Pressure effects on vacuum ultraviolet spectra

OF MOLECULAR

JOUHKAL

Pressure

Effects .\I. B.

Bell Telephone

33, 274-291

BPWTHOS(‘OPY

(1970)

on Vacuum KOBIX

Laborafclries,

AND

Ultraviolet

S.

Incorporated,

A.

Spectra

K~TEBLER

Murray

Hill,

Xew Jw.se!j 07.974

II was found that certain features in the vacuum ultraviolet spectra (2000 1300 .\) of many molecules are considerably modified in the presence of modest pressrlres (100-150 atm) of either nitrogen or helium perturber gas. Specifically, if a I ransition is a valence shell one, then t.he pressures employed here are far too low to cause any shift or broadening of the spectral featrlres, whereas at the same pressures, Kydberg t,ransitions respond by broadening completeI> asymmetrically to the high frequency side. The asymmetric broadening is thorlght to be dlle to the exchange repulsion esperienced by an absorber-pertrlrber pair when the absorber increases its effective diameter by several angstroms, as occlns in Rydberg excitations. Using this simple technique, variolbs bands ill the spectra of oxygen, benzene, ethylene, acetjone, and norhornadiene have beets classified as either valence shell or Rydherg. Pressurizing the ILydherg excitations of methyl iodide leads to the appearance of satellite bands displaced to the blue of the nnpertln+ed transitions. Similar effects arc observed in the analogous transitioll of the xenon atom.

Though

the effects of inert pressurizing

cules and atoms violet

regions,

On the other

have been studied

similar hand,

experiments the pressure

sorbers in the more accessible different

mechanisms

valve quantities

effects

a decrease

spectra

already

obtained

of mole-

and quartz

for just

measure

accompanied

nor calculate.

atomic

of the spectral

abn-it11

which iw

the pressure

line to either higher or lower values,

of the line, usually in the oscillator

by theories In general,

ult,r;k-

lacking.

regions are already very complicated,

vying for prominence,

:m as\-mmct’ric broadening

in the visible

below 2000 L&have been singularly

spectral

we can neither

c+fccts are a shift of frequency in some cases,

gases on the electronic

extensively

in the direction

strength.

In

of the shift,

addition,

:trld

one or more

satellite lines may appear to either the high or low frequency side of the original inc on increasing the pressure. However, examples cm be given of lines that shift to higher and then to lower frequencies with increasing pressure, lines that lshift’ to that low Fide, but broaden asymmetrically to the high frequency side, and lines that first broaden and then sharpen on increasing the pressure. Since studies ilI the past were concerned almost8 totally with the pressure broadening-pressure shifting mechanisms, they used :w tools, transitions in various atoms and molcc111t~ which \\-ere well-understood and unambiguously assigned. Our interest in prwsurr effects in the vacuum ultraviolet cent~ors not on the mechanisms, t,he

PRESSURE

EFFECTS

ON UV SPECTRA

275

quantitative theories of which will be even more complicated for polyatomic molecules, but rather on the possibility of using pressure effects in a phenomenological manner as an aid to the assignment of molecular spectra. In particular, the possibility of distinguishing valence shell and Rydberg spectral bands seems a good one. Another facet of our interest in pressure effects relates to the spectra of polyatomic molecules in rare gas matrices and in neat films. In these condensed phases, it has been found that valence shell excitations are relatively unperturbed, while the large orbit Rydberg excitations are quite often missing and only occasionally observed far from their gas-phase frequency (l-4). It was felt that compressed gas would offer an environment intermediate to those of the dilute gas and solid film phases, and could possibly clarify the spectral changes observed on going between the latter two environments. Because atomic transitions are so very sharp, relatively low pressures of perturbing gas (a few atm) and modest cell window thicknesses are sufficient for a study of pressure effects. For molecules, where the absorption lines in medium resolution are much broader, pressures of many thousand atmospheres are required, together with special cells having very thick quartz or sapphire windows (5). For vacuum ultraviolet work, where only salt windows offer any transmission, pressures of several thousand atmospheres would require prohibitively thick windows, which themselves would undoubtedly show only limited ultraviolet transmission due to their thickness. In view of this, it is fortunate indeed then, that the Rydberg excitations of polyatomic molecules are RO sensitive to even modest perturber pressures. Using a cell designed for only 300 atm pressure, but having transmission out to 1300 8, we find that 100 atm of either nitrogen

FIG. 1. Detail of the high pressure cell. The cell is pumped and filled through the ports (A) ; (B), the cell body, which carries the Teflon O-ring (C) ; (D), a GO” cone of LiF, 5.5 mm thick, polished flat to j$ wavelength of yellow light wit,h faces parallel to better t,hnn 0.01 mm. It is connected t,o window holder (F,) (410 stainless steel) with epoxy cement, while (F) is a copper washer held in place by ret,aining ring (G).

or helium perturbing gas is sufficient to profoundly affect the Rydberg band envelope, but is much too low a pressure to perturb the valence shell excitations in the same absorber. Thus the technique offers the opportunity to distinguish t~hcse two types of excitation under favorable conditions. EXPERIMENTAL

