internal energy effects in mass spectrometry

JOURNAL OF MASS SPECTROMETRY, VOL. 31, 445-463 (1996)

SPECIAL FEA TUR E: TUTORIAL

Internal Energy Effects in Mass Spectrometry

Karoly Vekey Central Research Institute for Chemistry, Pusztaszeri ht 59-67, H-1025 Budapest, Hungary

The internal energy of an ion has a very large effect on the appearance of the mass spectrum. The first part of this paper gives the theoretical background: (i) dependence of the reaction rate on internal energy; (ii) correspondence between the reaction rate and fragment ion abundances; (iii) role of the residence time of an ion in various parts of the instrument; (iv) the breakdown curve; and (v) the degrees of freedom or number of oscillators affected. In the second part internal energy distributions are discussed: those of molecular ions produced by various ionization techniques and of precursor ions in tandem mass spectrometry. The latter topic is closely connected with secondary excitation, and the particular case of collisional activation is discussed in some detail. In the final part, practical examples of internal energy effects in mass spectrometry are given, including high- and low-energy electron impact, chemical ionization using various reagent gases, metastable and collision-induced dissociation, keV and low-energy collision induced dissociation and matrix-assisted laser desorption/ionization.

KEYWORDS : internal energy effects; mass spectrometry

INTRODUCTION

The internal energy (Eint) of ions formed in a mass spectrometer has a most profound influence on the appearance of the spectrum. If ions have high internal energy, they will fragment to a large extent, producing a spectrum which typically displays a wide variety of abundant fragment ions. If, on the other hand, the internal energy is low, the ions will not fragment, or will produce only a few fragment ions of low abundance. T h ~ s may be most easily demonstrated in the case of electron impact ionization using high-energy (70 eV) or low-energy (12 eV) electrons. An example is shown in Fig. 1.

In spite of the importance of internal energy in all areas of mass spectrometry, few papers deal with it explicitly. This is partly due to the fact that it is very difficult to determine Eint experimentally or theoretically. The purpose of this tutorial article is to give a clear picture of the effect of internal energy on fragmentation processes observed in mass spectrometry; to clarify terminology, to show how varying (or selecting) the internal energy of the fragmenting ions may help in chemical analysis or ion structure elucidation, and to give a number of typical examples of the influence of internal energy on specific mass spectrometric processes. These topics are discussed, although to varying degrees, in most books dealing with basic aspects of mass spectrometry. Those by Cooks et al.,’ Levsen3 and Howe et aE.4 are particularly helpful in this respect.

To simplify the following discussion, and give easy reference points, terminology %relating to internal energy effects is listed in Table 1. Here the preferred terminology, common abbreviations and other terms

occasionally used in mass spectrometric publications are listed and briefly described. Expressions which are often used incorrectly in mass spectrometric papers are also indicated and corrected.

The formation of mass spectra involves three main steps: (1) formation and/or excitation of the molecular ion in the gas phase, (2) (unimolecular) fragmentation of

(a) 70 eV

100 I p /I7

H3C-[CHJl I-O-[CHJ, I-CH,

I69

(b) 12 eV 169

168 I 187 M 354

m/z

Figure 1. High (70) and low (12 eV) electron energy El spectra of di-n-dodecyl ether.‘ Reprinted with permission from VCH, Chemioche Berichte, 100. 79 (1 967).

CCC 1076- 5 174/96/05O445- 19 8 1996 by John Wiley & Sons, Ltd.

Received 15 February 1996 Accepted 26 March 1996

446 K. VfiKEY

Table 1, Terminology and abbreviations relating to internal energy effects Abbreviation Explanation and comments Term

Activated complex

Activation energy

Appearance energy

Branching ratio

Breakdown curve

Breakdown curve as a function of internal energy

Breakdown curve as a function of collision energy

Breakdown curve as a function of deflection angle

Breakdown curve as a function of reaction time

Collision energy

Critical energy

Degrees of freedom

Density of states in the precursor ion with internal energy E

'Early' transition state

A€

Molecular configuration corresponding to the highest energy point on the potential energy surface between the precursor and the product ion. A synonym of 'transition state'.

Also called Arrhenius activation energy. Defined rigorously in the case of thermal reactions: it is the difference in internal energy of the reacting molecules and the average internal energy of the whole assembly of precursor molecules. In other words, it is the difference in energy between the transition state and the average thermal energy of the reactant. In most cases it is close to (and often used as a synonym of) the critical energy of the reaction.

Minimum ionizing electron energy necessary to observe a fragment ion.

The relative proportion of various product ions generated from a precursor (ion) of given, well defined internal energy

The relative abundance of product (ion)s (the branching ratio) normalized at each internal energy and plotted as a function of internal energy. Instead of the 'internal energy' often the 'collision energy' or, in angle-resolved mass spectrometry, the 'deflection angle' or, in field ionization kinetics, the 'reaction time' are used. To avoid confusion, the discriminating parameter, i.e. internal energy, laboratory frame collision energy, etc., should always be specified.

The abundance of product (ion)s (the branching ratio) as a function of internal energy.

The relative abundance of product ions (the branching ratio) as a function of collision energy. Typically used in SID and in low collision energy CID (in quadrupole instruments, usually 10-200 eV laboratory frame collision energy). Should be specified whether laboratory or c.0.m. frame collision energy is used. High collision energy often correlates with high internal energy, although the correlation between these two quantities is not straightforward.

The relative abundance of product (ion)s (the branching ratio) as a function of deflection angle in angle-resolved mass spectrometry. Large deflection angles often correlate with high internal energy, although the correlation between these two quantities is not straightforward.

The relative abundance of product ions (the branching ratio) as a function of reaction time observed in field ionization kinetic studies. Fast reactions often correlate with high internal energy, although the correlation between these two quantities is not straightforward.

Kinetic energy of two collision partners. Usually expressed in the laboratory frame of reference [.€ool,(lab)J where it is often equal to the accelerating voltage. It is, however, often more appropriate to define the collision energy in the centre-of-mass (c.0.m.) frame of reference. In the latter case it should always be indicated [e.g. Eeoll(c.o.m.)]. It should be emphasized that the collision energy is not equal to the internal energy, or increase in the internal energy in a collision; and that high or low collision energy is not synonymous with high or low internal energy (or internal energy increase).

Difference in the heat of formation of the activated complex and that of the ground state; the minimum internal energy of the precursor ion needed to overcome the energy barrier of the reaction. For most purposes its value is very similar to (and often used as the synonym of) the activation energy.

Number of possible independent (orthogonal) movements of atoms (in a molecule). Translational motion is represented by three degrees of freedom; rotation (of a non-linear molecule) likewise by three degrees of freedom; none of these constitute internal degree of freedom. A (non-linear) molecule consisting of N atoms has 3N - 6 internal degrees of freedom.

Defines the number of states per unit energy internal.

The structure and geometry are far from those of the products. This is the case for rearrangement reactions. Its synonym is the 'tight' transition state. The frequency (or Arrhenius pre-exponential) factor is typically in the range 1 0*-lOi2 s-'.

INTERNAL ENERGY EFFECTS IN MASS SPECTROMETRY 447

Term Abbreviation Explanation and comments

'Effective' internal energy

'Effective' temperature

Frequency factor

'Hard' ionization

High energy

High collision energy

High electron energy

High internal energy

Internal energy

Internal energy distribution

Kinetic shift

'Late' transition state

'Loose' transition state

cff The internal energy value which would give the same result in an experiment (or phenomenon) as the actual internal energy distribution. It is possible that the same internal energy distribution might give different 'effective' internal energies if different processes are studied. It is related to 'effective' temperature.

V

Related to the internal energy distribution, it can be converted to 'effective' internal energy and vice versa. The effective temperature is a fictitious value which, when using equations developed for the case of thermal equilibrium, would describe the behaviour of ions with non-thermal internal energy distribution and under non-equilibrium conditions. It is a questionable but very useful and widely applied approximation. It is possible that the same internal energy distribution would give different 'effective' temperatures if different processes were studied.

Frequency used in the 'classical' form of the rate theory [Eqn (l)]. Represents the ratio of the product of vibrational frequencies in the precursor and in the transition state. Relates to the 'tightness' of the transition state: the tighter a transition state, the lower is the frequency factor. Its synonym is the Arrhenius pre-exponential factor.

