G1-3 These methods are based on ab initio molecular orbital calculations. Electron correlation is calculated using MP2 or MP4 and QCI.
|
|
- Leon Holland
- 6 years ago
- Views:
Transcription
1 23. High Accuracy Energy Methods 23.1 Gaussian-n Methods The method keywords G1, G2, G2MP2, G3, G3MP2, G3B3, G3MP2B3, G4, and G4MP2 perform high accuracy complex energy computations in Gaussian. Essentially, this means that they use other defined calculations in tandem to compute energies with an error tolerance of < 2 kcal/mol. All of these methods have been most rigorously tested on molecules constructed from row 1 and row 2 atoms of the periodic table (H, He, Li-F, Na-Cl). Each method was developed as an improvement over the one before: G2 is an improvement upon G1, G3 on G2, and G4 on G3. All methods were developed by Larry Curtiss et al. in 1989, 1991, 1998, and 2007 for G1-4 respectively. High accuracy in these methods is obtained by determining (experimentally and theoretically) a higher level correction E(HLC) based on calculations for the hydrogen atom and hydrogen molecule. The basis of all G-n calculations is that the energies from lower level calculations (MP2,MP4) are added to a higher level correction (HLC) calculation (QCISD(T)): all of it (E) equals some of it (MPn calculations) plus the rest of it (HLC). E e (Gn) = E 0 + E(HLC) (159) G1-3 These methods are based on ab initio molecular orbital calculations. Electron correlation is calculated using MP2 or MP4 and QCI. G1 uses three polarization functions: diffuse-sp, double-d, and f-polarization. Electron correlation is handled using Møller-Plesset Perturbation theory (MP4) and quadratic configuration interaction (QCI). The method is high accuracy for: atomization (dissociation), ionization energies, and electron affinities. This method uses MP2(full)/6-31G*. The inclusion of full means that all electrons are considered in energy calculations, not just valence electrons. The final energy is calculated by adding a zero-point energy (ZPE) that has been calculated using HF/6-3lG* and scaled by the scaling factor G2 improves on G1 by: 1. Correcting for the non-additivity of diffuse sp polarization by including a 2df basis set extension 2. Using a basis set that contains a third d function on non-hydrogen atoms and a second p function on hydrogen 3. Modifying the HLC The main improvements over G1 are: 1. More accurate atomization energies row 1 atom-containing molecules like LiF (35% better) 2. More accurate for hypervalent species 3. More accurate electron affinities for row 2 atom-containing molecules (44% better)
2 The increased accuracy for atomization of ionic species such as LiF comes from correcting the duplication of the contribution from the diffuse polarization function on the negative center (F) by the polarization extension of the positive center (Li). For LiF, the dissociation energy changes from kcal/mol in G1 to kcal/mol in G2- a big difference! G2MP2 uses MP2 instead of MP4 in calculations, significantly decreasing computational cost with negligible loss of accuracy. Both G2 and G2MP2 use the 6-311G* basis set. G3 uses 6-31G* instead of 6-311G*, thereby decreasing computational cost dramatically. G3 corrects for spin-orbit coupling in atoms and core electron correlation. Making these changes increases the accuracy of enthalpies of formation. The HLC is split into two parts: one for atoms and one for molecules. Doing this has significant impacts on calculated values for electron affinity and ionization potential. G3 has higher accuracy than G2 and G1 for: 1. Non-hydrogen systems like SiF4 and CF4 2. Substituted hydrocarbons 3. Unsaturated cyclic species The average error in enthalpy of formation is < 1kcal/mol away from experimentally and theoretically determined values. The average error is 1.02 kcal/mol- 31% more accurate in G3 than it was in G2 (1.48 kcal/mol). The process of G3: 1. Initial equilibrium structure is determined at the HF/6-31G(d) level a. RHF for singlets b. UHF for not singlets (same as G2) 2. HF/6-31G(d) used to calculate frequencies. A scaling factor of is applied to get ZPE (same as G2) 3. Equilibrium structure reoptimized at MP2(full) 6-31G(d). All electrons are taken into consideration when calculating correlation energies 4. Single point energy calculations carried out at MP4/6-31G(d). This is then modified by: a. Correction for diffuse function b. Correction for higher polarization function c. Quadratic CI correction by QCISD d. Correction for larger basis set effects caused by assumption of separate basis set extensions for diffuse functions and higher polarization functions Step 4 is what most differentiates G3 from G2. It uses the 6-31G basis set rather than the 6-311G, includes more polarizations on second row and less on first, and core