METHODS

The pressure cell used is :t commercial modc.1 (American Tnstrument (‘o., model 41-11341) ordinarily outfitted \yith l-in. thick fused quartz u-indoll-s. In our experiments, n-e replaced these window with the steel-LiY inserts shown in E‘ig. 1. From the mechanical strength of the window material, it was estimated that the ceil \vould be suitable up to about 300 :&,m pressure. Commer&,l p(‘rturbing g:Lses of ultrahigh purity were used straight from their cylinders, the pressures being read on a bourdon gauge. All absorbers were commercial matprials of research purity, and were subjected to either preparative gas-phase chrom:itography, or to several freeze-pump-thnw cycles prior to use. Our spectrometer is a lm normal incidence Alcl’herson instrument, operated with rare gas microjv:we discharge lamps and ancillary digitizing equipment for normalization of the 4ngle beam spectra by computer. DISCUSSION

The yuditatively different response of valence shell and Rydberg excitations to pressure must first be prefaced b>- a few \\-ords describing these types of electrouic states. In a valence shell trwsitiou , :m electron is transferred from a molecular orbital, which may be taken as a linear combination of :tppropriatc 11O’s, to B second molecular orbital composed of AO’s with the same principal quuntum number as forms the originating :\I(), but with different phases. A transition t,o an upper orbital composed of basis functions of hiqirer~ princil)aJ quantum number than any used in construction of the ground state, is a Rydberg transition. The utility of these definitions is restricted, AS ;\lulliken has s)w\\ Jl (Ci), because at a pxrticukw internuclear distance, a lower, seemingly. . lI>.dberg orbital can often be approximated tis a linear combination of Va]cJl~~~ sldl orbit:&. Thus the XWXIKydberg orbital of methane has the same symnlctry :md number of radial nodes as does the valence shell :\\I0 composed of the ‘-,s orbitnl on carbon taken out-of-phase with the 1s orbit& on the hydrogens. &TVever, in the case of the lsal orbital of methane, \\-hile the innermost part of the orbital might still be expressed in terms of valence shell AO’s, additional higllcr funct)ions must be added to these in order to attain the appropriate nodal properties. Qualitatively, ~\Iullikcn (6) expresses the radial part of the Rydberg \vave fuliction of a spherical system, R,,l , RS a sum of a core part and an expanded orbitid part:

PRESSURE

EFFECTS

277

ON UV SPECTRA

0.66

0.53 c BENZENE

0.40

0.27L

= 0.13 cn El D 1

0.00

2l I= 0.65 : BENZENE/l36

ATM

He

0.16

37.04

38.67

40.30 FREQUENCY,

41.93

43.57

45.20

cm-’ X IO3

FIG. 2. The electronic spectrum of benzene vapor upon the addition of 136 atm of helium gas (lower).

at a few mm pressure

(upper),

and

Each of the terms CY’~?’ represents a loop in the approximately sinusoidal variation of the radial part of the wave function. Suppose now that the Rydberg orbital is an ns function, and that there are Is, 2s, . . . ks occupied s-type orbitals in the core. The first sum of Eq. (1) is then to be taken so as to mime the ks valence shell core orbital, yielding a function having k loops and k - 1 nodal surfaces (7). In order to generate the complete orbital, the core function is augmented by additional loops [the second sum in Eq. (l)] which are the outermost n - k loops of the hydyogenic ‘ns function. The quantity 6 in the exponent of r in the second sum is the quantum defect of the familiar Rydberg equation,

ROBIN

AND

KUEBLER

0.72

0.36 OXYGEN

OXYGEN/l36

ATM

He

000 50.00

51.42

52.85 FREQUENCY,

Flu.

ddition

3. The electronic

54.27 Cd

55.70

5i

X IO3

spectrum of oxygen gas at a few mm pressnre of 136 atm of helium gas (lower).

(upper),

and ~lporl

and act:: here as :t phase shift. Thus, if a Rydberg orbital has occupied orbit& (real precursors) in the core, it will be a penetrating orbital with a large 6, having both core (valence shell) and beyond-the-core (Itydberg) character, whereas if there are no real precursors, the first sum in &I. (1) is nearly zero, as is 6, and the orbital is nonpenetrating and completely Rydberg in character. While there are complications introduced bot’h by the fact that t’he core functions for the molecules of interest are not closed shells, and that the core functions can be far from spherically symmetric for penetrating orbits, the rough qualitative features outlined above still seem to be valid (6). IIulliken also points out that the I* value at which the radial densit,v of the

PRESSURE

EFFECTS

ON UV SPECTRA

279

0.50 0.46

METHYL

0.35-

0.37

IODIDE

0.23-

0.25

0.12-

o.i2

NITROGEN

o.oorJ&

’

0.54 129 ATM NITROGEN

~ 0.43

47.6 ATM NITROGEN

0.32

NITROGEN

NITROGEN

4070

4985

5092

5190

5305

54.1 FREQUENCY

4870

49:86

5093

52.01

53.08

54 I

cm-’ x IO3

FIG. 4. The progressive broadening of the first Rydberg excitation of methyl iodide as t,he pressure of nitrogen gas is increased. One pressure of methyl iodide was used in the first two spectra, and a second higher pressure was used in the remaining four spectra.

