Development and Application of Optimizations in Computational Chemistry

Open Access
- Author:
- Younker, Jarod Michael
- Graduate Program:
- Chemistry
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 18, 2010
- Committee Members:
- Michael Thomas Green, Dissertation Advisor/Co-Advisor
Michael Thomas Green, Committee Chair/Co-Chair
Joseph M Bollinger Jr., Committee Member
Carsten Krebs, Committee Member
Philip C. Bevilacqua, Committee Member
James David Kubicki, Committee Member - Keywords:
- Chloroperoxidase
P450
Rate Equations
Principal Components Analysis
Numerical Optimizations
Adomian Decomposition
Density Functional Theory
Ribonucleotide Reductase - Abstract:
- <html> <body> <p>Computational chemistry is broadly defined as the application of numerical methods to solve chemical problems. This field encompasses the microscopic world of quantum mechanics to the macroscopic behavior observed when exploring the behavior of large ensembles of interacting molecules. The complexity of these problems requires, in most instances, the use of computers to simulate the physics of the phenomenon and model the dynamic behavior. For example, in quantum mechanics the only systems which can be solved exactly are those composed of only one or two particles. Nevertheless, high-level numerical approximations to the many-bodied problem can be achieved employing numerical methods. Other numerical methods enable researchers to understand large amounts of data, which modern-day instruments record, via decomposition and simulation. Each chapter of the thesis addresses an independent topic in computational chemistry.</p> <h3>Chapter 1</h3> <p>Deoxyribonucleotides are the building blocks of DNA. One of the last steps in their <I>de novo</I> synthesis is carried out by ribonucleotide reductase (RNR). RNR is ubiquitous in all living organisms and catalyzes the reduction of di- or triphosphate ribonucleoside to the respective deoxyribonucleoside. Recently a new subclass of RNR has been discovered. The class Ic RNR from the obligate parasite <I>Chlamydia trachomatis</I> (<I>Ct</I>) uses a stable Mn(IV)/Fe(III) cofactor to initiate nucleotide reduction by a free-radical mechanism. This novel cofactor may be a promising drug target. The generation of the Mn(IV)/Fe(III) active state begins with either a Mn(II)/Fe(II) or a Mn(III)/Fe(III) cofactor, which is oxidized via molecular oxygen or hydrogen peroxide to yield a Mn(IV)/Fe(IV) state. This latter state is quickly reduced by one electron. <I>Ct</I> RNR holds promise for new insights into the structures of high-valent dinuclear metal clusters. Unlike their analogues from <I>E. coli</I> RNR and methane monooxygenase (MMO), both complexes can be obtained in high yields. The presence of the two different metals in the cofactor could further our understanding of dinuclear metal clusters. Their presence allows researchers to study EPR-active oxidation states, that in the diiron <I>E. coli</I> RNR and MMO cofactors are EPR-inactive. In this chapter, extended X-ray absorption fine structure (EXAFS) spectroscopy and density functional theory (DFT) calculations are coupled with previous EPR and <SUP>57</SUP>Fe Mossbauer spectroscopy to postulate structures for the two cofactors. Fe and Mn <I>K</I>-edge EXAFS data yield intermetallic distances for the Mn(IV)/Fe(III) and Mn(IV)/Fe(IV) cofactors of ~2.9 and ~2.8 Angstrom, respectively. The Mn data also suggest the presence of a short 1.74 Angstrom Mn-O bond for the Mn(IV)/Fe(III) cofactor. These metrics are compared to the results of DFT calculations on 16 cofactor models derived from the crystal structure of the inactive Fe<SUB>2</SUB>(III/III) form of the protein. Models are differentiated by the protonation states of their bridging and terminal OH<SUB>X</SUB> (if present) ligands, as well as the location of the Mn(IV) ion (site 1 or 2). The models that agree best with experimental observations for the Mn(IV)/Fe(III) cofactor feature a mu-1,3-carboxylate bridge (E120), terminal solvent (H<SUB>2</SUB>O/OH) to site 1, one mu-O bridge, and one mu-OH bridge. The models that agree best with the experimental observations for the Mn(IV)/Fe(IV) cofactor feature an identical core structure to that of Mn(IV)/Fe(III), but with the terminal solvent to site 1 displaced by the second carboxylate oxygen of E89. If correct, reduction of the Mn(IV)/Fe(IV) cofactor by one electron is accompanied by significant core rearrangement and association of water to site 1. The site-placement of the metal ions cannot be discerned from the available data. Hyperfine couplings and <SUP>57</SUP>Fe Mossbauer parameters are also predicted.