Graduate Theses, Dissertations, and Problem Reports 2011 Potential Energy Surface of Urea Xiaojian Mao West Virginia University Follow this and additional works at: https://researchrepository.wvu.edu/etd Recommended Citation Mao, Xiaojian, "Potential Energy Surface of Urea" (2011). Graduate Theses, Dissertations, and Problem Reports. 4750. https://researchrepository.wvu.edu/etd/4750 This Dissertation is protected by copyright and/or related rights. It has been brought to you by the The Research Repository @ WVU with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you must obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Dissertation has been accepted for inclusion in WVU Graduate Theses, Dissertations, and Problem Reports collection by an authorized administrator of The Research Repository @ WVU. For more information, please contact [email protected]. Potential Energy Surface of Urea Xiaojian Mao A dissertation submitted to the Eberly College of Arts and Sciences at West Virginia University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry Approved by Charles Jaff´e,Ph. D., Chair Alfred H. Stiller, Ph. D. Ken Showalter, Ph. D. Terry Gullion, Ph. D. John Penn, Ph. D. C. Eugene Bennett Department of Chemistry Morgantown, West Virginia 2011 Key word: urea; potential energy surface; ab initio Abstract Potential Energy Surface of Urea Xiaojian Mao Using MP2 methods with aug-cc-pVDZ basis set, the inversion and rotation potential energy surface (PES) of urea molecule were plotted and fitted into polynomials. Important conformations on the PES were located and characterized. Their connecting paths were examined. Both inversion and rotation energy barriers were calculated. It was showed there could exist more than one internal rotation path for a floppy molecule. The topology of the PES were characterized using graphical description and symmetry analysis. To my wife, Jing Zhu, and my parents, whose love is always with me iii Acknowledgements I would like to express my sincere appreciation and great gratitude to my advisor Dr. Charles Jaff´e.This work would not have been possible without his unfaltering support and encouragement. His inspiring encouragement, his guidance on this research, and his patience are the most important factors which help me through the graduate study. He is not only the advisor, but also a good friend. His help is not limited in chemistry and is extended to my daily life in Morgantown. Appreciation is also due to my committee members, Dr. Alfred H. Stiller, Dr. Ken Showalter, Dr. Terry Gullion, and Dr. John Penn for their precious time, guidance, suggestions, help and encouragement. I would also like to thank many people for their friendship and assistance in the chemistry department during these years while it is hard to name every individual. My very special appreciation goes to my wife, Jing Zhu, and my parents. Their love are the key to support me to overcome the obstacles during all these years. Finally, many thanks to the Department of Chemistry at West Virginia University for providing me uninterrupted financial support. iv Contents List of Figures viii List of Tables x 1 Introduction 1 1.1 Urea as a protein denaturing agent . 1 1.2 Urea aqueous solution . 2 1.3 Structure of urea molecules . 3 1.4 Goal of this research . 5 2 Method and Model 7 2.1 Coupling of Inversion and Rotation . 7 2.2 Inversion and Rotation Variables . 9 2.3 Plotting PES . 11 2.4 Computational Details . 11 2.4.1 GAMESS . 11 2.4.2 Basis Set . 12 2.4.3 Aug-cc-pVDZ Basis Set . 12 2.4.4 Calculation Level . 14 3 Two-dimensional Inversion Potential Energy Surface 15 v CONTENTS 3.1 Inversion PES . 15 3.1.1 Important conformations . 15 3.1.2 Hybridization of nitrogen atoms . 17 3.1.3 Inversion Barrier . 20 3.1.4 Population Map . 20 3.1.5 Dipole Moment . 21 3.2 Fitting inversion PES . 24 3.3 Normal Mode Analysis . 26 3.3.1 Degrees of Freedom . 26 3.3.2 Kinetic Energy Terms . 26 3.3.3 Potential Energy Terms . 28 3.3.4 Normal mode coordinates . 30 3.3.5 Rank-2 Saddle . 31 3.4 Two-dimensional Schr¨odingerEquation . 33 4 Four-dimensional Rotation Potential Energy Surface 39 4.1 Internal rotation PES . 39 4.2 Important conformations . 39 4.3 Dipole moments . 42 4.4 Internal rotation barrier . 43 4.4.1 Early results . 43 4.4.2 Internal rotation barrier . 43 4.4.3 Conjugation . 44 4.4.4 Rotation barrier of floppy molecules . 44 4.5 Fitting rotation PES . 45 5 Symmetry Analysis 46 5.1 Complete Permutation-inversion Group . 46 vi CONTENTS 5.2 Subsurfaces of PES . 46 5.3 Longuet-Higgins Group . 47 5.4 Longuet-Higgins Group of Urea . 48 5.5 Tunneling . 