Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride transfer and relationship to the water-gas shift reaction

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Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride transfer and relationship to the water-gas

shift reaction

Christian Sant Gjermestad

Thesis submitted for the degree of Master in Master of Science in Chemistry

60 credits

Department of Chemistry

Faculty of Mathematics and Natural Sciences

UNIVERSITY OF OSLO

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Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride

transfer and relationship to the water-gas shift reaction

Christian Sant Gjermestad

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c 2018 Christian Sant Gjermestad

Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride transfer and relationship to the water-gas shift reaction

http://www.duo.uio.no/

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Preface

This thesis finalizes the degree of Master of Science in Chemistry at the Department of Chemistry, University of Oslo. The experimental and computational work was conducted in the research group associated with the mass spectrometry laboratory at the Depart- ment of Chemistry in the time period from august 2016 to june 2018.

First of all I would like to thank my supervisor, Professor Einar Uggerud for guidance throughout these two years. I highly appreciated the stimulating conversations with the rest of the research group and I am especially thankful to Glenn B.S. Miller and Mauritz Ryding for giving me training on the instrument and in the use of the computational methods used in this thesis.

Finally I wish to thank my family, and Jølin for supporting me and understanding the long nights involved in writing this thesis.

University of Oslo, June 2018 Christian Sant Gjermestad

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Abstract

In this work the gas phase reactivity of methoxide complexes of Mg(II) haas been studied via mass spectrometry, quantum chemical calculations and statistical models for unimolecular kinetics. The hydride transfer from these complexes to CO₂ was found to be exothermic with a submerged barrier in the case of the cationic MeOMg⁺. The equivalent reaction with the anionic MeOMgCl2–

was determined to be thermoneutral, with a reaction barrier substantially increased in comparison to the cation. Quantum chemical calculations revealed the equivalent reaction with MeOMgCl to be the energetic step between energetics of the two following reaction, with each added ligand increasing barrier heights and increasing the endothermicity of the reaction. The partial charge of the Mg(II) moiety is suggested to be the primary factor determining the barrier height for the hydride transfer from these magnesium methoxide complexes. The equivalent reaction in the absence of Mg(II) was found to exhibit a computational hydride transfer barrier of

−10 kJ mol⁻¹, with products at −57 kJ mol⁻¹ relative to the reactants. This indicates the presence of Mg(II) does not improve the energetics of this hydride transfer.

The unimolecular and bimolecular reactivity of magnesium formate complexes was explored. The magnesium formate complexes were found to preferentially dissociate via loss of CO2 over loss of CO. The barriers for loss of CO2 from these complexes were found to be greater than activation energies typical for the water-gas shift reaction where decomposition of formate is thought to be a key step. A decrease in barrier heights was found when Mg(II) was replaced by less electronegative alkaline earth metals in silico.

The presence of H₂O, MeOH and CH₃CHO electrostatically bound to the Mg moiety of these magnesium formate complexes was found to drastically reduce the reaction barriers for decarboxylation and decarbonylation of the formate moiety to the point where these reactions dominate over most reactions where the neutral molecule plays and active role.

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1 Introduction

Combustion of fossil fuels currently contributes to 81 % of the world’s energy production [1]. This process releases CO₂ which contributes significantly to global warming resulting in an increase of smelting rate at the ice caps and ultimately causing sea levels to rise. It is thought that the excessive CO2 emissions can be counteracted by:

1. Long-term storage of the emitted CO₂ 2. Reducing emissions

3. Utilization of CO2 as a starting point for synthesis of useful organic chemicals The first option involves isolating CO₂ from other exhaust gas from energy plants and storing it semi-permanently in some manner. One suggestion on how to achieve this includes the use of minerals on the form (Mg, Ca)SiO₄ to generate carbonates [2]. A second option is injecting CO₂ into oil- and gas reservoirs, simultaneously increasing the amount of gas and oil which may be extracted while trapping the CO₂ in the microporous rock typical of such reservoirs [3]. It has been suggested that as much as 3600 gigatons of CO₂ may be stored in empty oil- and gas reservoirs in the northern United States alone [4]. This is roughly 100 times the amount of CO₂ released by mankind in 2015 [5]. The effects of sequestering CO₂ in such a high-pressure environment is being studied diligently via computational methods [6, 7].

The second school of thought is concerned with reducing anthropogenic emission of greenhouse gases. Measures such as transitioning from private cars to public transporta- tion may reduce global emissions substantially, as passengers cars are reported to be responsible for 12 % of the EU’s emissions of CO₂ [8]. The energy required to sustain of a rapidly growing human population will how ever quickly out pace such measures and other solutions to the planet’s energy requirements must be found. Replacing fossil fuels with renewable fuel sources such as solar, wind, or water power are good alternatives.

The use of hydrogen as an energy source is also being explored but is facing a great chal- lenge in finding efficient methods for storage. The suggested solutions include storage of hydrogen in cryogenic pressure vessels to increase density [9] and storing the hydrogen as metal hydrides. Especially MgH₂ is considered a promising candidate for this use [10].

The need for finding efficients means of storing hydrogen leads to the final point: Using CO₂ as a starting point for creating more complex organic molecules. This is not a new concept as industry has used CO₂ for synthesis of urea [11] and salicylic acid derivatives since the late 19th century [12]. Using formic acid and formate as a storage medium is an attractive prospect currently being explored. This process would simultaneously fixate CO₂ and store hydrogen. For such a process to be feasible good catalysts are needed for both the hydrogenation and dehydrogenation steps, a topic which will be explored further in Section 1.1.

1.1 CO

₂

as a starting point for energy storage

The previously mentioned MgH₂ has a hydrogen content of 7.7 % and sports a dihy- drogen desorption enthalpy of 74(1) kJ mol⁻¹ [13]. Though this energy requirement may be lowered by doping with transition metals, for example Ti, V, Mn, Fe or Ni [14], this will result in relatively high operating temperatures. Formic acid has a somewhat

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lower hydrogen content of 4.3 %, but is dependent on good dehydrogenation catalysts as this process has been found computationally to exhibit a barrier of 280 kJ mol⁻¹ [15].