3 polarization functions are added. To account for core-related correlation contributions to total energy, step 4d is carried out at MP2(full). 5. MP4/6-31G(d), the energy from step 4, and a spin orbit correction are added together for atomic species. Spin orbit correction, determined experimentally or theoretically, is an important consideration for halide containing compounds. Molecular spin orbit interaction is neglected because isgives no overall improvement to energy. 6. HLC is added in. Includes corrections (A, B, C, and D) for pairs of valence electrons in molecules, unpaired electrons in molecules, pairs of valence electrons in atoms, unpaired electrons in atoms. For G3 theory, A=6.386 mhartrees, B=2.977 mhartrees, C=6.219 mhar- trees, D=1.185 mhartrees. Total energy is calculated by adding ZPE from step 2 to this total energy. G3MP2 uses MP2 instead of MP4 to reduce computational cost, G3B3 uses B3LYP to optimize geometry, and G3MP2B3 does both. Neither G2 nor G3 are size consistent. G4 is different from G1-3 in that it depends on cancellation of errors for its high accuracy, rather than on QCI. The mechanism of G4 calculation is the same as that of G3, detailed above. G4 gains accuracy over G3 by: 1. Determining the HF limit for total inclusion of energy 2. Increasing d-polarization to 3d on first row atoms, 4d on second row atoms 3. Replacing QCISD(T) with CCSD(T) in HLC 4. Calculating geometry and ZPE at B3LYP/6-31G(2df,p) level 5. Including two more HLC parameters a. A corrects inaccuracies for pairs of electrons in radical molecules that also have an ion b. E corrects inaccuracies for molecules with a valence 1s pair of electron The absolute energy error of G4 is 0.83 kcal/mol, which is lower than the 1.02 kcal/mol of G3. The error in enthalpies of formation for non-hydrogen species is significantly reduced from G3 as well CBS: Complete Basis Set Extrapolation Energy calculations run with this method are computationally cheap and have high accuracy. It is obvious that the most accurate energy is that of the solution of the Schrödinger Equation- or at an infinitely large basis set. CBS methods approximate an infinitely large basis set by combining energies from many lower-level theories. The most accurate CBS method is CBS-APNO (Atomic Pair Natural Orbital) which has a mean absolute deviation of only 0.5 kcal/mol. This is nearly twice as accurate as all previously
4 described methods. This increased accuracy comes at a computational cost, though. The computational difficulties arise from the expensive QCISD(T)/6-311+G(2df,p) calculation. This method is only applicable to first row compounds. The next most accurate CBS method is CBS-QB3, which is about two times less accurate than CBS-APNO but is also significantly faster. The fastest (and least accurate) CBS method is CBS- 4M. Its advantage is that it can be used on large systems, which cannot be said for most other high accuracy methods. The primary difference between CBS methods and Gaussian methods is that Gaussian increases accuracy by adding in more and more empirical terms trying to correct for known issues with the models being used, while CBS corrects the energy by trying to extrapolate the basis set to the infinite basis set W1: Weizmann-1 These are by far the most accurate methods with a mean error of only 0.3 kcal/mol. The mechanism of calculation is similar to that of CBS where the basis function is extrapolated to infinity. The high accuracy is due to the use of very large basis sets: up to cc-pvqz + 2d1g and cc-pv5z + 2d1f and calculations at the CCSD and CCSD(T) level. The variants are W1U, W1BD and W1 RO. The W1BD uses BD instead of Coupled Clusters (CC) and is extremely accurate as well as computationally expensive. The very high level of accuracy can be obtained without the use of any empirical parameters. This is a main point of difference between W1 and Gn methods. Unfortunately, the very high accuracy comes at a very high computational cost, limiting the application of these methods to small molecules Comparisons Computational Cost: W1> G2, CBS-APNO > G4 > G3, G2MP2 > CBS-QB3 > CBS-4M Accuracy: W1 > CBS-APNO > CBS-QB3, G4 > G3 > G2, G2MP2, CBS-4M 23.5 Gaussian keywords Can not specify basis set keywords with any method. Opt=(MaxCyc=n) can be used to modify cycles in optimization. QCISD=maxcyc, CCSD=maxcyc to modify cycles in energy calculations. ReadIsotopes to specify temperature, pressure, scaling factor. Restart to restart calculations using new parameters.
