Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics

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576 Part C Molecules

Table 38.1 Examples illustrating the range of ionic reactions that can occur in the gas phase

Reaction Process Reaction Type

+ O

→ O

+ Ar Nondissociative charge transfer/charge exchange

−

+ NO

→ NO

−

+ O

→ O

+ O + He Dissociative charge transfer

+ Corannulene → Corannulene

+ C

Multiple charge transfer

+ N

→ NO

+ N Ion/atom interchange or atom abstraction

−

+ CH

→ OH

−

+ CH

Atom abstraction

+ HCN → H

+ H

O Proton transfer

−

+HCN→ CN

−

+ H

−

+ H → H

O + e

−

Associative detachment

+ C

→ C

+ H Atom insertion

+ H

+ M → CH

+ M Ternary collisional association

−

+ BCl

+ M → BCl

−

+ M

+ e

−

→ He

(2He) + hν Radiative electron–ion recombination

HCO

+ e

−

→ H + CO Dissociative electron–ion recombination

+ NO

−

→ NO + NO

Ion–ion recombination (mutual neutralization)

−

+ CCl

→ Cl

−

+ CCl

Dissociative electron attachment

−

+ C

→ C

−

Nondissociative electron attachment

−

+ O

+ M → O

−

+ M Ternary collisionally stabilized attachment

CO Isotope exchange

−

+ NH

−

+ NH

the polarizability/dipole moment of the product neu-

tral(s) may differ from those of the reactant neutrals.

Generally, the ﬁnal part (c) of the interaction has lit-

tle inﬂuence on the magnitude of the reaction rate

coefﬁcient or on the product distribution once the

products have signiﬁcantly separated (i. e., beyond the

range at which processes such as long range elec-

tron transfer can occur). Thus, to a major degree, part

(b) of the mechanism and the reaction energetics de-

termine the products of the reaction. Theories which

address this part of the interaction are also discussed

in Chapt. 37 and these have met with mixed success.

Thus, at present, experimental measurements are pro-

viding a more deﬁnitive understanding of reactions and

their mechanisms.

Also, the situation is not in general clear as to the

form of the thermodynamic energy that governs whether

a reaction will proceed spontaneously, i. e., whether it is

controlled by the enthalpy change ∆ H in the reaction

or by the Gibbs’ free energy change ∆G = ∆ H − T∆S,

where ∆S is the entropy change in the reaction [38.8].

This is discussed in more detail in Sect. 38.2.

Rate coefﬁcients and product distributions for

these reaction processes are important in all ionized

media where molecular species exist, such as interstel-

lar gas clouds [38.9], planetary atmospheres [38.10]

(including that of the Earth [38.11, 12]), comets

(Chapt. 83), the space shuttle environment [38.13], laser

plasmas [38.14], plasmas used to etch semiconduc-

tors [38.15], hydrocarbon ﬂames [38.16], etc.

38.2 Reaction Energetics

The availability of sufﬁcient energy is a primary consid-

eration for determining whether a reaction can proceed

spontaneously. Criteria for determining whether energy

is given out or absorbed in a reaction are (i) exo-

or endoergicity, ∆E representing the internal energy

change involved in a single interaction, (ii) exo- or

endothermicity for an ensemble of particles in ther-

mal equilibrium as deﬁned by the enthalpy change per

mole, ∆H, in the reaction and (iii) exergonic or en-

dergonic as deﬁned by the Gibbs’ free energy change,

∆G [38.17]. ∆ E is related to ∆H at temperature T

∆H

≈−N∆E

, (38.2)

Part C 38.2

Gas Phase Ionic Reactions 38.2 Reaction Energetics 577

where N is Avogadro’s number. ∆E is usually

deduced from bond energies [38.18–20], ionization po-

tentials [38.21], electron afﬁnities [38.22, 23], proton

afﬁnities [38.22, 24, 25], gas phase basicities [38.22,

24–26], etc. ∆ H

is determined from the heats of

formation H

f,T

by [38.27]

∆H



products

f,T

−



reactants

f,T

, (38.3)

where the superscript 0 refers to the standard

state [38.17] of the reactants and products [for exam-

ple, see (38.1)]. ∆G

is determined from ∆H

and the

entropy change ∆S

∆G

= ∆H

− T∆S

, (38.4)

where

∆S



products

−



reactants

, (38.5)

and the S

are the standard entropies [38.17]. In cases

where all of the H

f,T

and S

are not available, they can

often be deduced by constructing other reactions involv-

ing the species of interest and other species for which the

required thermodynamic information is known ([38.17]

discusses the details of ways in which this can be

achieved). Alternatively, the magnitude of a thermo-

dynamic parameter can be calculated using equilibrium

statistical thermodynamics, if the energies of all of the

occupied molecular energy levels are known [38.28].

