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Benchmarking and Application of Density Functional Methods In BENCHMARKING AND APPLICATION OF DENSITY FUNCTIONAL METHODS IN COMPUTATIONAL CHEMISTRY by BRIAN N. PAPAS (Under Direction the of Henry F. Schaefer III) ABSTRACT Density Functional methods were applied to systems of chemical interest. First, the effects of integration grid quadrature choice upon energy precision were documented. This was done through application of DFT theory as implemented in five standard computational chemistry programs to a subset of the G2/97 test set of molecules. Subsequently, the neutral hydrogen-loss radicals of naphthalene, anthracene, tetracene, and pentacene and their anions where characterized using five standard DFT treatments. The global and local electron affinities were computed for the twelve radicals. The results for the 1- naphthalenyl and 2-naphthalenyl radicals were compared to experiment, and it was found that B3LYP appears to be the most reliable functional for this type of system. For the larger systems the predicted site specific adiabatic electron affinities of the radicals are 1.51 eV (1-anthracenyl), 1.46 eV (2-anthracenyl), 1.68 eV (9-anthracenyl); 1.61 eV (1-tetracenyl), 1.56 eV (2-tetracenyl), 1.82 eV (12-tetracenyl); 1.93 eV (14-pentacenyl), 2.01 eV (13-pentacenyl), 1.68 eV (1-pentacenyl), and 1.63 eV (2-pentacenyl). The global minimum for each radical does not have the same hydrogen removed as the global minimum for the analogous anion. With this in mind, the global (or most preferred site) adiabatic electron affinities are 1.37 eV (naphthalenyl), 1.64 eV (anthracenyl), 1.81 eV (tetracenyl), and 1.97 eV (pentacenyl). In later work, ten (scandium through zinc) homonuclear transition metal trimers were studied using one DFT 2 functional. Electronic ground states and bond lengths for equilateral triangles were: Sc3 ( A1′ , 2.83 Å), Ti3 7 2 17 16 11 6 3 ( E ′ , 2.32), V3 ( E ″ , 2.06), Cr3 ( E ′ , 2.92), Mn3 ( A2′ , 2.73), Fe3 ( E ″ , 2.24), Co3 ( E ″ , 2.18), Ni3 ( A2″ , 2 1 2.23), Cu3 ( E ′ , 2.37), Zn3 ( A1′ , 2.93). Vibrational frequencies, several low-lying electronic states, and trends in bond lengths and atomization energies are discussed. The predicted dissociation energies ∆E -1 -1 -1 -1 (M3 → M2 + M) are 49.4 kcal mol (Sc3), 64.3 kcal mol (Ti3), 60.7 kcal mol (V3), 11.5 kcal mol (Cr3), -1 -1 -1 -1 -1 32.4 kcal mol (Mn3), 61.5 kcal mol (Fe3), 78.0 kcal mol (Co3), 86.1 kcal mol (Ni3), 26.8 kcal mol -1 (Cu3), and 4.5 kcal mol (Zn3). INDEX WORDS: Density Functional Theory, precision, G2-97, Polycyclic Aromatic Hydrocarbon, PAH, electron affinity, transition metal trimers, M3. BENCHMARKING AND APPLICATION OF DENSITY FUNCTIONAL METHODS IN COMPUTATIONAL CHEMISTRY by BRIAN N. PAPAS B.S., Michigan State University, 2002 A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY ATHENS, GEORGIA 2006 © 2006 Brian N. Papas All Rights Reserved BENCHMARKING AND APPLICATION OF DENSITY FUNCTIONAL METHODS IN COMPUTATIONAL CHEMISTRY by BRIAN N. PAPAS Major Professor: Henry F. Schaefer III Committee: Geoff Smith Nigel Adams Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia May 2006 iv TABLE OF CONTENTS Page LIST OF TABLES......................................................................................................................... vi LIST OF FIGURES ...................................................................................................................... vii CHAPTER 1 INTRODUCTION AND BACKGROUND MATERIAL.............................................1 1.1 INTRODUCTION .....................................................................................................1 1.2 THEORY AND IMPLEMENTATIONS .........................................................................1 1.3 PROSPECTUS .........................................................................................................3 1.4 REFERENCES.........................................................................................................3 2 CONCERNING THE PRECISION OF STANDARD DENSITY FUNCTIONAL PROGRAMS: GAUSSIAN, MOLPRO, NWCHEM, Q-CHEM, AND GAMESS .4 2.1 ABSTRACT............................................................................................................5 2.2 INTRODUCTION.....................................................................................................5 2.3 METHODS .............................................................................................................5 2.4 RESULTS...............................................................................................................7 2.5 CONCLUSIONS ....................................................................................................10 2.6 ACKNOWLEDGEMENTS .......................................................................................10 2.7 TABLES AND FIGURES ........................................................................................10 2.7 REFERENCES.......................................................................................................21 3 THE NAPHTHALENYL, ANTHRACENYL, TETRACENYL, AND PENTACENYL RADICALS, AND THEIR ANIONS ..........................................23 v 3.1 ABSTRACT..........................................................................................................24 3.2 INTRODUCTION...................................................................................................24 3.3 METHODS ...........................................................................................................25 3.4 RESULTS AND DISCUSSION .................................................................................27 3.5 CONCLUSIONS ....................................................................................................31 3.6 ACKNOWLEDGMENTS .........................................................................................32 3.7 TABLES AND FIGURES ........................................................................................32 3.8 REFERENCES.......................................................................................................37 4 HOMONUCLEAR TRANSITION METAL TRIMERS ............................................40 4.1 ABSTRACT..........................................................................................................41 4.2 INTRODUCTION...................................................................................................41 4.3 METHODS ...........................................................................................................42 4.4 RESULTS.............................................................................................................44 4.5 CONCLUSIONS ....................................................................................................61 4.6 ACKNOWLEDGEMENTS .......................................................................................62 4.7 TABLES AND FIGURES ........................................................................................62 4.7 REFERENCES.......................................................................................................67 5 CONCLUSIONS..........................................................................................................79 vi LIST OF TABLES Page Table 2.1: G2/97 subset of neutral molecules considered in the present research.. ......................10 Table 2.2: Specification of the numerical integration grids used in this study..............................11 Table 2.3: “Exact” energies (Hartrees), computed as averages of energies from all programs with the “Large” grid quadratures...........................................................................................12 Table 3.1: Ipso C-C-C angles (in degrees) for the radicals and their anions.................................33 Table 3.2: C-C bond lengths (in Å) adjacent to the removed hydrogen atom...............................34 Table 3.3: EAs (in eV) with ZPVE corrected values in parentheses.............................................35 Table 3.4: ZPVE corrected energies (kcal/mol) relative to lowest energy species.. .....................36 Table 3.5: Global AEAs (eV), with ZPVE corrected values in parentheses.. ...............................36 Table 4.1: Low-lying electronic states of first row transition metal trimers.. ..............................62 Table 4.2: Harmonic vibrational frequencies (in cm-1) for transition metal trimers.....................63 Table 4.3: Summary of electronic ground states for the transition metal trimers in D3h symmetry.........................................................................................................................64 vii LIST OF FIGURES Page Figure 2.1: Gamess error curves. ...................................................................................................14 Figure 2.2: Molpro error curves.....................................................................................................15 Figure 2.3: NWChem error curves.................................................................................................16 Figure 2.4: QChem error curves. ...................................................................................................17 Figure 2.5: Gaussian 94 error curves.. ...........................................................................................18 Figure 2.6: BLYP results by molecule type...................................................................................19
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