Density Functional Theory (DFT)
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Semiempirical Implementations of Molecular
Semiempirical Implementations of Molecular Orbital Theory How one can make Hartree-Fock theory less computationally intensive without much sacrificing its accuracy? The most demanding step – calculation of two-electron (four-index) integrals (J and K integrals) appearing in the Fock matrix elements (N4 where N is the number of basis functions). One way to save time – to estimate their value accurately in an a priori fashion and thus to avoid numerical integration. Coulomb integrals measure the repulsion between electrons in regions of space defined by the basis functions. When the basis functions in the integral for one electron are very far from the basis functions for the other, the value of that integral will approach zero. In a large molecule, one might be able to avoid the calculation of a very large number of integrals simply by assuming them to be zero. HF theory is intrinsically inaccurate as it does not include correlation energy. Therefore, modifications of the theory introduced in order to simplify its formalism may actually improve it, provided the new approximations somehow introduce an accounting for correlation energy. Most typically, such approximations involve the adoption of a parametric form for some aspect of the calculation where the parameters involved are chosen so as best reproduce experimental data – ‘semiempirical’. Another motivation for introducing semiempirical approximation into HF theory was to facilitate the computation of derivatives (gradients, Hessians) so that geometries could be more efficiently optimized. Extended Hückel Theory Before considering semiempirical methods we revisit Hückel theory: H11 − ES11 H12 − ES12 L H1N − ES1N H21 − ES21 H22 − ES22 L H2N − ES2N = 0 M M O M H − ES H − ES H − ES N1 N1 N2 N 2 L NN NN The dimension of the secular determinant depends on the choice of the basis set. -
Supporting Information
Electronic Supplementary Material (ESI) for RSC Advances. This journal is © The Royal Society of Chemistry 2020 Supporting Information How to Select Ionic Liquids as Extracting Agent Systematically? Special Case Study for Extractive Denitrification Process Shurong Gaoa,b,c,*, Jiaxin Jina,b, Masroor Abroc, Ruozhen Songc, Miao Hed, Xiaochun Chenc,* a State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China b Research Center of Engineering Thermophysics, North China Electric Power University, Beijing, 102206, China c Beijing Key Laboratory of Membrane Science and Technology & College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, PR China d Office of Laboratory Safety Administration, Beijing University of Technology, Beijing 100124, China * Corresponding author, Tel./Fax: +86-10-6443-3570, E-mail: [email protected], [email protected] 1 COSMO-RS Computation COSMOtherm allows for simple and efficient processing of large numbers of compounds, i.e., a database of molecular COSMO files; e.g. the COSMObase database. COSMObase is a database of molecular COSMO files available from COSMOlogic GmbH & Co KG. Currently COSMObase consists of over 2000 compounds including a large number of industrial solvents plus a wide variety of common organic compounds. All compounds in COSMObase are indexed by their Chemical Abstracts / Registry Number (CAS/RN), by a trivial name and additionally by their sum formula and molecular weight, allowing a simple identification of the compounds. We obtained the anions and cations of different ILs and the molecular structure of typical N-compounds directly from the COSMObase database in this manuscript. -
Semiempirical Quantum-Chemical Methods Max-Planck-Institut Für
