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

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982 Part E Scattering Experiment

66.63 J. M. Farrar, T. P. Schafer, Y. T. Lee: AIP Conference

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66.65 S. Bosanac: Phys. Rev. A 22, 2617 (1980)

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Part E 66

983

Ion–Molecule

67. Ion–Molecule Reactions

The observation of ion–molecule reactions has

a history that goes back to the beginning of the

twentieth century, when J. J. Thomson discovered

that operating his positive ray parabola appara-

tus in a hydrogen atmosphere produced signals

at a mass to charge ratio of 3, which he correctly

attributed to the species H

[67.1]. Later studies

showed that this species was produced by a re-

action between the primary ionization product

and molecular hydrogen. Most ion-molecule

reactions proceed without an activation bar-

rier and their cross sections are governed by the

long range attractive potential of the approach-

ing reactants (Sect. 64.2.4). Reaction rates based

on long range potential capture models [67.2]

predict rates in excess of 10

−9

molecule

−1

corresponding to thermal energy cross sections

(Sect. 47.1.7)of10

−16

–10

−15

.Theimportance

of ion-molecule reactions in such widely di-

verse areas as planetary atmospheres, (Sect. 84.1),

electrical discharges and plasmas (Sect. 87.1.4),

particularly in semiconductor processing, in

the formation of molecules in interstellar

space (Chapt. 82), and in ﬂames and combustion

67.1 Instrumentation.................................. 985

67.2 Kinematic Analysis............................... 985

67.3 Scattering Cross Sections ...................... 987

67.3.1 State-to-State Differential Cross

Sections ................................... 987

67.3.2 Velocity–Angle Differential Cross

Sections ................................... 988

67.3.3 Total Cross Sections with

State-Selected Reactants............ 989

67.3.4 Product–State Resolved Total

Cross Sections ........................... 989

67.3.5 State-to-State Total Cross

Sections ................................... 990

67.3.6 Energy Dependent Total Cross

Sections .................................. 990

67.4 New Directions:

Complexity and Imaging ...................... 991

References .................................................. 992

systems (Sect. 88.1), has borne out that pre-

diction. This chapter discusses applications of

single-collision scattering methods to the study

of reactive collision dynamics of ionic species with

neutral partners.

A number of different physical processes can be cate-

gorized as ion-molecule reactions, with examples such

+ BC → A+ BC

, charge transfer

+ BC → A+ (B+ C)

, dissociative charge

transfer

+ BC → AB

+ C . particle transfer

The ± superscript indicates charge appropriate to anions

and cations. The parentheses indicate that the charge can

reside on either the B or C fragment. Particle transfer

reactions often involve the transfer of a hydrogen atom

or a proton, but heavy particle <transfer processes are

often important ones as well. An interesting example in

which new carbon-carbon bonds are formed, termed a

condensation reaction, is the following:

+ CH

→ C

+ H .

An additional process unique to anionic systems is de-

tachment, occurring when the intermediate collision

complex is internally excited above its autodetachment

threshold:

−

+ BC →[ABC

−

]

∗

→A+ BC + e

−

detachment

−

+ BC →[ABC

−

]

∗

→ABC + e

−

associative detachment

For exothermic reactions at low collision energies where

the long range attraction dominates the interaction po-

tential, cross sections are consistent with Langevin

orbiting, generally having E

−1/2

energy dependence.

Part E 67

984 Part E Scattering Experiment

At higher energies, cross sections drop below this limit,

as surface crossings and short-range repulsive features

become important. Endothermic reactions exhibit cross

section thresholds, as illustrated in Sect. 67.3.4 on the

+ D

system.

Scattering measurements probe the potential energy

surface, or surfaces, governing the collision dynamics

with techniques that measure the ﬂuxes from speciﬁc

reactant quantum states into product quantum states,

scattering angles, and product translational energies.

Scattering experiments deﬁne more precisely than in

a bulb the initial and ﬁnal conditions in a collision

[67.3]. A scattering experiment measures a cross section

(Sect. 91.1.1) rather than a rate constant. The measured

cross section represents an average over initial condi-

tions and a sum over ﬁnal states inherent in the technique

used.