?lth orbital is maximal is directly proportional to (n - 8)2, so that for those orbitals of the same ~2,the largest will have the smallest 6 value. These qualitative ideas will be of value to us in future work where we will discuss the importance of orbital size to the problems of pressure effects and line shapes. Pressure effects on the ]AI, + lBzu transition of benzene, commencing at 2589 A, have been studied by a large number of workers (8-10). Our results on this system are shown in Fig. 2, wherein the zero-pressure spectrum of benzene vapor is compared with that pressurized with 136 atm of helium. As already reported, helium at this pressure produces a miniscule blue shift, while nitrogen

ROBIN

FIG. 5. Response pressure.

AND

of the _V + B and _\-4

KUEBLER

n transitions

of ethylene

to increasing

nitrogen

gives

x slightly larger red shift. The band shapes in either ease look exactly as they do at zero pressure. Exactly similar results are obtained by pressurizing the ‘9,, -+ lBllL and lil,, 4 lEIU valence shell transitions of benzene. The Schumann-Runge (“2, + 35J bsdn dos 0 f oxygen, Fig. 3, offer another example of a valence shell transition which is completely unaffected by the low pressures of perturber gas used in our experiments.’ Figures 2 and 3 typify the exceedingly small solvent effects me have found for all valence shell excitations. Other examples of the unresponsiveness of valence shell transitions to our modest pressures arc pointed out below in the discussion of the spectra of particular molecule<. The reaction of Rydberg excitations to pressure is distinctly different from that8 of the valence shell excitations, us Evans has already pointed out (11). Figure -I illustrates the typical effect, the example being the 5p + 6s singlet to triplet R\,dberg excitation in methyl iodide. We see from this that as the per-

I Actually, in the low pressure oxygen spectrum a loral minimum in the Franck-Condon factors appears at V’ = 13 (56,000 cm-l), which is not, present in either the presslu%ed spectrltm (Figure 3) or the spectrum of oxygen in a nitrogen matrix [O. Schnepp and K. Ijressler, J. Chenj. Php. 42, 2482 (1965)]. Though band-width studies [P. G. Wilkinson and R. S. Mulliken, Asfrophys. J. 126, 594 (1957); P. K. Carroll, Aslrophys. J. 129, 794 (1959)] have demonstrated that the vibronic compouents V” = 0 + o’ = 4 - 13 are predissocinted, most likely through interaction with a repldsive Q, state, and that this might lead to intensity variations within the band envelope, it is not at all clear how pressure call affect this, unless the perturbing state is a Rydberg. A second possibility is that, V’ = 13 is a much sharper state, so that in our medium resolution spectrum the sharp lines are satllrated at low pressrlre, brat broaden and give the proper absorption intensity at higher Dressllre.

PRESSURE EFFECTS ON UV SPECTRA

251

FIG. 6. Hypothetical absorber-perturber potential energy curves for the absorber in its ground state, I; in a Rydberg excited state, II; and in a valence shell excited state, III. turber pressure is increased, the Rydberg

bands show a progressive asymmetric broadening to the high frequency side, whereas the low frequency side of the bands show no evidence of the perturbation. As with the lack of “pressure effects” consistently observed in valence shell transitions, this severely asymmetric broadening to higher frequency was consistently observed for Rydberg excitations in polyatomic molecules, and may be taken as a characteristic of this type of excitation. The ultraviolet spectrum of ethylene, Fig. 5, presents an example of the lack of response of a valence shell transition (‘A, + lBlu, in the 50 000 cm-l region), and the strongly asymmetric spread of the adjacent Rydberg excitation (T + 3s, ‘A, + lBa,, with (0, 0) at 57 300 cm-l) on applying a modest pressure of nitrogen. It is to be noticed that the frequency of the Rydberg absorption maximum suffers only a very slight shift on increasing the pressure, asymmetric broadening being the much larger effect. If the unperturbed vibronic lines of a Rydberg excitation are separated by no more than about 1500 cm-l, then the asymmetric pressure broadening to higher

1iOBIN AND KUEBLEIZ

2s2 frequency

nil1 result

manifcst Figs.

in a general

itself as an apparently

4, 5, and 7). Since

mnximal

intensity

Rydberg

wing

of the broadened

a five-channel

Intensities

dufont

limit set by the inherent less accurntely, Rydberg

spectral

developed

curve

of pressurizing

constant

perturbat#ion

states

is contained

sho\vs that

components

on increasing

the relative Though

theory” (IS),

pressure.

of hclium~

(16),

bro:dening in the ~votk.

and Hreenc

(1/j). In the

map be assumed

by ilbsorber-l,crburber

states of the absorber.