Tables 1 and 2 show examples of catalysts used for hydrogenation/dehydrogenation of CO₂/HCO₂H. For a more comprehensive overview of such catalysts please see the reviews by Enthaler et al. [16] and Jessop et al. [17]. Both classes of catalysts are centered by noble metals, increasing the price of the stored hydrogen. The dehydrogenation catalysts require a higher operating temperature which could be inhibitive for the use of hydrogen as an energy source in personal vehicles. Finding less expensive catalysts is an essential step towards a hydrogen economy, and in this work the possibility of Mg facilitating the hydride transfer step of hydrogenation is considered.

Table 1: A selection of catalysts for hydrogenation of CO₂ Catalyst T [^◦C] Ref.

RuCl(oAc)(PMe₃)₄ 50 [18]

[RuCl2(TPPMS)2]2 80 [19]

RuH₂(PMe₃)₄ 50 [20]

RhCl(TPPTS)₃ 81 [21]

Table 2: A selection of catalysts for dehydrogenation of HCO₂H Catalyst T [^◦C] Ref.

PtCl₂(Pbu)₃ 118 [22]

IrCl₃(PEt₂Ph)₃ 118 [22]

[Rh(CO)₂Cl]₂ 100 [23]

[Ru(H₂O)₆](tos)₂ 120 [24]

1.1.1 Hydride transfers

To set the state for further discussion of hydride transfers, the concept ofhydride affinity (HA) will be defined. In a reaction such as

AH⁻+ B−−→A + BH⁻

the hydride affinity of the two species A and B is the primary factor in deciding the energetics of the reaction. In Table 3, the hydride affinities of some common reducing agents and molecules relevant to this work are listed. Here hydride affinity is defined as the change in free energy associated with detachment of the hydride:

RH⁻−−→R + H⁻ HA(R) = ∆ H

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Table 3: Gas phase hydride affinity of selected molecules RH^– Compound (R) HA(R) [ kJ mol⁻¹] Ref.

BH₄^– Borane 310(12) [25]

AlH4–

Alane 314(17) [26, 27]

HCO₂^– Carbon dioxide 211(5) [26, 27]

H₃CO^– Formaldehyde 170(4) [26, 27]

CH3CH2O^– Acetaldehyde 157(5) [26, 27]

C₆H₇^– Benzene 91(19) [26, 27]

HCO^– Carbon monoxide 23(2) [26, 27]

1.1.2 Biological hydride transfer

The planet’s greatest success story in utilization of CO₂ for energy storage is often at- tributed to the plants. It has been estimated that plants annually fixate 100 gigatonnes of carbon via photosynthesis [28]. This dwarfs anthropogenic emissions, but primarily counteracts soil- and plant respiration. Photosynthesis is divided into two cycles: The light cycle, where energy from the sun is captured, and the dark, or Calvin cycle, where CO₂ is captured and converted to carbohydrates. In this cycle CO₂ enters the enzyme ribulose bisphosphate carboxylase oxygenase (RuBisCO) and binds to Mg(II) in the active seat. A C–C bond is then formed between CO₂ and ribulose 1,5-biphosphate (RuBP), resulting in formation of 3-phophoglycerate (3PGA). Progress has been made towards understanding the mechanisms of this step by Miller, F¨aseke and Uggerud [29] and Miller and Uggerud [30]. In the next step reduced nicotineamide adenine dinucleotide phosphate (NADPH), produced in the light cycle, transfers a hydride to the carbon of the CO₂ which is now part of 3PGA. With this hydride transfer a phosphate group detaches from 3PGA, forming the final product of this cycle, glyceraldehyde 3-phosphate (G3P), which ultimately is converted to glucose.

3CO₂

RuBisCO

COO^–

CHOH CH₂O P 3 x 3-PGA

6 ATP

6 ADP

6 NADPH

6 NAPD⁺ + 6 P_i CHO

CHOH CH₂O P

6 x G3P

1: Carbon fixation

2: Reduction CHOH

CHOH CH₂O P C CH₂O

O P

3 x RuBP

Figure 1: The relevant steps in the dark cycle of photosynthesis. Adapted from [31]

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N

H O

NH₂

R N

H O

NH₂

R

+ H^– H

O P

O O

O P O

O O

R Mg²⁺

O P

O O

O P O

O O

R Mg²⁺

Figure 2: The hydride transferred in NADPH −−→ NADP⁺+ H^– is highlighted in red.

The pyrophophate group which frequenty coordinate to Mg(II) is also shown [32]

As shown in Fig. 2, the hydride transferred from NADPH in the reductive step of the Calvin cycle is bound to a carbon atom. To model the active site of this enzyme, a methoxide ligand, emulating NADPH will be attached to Mg(II), in total MeOMg⁺. Ligands will be added to simulate the effect of metal coordination around Mg(II), a factor which is known to be of great import in enzymatic catalysis [32, 33].

From the hydride affinities in Table 3, the ∆ H for the hydride transfer from C3HO^– CO₂ may be calculated:

As we have the hydride affinities of both formaldehyde and carbon dioxide H₃CO⁻−−→ H⁻+ H₂CO ∆ H = 170(4) kJ mol⁻¹ HCO2−−−→ H⁻+ CO2 ∆ H = 211(5) kJ mol⁻¹

the ∆H of the hydride transfer from methoxide to carbon dioxide may be found H3CO⁻+ CO2 −−→ H2CO + HCOO⁻ ∆ H =−41(6) kJ mol⁻¹

In this study the effects of adding Mg(II) to these systems will be considered via the thermochemistry and kinetics. Understanding the factors governing the energetics and kinetics of the hydride transfer from complexes of magnesium methanolates to CO₂ may ultimately lead to improvement of hydrogenation catalysts.

1.2 The water-gas shift reaction

In order for hydrogen to be a viable source of energy, it must be produced in an energy- efficient manner. The industrially used water-gas shift reaction (WGSR) is a moderately exothermic reaction between steam and carbon monoxide thought to have HCO2H or HCO₂^– as an intermediate [34]:

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Computational studies have suggested that unimolecular dissociation of HCOOH to CO + H₂O and H₂+ CO₂ occurs through transition states as shown in Fig. 3. Akiya and Savage found in silico barriers of 280 kJ mol⁻¹ and 284 kJ mol⁻¹ for former and latter reaction, respectively [15]. Blake, Davies and Jackson found an experimental barrier of 253 kJ mol⁻¹ for decarboxylation of HCOOH in the gas phase [36].

