COMPUTATIONAL THERMODYNAMIC STUDIES OF ALKALI AND ALKALINE EARTH COMPOUNDS, OLEFIN METATHESIS CATALYSTS, AND BORANE AZOLES

Transcription

1 COMPUTATIONAL THERMODYNAMIC STUDIES OF ALKALI AND ALKALINE EARTH COMPOUNDS, OLEFIN METATHESIS CATALYSTS, AND BORANE AZOLES FOR CHEMICAL HYDROGEN STORAGE by MONICA VASILIU A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Chemistry in the Graduate School of The University of Alabama TUSCALOOSA, ALABAMA 2010

2 Copyright Monica Vasiliu 2010 ALL RIGHTS RESERVED

3 ABSTRACT Geometry parameters, frequencies, heats of formation and bond dissociation energies are predicted for the alkali (Li, Na and K) hydrides, chlorides, fluorides, hydroxides, and oxides and alkaline earth (Be, Mg and Ca) fluorides, chlorides, oxides and hydroxides at the coupled cluster theory [CCSD(T)] level extrapolated to the complete basis set (CBS) limit. The calculations including core-valence correlation corrections with the aug-cc-pwcvnz basis sets (n = D, T, Q and 5) are mostly in excellent agreement with the available experimental measurements. Additional corrections (scalar relativistic effects, vibrational zero-point energies, and atomic spin-orbit effects) were necessary to accurately calculate the total atomization energies and heats of formation. The results resolve a number of issues in the literature. CCSD(T)/CBS level calculations with additional corrections are used to predict the heats of formation, adiabatic and diabatic bond dissociation energies (BDEs) and Brønsted acidities and fluoride affinities for the model Schrock-type metal complexes M(NH)(CRR )(OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) and MO 2 (OH) 2 transition metal complexes. The metallacyclobutane intermediates formed by addition of C 2 H 4 to M(NH)(CH 2 )(OH) 2 and MO 2 (OH) 2 are investigated at the same level of calculation. The electronegative groups bonded to the carbene carbon lead to less stable Schrock-type complexes as compared to the complexes with a CH 2 substituent. The Schrock compounds with M = Cr are less stable than with M = W or Mo. The heats of formation and bond dissociation energies (BDEs) for the pyrrole, pyrazole, imidazole, triazole and tetrazole borane adducts were predicted using an isodesmic approach ii

4 based on G3MP2 calculations. As potential hydrogen storage substrates, dehydrogenation energies for the elimination of one H 2 molecule were predicted as well as thermodynamic properties relative to their acid-base behavior. The H 3 B N bonds to an sp 2 nitrogen are much stronger than those to an sp 3 nitrogen for the 5-membered rings. The B N BDEs for the azolylborate adducts are much larger than for the neutral azole borane adducts. The azole adducts with more number of nitrogens in the ring and with more BH 3 molecules to the azole nitrogens are more acidic. iii

5 DEDICATION To my family, especially to my grandparents, for their infinite love and support iv

6 LIST OF ABBREVIATIONS AND SYMBOLS aug-cc-pvnz aug-cc-pvtz-dk aug-cc-pvnz-pp aug-cc-pwcvnz aug-cc-pwcvtz-dk aug-cc-pwcvtz-pp awcvtz B3LYP BLYP BDE BP86 CBS CCSD(T) COSMO CI CISD CV DFT DK DZVP DZVP2 Augmented, correlation consistent, polarized valence n zeta basis sets, where n = double (D), triple (T) or quadruple (Q) aug-cc-pvtz basis sets with all electron DK basis set aug-cc-pvnz basis sets with pseudopotentials for heavy atoms Augmented, correlation consistent, polarized weighted core-valence n (D, T, Q or 5) zeta basis sets aug-cc-pwcvtz basis sets with all electron DK basis set aug-cc-pwcvtz basis set with pseudopotentials for heavy atoms aug-cc-pwcvtz basis sets Becke 93 (exchange), Lee-Yang-Parr (correlation) DFT functional Becke 88 (exchange), Lee-Yang-Parr (correlation) DFT functional Bond dissociation energy Becke 88 (exchange), Perdew 86 (correlation) DFT functional Complete basis set Coupled cluster singles, doubles, and disconnected triples Conductor-like screening model Configuration interaction Configuration interaction singles and doubles Core valence Density functional theory Douglas-Kroll-Hess DFT optimized double zeta valence basis set with polarization functions (except H) DFT optimized double zeta valence basis set with polarization functions v

7 ΣD 0 (ΣD 0,0K ) Total atomization energy G3MP2 Gaussian-3 theory calculation using 2 nd order Møller Plesset perturbation theory (MP2) E CBS E CV E Rel E SO E SR E ZPE E 0K / E 298K ECP FA G aq G gas G solv G 298K GIAO H 298K HA HF H f,0k H f,298k H rxn IR MO MP2 MVD NIST-JANAF NMR PA Complete basis set energy change Core valence energy change Scalar relativistic energy change Spin orbit energy change Scalar relativistic correction calculated as the MVD expectation values Zero point energy change BDE at 0 K/298 K Effective core potential Fluoride affinity Aqueous deprotonation Gibbs free energy (solution free energy) Gas phase free energy Aqueous solvation free energy Gas phase Gibbs acidity Gauge independent atomic orbital approximation Gas phase enthalpy acidity Hydride affinity Hartee-Fock Heat of formation at 0K Heat of formation at 298K Reaction enthalpy change Infrared spectrscopy Molecular orbital 2 nd order Møller-Plesset perturbation theory Mass-velocity and Darwin operators National Institute of Standards and Technology - Joint Army-Navy-Air Force Nuclear magnetic resonance Proton affinity vi