Max-Planck-Institut für Kohlenforschung This is the peer reviewed version of the following article: WIREs Comput. Mol. Sci. 4, 145-157 (2014), which has been published in final form at https://doi.org/10.1002/wcms.1161. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self- Archived Versions. Semiempirical quantum-chemical methods Walter Thiel Max-Planck-Institut für Kohlenforschung Kaiser-Wilhelm-Platz 1, 45470 Mülheim, Germany [email protected] Abstract The semiempirical methods of quantum chemistry are reviewed, with emphasis on established NDDO-based methods (MNDO, AM1, PM3) and on the more recent orthogonalization-corrected methods (OM1, OM2, OM3). After a brief historical overview, the methodology is presented in non- technical terms, covering the underlying concepts, parameterization strategies, and computational aspects, as well as linear scaling and hybrid approaches. The application section addresses selected recent benchmarks and surveys ground-state and excited-state studies, including recent OM2- based excited-state dynamics investigations. Introduction Quantum mechanics provides the conceptual framework for understanding chemistry and the theoretical foundation for computational methods that model the electronic structure of chemical compounds. There are three types of such approaches: Quantum-chemical ab initio methods provide a convergent path to the exact solution of the Schrödinger equation and can therefore give “the right answer for the right reason”, but they are costly and thus restricted to relatively small molecules (at least in the case of the highly accurate correlated approaches). Density functional theory (DFT) has become the workhorse of computational chemistry because of its favourable price/performance ratio, allowing for fairly accurate calculations on medium-size molecules, but there is no systematic path of improvement in spite of the first-principles character of DFT. -
Starting SCF Calculations by Superposition of Atomic Densities
Starting SCF Calculations by Superposition of Atomic Densities J. H. VAN LENTHE,1 R. ZWAANS,1 H. J. J. VAN DAM,2 M. F. GUEST2 1Theoretical Chemistry Group (Associated with the Department of Organic Chemistry and Catalysis), Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands 2CCLRC Daresbury Laboratory, Daresbury WA4 4AD, United Kingdom Received 5 July 2005; Accepted 20 December 2005 DOI 10.1002/jcc.20393 Published online in Wiley InterScience (www.interscience.wiley.com). Abstract: We describe the procedure to start an SCF calculation of the general type from a sum of atomic electron densities, as implemented in GAMESS-UK. Although the procedure is well known for closed-shell calculations and was already suggested when the Direct SCF procedure was proposed, the general procedure is less obvious. For instance, there is no need to converge the corresponding closed-shell Hartree–Fock calculation when dealing with an open-shell species. We describe the various choices and illustrate them with test calculations, showing that the procedure is easier, and on average better, than starting from a converged minimal basis calculation and much better than using a bare nucleus Hamiltonian. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 926–932, 2006 Key words: SCF calculations; atomic densities Introduction hrstuhl fur Theoretische Chemie, University of Kahrlsruhe, Tur- bomole; http://www.chem-bio.uni-karlsruhe.de/TheoChem/turbo- Any quantum chemical calculation requires properly defined one- mole/),12 GAMESS(US) (Gordon Research Group, GAMESS, electron orbitals. These orbitals are in general determined through http://www.msg.ameslab.gov/GAMESS/GAMESS.html, 2005),13 an iterative Hartree–Fock (HF) or Density Functional (DFT) pro- Spartan (Wavefunction Inc., SPARTAN: http://www.wavefun. -
Intro Bonding and Properties-2016-4U
Introduction to Bonding and Properties of Ionic and Molecular Covalent Compounds SCH4U_2016 1. Ionic Bonding - Ionic solids are generally stable and the bonds are relatively strong. - electrostatic attraction between oppositely charged ions forming a 3-D crystalline lattice structure - crystal lattice energy is the energy liberated when one mole of an ionic crystal is formed from the gaseous ions, high stability reached when energy is lost. Properties - do not conduct an electric current in the solid state, why? - in the liquid phase, i.e when molten, they are relatively good conductor of an electric current, why? - when soluble in water form good electrolytes, why? - relatively high M.P. and B.P. (>500°C, >100°C) - do not readily vaporize at room temperatures. These solids have relatively low volatility, low vapour pressure, this also indicates that a.... - brittle, easily broken under stress, why? 2. MOLECULAR CRYSTALS Covalent bonding, the sharing of electrons is known as an intra molecular force. Properties - neither solids nor liquids conduct an electric current. This indicates ... - many exist as gases at room temperature or as volatile solids and liquids, indicating ... - M.P. and B.P. are relatively low, thus indicating ... - Solids are soft and waxy - Large amount of energy required to decompose in simple substance, indicating ... Covalent Bonding How do these work? Covalent bonding occurs between atoms that have quite high electronegativities, i.e. between two non- metals. Example: H + H sssssd H— H In covalent bonding the two atoms involved share some of their valence electrons. The attraction of the two nuclei for these shared electrons results in the atoms being bonded together. -
