The RBED is then used to simulate Raman-Brillouin spectra and compare to experiments on silicon membranes.
The document discusses ab initio molecular dynamics simulation methods. It begins by introducing molecular dynamics and Monte Carlo simulations using empirical potentials. It then describes limitations of empirical potentials and the need for ab initio molecular dynamics which calculates the potential from quantum mechanics. The document outlines several ab initio molecular dynamics methods including Ehrenfest molecular dynamics, Born-Oppenheimer molecular dynamics, and Car-Parrinello molecular dynamics. It provides details on how these methods treat the quantum mechanical potential and classical nuclear motion.
This document provides information on the course "Digital System Design" including its objectives, modules, and outcomes. The key points are:
- The course covers topics like combinational logic design using K-maps and Quine McClusky, design of decoders, multiplexers, adders, and sequential circuits using latches and flip-flops.
- The modules include combinational logic analysis, design of combinational components, flip-flops and applications, sequential circuit design using Mealy and Moore models, and applications of digital circuits.
- The course aims to enable students to design various digital components, analyze sequential circuits, and appreciate applications of digital systems. Upon completion, students will be able to
This document provides an overview of 2D NMR spectroscopy techniques. It begins with an introduction to 2D NMR basics, including how 2D NMR experiments accumulate multiple 1D spectra with an incremental change in variable to allow Fourier transforms in two dimensions. It then discusses various specific 2D NMR experiments including COSY for proton-proton correlations, HETCOR for heteronuclear through-bond correlations, HSQC for 1-bond heteronuclear correlations, and HMBC for longer range multiple-bond heteronuclear correlations. Examples of these techniques applied to specific molecules are also presented.
The document provides an introduction to computational quantum chemistry, including:
- Definitions of computational chemistry and computational quantum chemistry, which focuses on solving the Schrodinger equation for molecules.
- An overview of methods like ab initio quantum chemistry, density functional theory, and approximations like the Born-Oppenheimer approximation and basis set approximations.
- Descriptions of approaches like Hartree-Fock, configuration interaction, Møller-Plesset perturbation theory, and coupled cluster theory for including electron correlation effects.
This document provides an outline for a talk on electronic and thermal properties of semiconductor nanostructures from atomistic modeling and simulation. It motivates the importance of integrated atomistic simulation to study next-generation devices facing CMOS scaling challenges. It describes using an atomistic tight-binding approach and charge-potential self-consistent solution to model silicon nanowire field effect transistors, validated against experimental devices. The talk aims to discuss applications to silicon and gallium arsenide nanostructures and disseminating findings through nanohub.org.
The document summarizes X-ray diffraction (XRD) techniques. XRD relies on the scattering of X-rays from the regular atomic structure of crystalline materials to produce a diffraction pattern that can identify materials and measure lattice parameters. Bragg's law relates the diffraction pattern peak positions to the atomic spacing. XRD equipment consists of an X-ray source, sample holder, and detector that measures diffraction as the sample or detector is rotated. Indexing assigns Miller indices to peaks to determine the unit cell. Lattice parameters are then calculated from peak positions and Bragg's law.
This presentation discusses Contoso's goals for the next quarter, including synergizing scalable e-commerce, disseminating standardized metrics, coordinating e-business applications, and deploying strategic networks. The presentation outlines Contoso's areas of growth in B2B supply chain, ROI, and e-commerce. It then provides a timeline for the product launch plan and areas of focus on B2B market scenarios and cloud-based opportunities.
This PowerPoint presentation covers various topics and includes an agenda, introduction, topic one with a chart and table, quotes, a team page, timeline, tips on using PowerPoint, and a concluding thank you slide. The presentation teaches how to create and share presentations using PowerPoint across devices by adding text, images, videos and saving to OneDrive for access on a computer, tablet or phone.
The document contains an agenda for a presentation with topics on charts and tables showing various data, quotes on getting started, and sections on the team, timeline, and how to use presentation features in PowerPoint like starting the slide show, presenter view, notes pane, and navigating between slides. It concludes with a summary and thank you.
Wind power has been used for centuries to grind grain and pump water, and modern utility-scale wind farms convert wind energy into electricity via wind turbines grouped together over wide areas. The document outlines the history of wind power and discusses topics such as wind energy, wind farms, wind power capacity and production levels globally, the economics of wind power including small-scale applications, environmental effects, political factors, and turbine design innovations.
The document is a presentation by Mirjam Nilsson at Contoso. It outlines the company's goals of annual revenue growth and improving performance in key areas like supply chain and e-commerce. It introduces the executive team and extended team. The presentation details plans for a new product launch, including timelines for planning, marketing, design, and launch. It focuses on developing strategies for B2B markets and cloud-based opportunities to drive growth.
The document outlines a travel timeline over 4 weeks, visiting North, Utah, Arizona, and California. It details activities like going to a sushi restaurant, pizza place, farmers market, and enjoying macaroons. The timeline shows plans for each day of the week, from Sunday to Friday, with various to-do items and locations mentioned.
The document outlines a travel timeline over 4 weeks, visiting North, Utah, Arizona, and California. It details activities like going to a sushi restaurant, pizza place, farmers market, and enjoying macaroons. The timeline shows plans for each day of the week, from Sunday to Friday, with various to-do items and locations mentioned.
This document contains a presentation template with slides on various topics including an agenda, chart, table, quote, team, timeline, content, and summary. The presentation discusses how to create and share presentations using PowerPoint, add various elements like text, images, and videos, and access presentations from different devices by saving to OneDrive.