8 PBE Perdew-Burke-Ernzerhof (exchange), Perdew-Burke-Ernzerhof (correlation) DFT functional PES Potential energy surface pk a Negative logarithm of the acid dissociation constant PP Pseudopetential PW91 Perdew-Wang 91 (exchange), Perdew-Wang 91 (correlation) DFT functional R Gas constant ROHF Open-shell HF R/UCCSD(T) Open-shell CCSD(T) SCF Self consistent field SCRF self consistent reaction field SO Spin orbit SP Square pyramidal SR Scalar relativistic T Temperature TAE Total atomization energy TBP Trigonal bipyramidal TZ2P Triple zeta basis set with 2 polarization functions VTZP Valence high triple zeta basis set with polarized function ZORA Zeroth order regular approximation to the Dirac equation ZPE Zero point energy > Greater than < Less than = Equal to Å Angstrom Degrees ± Plus or minus vii

9 ACKNOWLEDGMENTS I am pleased to have this opportunity to thank all those people who have guided, inspired and helped me during the years I spent at The University of Alabama. First of all, I am most indebted to my research advisor Dr. David A. Dixon for his tremendous support, constant guidance, endless patience and encouragement. He was always there to help and I am so fortunate to have the opportunity to work with him and to be part of his research group. I would like to thank Dr. Anthony J. Arduengo, III for being my research advisor for the time I spent in his group which allowed me to develop laboratory skills. He is a great scientist and his strive for perfection has been an inspiration for me. Special thanks to my committee members past and present, Dr. Joseph S. Thrasher, Dr. Martin G. Bakker, Dr. Masaaki Yoshifuji and Dr. Michael P. Jennings for their important contribution to my education at UA. I want to thank Dr. Owen W. Webster and Dr. Kevin H. Shaughnessy for their helpful discussions and valuable advices. I would like to thank all of the contributors to this work: Dr. Kirk A. Peterson and Dr. David Feller from Washington State University, Dr. James L. Gole from Georgia Institute of Technology and Dr. Shenggang Li, The University of Alabama, co-authors of Chapters 2 and 3; and Dr. Anthony J. Arduengo, III co-author of Chapters 4 and 5. Many thanks to the Dixon and Arduengo past and present group members, the best colleagues anyone could ask for, especially Dr. Shenggang Li for his great help, time and patience when I needed. viii

10 The financial support made my study possible at the University of Alabama and I would like to thank the Department of Chemistry for its assistantships and DOE for providing the funding. Last, but not least, I wish to thank my family and Ami for their love, support and understanding throughout my PhD years. ix

11 CONTENTS ABSTRACT... ii DEDICATION... iv LIST OF ABBREVIATIONS AND SYMBOLS...v ACKNOWLEDGMENTS... viii LIST OF TABLES... xii LIST OF FIGURES... xvi 1. INTRODUCTION Computational Chemistry Molecular orbital (MO) theory Density Functional Theory (DFT) Energy calculations Thermochemistry STRUCTURES AND HEATS OF FORMATION OF SIMPLE ALKALI METAL COMPOUNDS: HYDRIDES, CHLORIDES, FLUORIDES, HYDROXIDES, AND OXIDES FOR Li, Na, AND K...14 References...47 Appendix STRUCTURES AND HEATS OF FORMATION OF SIMPLE ALKALINE EARTH METAL COMPOUNDS: FLUORIDES, CHLORIDES, OXIDES, AND HYDROXIDES FOR Be, Mg, AND Ca...68 References...96 x

12 Appendix BOND ENERGIES IN MODELS OF THE SCHROCK-TYPE METATHESIS CATALYSTS References Appendix COMPUTATIONAL STUDIES OF AZOLE.xBH 3 ADDUCTS AND RELATED SPECIES FOR CHEMICAL HYDROGEN STORAGE: THERMOCHEMISTRY, ACIDITY BASICITY AND NMR References Appendix CONCLUSIONS REFERENCES xi

13 LIST OF TABLES 2.1. Calculated and Experimental Bond Distances for the Diatomic Compounds Calculated and Experimental Geometry Parameters for the Alkali Metal Hydroxides MOH Calculated and Experimental Geometry Parameters for the Alkali Metal Dioxides (Alkali Superoxides) MO 2 and Alkali Metal Trioxides (Alkali Ozonides) MO Calculated and Experimental Bond Distances for the Dialkali Metal Oxides M 2 O (M= Li, Na, and K) Calculated and Experimental Harmonic Frequencies (ω e ) and Anharmonicities (ω e χ e ) in cm 1 for Diatomic Alkali Metal Compounds Calculated (CCSD(T)/awCVTZ) and Experimental Vibrational Frequencies in cm 1 for the Triatomic and Tetratomic Alkali Metal Compounds: MOH, MO 2, MO 3, and M 2 O Calculated and Experimental Total Atomization Energies at 0 K in kcal/mol Calculated and Experimental Heats of Formation at 0 K and 298 K in kcal/mol Calculated and Experimental Bond Dissociation Energy in kcal/mol Calculated and Experimental Bond Distances for the Alkaline Earth Oxides, Monochlorides and Monofluorides Calculated and Experimental Geometry Parameters for the Alkaline Earth Halides (Fluorides and Chlorides)...83 xii