Computational Studies on Carbohydrates: I. Density Functional Ab Initio Geometry Optimization on Maltose Conformations
Computational Studies on Carbohydrates: I. Density Functional Ab Initio Geometry Optimization on Maltose Conformations F. A. MOMANY, J. L. WILLETT Plant Polymer Research, National Center for Agricultural Utilization Research, USDA, Agricultural Research Service, 1815 N. University St., Peoria, Illinois 61604 Received 10 September 1999; accepted 10 May 2000 ABSTRACT: Ab initio geometry optimization was carried out on 10 selected conformations of maltose and two 2-methoxytetrahydropyran conformations using the density functional denoted B3LYP combined with two basis sets. The 6-31G∗ and 6-311CCG∗∗ basis sets make up the B3LYP/6-31G∗ and B3LYP/6-311CCG∗∗ procedures. Internal coordinates were fully relaxed, and structures were gradient optimized at both levels of theory. Ten conformations were studied at the B3LYP/6-31G∗ level, and five of these were continued with ∗∗ full gradient optimization at the B3LYP/6-311CCG level of theory. The details of the ab initio optimized geometries are presented here, with particular attention given to the positions of the atoms around the anomeric center and the effect of the particular anomer and hydrogen bonding pattern on the maltose ring structures and relative conformational energies. The size and complexity of the hydrogen-bonding network prevented a rigorous search of conformational space by ab initio calculations. However, using empirical force fields, low-energy conformers of maltose were found that were subsequently gradient optimized at the two ab initio levels of theory. Three classes of conformations were studied, as defined by the clockwise or counterclockwise direction of the hydroxyl groups, or a flipped conformer in which the -dihedral is rotated by ∼180◦.Different combinations of ! side-chain rotations gave energy differences of more than 6 kcal/mol above the lowest energy structure found. -
The Molpro Quantum Chemistry Package
The Molpro Quantum Chemistry package Hans-Joachim Werner,1, a) Peter J. Knowles,2, b) Frederick R. Manby,3, c) Joshua A. Black,1, d) Klaus Doll,1, e) Andreas Heßelmann,1, f) Daniel Kats,4, g) Andreas K¨ohn,1, h) Tatiana Korona,5, i) David A. Kreplin,1, j) Qianli Ma,1, k) Thomas F. Miller, III,6, l) Alexander Mitrushchenkov,7, m) Kirk A. Peterson,8, n) Iakov Polyak,2, o) 1, p) 2, q) Guntram Rauhut, and Marat Sibaev 1)Institut f¨ur Theoretische Chemie, Universit¨at Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany 2)School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom 3)School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom 4)Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany 5)Faculty of Chemistry, University of Warsaw, L. Pasteura 1 St., 02-093 Warsaw, Poland 6)Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States 7)MSME, Univ Gustave Eiffel, UPEC, CNRS, F-77454, Marne-la- Vall´ee, France 8)Washington State University, Department of Chemistry, Pullman, WA 99164-4630 1 Molpro is a general purpose quantum chemistry software package with a long devel- opment history. It was originally focused on accurate wavefunction calculations for small molecules, but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding and anharmonic vibrational spectra. -
Massive-Parallel Implementation of the Resolution-Of-Identity Coupled