Occasionally used as the opposite of 'soft' ionization. Indicates an ionization method resulting in molecular ions of high average internal energy, The result is a spectrum with a variety of abundant fragment ions. The proto-typical example is 70 eV El ionization.

Often very vaguely used--may mean high internal energy, high collision energy, high ionization electron energy. Must always be specified which is meant. Becomes even more confusing, if 'high energy' in one place means high collision energy and in another place high internal energy. 'High' is also relative: preferably it should be specified.

In mass spectrometry, if not otherwise defined, this means laboratory-frame collision energy in the keV range (e.g. on sector or time-of-flight instruments). Better to use the expression 'keV collision energy'.

In electron impact ionization, usually means ionizing electron energy in the 50-100 eV range (most commonly 70 eV).

Usually a relative expression, compared with other species of lower internal energy. Ions which fragment in CID or in SID are usually considered to have (relatively) high internal energy (compared with stable ions or with those, which undergo slow fragmentation, e.g. as 'metastable' species). May also mean the high-energy part of an internal energy distribution. The expression 'high internal energy' is usually not confusing.

Total energy of a species above its electronic, vibrational and rotational ground state. Occasionally other reference points may be defined (e.g. internal energy with respect to an electronically excited state, or with respect to the ground state of an isomer), but in such a case the reference species has to be explicitly stated. In some expressions € is used instead of E,,, , as in k(E) . Probability of a species having a particular internal energy. The area under the P ( € ) curve is usually normalized to unity.

Energy difference between the energy threshold of decomposition (I€ + E,) and the internal energy required to observe fragmentation within the timescale of the mass spectrometer (e.g. - 1 0-6 s in a sector-type instrument). In most cases the 'kinetic shift' is less than 1 eV, but occasionally (especially in the case of large molecules) it can befar higher.

Relates to reactions of the direct bond cleavage type. Its synonym is the 'loose' transition state. The structure and geometry are close to those of the products. The frequency (or Arrhenius pre-exponential) factor is typically in the range 10'2-10'6 s-'.

Relates to reactions of the direct bond cleavage type. Its synonym is the 'late' transition state. The structure and geometry are close to those of the products. The frequency (or Arrhenius type pre-exponential) factor is typically in the range 1 012-10'E s-'.

448 K. VEKEY

-~

Table l.-(continued)

Term

Low energy

Low collision energy

Low electron energy

Low internal energy

Molecular ion

Number of states in the transition state in the E - E , internal energy range

Oscillators

Quasi-equilibrium theory

Phase-space theory

Pre-exponential factor

Reaction coordinate

Reaction half-life

Reaction rate

Reaction time

Rice-Ramspberger-Kassel reaction rate theory

Rice-Ramspberger-Kassel-Marcus reaction rate theory

Abbreviation Explanation and comments

G * ( E - E , )

QET

Often very vagely used-may mean low internal energy, low collision energy, low ionization electron energy. Must always be specified which is meant. Becomes even more confusing, if 'low energy' in one place means low collision energy and in another place low internal energy. 'Low' is also relative; preferably it should be specified.

In mass spectrometry, if not otherwise defined, usually means laboratory-frame collision energy in the low (0.1-200) eV range (as occurs in quadrupole, ion trap or Fourier transform instruments).

In electron impact ionization, usually means ionizing electron energy in the 5-20 eV range. In this range the spectra show a large degree of energy dependence.

Usually a relative expression, compared with other species of higher internal energy. Stable ions or those which fragment as 'metastable' ions are usually considered to have (relatively) low internal energy (compared with ions fragmenting in CID or in SID). May also mean the low-energy part of an internal energy distribution. The expression 'low internal energy' is usually not confusing.

Ion generated directly from the neutral analyte molecule of interest. Can refer either to the radical cation or to ionized molecules, sometimes termed pseudo-molecular ions, in which an electron, sodium cation, proton, etc., is attached to the molecule.

General name for vibrations and internal rotations. Typically user' in discussions on rate theories.

Reaction rate theory applied to mass spectrometric ('infinitely' low pressure) conditions. Originally very similar to the RRK formalism, now the RRKM formalism is more often used.

Reaction rate theory related to R R K M ; mathematically more complex, but often gives more accurate results.

A in the Arrhenius equation: k =A e-'Eo/*r). Has the same meaning as the frequency factor ( v ) in Eqn (1). Also referred to as the 'entropy factor'. Relates to the 'tightness' of the transition state: the tighter a transition state, the lower is the pre-exponential factor. It can be regarded as a synonym of the frequency factor.

Description of the motion of atoms in a molecule moving from the precursor state to the product state along one internal coordinate (which is orthogonal t o all other internal coordinates). In the case of direct bond cleavage, the reaction coordinate is the stretching of the breaking bond. In the case of rearrangements, the reaction coordinate is more difficult to define; it is a combination of various bond length and angles changes.

71 /Z

k . k ( E )

Z, t

RRK

Also called half-lifetime or lifetime. Time in which 50% of the precursor ions decompose. z1 ,2 = (In 0.5)/k = 0.69/k.

The expression k ( E ) emphasizes that the reaction rate is a function of the internal energy.

7 is usually preferred, as t is often used to indicate other parameters.

Reaction rate theory; for the sake of mathematical simplicity uses the concept of classical (non-quantized) oscillators. Now generally superseded by the much more accurate R R K M theory.

R R K M Now widely accepted reaction rate theory; quantitatively describes the reaction rate as a function of internal energy. Uses the concept of quantized harmonic oscillators.


Table l.-(continued)

Term Abbreviation Explanation and comments

‘Soft’ ionization

‘Tight‘ transition state

Indicates an ionization method resulting in low average internal energy molecular ions. The result is a spectrum dominated by an abundant molecular ion with no or few fragment ions of low abundance. Typical examples are field ionization, MALDl and electrospray.

Relates to rearrangement reactions. Its synonym is the ‘early transition state‘, where the structure and geometry of the transition state are far from those of products. The frequency (or Arrhenius pre-exponential) factor is typically in the range 1 Os-1 0’ s- l .

Transition state Molecular configuration corresponding to the highest energy point on the potential energy surface between the precursor and the product ion. A synonym of activated complex.

the molecular ion and (3) identification and detection of the product ions. Although this is a simplified scheme, these three steps are of prime importance in all mass spectrometric experiments. The molecules or precursor ions, depending on the mode of their formation (typically ionization) and on their history (ions selected by a magnetic sector, excited by photons, etc.) have a certain amount of internal energy. More precisely, the precursor ions have a certain distribution of internal energy.

