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## Blackbody infrared radiative dissociation (BIRD)

BIRD is one of the mass spectrometry techniques that is of special interest for quantitative study of the binding and dissociation properties of rather weak interactions.106 In this technique, ions of interest are trapped in an ultra-low pressure (≤ 1 × 10-8 Torr)107,108 trapping mass spectrometer where they can experience unimolecular dissociation in the absence of any collision.109 Therefore, the only source of activation is the absorption of infrared photons from the surroundings (Equation 2.1):110,111 + 1, / −1, [ + ] ∗ + (2.1)

In Equation 2.1, k1,rad and k-1,rad are rate constants for absorption and emission of infrared photons, respectively, and kd is the unimolecular dissociation rate constant. Using the steady state approximation, the overall rate constant for the whole process, k.

In this technique, in order to see a substantial amount of fragmentation, the time allowed for the observation of the dissociation should be rather long (e.g., several minutes). In addition, pressure must be maintained sufficiently low to make sure that there is not any exchange of energy via unintended collisions. Both of these conditions can be readily fulfilled inside the cell of a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer (Figure 2-1). In BIRD experiments, the only source of energy is the absorption of multiple low-energy infrared photons (in contrast to visible or ultraviolet dissociations in which a single high-energy photon is used for excitation), and from the practical point of view, only a limited temperature range can be achieved for BIRD dissociations. For these reasons, precursor ions of BIRD have to be fragile enough to dissociate in the available temperature range, and at the same time, they must be stable enough to be able to arrive intact into the ICR cell after formation in the ionization source. Since electrospray ionization (ESI)3–5 allows weak interactions to be preserved in the gas phase; it is one of the most convenient techniques for generation of precursor ions of BIRD.

Figure 2-1- Schematic of a hybrid quadrupole-FT-ICR mass spectrometer (ApexQe, Bruker Daltonics)

In treating BIRD data, the natural logarithm of the survival yield (Equation 1.47) is plotted as a function of the trapping time in the ICR cell. This plot will be linear for the reactions following first-order kinetics, and the obtained slope gives the rate constant (k). The dissociation rate constants are acquired at various temperatures and finally, the subsequent plot of ln k versus 1/T allows one to deduce observed activation energy (Eaobs) and pre-exponential factor (Aobs) parameters (Equation 1.50 and Figure 2-2).106

These experimentally-derived Arrhenius parameters (Eaobs and Aobs), can be useful for comparison of the kinetics of similar reactions. For more universal comparisons, it is necessary to derive the corresponding infinite-pressure parameters, Eaꝏ and Aꝏ. This will help to compare bond energies and the nature of the transition state in different unimolecular dissociation reactions. One may ask the questions: why are universal comparisons feasible at the high-pressure limit, and how is it possible to have this condition in BIRD experiments that are performed under ultra-low-pressure conditions? In the high-pressure limit condition (a high pressure of collision gas), the ion population experiences very rapid energy exchange, and as a consequence, it is in complete equilibrium with its surroundings at temperature T. Under this condition, the ion population has a Maxwell-Boltzmann distribution of internal energy, and observed activation energy and pre-exponential factor will approach to the corresponding infinite-pressure values which are characteristics of the dissociation reaction and therefore can be used for universal comparison purposes. In the low-pressure condition of BIRD experiments, this condition of fast energy exchange can be fulfilled by increasing the molecular size (due to a large number of photon absorption and emission events). Therefore, to avoid any confusion, this infinite-pressure limit is called the rapid energy exchange (REX) limit.106

For an ensemble of ions in thermal equilibrium (REX limit), the internal energy distribution is given by Maxwell Boltzmann relation: where P(E) is the probability density for an ion to have a special energy of E at temperature T,(E) is the density of states, kB is the Boltzmann constant, and Const. is the normalization constant. In BIRD experiments, the rate of energy exchange strongly depends on the size of the molecule. As the size of the ion increases, the rate of the absorption (k1,rad) and emission (k-1,rad) of infrared photons increases as well. However, the unimolecular dissociation rate (kd) stays almost constant at a given temperature, and is hardly influenced by the molecular size. This means that P(E) approaches to a Maxwell Boltzmann distribution without any significant loss of the highest energy part of the population via unimolecular dissociation. Therefore, when the size of the molecule is large enough, k-1,rad far exceeds kd, the population is thermalized, and the observed activation parameters Eaobs and Aobs, are equal to their infinite-pressure values Eaꝏ and Aꝏ.

