Department of Physics, Chemistry and Biology Bachelor’s Thesis Chemical bond analysis in the ten-electron series Thomas Fransson LITH-IFM-G-EX–09/2112–SE Department of Physics, Chemistry and Biology Link¨opings universitet, SE-581 83 Link¨oping, Sweden Bachelor’s Thesis LITH-IFM-G-EX–09/2112–SE Chemical bond analysis in the ten-electron series Thomas Fransson Adviser: Patrick Norman IFM Examiner: Patrick Norman IFM Link¨oping, 4 June, 2009 Avdelning, Institution Datum Division, Department Date Computational Physics 2009-06-04 Department of Physics, Chemistry and Biology Link¨opings universitet, SE-581 83 Link¨oping, Sweden Spr˚ak Rapporttyp ISBN Language Report category — Svenska/Swedish Licentiatavhandling ISRN ⊠ ⊠ Engelska/English Examensarbete LITH-IFM-G-EX–09/2112–SE C-uppsats Serietitel och serienummer ISSN D-uppsats Title of series, numbering Ovrig¨ rapport — URL f¨or elektronisk version Titel Title Chemical bond analysis in the ten-electron series F¨orfattare Thomas Fransson Author Sammanfattning Abstract This thesis presents briefly the application of quantum mechanics on systems of chemical interest, i.e., the field of quantum chemistry and computational chem- istry. The molecules of the ten-electron series, hydrogen fluoride, water, ammonia, methane and neon, are taken as computational examples. Some applications of quantum chemistry are then shown on these systems, with emphasis on the na- ture of the molecular bonds. Conceptual methods of chemistry and theoretical chemistry for these systems are shown to be valid with some restrictions, as these interpretations does not represent physically measurable entities. The orbitals and orbital energies of neon is studied, the binding van der Waals- interaction resulting in a Ne2 molecule is studied with a theoretical bond length of 3.23 A˚ and dissociation energy of 81.75 µEh. The equilibrium geometries of FH, H2O, NH3 and CH4 are studied and the strength and character of the bonds involved evaluated using bond order, dipole moment, Mulliken population analysis and L¨owdin population analysis. The concept of electronegativity is studied in the context of electron transfer. Lastly, the barrier of inversion for NH3 is studied, with an obtained barrier height of 8.46 mEh and relatively constant electron transfer. Nyckelord computational chemistry, computational physics, quantum chemistry, bond anal- Keywords ysis, electron population, electron transfer Abstract This thesis presents briefly the application of quantum mechanics on systems of chemical interest, i.e., the field of quantum chemistry and computational chem- istry. The molecules of the ten-electron series, hydrogen fluoride, water, ammonia, methane and neon, are taken as computational examples. Some applications of quantum chemistry are then shown on these systems, with emphasis on the na- ture of the molecular bonds. Conceptual methods of chemistry and theoretical chemistry for these systems are shown to be valid with some restrictions, as these interpretations does not represent physically measurable entities. The orbitals and orbital energies of neon is studied, the binding van der Waals- interaction resulting in a Ne2 molecule is studied with a theoretical bond length of 3.23 A˚ and dissociation energy of 81.75 µEh. The equilibrium geometries of FH, H2O, NH3 and CH4 are studied and the strength and character of the bonds involved evaluated using bond order, dipole moment, Mulliken population analysis and L¨owdin population analysis. The concept of electronegativity is studied in the context of electron transfer. Lastly, the barrier of inversion for NH3 is studied, with an obtained barrier height of 8.46 mEh and relatively constant electron transfer. v Acknowledgements First of all, I woulds like to thank my supervisor Patrick Norman for the oppor- tunity of completing this diploma work and for excellent supervision. It has been a great experience. I would also like to thank all the other people of Computa- tional Physics at IFM for the great welcome, the time discussing physics, the time discussing less serious things at breaks, floorball sessions and more. I wish to thank all my friends for simply being my friends and for weathering through this time where I may not always have been the most present person, thanks. Last but not least, I wish to thank my family. vii Contents 1 Introduction 1 1.1 Quantum chemistry . 1 1.2 Relevant elements and molecules . 2 2 Electronic structure theory 3 2.1 Many-particlesystems ......................... 3 2.1.1 The Born–Oppenheimer approximation . 4 2.1.2 Antisymmetry ......................... 4 2.2 The Hartree–Fock approximation . 5 2.3 Basisconsideration........................... 5 2.4 Molecular orbitals and applications . 6 2.4.1 Construction of molecular orbitals . 