C

O O

H H C

O O

H

O C O H

H C

O O

H

CO2 + H2

CO + H₂O

Figure 3: The mechanisms for unimolecular decomposition of formic acid suggested by Blake, Davies and Jackson [15] as well as by Goddard, Yamaguchi and Schaefer [37]

This reaction can operate at lower temperatures with one set of catalysts or at higher temperature with a different set of catalysts. For the colder process the catalysts are generally based on copper, zinc and aluminum while for high-temperature reactors the catalysts are primarily iron and chromium with small amounts of Mg [38]. The WGSR has been found to have an activation energy of 71.1 kJ mol⁻¹ with a low-temperature catalyst consisting of pure Cu (111) [39]. Shishido et al. studied the effect of incrementally increasing the amount of Mg added to industrial Cu/Zn-based WGSR catalysts and found 0.1 mol % Mg to substantially increase reaction rates and lower activation energies to 30−50 kJ mol⁻¹depending on the particle size. This activation is substantially lower than other Cu/Zn-based catalysts, such as Cu/MnO₂ (55 kJ mol⁻¹) [40] and Cu/ZnO/Cr₂O₃ (78.2−86.6 kJ mol⁻¹) [41]. Shishido et al. suggested that the presence of Mg in the catalyst facilitates the oxidation of Cu to Cu⁺, but the authors do not offer further explanation.

In high-temperature iron catalysts Cr2O3 is often used avoid sintering of the catalyst [42] which would reduce the surface area and therefore its efficiency. Boudjemaa et al. saw an increase in the efficiency of such catalysts by replacing Cr with Mg, suggesting that Mg promoted formation of smaller and more well-dispersed Fe particles [42]. Although the Cr(III) most often used in these catalysts is of a lesser health risk to humans than Cr(VI), replacing this metal with the very abundant, environmentally friendly and catalytically more potent Mg would be very favorable.

The presence of formate in water-gas shift reactors has been confirmed on multiple accounts via IR spectroscopy, both in the gas phase and bound to the catalyst [43–45].

Its role in the reaction is however disputed by several authors, with different results depending on the catalyst. Kalamaras, Panagiotopoulou, Kondarides and Efstathiou reported formate to be a spectator species in the WGSR utilizing a Pt/TiO₂ catalyst.

Noto, Fukada, Onishi initially found a similar result, where formate was found to not be actively involved in the decomposition of formic acid [46] on alumina and silica catalysts.

Some of the same authors, namely Ueno, Onishi and Tamaru, found evidence for this exchange on ZnO and MgO catalysts two years later [47]. Amenomiya and Pleizierand also argued the case for formate as an active species by demonstrating that the rate of

1Calculated using standard enthalpies of formation found in [35]

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the WGSR increases with the area of the alkali-metal catalyst covered in formate. This may however be a case of formate participating passively in the reaction, for example by manipulating the charge distribution in the catalyst.

Mross proposes in his 2006 review that including alkali metals causes donation of electron density from the Fe of a high-temperature WGSR catalyst to the alkali metal [48], thereby reducing the electron density available to Fe for binding hydrogen and thereby facilitating release of the products. One may on the other hand imagine that a more electropositive catalyst will bind CO₂ more strongly due to strong electrostatic interactions, and this is another consideration. Amenomiya and Pleizier found the rate of the WGSR to be higher with more electropositive alkali metals, i.e. Cs>K>Na>Li [45], indicating that the desorption of CO₂ is less problematic. Alkaline earth metals are more electronegative than alkali metals and would result in a lesser degree of electron donation as additives to WGSR catalysts. These additives may additionally have an effect on the lifetime of the catalyst, but these factors are not considered in this work.

A mechanism for the catalytic WGSR including a formate intermediate is suggested based on [49] and [50], shown in Fig. 4.

O H O H C

O H

H O C

CO + H₂O

H

O O H C

O H O

C

O O C

CO₂ + H₂ ^O

O C H

H

O O

C H H

O O C H

H

Figure 4: Illustration of a suggested mechanism for the water-gas shift reaction involving a formate intermediate. The gray rectangle represents the catalyst surface.

In short, limited research has been performed on the effect of Mg in these catalysts and the role of formate as an active intermediate is disputed. By studying how Mg alone catalyzes the water-gas shift reaction, insight may be gained into its role in the WGSR. To model these reactions HCO₂Mg⁺ will represent a a site in the catalyst where formate is attached to Mg. Experimental and computational values for the decarboxyla-

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Computationally replacing Mg for other earth alkali metals will reveal the effect of the electropositivity of the metal on the decarboxylation and decarbonylation barrier heights.

1.2.1 Microsolvation

In the gas phase bimolecular reactions are often initiated by the two species forming a complex due to electrostatic attraction. With sufficient energy the complex may then climb the reaction barrier and arrive in an energetic minimum corresponding to a new such complex. The two species may then separate to yield the final products. Incrementally adding solvent molecules to a system in silico has revealed that the energetic minima corresponding to these complexes become increasingly shallow, and disappearing entirely as the number of solvent molecules approaches a number equivalent to macroscopic solvent [51]. Adding solvent molecules to a system can primarily affect the reactivity in two ways.

The first involves the solvent molecules changing reaction mechanism. Water molecules often act as a proton relay where each proton travels only a short distance but the total distance from the donor to acceptor is relatively large. This mechanism is common in the active sites of enzymes, where protons often travel great distances [52]. See Fig. 5 for an example of a proton relay reducing the barriers for unimolecular decomposition of formic acid to CO + H₂O or H₂+ CO₂. Akiya and Savage found these barrier to decrease by 71 and 107 kJ mol⁻¹ for the decarboxylation and decarbonylation when compared to the analogous transition states in the absence of water [15].