Cross sections of various forms can be deﬁned with

respect to the rate of formation of product states un-

der single-collision conditions. The total rate of product

formation dN

/dt for a beam of ions with number den-

sity n

intersecting a gas of number density n

within a

scattering volume ∆V, deﬁned by the overlap of the ion

beam with the target gas, is given by

/dt = σv

rel

∆ V , (67.1)

where σ is the total reaction cross section (Sect. 47.1.7)

and v

rel

is the relative speed of the collision partners. Us-

ing the experimental ion beam current I

, cross section

σ, neutral number density n

, and attenuation length L,

this expression converts to the particularly useful form

/dt = 6.25 × E − 7σI

L (67.2)

for computing signal levels, where σ isexpressedinÅ

in nA, n

in cm

−3

,andL in cm. An ion beam of

current 1 nA, intersecting a target of length 1 cm at a

pressure of 10

−3

Torr, corresponding to a number den-

sity of 3.5×10

−3

at STP, and reacting with a cross

section of 1 Å

yields a total rate of product formation

of 2 × 10

−1

The detector observes only a fraction of this total

rate. If reaction products are scattered isotropically over

4π steradians in the laboratory, and the detector entrance

slit of area dS is located a distance r from the collision

center, subtending a solid angle dS/r

, the fraction of the

total signal scattered into the slit is dS/(4πr

) [67.4].

The fraction of the collision volume, or of the product

state distribution accessible to a particular experimen-

tal method, determines the tradeoffs between resolution

and signal level, and therefore the feasibility of a given

experiment.

In an “ideal” experiment, one collides reactants, with

well speciﬁed quantum numbers collectively denoted

n, at a precisely deﬁned relative velocity v

rel

, resolv-

ing products in quantum states n



scattered through

center-of-mass scattering angle θ. The resulting detailed

differential cross section (DCS) (Sect. 47.1.1) is denoted

by σ(n



,θ| n, v

rel

). However, most experiments involve

at least partial averages over initial states and/or sum-

mations over ﬁnal states. Figure 67.1 shows the result

of averaging σ(n



,θ| n, v

rel

) over θ to yield the state-to-

state cross section at ﬁxed v

rel

, denoted by σ(n



|n, v

rel

Averaging this cross section over a Maxwell–Boltzmann

distribution of molecular speeds at a speciﬁed temper-

ature T yields the detailed state-to-state rate constant

k(n



|n, T), while summation over the ﬁnal states n



and

averaging over the initial states n yields the thermal

rate constant k(T). These latter two quantities are ther-

mally averaged, multiple collision properties and not

the subject of this chapter, although they play an im-

portant role in practical applications. Another pathway

for averaging the detailed DCS σ(n



,θ|n, v

rel

) arises

from averaging over n and summing over n



to yield

cross sections differential in product velocity v



rel

and

θ at ﬁxed v

rel

, denoted by σ(v



rel

,θ|v

rel

).Anaverage

over θ and v



rel

yields the velocity dependent total cross

section σ(v

rel

), and its Maxwell-Boltzmann average pro-

duces the thermal rate constant k(T) once again. The

subject of this chapter is a discussion of the various

cross sections σ shown in Fig. 67.1. As one moves from

σ(n⬘,θⱍn,V)

σ(n⬘ⱍn,V)

k(n⬘ⱍn;T)

k(T)

σ(V)

σ(V⬘,θⱍV)

n⬘, n

 v

 θ

n⬘, n

 θ, v⬘

Fig. 67.1 Relationships among differential and total cross

sections, and rate constants. Brackets denote averages over

indicated variables, or averages over initial states and sum-

mations over ﬁnal states

Part E 67

Ion–Molecule Reactions 67.2 Kinematic Analysis 985

more highly averaged quantities to the detailed cross

sections, more sophisticated reactant preparation and

product detection schemes are required to extract the

desired information, at the expense of decreased sig-

nal levels. Technological advances, particularly in laser

preparation of quantum state-selected reactants and in

state-speciﬁc product detection, have made the “ideal”

experiment a near reality in favorable circumstances,

particularly in neutral-neutral interactions, e.g., in ex-

periments on H + H

and its isotopic variants. This

chapter discusses the cross sections σ(n



,θ| n, v

rel

σ(v



rel

,θ|v

rel

), σ(n



| n, v

rel

),andσ(v

rel

), emphasizing

the dynamical information that can be extracted from

each kind of measurement.