5 23.6 Examples As an example, consider proton affinity (PA) of water. PA is calculated as the change in energy (at 0K) between the molecule with and without an extra proton. The following input calls for a G2 calculation on water: %chk=h2o.chk #T G2 Test G2 on H2O - calculating proton affinity 0 1 H O 1 OH H 2 OH 1 OHO OH = 1.08 OHO = I didn t call for an extra optimization or restart. Notice that I didn t use any extra basis set keywords. The output summary is: Temperature= Pressure= E(ZPE)= E(Thermal)= E(QCISD(T))= E(Empiric)= DE(Plus)= DE(2DF)= G1(0 K)= G1 Energy= G1 Enthalpy= G1 Free Energy= E(Delta-G2)= E(G2-Empiric)= G2(0 K)= G2 Energy= G2 Enthalpy= G2 Free Energy= DE(MP2)= G2MP2(0 K)= G2MP2 Energy= G2MP2 Enthalpy= G2MP2 Free Energy= Notice that at the G2 level, G1 and G2MP2 energies are calculated along with G2 energy. Input of hydronium ion %chk=hydronium.chk #T HF/6-31G(d) G2 Test G2 on H3O+ - calculating proton affinity 1 1 O H 1 r1 H 1 r1 2 a1 H 1 r1 2 a1 3 d1 r1=0.904 a1= d1=
6 Output: Temperature= Pressure= E(ZPE)= E(Thermal)= E(QCISD(T))= E(Empiric)= DE(Plus)= DE(2DF)= G1(0 K)= G1 Energy= G1 Enthalpy= G1 Free Energy= E(Delta-G2)= E(G2-Empiric)= G2(0 K)= G2 Energy= G2 Enthalpy= G2 Free Energy= DE(MP2)= G2MP2(0 K)= G2MP2 Energy= G2MP2 Enthalpy= G2MP2 Free Energy= Find change in energy (at 0K): E = E(H 3 O + ) E(H 2 O) E(H + ) G = [( ) ( )] = kcal/mol The H + has no electrons and no ZPE therefore no energy at 0K. Experimental value: kcal/mol Deviation from experiment: 1.4 kcal/mol
Performance of Hartree-Fock and Correlated Methods
Chemistry 460 Fall 2017 Dr. Jean M. Standard December 4, 2017 Performance of Hartree-Fock and Correlated Methods Hartree-Fock Methods Hartree-Fock methods generally yield optimized geomtries and molecular
More informationAppendix C Calculating Excited States using Gaussian
Appendix C Calculating Excited States using Gaussian 403 This appendix contains methods for using Gaussian 03 78 and Gaussian 09 121 to calculate excited states of molecules. Such methods are useful for
More informationG3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry
G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry David J. Henry, Michael B. Sullivan, and Leo Radom Citation: The Journal of Chemical Physics 118,
More information4 Post-Hartree Fock Methods: MPn and Configuration Interaction
4 Post-Hartree Fock Methods: MPn and Configuration Interaction In the limit of a complete basis, the Hartree-Fock (HF) energy in the complete basis set limit (ECBS HF ) yields an upper boundary to the
More informationIntroduction to computational chemistry Exercise I: Structure and electronic energy of a small molecule. Vesa Hänninen
Introduction to computational chemistry Exercise I: Structure and electronic energy of a small molecule Vesa Hänninen 1 Introduction In this exercise the equilibrium structure and the electronic energy
More informationExercise 1: Structure and dipole moment of a small molecule
Introduction to computational chemistry Exercise 1: Structure and dipole moment of a small molecule Vesa Hänninen 1 Introduction In this exercise the equilibrium structure and the dipole moment of a small
More informationChoice of Theoretical Method
Choice of Theoretical Method 1 General Considerations PResources < Software < Computer P Expense (Time and Money) < Optimization/Single Point Calculations < Basis Set Choice < Method Choice P < Comparison
More informationOVERVIEW OF QUANTUM CHEMISTRY METHODS
OVERVIEW OF QUANTUM CHEMISTRY METHODS Outline I Generalities Correlation, basis sets Spin II Wavefunction methods Hartree-Fock Configuration interaction Coupled cluster Perturbative methods III Density
More informationChemistry 4560/5560 Molecular Modeling Fall 2014
Final Exam Name:. User s guide: 1. Read questions carefully and make sure you understand them before answering (if not, ask). 2. Answer only the question that is asked, not a different question. 3. Unless
More informationQUANTUM CHEMISTRY PROJECT 3: ATOMIC AND MOLECULAR STRUCTURE
Chemistry 460 Fall 2017 Dr. Jean M. Standard November 1, 2017 QUANTUM CHEMISTRY PROJECT 3: ATOMIC AND MOLECULAR STRUCTURE OUTLINE In this project, you will carry out quantum mechanical calculations of
More informationVol. 9 COMPUTATIONAL CHEMISTRY 319
Vol. 9 COMPUTATIONAL CHEMISTRY 319 COMPUTATIONAL QUANTUM CHEMISTRY FOR FREE-RADICAL POLYMERIZATION Introduction Chemistry is traditionally thought of as an experimental science, but recent rapid and continuing
More informationTowards multireference equivalents of the G2 and G3 methods
Towards multireference equivalents of the G2 and G3 methods Theis I. So/lling, David M. Smith, Leo Radom, Mark A. Freitag, and Mark S. Gordon Citation: The Journal of Chemical Physics 115, 8758 (2001);
More informationLec20 Fri 3mar17
564-17 Lec20 Fri 3mar17 [PDF]GAUSSIAN 09W TUTORIAL www.molcalx.com.cn/wp-content/uploads/2015/01/gaussian09w_tutorial.pdf by A Tomberg - Cited by 8 - Related articles GAUSSIAN 09W TUTORIAL. AN INTRODUCTION
More informationAB INITIO METHODS IN COMPUTATIONAL QUANTUM CHEMISTRY
AB INITIO METHODS IN COMPUTATIONAL QUANTUM CHEMISTRY Aneesh. M.H A theoretical study on the regioselectivity of electrophilic reactions of heterosubstituted allyl systems Thesis. Department of Chemistry,
More informationChapter 5 Predicted A-X Transition Frequencies and 2-Dimensional Torsion-Torsion Potential Energy Surfaces of HOCH 2 OO and HOC(CH 3 ) 2 OO
119 Chapter 5 Predicted A-X Transition Frequencies and 2-Dimensional Torsion-Torsion Potential Energy Surfaces of HOCH 2 OO and HOC(CH 3 ) 2 OO Abstract In Chapter 4, we presented the 1 (OH stretch) vibrational
More informationThis is a very succinct primer intended as supplementary material for an undergraduate course in physical chemistry.