The precursor ions, depending on their structure and internal energy, may fragment by various competing reactions. The probability of a precursor ion decomposing by a particular reaction depends on the rate of the reaction. Reaction rates determine the ratio of precursor and product ions, and also the relative abundance of various fragments. Reaction rates, in turn, depend on the internal energy content of the precursor ion. The fundamental relationships connecting these quantities are discussed in the first part of the paper.

~~~~~

FUNDAMENTALS

Reaction rates and internal energy

Reaction rate theories usually relate to thermal processes, where molecules are constantly energized and deactivated by collisions with other molecules (solvent, buffer gas, etc.). The internal energy, which is typically in equilibrium with the environment, is described by the temperature. The temperature not only specifies the average internal energy of a species, but also describes its distribution (usually referred to as the Maxwell- Boltzmann distribution). Ions produced in a mass spectrometer are typically energized in a single event (e.g. ionization or collision), and are not in equilibrium or even, very often, in energy exchange with their environment. Their internal energy (and its distribution) therefore cannot be described by a temperature. To apply statistical rate theories to mass spectrometry modifications are required, and these are incorporated in the so-called quasi-equilibrium theory (QET), developed by Rosenstock et aL5 A good description of statistical rate theories can be found in a book by Robinson and Holbrook6 and a more qualitative dis-

cussion, giving a number of semi-quantitative applications relating to mass spectrometry, in Cooks et al.’s book on metastable ions.’

The fundamental assumptions of the QET are the following: (1) the time required for dissociation is long compared with the time of interaction leading to excitation; (2) the rate of dissociation is slow relative to the rate of distribution of internal energy over all degrees of freedom; (3) an ion in the mass spectrometer represents an isolated system in a state of internal equilibrium (‘isolated’ means that there is no energy exchange with the environment, ‘internal equilibrium’ means that the energy within the ion is distributed statistically over the internal oscillators); and (4) fragmentation products are formed by a series of competing and consecutive unimolecular reactions.

Assumptions (l), (3) and (4) are usually easily satisfied in most mass spectrometric experiments. Some excep- tions are observed in a few cases such as high-pressure mass spectrometry, where ions are excited by sequential collisions and thermal equilibrium may be reached. Assumption (2) created (and still creates) some contro- versy. Some deviations from it were observed in the case of some very small ions and it is probably not applicable to very large molecules (consisting of -lo00 or more atoms). In most cases examined, however, QET appears to be a good approximation.

The early version of QET used the classical approximation of the absolute rate theory [the oscillators are not quantized, the Rice-Rampsberger-Kassel (RRK) theory]. The reaction rate constant, k(E), is expressed as a function of internal energy, E :

k(E) = v ( l - E,/E)”-’ where v is the ‘frequency factor’, E , is the critical energy of the reaction, and s is the number of oscillators in the molecule (sometimes also called the number of ‘degrees of freedom’). In thermal reactions, instead of critical energy E, often indicates the activation energy. Under non-thermal conditions (i.e. in most of mass spectrometry) the use of critical energy is nearly always more correct, although activation energy and critical energy are often used as synonyms. To account for the inaccuracy of the mathematical treatment (non-quantized oscillators), the concept of ‘effective’ oscillators has been introduced, decreasing the number of oscillators to -20-30% of the true value. The use of this expression is often very helpful for qualitative purposes. Equation

450 K. VBKEY

12 - 10 -

Y 8 - 0) 0 - 6 -

4-

2 -

(1) clearly indicates that the reaction rate increases exponentially with the internal energy, and this dependence is also shown in Figs. 2 and 5. For quantitative or semi-quantitative purposes, however, this form of the theory should not be used. A better description of the reaction rate, called the Rice-Rampsberger-Kassel- Marcus (RRKM) theory, uses a mathematical form taking into account the quantized nature of vibrations and rotations. In this formalism there is no need to assume ‘effective’ oscillators, and the rate constant takes

14 7

A

DIR

REARR

B

I I I I I I I I 1

0 2 4 6 8 10 12 14 16 5”t (ev’

Figure 2. Rate constant as a function of internal energy, modeled in the case of butylbenzene. DIR is propyl radical loss, a typical example of direct bond cleavage: high frequency factor (1014 s-‘) and high critical energy (1.7 eV). REARR is propene elimination, a typical example of rearrangement: low frequency factor (1 0” s-‘) and low critical energy (1.0 eV). Data were calculated using Christie’s RRKM Large p r ~ g r a m . ~ Frequency models similar to that described79a were used to describe the ground and the transition states and the frequency factors given above were calculated by the program from the transition state models. The dashed curves indicate hypothetical processes of high frequency factor and low critical energy (A) and low frequency factor and high critical energy (6).

100

80

60 s

40

20

_ _ _ - - - - - M-C, H,

---- ............_._._._ ....... -.._ --...__ I I 1 I I 1 ’ 1 1

Figure 3. Breakdown diagram (as a function of internal energy) of the butylbenzene molecular ion, calculated from the rate constants shown in Fig. 2, using a 1 ps residence time in the ion source and assuming that all ions leaving the source will be detected.

the form 0 G*(E - E,)

k(E) = - h P(E)

where n is the reaction path degeneracy, h is Planck’s constant, G*(E - E , ) is the number of states in the energy range E - E , and p(E) is the density of states in the reactant ion of internal energy E. G*(E - E,) and p ( E ) can be determined by a direct counting of states. State counting requires, however, a knowledge of vibrational frequencies in the reactant (typically known) and in the transition state (typically unknown). The latter are, therefore, often estimated. Many applications are not sensitive to the choice of vibrational frequencies, and in such cases quantitative studies can be performed without a detailed knowledge of the transition state.’,’

The k versus E curves are predominantly determined by three factors: the critical energy, the vibrational frequency change between the ground and transition states [expressed as the frequency factor, v, in Eqn (l)] and the molecular size. Fragmentation rates decrease significantly with the latter, as shown clearly by Eqn (1). This is called the degree of freedom effect, and will be discussed later in some detail.

Based on their frequency factors, fragmentation reactions are usually divided into two broad categories: direct bond cleavages and rearrangements. The transition state corresponding to a direct bond cleavage is usually defined as a ‘loose’ complex or transition state. Its structure and geometry are close to those of the products, and therefore it is also called a ‘late’ transition state. It involves stretching of a bond along the reaction coordinate, while the frequency of a few other vibrations may decrease or they may be converted into internal rotations. The frequency factor [ v in Eqn (l)] is high, usually between 10l3 and 1015 s-’. The transition state corresponding to rearrangement reactions is usually defined as a ‘tight’ complex or transition state. It usually involves the formation of a cyclic structure, where some internal rotations ‘freeze’ (become vibrations), and some other vibrational frequencies may also change. The frequency factor is low, usually between lo6 and 10” s-’. The structure and geometry of a tight transition state is usually far from that of the products, and therefore it is also called an ‘early’ transition state.

If the frequency factor is high and the critical energy is low (low energy direct bond cleavage), the rate constant compared with that of other reactions is high at all internal energies (Fig. 2, curve A). This is the case in open-chain amines, where immonium ion formation (Q-

cleavage) is predominant both at low and at high internal energy. If the frequency factor is low and the critical energy is high (high energy rearrangement), the reaction rate will be low at all internal energies (Fig. 2, curve B). In an ion where several fragmentation processes compete, A will always be predominant and B (if observable at all) will give minor fragments.

In a more usual case, direct bond cleavage and rearrangement reactions compete efficiently; one having a high critical energy and high frequency factor (Fig. 2, curve DIR), while the other has a low critical energy and low frequency factor (Fig. 2, curve REARR). These, in fact, correspond to model calculations on the n-butyl-


benzene molecular ion: DIR is propyl radical elimination by direct bond cleavage and REARR is propene elimination by a typical rearrangement process. The two curves (in the example discussed here) cross at 5.8 eV internal energy. Below this internal energy the rearrangement reaction (propene elimination) requiring low critical energy prevails, and above this internal energy direct bond cleavage (propyl radical loss), having a high frequency factor, is more probable. If the internal energy of a particular precursor ion is increased (e.g. by collisional excitation), products formed by direct bond cleavages are likely to become more abundant. The behaviour of direct bond cleavages and rearrangements described here (Fig. 2) can be considered typical for these reaction types.

Reaction rates and fragment ion abundances

A molecule or parent ion may dissociate by a series of competing and consecutive reactions. The reaction rates of the individual reactions define the product ion abundances in a straightforward manner, i.e. from the reaction rates the product ion abundances can be calculated. The calculations are further simplified in mass spectrometry where predominantly unimolecular reactions are observed (bimolecular reactions will not be discussed here). High accuracy is usually not attempted, so complications due to the loss of fragments during the fight time (e.g. decomposition in the magnetic sector) are neglected. In the simplest case, when the molecule ion has one unimolecular decomposition reaction only, M +A, characterized by the rate constant k, the abundance of M at time z is given by