49 5.6 Electric Dipole Selection Rules . 53 5.7 Symmetry of inversion PES . 54 5.8 Symmetry of rotation PES . 54 5.9 Graphical Description . 55 5.10 Graphical Description of Urea PES . 55 6 Conclusion 59 Appendices 60 Appendix A Potential energy of urea fitting around conformation D 61 Appendix B Coefficients of fitted rotation PES of urea 63 References 65 vii List of Figures 1.1 Structure of urea in solid state, which shows an extensive hydrogen bond- ing network . 4 1.2 Structure of urea in gas state: solid NH bonds come out of the page and the NH dashed bonds go into the page . 5 2.1 Atom numbering for urea molecule . 8 3.1 Inversional potential energy surface of urea molecule . 16 3.2 A - global minimum, C2 ........................... 19 3.3 B - local minimum, Cs ............................ 19 3.4 C - rank-2 saddle, C2v ............................ 19 3.5 D - rank-1 saddle, C1 ............................. 19 3.6 Population map . 22 3.7 Mesomeric structures of urea molecule . 23 3.8 Ground state wave function of urea molecule from inversion potential . 35 3.9 Contour map of ground state wave function of urea molecule from inver- sion potential . 35 3.10 First excited state wave function of urea molecule from inversion potential 36 3.11 Contour map of first excited state wave function of urea molecule from inversion potential . 36 viii LIST OF FIGURES 3.12 Second excited state wave function of urea molecule from inversion po- tential . 37 3.13 Contour map of second excited state wave function of urea molecule from inversion potential . 37 3.14 Third excited state wave function of urea molecule from inversion potential 38 3.15 Contour map of third excited state wave function of urea molecule from inversion potential . 38 4.1 Rotational potential energy surface of urea molecule . 40 4.2 E - rank-2 saddle, C2v ............................ 41 4.3 F - rank-2 saddle, Cs ............................. 41 4.4 G - rank-2 saddle, C2v ............................ 41 4.5 H - rank-1 saddle, Cs ............................. 41 4.6 I - rank-2 saddle, Cs ............................. 41 5.1 Eight energetically equivalent global energy minimum conformations of urea molecule which are accessible to each others. 47 5.2 Atom numbering for urea molecule's permutation-inversion operation . 48 5.3 Elements of urea's permutation group: cont. 50 5.4 Elements of urea's permutation group: contd. 51 5.5 Graphic description of connections on PES of urea molecule . 56 5.6 Inversion paths on PES of urea molecule . 57 5.7 One-side rotation paths on PES of urea molecule . 57 5.8 Two-side rotation paths on PES of urea molecule . 57 ix List of Tables 2.1 Urea geometry optimization using different basis sets . 13 3.1 Important conformations in inversion PES of urea molecule . 18 3.2 Out-of plane angles of different urea molecule conformations in its inver- sion PES . 19 3.3 Dipole moment of urea molecules . 21 3.4 Coefficients of fitted inversion PES of urea . 25 3.5 Conventional internal coordinates of urea molecule . 26 3.6 Energy levels of urea molecule's inversion potential . 33 4.1 Out-of plane angle of different urea molecule conformations in its rota- tion PES . 42 4.2 Dipole moments of important conformations in rotation PES of urea molecule . 42 4.3 Important conformations in rotation PES of urea molecule . 43 4.4 CN bond lengths of important conformations in rotation PES of urea molecule . 44 5.1 Character Table of Longuet-Higgins Group of Urea While Inversion and Rotation Included . 52 5.2 Reducible representation of symmetric and antisymmetric levels . 53 x LIST OF TABLES 5.3 Character Table of Longuet-Higgins Group of Urea While Only Inversion Included . 54 5.4 Character Table of Longuet-Higgins Group of Urea While Only Rotation Included . 55 5.5 Number of important conformations in PES of urea molecule . 56 A.1 Coefficients of fitted PES of urea around conformation D . 62 B.1 Coefficients of fitted rotation PES of urea . 64 xi Chapter 1 Introduction Urea was the first organic compound prepared outside of a living organism in history. It was synthesized from ammonium sulfate and lead cyanate by W¨ohlerin 1828 [1]. This is marked as the demise of the vital force theory and the beginning of modern organic chemistry. Since then it has been the subject of interest in almost every branch of fundamental and applied chemistry research field. 1.1 Urea as a protein denaturing agent Although urea is structurally simple and has been investigated for such a long time, many of its properties are still not understood and draw a great amout of interest in many fields of chemistry.