67.1 Instrumentation

Instrumentation for studying ion-molecule reactions

is quite diverse, and numerous literature sources

are available for further discussion [67.5]. A typ-

ical instrument has an ionization source, a primary

mass selector, a collision region, and detector,

consisting of a mass spectrometer or employ-

ing a spectroscopic technique allowing molecular

identiﬁcation.

67.2 Kinematic Analysis

The transformation of laboratory measured speeds,

angles and intensities to their center of mass (cm) coun-

terparts can be accomplished with appropriate geometric

constructions [67.6,7]. The geometric relationships can

be understood by considering a kinematic Newton di-

agram for the collision process A+ BC,asshown

in Fig. 67.2. The diagram is constructed for the spe-

cial case in which the reactant beams intersect at 90

◦

The laboratory scattering angle and velocity are Θ

and v respectively, while the corresponding center of

mass quantities are θ and u. The beam velocity vec-

tors v

and v

deﬁne the initial conditions, and the

relative velocity vector v

rel

is deﬁned by their vec-

tor difference. The velocity c of the center of mass,

or centroid, of the collision system is determined by

conservation of linear momentum; the vector c divides

the v

rel

in inverse proportion to the masses of A and

BC:

c =

+ m

(67.3)

=−

rel

, (67.4)

rel

, (67.5)

where M is the total mass of the reactants with masses

and m

. An observer moving away from the lab-

oratory origin in the direction of the center of mass

vector c would see the reactants A and BC approach

along the direction of v

rel

, with the products retreat-

ing along the direction of v



rel

. The angle θ between

these vectors deﬁnes the center of mass scattering an-

gle. For a single Newton diagram, detection of products

at recoil speed u and scattering angle θ requires that

measurements be made at laboratory coordinates (v,

Θ). For monoenergetic incident beams, the measure-

ment of both laboratory scattering angle and speed

results in a unique lab to cm coordinate transforma-

tion. Linear momentum conservation also relates the

center of mass speeds of products AB and C to the

relative velocity of the separating products according

dω

⍀

Fig. 67.2 Kinematic Newton diagram showing laboratory

and center of mass velocities and scattering angles

Part E 67.2

986 Part E Scattering Experiment



rel

, (67.6)



=−



rel

. (67.7)

The ﬁnal relative kinetic energy of the separating prod-

ucts is



rel



rel

· v



rel

, (67.8)

where µ



is the reduced mass of the prod-

ucts.

The total energy of a collision system is computed

from the energies of the incident reactants and the energy

accessible to the products:

tot

= T

rel

+ E

int

− ∆D

= T



rel

+ E



int

; (67.9)

rel

and E

int

refer to the incident kinetic and inter-

nal excitation energies of the reactants and the primed

quantities correspond to the products. ∆ D

is the zero

point energy difference of reactants and products. Spec-

iﬁcation of the vibrational and rotational energy of a

product determines the relative velocity v



rel

with which

the products separate, according to



rel





rel

+ E

int

− ∆D

− E



int

)



1/2

(67.10)

The quantization of internal energy of the product AB

leads to a series of concentric circles about the cen-

troid that describe the loci of ﬁnal translational speeds

for AB produced in speciﬁc internal states. An exam-

ple of the kinematic resolution of product vibrational

states in the reaction O

−

+ HF → F

−

+ OH is shown

in Fig. 67.3 [67.8, 9].

At a collision energy of 0.47 eV (45.0kJ/mol), the

laboratory ﬂux distribution shows structure that is at-

tributable to the formation of OH in v



= 0, 1, and 2

states. The kinematic Newton diagram at the bottom of

the ﬁgure shows the concentric circles corresponding to

the formation of F

−

in concert with OH in speciﬁc vibra-

tional states having quantum numbers v



= 0, 1, and 2.