[MI = eCkr (3) where z is measured from the formation (excitation) of the molecule (parent) ion and the initial abundance of M (corresponding to time zero) is normalized to unity. In a mass spectrum, this normalization means that the sum of all ion abundances is unity. The abundance of A will therefore be equal to 1 - e-kr. This expression also implies that the half-life of a precursor ion ( T , , ~ , the time in which 50% of the precursor ions fragment) is inversely related to the reaction rate constant (r,,, = In 2 /k = 0.69/k).

Competitive reactions are of great interest in mass spectrometry. These reactions can be expressed simply as

k l M-A

M-B k2 (4)

The molecular ion abundance in this case is determined by the sum of the individual rate constants ( X k = k , + k2), while the ratio of the fragments is determined by

the ratio of the rate constants ([A]/[B] a kJk,) . Expressed explicitly,

[MI = e-Zkr

[A] = (k , /Ck)( l - e-'&') ( 5 ) [B] = (k2/Ck)(1 - e-Zkr)

Product abundances in consecutive reactions (M + A + B) are more difficult to describe by analytical expressions. With some simplification, which does not introduce large errors, first the abundance of A is calculated (as before), then it is used as the initial abundance of the precursor for the second step (A + B). If the reaction rate constants of the two steps are k , and k , , the ion abundances will be

[MI = e-klr

[A] = (1 - e-klr)e-k2r (6 ) [B] = (1 - eCk1')(1 - e-k23

Further consecutive steps (e.g. B + C) can be treated in a similar manner.

Equations (3), (5) and (6) show that beside the reaction rate constants, the time-scale of the mass spectrometric experiment is also important in determining fragment ion abundances. This may vary from lo-'' s to several seconds, depending on the experiment. The residence times in various parts of the instrument vary somewhat according to the experimental collisions. The typical values listed below refer to medium mass molecules; large molecules (in excess of 1000 Da) may have significantly longer residence times. Fast reactions (lifetime 10-'2-10-9 s) can be studied by coincidence techniques or by field ionization kinetics. Fast and moderately fast reactions (rate constant larger than -lo6 s- , ) are observed in most conventional instruments as fragments formed in the ion source (the residence time in an ion source is - s). Metastable ions observed in sector instruments have a lifetime of - 10-6-10-4 s. Ions with lifetimes longer than - s are observed in sector and quadrupole type mass spectrometers as undecomposed molecular ions. Ions may have several second lifetimes in ion traps or Fourier transform ion cyclotron resonance (ICR) instruments.

The description of decompositions following secondary excitation is slightly more complicated. The precursor ion in a collisions induced decomposition (CID) process in sector-type instruments has a lifetime of over s when reaching the collision cell (otherwise it should already have decomposed). Its internal energy content is increased by collision, and consequently its fragmentation rate constant will also increase. To observe it fragmenting within the collision cell, its lifetime (after collision) should be less than

Ion lifetimes, the time window of an experiment, reaction rates and internal energies are closely connected. The time window of an experiment defines the observable ion lifetimes, which are, in turn, inversely pro- portional to the corresponding unimolecular reaction rates. As shown in Fig. 2, high reaction rates (short ion lifetimes) are possible only if the internal energy of the precursor ion is high, and in such cases direct bond cleavages are typical reactions. Long lifetimes are possible only if the internal energy of the precursor ion is low, and in such a case rearrangement reactions pre- dominate. These results also mean that by selecting the experiment one is also selecting the ion lifetime, and this typically determines the range of internal energies and reaction types accessed.

- 1 0 - ~ - 1 0 - ~ s.

452 K. VeKEY

Fragment ion abundances and internal energy: the breakdown diagram

From reaction rate constants and residence times, ion ratios can be determined as a function of the internal energy of the ion. This correlation is usually called the breakdown curve or, to be more precise, it is the breakdown curve as a function of internal energy. From the rate constants shown in Fig. 2 using a 1 ps residence time in the source, and assuming that all ions leaving the source will reach the detector, fragment ion ratios were determined. The result is shown in Fig. 3. In reality there are some complications that make precise calculations more difficult (some of the ions leaving the source will hit the slits, some will decompose during the flight time, the detector response is different for various ions etc.), but these usually do not change the results substantially. If the residence time were to be significantly different (e.g. -10-l2 s, as in field ionization), the breakdown curve would change greatly.

Breakdown curves (as functions of internal energy) can also be determined experimentally. The technique is to form a precursor ion of known and well defined internal energy, followed by the measurement of fragment ion abundances. The result will again depend on the characteristic residence time, which is usually around 10-6-10-7 s. If the precursor ion can be produced with various defined internal energies (typically by photoelectron - photoion coincidence spectroscopy or by chargee-exchange ionization), the breakdown diagram (as a function of internal energy) can be determined.

Unfortunately, breakdown curves (as a function of internal energy) are not easy to determine, and are known only for relatively few cases. There are, however, related correlations, which are often also (loosely and confusingly) referred to as breakdown curves. Foremost among these is the correlation between ion ratios and collision energy (as observed in quadrupole-type mass spectrometers). This should properly be called the breakdown diagram as a function of (laboratory frame) collision energy. The two breakdown diagrams are related, as higher collision energies typically result in higher internal energy products. The ratio between collision energy and internal energy is, however, not straightforward, so transformation of the two curves into each other is dificult (at present usually not possible). The correlation between collision energy and internal energy is very important, and will be discussed in the next section.

In an analogous manner, ion ratios can be measured as functions of other variables, also related to the internal energy. In chemical ionization the difference between the gas-phase basicity of the sample and the reagent gas defines the energy balance of protonation. This can be taken as a measure of (although it is not identical with) the internal energy of the product ion. In this way the breakdown diagram (ion ratios) as a function of the energy balance of the reaction can be determined. Scattering angles in CID have occasionally also been measured, and were found to be related to the energy conversion in the collision (larger angles correspond to higher internal energy products). This technique is usually called angle-resolved mass

spectrometry. Breakdown curves (ion ratios) as a function of the scattering angle have also been determined. A further technique is ion lifetime measurement by field ionization (usually called field ionization kinetics). Ion lifetimes are inversely (although loosely) related to the internal energy (as discussed above), so ion ratios as a function of ion lifetime are sometimes also referred to as breakdown curves.

Mass spectra and internal energy distribution

If the breakdown curve (as a function of internal energy) is known, then from the internal energy of the precursor ion the mass spectrum can be determined. Usually, however, precursor ions with a wide range of internal energies are formed. In such a case the mass spectrum would be a convolution of the breakdown diagram and the internal energy distribution: the ion ratios defined by the breakdown graph will be weighed by the probability of the ion having that particular internal energy, then summed over all possible internal energies.

Molecules formed by electron impact have a characteristic internal energy distribution (discussed in some detail in the next section), typically like that shown in Fig. 4. Using this distribution, together with the breakdown curve, the 70 eV electron impact (EI) mass spectrum can be calculated.

Degrees of freedom effect

In addition to the critical energy and frequency factor, the molecular size is very important in determining fragmentation rates. This decreases exponentially with increasing size (number of oscillators, or degrees of freedom) of the molecule. This dependence is obvious from Eqn (1) and less obvious (but still present) in Eqn (2). Using a critical energy (1.6 eV) and frequency factor (v = lOI4 s- '> found for leucine enkephalin,' the fragmentation rates for three different molecular sizes have been calculated: for a small organic molecule (butylbenzene, 66 oscillators, mass 134), for a small peptide (leucine enkephalin, 228 oscillators, mass 556) and for a medium-large peptide (substance P, 576 oscil-

I I I I 1 I I I I i

0 2 4 6 8 10 12 14 16 E,,, (e")

Figure 4. Typical internal energy distribution in 70 eV El spectra.


14 1

10

Y 8 en 0 - 6

4

2

0 5 10 15 20 25 30 35 Eint (W

Figure 5. Rate constant as a function of internal energy, modeled in the case molecules of different size: Butylbenzene-size (BB,66 oscillators, mass 134); small peptide, leucine enkephalin (LE, 228 oscillators, mass 556) : and medium-large peptide. substance P (SP, 576 oscillators, mass 1348). In the calculations identical critical energy (1.6 eV) and transition-state frequencies (v = 1 0’4 s-’) were used. Data were calculated using Christie‘s RRKM Large program.’

lators, mass 1348). The results are shown in Fig. 5 (the three molecules are indicated as BB, LE and SP, respectively).

