ABSTRACT GAFF, JOHN FRANCIS. Development of Methods to Simulate Resonance Raman Spectra Employing Density Functional Theory: Application to the Investigation of the Chemical Mechanism of Surface Enhanced Raman Scattering by Examination of Pyridine on Silver Clusters. (Under the direction of Dr. Stefan Franzen). A method for the calculation of resonance Raman cross sections is presented on the basis of structural differences between optimized ground and excited state geometries using density functional theory. A vibrational frequency calculation of the molecule is employed to obtain normal coordinate displacements for the modes of vibration. The excited state displacement relative to the ground state can be calculated in the normal coordinate basis by means of a linear transformation from a Cartesian basis to the normal one. The displacements in normal coordinates are then scaled relative to the classical turning point of the molecule to calculate dimensionless displacements for use in the two – time – correlator formalism for the calculation of resonance Raman spectra at an arbitrary temperature. This method is valid for Franck – Condon active modes within the harmonic approximation and is validated by calculation of resonance Raman cross sections and absorption spectra for nitrate ion, chlorine dioxide, trans – stilbene, 1, 3, 5 – cycloheptatriene, and the aromatic amino acids. This method permits significant gains in efficiency of calculating resonance Raman cross sections form first principles and, consequently, permits extension to large systems ( > 50 atoms). As an application, the chemical mechanism of surface enhanced Raman scattering (SERS) was investigated by studying super – molecules consisting of Ag clusters with a bound pyridine, Agn – Pyridine (n = 2, 4, 8, 14, and 20). Calculation of the excited state displacements of pyridine on Ag clusters were applied to the two – time – correlator formalism for the calculation of resonance Raman cross sections. The goal of the study is to understand the contribution of resonance Raman scattering to the chemical mechanism enhancement in SERS. Based on three theoretical observations, it is apparent that resonance Raman enhancement is a major contributor to the chemical enhancements observed in SERS when treating the silver clusters with bound pyridine as a super – molecule. First, structural changes in pyridine observed in the excited state displacement for all silver – pyridine molecules were essentially equivalent, and similar to those observed for the 168 nm transition of free pyridine. Secondly, the excited state displacement leads to resonance Raman scattering with cross sections on the magnitude of ~ 109 Å2/molecule. Thirdly, enhancements of the magnitude observed for a typical resonance Raman experiment, ~ 103 – 106, were calculated for all silver – pyridine clusters. Given that traditional SERS effects range from 103 – 106, the study suggests that SERS may be dominated by the contribution from resonance Raman. This study does not rule out the role of the electromagnetic enhancement, but rather suggests that the chemical enhancement should be reconsidered as a significant contribution. Development of Methods to Simulate Resonance Raman Spectra Employing Density Functional Theory: Application to the Investigation of the Chemical Mechanism of Surface Enhanced Raman Scattering by Examination of Pyridine on Silver Clusters. by John Francis Gaff A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Chemistry Raleigh, North Carolina 2011 APPROVED BY: _______________________________ Stefan Franzen Advisor, Committee Chair _______________________________ ______________________________ David A. Shultz Tatyana I. Smirnova ________________________________ ________________________________ Jerry L. Whitten David E. Aspnes DEDICATION I am dedicating this dissertation to my fiancée, Emily Etter. Thank you for all the love and support that you have provided to me, in both times of good and bad. Also, to both of my parents, John and Jan Gaff, for without you this journey would not have been possible. Lastly, as a special dedication to my loving friend Lars Olson. ii BIOGRAPHY John Francis Gaff was born at Resurrection Hospital in Chicago Illinois on September 24th, 1976 to John and Jan Gaff. In October of 1986, he, his parents, and three sisters moved to the state of North Carolina. He began his education at North Carolina State University where he received his Bachelors of Science in chemistry. During his time as an undergraduate his interest in physical chemistry was piqued by Professor Stefan Franzen. Having left a lasting impact, John, immediately after graduation, enrolled into the Chemistry Graduate Program at NCSU to work in the Franzen group and pursue a graduate degree in computational chemistry. iii ACKNOWLEDGMENTS I would like to personally thank Dr. Stefan Franzen for the opportunity you gave me, for believing in me. I would like to also extend much appreciation to Dr. Bernard Delley of the Paul Scherrer Institute. You have bestowed upon me a great deal of knowledge, and taught me new ways of analytical thinking I thought not possible. I would also like to thank Dr. Simon Lappi for many insightful and helpful conversations. iv TABLE OF CONTENTS LIST OF TABLES ................................................................................................... ix LIST OF FIGURES ............................................................................................... xii Chapter 1 .............................................................................................................. 1 1.1 Introduction to Raman Scattering .................................................... 1 1.2 Theory of Resonance Raman Scattering ......................................... 5 1.3 Time-Dependent Theory of Resonance Raman Scattering ............. 13 1.4 Connection to Time – Correlator Formalism .................................... 21 1.5 References ...................................................................................... 24 Chapter 2 .............................................................................................................. 26 2.1 Introduction to Density Functional Theory ....................................... 26 2.2 Calculation Parameters ................................................................... 34 2.3 Description of Multi – Projection of Normal Modes .......................... 36 2.4 Ab Initio Calculation of Resonance Raman Cross Sections Based on Excited State Geometry Optimization .............................. 38 2.4.1 Motivation For New Technique ..................................................... 38 2.4.2 Methodology: Example Based on the Nitrate Ion ......................... 39 2.5 References ...................................................................................... 46 Chapter 3 .............................................................................................................. 49 3.1 Introduction ........................................................................................ 49 - 3.2 Nitrate Ion, NO3 .............................................................................. 52 3.3 Chlorine Dioxide, ClO2 ..................................................................... 57 v 3.4 Trans – stilbene ............................................................................... 61 3.5 1, 3, 5 – cycloheptatriene ................................................................. 66 3.6 Aromatic Amino Acids ...................................................................... 72 3.6.1 Toluene ........................................................................................ 73 3.6.2 para – cresol ................................................................................. 76 3.6.3 3 – methylindole ........................................................................... 80 3.7 Conclusion ....................................................................................... 84 3.8 References ...................................................................................... 86 Chapter 4 .............................................................................................................. 91 4.1 Introduction ...................................................................................... 91 4.2 Experimental Methods ..................................................................... 96 4.3 Results and Discussion ................................................................... 96 4.3.1 Pyridine ........................................................................................ 99 4.3.2 Pyr – (Ag)n Clusters .................................................................... 101 4.4 Conclusion ..................................................................................... 115 4.5 References .................................................................................... 117 Appendices ......................................................................................................... 124 Appendix A .......................................................................................................... 125 A.1 Comparison Against Analytical Gradient Method .......................... 125 A.2 Nitrate Ion ...................................................................................... 126 A.3 Chlorine Dioxide ...........................................................................