Biosensors convert a biochemical recognition event into a measurable signal and consist of a biological probe and physical detector. There are several types including enzyme-based, immunosensors, and piezoelectric biosensors. Lab-on-chip technology integrates laboratory functions onto a small chip and contains microchannels to flow liquid samples along with integrated measuring components. Examples of lab-on-chip applications described are ones that can detect Ebola virus from a blood sample in 30 minutes and detect HIV using CD4+ cell numbers and magnetophoresis from 10 microliters of whole blood in 20 minutes. Organ-on-chip technology aims to mimic organ behaviors for medical research purposes.
Chloramphenicol was the first antibiotic to be manufactured synthetically for clinical use. It inhibits bacterial protein synthesis by binding to the 50S ribosomal subunit. While broad-spectrum, it carries risks of bone marrow toxicity in humans. Safer derivatives like thiamphenicol and florfenicol were later developed.
Chloramphenicol is a broad-spectrum antibiotic that inhibits bacterial protein synthesis. It binds reversibly to the 50S subunit of bacterial ribosomes, blocking the formation of peptide bonds between amino acids. While effective against many gram-positive and gram-negative bacteria, its use is now reserved for life-threatening infections due to risks of bone marrow suppression and gray baby syndrome in neonates. Proper dosing and alternative antibiotics are preferred whenever possible due to these toxicities.
This document discusses doxycycline, a broad-spectrum antibiotic derived from tetracycline. It inhibits protein synthesis by reversibly binding to the 30S subunit of bacteria to block aminoacyl-tRNA binding. It has activity against many gram-positive and gram-negative bacteria. Doxycycline is used to treat infections caused by Mycoplasma pneumoniae, Rickettsiae, Chlamydia, Vibrio cholerae, Bacillus anthracis, and spirochetes. Adverse effects include gastrointestinal issues, tooth discoloration in children, and photosensitization. It is contraindicated in pregnancy, infants, and those with hypersensitivity.
This document provides an outline for a chemistry lecture covering several topics:
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The document discusses key concepts in chemistry including the scientific method, atomic theory, and the classification of matter. It explains that chemistry uses the scientific method to study matter and its transformations. Matter is anything that has mass and takes up space, and can be classified as elements, compounds, or mixtures. Elements are substances made of only one type of atom, while compounds are made of two or more elements chemically bonded together. Mixtures can be either homogeneous, with consistent properties throughout, or heterogeneous, having distinct parts with different properties. Chemical and physical changes that matter undergoes are also described.
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2. its.unc.edu 2
Outline
Introduction
Methods in Computational Chemistry
•Ab Initio
•Semi-Empirical
•Density Functional Theory
•New Developments (QM/MM)
Hands-on Exercises
The PPT format of this presentation is available here:
http://its2.unc.edu/divisions/rc/training/scientific/
/afs/isis/depts/its/public_html/divisions/rc/training/scientific/short_courses/
3. its.unc.edu 3
About Us
ITS – Information Technology Services
• http://its.unc.edu
• http://help.unc.edu
• Physical locations:
401 West Franklin St.
211 Manning Drive
• 10 Divisions/Departments
Information Security IT Infrastructure and Operations
Research Computing Center Teaching and Learning
User Support and Engagement Office of the CIO
Communication Technologies Communications
Enterprise Applications Finance and Administration
4. its.unc.edu 4
Research Computing
Where and who are we and what do we do?
• ITS Manning: 211 Manning Drive
• Website
http://its.unc.edu/research-computing.html
• Groups
Infrastructure -- Hardware
User Support -- Software
Engagement -- Collaboration
5. its.unc.edu 5
About Myself
Ph.D. from Chemistry, UNC-CH
Currently Senior Computational Scientist @ Research Computing Center, UNC-CH
Responsibilities:
• Support Computational Chemistry/Physics/Material Science software
• Support Programming (FORTRAN/C/C++) tools, code porting, parallel computing, etc.
• Offer short courses on scientific computing and computational chemistry
• Conduct research and engagement projects in Computational Chemistry
Development of DFT theory and concept tools
Applications in biological and material science systems
6. its.unc.edu 6
About You
Name, department, research interest?
Any experience before with high
performance computing?
Any experience before with
computational chemistry research?
Do you have any real problem to solve
with computational chemistry
approaches?
7. its.unc.edu 7
Think BIG!!!
What is not chemistry?
• From microscopic world, to nanotechnology, to daily life, to
environmental problems
• From life science, to human disease, to drug design
• Only our mind limits its boundary
What cannot computational chemistry deal with?
• From small molecules, to DNA/proteins, 3D crystals and
surfaces
• From species in vacuum, to those in solvent at room
temperature, and to those under extreme conditions (high
T/p)
• From structure, to properties, to spectra (UV, IR/Raman,
NMR, VCD), to dynamics, to reactivity
• All experiments done in labs can be done in silico
• Limited only by (super)computers not big/fast enough!
8. its.unc.edu 8
Central Theme of
Computational Chemistry
DYNAMICS
REACTIVITY
STRUCTURE CENTRAL DOGMA OF MOLECULAR BIOLOGY
SEQUENCE
STRUCTURE
DYNAMICS
FUNCTION
EVALUTION
10. its.unc.edu 10
What is Computational
Chemistry?
Application of computational methods and
algorithms in chemistry
• Quantum Mechanical
i.e., via Schrödinger Equation
also called Quantum Chemistry
• Molecular Mechanical
i.e., via Newton’s law F=ma
also Molecular Dynamics
• Empirical/Statistical
e.g., QSAR, etc., widely used in clinical and medicinal
chemistry
Focus Today
H
t
i ˆ
11. its.unc.edu 11
How Big Systems Can We
Deal with?