For laboratory scattering angles in the range 0

◦

≤ Θ ≤

◦

and 80

◦

≤ Θ ≤ 90

◦

energy scans only intersect the

kinematic circles corresponding to OH in v



= 0and1

states, while data in the intermediate range of angles 18

◦

≤ Θ ≤ 70

◦

show contributions from all three states. The

laboratory speeds at which these vibrational states ap-

pear, for a given Θ, are marked in the ﬁgure, showing

clear correspondence with the structure in the experi-

mental data. Rotational excitation in the products will

broaden the contributions from individual vibrational

states in experiments lacking rotational resolution. The

best resolution achievedin electrostatic energy analyzers

is approximately 5 meV (40 cm

−1

); and consequently,

scattering measurements of product ﬂuxes based on ki-

netic energy analysis generally do not have rotational

state resolution. However, photoelectron spectroscopy

measurements on H

[67.10] have yielded spectra of

energy levels with rotational resolution.

The transformation of intensities and cross sections

between laboratory and cm coordinate systems relies on

conservation of ﬂux in a transformation between two

coordinate systems moving with respect to one another.

Figure 67.2 shows the nature of this conservation: in

laboratory coordinates, the ﬂux into solid angle dΩ is

given by I

lab

(Ω) dΩ, where the laboratory intensity I

lab

is the ﬂux per unit solid angle, while the corresponding

ﬂux in the cm frame is I

(ω) dω,whereI

is the cm

ﬂux per unit solid angle. The solid angles subtended by

the detector in the laboratory and cm frames expressed

in velocity space may be computed from the surface

element dS subtended by the detector:

dω =

, dΩ =

. (67.11)

The ﬂux equality I

lab

(Ω) dΩ = I

(ω) dω leads to the

intensity transformation

lab

(v, Θ) =

(u,θ). (67.12)

The widths of the beam velocity distributions must

be accounted for in extracting accurate cm cross sections

from laboratory data. In the case where the laboratory

ﬂux at a given Θ is comprised of contributions from

individual quantum states of the products, the laboratory

ﬂux is recovered from the relation

lab

(v, Θ) =v

∞



)

∞



)

rel







σ(n



,θ|n, v

rel

)δ(u − u



)



(67.13)

In this expression, the velocity distributions for the pri-

mary ion beam and the secondary neutral beam are

given by f

)and f

) respectively. The ﬁnal prod-

uct internal states are labeled by the index n



;thecm

cross section for producing collective quantum state



is given by σ(n



,θ|n, v

rel

) and the cm speed cor-

responding to the formation of this state is given by

Part E 67.2

Ion–Molecule Reactions 67.3 Scattering Cross Sections 987

18°

5 15 25 35 5 15 25 35 5 15 25 35 5 15 25 35

9° 11°0° 10 1 0 1 0 21 0

1021021010

Lab velocity (100 m/s)

Newton

Diagram

–

rel

v⬘= 2

v⬘= 1

v⬘= 0

80° 90°70°26°

Fig. 67.3 F

−

reactive ﬂuxes in the O

−

+ HF system at a collision energy of 45 kJ/mol. After [67.8, 9] by permission



. The solution of this equation for σ(n



,θ|n, v

rel

) can

be accomplished both by forward convolution integra-

tion ﬁtting procedures [67.11] and by iterative unfolding

[67.12]. Forward convolution methods assume paramet-

ric forms for σ(n



,θ|n, v

rel

) that are substituted into

(67.13). The parameters are then varied until the cal-

culated ﬂuxes agree with the data within experimental

error. Iterative deconvolution methods generally extract

the cm cross section summed over ﬁnal states,





σ(n



,θ|n, v

rel

), (67.14)

but the ﬁnite energy of the detection scheme also deter-

mines whether quantum states are completely resolved

or if the data represent a summation over product energy

levels.