14 3.3. Calculated and Experimental Geometry Parameters for the Alkaline Earths Hydroxides Calculated and Experimental Harmonic Frequencies (ω e ) and Anharmonicities (ω e χ e ) in cm 1 for the Diatomic Alkaline Earth Compounds Calculated (CCSD(T)/awCVTZ) and Experimental Vibrational Frequencies in cm 1 for the Halides and Hydroxides Alkaline Earth Compounds Calculated and Experimental Total Atomization Energies at 0 K in kcal/mol Calculated and Experimental Heats of Formation at 0 K and 298 K in kcal/mol Calculated and Experimental Bond Dissociation Energies in kcal/mol Calculated Bond Length (Å) for MO 2 (OH) 2 (M = Cr, Mo, W) at the B3LYP/aD Level Calculated Bond Length (Å) for M(NH)(CRR )(OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) at the B3LYP/aD Level Calculated Harmonic Vibrational Frequencies in cm -1 for the Metal-Oxygen Stretches in MO 2 (OH) 2 (M = Cr, Mo, W) at the B3LYP/aD Level Calculated Harmonic Vibrational Frequencies in cm -1 for Metal- Oxygen, Metal-Nitrogen, and Metal-Carbon Stretches in M(NH)(CRR )(OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) at the B3LYP/aD Level Total Atomization Energies at 0 K (ΣD 0,0K ) a and Heats of Formation at 0 and 298 K ( H f,0k and H f,298k ) in kcal/mol for the Ground States of M(NH)(CRR )(OH) 2 and MO 2 (OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) Calculated at the CCSD(T) Level Adiabatic and Diabatic Bond Dissociation Energies at 0 K in kcal/mol ( E 0K ) for the M=O bonds in MO 2 (OH) 2 (M = Cr, Mo, xiii

15 and W) and Singlet-Triplet Energy Differences at 0 K in kcal/mol ( E S-T ) for MO(OH) 2 Calculated at the CCSD(T) Level Adiabatic Bond Dissociation Energies at 0 K ( E 0K, kcal/mol) for the M OH Bonds in M(NH)(CRR )(OH) 2 and MO 2 (OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) Calculated at the CCSD(T) Level Adiabatic and Diabatic Bond Dissociation Energies at 0 K ( E 0K, kcal/mol) for the M=CRR Bonds in M(NH)(CRR )(OH) 2 (CRR = CH 2, CHF, CF 2 ; M = Cr, Mo, W) and Singlet-Triplet Energy Differences at 0 K ( E S-T, kcal/mol) for the Metal-Containing Fragments Calculated at the CCSD(T) Level Adiabatic and Diabatic Bond Dissociation Energies at 0 K ( E 0K, kcal/mol) for the M=NH Bonds in M(NH)(CRR )(OH) 2 (CRR = CH 2, CHF, CF 2 ;M = Cr, Mo, W) and Singlet-Triplet Energy Differences at 0 K ( E S-T, kcal/mol) for the Metal-Containing Fragments Calculated at the CCSD(T) Level Heats of Formation at 0 and 298 K ( H f,0k and H f,298k, kcal/mol) for the Ground States of the Metal Containing Fragments of the M(NH)(CRR )(OH) 2 and MO 2 (OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) Brønsted Acidities ( H 298K and G 298K in kcal/mol) for M(NH)(CH 2 )(OH) 2 and MO 2 (OH) 2 (M = Cr, Mo, W) Calculated at the CCSD(T) Level Fluoride Affinities at 0 K ( E 0K, kcal/mol) for M(NH)(CRR )(OH) 2 and MO 2 (OH) 2 (M = Cr, Mo, W; CRR = CH 2, CHF, CF 2 ) Calculated at the CCSD(T) Level Calculated Bond Length (Å) and Bond Angles ( ) for M(NH)(CH 2 )(OH) 2 (C 2 H 4 ) (M = Cr, Mo, W) at the B3LYP/aD Level Calculated Bond Length (Å) and Bond Angles ( ) for MO 2 (OH) 2 (C 2 H 4 ) at the B3LYP/aD Level Calculated Reaction Energies for the Formation of the Most Stable Metallocycles at the CCSD(T) Level xiv

16 4.16. Calculated Relative Energies at 0 K ( E 0K, kcal/mol) for the Different Conformations of the Metallacycles at the CCSD(T) Level Total Atomization Energies at 0 K (ΣD 0,0K ) and Heats of Formation at 0 and 298 K ( H f,0k and H f,298k ) in kcal/mol for the Ground States of the Azoles (Neutral and Anions) Calculated at the CCSD(T) Level Calculated Heats of Formation at 298K ( H f,298k ) in kcal/mol of the Azole Borane Adducts and Related Species at G3MP2 Level and from Isodesmic Reactions H 3 B N< Bond Dissociation Energies ( E 0K ) in kcal/mol for the Azole Borane Adducts and Related Species at G3MP2 Level and from the Heats of Formation Calculated using Isodesmic Reactions Dehydrogenation Reactions Energies at 298 K in kcal/mol at the G3MP2 Level and from the Heats of Formation Calculated using Isodesmic Reactions Calculated and Experimental Proton Affinity (PA) of the Azoles at N in kcal/mol (298K) at G3MP2 Level Calculated and Experimental Brønsted Acidities ( H 298K and G 298K ) in kcal/mol for the Neutral Azoles and Azole Borane Adducts at the G3MP2 Level Calculated and Experimental pk a Values Relative to Nitric Acid (pk a ) of the Neutral Azole Borane Adducts Hydride affinities (HA) in kcal/mol at 0 and 298 K for the Azolylborate Adducts Calculated at the G3MP2 Level Calculated 11 B-NMR Chemical Shifts in ppm of the Azole Borane Adducts and Related Species xv

17 LIST OF FIGURES 2.1. Bond dissociation energies for the sequential loss of O from MO 3 to form M in kcal/mol at 0 K Different Conformations of the Metallacycles Relative Energies for the Intermediates Formed in the Reactions of M(NH)(CH 2 )(OH) 2 (M = Cr, Mo, W) with C 2 H Relative Energies for the Intermediates Formed in the Reaction of MO 2 (OH) 2 (M = Cr, Mo, W) with C 2 H Neutral Azoles, Protonated, and Deprotonated Azoles Neutral Azole Borane Adducts Azolylborate Adducts Azolylborane Adducts xvi