Assuming typical computing setup (number of CPUs,
memory, disk space, etc.)
Ab initio method: ~100 atoms
DFT method: ~1000 atoms
Semi-empirical method: ~10,000 atoms
MM/MD: ~100,000 atoms
12. its.unc.edu 12
i
j
n
1
i ij
n
1
i
N
1 i
2
i
2
r
1
r
Z
-
2m
h
-
H
n
i
j
n
1
i ij
n
1
i r
1
i
h
H
Starting Point: Time-Independent
Schrodinger Equation
E
H
H
t
i ˆ
13. its.unc.edu 13
Equation to Solve in
ab initio Theory
E
H
Known exactly:
3N spatial variables
(N # of electrons)
To be approximated:
1. variationally
2. perturbationally
14. its.unc.edu 14
Hamiltonian for a Molecule
kinetic energy of the electrons
kinetic energy of the nuclei
electrostatic interaction between the electrons and
the nuclei
electrostatic interaction between the electrons
electrostatic interaction between the nuclei
nuclei
B
A AB
B
A
electrons
j
i ij
nuclei
A iA
A
electrons
i
A
nuclei
A A
i
electrons
i e
R
Z
Z
e
r
e
r
Z
e
m
m
2
2
2
2
2
2
2
2
2
ˆ
H
15. its.unc.edu 15
Ab Initio Methods
Accurate treatment of the electronic distribution using the
full Schrödinger equation
Can be systematically improved to obtain chemical accuracy
Does not need to be parameterized or calibrated with
respect to experiment
Can describe structure, properties, energetics and reactivity
What does “ab intio” mean?
• Start from beginning, with first principle
Who invented the word of the “ab initio” method?
• Bob Parr of UNC-CH in 1950s; See Int. J. Quantum Chem.
37(4), 327(1990) for details.
16. its.unc.edu 16
Three Approximations
Born-Oppenheimer approximation
• Electrons act separately of nuclei, electron and
nuclear coordinates are independent of each other,
and thus simplifying the Schrödinger equation
Independent particle approximation
• Electrons experience the ‘field’ of all other
electrons as a group, not individually
• Give birth to the concept of “orbital”, e.g., AO,
MO, etc.
LCAO-MO approximation
• Molecular orbitals (MO) can be constructed as linear
combinations of atom orbitals, to form Slater
determinants
17. its.unc.edu 17
Born-Oppenheimer
Approximation
the nuclei are much heavier than the electrons and move more
slowly than the electrons
freeze the nuclear positions (nuclear kinetic energy is zero in the
electronic Hamiltonian)
calculate the electronic wave function and energy
E depends on the nuclear positions through the nuclear-electron
attraction and nuclear-nuclear repulsion terms
E = 0 corresponds to all particles at infinite separation
nuclei
B
A AB
B
A
electrons
j
i ij
nuclei
A iA
A
electrons
i
i
electrons
i e
el
r
Z
Z
e
r
e
r
Z
e
m
2
2
2
2
2
2
ˆ
H
d
d
E
E
el
el
el
el
el
el
el
el *
* ˆ
,
ˆ
H
H
18. its.unc.edu 18
Approximate Wavefunctions
Construction of one-electron functions (molecular orbitals,
MO’s) as linear combinations of one-electron atomic basis
functions (AOs) MO-LCAO approach.
Construction of N-electron wavefunction as linear
combination of anti-symmetrized products of MOs (these
anti-symmetrized products are denoted as Slater-
determinants).
down)
-
(spin
up)
-
(spin
;
1
i
i
u i
k
N
k
kl
i
l r
q
19. its.unc.edu 19
The Slater Determinant
z
c
b
a
z
c
b
a
z
z
z
z
c
c
c
c
b
b
b
b
a
a
a
a
n
z
c
b
a
z
c
b
a
n
z
c
b
a
n
n
n
n
n
n
n
n
3
2
1
3
2
1
3
2
1
3
2
1
3
2
1
3
1
2
3
2
1
3
2
1
Α̂
!
1
!
1
20. its.unc.edu 20
The Two Extreme Cases
One determinant: The Hartree–Fock method.
All possible determinants: The full CI method.
N
N
3
2
1 3
2
1
HF
There are N MOs and each MO is a linear combination of N AOs.
Thus, there are nN coefficients ukl, which are determined by
making stationary the functional:
The ij are Lagrangian multipliers.
N
l
k
ij
lj
kl
ki
N
j
i
ij u
S
u
H
E
1
,
*
1
,
HF
HF
HF
ˆ
21. its.unc.edu 21
The Full CI Method
The full configuration interaction (full CI) method
expands the wavefunction in terms of all possible Slater
determinants:
There are possible ways to choose n molecular
orbitals from a set of 2N AO basis functions.
The number of determinants gets easily much too large.
For example:
n
N
2
1
ˆ
;
2
1
,
CI
CI
CI
2
1
CI
c
S
c
H
E
c
n
N
*
n
N
9
10
10
40
Davidson’s method can be used to find one
or a few eigenvalues of a matrix of rank 109.