Figure 5 shows that with increasing molecular size, the fragmentation rates decrease drastically. (Note also that the internal energy range shown is increased up to 30 eV to show the curve for substance P.) In practice, a fragment ion to be observable in a spectrum should have an intensity - 1% of that of the molecular ion, and to be called an abundant peak it should have a relative abundance of at least - 10%. The residence time in the ion source can be assumed (as before) to be -1 ps. Using these values, rate constants should be lo4 to give an observable fragment. This requires 2.6 eV internal energy for a butylbenzene-sized molecule, -8 eV for leucine enkephalin and - 18 eV for substance P.

The high internal energies necessary to fragment large molecules at observable rates are especially striking if compared with the critical energy (1.6 eV). The difference is called the ‘kinetic shift’: the internal energy above the critical energy necessary to drive the reaction fast enough to observe fragmentation. To observe abundant fragments, even higher internal energy is required.

As a rule of thumb, the internal energy necessary for fragmentation increases nearly linearly with the number of degrees of freedom (i.e. the size) of the molecule. This can be qualitatively explained as follows: to induce fragmentation, the internal energy per oscillator (degree of freedom) should be roughly the same in various molecules. The effect of fragmentation rates decreasing with the size of the molecule is therefore often called the ‘degrees of freedom’ effect.

At this point, three further aspects should be mentioned, each facilitating the fragmentation of large molecules (mass > lo00 Da). (1) The thermal energy of large molecules is significant, -0.007 eV per oscillator at typical mass spectrometric temperatures.’ This results in a thermal energy of only 0.5 eV for butylbenzene, but progressively larger values in leucine enkephalin (1.5 eV) and in substance P (4 eV). (2) In some instru-

ment types (notably in Fourier transform ICR and in ion-trap instruments) long residence times can be achieved (up to several seconds). This decreases the rate constant necessary to observe some fragmentation from lo4 to - lop2 s-’. This reduces the internal energy necessary to induce fragmentation to about half the values needed in sector or quadrupole type instruments. In the case of substance P, 8 eV (instead of 18 eV) is sufficient to fragment the molecule. Taking into account the thermal energy of the molecule, ‘only’ -4 eV of additional internal energy accompanying ionization would be sufficient to produce fragmentation. Observ- ation of the fragmentation of large peptides, like insulin, would require an increase in the internal energy of - 8 eV. (3) If excitation occurs at a given position in the molecule, the assumption of QET is that randomization of the internal energy inside the molecule is faster than fragmentation. This assumption in likely to break down for large molecules (above - 500 oscillators, mass -lo00 Da). In large molecules if the energy is ‘local- ized’ in a given part of the molecule, a much smaller energy increase due to ionization or collisional excitation may cause fragmentation than that calculated above. This, however, relates only to those cases when excitation occurs in one step (e.g. in CID on sector instruments at low collision gas pressures, but not in quadrupoles or Fourier transform instruments, as discussed later).

Comparison of calculations and experiment

The sequence of Figs. 2, 3 and 4 shows the various ways in which mass spectra and mass spectral characteristics are affected by the internal energy. The calculations can be compared with experimental data on n-butylbenzene (70 eV EI spectrum, 14 eV EI spectrum, metastable spectrum and the CID spectrum, see Fig. 6). At 70 eV ionizing electron energy [Fig. 6(a)] mainly propyl radical loss is observed (at m/z 91). At low ionizing electron energy (14 eV) [Fig. 6(b)], when the internal energy of the molecular ion is lower than at 70 eV, propene elimination (at m/z 92) has a higher probability. Com- pared with the molecular ion, however, the abundance of both products decreases. In the case of metastable ions, the abundance ratio of rearrangement to direct cleavage is even higher, as shown in Fig. 6(c), but the abundance of fragments to that of the molecular ion is very low. Following collisional activation, the abundance of both processes increases, dlrect bond cleavage becoming predominant [Fig. qd)].

The results of QET rate calculations on butylbenzene (Fig. 2) indicate that the product ion ratio observed in the 70 eV EI spectrum corresponds to 6.5 eV internal energy. This is the ‘effective’ internal energy, which is not equal to the algebraic average (centre of mass) of the internal energy distribution curve. The ‘effective’ internal energy can be defined as the internal energy value which would yield the same result (spectral characteristics) as the actual internal energy distribution. Product ion ratios observed in the 14 eV electron impact spectra correspond to 5.5 eV, those in the CID spectra to 5.8 eV and those in the metastable ion spectrum to 3.7 eV effective internal energy butylbenzene molecular ions.

454

10 -4

K. VEKEY

I

5

0

9 1

I;,, , , * , , , , ,

$5 d o 1bs li0 115

(b) Figure 6. Experimental spectra for butylbenzene: (a) 70 eV El spectrum; (b) 14 eV El spectrum; (c) metastable spectrum [obtained by the mass-analysed ion kinetic energy spectroscopy (MIKES) technique]; and (d) the CID spectrum. (Spectra obtained by L. Ludanyi, whose help is gratefully acknowledged).


(4 Figure 6.-(contInued)

456 K. VEKEY

The ‘effective’ internal energy can also be estimated by a different fragmentation characteristic, the ratio of molecular ion to the sum of fragment ion abundances. Using a 1-ps residence time in the ion source and the assumption that all ions leaving the source will reach the detector, the ‘effective’ internal energy of butylbenzene molecular ions will be 3.0 eV in the 70 eV data and 2.6 eV in the 14 eV EI spectra. Comparison of this result with those in the previous paragraph indicates that the value of the ‘effective’ internal energy depends not only on the internal energy distribution but also on the spectral characteristic studied.

As discussed in the previous section, from the calculated breakdown diagram (Fig. 3) and the estimated internal energy distribution (Fig. 4), the 70 eV EI mass spectrum of butylbenzene can be determined. The abundance ratio of the M+‘ to [M - C,H6]+ (rearrangement) to [M - C,H,]+ (direct cleavage) is 27 : 34 : 39. Comparing it with the experimentally observed spectrum [Fig. 6(a)], good semi-quantitative agreement can be found: the ratio of molecular ion to sum of fragment ion abundances (considering only the M“, [M - C3H7]+ and [M - C3H6]+‘ ions) is 0.20 in the experimental spectrum, while the calculated value is 0.37. (If the calculations are modified to take into account molecular ions decomposing between the ion source and the detector, the calculated value is 0.26, much closer to the experimental result.) The abundance ratio of direct bond cleavage to rearrangement is calculated to be 1.1, while it is measured as 2.1. The agreement between the calculated and experimental results illustrates the sort of accuracy one can hope for in a simple QET type calculation.

The algebraic mean (centre of mass) of the internal energy distribution shown in Fig. 4 is 5.5 eV. This can be compared with the ‘effective’ internal energy (based on the fragment ion abundance ratio) of 5.7 eV, determined from the calculated mass spectrum. The ‘effective’ internal energy based on parent to fragment ion abundance ratios, again determined from the calculated mass spectrum, is 2.8 eV. These values illustrate how the same internal energy distribution corresponds to different ‘effective’ internal energies.

The time window for metastable fragmentations in the present example is from 10 to 15 ps (measured from the formation of the molecular ion in a reversed geometry ZAB instrument). The internal energy distribution of metastable ions can be calculated from Figs 3 and 4, as described in the next section and shown in Fig. 7. Using this internal energy distribution, the ratio of metastable fragment ions to the undecomposed precursor ion is calculated to be 9%, which can be compared with the experimentally observed peak area ratio of 2.5%, i.e. the agreement is fair. The calculated ratio of direct bond cleavage to rearrangement is lo-’, much lower than the experimental value of 0.05 (the latter, relatively high value, may be in part due to ‘unintended’ collisions on residual gases ‘contaminating’ the metastable spectrum). The mean internal energy of metastable ions, based on Fig. 7, is 2.0 eV, close to the ‘effective’ internal energy based on calculated fragment ion ratios (2.2 eV), and that based on the parent to fragment ion ratio (1.6 eV).

To conclude the comparison of experiment with the

1 A h

a

I YA 0 2 4 6 8 10 12 14 16

l ’ l ’ l ’ l ’ l i

E int (ev)

Figure 7. Typical internal energy distribution of ions reaching the field-free region (continuous curve) and that fraction (shaded area) decomposing spontaneously in the field-free region. Dis- tributions were calculated from the distribution shown in Fig. 4 using the rate constants shown in Fig. 2; 10 ps time necessary for the ions to reach the field-free region and 5 ps residence time in the field-free region.

theory, the change in fragmentation characteristics with the internal energy is well reproduced by the calculations. Precise quantitative agreement is difficult to achieve. The calculations are, however, very useful for modelling the behaviour of ion fragmentations and the effect of internal energy and its distribution on the mass spectra.

INTERNAL ENERGY DISTRIBUTIONS

The extent of fragmentation of a given precursor ion, which is described by the rate constants and the breakdown diagram as discussed above, is determined by its internal energy. The internal energy, almost by defini- tion, is perhaps the most important parameter in mass spectrometry. It is, however, not easy to change, and even its determination is p r o b l e m a t i ~ . ~ . ~ * * ~ ’ ~ Neverthe- less, underlies in many aspects of mass spectrometry.