18 CHAPTER 1 INTRODUCTION This dissertation focuses on the prediction of thermodynamic and chemical properties of compounds that are of interest in atmospheric and energy chemistry, catalysis and chemical hydrogen storage. We describe computational studies of alkali and alkaline earth compounds, Schrock-type transition metal complexes and azole borane adducts. The alkali metal compounds are involved in atmospheric and combustion chemistry and high quality information about their energetics are of interest. The source of alkali metals in the mesosphere is considered to be mostly meteoritic 1 and layers containing atomic alkali metals have been observed at about 90 km. 2 Atomic alkali metals (especially Na) are oxidized in the upper atmosphere forming the neutral oxides and hydroxides. There is also substantial interest in the role of alkali metal compounds that can be formed in the combustion of coal and other fuel sources, for example added biofuels. Alkali compounds can be formed from precursors in the fuel and from additives. The alkali metal compounds formed during combustion have been involved in fouling, corrosion, erosion, and agglomeration processes in power plants. We focused on the thermochemical properties of the hydrides, chlorides, fluorides, oxides and hydroxides of Li, Na and K. Compounds containing the alkaline earth metals are commonly occurring substances in nature and are used on a daily basis in the chemical industry. Magnesium hydroxide is the main component of milk of magnesia, magnesium oxide is used for lining furnaces, and calcium 1

19 hydroxide (slaked lime) is the principal ingredient in plaster and mortar. Calcium chloride absorbs water from the air and it is used in the prevention of dust on roads, coal, and tennis courts and also as a drying agent in the laboratory. The alkaline earth monoxides play an important role in flame chemistry 3, in fuels (MgO) 4 and possibly in stellar atmospheres. 5 The gas phase alkaline earth compounds are highly reactive species and the composition of the vapors is very complex, especially for the oxides and hydroxides. We are particularly interested in the thermochemical properties of the chlorides, fluorides, oxides and hydroxides of Be, Mg and Ca. There is substantial interest in olefin metathesis by transition metal complexes due to the importance of being able to manipulate C C bonds catalytically and the applicability of this reaction in medicine, biology, and material sciences. Catalytic olefin metathesis 6,7,8 has become an increasingly indispensable tool in organic chemistry ranging from the synthesis of macrocyclic rings to olefin polymerization. The Schrock type catalysts are of special interest to us because their basic structure, M(NR)(CR 2 )(OR ) 2 (M = Cr, Mo, W), is very similar to the high metal oxidation state MO 3 and MO 2 (OH) 2 based clusters, which we have been studying computationally 9,10,11,12 to better understand their role in heterogeneous catalysis. Thus, we are interested in energetics underlying the Schrock type complexes catalytic behavior. Amine borane adducts are not very stable, especially at high temperatures or in reaction with protic solvents where they eliminate hydrogen, but they are attractive chemicals due to their unique reactivity. 13 As compared to other amines, azoles are less toxic and they are often used in pharmaceuticals as antifungal agents especially triazole and imidazole derivatives. Our interest on azole borane adducts is as potential chemical hydrogen storage materials. As we increase the number of nitrogen atoms in the 5-membered cycle, we increase the possibility to coordinate more BH 3 molecules to form amine borane complexes and to store more hydrogen. Thus, similar 2

20 to ammonia borane 14,15 these azole borane adducts could be used as chemical hydrogen carriers and their energetic properties and acid-base chemistry are of interest. 1.1 Computational Chemistry Chemistry is the science which involves the construction, transformation and properties of molecules. Plastic models and chemical drawing programs together with a set of pre-defined objects and rules are used to approximate real chemical entities and processes. Chemical structures and reactions can be simulated numerically using computers so that one is not restricted to examining reactions and compounds only experimentally. Computational chemistry is the study of chemical phenomena using mathematical methods to solve fundamental laws of physics. It has an advantage of being able to provide information not only about stable, but also unstable molecules as intermediates or even transition states which is difficult to obtain from experiment. Overall, computational chemistry is a vital adjunct to experimental chemistry. Molecular mechanics and electronic structure theory are the two broad areas of computational chemistry dealing with structure of molecules and their reactivity. Both approaches can predict energies (and properties related to energies), geometries, and frequencies. Molecular mechanics is based on solving Newton s laws to predict the structures and properties of molecules, using classical force fields. Molecular mechanics does not usually explicitly treat the electrons in a molecular system and relies on the accuracy of the parameterization approach. Electronic structure methods use the laws of quantum mechanics in their computations and include two major classes: semi-empirical methods which use parameters derived from experimental data to simplify the computation and ab initio methods based only on the laws of quantum mechanics and fundamental physical constants. 16 3

21 In computational chemistry, the primary task is to solve the Schrödinger equation to get information about the energy and related properties of a molecule. The time-independent, nonrelativistic Schrödinger equation is given by: HΨ = EΨ (1.1) where H is the Hamiltonian operator which includes the kinetic and potential energies of the nuclei and electrons, Ψ is the total wavefunction and E is the total energy. For a system with N nuclei nuclei and N elec electrons, the electronic Hamiltonian operator after the application of Born-Oppenheimer approximation can be written as: where the first term on the right hand side is the electronic kinetic energy and the other terms describe the nuclear-electron attraction, electron-electron repulsion and the nuclei-nuclei repulsion potential energies. R and r refer to nuclear positions (A, B) and electronic coordinates (i, j) corresponding to different centers. Z is the atomic number and is the gradient operator. Within the Born-Oppenheimer approximation the last term is a constant as the nuclei are fixed and the Hamiltonian operator is determined by the number of electrons and the potential created by the nuclei in terms of the nuclear charges and positions. The changes in electronic energies as a function of nuclear positions give the potential energy surface (PES) of a molecule. The global minimum of energy on the PES gives the most stable structure of the molecule. The second derivatives of the energy with respect to the nuclear coordinates provide the Hessian which can be transformed into the harmonic vibrational modes of the molecule. Our goal is to solve the Schrödinger equation to obtain information about the structure and energetics of the compounds described above. 4