For studies where all reacting particles of a given type

have the same energy, such as in beam/beam interac-

tions where cross sections σ(E) are measured, then ∆E

is most appropriate. Alternatively, for reactions involv-

ing an ensemble of particles in thermal equilibrium at

a temperature T, such as those studied in high pressure

mass spectrometer ion sources or afterglows where rate

coefﬁcients k(T ) are measured, ∆H and ∆G are more

appropriate. (The terms “rate coefﬁcient” and “rate con-

stant” are used interchangeably in the literature.) σ(E)

and k(T ) are directly related via

k(T) =

∞



v(E) f(E)σ(E) dE , (38.6)

where v(E) is the relativespeed of the reactants and f(E)

is the Maxwell–Boltzmann energy distribution. Whether

∆H or ∆G is more important for determining reaction

spontaneity depends on the degree of interaction of the

reacting systems with the surroundings during the course

of the whole reaction process. For example, if the reac-

tions occur at low pressure such that the reaction time is

much less than the collision time with the background

gas, there will be no interactions with the surroundings,

and the only energy available in the reactions will be

∆H. Here, ∆S can only determine the probability that

the intermediate complex dissociates forward to prod-

ucts or back to reactants. At the other extreme, if the

reactions are conducted at high pressure such that the

reaction species are always in thermal equilibrium with

the surroundings (the limiting case of this is reaction in

solution), then the additional energy T∆S is available,

and ∆G determines whether the reactions are sponta-

neous. Obviously, for intermediate pressures, there is

a varying degree of contact with the surroundings, and

which of ∆ H and ∆G is most applicable is more ob-

scure. The deﬁnition of surrounding is also somewhat

loose, since in the present context it represents any-

thing that can provide a source of energy during the

reaction (for example, vibrational modes of the react-

ing species that are not involved in the interaction and

which could be cooled as the reaction proceeds). Usu-

ally, the T∆S term is not sufﬁciently large that ∆H

and ∆G have different signs so that confusion about

the spontaneity of reactions often does not arise. Re-

cently, however, reactions have been discovered which

appear to proceed spontaneously even though ∆ H is

positive, and there has been considerable discussion of

this [38.8].

Eventually, all reaction processes will reach equilib-

rium as deﬁned by

∆G =−RT ln K ,

(38.7)

where

K =







(38.8)

is the equilibrium constant for the reaction

aA+ bB

 cC + dD. (38.9)

The subscripts to the pressures p denote the components

A to D, and the superscripts represent the stoichiome-

tries [38.17,28]. The equilibrium constant K also equals

, the ratio of the forward to reverse rate coefﬁcients,

obtained for thermalized particles at temperature T.

Thus, from measurements of k or the equilibrium con-

stant at a series of temperatures, ∆ H and ∆S of the

reaction can be separately obtained.

Part C 38.2

578 Part C Molecules

38.3 Chemical Kinetics

The rate coefﬁcient k for the reaction process

A+ B → C + D

(38.10)

is deﬁned by the rate equation [38.29]

d[A]

d[B]

=−k[ A][B] ,

(38.11)

where the square parentheses represent the concentra-

tions of the enclosed species, and the units of k are

typically cm

molec

−1

(often molec

−1

is not writ-

ten explicitly in the units). These k are deduced from the

time variation of speciﬁc concentrations of thermalized

reactants under a variety of conditions. For ion–neutral

reactions, with A being the positive or negative ion

species, the situation can usually be achieved in the

laboratory where [B][A], i. e., a pseudo ﬁrst-order

reaction. Simple integration yields

[A]

=[A]

exp(−k [B]

t ), (38.12)

where the subscript 0 indicates that this concentration

is time invariant. Similar circumstances apply to binary

electron attachment reactions, where [A]=[e], the elec-

tron number density (the symbol β is often used here in

place of k). If the reaction proceeds by association that

is stabilized by collision with a third body M then

A+ B+ M → AB + M ,

(38.13)

and the solution is

[A]

=[A]

exp(−k [B]

[M]

t ) (38.14)

with k now having units of cm

molec

−2

−1

. Note that

situations exist where binary and ternary reactions can

occur simultaneously.

If [B] [A], the solution of (38.11) is different. For

the special case [B]=[A], integration yields

1/[A]

− 1/[A]

= kt , (38.15)

and similarly for [B]. This situation is usually achieved

in the laboratory for the determination of k for electron–

ion and ion–ion recombination (the symbols α

and α

respectively are often used to replace k here). In manyap-

plications where several processes contribute to changes

in [A] and [B], and where the simple limits are not

applicable, the situation has to be analyzed numerically.