1 Computational Chemistry (Quantum Chemistry) Primer This is a very succinct primer intended as supplementary material for an undergraduate course in physical chemistry. TABLE OF CONTENTS Methods...1 Basis
More informationIntroduction to Computational Chemistry: Theory
Introduction to Computational Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC andrew.gilbert@anu.edu.au 3023 Course Lectures Introduction Hartree Fock Theory Basis Sets Lecture 1 1 Introduction
More informationComputational Chemistry I
Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of
More informationIntroduction to Computational Chemistry
Introduction to Computational Chemistry Vesa Hänninen Laboratory of Physical Chemistry Chemicum 4th floor vesa.hanninen@helsinki.fi September 10, 2013 Lecture 3. Electron correlation methods September
More informationJack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah
1. Born-Oppenheimer approx.- energy surfaces 2. Mean-field (Hartree-Fock) theory- orbitals 3. Pros and cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usually does HF-how? 6. Basis sets and notations
More informationHomework Problem Set 5 Solutions. E e + H corr (a.u.) a.) Determine the bond dissociation enthalpy of ethane in kcal/mol (1 a.u. = kcal/mol).
Chemistry 380.37 Dr. Jean M. Standard Homework Problem Set 5 Solutions 1. Given below are the sum of electronic and thermal enthalpies, E e + H corr, from Hartree-Fock calculations using a 6-31G(d) basis
More informationChemistry 334 Part 2: Computational Quantum Chemistry
Chemistry 334 Part 2: Computational Quantum Chemistry 1. Definition Louis Scudiero, Ben Shepler and Kirk Peterson Washington State University January 2006 Computational chemistry is an area of theoretical
More informationBeyond the Hartree-Fock Approximation: Configuration Interaction
Beyond the Hartree-Fock Approximation: Configuration Interaction The Hartree-Fock (HF) method uses a single determinant (single electronic configuration) description of the electronic wavefunction. For
More informationCHEMISTRY 4021/8021 MIDTERM EXAM 1 SPRING 2014
CHEMISTRY 4021/8021 Q1) Propose a simple, united-atom molecular mechanics force-field needed to generate a potential energy surface for an isolated molecule of acetone (Me 2 CO). I.e., provide an energy
More informationComparison of G3 and G4 Theories for Radical Addition and Abstraction Reactions
Article Subscriber access provided by AUSTRALIAN NATIONAL UNIV Comparison of G3 and G4 Theories for Radical Addition and Abstraction Reactions Ching Yeh Lin, Jennifer L. Hodgson, Mansoor Namazian, and
More informationSolution of the Electronic Schrödinger Equation. Using Basis Sets to Solve the Electronic Schrödinger Equation with Electron Correlation
Solution of the Electronic Schrödinger Equation Using Basis Sets to Solve the Electronic Schrödinger Equation with Electron Correlation Errors in HF Predictions: Binding Energies D e (kcal/mol) HF Expt
More informationuse the backs of pages as needed
CHEMISTRY 4021/8021 Q1) Propose a simple, united-atom molecular mechanics force-field needed to generate a potential energy surface for an isolated molecule of acetone (Me 2 CO). I.e., provide an energy
More informationThe Potential Energy Surface
The Potential Energy Surface In this section we will explore the information that can be obtained by solving the Schrödinger equation for a molecule, or series of molecules. Of course, the accuracy of
More informationComputational Methods. Chem 561
Computational Methods Chem 561 Lecture Outline 1. Ab initio methods a) HF SCF b) Post-HF methods 2. Density Functional Theory 3. Semiempirical methods 4. Molecular Mechanics Computational Chemistry " Computational
More informationIntroduction to Computational Quantum Chemistry: Theory
Introduction to Computational Quantum Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC 3108 Course Lectures 2007 Introduction Hartree Fock Theory Configuration Interaction Lectures 1 Introduction
More informationMethods for Treating Electron Correlation CHEM 430
Methods for Treating Electron Correlation CHEM 430 Electron Correlation Energy in the Hartree-Fock approximation, each electron sees the average density of all of the other electrons two electrons cannot
More informationComputational Chemistry. An Introduction to Molecular Dynamic Simulations