22 The Schrödinger equation can be solved exactly only for a very small number of systems, for example the hydrogen atom. Thus, approximate methods are required in order to study manyelectron systems such as the molecules we are interested in studying. There are currently two distinct approaches to solve this equation: molecular orbital (MO) and density functional theory (DFT). 1.2 Molecular orbital (MO) theory One of the earliest approaches to solving the Schrodinger equation for the electronic structure of molecules is molecular orbital theory. 17,18,19,20 The simplest approach used in solving Schrödinger equation is the Hartree-Fock (HF) method where each electron in an n-electron system moves in an average field created by the n-1 other electrons and the nuclei. Electron correlation is neglected, as the electron-electron repulsion is only included as an average of all of the electrons. Each MO is constructed as a linear combination of atomic orbitals, expressed as a predefined set of one electron atomic functions known as basis functions (χ µ ) usually centered on an atom. We define a molecular orbital as: where the c iµ are the molecular expansion coefficients. In the HF method, the Schrödinger equation is reduced to a set of Fock equations using the variational principle, the solution of which gives the above MO coefficients. The HF equations have to be solved iteratively to optimize the coefficients to minimize the electronic energy, and this procedure is called the Self Consistent Field (SCF) method. With a sufficiently large basis set, the HF wavefunction can account for up to 99% of the total energy, but the remaining energy is very important in describing chemical phenomena. The difference between the HF and the exact energy is defined as the electron correlation energy and 5

23 describes the motion of the electrons as they interact with each other. The motion of electrons of opposite spin is uncorrelated in HF theory. Thus, an electron in a given doubly occupied orbital does not know the position of the electron with opposite spin other than as given by the average of n-1 electrons. However, the two electrons in the orbital must be aware of each other as classically they repel each other so their motion is actually correlated. Methods which explicitly calculate the electron correlation energies are known as post-hf methods. Electron correlation methods usually begin with the HF wavefunction as the reference wavefunction and give much better energies than the HF method. To calculate total energies at the chemical accuracy of ± 1 kcal/mol it is necessary to use methods which include electron correlation and large basis sets, which is possible only for modest size molecular systems. In order to reduce the computational cost, the core orbitals, mostly chemically inert, are usually excluded from the correlation treatment. The resulting energy is the valence electronic energy, and the effect of the core electron correlation can be calculated using a smaller basis set if necessary. The three main methods to calculate the electron correlation energy are: configuration interaction (CI), many body perturbation theory (MBPT) and coupled cluster (CC). Configuration interaction (CI) 21 methods are based on constructing a linear combination of determinants by replacing one or more occupied orbitals within the HF determinant with the virtual orbitals and the coefficients are solved by minimizing the energy of the resultant wavefunction. Full CI is both variational and size-consistent, but it is extremely expensive computationally. Truncated CI methods are variational, but they are neither size-consistent nor size extensive and, thus, the other two correlated methods are preferable as they are sizeconsistent and size extensive. A method is size extensive if the energy calculated thereby scales 6

24 linearly with the number of particles. A method is called size consistent if it gives an energy E A + E B for two non-interacting subsystems A and B. Many body perturbation theory (MBPT) accounts for electron correlation by treating it as a perturbation to the HF wavefunction. MBPT consists of corrections to the energy obtained by adding higher excitations to the HF determinant non-iteratively. In perturbation theory, the Hamiltonian is divided in two parts: the unperturbed term, exactly solvable (H 0 ) and a perturbation term (H'): H = H 0 + λh' (1.4) where λ is a parameter which determines the strength of the perturbation. Second order Møller- Plesset perturbation theory (MP2) 22 is the simplest treatment of electron correlation. The perturbation is assumed to be very small. MP2 recovers up to 80% of the correlation energy and it scales as N 5 (N is the number of basis functions) due to the integral transformation step. Higher order perturbation theories such as MP4 are computationally very expensive, but not as accurate as the coupled cluster method discussed below, and thus are not used as much today. We mostly used the third type of correlation methods in our study, the coupled cluster (CC) method. 23 CC theory has become one of the most reliable computational methods for the prediction of chemical properties of molecular systems. The coupled cluster wave function is written as: Ψ CC = e T Φ 0 (1.5) where we expand the exponential in a Taylor series. Here, T is the cluster operator and Φ 0 is the reference wavefunction. T is given by: T = T 1 + T 2 + T T n (1.7) 7

25 and n describes a specific degree of excitation: n = 1 are singles, n = 2 are doubles, n = 3 are triples and so on. The CC equations are solved iteratively. The cluster operator must be truncated at some excitation level, otherwise it scales as the full CI method. The CCSD(T) method is one of the most successful CC method for the predictions of a wide range of molecular properties to the chemical accuracy. In this method, only the single and double excitations are included in the iterative procedure which scales as N 6, and the effect of the triple excitations are included perturbatively from an MP4(SDTQ) calculation using the CCSD amplitudes which scales as N 7. To fully include the iterative triple excitations will significantly increase the computational cost to N 8, often without improving the results qualitatively. If the wavefunction is dominated by a single determinant, the CCSD(T) energy is usually very close to the full CI result. 1.3 Density Functional Theory (DFT) DFT 24,25,26 is the alternative to ab initio MO methods. DFT incorporates the effects of electron correlation without dramatically increasing the computational cost and provides a good description of the geometries and frequencies of a wide range of molecules. The DFT method is based on the fact that the ground state electronic energy is a functional and it is, thus, uniquely determined by the electron density (ρ). The DFT method has a computational cost similar to HF but with the possibility of providing much more accurate results. The general DFT electronic energy expression can be written as: E DFT [ρ] = T S [ρ] + E ne [ρ] + J[ρ] + E xc [ρ] (1.8) where T S is the kinetic energy, E ne is the electronic-nuclear potential energy, J is the Coulombic interaction and E xc is the exchange correlation energy including the remaining part of the electron-electron interactions. If the exact form of E xc is known, DFT can give the exact energy in contrast to the HF theory. However, there are no a priori definitions of E xc and we do not 8