38.4 Reaction Processes

Recently, a nine volume series, concerned with all as-

pects of mass spectrometry, is being published of which

Volume 1 deals with theoretical and experimental as-

pects of ionic reactions in great detail [38.30]. The reader

is recommended to ﬁrst consult the present chapter to

get an overview of the reaction processes, and to go to

this other text if more detail is required.

The wide variety of possible reaction processes is

listed in Table 38.1 by speciﬁc examples. However, the

reaction mechanisms illustrated are completely general.

Magnitudes of the rate coefﬁcients for binary interac-

tions between charged and neutral particles, vary from

−7

−1

for electron attachment [38.31,32]to10

−8

or 10

−9

−1

for unit efﬁciency ion–molecule reac-

tions [38.33–36]. The efﬁciency is deﬁned as the ratio of

the measured k to the theoretical collisional value, i. e.,

that determined using the appropriate interaction poten-

tial. Ion–molecule reactions involving molecules with

large permanent dipoles (for example, HCN at 2.98 D

and HCl at 1.08 D [38.37]), can have k > 10

−7

−1

at low T [38.37–39] due to locking of the dipole along

the line joining the reactant species, thereby maximiz-

ing the strength of the interaction. Rate coefﬁcients

can be much smaller (by orders of magnitude) than

these upper limits if the efﬁciency of part (b) of the

mechanism is small. The part of the mechanism after

collision occurs is treated by transition state theory in

terms of the partition function of the transition state;

where the transition state is, and its partition function,

relates to the number of ways that the available en-

ergy can be distributed in the transition state [38.40].

More details of the theories are given in Chapt. 37

and [38.41].

For dissociative electron–ion recombination, the

upper limits on k are generally much larger as

a consequence of the long range Coulombic inter-

action potential, varying from ≈ 10

−7

−1

for

diatomic ions to > 10

−6

−1

for more polyatomic

species [38.42–45]. For ion–ion recombination, the rate

coefﬁcients are about an order of magnitude smaller

than these values because of the larger mass of the

negative ion relative to the electron, and thus the

smaller interaction velocity (the σ of the two processes

are, in fact, similar) [38.46]. Electron–ion recombi-

nations that are radiatively stabilized generally have

asmallk,assmallas≈ 10

−12

−1

[38.47], be-

Part C 38.4

Gas Phase Ionic Reactions 38.4 Reaction Processes 579

cause of the large magnitude of the radiative lifetime

of the reaction intermediate compared with the time for

autoionization. For most reaction types, experimental

rate coefﬁcients are available at room temperature, and

for some, the temperature and/or energy dependencies

have also been determined [38.31, 32, 43, 44, 46, 48].

Generally, only the ion products are identiﬁed using

mass spectrometry, and the product neutrals are not de-

termined (unless the energetics allow only one neutral

product), and the states of excitation of the products are

not identiﬁed.

For ternary processes involving association, k varies

from totally saturated at the binary collision limit

to very small (≈ 10

−32

−1

) for ion–neutral

reactions [38.33, 34] and similarly for electron attach-

ment [38.49]. Little is known about collision stabilized

recombination [38.50]. Each type of reaction process

has its own characteristic behavior and dependence on

temperature. Rate coefﬁcients, temperature dependen-

cies, and product distributions (where available) have

been tabulated for ion–neutral reactions [38.33, 34, 51]

and electron attachment [38.31,32]. Less data are avail-

able for electron–ion and ion–ion recombination, so no

attempts have been made to compile these. Data are

available in [38.6, 42–44,46].

38.4.1 Binary Ion–Neutral Reactions

Over the years, these reaction processes have been re-

viewed several times, but from different perspectives.

Most recently, studies of positive ion–molecules in ﬂow

tubes [38.52] and negative ion–molecule reactions from

an organic mechanistic viewpoint [38.53] have been

discussed.

Charge Transfer and Charge Exchange

These processes involve the exchange of an electron

which can occur at relatively large interparticle separ-

ations (i. e., up to ≈ 6 Å [38.54]). Thus, in principle,

k values can be larger than the collision limiting value.