22. its.unc.edu 22
N
N
3
2
1 3
2
1
HF
N
l
k
ij
lj
kl
ki
N
j
i
ij u
S
u
H
E
1
,
*
1
,
HF
HF
HF
ˆ
N
i
li
ki
kl
N
l
k
kl
mn
N
n
m
mn u
u
P
nl
mk
P
h
P
E
H
1
*
1
,
2
1
1
,
nuc
HF
HF ;
ˆ
0
HF
E
uki
Hartree–Fock equations
The Hartree–Fock Method
23. its.unc.edu 23
|
S
Overlap integral
|
2
1
|
P
H
F
i
i
occ
i
c
c
2
P
Density Matrix
S
F
i
i
i c
c
The Hartree–Fock Method
24. its.unc.edu 24
1. Choose start coefficients for MO’s
2. Construct Fock Matrix with coefficients
3. Solve Hartree-Fock-Roothaan equations
4. Repeat 2 and 3 until ingoing and outgoing
coefficients are the same
Self-Consistent-Field (SCF)
S
F
i
i
i c
c
25. its.unc.edu 25
Semi-empirical methods
(MNDO, AM1, PM3, etc.)
Full CI
perturbational hierarchy
(CASPT2, CASPT3)
perturbational hierarchy
(MP2, MP3, MP4, …)
excitation hierarchy
(MR-CISD)
excitation hierarchy
(CIS,CISD,CISDT,...)
(CCS, CCSD, CCSDT,...)
Multiconfigurational HF
(MCSCF, CASSCF)
Hartree-Fock
(HF-SCF)
Ab Initio Methods
27. its.unc.edu 27
Size vs Accuracy
Number of atoms
0.1
1
10
1 10 100 1000
Accuracy
(kcal/mol)
Coupled-cluster,
Multireference
Nonlocal density functional,
Perturbation theory
Local density functional,
Hartree-Fock
Semiempirical Methods
Full CI
28. its.unc.edu 28
ROO,e= 291.2 pm
96.4 pm
95.7 pm 95.8 pm
symmetry: Cs
Equilibrium structure of (H2O)2
W.K., J.G.C.M. van Duijneveldt-van de Rijdt, and
F.B. van Duijneveldt, Phys. Chem. Chem. Phys. 2, 2227 (2000).
Experimental [J.A. Odutola and T.R. Dyke, J. Chem. Phys 72, 5062 (1980)]:
ROO
2 ½ = 297.6 ± 0.4 pm
SAPT-5s potential [E.M. Mas et al., J. Chem. Phys. 113, 6687 (2000)]:
ROO
2 ½ – ROO,e= 6.3 pm ROO,e(exptl.) = 291.3 pm
AN EXAMPLE
30. its.unc.edu 30
LCAO Basis Functions
’s, which are atomic orbitals, are called basis
functions
usually centered on atoms
can be more general and more flexible than atomic
orbital functions
larger number of well chosen basis functions yields
more accurate approximations to the molecular
orbitals
c
31. its.unc.edu 31
Basis Functions
Slaters (STO)
Gaussians (GTO)
Angular part *
Better behaved than Gaussians
2-electron integrals hard
2-electron integrals simpler
Wrong behavior at nucleus
Decrease too fast with r
r)
exp(
2
n
m
l
r
exp
*
z
y
x
32. its.unc.edu 32
Contracted Gaussian Basis Set
Minimal
STO-nG
Split Valence: 3-
21G,4-31G, 6-
31G
• Each atom optimized STO is fit with n
GTO’s
• Minimum number of AO’s needed
• Contracted GTO’s optimized per atom
• Doubling of the number of valence AO’s
33. its.unc.edu 33
Polarization /
Diffuse Functions
Polarization: Add AO with higher angular
momentum (L) to give more flexibility
Example: 3-21G*, 6-31G*, 6-31G**, etc.
Diffusion: Add AO with very small exponents for
systems with very diffuse electron densities
such as anions or excited states
Example: 6-31+G*, 6-311++G**
34. its.unc.edu 34
Correlation-Consistent
Basis Functions
a family of basis sets of increasing size
can be used to extrapolate to the basis set limit
cc-pVDZ – DZ with d’s on heavy atoms, p’s on H
cc-pVTZ – triple split valence, with 2 sets of d’s
and one set of f’s on heavy atoms, 2 sets of p’s
and 1 set of d’s on hydrogen
cc-pVQZ, cc-pV5Z, cc-pV6Z
can also be augmented with diffuse functions
(aug-cc-pVXZ)
35. its.unc.edu 35
Pseudopotentials,
Effective Core Potentials
core orbitals do not change much during chemical
interactions
valence orbitals feel the electrostatic potential of the
nuclei and of the core electrons
can construct a pseudopotential to replace the
electrostatic potential of the nuclei and of the core
electrons
reduces the size of the basis set needed to represent the
atom (but introduces additional approximations)
for heavy elements, pseudopotentials can also include of
relativistic effects that otherwise would be costly to treat
36. its.unc.edu 36
Correlation Energy
HF does not include correlations anti-parallel electrons
Eexact – EHF = Ecorrelation
Post HF Methods:
• Configuration Interaction (CI, MCSCF, CCSD)
• Møller-Plesset Perturbation series (MP2, MP4)
Density Functional Theory (DFT)
37. its.unc.edu 37
Configuration-Interaction (CI)
In Hartree-Fock theory, the n-electron wavefunction is approximated by one
single Slater-determinant, denoted as:
This determinant is built from n orthonormal spin-orbitals. The spin-orbitals that
form are said to be occupied. The other orthonormal spin-orbitals that
follow from the Hartree-Fock calculation in a given one-electron basis set of
atomic orbitals (AOs) are known as virtual orbitals. For simplicity, we assume that
all spin-orbitals are real.
In electron-correlation or post-Hartree-Fock methods, the wavefunction is
expanded in a many-electron basis set that consists of many determinants.
Sometimes, we only use a few determinants, and sometimes, we use millions of
them:
In this notation, is a Slater-
determinant that is obtained by
replacing a certain number of
occupied orbitals by virtual ones.
Three questions: 1. Which determinants should we include?