minimum

tributed

to long-range

to exchange chwgc

as shown in Iq‘ig. 6 The attractive

forces

distribut’ions.

essentially

dispersion

which become

For the ground

The

forces I\-ill be stronger electron

curve

the same as that

and the minimum

goes into a large Rydberg

increases

appreciably

shell

state,

upper

I, except

:I little deeper.

then the repulsive

than in the ground state,

kss

repulsion

is due

of the int,cr:wting

state,

III,

that

the

\viII IOOI~ &sINTSi(Jll

Ho\%-ever, if t,he optic:ll

orbit so that the effective

on excitation,

:tt much larger distances

upon the overlap

for a valence

for the ground

(4 the 01’

part of this pot,cnt,ial is :it,-

forces, whereas the short-range operative

to

potetl-

.+tnte of the two-body system, we can imagine a potential composed van der Waals attractive b/P and repulsive U/I”” terms, \vitll :1 nlOrP stable

of ;I

In general.

of pressure

and reviewed

the broadening

characterized

tin1 energy curves for each of the electronic

measured

intensit!.

by a given pressure

(14), Ch’en and Takeo process

inte!/~cc/

to I\-ithin the

the pressure of nitrogen. pressure broadening obwrved

irt the “statistical

theory,

dc-

compotwtlts

are preserved

the perturber

could be affected

of the statistical

of a tao-body

(see witll

such a transition

of the curve decomposition.

(12), and by .Jablonski

and Watson

exposition

bc the result

vertical,

into ske\ved Gaussian

analyzer

vibronic

ambiguity

by Margenau

of .\Iargennu simplest

quite

at the expense of the (0, 0) b:md. However,

tllc same effect was achieved with rough]!. T +,l,i The explanation for the severely asymmetric for Itydberg

factors

it also appears in all cases that the total integrated

band remains

whatever

are usually

effect

which can

of Frank-Condon

excitations

band envelope

of the individual

in this direction,

alteration

at (0, 0), the general

is to increase the (1, 0) intensity composition

shift of intensity

radical

size of the absorber

exchange

forces \viII set irl

curve II, ITig. 6. Constcluentl>

,

Rydberg transitions taking place from the configur:itional coordinate ;1 _-a fj \vill have t,hc unperturbed transition energy, while ~11 others, such as (’ 2 I), \vill necrss:trilg

appear

thawvertical

transition

on the higher rnezgy probability

thr details of the perturbed vesities

of the two potential

side of the d + 3 transit,iorl. T:king from all points of the lo\+-erpotential 3s eclu:tl,

band shape will then depend upon the relutivc> curves,

and the statistical

distribution

c(JII-

of :tbsorher-

perturber pairs along the internuclear coordinate, but in general will slro\\- an appreciable wing to the blue side of the unperturbed line. AR the Ijressure itIcreases, t’he pair distribution function grows in the region of smaller nbsorberpcrturber distances, in which region the pressure shift is most sensitive to ({istame. (2)nsequently, the blue wing broadens and accounts of the band profile BS the perkwber pressure is increased.

for more

:tnd

tnt)t’t’

PRESSURE

EFFECTS

F :

283

ON UV SPECTRA

ACETONE /I46 ATM NITROGEN

0.32

0.24

0.16

0.08

o.oc

I_

46.51

1

49.22

1

51.92 FREQUENCY,

FIG.

1

54.62 Cm-‘X

I

I

57.33

I

60.03

IO3

7. Pressure effect on the 51 000 cm-l band of acetone.

While the line shape problem has been solved analytically for the case where all atoms in the gas perturb the absorber via the attractive part of the van der Waals potential, the additional consideration of the repulsive part of the potential considerably complicates the matter. Robin, et al. (17) solved this problem for the Na/Ar system, but did not obtain an analytical solution for the band shape, or a very good fit to the data. In general, even for the simplest atom-atom systems, it has been difficult to get any meaningful quantitative agreement between ab z’nitio theory and experiment, or to extract any meaningful parameters from the observed broadening and shift. Though we have no hope of a quantitative explanation of the band shapes presented here, the experimental results do suggest an empirical relationship between pressure effect and band type which can be rationalized qualitatively using the skeleton of the statistical theory described

2s1

ROBIN

ANI)

KUEBLER

above. One might compare the utility of the vacuum ultraviolet pressure effects to the ‘w+ r* blue shift phenomenon (18) for which one also has only a qualitative picture for the blue shift mechanism, but which is nonetheless of everydn) utility in the description of molecular transitions. Specific Examples