A further complication is that it is rarely possible to form ions with a well defined internal energy value. Typically ions with a distribution of internal energies are formed (or selected). Instead of the correct expression ‘internal energy distribution’ [often indicated as the P(E) curve], which is somewhat clumsy, often only ‘internal energy’ is mentioned. This may mean either the distribution, or some average of the distribution. The ‘average’ of the distribution, also vaguely defined, usually means an ‘effective’ internal energy. The latter is the internal energy value which would give the same result in an experiment (or phenomenon) as the internal energy distribution, but it is rarely equal to the algebraic mean (the centre of mass) of the distribution (as shown above), and usually the same internal energy distribution gives different ‘effective’ internal energies if different processes are studied.

The ‘effective’ internal energy is related to ‘effective’ temperature. The temperature of a molecule (under thermal conditions) defines its average internal energy


and vice versa:’

Eint = c(T, v)skT (7) [where s is the number of oscillators, k the Boltzmann constant, T the absolute temperature and c(T, v) a temperature- and frequency-dependent factor, with a value of -0.2 in organic molecules between 300 and 450 K). The effective temperature is a fictitious value which, when using equations developed for the case of thermal equilibrium, would describe the behaviour of ions with a non-thermal internal energy distribution and under non-equilibrium conditions. This value in turn defines the effective rate constant, keff :

This is a questionable but very useful and widely applied approximation. It is possible that the same internal energy distribution would give different ‘effective’ temperatures if different processes were studied.

Molecular ions

The internal energy content of molecular ions derives from two different sources: the thermal energy of the molecule before ionization and the amount of energy deposited in the ionization process. The former has a relatively narrow distribution and is fairly simple to cal- culate from the degrees of freedom and the vibrational f requencie~ .~ .~ ,~ To give an example, the mean thermal energy of an organic molecule of mass 200 Da at 200 “C is - 1 eV. In most cases (organic molecules below mass 500, at ion source temperature) the contribution of the thermal energy to the internal energy of an ion is much lower than the energy transfer due ionization, and is usually neglected. There are two cases when the thermal energy is very important: (1) in the case of large molecules (above 1000 Da), where the thermal energy may exceed energy deposition by ionization even at room temperature, and (2) in the case of ionization of labile molecules, which decompose easily (e.g. some alcohols). In such a case the molecular ion (M-.} can be detected only if the internal energy of the molecule ion is kept very low, by obtaining low electron energy, low temperature spectra.

The expressions ‘hard’ and ‘soft’ ionization are connected with internal energy content. The distinction between them is not rigid, and often depends on the comparison intended. ‘Hard’ ionization indicates a method resulting in high average internal energy molecular ions. The result is a spectrum with a low abundance molecular ion and abundant fragments, as occurs in 70 eV EI spectra. ‘Soft’ ionization means the opposite : low average internal energy, where the molecular ion is of high abundance (typically the base peak in the spectrum), while fragments are absent or are of low abundance. In soft ionization, not only do the fragment ions have low abundance, but also the number of reaction channels (fragment ion types) is small. Typical examples are low-energy EI, chemical ionization, field ionization, matrix-assisted laser desorption/ionization (MALDI) and electrospray. The internal energy deposited in the molecule can, however, be changed by the experimental conditions.

EI is by far the most thoroughly studied and best understood ionization technique. It is generally assumed that at 70 eV ionizing electron energy the internal energy distribution of molecular ions derived from organic compounds is similar to that shown in Fig. 4: a wide distribution having a long tail to high internal energies. Increasing the ionizing electron energy above this value (to 100 or 1000 eV) hardly changes the internal energy distribution or the mass spectra. Low- energy EI is assumed to have a similar distribution, only the high-energy side of the curve is cut off at the value corresponding to the difference of the ionizing electron energy and the I E of the compound (the ionizing electrons also have an energy distribution, so this ‘cut-off’ is never sharp, and may be -2 eV wide). The precise internal energy distribution of a particular compound, however, may be different. There may be structure in the P(E) curve, and the average and the maximum value may not be exactly like that shown in Fig. 4. For semi-quantitative purposes the curve shown in Fig. 4 can, however, be taken as a general guide.

Chemical ionization (CI) is a soft ionization technique, where an ion such as the protonated molecule (MH’) is typically the base peak in the spectrum and there are few fragments. The internal energy deposited in the ionized molecule is usually approximated by the energy balance of proton exchange: the difference of the gas-phase basicity (GB) of the sample and the reagent gas which, in turn, is often approximated by the difference of proton affinities (PA). The GB (and PA) difference in typical cases is less than 2 eV, so the molecular ion will be much less excited than in EI. A high proton affinity reagent (e.g. ammonia, P A = 865 kJ mol-’) results in a smaller internal energy molecular ion (smaller fragments) than a low proton affinity reagent, such as methane ( P A = 530 kJ mol-I).

Fast atom bombardment (FAB) ionization (essentially the same technique is also called liquid secondary ion mass spectrometry, liquid-SIMS or LSIMS) is often considered a soft ionization technique, as the ionized molecule (MH+ or MMe’ ) is usually the base peak in the spectrum. The internal energy distribution is, in most cases, similar to that observed in EI (Fig. 4), but fragmentation is often masked by the matrix. The high abundance of the molecular ion and the relatively low abundance of fragments is in large part is due to the molecular size. Large molecules (mass -1000 Da) usually need over 10 eV internal energy to fragment in the mass spectrometer (Fig. 5), and this is the main reason why only a few fragments are Low molecular mass compounds, if studied by FAB, usually show a high degree of fragmentation.

Electrospray and MALDI are also soft ionization techniques, producing little fragmentation [Fig. 8(a)]. As in FAB, this reflects mainly the slow reaction rates of large molecules, rather than an internal energy distribution weighted to low energy.

Secondary excitation

In mass spectrometry, it is often desirable to increase the internal energy content of a selected ion. This is fundamental to tandem mass spectrometry (MS/MS),

458 K. VEKEY

p+l-fJ* = 1498.6

F(+y’ = 1496.6

200 3Im 400 500 600 700 l000BM)loOo 1- j a w

mh

Figure 8. (a) MALDI spectrum of a synthetic peptide and (b) its MALDI-PSD spectrum. The latter shows abundant fragment peaks, which give information on the amino acid sequence.”

where the fragmentation of a selected precursor ion (not necessarily the molecular ion) is studied. The fragmentation rate of the selected ion is often not sufficient, so its internal energy is increased by secondary excitation to enhance the fragmentation rate. This is usually done by ion-molecule or ion-atom collisions (CID) or surface- induced dissociation (SID). The internal energy of the precursor ion after excitation is determined by three effects: (1) internal energy deposited during formation of the precursor ion (often, but not always, ionization or protonation), (2) ‘loss’ of the high energy ions by fragmentation and (3) internal energy deposition by excitation.

(1) The internal energy of the precursor molecular ions has been discussed in the previous section. If the precursor ion (to be studied by MS/MS) is formed by fragmentation of a molecular ion, its internal energy is determined by three factors: the internal energy of the original molecular ion, the energy requirement of the fragmentation reaction and the partitioning of the remaining internal energy between the products (the neutral and the fragment ion, the latter becoming the precursor ion in the MS/MS experiment). Determining or estimating these values may not be straightforward, but is sometimes possible.

(2) If molecular ions are formed with high internal energy, they are likely to fragment before being selected for MS/MS. This means that precursor ions selected for MS/MS will have a lower average internal energy (lack the high-energy tail of the internal energy distribution) than the same ions studied in the source. The effect can be illustrated by the example of butylbenzene: the molecular ion needs 10 ps to reach the field-free region (this can be calculated from the instrument geometry, accelerating voltage and ion mass), so those molecular ions which reach there will have a lifetime of over 10 ps. Those ions which have a shorter lifetime will have decomposed beforehand and so are lost for subsequent analysis. The internal energy of undecomposed molecular ions can be calculated using the rate constants shown in Fig. 2 and the internal energy distribution following ionization (Fig. 4), and the result is shown Fig. 7.

(3) Internal energy deposition by secondary excitation is of profound interest in MS/MS. The resulting internal energy (distribution) will be the sum of the internal energy before excitation [as discussed in (2) above] and the energy deposition. Theoretically, the simplest case is laser excitation by high-energy photons, where the amount of internal energy increase is precisely known; this is its main advantage. When infrared


lasers are used, the ion will absorb a number of photons, so the energy deposition will have a fairly wide distribution. The disadvantage of photon excitation (especially that in the visible or UV region) is the com- plexity and cost of the equipment and corresponding practical difficulties.