67.3 Scattering Cross Sections

Measurements of the single-collision cross sections

shown schematically in Fig. 67.1 require a variety of

sophisticated techniques. Each of these are discussed in

the context of measurement techniques and information

content, with illustrative examples.

67.3.1 State-to-State Differential Cross

Sections

Information most diagnostic of the potential energy sur-

face for chemical reaction comes from σ(n



,θ|n, v

rel

The experimental data of Fig. 67.3 on the O

−

HF system provide an example of a case in which



refers to product OH vibrations in the ground

electronic state, but without resolution of product

rotations. Iterative deconvolution of the laboratory

ﬂuxes results in a ﬂux distribution that is a sum

of cross sections, as described in (67.14). Fig-

ure 67.4 shows this distribution in cm velocity space

as a function of u and θ. In this representation,

the relative velocity vector lies along the 0

◦

- 180

◦

line, and the symmetric peaks of the data near

◦

(forward scattering) and 180

◦

(backward scatter-

ing) indicate that the reaction proceeds through a

transient collision complex living for at least sev-

eral rotational periods. The symmetry of the ﬂux

distribution with respect to 90

◦

is the most impor-

tant diagnostic for the participation of a long-lived

transient complex. Whether the distribution is forward-

backward peaked, as in the present example, or

more isotropic reﬂects the geometry of the com-

plex (i. e., oblate or prolate symmetric top) and the

manner in which angular momentum is partitioned

in the products [67.13]. In Fig. 67.4, the forward-

backward scattering is indicative of the fact that

the orbital angular momentum L of the approach-

ing reactants is partitioned preferentially into orbital

angular momentum of the products, L



, through

a near-linear [O···H···F]

−

intermediate. The vari-

ous peaks in the ﬂux distribution of Fig. 67.4 can

Part E 67.3

988 Part E Scattering Experiment

be assigned to OH vibrations v



= 0, 1, and 2.

Integration of the cross sections over the appro-

priate angular and velocity ranges yields the result

P(v



= 0) : P(v



= 1) : P(v



= 2) = 0.38 : 0.43 : 0.18.

Crossed–beam experiments (Sect. 60.2.2) with sufﬁ-

cient angular and kinetic energy resolution yield angular

distributions for individual vibrational states. Similarly,

laser-induced ﬂuorescence experiments [67.15] yield ro-

tational distributions. Recent work on the Ar

+ N

→ Ar + N



= 0, J



) system illustrates this capabil-

ity [67.16] (Sects. 64.2.1 and 38.4.1). However, these

experiments probe N

in the collision volume, thereby

averaging over all possible scattering angles, and are

more properly examples of product-state resolved cross

sections, discussed in Sect. 67.3.4. Experiments that

provide complete product vibrational-rotational state

speciﬁcation and product scattering angles have yet to

be carried out.

In the above examples the neutral beam is produced

by supersonic expansion, producing reactants in their

ground vibrational states, with rotational temperatures of

only a few kelvins. Experiments with reactants prepared

in excited states, either by laser absorption [67.17]or

photoionization, and with full ﬁnal state selection and

angular resolution, remain a major goal of ion-molecule

chemistry.

The production of reagent ions in selected vibra-

tional and vibrational-rotational states by resonance en-

hanced multiphoton ionization (REMPI) (Sect. 74.1.2)

90°

0°

180°

–

Fig. 67.4 Axonometric plot of F

−

ﬂuxes in velocity space

in the reaction O

−

+ HF → OH + F

−

at 45 kJ/mol. Data

from [67.8,9]

has been accomplished in a number of systems [67.17,

18]. The use of photoelectron spectroscopy to assess the

purity of the state-selection process is essential [67.19].