We wish to list here several examples of the pressure effects to be found in vacuum ultraviolet spectra, and how they can be used in the determination of spectral assignments. _lcefone. The electronic spectra of formaldehyde and the various alkylated aldchyden and ketones are in close correspondence, showing a weak valence shell I/ -+ T* transition near 33 000 cm-’ and a much stronger band in the 51 OOO57 000 cnl-’ region. While this second band in both formaldehyde (19) and acetaldehyde (20) is assigned as an 11,+ 3s Rydberg excitation, various interpretations have been put forward for its assignment in the larger ketones, the most recent being the valence shell excitation II + g,*=o (21-23). La Paglia (LG‘), arguing by analogy, deduces that the 51 000 cm-’ band of acetone (Fig. 7, upper) instead has a 3s Rydberg upper state. Thus the later workers all agree that the second band of aldehydes and ketones can be assigned as 11+ c *, the difference being whether u* is a valence shell or a Rydberg orbital. Of course, following Ilulliken’s prescription, the 3s orbital of acetone has a real precurser in the core (L’s) and hence is penetrating and would be of mixed valence shell-Rydbwg character. The pressure effect on the 51 000 cm-l band of acetone, liig. 7, is shown to be that the characteristic of a big orbit upper state. HoLvever, since tll(: pressure effect is not extreme, and since this band of acetone appears readily irr condensed phase spectra (25), the upper state must have a significant amount, of valence shell character, just as ~\IulliBen predict s. Similarly, all of the sharl) absorption features in the 62 000-76 000 cm-’ region of the pressurized acetone spectrum are severely broadened t’o higher frequencies, as expected from tmllcil Rydberg nature. Norbort,acZiene. The near UV spectrum of norbornadiene,

PRESSURE

D

Ol7-

i

oo*l_j

EFFECTS

NORBORNADIENE/l36

i”

0 IO-

ooo., 42.63

C-J. 4427

NORBORNADIENE,

5

45.84

285

ON UV SPECTRA

j

47.4f

FREQUENCY

24-K

J

4899 cm-‘r

ATM He

50.56

1

IO3

FIG. 8. The first transition of norbornadiene vapor (upper); pressurized of helium gas (middle); as a polycrystalline film at 24°K (Iower).

with 130 atm

has recently been investigated (!Z%), and the claim was made that the lowest absorption band at 48 000 cm-l (see Fig. S) was possibly a = * U* Rydberg transition, rather than the N + VI valence shell excitation postulated by earlier workers. In a rare gas matrix or a neat film at low temperature, the well-defined 385 cm-l progression of the first norbornadiene transition disappears, and in its place, there appears a band showing a 1200 cm-l progression, Fig. 8. Though it was first thought that the two bands represented the same electronic transition with the altered vibrational frequency attributable to a vague frozen-matrix effect, the spectrum of norbornadiene pressurized with nitrogen gas shows that this interpretation is in error. As norbornadiene is pressurized, the spectral band decorated with the 385 en-’ progression becomes more and more indistinct as it broadens to the high frequency side, until at a helium pressure of 136 atm, there appears the outline of a second band with a characteristic vibrational spacing of 1200 cm-l. Our interpretation here is that the more prominent band with the 3S5 cm-’ spacing is an

286

ROBIN

AND KUEBLER

allowed Rydberg excitation which sits upon the valence shell N + VI band, and that the latter is apparent only when the molecule is sufficiently perturbed so as to completely broaden the Rydberg absorption (27) as is the case in a matrix or in a high pressure gas. The similarity of the band shapes of the 47 000 cm+ transition of norbornadiene in a matrix and in a high pressure gas is evident, once the spectra are shifted into coincidence as has been done in Fig. S. MefhyZ Iodide. Pressure effects on the methyl iodide spectrum are instructive for they not only demonstrate very clearly how the high frequency asymmetry of a Rydberg excitation develops on increasing the perturber pressure, but they also introduce us to the appearance of satellite bands in molecular spectra. The sharp band at 49 720 cm-l in the CHSI spectrum is the origin of the 5~ --j 6s RTdberg transition, the CHJ+ core having the 2E3/zsymbol; one quantum of v2 , the totally symmetric CH, deformation appears at 1100 cm-’ higher frequency (28). The spectra of Fig. 4 demonstrate first how totally asymmetric the pressure-induced broadening of a Rydberg transition can be. Regardless of the drastic broadening on the high frequency side of the line, the low frequency edge maintains its very sharp character up to the highest pressures. According to the explanation of the broadening discussed above, this implies that the two pertinent potential curves for CHJ/N, collisions are diverging for all accessible coordinates as the perturber approaches the absorber from infinity. As the nitrogen pressure is increased in the CHJ/N? system, a broad satellite band is seen to grow out of the high frequency asymmetry, until at 139 atm, it has almost completely eclipsed the parent band. The same effect of totally highfrequency broadening giving way to a high frequency satellite band is also apparent in the ~2’vibronic band of methyl iodide. Though hundreds of examples of such pressure-induced satellite bands are non- well known in atomic spectra (16 , 29), it is not at all clear as yet which or how many of the explanations advanced for them arc important. Some of the more practical suggestions are mentioned below. If the upper and lower potential curves in Fig. 6 are parallel for any range of I’, then all coordinates in the parallel region will give the same transition energy displacement, and a satellite band may result (30). Kielkopf and Gwinn (31) in their recent work have built their explanation upon this assumption, and were able to satisfactorily explain the magnitudes of the parent-satellite displacements. However, Klein and Margenau (32) claim that the parallel-curves argument will lead to only a shifted, asymmetric line, but no auxilliary maximum. Another factor of possible concern has to do with term splitting induced b! collisions. If a spherical system is degenerate, as is, for example, the l&p ‘P state of helium, then on the approach of a perturber atom, the degeneracy will be lifted partially, and there will result the two pseudomolecular states IS and ‘II, differing in whether or not the occupied 1~orbital has zero momentum along