26 know how to explicitly define it. Thus, a major problem of using DFT is choosing the proper form of the exchange-correlation functional. A variety of exchange-correlation functionals are available, and the design of better functionals is an open area of research. These functionals can be classified into local density functionals which depend only on the electron density, and gradient-corrected functionals which also depend on the gradient of the electron density. Some of the gradient-corrected functionals also include the HF exchange, and these are known as hybrid functionals. In this work, we use the B3LYP hydrid functional, one of the most popular functionals, to calculate the geometries and frequencies. 1.4 Energy calculations Different energies including total atomization energies, bond dissociation energies, fluoride affinities, and gas phase acidities all correspond to the energy difference between a molecule (reactant) and isolated atom/fragments (products). These energies are calculated as the sum of contributions: E = E CBS + E ZPE + E Rel + E CV + E SO (1.9) The main contributor to E is the valence electron energy at the complete basis set (CBS) limit ( E CBS ) at the CCSD(T) level. E ZPE is the nuclear zero point energy and requires calculation of the frequencies. The remaining terms from Eq. (1.9) are energy corrections necessary to reach the chemical accuracy of ± 1 kcal/mol. For molecules involving elements from the third row or higher in the Periodic Table there are a large number of core electrons which are chemically unimportant. ECPs (effective core potentials) 27 or PPs (pseudopotentials) 28 are introduced to account for these core electrons and in this way only the valence electrons are treated explicitly which lowers the computational cost. Scalar relativistic corrections are calculated as the expectation values of the mass-velocity and 9

27 Darwin operators (MVD) from the Breit-Pauli Hamiltonian 29 for the CISD (configuration interaction with single and double excitations) wavefunction. A potential problem arises in computing the scalar relativistic correction for molecules as there is a possibility of double counting the relativistic effect on the atoms with an ECP when applying a MVD correction to an energy which already includes some relativistic effects via the ECP. However, this has been shown to be negligible. Additional calculations were done at the CCSD(T) level with the secondorder Douglas-Kroll-Hess Hamiltonian 30 and all electron DK basis sets to correct for errors associated with the use of the effective core potential (ECP) and the above MVD approach. 31,32 An additional relativistic correction, the atomic spin-orbit corrections (SO), were calculated from the experimental values for the ground states of the atoms using Moore tables. 33 Core-valence correlation corrections ( E CV ) were calculated at the CCSD(T) level. For first row atoms, the core-valence correction accounts for the electron correlation effect of the 1s electrons, whereas for the transition metal atoms, it accounts for that of the (n-1)s 2 (n-1)p 6 electrons with n the row number of the transition metal. Heats of formation were calculated by combining the computed total atomization energy (ΣD 0,0K ) values with the known enthalpies of formation at 0 K for the elements from the JANAF table. 34 Heats of formation at 298 K were calculated by following the procedures outlined by Curtiss et al. 35 Other composite approaches are the Gn methods and their reduced approaches. Gaussian- 3 (G3) theory 36 is a procedure used to calculate energies of molecules containing atoms of the first and second rows of the periodic table based on ab initio molecular orbital theory. The G3MP2 theory 37 is a variation of G3 in which the basis set extensions are obtained at a reduced second order Møller-Plesset level. The total G3MP2 energy equation 36,37 is given by: 10

28 E 0 (G3MP2) = E(QCISD(T)/6-31G(d)) + [E(MP2/G3MP2large) E(MP2/6-31G(d))] + E(SO) + E(HLC) + E(ZPE) (1.10) The single point energy calculations were performed at QCISD(T)/6-31G(d), MP2/G3MP2large and MP2/6-31G(d) level of theory, respectively, at the MP2(full)/6-31G(d) geometry. The combination of these three energies gives a approximation to the total energy at QCISD(T)/G3MP2large level. All the single point energy calculations in the G3MP2 theory were done with a frozen core, except for the MP2 calculation with the G3large basis set which treats all electrons, also it includes the core-related corrections. The E(HLC) is the high level correction and empirically takes into account any remaining deficiencies in the energy calculation. The E(SO) is the spin orbit correction for the atoms and E(ZPE) is the zero point energy correction obtained from scaled (0.8929) HF/6-311G(d,p) frequencies. 1.5 Thermochemistry Thermodynamics 38 is the study of the energy effects which accompany chemical and physical changes. The internal energy of a molecule at 0 K is calculated as the sum of the electronic energy and the zero point energy: The molecular energy, for an ideal gas and over a temperature range T, say 0 K to 298 K, can be decomposed into energy contribution from electronic, vibrational, translational, and rotational motions: U T = U 0 + U 0 T (elec) + U 0 T (vib) + U 0 T (rot) + U 0 T (trans) (1.12) The enthalpy at T for an ideal gas is given by H 298 = U pv = U RT. The molecular entropy is calculated as a sum of electronic, vibrational, translational, and rotational contributions as a function of temperature. Thus, the free energy can be calculated as: 11

29 G T = H T TS (1.13) The enthalpy, entropy and free energy are state functions so they are independent of the path; these quantities can be used to determine if a reaction is endothermic or exothermic. For a given reaction at a specific temperature, the energy change is defined as the energy difference between the energy of products and the reactants taking into account the reaction coefficients. The free energy change can be obtained from the equilibrium constant (K) where R is the gas constant and T is the temperature at K: G = - RT ln K (1.14) Thermodynamic calculations in the liquid state require further approximations in addition to those for ideal gases. Solvation methods together with ideal gas calculations can be used to assess chemistry in the liquid state. Thus, in aqueous solution, the pk a values were calculated by combining the gas phase acidities with aqueous solvation free energies. To estimate the effects of solvation, we used the self consistent reaction field (SCRF) 39 approach with the COSMO parameterization 40 to calculate the electrostatic and non-electrostatic contributions to the free energies of solvation. Using these thermodynamic techniques for azole borane adducts and M(NH)(CH 2 )(OH) 2 transition metal complexes, we were able to predict and compare the acidities in both liquid and gas phase. For large molecules, it is very expensive or sometimes impossible computationally to calculate the heats of formation at the CCSD(T) level. Thus, to calculate the heats of formation of the azole borane adducts we used isodesmic reactions. Isodesmic reactions are define as " chemical changes in which there is retention of the number of bonds of a given formal type, but with a change in their relation to one another". 41 In other words, the types of chemical bonds broken in the reactants are the same as the types of bonds formed in the products. Thus, we used 12