67.3.2 Velocity–Angle Differential Cross

Sections

The velocity-angle DCS σ(v



rel

,θ|v

rel

) obtained by

measuring kinetic energy distributions as a function

of Θ can be plotted as a distribution in u and

θ. Figure 67.5 shows σ(v



rel

,θ|v

rel

) for the reaction

+ H

O →[COH]

+ H at a collision energy of

2.14 eV (206.5kJ/mol) [67.14]. The scattering is pre-

dominately backward, and the data indicate a reaction

taking place in part through a transient complex, but

principally through low impact parameter direct colli-

sions leading to backward scattered products. Collisions

leading to such backward scattered products are called

rebound collisions and are dominated by the repulsive

part of the potential surface. Although the reaction of C

with H

O is exothermic, high kinetic energy release in

the rebound component suggests that a potential energy

barrier is in the exit channel, i. e., it acts as the products

separate.

At lower collision energies, the forward peak in

the ﬂux distribution becomes more pronounced for the

+ H

O reaction, suggesting that the reaction is me-

diated by a collision complex living for a fraction of a

rotational period. Under these conditions, it is possible

O C

90°

0°

180°

Fig. 67.5 Axonometric plot of [COH]

ﬂuxes in velocity

space in the reaction C

+ H

O → [COH]

+ Hat2.14 eV

(206.5kJ/mol). Data from [67.14]

Part E 67.3

Ion–Molecule Reactions 67.3 Scattering Cross Sections 989

to extract collision complex lifetimes from the angular

distributionasymmetry through the osculating model for

chemical reactions [67.20]. In this model, the lifetime is

a parametric function of the complex’s rotational period,

evidenced by the forward-backward asymmetry

I(180

◦

)/I(0

◦

) = 1/ cosh(τ

/2τ) . (67.15)

In this expression, τ is the lifetime of the complex and τ

is the rotational period, estimated from the moment of

inertia I and the maximum orbital angular momentum

max

of the complex. The total reaction cross section σ

can be used to estimate this latter quantity from

σ =



2µT

rel



max

+ 1)

. (67.16)

In the present case, the lifetime estimate for the

[CHOH]

complex is less than 1× 10

−13

s(Chapt.35).

At high energies, rebound collisions dominate

the dynamics of the C

+ H

O reaction. Another

limit often encountered in high energy ion-molecule

reactions is the stripping process in which the in-

coming ionic projectile removes a particle from its

molecular collision partner, and the new ionic prod-

uct travels in the same direction as the incident

ionic reactant. The spectator stripping limit [67.22]

for a reaction of the type A+ BC → AB + C cor-

responds to the case in which the cm speed of

product C is unchanged from the cm speed of

reactant BC,i.e.,C “spectates” as the reaction

occurs.

67.3.3 Total Cross Sections with

State-Selected Reactants

State-selected cross sections σ(n



|n, v

rel

) were ﬁrst

measured by Chupka and collaborators [67.23, 24]in

the endothermic reaction of H

+ He → HeH

H, with H

prepared in states v ≥ 2 by photoioniza-

tion, and HeH

detected without product state analysis.

Thus, n



represents a summation overallaccessible prod-

uct states in state-selected reactant experiments. At a

given vuv ionization wavelength, H

is prepared, sub-

ject to Franck-Condon factor limitations (Sect. 33.6.1),

in all possible vibrational states up to the maximum al-

lowed by the photon energy. Therefore, extraction of

cross sections for individual vibrational states requires

VUV wavelength dependent studies in which the num-

ber of reactant vibrational states is increased smoothly

from the ground state up to the limit allowed by in-

strumental resolution or photon sources. A number of

reactive and charge transfer systems have been studied

with photoionization techniques at the reactant state-

selected level with unresolved product states. Data are

typically in the form of P(v



) vs. v



, as a function of colli-

sion energy. A comprehensive review by Ng is available

[67.25].

67.3.4 Product–State Resolved Total Cross

Sections

The resolution of product states in cross section mea-

surements can be accomplished in a variety of ways.