O H

H C

O O

H H C

O O

H H H O H

CO-loss CO₂-loss

209 kJ mol^-1 178 kJ mol^-1

C

O O

H

H C

O O

H

280 kJ mol^-1 284 kJ mol^-1

Figure 5: Water-catalyzed transition states compared to non-catalyzed transition states.

The water molecule has been marked in blue. Adapted from [15]

In reactions where a metal catalyst is used a second effect becomes important. When the solvent molecule attaches to the catalyst some electron density is transferred from the solvent molecule to the metal, which will particularly affect the bonds between the metal and any substrates containing partially negative groups, such as a CO. Weaker M–substrate bonds will affect the relative energy of the transition states as well as how much energy is required to desorb the products from the catalyst surface. This may be related to the fact that a higher ratio of H₂O/CO has been found to result in a more complete conversion of CO to H₂ in the WGSR, while reducing the amount of solid carbon and methane formed [53–55]. The role of water as a proton relay has been established as a likely explanation for the increased reaction rate, as illustrated in Fig. 5.

Any molecules of water not actively participating in the reaction will nonetheless donate

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electron density to the catalyst and affecting the reactivity in this manner. Some work has been done by Shido, Asakura and Iwasawa on the effect of water on the decomposition of formate in a water-gas shift reactor using the catalysts MgO, ZnO, CeO₂ and Rh/CeO₂ [56–59]. In general the presence of H₂O was found to decrease the activation energies, increase reaction rates as well as resulting in almost exclusively decarboxylation. One notable exception is the case of MgO where the activation energy increased. Several computational studies have been undertaken on reaction mechanisms different from the ones suggested by Shido et al., particularly involving Au/CeO₂ catalysts [60–62].

The role of water in the unimolecular dissociation of HCO₂Mg⁺ will be considered experimentally via a near-thermal reaction between this ion and H2O with computational elucidation using quantum chemical calculations. The effect of adding a second molecule of water, as well as other common solvating molecules, to the Mg moiety will be evaluated computationally. The proton relay mechanism will be compared with the water-assisted unimolecular decomposition to HMg⁺+ CO₂.

1.3 Aim of study

1. Explore the factors governing the energetics of the hydride transfer from magnesium methoxide complexes to CO₂: Replacement of the metal and addition of the ligands Cl, OH or OH to the Mg moiety.

2. Evaluate the role of Mg(II) in the water-gas shift reaction. Compare the selec- tivity for decarboxylation over decarbonylation of the formate intermediate of this reaction in absence and presence of water.

3. Consider the electron donating effect of addition of one and two solvating molecules to the Mg moiety on the unimolecular dissociation of formate

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2 Experimental methods

The Waters MicroMass Q-Tof 2 mass spectrometer with an electrospray ionization source was used for all experimental measurements. A sketch of this instrument is shown in Fig.

6. The five primary components of this instrument will be explained in due order: The ion source, quadrupole mass-analyzer, collision cell hexapole, time-of-flight (TOF) mass analyzer and the multi-channel plate (MCP) detector. These will be explained in due order.

Figure 6: Instrument sketch for the Waters MicroMass Q-Tof 2 [63]

The instrument in our lab has been modified with a inlet system allowing introduction of chemicals not readily available in gas flasks into the collision cell hexapole. A sketch of this setup is shown in figure 7.

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Figure 7: Sketch of the custom inlet system of the laboratory’s Q-Tof 2

2.1 Electrospray ionization

The first step of a mass-spectrometric analysis is generation of ions. Conventional electron ionization (EI) generally results in substantial fragmentation of the ions which may be impractical when the aim is to study the reactivity of this ion. Therefore electrospray ionization is chosen, a much gentler ionization method which causes little fragmentation and is routinely used for analytes ranging from small organic compounds to biopolymers [64]. Fig. 8 shows a sketch of the Waters Z-spray electrospray ion source connected to the instrument in our laboratory. A feature not shown in this picture is the possibility of adjusting the position of the needle, a parameter which is essential in achieving high signal for parent ions for further study.

To initiate ionization, and electric potential of opposite polarity is placed over the tip of the capillary and on the backplate opposite to it. With a sufficient potential difference a Taylor cone forms [66] and ions of the charge corresponding to the sign of the potential difference move to the front of the cone. At a second potential difference threshold droplets will start leaving the cone and a spray is formed. Equation 1 below describes the capillary voltage Von needed to initiate the electrospray [67]:

Von ≈

rcγcosθ ₀

1/2

ln(4d/rc) (1)

Where r_c is the radius of the capillaryγ is the surface tension of the solvent, θ is the half-angle of the Taylor cone,₀ is permittivity of vacuum andd is the distance between the capillary and the back plate [66]. Using this equation the capillary potential required to electrospray a solvent may be estimated. For the potentials required to electrospray some common solvents, see Table 4.

The released droplets contain both ions and solvent. This solvent gradually evaporates

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Figure 8: Instrument sketch for the Waters Z-spray [65]

Table 4: Capillary voltages required to initiate electrospray [67, p. 12]

Solvent CH₃OH CH₃CN DMSO H₂O Von [kV] 2.2 2.5 3.0 4.0

The process repeats until only the ions remain.

γ < Q²

16πa³₀ (2)

Here Q is the charge of the droplet and a₀ is the radius of the droplet.

2.2 Quadrupole

The quadrupole may act as a mass analyzer or simply as an ion guide. It consists of four precisely machined rods. A positive direct current (DC) voltage with a superimposed radio frequency (RF) component is placed on two rods opposite to eachother (+(U + V cos(ωt))). On the other pair of rods, a negative DC voltage with an RF component 180^◦ out of phase in comparison to voltage on the other pair of rods is applied [69, p.

147].

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Figure 9: Principle sketch of a quadrupole [68]

Ions entering the electric field generated by these voltages will move through the quadrupole in an oscillatory manner described by the Mattieu equations [69, p. 148]:

d²x

dτ² + (a_x+ 2q_xcos(2τ))x= 0 (3) d²y

dτ² + (ay+ 2qycos(2τ))y = 0 (4) where

a_x =−a_y = 4eU

mir²₀ω², q_x =−q_y = 2eV

mir²₀ω², τ = ωt

2 (5)

Herer₀ is the distance from the center of the quadrupole to a rod,eis the elementary charge, m_i is the mass of the ion and ω is the RF frequency. A combination of DC (U) and RF voltages (V) may allow only ions of a specific m/z through the quadrupole, or a range of ions with successivem/z . Setting the DC voltage to zero lets all ions through.