Such reactions are, in general, relatively fast, although

there are some notable exceptions (for example, He

, k = 1×10

−13

−1

;Ne

+ H

, k < 2×10

−14

and

+ N

, k = 1.1×10

−13

[38.33]). Attempts have been

made to relate the efﬁciency of charge transfer to the

Franck–Condon overlap between the neutral reactant

and the product ion, with mixed success [38.55]. More

energy is generally available in the positive ion reac-

tions than the negative ion reactions since ionization

potentials are much larger than electron afﬁnities, and

thus more dissociative products would be expected, as

is usually observed. The reaction

+ N

→







+ N+ He + 0.28 eV

+ He+ 9.00 eV ,

is particularly interesting and has been studied in consid-

erable detail. The product distribution slightly favors N

(60%) rather than N

[38.56], with the N

channel be-

coming even more important with increasing vibrational

temperature of the N

[38.57]. Spectroscopic emission

studies [38.58] have shown that a signiﬁcant fraction

(≥5%) of the reactions proceed by charge transfer into

the N





state followed by the radiative decay





→ N





+ hν.

(38.16)

This channel competes with the predissociation





→ N

+ N . (38.17)

A new mechanism has recently been observed in

which charge transfer occurs in parallel with chemi-

ionization (or, equivalently, electron detachment):

+ C

→ C

+ e

−

+ He . (38.18)

Such a process is, of course, only energetically pos-

sible for high recombination energy ions like He

and

[38.59]. Also, multiply charged C





has been

seen to undergo two electron transfer with Corannulene

and some Polycyclic Aromatic Hydrocarbons (PAH’s),

generally in parallel with a whole series of other reaction

channels [38.60].

Proton Transfer

Where proton transfer is signiﬁcantly exoergic, as de-

termined by the difference in the proton afﬁnities of

the reactant and product neutrals, reaction usually pro-

ceeds at the collisional rate [38.61]. If the reaction is

close to thermoneutral, then the amount of phase space

available when the intermediate complex dissociates to

products is similar to that available when it dissoci-

ates back to the reactants, and the k approximates to

one-half the collisional value. For proton transfer re-

actions which are not highly exo- or endoergic, k

and

can be measured and thus ∆G determined [using

(38.7)]. If ∆S can be determined in some way, or if

can be determined as a function of T,then∆H

can be deduced and used to obtain the proton afﬁn-

ity difference (∆S can also be determined in the latter

case). This has been used to construct proton afﬁnity

scales [38.24, 25]. Care is required in such studies to

Part C 38.4

580 Part C Molecules

ensure that no vibrational excitation remains in the re-

actant ion due to its formation, and that the identities

(i. e., isomeric forms) of the reactant and product ions

are known (e.g. whether the ion is HCO

or the higher

energy form COH

[38.62]).

Often the individual reaction processes do not oc-

cur in isolation. For example, in the reactions of CH

with COS, H

S, NH

CO and CH

OH, both charge

transfer and proton transfer are energetically possible,

and both channels are observed. Here, the least exoergic

channel is favored in all cases [38.63]. Proton transfer

also occurs in negative ion reactions, for example those

of OH

−

and NH

−

giving H

OandNH

respectively

(e.g. see Table 38.1), and these types of reactions are

production sources for many negative ions [38.53,64].

Ion–Atom Interchange and Atom Abstraction

In many simple cases, these two processes are the same,

for example

+ H

→ ArH

+ H , (38.19)

but not so for the more complicated molecules (e.g., O

−

+ CH

;seeTable38.1). Such reactions, when exoergic,

usually occur close to the collisional rate although some-

what slower. Series of such reactions with H

occur in

the interstellar medium and are responsible for produc-

ing the hydrogenation in many of the species observed

there, for example, in CH

production from CH

,NH

from NH

and H

from OH

(see Chapt. 82). The

reaction,

+ H

→ NH

+ H , (38.20)

is particularly interesting. At temperatures greater than

300 K, the reaction shows an activation energy barrier of

2 kcal mol

−1

. The rate coefﬁcient k decreases with de-

creasing T, reaching a minimum of 2×10

−13

−1

at 80 K and then increases at lower T due to tunneling

through the barrier [38.48]. This behavior occurs be-

cause, at the higher temperatures, the lifetime of the

intermediate complex is not sufﬁcient for signiﬁcant

tunneling to occur, but there is sufﬁcient energy in

the reacting species to overcome the barrier. At lower

temperatures, there is not sufﬁcient energy available to

overcome the barrier, but the lifetime of the intermediate

complex becomes long enough for signiﬁcant tunneling

to occur [38.65]. This explanation has been substanti-

ated by the isotopic studies of the reactions NH

+ D

and ND

+ H

and D

[38.66].

For some reactions, isotopic labeling has been

used to identify the reaction mechanism. For example,

the reaction

+ O

→ O

+ O (38.21)

has been shown to be predominantly charge transfer,

rather than ion–atom interchange, by labeling the ion as

[38.67,68].