We will ﬁrst discuss the case in which the reactants have

not been state-selected. In principle, spectroscopic meth-

ods such as laser-induced ﬂuorescence can be used for

complete product quantum state speciﬁcation. Earlier

reference to N

vibration-rotation state-resolved charge

transfer experiments [67.16] provides an excellent ex-

ample of the state of the art of such methods, and their

extension to chemical reactions represents an impor-

tant future development. A beautiful example is mass

spectrometric detection of N

in the Ar

+ N

charge

transfer system [67.21]. Guided ion-beam production

and detection methods [67.26] in conjunction with a su-

personic beam of N

allow 4π detection of the charge

transfer products as a function of collision energy, yield-

ing accurate total cross sections. The results, plotted in

Fig. 67.6, show thresholds for the production of excited

vibrational states of N

Sigma

, v



= 1, 2, and 4) as

well as the formation of the excited B

state. The

detection of chemiluminescence from electronically ex-

0.1 1 10 100

Cross section (arb. units)

Collision energy (eV)

v = 4)

v = 2)

)

v = 1)

D(N

–N)

Fig. 67.6 Energy dependent cross section for production

of N

in states as indicated in the Ar

+ N

charge

transfer system. After [67.21] by permission

Part E 67.3

990 Part E Scattering Experiment

cited states of ion-molecule reactions is also a powerful

method for determining such cross sections; methods

and results are reviewed in [67.27].

67.3.5 State-to-State Total Cross Sections

The most detailed probe of an ion-molecule reaction

is the state-to-state cross section. The measurement

of angularly-resolved state-to-state cross sections has

only been achieved for reactants in their ground states,

but true state-to-state total cross sections have now

been measured in a few favorable cases. A particu-

larly novel method for product-state determination with

reactant-state selection has been developed [67.25]. In

the differential reactivity method, product vibrational

states are distinguished by their differing cross sections

for charge transfer with selected molecules. Although

the method is limited at present because state-selected

charge transfer cross sections have been measured in

only a few systems, the technique has great potential.

The charge transfer reaction H

(v)+ H

→ H

+ H



),inwhichH

is prepared in v = 0and1byVUV

photoionization, provides a particularly good example

of its power. The H

charge transfer products, formed

in states v



= 0− 3, are ﬁrst mass-analyzed, accelerated

to 10 eV, and then passed through a collision cell con-

taining N

, Ar, or CO, where charge transfer occurs

once again. The N

,Ar

,orCO

products are mass

analyzed and the cross sections σ

for forming these

ions by charge transfer from the H

reaction products

are measured. The charge transfer cross sections for H

with these gases have different dependences on v



,as

01234

v⬘

Relative cross section (arb. units)

Fig. 67.7 Cross sections for charge transfer of H



) vs.



with N

, Ar, and CO at a collision energy of 10 eV. After

[67.25] by permission of John Wiley & Sons, Inc

shown in Fig. 67.7, and therefore, the gases can be used

to probe the product states of H

formed in the sym-

metric charge exchange reaction. Letting X



denote the

fraction of H

formed in the vibrational state v



, n de-

notethe number density of the neutral collision gas, and l

denote the attenuation length, the following set of simul-

taneous equations can be solved for X



, since thecross

sections σ



are known and the σ

are measured:

+ X

= 1 (67.17)

and, for a particular ion (e.g., N

,Ar

,CO

nlσ

+ X

nlσ

+ X

nlσ

+ X

nlσ

= nlσ

(67.18)

[An equation like (67.18) will exist for each collision

gas.] An extensive set of data at collision energies from

2 eV up to 16 eV has been obtained [67.29]. When the

reactant ions are in the vibrational ground state, at low

kinetic energies the charge transfer product is also in

the ground state, indicating that resonant charge transfer

is the dominant process. At increasing collision ener-

gies, X

increases from 0.0 to 0.17. For vibrationally

excited H

reactants, inelastic relaxation to form H



= 0 is important at all collision energies, increasing in

magnitude with increasing collision energy. Of particu-

lar interest is the fact that inelastic relaxation forming



= 0 is substantially more important than inelastic

excitation producing v



= 1 or 2. This trend is pre-

dicted by theory, but underestimated at lower collision

energies.

1 10 100 1000

Collision energy (meV)

Cross section (Å

)

Fig. 67.8 Total cross section for ND

formation in the N

+ D

system, showing a low energy threshold at 15 meV.

