VERIFICACIÓN Y ACCIONES CORRECTIVAS

The co n figu ra tio n o f electrons in a m o le cu le is d e p e n d e n t upon th e internal e n e rg y o f th e m olecule. The m o le cu le is most stable in its gro un d state w here the internal energy is smallest a n d th e electrons o c c u p y those orbitals closet to the nucleus. The interaction o f a p h oto n o r ele ctron m a y result in th e internal

Chapter One

th e g eneral form o f fhe p o fe n fioi energ y curves for w hich are shown in figure

1.2 1: E _{‘Repulsive ’ Surface} ‘Bound ’ Surface X + Y X + Y X + Y XY XY X Y

(b)

Figure 1.21 : Electronic excitation to bound and repulsive states of a molecule

If a transition occurs fo a state wifh a ‘repulsive’ po te n tial e n erg y curve, figure 1.21a, fhe m o le cu le will im m ed ia te ly dissociate wifh a release o f kinetic energy (KER) resulting in fh e form ation o f fw o neutral species, wifh e ith er or both in e x c ite d states.

For excitation to a b o un d state, if th e equilibrium b o nd lengths req are a p p ro xim a te ly the sam e (figure 1.21b) then there m a y b e g o o d o ve rla p b e tw e e n the m inim a o f the curves a n d the resulting e x cite d state m a y be stable for a short tim e (m etastable) b e fo re radiatively relaxing b a c k to the gro u n d state. H ow ever if req for the tw o e le ctro n ic states are significantly d iffe re nt then the p o te n tial energy wells for th e states no lon g e r o ve rla p an d the transition m a y o c c u r to a point on th e cu rve a b o v e th e dissociation energy.

De, for the m olecule, figure 1.21 c.

Transitions m a y o c c u r b e tw e e n vibrational levels o f the tw o states w hich, w hen associated with an e le c tro n ic transition, are known as ‘vibronic transitions’. If ro ta tio n a l cha ng e s are ignored then the energ y involved m a y b e w ritten:

^TOTAL ~ ^ELEC + ^VIB

zviB has a lre a d y b een d e fin e d in e q u a tio n 1.33. a n d so 1.35. is rewritten:

1.35)

^TOTAL =^ELEC+(y + yi)^e - Xe i^ + YlŸ^e ^=0, I, 2. ( 1.36)

with th e energ y o f a transition d e fin e d as:

Chapter One

V s p ec - (ggkc - K l e e ) + { ( ^ + Y ù ^ ' e ~ X ' e + X ) ^ ^ ' e) - {(v" + X X - + X ) ^ < }

1.37) If several transitions are observed spectro scop ica lly then it is possible to d e te rm in e th e values for m l an d x l as well as th e separation o f the e le c tro n ic states a nd e_'elecIu

A transition b e tw e e n tw o energ y levels m a y be represented by a vertical line on a p o te n tial energy d ia g ra m a c c o rd in g to th e Franck-Condon principle,

“ Because th e nuclei are so m uch m ore massive than th e electrons, on e le c tro n ic transition takes p la c e faster th a t the nuclei c a n respond" (Atkins 1990). Examples o f such transitions are shown in figure 1.22. The intensity o f a v ” ^ v ’ transition is given by the square o f th e o verlap integral o f v ” a n d v ’ a n d is known os the Franck-Condon Factor (FCF):

(1.38) w he re v ’ is th e vibrational energy level for the e xcite d state a n d v" for the g ro un d state o f the m olecule. If there is little or no c h a n g e in th e inter-nuclear separation, figure 1.22a, then only th e v ’^ 0 ^ v ’' ^ 0 transition will have significant intensity. E v ’=0 v ” = 0 r E ■=o v ” = 0 r feq E ■=o v ” = 0 r (i) ( ii) Continuum, (H i) 0,0 1,0 2,0 3,0 cm^ — 0,0 1,0 2,0 3,0 ... cm^ — cm

Chapter One

c. If the d iffe re n c e in inte rnu cle ar separation is slight as in figure 1.22b then vertica l transitions will o c c u r to higher (v ’ >0) vibrational levels in th e e xcite d state. In this e xa m ple th e transition the highest intensity will be v ” = ^ v ’ = 3,

with th e pro ba b ility o f transitions o ccu rrin g to levels a b o v e a n d b e lo w v ’ = 3 being lower, resulting in structure as in figure 1.22(ii). If th e separation is significantly d ifferent as in figure 1.22c then transitions o c c u r to high values of v ’ a n d also to a point a b o v e the dissociation level o f th e state. If this occurs then the resulting spectrum figure 1.22{iii) will co n ta in structure representing vibronic transitions a n d also a co ntinuum as th e species form e d via dissociation m ay ta ke an y a m o u n t o f kinetic energy a n d is no longer quantised.