Associative Detachment

For negative ions, an additional process is possible for

which there is no equivalent positive ion analog (al-

though there is the related process of chemi-ionization,

i. e., AB + C → ABC

+ e

−

). In this process, the nega-

tive ion and the neutral associate, and the association is

stabilized by the ejection of the electron (see Table 38.1).

Such reactions can only occur when the electron detach-

ment energy is less than the energy of the bond that

is produced. Therefore, these reactions usually involve

radical species which produce stable molecules. k values

are usually an appreciable fraction of the collisional val-

ues [38.69, 70]. Infrared emissions have been detected

from a series of these reactions [38.71], for example O

−

with CO and F

−

,Cl

−

and CN

−

with H, and show that

the reactions populate the highest vibrational levels that

are energetically accessible.

Other Binary Ion–Molecule Reaction Channels

As reactant species become more polyatomic, there is

a greater variety of reaction processes that can occur, and

these often occur in parallel. The processes that occur

are too numerous to list so a few examples will have

to sufﬁce. Reactions that occur in isolation are insertion

reactions of the type [38.72]

+ C

→ C

n+1

m−x

+ xH (38.22)

and

+ C

→ H

m−1

+ H . (38.23)

Multiple channels are very evident in reactions of ions

produced from species with large ionization potentials

and small proton afﬁnities, for example, NH

[38.73],

+ CH

→











+ NH

+ NH (charge tsfr.)

+ N (proton tsfr.)

+ (NH

+ H)

+ NH

In addition to charge and proton transfer, other channels

requiring more rearrangement are evident.

Part C 38.4

Gas Phase Ionic Reactions 38.4 Reaction Processes 581

Isotopically Labeled Reactants

A great deal can be learned about reaction mechan-

isms in signiﬁcantly exoergic ion–neutral reactions by

isotopic labeling. Some such reactions have been men-

tioned above, but a particularly graphic example is the

reaction

+ CH

→ CH

+ CH

, (38.24)

which was assumed to be either proton transfer and/or

H-atom abstraction, depending on the interaction en-

ergy. By studying the reaction with both the ion and

the neutral reactants separately deuterated, the reaction

was shown to be much more complex, with the prod-

uct ions being CH

(10%), CH

(22%), CH

(43%) and CHD

(25%) for the reaction of CH

with

[38.74]. The reaction clearly proceeds via a long-

lived intermediate in which there is a large degree of

isotope mixing before unimolecular decomposition to

products.

A further class of isotopic reactions are those for

which the exoergicity is provided only by the differ-

ent zero point energies of the reactants and products.

Many such reactions have been studied. Examples of the

various types are: (i) The symmetrical charge transfer

→

, (38.25)

which proceeds in both directions at more than half the

collisional rate. This implies that the reaction proceeds

via long-range charge transfer, a conclusion substan-

tiated by the fact that no mixed product

produced [38.67]. (ii) Proton transfer reactions exempli-

ﬁed by

and H

CO, which

are both exoergic by about 1 meV [38.48]. Some iso-

topic scrambling has been observed in the latter reaction

by using the double isotopic substitution [38.75],

O →











(≥ 90%)

(≤ 10%).

Other examples where considerable isotope scram-

bling occurs are H/D exchange in the reaction

systems H

+ H

,CH

+ H

O, CH

,etc.[38.48]. Such scrambling reactions are be-

lieved to proceed via proton bound dimer intermediates

(e.g., H

O ···H

···D

O). (iii) Isotope exchange reac-

tions such as

CO →

CO have also

been studied. For this reaction, both k

and k

increase

with decreasing T due to an increase in the intermedi-

ate complex lifetime; k

decreases at lower T due to the

endoergicity in this reaction direction [38.74].

Isotope exchange is also observed to occur with

negative ions, viz.

−

+ MH → HO

−

+ MD , (38.26)

and is a common process. Particularly signiﬁcant is the

comparison where MHisH

and NH

. These species

have very similar gas phase acidities, and thus the exo-

ergicities of the reactions are similar. However, NH

has a larger polarizability than H

and, in addition, has

a permanent dipole moment. The observation that the

k for the NH

reaction is a factor of ten larger than

that for the H

reaction is explained as being due to the

stronger interaction potential which makes more energy

available in the intermediate complex and facilitates H/D

exchange [38.64].