Computational Chemistry An Introduction to Molecular Dynamic Simulations Computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws
More information( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r)
Born Oppenheimer Approximation: Ĥ el ( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r) For a molecule with N electrons and M nuclei: Ĥ el What is E el (R)? s* potential surface Reaction Barrier Unstable intermediate
More informationA complete basis set model chemistry for excited states
A complete basis set model chemistry for excited states George A. Petersson Hall-Atwater Laboratories of Chemistry, Wesleyan University, Middletown, Connecticut 06459-0180 1 Report Documentation Page Form
More informationQUANTUM CHEMISTRY PROJECT 3: PARTS B AND C
Chemistry 460 Fall 2017 Dr. Jean M. Standard November 6, 2017 QUANTUM CHEMISTRY PROJECT 3: PARTS B AND C PART B: POTENTIAL CURVE, SPECTROSCOPIC CONSTANTS, AND DISSOCIATION ENERGY OF DIATOMIC HYDROGEN (20
More informationComputational Material Science Part II. Ito Chao ( ) Institute of Chemistry Academia Sinica
Computational Material Science Part II Ito Chao ( ) Institute of Chemistry Academia Sinica Ab Initio Implementations of Hartree-Fock Molecular Orbital Theory Fundamental assumption of HF theory: each electron
More informationAN INTRODUCTION TO QUANTUM CHEMISTRY. Mark S. Gordon Iowa State University
AN INTRODUCTION TO QUANTUM CHEMISTRY Mark S. Gordon Iowa State University 1 OUTLINE Theoretical Background in Quantum Chemistry Overview of GAMESS Program Applications 2 QUANTUM CHEMISTRY In principle,
More informationCOMPUTATIONAL THERMODYNAMIC STUDIES OF ALKALI AND ALKALINE EARTH COMPOUNDS, OLEFIN METATHESIS CATALYSTS, AND BORANE AZOLES
COMPUTATIONAL THERMODYNAMIC STUDIES OF ALKALI AND ALKALINE EARTH COMPOUNDS, OLEFIN METATHESIS CATALYSTS, AND BORANE AZOLES FOR CHEMICAL HYDROGEN STORAGE by MONICA VASILIU A DISSERTATION Submitted in partial
More informationCOPYRIGHTED MATERIAL. Quantum Mechanics for Organic Chemistry &CHAPTER 1
&CHAPTER 1 Quantum Mechanics for Organic Chemistry Computational chemistry, as explored in this book, will be restricted to quantum mechanical descriptions of the molecules of interest. This should not
More informationRapid and precise thermochemical calculations by quantum chemical methods
Rapid and precise thermochemical calculations by quantum chemical methods Ph.D. thesis By: Adrienn Ruzsinszky Supervisor: Dr. Gábor Csonka Budapest University of Technology and Economics Department of
More informationLec20 Wed 1mar17 update 3mar 10am
564-17 Lec20 Wed 1mar17 update 3mar 10am Figure 15.2 Shows that increasing the diversity of the basis set lowers The HF-SCF energy considerably, but comes nowhere near the exact experimental energy, regardless
More informationSession 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education
Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools
More informationChemistry 4021/8021 Computational Chemistry 3/4 Credits Spring Semester 2007 Key PS3
Chemistry 4021/8021 Computational Chemistry 3/4 Credits Spring Semester 2007 Key PS3 1. Below are two isomeric geometries that we previously examined in Problem Sets 1 and 2 as both C 10 H 16 and Si 10
More informationLecture 4: methods and terminology, part II
So theory guys have got it made in rooms free of pollution. Instead of problems with the reflux, they have only solutions... In other words, experimentalists will likely die of cancer From working hard,
More information154 J. Chem. Phys. 108 (1), 1 January /98/108(1)/154/23/$ American Institute of Physics
An examination of intrinsic errors in electronic structure methods using the Environmental Molecular Sciences Laboratory computational results database and the Gaussian-2 set David Feller and Kirk A. Peterson
More informationElectron Correlation Methods
Electron Correlation Methods HF method: electron-electron interaction is replaced by an average interaction E HF c = E 0 E HF E 0 exact ground state energy E HF HF energy for a given basis set HF E c
More informationJack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah
1. Born-Oppenheimer approx.- energy surfaces 2. Mean-field (Hartree-Fock) theory- orbitals 3. Pros and cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usually does HF-how? 6. Basis sets and notations
More information计算物理作业二. Excercise 1: Illustration of the convergence of the dissociation energy for H 2 toward HF limit.
