METO 637

Lesson 4

Electronically Excited Species

• Electronically excited species can be formed as the result of optical pumping, photo-fragmentation, and electron impact e.g.

N2 + e → N2* + e

• There are two ways in which the reactivity of a species can be influenced by its electronic state:

(1) The energetics of the reaction are altered

(2) The electronic structure.

Electronically Excited Species

• A reaction favors products only if ΔG for the reaction is positive.

• For example, the reaction

O(1P) + H2O → OH + OH is 70 kJ mol-1 endothermic, while the reaction

O(1D) + H2O → OH + OH is 120 kJ mol-1 exothermic because of the 190 kJ

mol-1 excitation energy of the O(1D)

Photodissociation

Adiabatic processes and the correlation rule

• Examine the potential curve for molecular oxygen.

• the B state correlates with O(1D) + O(3P) while the ground state X correlates with O(3P) + O(3P)

• Bringing an O(1D) atom together with an O(3P) cannot therefore produce an O2 molecule.

• An adiabatic reaction is one in which the reactants are connected on a single surface

• In the example above the reaction cannot be adiabatic, because of the selection rule that the total electronic spin must not change, ΔS=0

Spin Angular Momentum

• Correlation or conservation rules are formulated in terms of the angular momentum or symmetry properties.

• The spin angular momentum, S, is one of these• Consider a hypothetical reaction

A + BC → [ABC] → AB + C• The transient ABC must have a total spin SABC

produced either from SA and SBC, or from SAB and SC.

• Angular momenta sum vectorially, and for molecules are quantized.

Spin Angular Momentum

• Spins SA and SBC produce resultants

| SA + SBC |, | SA + SBC -1|,……….. | SA - SBC |

• Spins SAB and SC produce

| SAbB+ SC |, | SAB + SC -1|,……….. | SAB - SC |

• If the two lists do not have a value for S in common, an adiabatic reaction cannot occur.

• Note however, that if they do have an S in common then the reaction may occur.

• Consider the reactions

O(3P,1D) + O3(1A) → O2 + O2

Spin Angular Momentum

• For the O(3P) reaction the spins of the reactants are 1 and 0, which combine to give a total spin of 1.

• The ground state for molecular oxygen is a triplet (S=1), so the two molecules can combine to give total spins of 2,1,or 0.

• The reaction could therefore proceed on a triplet surface (S=1). Note that the reaction can occur for any two triplet states of molecular oxygen

• One triplet and one singlet product give S=1 also• Two singlet products can give only S=0

Spin Angular Momentum

• For the O(1D) reaction the only spin product is S=0. Hence the reaction must proceed on a singlet surface.

• The product oxygen molecules must both be singlets or both be triplets.

• All other reaction possibilities involve spin-forbidden crossings.

• Same rules also apply to photochemical processes

Spin Conservation and Photochemistry

• Consider the reaction

O3 + hν →[O3*] → O2 + O

• Ground-state ozone is a singlet state (S=0). The absorption in the ultraviolet is strong hence the transition is likely to be spin allowed.

• Transient state [O3*] must be a singlet also

• If we look at the products both must be in a singlet state, or both in a triplet state.

• In the O(1D) production process, the O2 must be in a singlet state (1Δg)

Potential Energy Surface

• We have already considered the potential energy diagram for a diatomic surface, which can be represented as a two dimensional surface.

• But for a polyatomic molecule we must consider a three dimensional potential energy surface.

• The next figure represents the potential energy surface for the reaction

A + BC → ABC* → AB + C

• The symbol * indicating that ABC has energy above that of the reactants A and BC, and therefore ABC* is unstable.

• ABC* will either drop back to A + BC or drop down to AB + C

Potential Energy Surface

Chemical Kinetics• A reaction

A + B → products

proceeds at a rate proportional to the concentrations raised to some power

][][][][

BAkdt

Bd

dt

AdRate

• k is the rate coefficient (rate constant). The powers and are the order of the reaction with respect to the reactants i.e.

A + B → products

• If for example then the reaction is called a second order reaction () .

Chemical Kinetics

• If the concentration of B is very much greater then A then [B] can be considered a constant.

• One can now combine [B] with k to form a first order reaction rate

][]}[][{][

12 AkABkdt

AdRate

• k1 is called a pseudo first order rate coefficient

Bimolecular reactions

• As two reactants approach each other closely enough, the energy of the reaction system rises ( see the previous figure).

• The contours of the surface show that there is a valley that provides the lowest energy approach of the reactants, the dotted line in the figure is that lowest path.

• There comes a point , marked ‘*’ beyond which the energy starts to decrease again, and so product formation is now energetically favorable.

• The next figure shows the energy of the ABC system as a function of distance traveled along the lowest path for an exothermic reaction.

Bimolecular reactions

Bimolecular reactions

• In the previous figure

reactionrC

fC

productsABCrC

tsreacABCfC

tsreacproductsreaction

HEEhence

HHE

HHE

HHH

*

tan*

tan

It is only possible to calculate the potential surfaces for the simplest systems. So how can we calculate the rates of the reactions. We adopt two simple approximations

Bimolecular reactions – collision theory

• Reactant molecules are assumed to be hard spheres of radii rA and rB.

• Reaction is possible it two conditions occur; a collision takes place, and the energy of collision along the line of site of the reactants must equal or exceed the energy EC. The rate of the reaction is given by:

T re temperatuat the molecules theofvelocity

relativemean theis c and section) cross (collision

collisionfor area sectional cross theis where

)/exp(

c

ccBCABCA RTEcnndt

dn

dt

dn

Bimolecular reactions – collision theory

)/exp(k

as written becan t coefficien rate The BC. andA

of ionsconcentrat theare and that note

where

8 )(

and

c

2/1

RTEc

nn

mm

mm

kTcrr

a

BCA

BCA

BCA

BCAc

Bimolecular reactions – collision theory

• Experimentally many second order reactions follow a temperature law, known as the Arrhenius expression

k = A exp(-Ea/RT)• One can identify Ea with Ec • Note that the mean relative velocity in the

collision theory is proportional to the square root of the temperature, while A is considered to be temperature independent.

• Over the limited range of most reaction rate measurements this is likely not to be a problem

Bimolecular reactions – collision theory

• For typical atmospheric reactants, with collision radii ~400 pm and relative molecular masses of 30, σcĉ is ~3 x 10-10 cm-3 molecule-1 sec-1 at 300K.

• The product of σ and č is known as the collision frequency.

• In general A is much less than the collision frequency.

• The principle explanation for the disagreement is that the reaction rate depends on the direction in which the molecules collide (steric effect).