2. How do we determine the expansion coefficients?
3. How do we evaluate the energy (or other properties)?
HF
HF
c
HF
CI
38. its.unc.edu 38
Truncated configuration interaction:
CIS, CISD, CISDT, etc.
We start with a reference wavefunction, for example the Hartree-
Fock determinant.
We then select determinants for the wavefunction expansion by
substituting orbitals of the reference determinant by orbitals that
are not occupied in the reference state (virtual orbitals).
Singles (S) indicate that 1 orbital is replaced, doubles (D) indicate
2 replacements, triples (T) indicate 3 replacements, etc., leading
to CIS, CISD, CISDT, etc.
N
N
k
j
i
3
2
1
HF
etc.
,
3
2
1
,
3
2
1 N
N N
k
b
a
ab
ij
N
k
j
a
a
i
39. its.unc.edu 39
Truncated
Configuration Interaction
Level of
excitation
Number of
parameters
Example
CIS n (2N – n) 300
CISD … + [n (2N – n)] 2
78,600
CISDT …+ [n (2N – n)] 3
18106
… … …
Full CI
n
N
2
109
Number of linear variational parameters
in truncated CI for n = 10 and 2N = 40.
40. its.unc.edu 40
Multi-Configuration
Self-Consistent Field (MCSCF)
The MCSCF wavefunctions consists of a few selected determinants or CSFs. In the
MCSCF method, not only the linear weights of the determinants are variationally
optimized, but also the orbital coefficients.
One important selection is governed by the full CI space spanned by a number of
prescribed active orbitals (complete active space, CAS). This is the CASSCF method.
The CASSCF wavefunction contains all determinants that can be constructed from a
given set of orbitals with the constraint that some specified pairs of - and -spin-
orbitals must occur in all determinants (these are the inactive doubly occupied
spatial orbitals).
Multireference CI wavefunctions are obtained by applying the excitation operators to
the individual CSFs or determinants of the MCSCF (or CASSCF) reference wave
function.
k
C
C
c
k
k
k
k )
ˆ
ˆ
(
CISD
-
MR 2
1
k
k
k
k
k k
d
C
k
C
c 2
1
ˆ
)
ˆ
(
MRCI
-
IC
Internally-contracted MRCI:
41. its.unc.edu 41
Coupled-Cluster Theory
System of equations is solved iteratively (the convergence is
accelerated by utilizing Pulay’s method, “direct inversion in
the iterative subspace”, DIIS).
CCSDT model is very expensive in terms of computer
resources. Approximations are introduced for the triples:
CCSD(T), CCSD[T], CCSD-T.
Brueckner coupled-cluster (e.g., BCCD) methods use
Brueckner orbitals that are optimized such that singles don’t
contribute.
By omitting some of the CCSD terms, the quadratic CI method
(e.g., QCISD) is obtained.
42. its.unc.edu 42
Møller-Plesset
Perturbation Theory
The Hartree-Fock function is an eigenfunction of the
n-electron operator .
We apply perturbation theory as usual after decomposing the
Hamiltonian into two parts:
More complicated with more than one reference determinant
(e.g., MR-PT, CASPT2, CASPT3, …)
F̂
F
H
H
F
H
H
H
H
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1
0
1
0
MP2, MP3, MP4, …etc.
number denotes order to which
energy is computed (2n+1 rule)
43. its.unc.edu 43
Semi-Empirical Methods
These methods are derived from the Hartee–Fock model, that is,
they are MO-LCAO methods.
They only consider the valence electrons.
A minimal basis set is used for the valence shell.
Integrals are restricted to one- and two-center integrals and
subsequently parametrized by adjusting the computed results to
experimental data.
Very efficient computational tools, which can yield fast
quantitative estimates for a number of properties. Can be used
for establishing trends in classes of related molecules, and for
scanning a computational poblem before proceeding with high-
level treatments.
A not of elements, especially transition metals, have not be
parametrized
44. its.unc.edu 44
Semi-Empirical Methods
Number 2-electron integrals (|) is n4/8, n = number of basis
functions
Treat only valence electrons explicit
Neglect large number of 2-electron integrals
Replace others by empirical parameters
Models:
• Complete Neglect of Differential Overlap (CNDO)
• Intermediate Neglect of Differential Overlap (INDO/MINDO)
• Neglect of Diatomic Differential Overlap (NDDO/MNDO, AM1, PM3)
45. its.unc.edu 45
A
B
AB
V
U
H
U from atomic spectra
VAB value per atom pair
0
H
, on the same atom
S
H AB
B
A
AB 2
1
One parameter per element
Approximations of 1-e
integrals
46. its.unc.edu 46
Popular DFT
Noble prize in Chemistry, 1998
In 1999, 3 of top 5 most cited
journal articles in chemistry (1st,
2nd, & 4th)
In 2000-2003, top 3 most cited
journal articles in chemistry
In 2004-2005, 4 of top 5 most
cited journal articles in chemistry:
• 1st, Becke’s hybrid exchange
functional (1993)
• 2nd, LYP correlation functional
(1988)
• 3rd, Becke’s exchange
functional (1988)
• 4th, PBE correlation functional
(1996)
http://www.cas.org/spotlight/bchem.html
Citations of DFT on JCP, JACS and PRL
47. its.unc.edu 47
Brief History of DFT
First speculated 1920’
•Thomas-Fermi (kinetic energy) and Dirac
(exchange energy) formulas
Officially born in 1964 with Hohenberg-
Kohn’s original proof
GEA/GGA formulas available later 1980’
Becoming popular later 1990’
Pinnacled in 1998 with a chemistry Nobel
prize
48. its.unc.edu 48
What could expect from DFT?