In the case of small molecules (less than 100 degrees of freedom), the rate of energy exchange is small compared to the dissociation rate (k-1,rad << kd). In fact, any excitation to any internal energy above the critical energy, leads to a very fast dissociation of ions. In this condition, which is called “sudden death” kinetic limit, the overall dissociation rate of the precursor ion depends only on the rate of photon absorption and emission, and is independent of the unimolecular dissociation rate. In this situation, the high energy portion of the population is lost via unimolecular dissociation, and this reactive depletion106 leads to a significant deviation of Eaobs and Aobs from Eaꝏ and Aꝏ, respectively; as a consequence, difficulties arise in the interpretation of BIRD data. Here, the simplest approach for extracting the critical energy from the BIRD data is a method called the « truncated Boltzmann approximation ».106,108 Based on this model, critical energy is given by: =+ 〈 ′〉 − ∆ − ∆ (2.4) 0 where <E’> is the average energy of the truncated Boltzmann distribution,Erad is the temperature dependence of the radiation field, andEdepl is that of the reactive depletion of the higher energy levels. These two latter terms are small and partially cancel each other. In Equation 2.4, <E’> term is dependent on the E0, but Eaobs,Erad andEdepl are independent of E0. Therefore, critical energy can be obtained by iteration: first, using the approximations of harmonic oscillator and Boltzmann statistics, the internal energy distribution of the system is calculated, and then <E’> is calculated using an initial estimate for critical energy. Afterwards, using the calculated <E’>, and Equation 2.4, a new value for critical energy is calculated, and is compared with the initially estimated value. This process will be repeated until the newly obtained E0 is less than 5 cm-1 different from the value that is used to calculate <E’> in the previous step. In addition to the truncated Boltzmann approach, master-equation modeling can also be used to extract critical energies from BIRD data in small systems. This method is the most reliable procedure for extraction of critical energies provided that accurate information about the transition state is available. However, it is a more demanding approach compared to the truncated Boltzmann method.106,108 For the ions of intermediate size, the rate of energy exchange is comparable to the dissociation rate (k-1,rad ≈ kd). Here, the ion population is not completely thermalized and a small part of the population in the higher energy side is lost by unimolecular dissociation. Therefore, the internal energy distribution is Maxwell-Boltzmann-like with a small depletion in its higher energy portion. In this case, master equation analysis has to be performed on the experimentally obtained activation parameters to drive the correct value of the critical energy. In the master equation model, any particular ion can undergo photon absorption, photon emission and unimolecular dissociation, and in fact, each ion, is considered to have a random walk along the internal energy axis. To perform this modeling, one needs to have information about the microcanonical dissociation rate of the molecule as a function of internal energy. It is convenient to use the master equation in a matrix form as follows: where dNi(t) is the change in the population of an ion with time relative to the initial population Ni(0), and the first matrix in the right side of Equation 2.5 is called the J matrix which includes rate constants of all the energy exchange and dissociation events. Matrix-algebra techniques and computer software can be used to solve Equation 2.5 numerically to predict unimolecular dissociation rate constants at different temperatures, which then can be compared with the experimentally observed rates. For this purpose, some inputs are required as follows: 1) an estimated value of E0 which can be varied to obtain the best fit with the observed data, 2) radiative energy exchange coefficients which can be determined by ab initio quantum calculations, and 3) dissociation rate constants that can be calculated using RRKM theory. Therefore, using these inputs, the master equation is set up and solved by adjusting E0 and the transition state parameters to give calculated rate constants at different temperatures which are best fitted to the experiment.