By systematically varying these voltages the entire spectrum is sampled.

2.3 Hexapole collision cell

The hexapole is a radio frequency-only quadrupole with two additional rods for more a more stable ion path. It may be used as an ion guide, but collision gas can be introduced to study bimolecular reactions or -induced dissociation (CID), a concept which will be explained in Chapter 1.6. When studying reactivity it is important to have some idea about how many collisions the parent ion is exposed to at a given pressure. One way of

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λ= k_BT

σp , σ =π(2r)² (6)

Here k_B is the Boltzmann constant, T is the temperature in Kelvin, r is the radius of the particles and σ is the collisional cross-section of the particle. The gas used for collisional activation in this study is argon, which based on van der Waals radius has a geometric cross-section of 0.44 nm. With a 16 cm long hexapole, this means that at p = 5.8·10⁻⁴ mBar, on average one collision will occur. Note that this expression does not account for Coulomb interactions, meaning that ions will experience collisions with neutrals more often at a given pressure than predicted by this expression. This is especially important for the ion-neutral reactions studied here, as multiple collisions will both add more energy to the ion and cool it via collision in an unknown ratio.

We therefore generally strive to operate under single-collision conditions. In some cases higher pressures have been used to get a qualitative picture of the reaction, especially in cases where no reactivity is observed at lower pressures.

2.4 The Time of Flight mass analyzer

The time of flight (ToF) mass analyzer is a fast method of acquiring mass spectra. De- pending on the design, the mass resolution (see eq. 2.4) may reach 20 000. To illustrate, a resolution of 20 600 is required to separate the peak of ¹³CC₆H₇⁺ (m/z 92.0581) from that of C₇H₈^•+ (m/z 92.0626) [69, p. 91]. The Waters Q-Tof 2 has a mass resolution limit of 10 000 [63, p. 81].

Mass resolution = m/z

∆(m/z) (7)

∆(m/z) is the full peak width at half maximum for the chosenm/z. If the resolution of the instrument is not high enough to get an accurate molecular formula, isotope dis- tributions may be of some help. An ion containing Mg will have a [100 : 10 : 11] isotope pattern of [²⁴Mg : ²⁵Mg : ²⁶Mg]. Ions containing MgCl₂ will have a very distinct [100 : 13 : 80 : 8 : 19] pattern. The contamination of a peak containing these elements can therefore be estimated by the deviation from the isotope distribution pattern. Fragmentation of the ion can also help confirm that the peak corresponds to the supposed ion.

The operating principle of the ToF mass analyzer is that the m/z of an ion may be determined by the time it takes to travel through the flight tube. To arrive at an expression for calculating m/z based on flight time, we begin by describing the energy transferred to the ion by its travel through the electric field constituting an acceleration region prior to the flight tube:

E_el =qU =eZU (8)

e is the elementary charge, and Uis the potential difference accelerating the ion. To couple this energy to the velocity of the ion, the classical expression for kinetic energy is used:

E_k = 1

2mv² (9)

With the assumption that E_el=E_k, the following expression is found:

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v =

r2zeU m =√

2eU ·m z

−1/2

(10) This shows that the velocity of the ion after leaving the accelerating region is inversely proportional to the square of them/z. With the length of flight tube known, the time of flight may be found:

t = d

ν = D q2zeU

m

= Ds

√2eU rm

z (11)

With some rearrangement, we arrive at the final result, which is used to calculate the m/z of the ions:

m/z = 2eU t²

d² (12)

2.5 The Multi-channel plate signal detector

The multi-, or micro-channel plate (MCP) consists of several signal-multiplying channel- trons such as the one shown in fig. 10. When entering the channeltron the ion beam hits the wall causing ejection of two electrons. When these electrons hit the opposite side, a total of four electrons are released. This process continues doubling the number of electrons until the end of the channeltron is reached and the electrons are picked up by the detector. Signal amplification in an MCP is typically of the order of 10³ – 10⁴, while it is possible to stack two or more MCPs to achieve 10⁶ – 10⁸ [69, p. 204]

Ion beam

Electrons Multiplier tube

1-2 kV

-

⁺

Figure 10: Sketch of a linear channeltron

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Figure 11: Illustration of a multiple-channel plate signal amplifier. (TikZ code adapted from [70])

2.6 Collision-Induced Dissociation

As electrospray ionization causes very little fragmentation, information about the fragmentation products must be acquired in another manner. Some inert gas, often argon or helium, is introduced into the collision cell. The ions are accelerated to a given translational energy by potential differences prior to entry in the collision cell. The collision between the ion and neutral atom or molecule converts some unknown portion of translational energy into rotational and vibrational energy of the ion, which is then available for unimolecular reaction. The energy transferred to the ion this collision is commonly presented in the center-of-mass frame:

E_CM =E_LAB mneutral

m_neutral+m_ion (13)

E_LAB is the translational energy of the ion after leaving the acceleration field. Note that this expression does not describe how much energy is converted into vibrational and rotational energy, meaning that the actual energy available for reaction is unknown. This makes E_LAB an upper limit.

2.6.1 Breakdown curves and threshold energy

CID experiments often reveal several product ions resulting from competing unimolecular reactions. A qualitative impression of the relative rates of these reactions may be gained by recording breakdown curves; plots of parent ion energy versus the observed intensity of each ion. A linear fit may then be made to the data points making up the upward slope of a product curve, with extrapolation tox= 0 yielding the threshold energy of the

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reaction. This energy is generally comparable to the computational dissociation energy [71–75], giving a valuable indication of the validity of a suggested reaction mechanism.

Fig. 12 shows a breakdown curve of a single product ion and the points chosen for the linear fit. Here it is shown that by excluding the first data point in the linear fit a significantly different threshold energy is found. Which points to include is not always certain, and in in cases where there is reasonable doubt, the average 1.52 and 1.60 eV is taken and reported as 1.56(4) eV.