Article Cite This: J. Chem. Theory Comput. 2019, 15, 4721−4734 pubs.acs.org/JCTC Massive-Parallel Implementation of the Resolution-of-Identity Coupled-Cluster Approaches in the Numeric Atom-Centered Orbital Framework for Molecular Systems † § † † ‡ § § Tonghao Shen, , Zhenyu Zhu, Igor Ying Zhang,*, , , and Matthias Scheffler † Department of Chemistry, Fudan University, Shanghai 200433, China ‡ Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Science, Fudan University, Shanghai 200433, China § Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany *S Supporting Information ABSTRACT: We present a massive-parallel implementation of the resolution of identity (RI) coupled-cluster approach that includes single, double, and perturbatively triple excitations, namely, RI-CCSD(T), in the FHI-aims package for molecular systems. A domain-based distributed-memory algorithm in the MPI/OpenMP hybrid framework has been designed to effectively utilize the memory bandwidth and significantly minimize the interconnect communication, particularly for the tensor contraction in the evaluation of the particle−particle ladder term. Our implementation features a rigorous avoidance of the on- the-fly disk storage and excellent strong scaling of up to 10 000 and more cores. Taking a set of molecules with different sizes, we demonstrate that the parallel performance of our CCSD(T) code is competitive with the CC implementations in state-of- the-art high-performance-computing computational chemistry packages. We also demonstrate that the numerical error due to the use of RI approximation in our RI-CCSD(T) method is negligibly small. Together with the correlation-consistent numeric atom-centered orbital (NAO) basis sets, NAO-VCC-nZ, the method is applied to produce accurate theoretical reference data for 22 bio-oriented weak interactions (S22), 11 conformational energies of gaseous cysteine conformers (CYCONF), and 32 Downloaded via FRITZ HABER INST DER MPI on January 8, 2021 at 22:13:06 (UTC). -
Lawrence Berkeley National Laboratory Recent Work
Lawrence Berkeley National Laboratory Recent Work Title From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape. Permalink https://escholarship.org/uc/item/4sm897jh Journal Chemical reviews, 121(8) ISSN 0009-2665 Authors Kowalski, Karol Bair, Raymond Bauman, Nicholas P et al. Publication Date 2021-04-01 DOI 10.1021/acs.chemrev.0c00998 Peer reviewed eScholarship.org Powered by the California Digital Library University of California From NWChem to NWChemEx: Evolving with the computational chemistry landscape Karol Kowalski,y Raymond Bair,z Nicholas P. Bauman,y Jeffery S. Boschen,{ Eric J. Bylaska,y Jeff Daily,y Wibe A. de Jong,x Thom Dunning, Jr,y Niranjan Govind,y Robert J. Harrison,k Murat Keçeli,z Kristopher Keipert,? Sriram Krishnamoorthy,y Suraj Kumar,y Erdal Mutlu,y Bruce Palmer,y Ajay Panyala,y Bo Peng,y Ryan M. Richard,{ T. P. Straatsma,# Peter Sushko,y Edward F. Valeev,@ Marat Valiev,y Hubertus J. J. van Dam,4 Jonathan M. Waldrop,{ David B. Williams-Young,x Chao Yang,x Marcin Zalewski,y and Theresa L. Windus*,r yPacific Northwest National Laboratory, Richland, WA 99352 zArgonne National Laboratory, Lemont, IL 60439 {Ames Laboratory, Ames, IA 50011 xLawrence Berkeley National Laboratory, Berkeley, 94720 kInstitute for Advanced Computational Science, Stony Brook University, Stony Brook, NY 11794 ?NVIDIA Inc, previously Argonne National Laboratory, Lemont, IL 60439 #National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6373 @Department of Chemistry, Virginia Tech, Blacksburg, VA 24061 4Brookhaven National Laboratory, Upton, NY 11973 rDepartment of Chemistry, Iowa State University and Ames Laboratory, Ames, IA 50011 E-mail: [email protected] 1 Abstract Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. -
Inter and Intra Molecular Forces
Properties of Solutions Why do things Melt or boil? Made by Schweitzer 10-25-04 What factors affect whether a substance will be a solid, liquid or a gas? Simple…Attraction The more attraction there are between the atoms the more likely they will be a liquid or a solid. If there isn’t any attraction then they will be a gas. Think of these attractions like glue. The more glue the harder it is to separate. Therefore higher boiling points and more likely to be a liquid or even solid at room temperature. Types of Solids Type of solid is determined by type of bond Ionic: metal= Non-metal Covalent: non-metal = non-metal Metallic: metals Network covalent: only C, Si, Ge Types of Bonds Ionic Very strong bond. Results in a solid with very high melting points. High Attractions are due to + and negative ions bundled together in a lattice crystal. Lattice Crystal / Lattice Energy Energy that is tied up in crystal structure. Greater the difference of charge the stronger the crystal structure. +1…-1 