Temperature Dependencies of Binary Reactions

When the k values at room temperature are close to the

collisional value, appreciably exoergic reactions gener-

ally exhibit little temperature dependence. For slower

reactions, a signiﬁcant inverse temperature dependence

is observed, being ≈ T

−1/2

for several reactions. This

behavior is rationalized as a decreasing lifetime of the

intermediate complex with increasing temperature, thus

allowing less time for reaction [38.48].

38.4.2 Ternary Ion–Molecule Reactions

In cases where binary channels are not energetically

possible, association reactions can still occur, both for

positive and negative ions. The reactions can be as

simple as

+ He+ He → He

+ He , (38.27)

to associations more complex than those listed in Ta-

ble 38.1. Rate coefﬁcients k

at room temperature vary

from 1 × 10

−31

−1

for reactions such as (38.27)to

in excess of 1 × 10

−25

−1

, this upper limit being

due to experimental constraints rather than the reaction

itself. The mechanism usually postulated is

+ B 





∗

, (38.28)





∗

+ M → AB

+ M

∗

(38.29)

where M stabilizes the excited intermediate,





∗

by removing energy in the collision. For this type of

reaction, there is a considerable dependence of k on T.

Part C 38.4

582 Part C Molecules

Statistical theory predicts (see Chapt. 37),

∝ T

−(/2+δ)

, (38.30)

where  is the number of rotational degrees of freedom

in the separated reactants, and δ is a parameter attributed

to the temperature variation of the collision efﬁciency of

the stabilizing third body M. Experimentally, many as-

sociation reactions exhibit such power law dependencies

of the k

[38.48, 51] with δ being small (≈ 0.2or0.3)

for a helium third body. Also, some evidence exists for

a contribution of vibrational degrees of freedom to the

temperature coefﬁcient in cases where the vibrational

levels in the reactant neutral are closely spaced [38.76].

For complex reactant species, lifetimes of interme-

diate complexes become very long so that, in the higher

pressure experiments (see below), all intermediate com-

plexes are stabilized, and thus the reaction is independent

of the pressure of M. This form of “saturation” can be

eliminated in many cases by using low pressure experi-

ments, so that the time between collisions is long, and

normal ternary kinetics (38.14) are restored. Under these

conditions, sometimes there is still a pressure indepen-

dent component to the k which is postulated as being

due to radiative stabilization of the intermediate, viz.





∗

→ AB

+ hν. (38.31)

An example of this is the reaction [38.77]

+ CH

CN → CH

· CH

CN + hν. (38.32)

The stabilizing photon is often considered to be in the

infrared due to a vibrational transition within the ground

electronic state (with a radiative lifetime of ≈ 10

−2

−3

s). Note that only a photon with hν>3/2k

T is

required for the complex (although still vibrationally

excited) to be stable against unimolecular dissociation.

However, there are cases where it is believed that an elec-

tronically excited state is accessed [38.78,79]. Examples

are

+ H

→ CH

+ hν (38.33)

and

−

+ BCl

→ BCl

−

+ hν. (38.34)

As yet, radiative association has not been observed di-

rectly (i. e., by the detection of the emitted photon),

however, the kinetic evidence is strong for the existence

of this process.

For the more rapid collisional associations, compe-

tition with binary channels is possible, for example

+ NH

→











+ H

(70%)

+ CH

(10%)

−→ CH

· NH

+ He (20%)

where the percentages refer to product abundances at

aHepressureof0.2 Torr [38.80].

38.5 Electron Attachment

These reactions have generally been studied by differ-

ent techniques from those used to examine ion–neutral

reactions and also by different workers [38.31, 32].

Analogous to the ion–neutral situation, there are dis-

sociative processes,

−

+ CCl

→ Cl

−

+ CCl

, (38.35)

and nondissociative processes,

−

+ C

→ C

−

, (38.36)

the former being stabilized by dissociation, and the latter

occurring because of the long lifetime of the interme-

diate against autodetachment with eventual collisional

stabilization (cf. saturation in ion–neutral association

reactions; Sect. 38.4.2). Measured rate coefﬁcients vary

in the range 1 × 10

−7

to the smallest measurable value

of ≈ 1×10

−12

−1

[38.31, 32]. The upper limit

on k for this process is determined, from a consider-

ation of the electron de Broglie wavelength

λ = λ/2π,

to be ≈ 5×10

−7

(300/T )

1/2

−1

[38.81], or, more

rigorously,

k(E) =





σ/π



/[hρ(E)] , (38.37)

where ρ(E) is the density of states and

σ/πλ

≈ 1− exp



−



4γ



1/2



(38.38)

with γ

∞

= (2µ/m)

[38.5]; σ is the collision

cross section, T the kinetic energy, α

the polarizability,

the Bohr radius, µ the reduced mass, and i represents

the available product channels. Where k is less than the

upper limit value, this is usually due to activation energy

barriers, and k shows Arrhenius behavior

k(T) = k

exp

(

−∆E/k

)

, (38.39)

Part C 38.5

Gas Phase Ionic Reactions 38.6 Recombination 583

where k

is the Boltzmann constant, with the barrier

height ∆E being in the range 0 to ≈ 300 meV [38.32].