So far, we know that by increasing the molecular size we can approach the REX limit, but the question is that at which size can one be sure that the REX limit condition is fulfilled? Actually, the answer to this question depends on different parameters such as temperature, type of the transition state, critical energy, dissociation rate, and radiative absorption and emission properties of the ions.112 All of these parameters influence the relative rates of absorption (k1,rad) and emission (k-1,rad) of infrared photons compared to the unimolecular dissociation rate (kd), thereby indicating whether a molecular system is in the REX limit or not. For instance, Price and Williams have shown that as E0 increases and A decreases, kinetics approaches closer to the REX limit,112 or if we consider the effect of temperature, as it decreases, the dissociation rate decreases faster than the energy exchange rates. Under this condition, a longer observation window is needed to see enough fragmentation. Therefore, at low temperatures, the internal energy distribution is Maxwell-Boltzmann, and kinetics goes toward the REX limit. On the contrary, at high temperature, the situation is reversed and there is a considerable depletion (truncation) in the high energy portion of the distribution, and accordingly a significant deviation from the REX limit especially for smaller ions. Therefore, in BIRD experiments, it is preferable to work in the low temperature range, and high storage time conditions. It should be noted that at very long trapping times, there may be some possible problems related to the signal loss and consecutive fragmentations of the fragment ions. For these reasons, it is better to avoid using overly long storage times. From the above discussion, increasing the molecular size or critical energy, and decreasing of the pre-exponential factor or experimental temperature leads to the approach of the REX limit.112

To sum up, BIRD is one of the most reliable and appealing techniques in providing direct information about the dissociation energetics and type of transition state especially for large molecular systems. In this thesis, we will employ BIRD technique, and use it for calibration of temperature in other dissociation techniques.

### Low-energy collision induced dissociation (low-energy CID)

Here in this thesis, by low-energy CID, we mean the collisional activation occurring in quadrupole ion traps, although it can be performed in both quadrupole ion trap and ICR cell. In addition, since almost all the experiments in this thesis were performed using a linear quadrupole ion trap, here, a short introduction of this kind of ion trap is presented.

**Linear ion trap mass spectrometer**

The quadrupole ion trap is a device which can function either as a mass analyzer or as an ion trap for confinement of ions. By applying suitable potentials to the two ends of the electrodes of the ion trap, a potential well is built inside the trap which enables storing of the ions for a period of time. Afterwards, by linear scanning of the amplitude of radiofrequency (RF) potential, each ion with specific mass to charge ratio (m/z) will be ejected from the potential well at a special RF amplitude; enabling the quadrupole ion trap to act as a mass analyzer.113

The operating region of the quadrupole mass analyzer is represented by I in Figure 2-4-a, and also is shown separately in Figure 2-4-b. In general, ions remain in the trap only if they have stable trajectories in both radial and axial directions. Therefore, in the stability diagram, ions which fall in the overlap regions of x and y stability, will not collide with electrodes and will stay in the trap.

Let’s consider the position of the ions in different conditions of DC and RF voltages. When U=0, and only RF field is applied: under this condition, according to Equation 2.10, au=0, and according to equation 2.11, qu value for heavy ions are lower than those for light ions. Therefore, in the diagram, along the line au=0, different ions will be arranged in a way that high m/z ions fall in the left side (low qu value), and low m/z ions fall in the right side (high qu value) of the diagram. If we increase the RF amplitude, qu will also increase, therefore, ions will move further to the right side of the diagram. Now, if we also apply a DC voltage, this causes the ions to move along the au axis, in a way that lighter ions move further compared to the heavy ions. The sequence that usually is used in linear ion trap mass spectrometer is that, first, by applying an RF voltage to the rods, a range of m/z values (Equations 2.8 and 2.9) are allowed to be trapped. Afterwards, by linearly increasing the RF amplitude, gradually, ions will move to the right side (high qu value) in the stability diagram, and pass the boundary of qu = 0.908. This leads the ions to have unstable trajectories in both dimensions, and eject through the slits present on the rods. Usually, in addition to the RF voltage, an intense auxiliary (alternating current) AC voltage is used in resonance with the secular frequency of the ions, just as the ions are being ejected. This AC voltage is applied radially in order to energize the ions and help them to eject much more tightly through the slits on the rods, thereby increasing the spectral resolution. This phenomenon is called mass-selective ion ejection. In addition, this supplementary AC voltage can be used to remove unwanted ions from the ion trap, for example, for isolating a precursor ion prior to doing tandem mass spectrometry experiments. Finally, when a low amplitude of the AC voltage is used, it can resonantly dissociate precursor ions of interest.