vs. +3…-3 Atomic radius Greater distance lower attraction What about the melting point of these substances? Compound NaF NaCl NaBr NaI MgO Why the difference? Melting Point Lattice Energy Compound (Centigrade) (kcal/mol) NaF 988 -201 NaCl 801 -182 NaBr 790 -173 NaI 660 -159 MgO 2800 -3938 Why the difference? Interionic Lattice Melting Point Atomic Compound Distance Energy (Centigrade) Radius and (Angstroms) (kcal/mol) Differnce of charge NaF 2.31 988 -201 The larger the distance NaCl 2.79 801 -182 between nuclei the lower the NaBr 2.94 790 -173 attraction between atoms NaI 3.18 660 -159 MgO 3.0 2800 -3938 Atomic radius Summary of Ionic compounds When you melt ionic compounds you are breaking an ionic bond! Very hard Factors affecting ionic bonds. -
Faster. Smarter. Just Better
AMPAC Faster. Smarter. Just better. Feature AMPAC 9 MOPAC 2007 Graphical User Interface (GUI) Molecule Building / Viewing ▪ Visual display of properties, surfaces, MOs ▪ Animation of reaction coordinates and vibrations ▪ Gaussian03 – shares common interface ▪ Graphic images for publication ▪ Submit and manage jobs from the GUI ▪ Read pdb files and accurately complete hydrogens ▪ Semiempirical Methods AM1, MNDO, MINDO3, PM3, MNDO/d, RM1, PM6 ▪ ▪ SAM1 (transition metals Fe and Cu), MNDOC ▪ Geometry Optimization and SCF Convergence Automatic Heuristic SCF Convergence ∆ ▪ RHF/UHF ▪ ▪ TRUSTE and TRUSTG geometry optimization ∆ ▪ ▪ Eigenvector Following (EF) ▪ CHN and LTRD transition state location methods ∆ ▪ PATH, IRC for potential surfaces and reaction pathways ▪ Reaction pathway definition ▪ GRID 2D reaction pathway investigation ▪ LFORCE for rapid characterization of TSs and minima ▪ Sparse matrix method for large molecules * ▪ Additional Methods Configuration Interaction (CI) ∆ ▪ Selected State Optimized CI ∆ ▪ Analytic CI Gradients and higher spin multiplicities (20) ∆ ▪ Simulated Annealing for Multiple Minima Searches ▪ AMSOL Method for Solvated Molecules ▪ COSMO Solvation Method ▪ ▪ Tomasi Solvation Method ▪ Property Calculations Thermodynamic Properties ▪ ▪ Unpaired Electron Spin Density ▪ ▪ Population Analysis: Coulson / Mulliken / ESP ▪ ▪ Non-linear Optical Properties ▪ Polymers and solid states ▪ Limited molecular dynamics ▪ Compatibility and Support Fully Compatible with CODESSA™ QSAR Program ▪ Multiple File formats for read/write (mol, mol2, G03, pdf, CIF) ▪ Manual: new, fully updated and indexed in hypertext format ▪ Updating and addition of new features regularly ▪ Customer Support - knowledgeable and available ▪ Generous site-licensing for academics ▪ * Under active development. Common feature enhanced and improved in AMPAC. ∆ AMPAC much faster and more reliable . -
Semiemprical Methods Chapter 5 Semiemprical Methods
Semiemprical Methods Chapter 5 Semiemprical Methods Because of the difficulties in applying ab initio methods to medium and large molecules, many semiempirical methods have been developed to treat such molecules. The earliest semiempirical methods treated only the π electrons of conjugated molecules. In the π-electron approximation, the nπ π electrons are treated separately by incorporating the effects of the σ electrons and the nuclei into some sort of effective π- electron Hamiltonian Ĥπ (recall the similar valence-electron approximation where Vi is the potential energy of the ith π electron in the field produced by the nuclei and the σ electrons. The core is everything except the π electrons. The most celebrated semiempirical π-electron theory is the Hückel molecular-orbital (HMO) method, developed in the 1930s to treat planar conjugated hydrocarbons. Here the π-electron Hamiltonian is approximated by the simpler form where Ĥeff(i) incorporates the effects of the π-electron repulsions in an average way. In fact the Hückel method does not specify any explicit form for Ĥeff(i). Since the Hückel π-electron Hamiltonian is the sum of one-electron Hamiltonians, a separation of variables is possible. We have The wave function takes no account of spin or the antisymmetry requirement. To do so, we must put each electron in a spin-orbital ui=ii. The wave function π is then written as a Slater determinant of spin-orbitals. Since Ĥeff(i) is not specified, there is no point in trying to solve above eq. directly. Instead, the variational method is used. The next assumption in the HMO method is to approximate the π MOs as LCAOs.