LDA, ~20 kcal/mol error in energy
GGA, ~3-5 kcal/mol error in energy
G2/G3 level, some systems, ~1kcal/mol
Good at structure, spectra, & other
properties predictions
Poor in H-containing systems, TS, spin,
excited states, etc.
49. its.unc.edu 49
Density Functional Theory
Two Hohenberg-Kohn theorems:
•“Given the external potential, we know the
ground-state energy of the molecule when
we know the electron density ”.
•The energy density functional is variational.
E
Ĥ
Energy
50. its.unc.edu 50
But what is E[]?
How do we compute the energy if the density is
known?
The Coulombic interactions are easy to compute:
But what about the kinetic energy TS[] and exchange-
correlation energy Exc[]?
,
]
[
,
]
[
,
]
[ 2
1
ext
ne
nn r
r
r
r
r
r
r
r
r
d
d
J
d
V
E
r
Z
Z
E
nuclei
B
A AB
B
A
E[] = TS[] + Vne[] + J[] + Vnn[] + Exc[]
52. its.unc.edu 52
All about Exchange-Correlation
Energy Density Functional
LDA – f(r) is a function of
(r) only
GGA – f(r) is a function of
(r) and |∇(r)|
Mega-GGA – f(r) is also a
function of ts(r), kinetic
energy density
Hybrid – f(r) is GGA
functional with extra
contribution from Hartree-
Fock exchange energy
r
r
r
r d
f
QXC
,
,
, 2
Jacob's ladder for the five generation of DFT functionals,
according to the vision of John Perdew with indication of
some of the most common DFT functionals within each rung.
53. its.unc.edu 53
LDA Functionals
Thomas-Fermi formula (Kinetic) – 1
parameter
Slater form (exchange) – 1 parameter
Wigner correlation – 2 parameters
3
/
2
2
3
/
5
3
10
3
,
F
F
TF C
d
C
T r
r
3
/
1
3
/
2
3
/
1
3
/
4
4
3
8
3
,
X
X
S
X C
d
C
E r
r
r
r
r
d
b
a
EW
C 3
/
1
1
54. its.unc.edu 54
Popular Functional: BLYP/B3LYP
Two most well-known functionals are the Becke exchange functional
Ex[] with 2 extra parameters &
The Lee-Yang-Parr correlation functional Ec[] with 4 parameters a-d
Together, they constitute the BLYP functional:
The B3LYP functional is augmented with 20% of Hartree-Fock
exchange:
r
r
r
r d
e
d
e
E
E
E c
x
c
x
xc
,
, LYP
B
LYP
B
BLYP
3
/
4
2
2
2
3
/
4
,
1
LDA
X
B
X E
E
r
d
e
t
t
C
b
d
a
E c
W
W
F
LYP
c
3
/
1
2
3
/
5
3
/
2
3
/
1
18
1
9
1
2
1
1
nl
km
P
P
b
E
E
a
E
N
l
k
kl
N
n
m
mn
c
x
xc
1
,
1
,
LYP
B
B3LYP
55. its.unc.edu 55
Density Functionals
LDA
local density
GGA
gradient corrected
Meta-GGA
kinetic energy density
included
Hybrid
“exact” HF exchange
component
Hybrid-meta-GGA
VWN5
BLYP
HCTH
BP86
TPSS
M06-L
B3LYP
B97/2
MPW1K
MPWB1K
M06
Better scaling with system
size
Allow density fitting for even
better scaling
Meta-GGA is “bleeding
edge” and therefore largely
untested (but better in
theory…)
Hybrid makes bigger
difference in cost and
accuracy
Look at literature if
somebody
has compared functionals
for
systems similar to yours!
Increasing
quality
and
computational
cost
56. its.unc.edu 56
Percentage of occurrences of the names of the several functionals indicated in Table 2, in
journal titles and abstracts, analyzed from the ISI Web of Science (2007).
S.F. Sousa, P.A. Fernandes and M.J. Ramos, J. Phys. Chem. A 10.1021/jp0734474 S1089-5639(07)03447-0
Density Functionals
57. its.unc.edu 57
Problems with DFT
ground-state theory only
universal functional still unknown
even hydrogen atom a problem: self-interaction
correction
no systematic way to improve approximations
like LDA, GGA, etc.
extension to excited states, spin multiplets,
etc., though proven exact in theory, is not
trivial in implementation and still far from
being generally accessible thus far
58. its.unc.edu 58
DFT Developments
Theoretical
• Extensions to excited states, etc.
• Better functionals (mega-GGA), etc
• Understanding functional properties, etc.
Conceptual
• More concepts proposed, like electrophilicity, philicity, spin-
philicity, surfaced-integrated Fukui fnc
• Dynamic behaviors, profiles, etc.
Computational
• Linear scaling methods
• QM/MM related issues
• Applications
60. its.unc.edu 60
Chemical Reactivity Theory
Chemical reactivity theory quantifies the reactive propensity of
isolated species through the introduction of a set of reactivity indices
or descriptors. Its roots go deep into the history of chemistry, as far
back as the introduction of such fundamental concepts as acid, base,
Lewis acid, Lewis base, etc. It pervades almost all of chemistry.