30 a combination of G3MP2 level energies and isodesmic reactions using our highest level calculations of the heats of formation for the isodesmic reactions to predict the heats of formation of larger molecules. Using the above approaches, we predicted the heats of formation, adiabatic and diabatic bond dissociation energies (BDEs), Brønsted acidities, and fluoride affinities for many of the compounds of interest. In the following chapters we will apply these electronic structure techniques, coupled cluster with standard statistical mechanics treatments for gas phase thermodynamics and approximate techniques for condensed phase thermodynamics, to optimize the structures, to calculate the frequencies and accurate thermodynamic properties of alkali and alkaline earth compounds, Schrock type metal complexes and azole borane adducts. For the alkali metal compounds (hydrides, chlorides, fluorides, hydroxides and oxides) of Li, Na and K and alkaline earth metal compounds (chlorides, fluorides, hydroxides and oxides) of Be, Mg and Ca, the coupled cluster calculations were carried out with core-valence correlation always included due to the fact that the (n-1)s(n-1)p orbitals on the metals are higher in energy than some of the valence orbitals on the O, Cl or F. 13

31 CHAPTER 2 STRUCTURES AND HEATS OF FORMATION OF SIMPLE ALKALI METAL COMPOUNDS: HYDRIDES, CHLORIDES, FLUORIDES, HYDROXIDES, AND OXIDES FOR Li, Na, AND K From Vasiliu, M.; Li, S.; Peterson, K. A.; Feller, D.; Gole, J. L.; Dixon, D. A. J. Phys. Chem. A 2010, 114, Abstract Geometry parameters, frequencies, heats of formation and bond dissociation energies are predicted for simple alkali metal compounds (hydrides, chlorides, fluorides, hydroxides and oxides) of Li, Na and K from coupled cluster theory [CCSD(T)] calculations including corevalence correlation with the aug-cc-pwcvnz basis set (n = D, T, Q and 5). In order to accurately calculate the heats of formation, the following additional correction were included: scalar relativistic effects, atomic spin-orbit effects, and vibrational zero-point energies. For calibration purposes, the properties of some of the lithium compounds were predicted with iterative triple and quadruple excitations via CCSDT and CCSDTQ. The calculated geometry parameters, frequencies, heats of formation and bond dissociation energies (BDE) were compared with all available experimental measurements and are in excellent agreement with high quality experimental data. High level calculations are required to correctly predict that K 2 O is linear and that the ground state of KO is 2 Σ + not 2 Π as in LiO and NaO. This reliable and consistent set of calculated thermodynamic data is appropriate for use in combustion and atmospheric simulations. 14

32 Introduction The gas phase alkali metal compounds for M = Li, Na and K, especially the hydrides and halides have been extensively studied experimentally in terms of their spectroscopy, structure and thermodynamics. 1,2 Gas phase alkali metal hydroxides have been more difficult to study because monomers (MOH), dimers (M 2 O 2 H 2 ), and even trimers may be simultaneously present under the majority of the experimental conditions that were used. 3,4 The dialkali oxides M 2 O, especially Li 2 O, have been studied extensively, 5,6,7 although, there are uncertainties regarding their thermochemistry. For example, experiments under different conditions have been performed to determine the alkali superoxide bond dissociation energies (BDEs), but their results are somewhat uncertain. 8,9,10,11,12,13,14 The isolated alkali dioxides have been identified using low temperature matrix isolation spectroscopy. 15 There is substantial technological interest in the simple compounds of the alkalis. The alkali metal oxide diradicals (MO, MO 2, MO 3 ) have been observed in the upper atmosphere. 16,17,18 The source of alkali metals in the mesosphere is considered to be mostly meteoritic 19 and layers containing atomic alkali metals have been observed at about 90 km. 20 Atomic alkali metals (especially Na) are oxidized in the upper atmosphere forming the neutral oxides and hydroxides. Superoxides, formed by recombination reactions with O 2, are considered to be the main sink of the metal atoms beneath these layers. 21 There is also substantial interest in the role of alkali metal compounds that can be formed in the combustion of coal and other fuel sources, for example added biofuels. Alkali compounds can be formed from precursors in the fuel and from additives; examples include calcite or dolomite, which are used to remove sulfur. The alkali compounds formed during combustion have been implicated in fouling, corrosion, erosion, and agglomeration processes in power 15

33 plants. The alkali compounds can form fine particulates which are readily trapped on tube surfaces and can inhibit the stable operation of a coal-fired power plant leading to undesirable slagging, fouling, and corrosion in the boilers. In addition, alkali-based particulates can lead to the corrosion of gas turbine blades in commercial pressurized fluidized bed combustion reactors. Ash particles containing alkalis can be deposited on various combustor components causing serious damage, especially for gas turbine blades directly exposed to the combustion region. 22 The roles of alkali metal compounds in atmospheric and combustion chemistry are important reasons as to why high quality information about bond energies and heats of formation of alkali compounds are of interest. We have developed a composite approach 23,24 to the prediction of the thermodynamic properties of molecules based principally on molecular orbital theory using coupled cluster methods at the CCSD(T) level 25,26 together with the correlation consistent basis sets which allow the extrapolation of the electronic energy to the complete basis set (CBS) limit. 27 In selected cases the n-particle expansion is extended to include the explicit inclusion of iterative triple and quadruple excitations. 28,29 An estimate of the residual correlation error, defined as the difference between CCSDTQ and full configuration interaction (FCI), is obtained by application of a continued fraction approximant (cf est. FCI) originally formulated by Goodson in terms of SCF, CCSD and CCSD(T). 30 For particularly small molecules, such as LiH in this study, it is possible to replace the continued fraction approximant with explicit FCI. The recent design of systematically convergent, correlation consistent basis sets for the third, fourth and fifth row main group and transition elements using relativistic effective core potentials (RECPs) 31 has been essential to the application of highly accurate correlation methods to most of elements in 16