PRESSURE

EFFECTS

ON UV SPECTRA

257

the absorber-perturber line. The separation of these states at small 1’ may conceivably lead to the appearance of satellite bands in the absorption spectrum. It should be noted that in a Rydberg transition, the upper state degeneracy may arise in two ways. In the first case, the optical electron is promoted to a degenerate set of orbitals, say 5s2 + 5s16p1,whereas in the second case, the excitation is to a nondegenerate orbital, but originates in a degenerate set, as for example 5p6 -+ 5~~6s’. The pressure-induced term splitting would be expected to be much smaller in the latter case, since the matrix elements over the perturbation will be much smaller for degeneracy in the core orbitals than for degeneracy in the Rydberg orbitals. The term-splitting argument was first used by Weizel (33) in a discussion of the emission spectrum of high pressure helium, and was later discussed in more detail by Kuhn and Oldenberg (S4) in regard to the spectra of mercury and thallium vapors pressurized with rare gases. Klein and Margenau (38) point out that the van der Waals potential wells may be deep enough to allow vibrational levels of the absorber-perturber complex, and in fact assign several low frequency satellite transitions as vibronic hot bands within atomic absorber-atomic perturber pairs. To us, the most attractive argument involves the ground state pair distribution function, g(1.1).It is usually assumed that Y(Q) is zero for r1 values up to the radius of the absorber and is uniformly equal to one at all distances beyond this. In fact, if there is a minimum in the potential curve at RI as everyone proposes, then g(yl) has a maximum value at this configuration (35). That is, we must imagine the g(rl) in a compressed gas to be somewhat like that of a liquid, in which there is a strong statistical preference for a neighbor at the van der Waals distance, RI . A statistical preference for the coordinate RI will give rise to a satellite absorption peak having an energy shift characteristic of the RI COordinate. Robinson and McCarty (38, S7) discussed the satellite structure in the spectrum of mercury atoms in an argon matrix, and found a definite correlation with the satellite spectrum observed for mercury in high pressure argon gas. They concluded that the clustering unavoidably present in the solid is also present in the high pressure gas. In fact, for pure argon gas at 43.8 atm and 149.3”K, this argon-argon clustering has been found from the radial distribution function using X-ray diffraction techniques (38). If clustering about RI is appreciable and there is term splitting as well, then several satellites may appear on one, or perhaps both sides of the unperturbed line. In an attempt to explain the red satellite bands observed in the spectra of alkali atoms pressurized with rare gases, Kielkopf and Gwinn (31) presented a simple theory which we can rephrase to suit our own purposes. Presume first that the upper and lower potential curves of interest are of the van der Waals

ROBIN

L’ss

AND

KUEBLER

type:

I\-hich becomes

I’(r) using B = AR6/2, mal. Sow particle parallel.

and Gwinn calculated

.1’

1 -

$1

13)

coordinate

the satellite

at which

C:(I.) is mini-

band energy at that inter-

at wllich the upper, U(r2), and lower, 7,:(~,), potential

We instead

:wumption,

[

whew R is the interparticle

liielkopf

distance

= -;

calculated

the satellite

In order to simplify and for t’lle excited

it where !/(I,~) is maximal,

band will be displaced

the calculation,

state

of methyl

from the unperturbed

we take the perturber iodide,

curves :w

i.e., at RI . Under this

parameters

line b)

as a helium

appropriate

:lt,om

for bhe cor-

responding excited state of the xe~lorl atom. The sum of the van der Waals radii of :tn iodine atom and a helium atom, both in their ground states, is RI = S.?S ,%, \\-bile Iiielkopf and Gwinn show that in the 51) --, 6s excited state of xenon, t,hc -3 ii, making R, = :i..iS 8 in the helium-iodine s>-stem. radius increases by ‘) l~‘inally, the force constant il is given by 2cuao”e2tL4, where a! is the static polarixxbility of the helium atom and //.‘? is the square of the hydrogenic effective clutntjlun

number.

obwrved

)C is set equal to Rjl’,

Rydberg

term value.

gives :L I/i!///. fqut~ccy J\‘llil(~ we observe tlie :qqwmcnt

satellite

of the appropriate

displaced

constant

values

from the unperturbed

:L shift of only :300 cm-l

is more than

line by 515 cnl-I.

to t,he blue in the CHJ/He

does demonstrate

that

the proposed observed

mechanism

in the CHJ/He

Srr/n,c. It is at this point th:tt \w are able to demonstrate

is capable

of the rotational infrared

spectra

band envelope

of the absorber,

of

system.