If the attachment is nondissociative, and the lifetime of

the intermediate complex against autoionization is small

compared with the collision time (as occurs for less

complex species), the reaction exhibits normal ternary

behavior, for example,

−

+ O

+ M → O

−

+ M . (38.40)

Some interesting mechanisms have been identiﬁed for

attachment. Different product ions have been observed

in experiments conducted at very different pressures, for

example, in the reaction

I+ e

−

→ C

−

+ I (≥ 95%) (38.41)

→ C

−

(≤ 5%). (38.42)

at high pressures (≈ 1 Torr), the products, as indicated,

were observed with an association channel [see (38.42)]

being detected [38.82]. This association channel was

not seen in low pressure experiments [38.83]. Such

behavior is explained in terms of the relative mag-

nitudes of the autodetachment lifetime and the time

between collisions. When the former time is larger, the

association product will dominate, whereas if the con-

verse is true, dissociation products dominate. Thus, the

differentproduct distributions,rather than indicating dis-

crepancies, yield information about the autodetachment

lifetime.

In attachments to the Br-containing compounds,

,CFBr

,andCF

BrCF

Br and CH

BrCH

Br,

in which the Br atoms are on different carbon atoms, up

to a 20% Br

−

product is observed [38.84]. This shows

that atoms in product molecules can come from spatially

separated parts of the reactant molecule. Thus, consid-

erable distortion and rearrangement must occur in the

intermediate complex.

38.6 Recombination

This process has been much less studied than ion–

neutral reactions with only ≈ 100 reactions being

studied [38.44] compared to about 10 000 in the former

case [38.33]. Also, relatively little information is avail-

able concerning the products since these are neutral and

very much more difﬁcult to detect than ions.

38.6.1 Electron–Ion Recombination

Electron–ion recombination can proceed by series of

mechanisms, which have been discussed in detail re-

cently [38.85], and these are included in Table 38.1.

In brief, these are radiative recombination, where the

neutralized ion (excited into the continuum) is stabi-

lized by radiation emission, dielectronic recombination,

which is similar to radiative recombination, except that

there is a double electron excitation into the contin-

uum, collisionally stabilized recombination, where the

intermediate is stabilized by collisions with electrons

or a heavy third body (combined collisional radiative

recombination is also possible), and dissociative recom-

bination. Dissociative recombination can obviously only

occur when the recombining ion is molecular, however,

when it occurs it is usually several orders of mag-

nitude faster than the other recombination processes.

Thus, only dissociative recombination will be discussed

here.

Rate coefﬁcients for dissociative electron–ion re-

combination at room temperature vary from > 1×10

−6

for polyatomic ions to ≈ 1×10

−7

−1

for diatomic

ions [38.42, 43]. For large k, there is little tempera-

ture dependence, temperature dependencies being more

marked for the slower reactions. Two mechanisms were

initially proposed: (i) the direct mechanism [38.86]

where the neutralized ion undergoes a radiationless

transition to a repulsive potential curve on which

dissociation to products occurs, and (ii) the indirect

mechanism [38.87] where the neutralized ion initially

transfers to a Rydberg state and then undergoes a ra-

diationless transition to the repulsive curve. For the

former process, the theoretical temperature dependence

is T

−0.5

, while it is T

−1

−1.5

for the latter, where the

subscripts T and e refer to the thermal ion vibrational

and electron temperatures respectively [38.6]. There

is no reason why these two processes cannot occur

in parallel, although it is not straightfoward to deter-

mine the relative contributions [38.87]. Fortunately, both

processes are automatically included in multichannel

quantum defect theory (MQDT) [38.88]. Experimen-

tal T-dependencies for reactions which are not close

to the collisional limit have power law dependencies

in the range ≈ 0.7to1.5 [38.43, 89, 90], i. e., between

the theoretical predictions. In cases where there is de-

tailed temperature data, e.g., for some hydrocarbon

ions





[38.89, 90],

the dependence changes from the lower dependence

at low temperature to the higher dependence at higher

temperature.