By far the most commonly used method of secondary excitation is collisional activation (CA), and the resulting fragmentation is called collision-induced (or collisionally activated) dissociation (CID or CAD). In this process, accelerated ions collide with a neutral (collision or target) gas. CID processes are divided into high-energy (better defined as keV) and low-energy collisions (this expression refers to the kinetic energy of the collision partners, not the internal energy transfer). Typically, the laboratory frame collision energy is discussed; in the case of singly charged ions it is equal to the accelerating voltage (in a quadrupole type instrument, e.g. 200 eV). The collision process is however, better described terms of the centre-of-mass (c.0.m.) collision energy. This value is much lower; if, e.g., a mass 400 ion is colliding with He gas, the c.0.m. collision energy will be only -2 eV.

In the collision process, part of the c.0.m. collision (i.e. kinetic) energy is converted into the internal energy of the ion. The correlation between collision energy and internal energy deposition is very important, even if not perfectly understood. In keV (high) collision energy CID (used on sector-type instruments), typically one or only a few collisions occur: at 70-90% main beam transmission predominantly one, at 30% on average two. Also, the internal energy deposition in this collision energy range does not depend significantly on the collision energy. Average internal energy deposition is usually estimated to be a few (1-3) eV. The distribution of internal energy deposition in keV CID is wide and characterized by a high-energy tail (energy deposition of 10 eV or more also occurs). This means that in keV energy CID, (a) the undecomposed molecular ion will have a high abundance and (b) fragmentation processes requiring large critical energy are also observed.

Low kinetic energy (usually 10-200 eV in the laboratory frame) collisions are observed in quadrupole type mass spectrometers. In this case the internal energy deposition increases with the collision energy, although not necessarily linearly. The maximum amount of energy which may be converted to internal energy in one collision, is equal to the c.0.m. collision energy. Usually, however, only a fraction, maybe a few per cent, of this is energy will become internal energy of the incoming ion. In experiments utilizing low (kinetic) energy CID, the precursor ion typically collides many times, so the pressure of the collision gas may also have a large effect. The average internal energy deposition is estimated to be between 1 and 10 eV, depending on the experimental conditions. The distribution of internal energy deposited is, however, much narrower than in high kinetic energy collisions. This means that (a) the molecular ion is often absent or of low abundance but (b) fragmentation processes requiring large critical energy are frequently not observed.

Low kinetic energy collisions are also observed in ion-trap and Fourier transform type mass spectrometers. The collision energy in these experiments is

often very low (a few eV or less), but after collision the ions are re-accelerated and collide again, often several hundred times. The internal energy increase of the precursor ions are nearly continuous, occurring until they fragment. The large number of collisions makes this process resemble thermal activation. Low critical energy processes dominate.

Colliding an ion beam with a surface leads to surface- induced dissociation (SID). In this case, usually a low kinetic energy (10-100 eV) single collision occurs. In this case the laboratory frame and the c.0.m. collision energy are more nearly equal. The kinetic to internal energy transfer is relatively well described: depending on the surface and the precursor ion, 15-25% of the collision energy is converted into internal energy. The average value of energy conversion depends linearly on the collision energy and the resulting internal energy distribution (relatively to CID) is narrow.

MALDI is a soft ionization method, typically giving an abundant singly charged molecular ion, a less abundant doubly (perhaps triply) charged molecule and some adducts, but no fragments. An example has been shown in Fig. 8(a). The accelerated molecular ion, however, may fragment in the beginning of the flight path, and the resultant products may be detected. This technique is usually called ‘post-source decay’ (PSD). It seems likely that the ions, accelerated to 10-50 kV, collide with neutrals in the relatively high pressure region close to the surface, and may be excited in a CID-like process. PSD is, however, a fairly new technique, and the precise mechanism of excitation is not yet known. The MALDI-PSD spectra [an example is shown in Fig. 8(b)] are usually not unlike those observed using FAB-CID. The useful mass range for PSD extends to higher masses than that of CID; this may be related to different and more efficient excitation mechanisms or simply to the much higher sensitivity and mass range of MALDI compared with FAB.

Determination of internal energy distributions

As mentioned above, reliable determination of the internal energy distribution is dificult. According to the laws of threshold ionization, the internal energy distribution of molecular ions is given by the first derivative of the total ionization efficiency curve in photoionization and the second derivative of that in electron impact. With some approximations, the internal energy distribution can be determined this ~ a y , ~ , ~ but these experimental data are not easy to obtain and quantitatively the data may not be accurate. Internal energy distributions obtained by these two methods are qualitatively similar. In general, maxima in the internal energy distribution curves correspond to excited electronic states, which are initially populated. It is assumed (according to QET discussed above) that soon after ion formation these excited states convert into the ground electronic state, the excess energy being distributed into vibrational and rotational degrees of freedom. In medium and in large molecules (above -100-200 Da) there is a very large number of excited electronic states, and their distribution (weighed with the corresponding probability of being populated in the ionization process) gives rise to

460 K. VEKEY

the generalized smooth internal energy distribution shown in Fig. 9.

Recently, a new technique for estimating internal energy distributions, the so-called thermometer- molecule method, has become more widespread. It has the advantage of being applicable in conventional mass spectrometers and can be used for studying energy transfer not only in ionization, but also in other processes, such as CID or SID. The basic argument leading to the thermometer-molecule method is the following. l Z

Consider an ion, as such W(CO)6+, which fragments in consecutive fragmentation reactions, losing CO (or in general some other simple neutral fragment) in each step. If the internal energy of the ion is lower than the critical energy corresponding to W(CO), + formation [Eo(l) in Fig. 91, then the molecular ion will be observed. If W(CO),+ has more internal energy than Eo( l ) , but less than E0(2), then W(CO),+ ions will be produced [E0(2) indicating the critical energy necessary for the consecutive loss of two CO molecules]. The argument can be carried further through to the formation of W+, and is shown schematically in Fig. 9.

Thinking in reverse, observation of W(CO),+ indicates that the internal energy of the molecule ion is in the 0-Eo(l) energy range. Observation of W(CO),+, analogously, suggests that the internal energy of the excited molecular ion is in the Eo(l)-Eo(2) range. The relative abundance of the W(CO),+ ion, divided by the width of the internal energy range over which it is formed, gives the corresponding probability value (Fig. 9). Working through all fragment ions, the internal energy distribution can be obtained. While conceptually and technically simple, the thermometer-molecule method has some disadvantages: only molecules fragmenting exclusively by similar consecutive processes can be used, the ‘resolution’ of the curves is limited (e.g. the kinetic shift discussed above) and are not taken into account. A different method, which is sometimes referred to as the ‘deconvolution method’,l0,’ can overcome some of these limitations. This can be regarded as a variation of the thermometer-molecule method: instead of critical energies of consecutive processes, energy ranges obtained from experimental breakdown curves are used. A characteristic energy range is identi- fied with a characteristic fragment ion, and the internal

);Ed2) 2

Figure 9. Diagram describing the fundamentals of the thermometer-molecule method. The curve shows the internal energy distribution [P(€)]; P+ indicates the precursor ion, F, +, F,+ and F,+ the fragments and Eo(l ) , E0(2) and E0(3) the respective critical energies.” Reprinted from J. of Mass Spectrometry /on Proc., 75, 181 (1987). 8 1987 Elsevier Science, with kind permission of Elsevier Science, The Netherlands.

energy distribution is determined in a fundamentally similar way to that used in the thermometer molecule approach. The two techniques yield qualitatively similar results, although internal energies determined by the ‘deconvolution’ method are somewhat higher. If the internal energy of the product neutral in the thermometer-molecule approach is taken into account, internal energies determined will become larger, and the two techniques will yield quantitatively similar results.

INTERNAL ENERGY EFFECTS IN PRACTICE

Low and high electron energy EI

The 70 eV EI spectra, such as that in Fig. 1, show a large number of fragments. This particular ionizing electron energy is most often used, as it provides optimum sensitivity, and the spectra so obtained are reproducible and informative. Its disadvantage is that the molecular ion may have low abundance and often too many fragments are observed, making interpretation difficult. Decreasing the electron energy to and below 20 eV has a profound effect on the appearance of the spectrum: around 20 eV most fragments of low abundance disap- pear and it is easier to identify the most characteristic fragment ions. At electron energies 2-5 eV above the ionization threshold (most organic molecules have ionization energies in the range 9-11 eV, so this corresponds to 12-15 eV electron energy) the molecular ion is typically very abundant and only a few fragments (requiring low critical energy) are observed (Fig. 1). This often makes interpretation easier, especially if high and low electron energy spectra are interpreted together. Below this electron energy (close to the ionization threshold) the sensitivity drops significantly, and only the molecular ion is observed.