t,h:tt the asymmetrit

prwsure broadening of the mcth-J iodide spectrum is directly attributable absorber-perturber potential cncrgy effect, rather than a collision-inducctl pressure

system,

considering the strong dependenw of known values of RI and R, . Sonethrlcss,

giving sllifts of the sign and magnitude

fication

to thr

into t
satisfactory,

tllc c:~lcul:ttcd shift on the imprecisely tllcl c:dculution

the ratio of the Rydberg

Inwrtion

as is observed

t,o an modin high

(39). The 5pfi(1Lq) +

;ip”(“P$Jtis’ transition of xenon is tile atomic analog of the first Rydbcrg band origin in the methyl iodide molecule, bllt, of course, it does not have a rotational envelope. According to Moore (@), tllis transition in xenon has two components, at 67 OGS.0 and BS OG.0 cm-‘, only the second of which was observed in our spectra. Addition to senon of helium perturbrr gas at pressures up to 1X atm result,ed in the spectra displaycld in I’&. 9. It is clear from t8hew that’ even for atomic

absorbers

which have no rot,a-

PRESSURE

6711

67.72

68.32

68.92

EFFECTS

6952

70.10

ON UV SPECTRA

6711

6771

6831

6891

289

6951

7010

FREOUENCY. cm-‘X lo3

FIG. 9. Behavior of the 5p6 + 5p5 (zP~,~)6s1 transition of xenon on being pressurized with helium gas. A different pressure of xenon was used for each of t,he spectra.

tional envelope, the broadening is once again totally asymmetric, and that a satellite absorption appears at about 300 cm-’ higher frequency, with an intensity that increases with increasing perturber pressure, just as observed in the CHJ/He and CH,I/N2 systems. It is interesting to note that JIcLennan and Turnbull (41) observed this same xenon transition pressurized not with helium, but with more xenon, and found that the low frequency edge of the absorption band moved monotonically from 68 027 to 63 131 cm-i on increasing the pressure from 0.0013 to 50 atm. One sees in this that when the perturber is a helium atom, only repulsive forces are important for an excited xenon atom, whereas for a xenon perturber in the same situation, both excitonic resonance and chemical bonding effects can stabilize the upper state, thereby leading to absorption on the low frequency side of the free atom transition (4.2). In experiments in which much higher pressures of xenon absorber were used than in those of Fig. 9, a Zotcfrequency satellite displaced by 430 cm-l from the free atom absorption was also observed on pressurizing with helium. Baldini and Knox (4.5’)reported such a red satellite in the spectrum of 0.3 mole % xenon in an argon matrix at IO”!& and feel that it is probably due to Xen pair absorption. The matrix spectra however, do ,wot show either the high frequency satellite absorption or the high frequency broadening.

290

ROBIN

AND

KUEBLER

Relation to Condensed Phase Spectra Because we hope to discuss more fully the relationship between pressure arlcl condensed phase effects on Rydberg spectra in a future paper, we will touch upon it only briefly here. First, Rice and Jortner (44) demonstrated that collisions of the excited electron in a Rydberg orbital with surrounding perturhers will shorten the lifetime of that state, with a concomitant broadening of the absorption line. This mechanism, however, does not lead to an asymmetrically broadened line of the sort described herein, and so must be of secondary importance in our systems. Since KC interpret the asymmetry in the pressurized Rydberg spectra as due to the random distribution of perturbers about the absorber, in a condensed phase in which the absorber is surrounded in a regular way by the perturbers, one would expect the transition to be shifted to higher frecluency due to the exchange repulsion effect,” but to show only the symmetric lifetime broadening discussed above. In fact, these features characterize the first band of xenon atoms in an argon matrix (45). Similariy, the spectrum of 0.2% CH,I an argon matrix is shifted to higher frequency by 3200 cm-‘, but is still discrete with well-marked vibronic structure. One must admit, however, that even the most elementary appreciation of the relationships between the pressnrizcd and condensed phase spectra can be attained only after the collection of much more experimental data than is currently at hand. effects