Part C 38.6

584 Part C Molecules

Less is known about the products. Detailed theory

carried out for the diatomic ions O

,NO

and N

,and

to a large degree HCO

, are in general agreement with

experiment [38.91, 92]. For the more polyatomic ions,

the theory is not yet sufﬁciently quantitative [38.93,94]

and reliance is placed on experiment. H-atom contribu-

tions to the product distributions for ten ions



HCO

,HCO

,OCSH

,NH

and CH



vary from ≈ 20% for OCSH

to 120% for CH

[38.95]. OH is a substantial prod-

uct (30 to 65%) in the above reactions where it is

energetically possible [38.96] (i. e., excluding HCO

except in the case of OCSH

, perhaps indicating that

the proton is exclusively on the S-atom rather than the

O-atom (i. e., in the lowest energy form [38.97, 98]).

More complete product distributions are now being

obtained, initially using ﬂowing afterglows



HCO



[38.99], but more recently using

storage rings



including H

,CH

,NH

,CH



[38.100]. These studies are showing

that fragmentation to give three products is a common,

indeed dominant, mechanism [38.101]. Dissociative re-

combination has recently benn reviewed by [38.102].

Electron–ion recombination is an energetic process

and electronically excited states can also be populated.

Vibrational population distributions for these states can

readily be determined if Einstein A coefﬁcients are

known for the observed transitions (I ∝ A[∗],where

I is the photon intensity, and [∗] is the number dens-

ity of the excited state). The N

) state and the

CO (a

) state vibrational population produced in

the recombinations of N

,HCO

and CO

have been determined [38.103, 104]. Possible mechan-

isms [38.105] have been suggested for this vibrational

excitation: (i) the impulsive force on the molecular frag-

ments as the neutralized ion rapidly dissociates, and (ii)

the Franck–Condon overlap between the wave functions

of the molecular products (in various vibrational states)

and the wave function of this particular fragment in the

neutralized ion before it dissociates. Theory underes-

timates the populations of the higher levels, but does

predict the small observed oscillation in the occupancy

of the various vibrational levels in the CO (a

) state

generated in the recombination of HCO

[38.106].

The theories of recombination discussed above as-

sume favorable potential curve crossings, however, it

has been shown both experimentally [38.107, 108]and

theoretically [38.109] that such are not necessary when

quantum tunneling can occur. Experimental evidence

has been obtained in the recombinations of N

and

where the populations of the ν



= 6 vibrational

level of the N

electronically excited (B

) state is

greatly enhanced (≈ 6 at 100 K) for N

over N

This level is resonant with the ν = 0 vibrational level

of the recombining ion, making tunneling more facile;

and H atom tunneling is further enhanced because of the

smaller mass [38.108].

38.6.2 Ion–Ion Recombination

(Mutual Neutralization)

Less information is available on this process than

on electron–ion recombination; a detailed review

has recently been published [38.110]. k values vary

from about 4×10

−8

to 1×10

−7

−1

at room

temperature [38.44, 46] with power law temperature

dependencies of ≈ 0.4 for the only two systems that

have been studied as a function of T (NO

+ NO

−

and NH

+ Cl

−

) [38.46]. This is consistent with the-

ory [38.111] in which the Landau–Zener approximation

is used to determine the probability of a crossing be-

tween the Coulombic ion–ion attractive potential and

the potentials of the neutral products. This transition oc-

curs by an electron transfer (the optimum distance for

such a transfer when a favorable crossing exists is about

10 Å). Theory gives that

k ≈ 2





µ/2πk



1/2

, (38.43)

where Q is the cross section

Q = πR



1+ (R

−1



(38.44)

is the crossing distance, E is the interaction en-

ergy and v is the relative velocity at the crossing

point [38.111]. Once neutralized by electron transfer,

the products continue undeﬂected with the velocity

gained from the Coulombic ﬁeld. Photon emission has

been detected from a series of excited state prod-

ucts. Following the early detection [38.112]ofNO

) emissions from NO

+ NO

−

,avarietyofNO

emissions have been detected from NO

recombina-

tions with molecular



−

,andC

−



and

atomic (Cl

−

and I

−

) negative ions [38.113, 114]and

emissions from He

recombinations with C

−

and C

−

[38.113]. These emissions were inter-

preted in terms of long-range electron transfer [38.112],

however, in the recombination of Kr

and Xe

with

−

, KrF, and XeF, excimer emissions have been

seen [38.113], suggesting an intimate encounter in these

cases. Also, few data are available on the effects of pres-

sure. For the reactions SF

+ SF

−

and NO

+ NO

−

k increases by about a factor of 4 between 1 and

8 Torr [38.46, 50].

Part C 38.6

Gas Phase Ionic Reactions References 585

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Part C 38