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Potential Energy Surfaces Governing Chemical Reactions Involving Carbon, Oxygen and Hydrogen Sotiris S Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1991 Potential energy surfaces governing chemical reactions involving carbon, oxygen and hydrogen Sotiris S. Xantheas Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Physical Chemistry Commons Recommended Citation Xantheas, Sotiris S., "Potential energy surfaces governing chemical reactions involving carbon, oxygen and hydrogen " (1991). Retrospective Theses and Dissertations. 9602. https://lib.dr.iastate.edu/rtd/9602 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfihn master. UMI 61ms the text directly from the original or copy submitted. Thias, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9126270 Potential energy surfaces governing chemical reactions involving carbon, oxygen and hydrogen Xaiitheas, Sotiris S., Ph.D. Iowa State University, 1991 UMI 300N.ZeebRd. Ann Arbor, MI 48106 Potential Energy Surfaces Governing Chemical Reactions Involving Carbon, Oxygen and Hydrogen by Sotiris S. Xantheas A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department: Chemistry Major: Physical Chemistry Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. ror the Major Department Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1991 Copyright ® Sotiris S. Xantheas, 1991. All rights reserved. ii TABLE OF CONTENTS Page I. INTRODUCTION 1 II. POTENTIAL ENERGY SURFACE OF THE GROUND STATE OF O3 9 A. Introduction 9 B. Experimental Data and Previous Theoretical Calculations 10 C. Method of Calculation 13 D. The Lowest Singlet States in C2^ 14 E. The C2y Potential Energy Surface for the ^Aj^ State 17 1. The ring minimum 17 2. Location of the transition state for the ring opening 18 3. The intersection between the l-^A^ and 2-^k-^ surfaces 23 F. Exploration of Parts of the Complete Ground State ^A' PES 36 1. Usefulness of the ^A' ground state PES 36 2. The panel for ^-116.3° 38 G. Conclusions AO III. POTENTIAL ENERGY SURFACE OF THE GROUND STATE OF CO2 43 A. Introduction 43 B. Method of Calculation 44 C. Mapping of the Complete Ground State ^A' PES 45 D. The Lowest Singlet States in C2y 47 E. The C2y Potential Energy Surface for the ^A^ State 50 1. The ring minimum 50 2. PES governing the ring opening process 54 3. Location of the ring opening transition state 56 F. Exploration of the Complete Ground State PES E(^,R]^,R2) 58 ill 1. Introduction 58 2. The panel for ^-94° 61 3. The panel for ^-180°: collinear approach of 0(^D) to COC^S"*") 66 4. The panel for 4-0°: collinear C(3p)+02(^2g") C0(^S+)+0(1d) 70 G. Conclusions 72 IV. THE RING OPENING OF CYCLOPROPYLIDENE TO ALLENE 74 A. Key Regions of the Singlet Ring Opening Surface 74 1. Introduction 74 2. Method of calculation 78 2.1. Scope of calculations 78 2.2. Basis sets 79 2.3. Configuration spaces 81 3. Critical regions 83 3.1. The ring opening transition state 83 3.2. The other critical points 90 4. Reaction paths 98 4.1. The steepest descent: qualitatively 98 4.2. The steepest descent: quantitatively 102 From R to TS 102 From TS to CR 104 From CR to TS* 107 From TS* to A 107 From I/CR to P/P' 107 5. The intersecting coordinate subspace (ICS) 108 5.1. Dimensionality 108 5.2. Linear approximation near CR 110 5.3. Determination of the linear approximation 113 5.4. Steepest descent lines near CR 114 5.5. Intersecting coordinate subspace & reduced energy surface 115 6. The free internal rotation of the CH2 groups 119 B. Ab-initio Interpretation of the Electronic Rearrangements in Terms of Quasiatomic Orbitals 123 1. Introduction 123 2. Method of analysis 125 2.1. Localized FORS MO's as molecule-adapted deformed mini­ mal basis-set atomic orbitals; quasi-atomic orbitals 125 2.2. Density and population analysis of a FORS wavefunction 127 2.3. Configurational analysis of a FORS wavefunction 132 2.4. The localization process 134 3. The ring opening barrier 135 3.1. Quasi-atomic FORS MO's 135 Reactant 136 Transition state 138 iv 3.2. Population and bond order analysis 139 Reactant 139 Transition state 144 3.3. FORS configuration analysis 148 Reactant 149 Transition state 151 4. The aliéné isomerization barrier 152 4.1. Staggered linear aliéné 153 4.2. Bent planar aliéné (^-133.3° ) 158 4.3. Symmetry considerations, conical intersection between the two transition states 164 5. The free internal cogwheel motion 165 5.1. Quasi-atomic FORS MO's 166 («1, - (90° ,0° ) 166 (gi - *2 - 45" ) 168 («1, «2> - <0° ,90°) 171 5.2. Analysis for iS^, «2)-(90° ,0° ) and (fi^, 62>-(0° ,90°) 171 Population and bond order analysis 171 Configurational analysis 181 5.3. Analysis for SyS2~^^° 182 Population and bond order analysis 182 Configurational analysis 185 6. The population and configuration analysis for the extended basis set calculations 186 6.1. Quasiatomic character of localized MO's 187 6.2. Population analysis 189 6.3. Configurational analysis 193 7. Summary and Conclusions 193 V. REFERENCES 197 VI. ACKNOWLEDGEMENTS 201 1 I. INTRODUCTION Computational Chemistry has evolved over the last few years into a powerful tool which can accurately describe both atomic and molecular properties in very close agreement with experimental observations. Although the basic ideas of quantum mechanics were set in the beginning of this century, definite difficulties in their application to real systems prevented theorists from making early computational breakthroughs. This problem was recognized by Dirac (1929) who wrote: "The underlying physical laws necessary for the mathematical theory of the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble". The inability to solve the exact equations analytically yielded a plethora of approximate solutions. These are due to the fact that in order for the quantum mechanical ideas to be applied to real systems various approximations need to be employed which in turn introduce errors to the values of the computed physical quantities. Furthermore the crudity of these approximations and as a consequence the magnitude of the errors they introduce increase rapidly with the size of the system. The approximations used in molecular modelling are tested in cases where experimental data are available - usually compared against spectroscopic measurements or X-ray diffraction studies - at nuclear configurations describing stable and/or metastable species of real molecules. By comparing the experimental data with the theoretical predictions, theoreticians were able to build over the years a level of 2 theory which although is far from being simple and understandable by someone without explicit knowledge of advanced applied mathematical techniques, has succeeded in providing the theoretical background needed to give some insight into important chemical concepts such as molecular bonding, reactivity, reaction mechanisms as well as equilibrium geometries and amounts of energy needed or released during various chemical reactions. By testing the validity of the theoretical approximations in cases where experimental data are available (i.e. ground states of small molecules) one can furthermore employ them in a predictive manner in order to speculate about species lacking direct experimental verification (i.e. short-life intermediates). The latter consist of structures for transition states or other metastable species occurring during chemical reactions, yielding therefore energy barriers, reaction paths, rates as well as the energy contents of various chemical processes. In order to achieve these goals it is desirable to be able to visualize the way the nuclei move around during a chemical reaction as well as the energy content associated with these nuclear motions. One of the most important approximations used in electronic structure calculations which has almost universal validity is the one proposed by Born and Oppenheimer (1927). It states that due to the fact that the electrons are much lighter than the nuclei, the latter can be consider standing still. Therefore it is possible to uncouple the theoretical treatment of the electronic and nuclear motions.
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