0 1 2

0 100 200 300 400 500

0 1 2

Product ion

Points used in linear fit

Counts/scan

R 2

= 0.95

y = .0161x - 2.348

E

threshold

= 146 kJ mol -1

Counts/scan

E CM

[kJ mol -1

] R

2

= 0.962

y = .0178x - 2.738

E

threshold

= 154 kJ mol -1

Figure 12: Illustration of how definition of the slope may influence the threshold energy

The pressure in the collision cell dictates the number of collisions the ion is exposed to and the threshold energy is dependent on this quantity. To find a vacuum threshold energy several breakdown curves may be recorded at increasing pressure, resulting in five threshold energies. These may then be plotted against the corresponding pressures

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0.0 1.0x10 -4

2.0x10 -4

3.0x10 -4

4.0x10 -4

5.0x10 -4

6.0x10 -4 1.2

1.3 1.4 1.5 1.6 1.7

Onsetenergy[eV]

Nominal pressure [mBar]

y = -816.6 + 1.7569

R 2

= 0.961

Figure 13: Threshold energies for the loss of CH₂O from CH₃OMg⁺ at various pressures.

2.7 Kinetic Isotope Effect

Replacing one isotope of an element with another can have dramatic consequences for the rate of a reaction. This may be a valuable tool in the elucidation of reaction mechanisms.

The kinetic isotope effect (KIE) describes this change and may be expressed in terms of the ratio of the rate constantskfor the reactions with the original and isotope-substituted species. Here this is exemplified with a protium and deuterium:

KIE = kD

k_H (14)

In some cases the KIE for a H/D exchange may be below 1, meaning that the reaction is faster with deuterium than with protium. KIEs as high as 8 are relatively common, and even higher KIEs may be found if the reaction barrier is particularly sharp and narrow.

Here quantum-mechanical tunneling is likely and doubling the mass of the tunneling object will drastically reduce this effect.

The change in the rate constant when exchanging one isotope for another is due to the changes in the zero-point vibrational energies of the transition state and the ground state:

∆ZPE_GS−∆ZPE_TS = ∆∆G^‡∝KIE (15)

Here ∆ZPE =ZPE_D −ZPE_H is the change in zero-point energy due to isotope substitution. See fig. 14 for an illustration of this effect. Zero-point vibrational energy is defined as:

ZP E = 1

2hν (16)

ν is the vibrational frequency of the oscillator, which depends on the reduced massµ of the system:

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ν = 1 2π

s k

µ; µ= m1m2

m₁+m₂ (17)

ZPE_GS,D ZPE_GS,H

ZPE_TS,D ZPE_TS,H

Reaction coordinate

Energy ZPED

ZPE

H

Figure 14: Schematic potential energy diagram illustratingg change in relative energy upon isotope substitution

In cases where the ground state and transition state have dissimilar vibrational frequencies, the increase in reduced massµmay cause the ZPE_{T S} to decrease by more than ZPE_GS, thereby resulting in a greater ∆∆G^‡ and a greater KIE. The transition states with frequencies most dissimilar from their ground states should exist in thermoneutral reactions where the proton is shared equally between donor and acceptor. In fact the vibrational frequency describing the reaction path may indeed be entirely independent of the reduced mass of the proton.

2.8 Experimental details

2.8.1 Solutions

The solutions used to generate the ions studied in this work are listed in table 5. In some cases other concentrations were used for initial experiments, but the concentrations listed in table 5 are the ones which were found to result in the highest and most stable signals.

For isotope labeling experiments the relevant component was replaced by an identical concentration of the isotope-labeled component.

2.8.2 Analog instrument settings

The pressure of desolvation gas, nebulizer gas and other source settings not described in the appendix are shown in table 6 below. Note that the description of the needle position

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Parent ion Added compounds CH₃OH : H₂O

CH₃OMg⁺ 2 mM MgCl₂ 1 : 1

CH3OMgCl2–

2 mM MgCl2, 5µL/mL Et3N 1 : 1 MgO₂CH⁺ 2 mM MgCl₂, 4 mM HCOOH 0 : 1 Cl₂MgO₂CH^– 4 mM MgCl₂, 1 v.% HCOOH 0 : 1

Table 5: Solutions used to generate the parent ions studied in this work.

Parent ion Desolv. gas [psi] Nebulizer gas [^◦] Needle pos.

CH₃OMg⁺ 600 120 Distant

CH₃OMgCl₂^– 350 120 Close

MgO₂CH⁺ 600 120 Close

Cl₂MgO₂CH^– 50 120 close

Table 6: Analog source settings for generation of ions.

2.8.3 Degassing of inlet chemicals

In order to remove N₂, O₂ and other atmospheric gases, the chemicals connected to the inlet system (fig. 7) were degassed via freeze thawing. The procedure is as follows:

1. Open gate valve to exhaust

2. Freeze chemical by submersion of the flask in liquid N₂

3. Open gate valve (1) between flask and the rest of the inlet system 4. Note the maximum pressure increase

5. Wait for pressure to stop falling

6. Close gate valve (1) between theflask and the rest of the inlet system 7. Smelt substance in pear flask by submersion of the flask in tepid water

8. Repeat steps 2-8 until the maximum exhaust pressure does not change appreciably from cycle to cycle

3 Computational methods

3.1 Quantum chemical calculations

While mass spectrometry serves as an experimental platform for studying gas-phase reactions, it provides minimal structural information. The systems studied in this work are relatively small with a similarly small number of isomers, meaning that high-level quantum chemical calculations may be used for determination of molecular structure and reaction mechanisms. After a concise benchmark and consultation of the literature, Gaussian 4 (G4) was chosen as the primary computational method. This is a compound method utilizing several levels of theory [76] which will be explained in due order. Calcu- lation of partial charges, implicit consideration of solvent and the use of internal reaction

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coordinate-calculations to ensure that a transition state connects the expected minima will also be outlined. Gaussian 09 [77] was used for all quantum chemical calculations.