</p> <h3>Chapter 2</h3> <p>Hydroxylation of hydrocarbons is of great interest both industrially and biologically. The C-H bond in alkanes is relatively inert, such that harsh reaction conditions are required to activate it industrially. Conversely, Nature is able to activate C-H bonds at ambient temperature and pressure. The P450 family of enzymes is largely responsible for hydroxylating exogenous alkanes <I>in vivo</I>. In P450s, hydroxylation occurs at an Fe(IV)=O porphyrin radical cation cofactor. It is hypothesized that the ability of metal-O(H) complexes to abstract hydrogen is directly related to the strength of the O-H bond formed in the resulting metal complex. For P450s, this Fe(IV)-OH species is called compound-II (P450-II). It is also hypothesized that P450s utilize an axial sulfur in order to increase the driving force to oxidize hydrocarbons. The sulfur increases the basicity of the Fe(IV)-O cofactor, making it basic under biological conditions. Thermodynamically, the metal O-H strength is directly dependent on the pK<SUB>a</SUB> of P450-II. Peroxidases, which usually possess an axial nitrogen, are incapable of performing alkane hydroxylations and are deprotonated at neutral pH. DFT calculated O-H bond strengths in P450 and peroxidase models are nearly identical, which is contrary to the aforementioned hypotheses. However, calculations on twenty iron and manganese complexes with experimentally known O-H bond dissociation enthalpies (BDEs) are found to be inaccurate at the B3LYP/6-311G and B3LYP/6-311+G(1D,1P)//6-311G levels of theory. The calculated O-H bond energies are analyzed to understand the discrepancy with experiment. The contribution to the dissociation enthalpies from the sum of the zero-point, rotational, translational, and vibrational energies are shown to be similar for all complexes (-5.4 +/- 0.6 kcal/mol). Finally, a Becke-inspired three-parameter hybrid functional is proposed to accurately predict metal O-H BDEs.</p> <h3>Chapter 3</h3> <p>This chapter documents the development of the author's optimization code and will be utilized throughout the rest of the dissertation (Chapters 4-5). The motivation for development of the code stemmed from a desire to include chemically intuitive constraints in nonlinear regression problems. Regression is frequently used to fit theoretical models to experimental data by minimizing the difference between the actual experimental results and the predictive model. The fitting of rate constants to kinetic traces is a typical chemical example. As will be seen in the subsequent chapters, constraints range from experimentally obtained molecular expectation values to the fact that absorption spectra cannot be negative. The versatility of the method is seen in the wide range of problems it allows the researcher to address. The code is classified as an interior-point method. It is necessarily constraint oriented and aware of the geometry of the problem (convex vs. nonconvex). The algorithm employs finite derivatives and can be used to find solutions to which there is no explicit formulation of the problem. The novelty of the code is in the use of a class object which contains virtual merit and constraint functions which are easily tailored to any problem. The class object also allows complex algorithms (even outside executables) to be passed to the optimization routine instead of the simple functions passed to available software.</p> <h3>Chapter 4</h3> <p>Chloroperoxidase (CPO) is frequently studied to understand the important alkane-hydroxylating enzyme P450 (see Chapter 2). One intermediate of interest is compound-II (CPO-II). Compound-II is the Fe(IV)-OH species which immediately follows hydrogen atom transfer. When CPO-II was first characterized with <SUP>57</SUP>Fe Mossbauer, two species with significantly different quadrupole splittings were found (Stone <I>et al., J. Am. Chem. Soc.,</I> <B>2006,</B> <I>128,</I> 6147-6153). The major species' splitting was accurately predicted with DFT, but the identity of the minority species has remained enigmatic. In order to find a model consistent with the minority species, a spectroscopically constrained geometry optimization is developed and employed. A model which is consistent with the experimental Fe(IV)-OH quadrupole splitting of 1.59 mm/s, as well as the Fe-O Raman stretch at 565 cm<SUP>-1</SUP>, is found. As a proof of concept, said quadrupole-constrained geometry optimization is shown to transition between different configurations of Fe(CO)<SUB>4</SUB><SUP>2-</SUP> and Fe(CO)<SUB>5</SUB>. The constrained optimization approach developed here has potential to be used whenever a molecular expectation value is known experimentally which is not reproduced by the minimum energy model.</p> <h3>Chapter 5</h3> <p>Chemists are frequently interested in rate equations, which are first-order differential equations. Numerical integration of these equations allows the researcher to accurately predict the concentrations of chemical species at any time given the initial conditions. Runge-Kutta (RK) integration is widely used for solving the rate equations. In this chapter, Adomian decomposition methods (ADM) are used to obtain the solutions of chemical rate equations. The Adomian method outlined here outperforms high-order RK routines in the arenas of accuracy and truncation error. Additionally, four modifications are introduced that place the Adomian integration on par with RK in terms of speed (a primary reason for which Adomian decomposition methods are currently underemployed). This increase in computational performance is highly significant to kinetic inversion and global analysis problems where rate constants are obtained via the fitting of experimental data and hundreds of numerical integrations are needed. The inclusion of up to the fifth term in the Adomian expansion gives a truncation error of order <I>O(h<SUP>10</SUP>)</I>. The method as presented yields solutions which are step-size independent in the non-stiff regime. The problem of rapid polynomial divergence is addressed through discretizing the time axis.</p> </body> </html>