Molecular Orbital Theory
• Fukui’s Frontier Orbital (HOMO/LUMO) model
• Woodward-Hoffman rules
• Well developed: Nobel prize in Chemistry, 1981
• Problem: conceptual simplicity disappears as computational
accuracy increases because it’s based on the molecular orbital
description
Density Functional Theory (DFT)
• Conceptual DFT, also called Chemical DFT, DF Reactivity Theory
• Proposed by Robert G. Parr of UNC-CH, 1980s
• Still in development
-- Morrel H. Cohen, and Adam Wasserman, J. Phys. Chem. A 2007, 111,2229
61. its.unc.edu 61
DFT Reactivity Theory
General Consideration
• E E [N, (r)] E []
• Taylor Expansion: Perturbation resulted from an
external attacking agent leading to changes in N and
(r), N and (r),
'
'
2
!
,
,
2
2
2
2
r
r
r
r
r
r
r
r
2
1
r
r
r
r
r
r
2
d
d
E
d
N
E
N
N
N
E
d
E
N
N
E
N
E
N
N
E
E
N
N
N
Assumptions: existence and well-behavior of all above partial/functional derivatives
62. its.unc.edu 62
Conceptual DFT
Basic assumptions
•E E [N, (r)] E []
•Chemical processes, responses, and changes
expressible via Taylor expansion
•Existence, continuous, and well-behavedness
of the partial derivatives
63. its.unc.edu 63
DFT Reactivity Indices
Electronegativity (chemical potential)
Hardness / Softness
Maximum Hardness Principle (MHP)
/
1
,
2
2
1
2
2
S
N
E HOMO
LUMO
2
LUMO
HOMO
N
E
64. its.unc.edu 64
DFT Reactivity Indices
Fukui
function
N
f
r
r
– Nucleophilic attack
r
r
r N
N
f
1
– Electrophilic attack
r
r
r 1
N
N
f
– Free radical activity
2
r
r
r
f
f
f
65. its.unc.edu 65
Electrophilicity Index
Physical meaning: suppose an
electrophile is immersed in an electron
sea
The maximal electron flow and
accompanying energy decrease are
2
2
1
N
N
E
2
2
max
N
2
2
2
2
min
E Parr, Szentpaly, Liu, J. Am. Chem. Soc. 121, 1922(1999).
66. its.unc.edu 66
Experiment vs. Theory
Pérez, P. J. Org. Chem. 2003, 68, 5886. Pérez, P.; Aizman, A.; Contreras, R. J. Phys. Chem. A 2002, 106, 3964.
2
2
log
(k)
=
s(E+N)
67. its.unc.edu 67
Minimum Electrophilicity Principle
Analogous to the maximum hardness principle (MHP)
Separately proposed by Noorizadeh and Chattaraj
Concluded that “the natural direction of a chemical reaction is
toward a state of minimum electrophilicity.”
Noorizadeh, S. Chin. J. Chem. 2007, 25, 1439.
Noorizadeh, S. J. Phys. Org. Chem. 2007, 20, 514.
Chattaraj, P.K. Ind. J. Phys. Proc. Ind. Natl. Sci. Acad. Part A 2007, 81, 871.
non-
LA
1 2 3 4 5 6 7
Aa -0.091 -
0.085
-0.093 -0.093 -
0.088
-0.087 -0.083 -0.090
Bb -0.089 -
0.084
-0.088 -0.089 -
0.087
-0.087 -0.0842 -
0.0892
Aa -0.172 -
0.247
-0.230 -0.220 -
0.218
-0.226 -0.2518 -
0.2161
Bb -0.171 -
0.246
-0.247 -0.233 -
0.221
-0.226 -0.2506 -
0.2157
Yue Xia, Dulin Yin, Chunying Rong, Qiong Xu, Donghong Yin, and Shubin Liu, J. Phys. Chem. A, 2008, 112, 9970.
68. its.unc.edu 68
Nucleophilicity
Much harder to quantify, because it related to local
hardness, which is ambiguous in definition.
A nucleophile can be a good donor for one electrophile
but bad for another, leading to the difficulty to define a
universal scale of nucleophilicity for an nucleophile.
A
B
A
B
A
2
2
1
Jaramillo, P.; Perez, P.; Contreras, R.; Tiznado, W.; Fuentealba, P. J. Phys. Chem. A 2006, 110, 8181.
= -N - ½ S()2
Minimizing in Eq. (14) with respect to ,
one has
=-N and = - ½ N2.
Making use of the following relation
B
A
B
A
N
69. its.unc.edu 69
Philicity and Fugality
Philicity: defined as ·f(r)
• Chattaraj, Maiti, & Sarkar, J. Phys. Chem. A 107, 4973(2003)
• Still a very controversial concept, see JPCA 108, 4934(2004); Chattaraj,
et al. JPCA, in press.
Spin-Philicity: defined same as but in spin resolution
• Perez, Andres, Safont, Tapia, & Contreras. J. Phys. Chem. A 106,
5353(2002)
Nuclofugality & Electrofugality
2
)
( 2
A
En
2
)
( 2
I
Ee
Ayers, P.W.; Anderson, J.S.M.; Rodriguez, J.I.; Jawed, Z. Phys. Chem. Chem. Phys. 2005, 7, 1918.
Ayers, P.W.; Anderson, J S.M.; Bartolotti, L.J. Int. J. Quantum Chem. 2005, 101, 520.
70. its.unc.edu 70
Dual Descriptors
N
N
N
N
f
N
E
E
N
f
r
r
r
r
r
2
2
2
2
2
3rd-order cross-term derivatives
0
2
r
r d
f
r
r
r
f
f
f 2
r
r
r HOMO
LUMO
f
2
Recovering Woodward-Hoffman rules!
Ayers, P.W.; Morell, C., De Proft, D.; Geerlings, P. Chem. Eur. J., 2007, 13, 8240
Geerling, P. De Proft F. Phys. Chem. Chem. Phys., 2008, 10, 3028
71. its.unc.edu 71
Steric Effect
one of the most widely used
concepts in chemistry
originates from the space occupied
by atom in a molecule
previous work attributed to the
electron exchange correlation
Weisskopf thought of as “kinetic
energy pressure”
Weisskopf, V.F., Science 187, 605-612(1975).