6 2.4.2 Molecular orbitals . 8 2.4.3 Electron density . 8 2.4.4 Potential energy surface . 10 2.5 Electron correlated methods . 10 2.5.1 Post-Hartree–Fock methods . 10 2.5.2 Density functional theory . 11 2.5.3 Hybridmethods ........................ 11 2.6 Molecular properties . 11 3 Computational details 13 3.1 Programsused ............................. 13 3.2 Basissetsused ............................. 13 3.3 Methods used . 14 4 Results and discussion 15 4.1 Neonmonomer ............................. 15 4.1.1 Orbitals............................. 15 4.1.2 Electron density . 15 4.1.3 Orbital energies . 16 4.2 Neondimer ............................... 19 4.2.1 Basissetsuperpositionerror . 19 4.2.2 Hartree–Fock .......................... 20 4.2.3 Second-order Møller–Plesset . 20 ix x Contents 4.2.4 Perturbation theory . 20 4.2.5 Results ............................. 20 4.3 Molecular equilibrium geometries . 22 4.4 Orbitalanalysis............................. 22 4.4.1 Hybridization.......................... 23 4.4.2 Natural atomic orbitals . 23 4.5 Bondorder ............................... 25 4.6 Bondcharacter ............................. 26 4.6.1 Electronegativity . 27 4.6.2 Dipolemoment ......................... 27 4.6.3 Mulliken population analysis . 28 4.6.4 L¨owdin population analysis . 28 4.6.5 Results ............................. 29 4.7 Inversionofammonia ......................... 30 4.7.1 Potential barrier . 31 4.7.2 Electron distribution . 33 5 Conclusions 35 Bibliography 37 Chapter 1 Introduction 1.1 Quantum chemistry The branch of physics or theoretical chemistry known as quantum chemistry at- tempts to, as far as possible, explain chemical phenomenas by physical laws. This is done considering the laws of quantum mechanics, which are most prominent on a small scale, such as the atomic scale, even though the govern all scales of interactions. To fully evaluate the behaviour of matter at the intramolecular level, a treat- ment utilizing non-relativistic quantum mechanics will prove insufficient. This is due to the fact that the electrons in the vicinity of nuclei (especially for the heav- ier elements), acts by such a strong potential that only a relativistic treatment is correct. This thesis has not included relativistic corrections apart from a study of the ionization energies of neon. The relativistic corrections will in most cases act as a perturbation and can be treated as such, it will not greatly alter any of the presented results. The present works has also disregarded any strong, weak or gravitational in- teractions. Not including gravitational interaction is valid as its strength relative to electromagnetic interaction is several tens of order weaker. Strong and weak interactions, however, are more of the scale of electromagnetic interactions, but the reach is very small (10−15 and 10−18 meter, respectively) and as molecular analysis works at a scale of about 10−10 m, it will not interfere [1, 2]. Quantum chemical calculations and theories have a variety of uses in modern science. Depending on the methods used, examples of applications are: Calculation of equilibrium geometries and energies [3, 4, 5]. Accuracy may • surpass experiments [6]. Study of chemical reactions and formation of molecule [7, 8], including reac- • tions too unstable for experiment [9]. 1 2 Introduction Determination of molecular properties and construction of molecules with • desired properties [10, 11]. This project have utilized ab initio methods, where no prior knowledge of the system of interest is assumed, and semi-empirical methods where some prior knowledge from ab initio calculations or experiment is assumed. Especially the ab initio methods are computationally very demanding, but also semi-empirical methods that consider the nuclei and electrons can result in to large calculations for macromolecules, e.g. proteins. Due to this there also exists methods that consider the molecular systems to be composed of atoms (“balls”) and molecular bonds (“sticks”). Electrons are not explicitly considered. These methods, such as molecular mechanics and molecular dynamics, are less demanding for larger systems and can thus be very useful in simulations of e.g. protein folding. 1.2 Relevant elements and molecules Table 1.1. Atoms treated. Atomic mass given in atomic mass units, u. Element Symbol Configuration Atomic mass Electronegativity Hydrogen H 1s 1.008 2.1 Carbon C 1s22s22p2 12.011 2.5 Nitrogen N 1s22s22p3 14.007 3.0 Oxygen O 1s22s22p4 15.999 3.5 Fluorine F 1s22s22p5 18.998 4.0 Neon Ne 1s22s22p6 20.180 - Values are obtained from [2]. Electronegativity according to Pauling [12]. The elements and molecules considered in the present work are listed in Table 1.1 and Table 1.2, respectively. Observe that hydrogen fluoride