In spite of the quadrupole field, in higher order multipoles, movements of ions in directions x and y are greatly coupled. In addition, in these cases, the solutions of the equations of motion strongly depend on initial condition. Therefore, stability diagrams are not readily derived. When trapping voltages are low, ion trajectories in RF multipoles can be approximately expressed as follows:118

( ) = ( ) = 2 ( )2 2 ( )2 −2 (2.17) where Ueff (r) is the effective mechanical potential, Veff (r) is the effective electric potential, and N is the order of multipole. Therefore, for a linear hexapole with N= 3, the effective potential is proportional to r4, for a linear octopole with N= 4, it is proportional to r6 and so on. This implies that in higher order multipoles, effective potentials near the central axis are relatively flat, and near the rods, they increase rapidly (Figure 2-5).

A schematic of the linear trapping quadrupole (LTQ) instrument (Thermo Fisher®, San Jose, CA) is represented in Figure 2-6. The inlet part of the instrument is an ionization source that can be electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI), atmospheric pressure photo ionization (APPI) ion source and so on. Ions produced in the source pass through a cone and a heated capillary (pressure of ~1 mbar), and then through the tube lens, skimmer, first quadrupole ion guide (Q00) and first lens (L0). Then they proceed to the next quadrupole ion guide (Q0) (pressure of ~0.001 mbar).

Then, after passing Lens L1 and gate lens, they enter into the Q1 octopole ion guide which is at lower pressure compared to the Q0 (pressure of ~3 x 10-5 mbar). During the injection time, Q1 directs the ions axially into the linear ion trap. Here we used the expression of “ion guide” that can be defined as a linear RF multipole which is used to transfer the ions from the ionization source into the mass analyzer. To convert a linear multipole into a linear ion trap, stopping potentials should be applied to the front and end of the electrodes to axially confine the ions. Then by applying RF voltages to the rods, radial confinement is fulfilled.

Figure 2-6- Schematic of the linear trapping quadrupole (LTQ) instrument (Thermo Fisher®, San Jose, CA).

In a linear quadrupole device, each rod has a front, a center and a back segment (Figure 2-7). The central segment of the electrodes defines the trapping volume, and at least one of the rods has a slot in its center segment to allow radial ejection of the ions into the detector. Trapping of the ions in axial directions is achieved by applying electric fields to the ends of the four hyperbolic rods and in the radial direction confinement of ions is done by applying a quadrupole field to the rods.

**Table of contents :**

**Introduction générale **

Chimie hôte-invité

Hémicryptophanes

Spectrométrie de masse en tandem

Ionisation par électronébulisation

Préface

**Chapter 1: Fundamentals of unimolecular ion dissociation **

Lindemann mechanism

Hinshelwood theory

RRK theory

Transition state theory

The RRKM/QET theory

**Chapter 2: A general introduction to the utilized fragmentation techniques **

Blackbody infrared radiative dissociation (BIRD)

Low-energy collision induced dissociation (low-energy CID)

Higher-energy collision dissociation (HCD)

**Chapter 3: Low-energy CID, CID and HCD mass spectrometry for structural elucidation of saccharides and clarification of their dissolution mechanism in DMAc/LiCl**

Introduction

Experimental section

Results and discussion

Conclusion

**Chapter 4: Investigation of hemicryptophane host-guest binding energies using high-pressure collision induced dissociation in combination with RRKM modeling **

Introduction

Experimental Section

Modeling Detail

Results and Discussion

Conclusion

**Chapter 5: Investigating binding energies of host-guest complexes in the gas-phase using low-energy collision induced dissociation **

Introduction

Methodology Background

Experimental section

Results and discussion

Conclusion

**Chapter 6: Investigating binding energies of host-guest complexes using higher-energy collision dissociation in the gas-phase **

Introduction

Experimental section

Modeling detail

Results and discussion

Conclusion

**Chapter 7: Dissociation energetics of lithium-cationized -cyclodextrin and maltoheptaose studied by low-energy collision induced dissociation **

Introduction

Experimental section

Results and discussion

Conclusion

**General conclusion **

**References**

List of Figures

List of Tables

Curriculum Vitae