计算物理作业二 Excercise 1: Illustration of the convergence of the dissociation energy for H 2 toward HF limit. In this exercise, basis indicates one of the following basis sets: STO-3G, cc-pvdz, cc-pvtz, cc-pvqz
More informationDensity Functional Theory
Chemistry 380.37 Fall 2015 Dr. Jean M. Standard October 28, 2015 Density Functional Theory What is a Functional? A functional is a general mathematical quantity that represents a rule to convert a function
More informationNobel Lecture: Quantum chemical models*
Nobel Lecture: Quantum chemical models* John A. Pople Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113 [S0034-6861(99)00904-6] I. INTRODUCTION The fundamental underpinnings
More informationQuantum Chemical Design of Hydroxyurea Derivatives. For the Treatment of Sickle Cell Anemia. B. A. Rohrman
1 Quantum Chemical Design of Hydroxyurea Derivatives For the Treatment of Sickle Cell Anemia B. A. Rohrman I. Introduction Sickle cell anemia is an inherited disorder in which red blood cells become stiff
More informationLecture 5: More about one- Final words about the Hartree-Fock theory. First step above it by the Møller-Plesset perturbation theory.
Lecture 5: More about one- determinant wave functions Final words about the Hartree-Fock theory. First step above it by the Møller-Plesset perturbation theory. Items from Lecture 4 Could the Koopmans theorem
More informationBefore I entered the Texas Academy of Mathematics and Science as a junior, I had very little
Vinay Ramasesh Getting Involved with Research Before I entered the Texas Academy of Mathematics and Science as a junior, I had very little experience with actual scientific research. As a freshman, I d
More informationExcited States Calculations for Protonated PAHs
52 Chapter 3 Excited States Calculations for Protonated PAHs 3.1 Introduction Protonated PAHs are closed shell ions. Their electronic structure should therefore be similar to that of neutral PAHs, but
More informationUptake of OH radical to aqueous aerosol: a computational study
Uptake of OH radical to aqueous aerosol: a computational study Grigory Andreev Karpov Institute of Physical Chemistry 10 Vorontsovo pole, Moscow, 105064, Russia Institute of Physical Chemistry and Electrochemistry
More informationElectron Affinities of Selected Hydrogenated Silicon Clusters (Si x H y, x ) 1-7, y ) 0-15) from Density Functional Theory Calculations
J. Phys. Chem. A 2000, 104, 6083-6087 6083 Electron Affinities of Selected Hydrogenated Silicon Clusters (Si x H y, x ) 1-7, y ) 0-15) from Density Functional Theory Calculations Mark T. Swihart Department
More informationwith the larger dimerization energy also exhibits the larger structural changes.
A7. Looking at the image and table provided below, it is apparent that the monomer and dimer are structurally almost identical. Although angular and dihedral data were not included, these data are also
More informationStudy of Ozone in Tribhuvan University, Kathmandu, Nepal. Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal
Study of Ozone in Tribhuvan University, Kathmandu, Nepal Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal 1 Country of the Mt Everest 2 View of the Mt Everest 3 4 5
More informationSemi-Empirical MO Methods
Semi-Empirical MO Methods the high cost of ab initio MO calculations is largely due to the many integrals that need to be calculated (esp. two electron integrals) semi-empirical MO methods start with the
More informationThe Periodic Table. Periodic Properties. Can you explain this graph? Valence Electrons. Valence Electrons. Paramagnetism
Periodic Properties Atomic & Ionic Radius Energy Electron Affinity We want to understand the variations in these properties in terms of electron configurations. The Periodic Table Elements in a column
More informationSchrodinger equation
CH1. Atomic Structure orbitals periodicity 1 Schrodinger equation - (h 2 /2p 2 m e2 ) [d 2 Y/dx 2 +d 2 Y/dy 2 +d 2 Y/dz 2 ] + V Y = E Y h = constant m e = electron mass V = potential E gives quantized
More informationReactions in the Al-H-Cl System Studied by ab Initio Molecular Orbital and Density Functional Methods
264 J. Phys. Chem. A 2001, 105, 264-273 Reactions in the Al-H-Cl System Studied by ab Initio Molecular Orbital and Density Functional Methods Mark T. Swihart* Department of Chemical Engineering, UniVersity
More informationFragmentation methods
Fragmentation methods Scaling of QM Methods HF, DFT scale as N 4 MP2 scales as N 5 CC methods scale as N 7 What if we could freeze the value of N regardless of the size of the system? Then each method
More informationExperimental and Ab initio Computational Study of Azobenzene and Several of its Derivatives
University of Tennessee, Knoxville Trace: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2015 Experimental and Ab initio Computational Study of Azobenzene and Several
More informationMolecular Simulation I