It must be emphasized that the spectra depend pri- marily on the structure (and therefore the potential energy surface) of the molecular ion, and the discussion above relates to a typical case. There are a few molecules which are not stable in ionic form (i.e. will decompose even at the ionization threshold, so no molecular ions can be observed). Other molecular ions are stable species, but the critical energy of decomposition is so low, that only a tiny fraction will be observed as molecular ions, which may practically be unde- tectable even at low electron energy. In contrast, some other molecular (e.g. some aromatics), have high critical energy fragmentation processes, and the molecular ion is the most abundant peak in the 70 eV mass spectrum. Large molecules (-1000 Da) nearly always give an abundant molecular ion, even if they have low critical energy decompositions. The reaction rate will be low (owing to the large number of oscillators, as described above), so the molecular ions will reach the detector before decomposition, yielding an abundant molecular ion peak.

Chemical ionization with reagent gases of different GB

As discussed above, the internal energy deposited following chemical ionization is close to the difference in


gas-phase basicity (GB) between the sample and the reagent gas. This is usually less than 2 eV, so the amount of internal energy of the resulting MH+ ion is fairly low. In consequence, the rates of fragmentation in CI are generally slower than in EI, and an abundant molecular ion (MH+) is observed. This is, in fact, the most important practical advantage of CI: it gives molecular mass information even in cases where the molecular ion (M") is not observed in EL

To observe MH' ions, the sample has to have a higher basicity than the reagent gas. If the reagent gas has a high gas-phase basicity (e.g. ammonia or isobutane), very little fragmentation is observed [Fig. lqb)]. However, if the basicity of the sample is higher than that of the reagent gas, no MH' ion is observed. In such a case, however, occasionally adducts such as [M + NHJ' can be observed. Often it is advantageous to obtain structural information in CI by observing fragmentation processes. If a reagent gas of low gas phase basicity is used, such as hydrogen or methane, protonation of the sample is strongly exothermic. In such a case various fragments are usually observed [as shown in Fig. 10(a)], although the molecular ion abundance is typically still high.

Metastable and CID fragmentation

Metastable fragmentations indicate those 'spontaneous' processes which occur in the field-free regions of a mass spectrometer; the product ions are described as meta-

stable ions. 'Spontaneous' indicates that these are unimolecular reactions, and the precursor ions were not excited after leaving the ion source. As discussed above, ions having high internal energy decompose before reaching the field-free region, so the internal energy distribution (as shown in Fig. 7) does not have a high- energy tail. The highest internal energy ions among these ions will, however, have sufficient energy to fragment in the field-free region, and their internal energy distribution is shown in Fig. 7 (shaded area). They cover a very narrow internal energy range, so metastable ions are characterized by a medium, well defined amount of internal energy just sufficient to cause decomposition with a rate constant of -lo5 s-'. The consequence of this internal energy distribution is that only few fragmentation processes occur, and these will have relatively low abundance. The observed reactions have low critical energy, and most often are rearrangements.

When the internal energy of the selected precursor ions reaching the field-free region is increased, for example by collisions, the resulting (CID) spectra will be different from those of the metastable spectrum in two major respects : the total abundance of fragment ions (i.e. the sensitivity) will increase, and there will be a larger variety of fragment ions, among which direct bond cleavages requiring higher critical energy will also occur. Another way of expressing this is that those processes which occur in CID, but not in metastable fragmentation, require high critical energy, and therefore are likely to be direct bond cleavages. This classification may be important, as bond cleavages relate to the structure in a more direct fashion than rearrangements.

C.I. (Methane)

261 *i" 50 100 150 200 250 300 350 400 m h

C.I. (Isobutane)

Di-(2-ethylhexyl Phthalate), M=390 Figure 10. Chemical ionization spectra of diisooctyl phthalate (mass 390) using (a) methane and (b) isobutane reagent g a s e ~ . ' ~

462 K. VEKEY

b0 x ~ 0 0 0 . 0 0

9 5

90

u i

1290

70

6 5

60

55

50

45

40

35

30:

25.:

20

15

10

~150.00

75

70

65:

6 0:

d d

d

IT0 1291 . I

AO. 1400 OEO m / i

5.4E4

5.OE4

4.6E4

4.1E4

3.7E4

3.3E4

2.9E4 t 2.5E4

2.1E4

3.7E4

1.2E4

8.3E3

4.1E3

Figure 11. (a) Metastable and (b) CID spectra of substance P (m/z 1348) using a four-sector instrument (VG-ZAB-T). Sequence ions of the "a" and "d" type are indicated (Spectra obtained by G. Pbcsfalvi, whose assistance is gratefully acknowledged.)

The case of butylbenzene has been discussed before [Fig. qc) and (d)]. Another example which shows the difference between the metastable and CID spectra is the case of substance P, a medium-large peptide (Fig. 11). The intensity of peaks in the metastable spectrum is very low, and there are few fragment ions, giving little sequence information. The peaks in the CID spectra, on the other hand, not only have higher intensity, but also there are many fragments, making peptide sequencing possible by mass spectrometry.

A less obvious difference between metastable and CID fragmentation relates to the energy content of the respective precursor ions when reaching the field-free region. Those fragmenting as metastable ions have a medium amount of energy and a relatively long lifetime, so they often isomerize in flight. Subsequent fragmentation may, therefore, start from an isomeric structure. In consequence, metastable ion spectra of some isomeric compounds may be identical. CID, on the other hand, samples the low-energy (non-fragmenting) ions. Depending on the isomerization barriers, these may not have enough energy for isomerization during the flight time, and so may represent the original structure. After excitation (by collisions or by other means) the internal energy is increased, but the ions may not have time for isomerization before fragmentation. The consequence is that in some cases isomers may be distinguished by CID, but not by metastable fragmentation.

keV and low-energy CID

In low (collision) energy CID, the amount of internal energy deposition can be increased either by increasing the collision energy or by increasing the number of collisions. This results in efficient fragment ion formation (low precursor ion abundance), and the spectra of vari- ously excited precursor ions can be studied. A significant limitation is that very high internal energies cannot be reached (ions obtaining a relatively high internal energy will fragment before they can be further excited). In high (keV) collision energy CID, internal energy transfer can be varied to a much smaller degree, and the average energy deposited into the ion is only a few eV. The energy deposition curve has, however, a long tail to high energies. This results in a spectrum in which fragmentation reactions requiring high critical energy will

also be observed. Observation of high critical energy processes is

important in some applications. Peptide sequencing is one such e~ample : '~ internal fragments and immonium ions (which contain significant information on the molecular structure) are frequently observed in keV CID, but not in low-energy CID. Determination of branching or double bond positions in long-chain fatty acids can be done elegantly and straightforwardly by CID.16 The informative cleavages are observed, however, only in keV and not in low-energy CID.

CONCLUSIONS


REFERENCES

Together with the method of sample introduction and the ionization technique, the internal energy content of an ion is the most important parameter in mass spectrometry. It has a similar effect as does temperature in thermal reactions. Unlike temperature, the internal energy of an ion is very difficult to determine and difficult to vary over a large range, and even changing it can be problematic.

The internal energy of an ion is rarely characterized by a well-defined single value, but typically by a wide distribution. To make things even more complicated, a change in the internal energy content of an ion is frequently accompanied by changes in other parameters. This hinders the study and the understanding of internal energy effects, as these may be masked by other changes. An example is the comparison of metastable and collision-induced fragmentations. The main (or intended) difference is the change in the internal energy of the precursor ion by collisional excitation. The two techniques, however, sample a different selection of the precursor ions : those giving metastable fragments initially had more internal energy, and so may have isom- erized to a different structure than the rest, which fragment by CID.

Theoretical modelling is very helpful, as in a calculation one can freely change the internal energy or the internal energy distribution of an ion, which is usually not possible in an experiment. Calculating the conse- quences of such a change, e.g. in the abundance ratio of fragment ions, can be enlightening, but can also help in actual research.

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3. K. Levsen, Fundamental Aspects of Organic Mass Spectrom- etry. Verlag Chemie, Weinheim (1 978).

4. 1. Howe, D. H. Williams and R. 0. Bowen, Mass Spectrometry. Principles andApplications. McGraw-Hill, New York (1981).

5. H. M. Rosenstock. M. 6. Wallenstein, A. L. Wahrhafig and H. Eyring, Proc. Natl. Acad. Sci., USA 38,667 (1 952).

6. P. J. Robinson and K. A. Holbrook, Unimolecular Reactions. Wiley, London (1 972).

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internal energy effects in mass spectrometry

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