After [67.28] by permission

Part E 67.3

Ion–Molecule Reactions 67.4 New Directions: Complexity and Imaging 991

67.3.6 Energy Dependent Total Cross

Sections

Although non-state-selected cross sections, denoted

σ(v), lack information about product energy disposal,

important features of the potential energy surface can

be obtained from their measurement. Guided ion beam

methods have been especially important in the deter-

mination of accurate cross sections, particularly those

that employ a supersonic beam rather than a gas as a

neutral target. Energy-dependent cross sections provide

crucial information on ion and neutral thermochemistry

through accurate measurements of reaction thresholds,

and help to elucidate important potential surface fea-

tures such as thresholds, barriers, and crossings [67.30].

A particularly illustrative example of threshold forma-

tion concerns the reaction N

(

P) + H

→ NH

+ H

and its isotopic variants. This reaction is important at

low (< 0.1 eV) collision energies as the ﬁrst step in

the chain reaction that leads to formation of ammo-

nia in dense interstellar clouds, but the bond energy of

is uncertain enough to prevent knowing whether

the above reaction is endothermic or exothermic. Re-

cent total cross section measurements on the isotopic

variant N

(

P) + D

→ ND

+ D at very low col-

lision energies now appear to answer this question

[67.28]. Figure 67.8 shows experimental results per-

formed on two different instruments, one a guided

ion beam-crossed neutral beam machine and the other

a guided merged-beam apparatus. The data show a

very clear threshold at 15 meV, demonstrating that

the reaction is endothermic and allowing for a more

accurate estimate of the ND

bond energy. This

experiment shows that the high energy resolution af-

forded in total cross section measurements employing

crossed and merged beams, rather than thermal col-

lision cells, can answer thermochemical questions of

importance in a wide variety of applications, includ-

ing astrophysics, combustion, electrical discharges, and

atmospheric processes.

67.4 New Directions: Complexity and Imaging

The crossed beam technique provides the precise kine-

matic deﬁnition required to extract the most intimate

details of reactive collisions. Although the highest res-

olution examples of the technique involve systems

with three or four atoms, several recent examples of

systems of greater complexity have appeared in the

literature. The multiply-charged CF

+ D

system

[67.31] is appreciably more complex experimentally

than its singly-charged analog, owing to the possibility

of forming two charged fragments with correlated prod-

uct distributions. The nine-atom C

+ CH

system

has been studied previously with guided ion beam-

gas cell methods under conditions where the reactant

ions are produced by multiphoton ionization [67.32].

Those early experiments, which yielded total reaction

cross sections for vibrational state-selected ions, gave

signiﬁcant indications of mode-selectivity in complex

reactions. A more recent study [67.33], conducted with-

out reactant state-selection or product state analysis,

maps out product angular distributions and disposal of

energy in relative translation with ion trapping tech-

niques that measure longitudinal velocity components

directly and provide upper bounds on the transverse

velocity components.

The majority of extant crossed beam experimen-

tal studies construct three-dimensional velocity space

distributions with a series of one-dimensional sections

through the full distribution such that, in any interval of

time, only a single detection element in velocity space

can be measured. Recent advances in imaging methods

[67.34–36], in which many velocity space elements can

be observed in a single time interval, promise to increase

the sensitivity of the crossed beams method by orders

of magnitude. The signal gains that can be achieved

with the implementation of such multiplex advantage

methods will allow the lower reactant and product sig-

nal levels associated with increasing state-speciﬁcation

and/or system complexity to be tolerated without undue

increases in data acquisition times.

Figure 67.9 shows a schematic of an instrument that

illustrates the imaging principle.

As indicated in the diagram, the locus of points of

reaction products with a constant center of mass speed

is a sphere whose radius increases with time. Individ-

ual quantum states of a given reaction product form a

set of nested spheres in velocity space. Projecting this

set of product spheres onto a detection plane allows all

product velocity elements to be observed in a single

time window. Application of the inverse Abel trans-

form [67.37] allows the full three-dimensional velocity

distribution to be extracted from the two-dimensional

projection on the detection plane. Velocity focusing

methods [67.38] allow reaction products originating

from spatially distinct regions of the collision volume

Part E 67.4