Molecular Simulation I Quantum Chemistry Classical Mechanics E = Ψ H Ψ ΨΨ U = E bond +E angle +E torsion +E non-bond Jeffry D. Madura Department of Chemistry & Biochemistry Center for Computational Sciences
More informationConformational energy analysis
Lab 3 Conformational energy analysis Objective This computational project deals with molecular conformations the spatial arrangement of atoms of molecules. Conformations are determined by energy, so the
More informationQUANTUM CHEMISTRY FOR TRANSITION METALS
QUANTUM CHEMISTRY FOR TRANSITION METALS Outline I Introduction II Correlation Static correlation effects MC methods DFT III Relativity Generalities From 4 to 1 components Effective core potential Outline
More informationThe calculation of the universal density functional by Lieb maximization
The calculation of the universal density functional by Lieb maximization Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
More informationTheoretical study of the OH-initiated atmospheric oxidation mechanism. of perfluoro methyl vinyl ether, CF 3 OCF=CF 2
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2015 Theoretical study of the OH-initiated atmospheric oxidation mechanism of perfluoro
More informationLab #3: Choice of Theoretical Method
Lab #3: Choice of Theoretical Method These directions assume the user is familiar with the WebMO interface and can build molecules, set up calculations, etc. Exercise 1 - Determine the Proton Affinity
More informationSystematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc Zn
THE JOURNAL OF CHEMICAL PHYSICS 123, 064107 2005 Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc Zn Nikolai B. Balabanov
More informationThe rôle of surfaces in prebiotic chemistry. Piero Ugliengo University of Torino Dip. Chimica Via P. Giuria, 7 - Torino
The rôle of surfaces in prebiotic chemistry Piero Ugliengo University of Torino Dip. Chimica Via P. Giuria, 7 - Torino 1 A collaborative work Dip. Chimica - NIS Centre Torino University TO BCN Dep. Quimica
More informationGeneral Chemistry (Third Quarter)
General Chemistry (Third Quarter) This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence
More informationApproximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules
JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 18 8 NOVEMBER 2000 Approximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules
More informationCOUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI
COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI Marta Włoch, a Jeffrey R. Gour, a and Piotr Piecuch a,b a Department of Chemistry,Michigan State University, East Lansing, MI 48824 b
More informationAPPLICATION OF THE CORRELATION CONSISTENT COMPOSITE APPROACH TO BIOLOGICAL SYSTEMS AND NONCOVALENT INTERACTIONS. Amanda G. Riojas
APPLICATION OF THE CORRELATION CONSISTENT COMPOSITE APPROACH TO BIOLOGICAL SYSTEMS AND NONCOVALENT INTERACTIONS Amanda G. Riojas Dissertation Prepared for the Degree of DOCTOR OF PHILOSOPHY UNIVERSITY
More information362 Lecture 6 and 7. Spring 2017 Monday, Jan 30
362 Lecture 6 and 7 Spring 2017 Monday, Jan 30 Quantum Numbers n is the principal quantum number, indicates the size of the orbital, has all positive integer values of 1 to (infinity) l is the angular
More information2~:J~ -ryej- r- 2 Jr. A - f3. sr(djk nv~tor rn~ +~ rvjs (::-CJ) ::;-1-.'--~ -. rhd. ('-.Ji.L.~ )- r'-d)c, -r/~ JJr - 2~d ~2-Jr fn'6.
.~, ~ I, sr(djk nv~tor rn~ +~ rvjs (::-CJ) ::;-1-.'--~ -. rhd. ('-.Ji.L.~ )- r'-d)c, -r/~ JJr - 2~d ~2-Jr fn'6.)1e'" 21t-ol Je C'...-------- lj-vi, J? Jr Jr \Ji 2~:J~ -ryej- r- 2 Jr A - f3 c _,~,= ~,.,w._..._.
More informationCHAPTER 6 CHEMICAL BONDING TEXT BOOK EXERCISE Q.1. Select the correct statement. i. An ionic compound A + B - is most likely to be formed when ii. iii. a. the ionization energy of A is high and electron
More information8.1 Types of Chemical Bonds List and define three types of bonding. chapter 8 Bonding General Concepts.notebook. September 10, 2015
chapter 8 Bonding General Concepts.notebook Chapter 8: Bonding: General Concepts Mar 13 11:15 AM 8.1 Types of Chemical Bonds List and define three types of bonding. Bonds are forces that hold groups of
More informationMO Calculation for a Diatomic Molecule. /4 0 ) i=1 j>i (1/r ij )
MO Calculation for a Diatomic Molecule Introduction The properties of any molecular system can in principle be found by looking at the solutions to the corresponding time independent Schrodinger equation
More informationIntroduction to Electronic Structure Theory
CSC/PRACE Spring School in Computational Chemistry 2017 Introduction to Electronic Structure Theory Mikael Johansson http://www.iki.fi/~mpjohans Objective: To get familiarised with the, subjectively chosen,
More informationJoint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data January 2012
2327-3 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data 23-27 January 2012 Qunatum Methods for Plasma-Facing Materials Alain ALLOUCHE Univ.de Provence, Lab.de la Phys.