RECKIVED: June 5, 19G9. KEFERISNCES 1. -J.-Y. RONCIN, J. illol. Spec.lry. 26, 105 (1968). 2. B. K.\Tz, M. BRITH, A. RON, B. SH.\RF, .\ND J. JOFLTXER,Chem. Phys. Letters 2, 189 (1968); also, B. K)ZTZ, M. BRITH, B. SH~~IKF, .\ND J. JORTNEX, to be published. 8. II. BUCH, M. B. ROBIN, .\ND N. A. KUE++LER, J. Chena. Phys. 49, 5007 (1968). 4. 13. Ka,rz AND J. JOXTNI,X, Chen~. Phys. Leffers 2, 437 (1968). 5. W. W. RoEI~RTS~~, in “ Technique of Inorganic Chemistry,” (H. B. JON.ISSICN.\ND 9. WCISSRERGP:R, eds.), Vol. 1, p. 157. Wiley (Interscience), New York, 1963. 0’. R. S. MULLIKEN, J. A??t. Chem. SOV. 86, 3183 (1964). 7. 3. C. sL.YrrsR, “@antllm Theor;- of Atomic Structure,” Vol. 1, p. 229. McGraw-Hill, New York, 1960. 8. S. I<;.B;\HB, JR., J. M. HORINSON, .\ND W. W. I~OBERTSON, J. Chem. Phys. 30,427 (1950). 9. IS. OI~SEXGORN, Cotnpf. Rend. 240, 2300 (1955). ICI. W. W. I?OISERTSON ANI) S. E. B.\HIs, JR., 6. Chem. Phys. 28, 753 (1958). Il. Il. F. I':v.\Ns, Proc. Ch.em.. Sot. 1963, 378. I.?. 1-I. Mli\~~~x;\~, Phys. Rev. 48, 755 (1935). 13. A. lJI\~~~~)~~~~, Phys. Rev. 68, 78 (1945). 14. TT. M.\RGEX~\U.IND W. W. W.\TSON, Rev. Mod. Phys. 8, 22 (1936). 15. S-Y. CFI’ISX .\NIl &I. T.~ixo, Ret’. nlod. Phys. 29, 20 (1957). _ p However, ET. Sun, S. A. Rice, and J. Jortner, J. Chem. Phys. 41,377Q (1964), calculate the “solvent shift” to be a delicate balance of several large competing terms, only one of which is the exchange rep~~lsion considered in our work.

PRESSURE

EFFECTS

ON UV SPECTRA

291

16. BREENE, R. G., JR., “The Shift and Shape of Spectral Lines,” p. 76. Pergamon Press, New York, 1961. 17. J. ROBIN, R. BERGEON, L. GALATRY, AND B. VO~AR, Discussions Faraday Sec. 22, 30 (1956). 18. H. MCCONNELL, J. Chem. Phys. 20, 700 (1952). 19. K. ALLISON AND A. D. WALSH, Chem. Inst. Canada Symp., Ottawa, Canada, 1957. 20. A. D. WALSH, Proc. Roy. Sot. (London), Ser. A 185, 176 (1946). 21. A. UDV~RHAZI AND M. A. EL-SAYED, J. Chem. Phys. 42, 3335 (1965). 22. W. C. JOHNSON, JR., AND W. T. SIMPSON, J. Chem. Phys. 48, 2168 (1968). 23. H. PRUGGER AND F. D~RR, Zeit. Elektrochem. 64, 425 (1960). .24. S. R. La PAGLIA, J. Mol. Spectry. 10, 240 (1963). 26. D. W. TURNER, “Determination of Organic Structures by Physical Methods.” (F. C. NACHOD AND W. D. PHILLIPS, eds.), Vol. 2, p. 339. Academic Press, New York, 1962. 26. 111. B. ROBIN AND N. A. KUEBLER, J. Chem. Phys. 44, 2664 (1966). 27. M. B. ROBIN, H. Basc~, N. A. KUEBLER, B. E. KAPLAN, AND J. MBINWALD, J. Chcm. Phys. 48, 5037 (1968). 28. G. HF,RZBF,RG, “Electronic Spectra of Polyatomic Molecules,” p. 528. Van Nostrand, Princeton, N. J., 1966. 29. S-Y. CH’EN AND R. A. WILSON, JR., Physica 27, 497 (1961). SO. W. M. PRESTON, Phys. Rev. 61, 298 (1937). 31. J. F. KIELKOPF AND J. A. GWINN, J. Chem. Phys. 48, 5570 (1968). 5.2. L. KLEIN AND H. MARGENAU, J. Chem. Phys. 30, 1556 (1959). $3. W. WEIZEL, Phys. Rev. 38, 642 (1931). 34. H. KUHN AND 0. OLDENBERG, Phys. &J. 41, 72 (1932). p. 209. McGraw-Hill, New York, 1956. ~35. T. L. HILL, “Statistical Mechanics,” 86. M. MCCARTY, JR. AND G. W. ROBINSON, Mol. Phys. 2, 415 (1959). 37. G. W. ROBINSON, Mol. Phys. 3, 301 (1960). S8. A. EISENSTEIN AND N. S. GINGRICH, Phys. Rev. 62, 261 (1942). 3.9. B. VODAR, Proc. Roy. Sot. (London), Ser. A 266, 44 (1960). 40. C. E. MOORE, Nat. BUT. Std. U. S., Circ. 467, 114 (1958). 41. J. C. MCLENNAN AND R. TURNBULL, Proc. Roy. Sot. (London), ser. A 129, 266 (1930). .@?. 0. SCHNEPP AND K. DR~SSLER, J. Chem. Phys. 33, 49 (1960). .@ G BALDINI AND R. S. KNOX, Phys. Rev. Letters 11, 127 (1963). ,#.& S. A. RICE AND J. JORTNER, J. Chem. Phys. 44, 4470 (1966).