72. its.unc.edu 72
Steric effect: a DFT description
Assume
since
we have
E[] ≡ Es[] + Ee[] + Eq[]
E[] = Ts[] + Vne[] + J[] + Vnn[] + Exc[]
Ee[] = Vne[] + J[] + Vnn[]
Eq[] = Exc[] + EPauli[] = Exc[] + Ts[] - Tw[]
Es[] ≡ E[] - Ee[] - Eq[] = Tw[]
r
r
r
d
TW
2
8
1
S.B. Liu, J. Chem. Phys. 2007, 126, 244103.
S.B. Liu and N. Govind, J. Phys. Chem. A 2008, 112, 6690.
S.B. Liu, N. Govind, and L.G. Pedersen, J. Chem. Phys. 2008, 129, 094104.
M. Torrent-Sucarrat, S.B. Liu and F. De Proft, J. Phys. Chem. A 2009, 113, 3698.
73. its.unc.edu 73
In 1956, Taft constructed a scale for the steric effect of different substituents,
based on rate constants for the acid-catalyzed hydrolysis of esters in aqueous
acetone. It was shown that log(k / k0) was insensitive to polar effects and thus,
in the absence of resonance interactions, this value can be considered as being
proportional to steric effects. Hydrogen is taken to have a reference value of
EsTaft= 0
Experiment vs. Theory
75. its.unc.edu 75
Glu 165 (the catalytic base), His 95 (the proton shuttle)
DHAP GAP
TIM 2-step 2-residue Mechanism
76. its.unc.edu 76
QM/MM: 1st Step of TIM
Mechanism
QM/MM size: 6051 atoms QM Size: 37 atoms
QM: Gaussian’98 Method: HF/3-21G
MM: Tinker Force field: AMBER all-atom
Number of Water: 591 Model for Water: TIP3P
MD details: 20x20x20 Å3 box, optimize until the RMS energy
gradient less than 1.0 kcal/mol/Å. 20 psec MD. Time step 2fs.
SHAKE, 300 K, short range cutoff 8 Å, long range cutoff 15 Å.
77. its.unc.edu 77
QM/MM: Transition State
=====================
Energy Barrier (kcal/mol)
-------------------------------------
QM/MM 21.9
Experiment 14.0
=====================
78. its.unc.edu 78
What’s New: Linear Scaling
O(N) Method
Numerical Bottlenecks:
• diagonalization ~N3
• orthonormalization ~N3
• matrix element evaluation ~N2-N4
Computational Complexity: N log N
Theoretical Basis: near-sightedness of density
matrix or orbitals
Strategy:
• sparsity of localized orbital or density
matrix
• direct minimization with conjugate
gradient
Models: divide-and-conquer and variational
methods
Applicability: ~10,000 atoms, dynamics
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600 700 800 900
Atoms
CPU
se
conds
pe
r
CG
ste
p
OLMO
NOLMO
Diagonalization
79. its.unc.edu 79
What Else … ?
Solvent effect
•Implicit model vs. explicit model
Relativity effect
Transition state
Excited states
Temperature and pressure
Solid states (periodic boundary condition)
Dynamics (time-dependent)
81. its.unc.edu 81
Popular QM codes
Gaussian (Ab Initio, Semi-empirical, DFT)
Gamess-US/UK (Ab Initio, DFT)
Spartan (Ab Initio, Semi-empirical, DFT)
NWChem (Ab Initio, DFT, MD, QM/MM)
MOPAC/2000 (Semi-Empirical)
DMol3/CASTEP (DFT)
Molpro (Ab initio)
ADF (DFT)
ORCA (DFT)
82. its.unc.edu 82
Reference Books
Computational Chemistry (Oxford Chemistry Primer) G. H.
Grant and W. G. Richards (Oxford University Press)
Molecular Modeling – Principles and Applications, A. R. Leach
(Addison Wesley Longman)
Introduction to Computational Chemistry, F. Jensen (Wiley)
Essentials of Computational Chemistry – Theories and Models,
C. J. Cramer (Wiley)
Exploring Chemistry with Electronic Structure Methods, J. B.
Foresman and A. Frisch (Gaussian Inc.)
83. its.unc.edu 83
Questions & Comments
Please direct comments/questions about research computing to
E-mail: research@unc.edu
Please direct comments/questions pertaining to this presentation to
E-Mail: shubin@email.unc.edu
The PPT format of this presentation is available here:
http://its2.unc.edu/divisions/rc/training/scientific/
/afs/isis/depts/its/public_html/divisions/rc/training/scientific/short_courses/
84. its.unc.edu 84
Hands-on: Part I
Purpose: to get to know the available ab
initio and semi-empirical methods in the
Gaussian 03 / GaussView package
• ab initio methods
Hartree-Fock
MP2
CCSD
• Semiempirical methods
AM1
The WORD .doc format of this hands-on exercises is available here:
http://its2.unc.edu/divisions/rc/training/scientific/
/afs/isis/depts/its/public_html/divisions/rc/training/scientific/short_courses/labDirections_compchem_2009.doc
85. its.unc.edu 85
Hands-on: Part II
Purpose: To use LDA and GGA DFT
methods to calculate IR/Raman spectra
in vacuum and in solvent. To build
QM/MM models and then use DFT
methods to calculate IR/Raman spectra
• DFT
LDA (SVWN)
GGA (B3LYP)
• QM/MM