The very basis of all quantum chemical methods is that some wavefunction Ψ can represent a particle. The wavefunction itself has no physical meaning, but can be used to predict observable properties of the particle when used in manners such as:

hHi= Z

Ψ^∗HΨdτ =hΨ^∗|H|Ψi=E (18)

Here hHi is the expectation value of the Hamiltonian operator, which when used on a normalized wavefunction gives the total energy of the system. Two one-particle wavefunctions can be combined to describe systems such as the hydrogen atom or the electronic structure of Li⁺ or He. For systems with more than two particles no exact solution of the Schr¨odinger equation can commonly be found, meaning that the wavefunction must be approximated in some manner. The various methods for doing this will now be discussed.

3.1.1 Hartree-Fock theory

Hartree-Fock theory is based on the assumption that the exact wavefunction can be approximated by a single Slater determinant [78, p. 296]:

|Ψ₀i=N_e!^−1/2det|φ_a(1)φ_b(2)· · ·φ_z(N_e)| (19) The spin orbitalsφ, which are products of the spatial orbitalψand a spin state αog β, are regularly expressed as a linear combination of some basis functions χ_i as shown in eq. 20 [78, p. 298].

φ=X

i

c_iχ_i (20)

These basis functions are most commonly Gaussian-type [78, p. 303] (χ = exp(−ax²)) or Slater-type (χ =kexp(−ax)), though in principle other types of functions can be used. The coefficients c_i resulting in the lowest-energy wavefunction is typically varied using what is know as the variational principle, which states that the exact energy may be assumed to be lower than the calculated energy [79]. Many quantum chemical methods are not variational and the energies acquired may be lower than the exact energy.

To determine the energy of the system the single-electron wavefunction is evaluated using the Fock operator:

f1 =h1+X

m

[2Jm(1)−Km(1)] (21)

Here h1 is the one-electron Hamiltonian, Jm is the Coulomb operator, and Km is the exchange operator for the m occupied orbitals. The Fock operator gives the orbital energy as an eigenvalue of the wavefunction:

f₁ψ_n(1) =_nψ_n(1) (22)

By using eqs. 20, and 22, the Roothan-Hall equations are found [78, p. 299]:

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Here F is a matrix of Fock operators f₁. c consists of the coefficients c_i, is a matrix of orbitals energies, and S is a matrix of orbital overlaps. As the Fock operator requires the wavefunction for evaluation of the energy, a set of coefficients for the basis set functions χ_i must be guessed. These are used to calculate a Fock matrix which can then be used to evaluate the energy of the system. The coefficientsc_iare then calculated from eq. 22, a new Fock matrix is found and used to calculate the new energy of the system. Once the energy changes little from iteration to iteration the calculation is done.

A central issue in this method is that it is difficult to differentiate between a global and local energetic minimum.

3.1.2 Basis sets

The basis functions mentioned above belong to basis sets. They primarily belong to one of two families: Pople or Dunnings. Slater-type functions are computationally demanding and are often approximated by a linear combination of primitive Gaussian functions [78, p. 304]. Some basis sets use more than one Slater-type function to describe the valence electrons. Those using only one basis function is called single-ζ (SZ), those with two are called double-ζ (DZ), those with three triple-ζ, et cetera.

Pople sets

The notation for Pople sets may be generalized ask-nlmG[79, p. 203]. kis the number of primitive Gaussians describing the core orbitals. nlm indicates the splitting of the valence. If only one number is present (n), there is no splitting (SZ), if two are present, it is split into two (DZ) and equivalently when all three numbers are present (TZ). The values of nlm give the number of primitive Gaussians used. Consider 3-21G. 3 is the number of primitive Gaussians for the core orbitals,2and 1give the number of primitive Gaussians used for the inner and outer part of the valence orbitals respectively.

Dunnings sets

The notation for Dunnings’ correlation-consistent basis sets is simpler: cc-pVNZ, N giving the valence splitting. If aug- is added as a prefix diffuse functions are included.

These are broad and less intense than the usual functions, which is often necessary to describe systems where the electrons are more delocalized, such as the anions studied here.

3.1.3 Electron correlation methods

Hartree-Fock theory describes electronic ground-state systems, but does not account for correlation energy, the interaction between the electrons of the system. To find this energy more than one Slater determinant is needed to describe the system. Once theN_e molecular orbitals have been determined, where N_e is the number of electrons, the first 1/2N_e orbitals are doubly occupied and the ground-state wave function is found [78, p.

309]:

Ψ = N_e!^−1/2det|φ_a(1)φ_b(2)· · ·φ_z(N_e)| (24)

=||φ_aφ_b· · ·φ_lφ_mφ_n· · ·φ_z|| (25) If electronm is excited to thevirtual orbitalp, the singly-excited Slater determinant is expressed simply as:

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Ψ^p_m =||φ_aφ_b· · ·φ_lφ_n· · ·φ_p· · ·φ_z|| (26) Similarly a doubly excited determinant may be expressed as:

Ψ^pq_mn =||φ_aφ_b· · ·φ_l· · ·φ_p· · ·φ_q· · ·φ_z|| (27) Configuration Interaction

The exact ground-state wavefunction may be written as a linear combination of N_e Slater determinants, i.e. a superposition of the ground state, singly excited state, doubly excited state, etc [78, p. 310]:

Ψ =c₀Ψ₀+X

a,p

c^p_aΨ^p_a+X

a < b p < q

c^pq_abΨ^pq_ab+ X

a < b < c p < q < r

c^pqr_abcΨ^pqr_abc+· · · (28) The energy acquired using this wavefunction is the exact non-relativistic energy. The difference between this and the Hartree-Fock energy is therefore the totalcorrelation energy. If all N_e excited determinants are considered the computational method is called full configuration interaction (CI). For example, full CI for H₂ involves considering single and double excitations. These methods traditionally have issues with size-consistency;

i.e. if a calculation is run on a system consisting of two species greatly separated, the total energy may not be the same as if two calculations were done on the two species separately, (E(A+B)6=E(A) +E(B).