A n o th e r m e th o d o f dissociation m a y o c c u r w hich does not require the excitation o f an e le ctron a b o v e th e dissociation level for a b o u n d state. If the p o te n tia l energy surfaces for tw o e le ctro n ic states intersect, as in figure 1.23, then a process known as predissociation m a y o ccu r.

E

’=0

From a lower electronic state

r

Figure 1.23 : Cross-over of two electronic states such that predissociation m ay occur.

A b o u n d surface with a m inim um is crossed, b e lo w its dissociation level, with a repulsive surface. Excitation to vibrational levels in th e b o u n d surface c a n o c c u r. H ow ever if excitation occurs to a vibrational level close to th e energy a t w hich the tw o surfaces intersect (e.g. v = i in figure 1.23), then a radiation less transfer m a y o c c u r to th e repulsive surface, causing the m o le cu le to dissociate. This transfer to th e repulsive surface is generally slower than vibrations within the m olecule, therefore vibrational transitions to those levels a w a y from the cross­ o v e r point are u n a ffe c te d a n d will a p p e a r as norm al in a spectrum . If, how ever, the transfer occurs faster than a vibrational transition then a co n tinu u m will be observed.

Chapter One

Unlike vibrational spectro scop y w here the transitions b e tw e e n vibrational levels are g o ve rn e d by th e selection rule Av=±7 , no such lim itation is im posed on vibro n ic transitions i.e. Av=0, ±1, ±2, ±3..., V ibrational coarse structure m ay be observed with high resolution to investigate th e spe ctro scop y o f m olecules, h o w e ve r with low resolution th e vibronic transitions a p p e a r as a b ro a d b a n d in a spectrum as the individual peaks m e rge to g e th e r. V ibronic transitions m a y either a p p e a r as a progression or a se q ue n ce o f transitions; figure 1.24. shows a com parison o f th e tw o types.

Progressions Sequences

v” =0

V =

v ” = l v'=3 Av= 0 A v = l

(a) (b)

Figure 1.24 : Vibrational Progressions and Sequences

A vibrational progression occurs w hen all transitions begin or e n d a t the sam e vibrational level, figure 1.24a, with the figure showing th re e vibrational progressions from th e v'=0 a n d the v'= 7 levels a n d from th e v ’ - 5 level o f the higher e le ctro n ic state; these transitions h a ve an increasing va lu e o f v. By com parison a se q ue n ce occurs w hen Av is th e som e for all transitions in the b a n d as shown in figure 1.24b.

1.4,3.1. Electronic selection ruies

There are several selection rules w hich govern th e a llo w e d transitions b e tw e e n e le c tro n ic states. The first, (1.39), implies th a t an e le c tro n ic transition m a y o c c u r b e tw e e n e le c tro n ic states having th e sam e axial c o m p o n e n t o f orbital a n g u la r m o m en tum or differing by o n e only:

Chapter One

AS-^0 (1.40)

a n d h e n ce transitions m a y only o c c u r b e tw e e n states w ith th e sam e spin m ultiplicity {2S+1) e.g. singlet singlet. The c h a n g e in to ta l spin a n g u la r m om en tum alo n g th e internuclear axis, S, is also g o vern e d by th e selection rule

A I = 0. A c o n s e q u e n c e o f these rules is to limit the c h a n g e in to ta l m om entum a lo n g th e inte rnu cle ar axis for fh e m o le cu le to:

AQ = 0 ,±I (1.41)

w here Q is th e sum o f the axial co m p o n e n ts o f e lectron spin a n d orbital a n gu la r m o m en ta:

Q = 11 + A I (1.42)

For e le ctro n ic transitions b e tw e e n states in h o m o n u c le a r d ia to m ic m olecule there are tw o further selection rules:

+ <-> + : + — : — <-> — ( 1.43) g < - > u ; g 4 > g ; u - i u (1.44) Selection rule (1.43) is relevant only for S ^ S transitions a n d requires th a t the sym m etry o f the w a v e fu n c tio n with respect to th e p la n e through th e nuclei is u n c h a n g e d . Rule (1.44) allows transitions to o c c u r such th a t the sym m etry o f the w a v e fu n c tio n is c h a n g e d from sym m etric to antisym m etric with respect to an inversion operation.