34 the periodic table. Using the new basis sets developed by Prascher et al. 32 for the alkali metals, we can expand our predictions to compounds of these elements. There are a wide range of calculations on alkali metal (Li, Na, K) hydrides, chlorides, fluorides, hydroxides and oxides. 33,34,35,36,37,38,39 A number of previous high level calculations are available especially for the alkali oxide and hydroxide heats of formation 35,36,40 with the most recent using slightly altered versions of the WnC methods 41 up through n = 2. Our goal is to expand on the previous work to provide reliable molecular constants, frequencies, and heats of formation for these alkali compounds. Computational Methods The thermodynamic properties and structure of the simple alkali metal (Li, Na and K) compounds (oxides, halides, hydrides and hydroxides) were calculated using coupled-cluster methods at the CCSD(T) level including core-valence (CV) correlation corrections with the augcc-pwcvnz basis set for n = D, T, Q and 5. These basis sets are abbreviated as awcvnz. The outer core electrons are included in the correlation calculations because they may be higher in energy than the valence s orbitals of the F or O bonded atoms as is found for K with both atoms and for Na with F. Equilibrium geometries were optimized at the CCSD(T)(CV)/awCVnZ level with n = D, T and Q except for the MO 3 compounds which were optimized at n = D and T. Tight d functions were included for chlorine and sodium. 42 Harmonic vibrational frequencies were calculated with all-electron basis set at the CCSD(T)/awCVTZ level except for the diatomic compounds. For the diatomic compounds, the harmonic frequencies and anharmonic constants were obtained at the CCSD(T)/awCVQZ level using a Dunham expansion. 43 The CCSD(T) energies were extrapolated to the CBS limit by fitting to a mixed Gaussian/exponential equation (1) 44 17

35 E(n) = E CBS + A exp[ (n 1)] + B exp[ (n 1) 2 ] (1) with n = 2, 3, and 4, giving the CBS-DTQ value. In select cases, CBS estimates were also obtained by extrapolating the total energy from basis sets through n = 5 using equations (2a), 45 (2b) 46 and (2c) 47,48 E(n) = E CBS + A exp[ B*n] E(l max ) = E CBS + B/[l max + 0.5] 4 E(l max ) = E CBS + B/l max 3 (2a) (2b) (2c) with an l max = n. We label the values obtained from Equation (2c) as CBS-Q5. Additionally, a fifth CBS estimate was obtained from the formulas proposed by Schwenke. 49 Scalar relativistic corrections were calculated at the CCSD(T)/second order Douglas- Kroll-Hess (DK) level with the all-electron aug-cc-pwcvtz-dk basis set. 32,50 E rel is the difference between E awcvtz-dk (the electronic energy calculated at the CCSD(T)/awCVTZ-DK level where the latter basis set is identical to awcvtz but employs DK contraction coefficients) and E awcvtz (the electronic energy calculated at the CCSD(T)/awCVTZ level). The atomic spin-orbit corrections (SO) were calculated from the experimental values for the ground states of the atoms using Moore tables 51 ( E SO (O) = -0.22, Eso(F) = -0.39, and E SO (Cl) = kcal/mol). The alkali metals and hydrogen have an outer (ns) 1 valence configuration and thus E SO = 0 kcal/mol to first order. Total atomization energies (TAEs) at 0 K were calculated from the following expression with delta referring to the difference between the molecule (reactant) and the atoms (products) for each energy component. 52 ΣD 0 = E CBS + E rel + E ZPE + E SO (3) 18

36 Heats of formation were calculated by combining our computed ΣD 0 values with the known enthalpies of formation at 0 K for the elements ( H f,0k (O) = ± 0.02, H f,0k (F) = ± 0.07, H f,0k (Cl) = 28.59, H f,0k (H) = 51.63, H f,0k (Li) = ± 0.2, H f,0k (Na) = ± 0.17, and H f,0k (K) = ± 0.1 kcal/mol) 1 Heats of formation at 298 K were calculated by following the procedures outlined by Curtiss et al. 53 The CCSD(T) calculations were performed with the MOLPRO program package. 54 The open-shell calculations were done with the R/UCCSD(T) approach where a restricted open shell Hartree-Fock (ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation. 25c,55 CCSDT and CCSDTQ calculations were performed with the MRCC program of Kállay and co-workers interfaced to MOLPRO. 56,57 The calculations were performed on Linux clusters at The University of Alabama and at Washington State University. Results and Discussion Geometries The optimized geometry parameters for the diatomic molecules (MH, MX, and MO) are shown in Table 2.1, for the alkali hydroxides (MOH) in Table 2.2, for the alkali dioxides (MO 2 ) and trioxides (MO 3 ) in Table 2.3 and for the dialkali oxide (M 2 O) in Table 2.4. For the 15 diatomics, the CCSD(T)(CV)/awCVQZ R MA bond lengths (where M is the metal and A the atom bonded to it) are universally slightly larger than the experimental values 2,58,59,60 but generally fall within Å of experiment. For LiH, LiF and LiCl use of larger basis sets, CBS extrapolation and inclusion of higher order correlation effects improves agreement with experiment but at a very high computational cost. A breakdown of the various components is provided in footnotes to Table 2.1. The largest discrepancy between CCSD(T)/awCVQZ theoretical values and experiment occurs for K Cl with a predicted bond length Å longer 19