More informationCalculating Bond Enthalpies of the Hydrides
Proposed Exercise for the General Chemistry Section of the Teaching with Cache Workbook: Calculating Bond Enthalpies of the Hydrides Contributed by James Foresman, Rachel Fogle, and Jeremy Beck, York College
More informationOther methods to consider electron correlation: Coupled-Cluster and Perturbation Theory
Other methods to consider electron correlation: Coupled-Cluster and Perturbation Theory Péter G. Szalay Eötvös Loránd University Institute of Chemistry H-1518 Budapest, P.O.Box 32, Hungary szalay@chem.elte.hu
More informationDouble Bond: C 2 H 4. An sp 2 hybridized C atom has one electron in each of the three sp 2 lobes
Double Bond: C 2 H 4 An sp 2 hybridized C atom has one electron in each of the three sp 2 lobes Top view of the sp 2 hybrid Side view of the sp 2 hybrid + the unhybridized p orbital 1 Double Bond: C 2
More information4 - BENZENE: AROMATICITY, CONJUGATION AND ASSOCIATED REACTIVITY
4 - BENZENE: AROMATICITY, CONJUGATION AND ASSOCIATED REACTIVITY During the early 1800's, a group of compounds of natural origin became collectively known as aromatic compounds. As several of these compounds
More informationPotential Energy Surfaces for Quantum Dynamics Simulations: From ab initio Computations to Vibrational State Determinations
Potential Energy Surfaces for Quantum Dynamics Simulations: From ab initio Computations to Vibrational State Determinations by Ekadashi Pradhan A thesis submitted in partial fulfillment of the requirements
More informationSession 7 Overview: Part A I. Prediction of Vibrational Frequencies (IR) Part B III. Prediction of Electronic Transitions (UV-Vis) IV.
Session 7 Overview: Part A I. Prediction of Vibrational Frequencies (IR) II. Thermochemistry Part B III. Prediction of Electronic Transitions (UV-Vis) IV. NMR Predictions 1 I. Prediction of Vibrational
More informationAb initio calculations for potential energy surfaces. D. Talbi GRAAL- Montpellier
Ab initio calculations for potential energy surfaces D. Talbi GRAAL- Montpellier A theoretical study of a reaction is a two step process I-Electronic calculations : techniques of quantum chemistry potential
More informationA Gentle Introduction to (or Review of ) Fundamentals of Chemistry and Organic Chemistry
Wright State University CORE Scholar Computer Science and Engineering Faculty Publications Computer Science and Engineering 2003 A Gentle Introduction to (or Review of ) Fundamentals of Chemistry and Organic
More informationFull configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods
JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 4 22 JANUARY 2003 Full configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods
More informationPhysical Chemistry II Recommended Problems Chapter 12( 23)
Physical Chemistry II Recommended Problems Chapter 1( 3) Chapter 1(3) Problem. Overlap of two 1s orbitals recprobchap1.odt 1 Physical Chemistry II Recommended Problems, Chapter 1(3), continued Chapter
More informationHartree, Hartree-Fock and post-hf methods
Hartree, Hartree-Fock and post-hf methods MSE697 fall 2015 Nicolas Onofrio School of Materials Engineering DLR 428 Purdue University nonofrio@purdue.edu 1 The curse of dimensionality Let s consider a multi
More informationORGANIC CHEMISTRY. Meaning of Organic?
ORGANIC CHEMISTRY Meaning of Organic? Initially scientists believed there was a special force in living organisms -this was assumed the unique component of organic material In 1828 Wöhler synthesized urea
More informationFEATURE ARTICLE. Ab Initio Calculation of Nonbonded Interactions: Are We There Yet? A. K. Rappé* and E. R. Bernstein*
J. Phys. Chem. A 2000, 104, 6117-6128 6117 FEATURE ARTICLE Ab Initio Calculation of Nonbonded Interactions: Are We There Yet? A. K. Rappé* and E. R. Bernstein* Department of Chemistry, Colorado State UniVersity,
More informationDefense Technical Information Center Compilation Part Notice ADP023773
UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADP023773 TITLE: Computational Chemistry Modeling of the Atmospheric Fate of Toxic Industrial Compounds [TICs] DISTRIBUTION: Approved
More informationSupporting Information: Predicting the Ionic Product of Water
Supporting Information: Predicting the Ionic Product of Water Eva Perlt 1,+, Michael von Domaros 1,+, Barbara Kirchner 1, Ralf Ludwig 2, and Frank Weinhold 3,* 1 Mulliken Center for Theoretical Chemistry,
More informationAccurate multireference configuration interaction calculations on the lowest 1 and 3 electronic states of C 2,CN, BN, and BO
Accurate multireference configuration interaction calculations on the lowest 1 and 3 electronic states of C 2,CN, BN, and BO Kirk A. Peterson a) Department of Chemistry, Washington State University and
More informationLUMO + 1 LUMO. Tómas Arnar Guðmundsson Report 2 Reikniefnafræði G
Q1: Display all the MOs for N2 in your report and classify each one of them as bonding, antibonding or non-bonding, and say whether the symmetry of the orbital is σ or π. Sketch a molecular orbital diagram
More information