Møller-Plesset perturbation theory

Many-body perturbation theory provides an alternative way of finding the correlation energy. Møller and Plesset chose to define the zero-order Hamiltonian from the Fock operators of the system [78, p. 313]:

H⁽⁰⁾ =H_HF=

Ne

X

i=1

f_i (29)

With the first order Hamiltonian as:

H⁽¹⁾ =H−H_HF (30)

Where H is the electronic Hamiltonian. For electron i, the first order correction is:

H⁽¹⁾(i) =j₀X

j

1 rij

−X

m

[2J_m(i)−K_m(i)] (31) This Hamiltonian may then be used to calculate the second-order energy correction:

E⁽²⁾ = X

j6= 0

hΨj|H⁽¹⁾|Ψ0i hΨ0|H⁽¹⁾|Ψji

E₀⁽⁰⁾−E₀⁽⁰⁾−E_j⁽⁰⁾ (32) The correction may be calculated to any arbitrary order to recover more of the correlation energy, but the algebraic expressions rapidly become very complicated resulting large computational costs. Second-order corrections are generally considered a good com-

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Coupled Cluster

While perturbation theory includes corrections for all excited states to a given order, Coupled Cluster does the opposite by correcting for a given number of excited states to infinite order [79, p. 169]. Initially an excitation operator Ti is defined which generates all excited Slater determinants to order i when acting on the HF wavefunction Ψ₀.

T_i =T₁+T₂+T₃+· · ·T_i (33) As an example, the effect of the T₂ operator is demonstrated below:

T2Ψ0 =

occ

X

i<j vir

X

a<b

t^ab_ijΨ^ab_ij (34)

ti are coefficients similar to theci used previously, making this expression essentially the same as the third term in eq. 28. In fact in can be shown that the excitation operator acting on the HF wavefunction will generate the complete CI wavefunction.

The Coupled Cluster wavefunction is now defined in terms of this excitation operator and the HF wavefunction:

Ψ_CC =e^TΨ₀ (35)

Where e^T is the Taylor expansion of the excitation operator:

e^T =

∞

X

k=0

1

k!T^k (36)

Writing out the terms and sorting by excitation level gives the following:

e^T = 1 +T₁+ (T₂+1

2T₁²) + (T₃+T₂T₁) + 1

6T₁³) +· · · (37) Both T2 and ¹₂T₁² create determinants for doubly excited states, with the former corresponding to two single excitations while the latter corresponds to a double excitation.

This procedure is computationally costly and only singles and doubles are routinely considered. Triples are often calculated using a perturbational method, resulting in what is known as CCSD(T), i.e Coupled Cluster with Singles, Double and perturbative (T)riples.

This is a highly accurate method which is considered the gold standard for quantum chemical calculations [81, 82].

3.1.4 Density Functional Theory

During the last two decades density functional theory (DFT) methods have grown to become some of the most popular quantum chemical methods due to their low computational costs and reasonable accuracy for a multitude of systems. A great advantage of DFT methods is that only a single three-dimensional function is used while wavefunction methods rely on a 3N_e-dimensional function. This enables study of larger systems to a greater degree of accuracy. On the other hand density functional methods are particularly deficient in describing dispersion forces, i.e. weak long-range interactions. In a some dispersion-bound systems such as Ar_n, certain functionals fail to predict bonding at all [83]. As DFT is not variational, i.e. the energy may in fact be below the actual energy, functionals must be compared to high-level computational methods and/or experiment

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to assert their accuracy. For such examples of such comparisons, see [81, 82]. A brief benchmark for a system studied in this work will also be shown inResults and Discussion.

The basis of this theory is the Hohenberg-Kohn theorem[79, p. 317]:

The ground-state energy and all other ground-state electronic properties are uniquely determined by the electron density.

This means that molecular properties such as energy, dipole moment, vibrational frequencies may be determined solely by electron density. The theorem allows us to express the energy of the ground-state system as:

E[ρ] =

EHK[ρ]

z }| { T[ρ] +V_ee[ρ] +

Z

ρ(r)ν(r)dr (38)

Here the total energy consists of the kinetic energy T[ρ], the electron-electron potential energyV_ee[ρ], with the final term describing the external potential. Kohn and Sham reformulated this equation into the form currently used:

h₁+j₀

Z ρ(r₂)

|r1−r2|dr₂+ν_xc(r₁)

ψ^KS_m (r₁) =^KS_m ψ_m^KS(r₁) (39) Herej₀ is the spherical Bessel function andν_xc(r)is the exchange-correlation potential. If the electron density is known, the exchange-correlation energy may be calculated by:

E_xc[ρ] =A Z

ρ(r)^4/3dr, A =−(8/9)α 3

π 1/3

j₀ (40)

The exchange-correlation potential ν_xc(r) may now be found using:

ν_xc(r) = 4

3Aρ(r)^4/3 (41)

A DFT calculation generally progresses in this fashion:

1. Guess electron density ρ(r), or approximate by linear combination of atomic den- sities

2. Use the selected exchange-correlation functionalExc[ρ], for example B3LYP, to find the exchange-correlation potential ν_xc(r)

3. Solve the set of Kohn-Sham equations to acquire a set of Kohn-Sham orbitals 4. Use these orbitals to calculate a new electron density ρ(r)

Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride transfer and relationship to the water-gas shift reaction

Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride transfer and relationship to the water-gas

shift reaction

Christian Sant Gjermestad

Thesis submitted for the degree of Master in Master of Science in Chemistry

60 credits

Department of Chemistry

Faculty of Mathematics and Natural Sciences

UNIVERSITY OF OSLO

Gas phase reactivity of methoxide and formate complexes of Mg(II). Hydride

transfer and relationship to the water-gas shift reaction

Christian Sant Gjermestad

Preface

Abstract

Contents

1 Introduction

1.1 CO

as a starting point for energy storage

1.2 The water-gas shift reaction

1.3 Aim of study

2 Experimental methods

2.1 Electrospray ionization

2.2 Quadrupole

2.3 Hexapole collision cell

2.4 The Time of Flight mass analyzer

2.5 The Multi-channel plate signal detector

-

2.6 Collision-Induced Dissociation

2.7 Kinetic Isotope Effect

2.8 Experimental details

3 Computational methods

3.1 Quantum chemical calculations