3Π Levels and Predissociations of N2 near the 12.135eV Dissociation LimitP. K. Carroll and R. S. Mulliken Citation: J. Chem. Phys. 43, 2170 (1965); doi: 10.1063/1.1697107 View online: http://dx.doi.org/10.1063/1.1697107 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v43/i7 Published by the AIP Publishing LLC. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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2170 R. A. BEAUDET AND R. L. POYNTER

DIPOLE MOMENT

The molecular dipole moment was determined by observing the Stark effect of several J = 3f-2 transitions The only effect of the weak boron nuclear quadrupole moments was to produce a slight broadening of the low J transitions, an effect which rapidly decreased with increasing J, and was only barely noticeable for the J=3f-2 transitions. The quadrupole moments did not produce a noticeable effect on the Stark splittings. The linearity of the plots of .6,,, vs 82, for the Stark effect confirmed that the quadrupole coupling effect was negligible.

All measurements were made at dry-ice temperatures. The absorption cell was calibratedll with OCS immedi­ately before and after the Stark measurements were made on the carborane. No B or e dipole component was observed, thus the dipole moment appears to be

11 S. A. Marshall and J. Weber, Phys. Rev. 105, 1502 (1957).

THE JOURNAL OF CHEMICAL PHYSICS

directed along the A axis. These measurements are believed to be accurate to within ±3%. The results are given in Table VI.

DISCUSSION

This is the largest molecule for which a skeletal structure has been determined by microwave spectros­copy. While microwave spectroscopy has been used to study heavier molecules, very few structures have been determined for heavy molecules by this method. Pre­liminary approximate bond distances and angles which were determined by other methods were available to assist in the spectral analysis of those molecules. For dicarbaheptaborane, such preliminary information was not available, a fact which, while it caused considerable experimental trouble, provided a challenge to test the suitability of microwave spectroscopy for the study of relatively large unknown molecules.

VOLUME 43, NUMBER 7 1 OCTOBER 1965

an Levels and Pre dissociations of N 2 near the 12.13S-eV Dissociation Limit* P. K. CARROLLt AND R. S. MULLIKEN

Laboratory of Molecular Structure and Spectra, Department of Physics, University of Chicago, Chicago, Illinois

(Received 3 June 1965)

The t~o predissociations in the second positive bands, C 311,,-+B 311., have been re-examined in the light of recent spectroscopic studies of the N. spectrum. It is concluded that the predissociation of Biitten­bender and Herzberg is due to a oIl" state and not to a 311" state as formerly believed. However, a few details of the predissociation are not yet clearly explained. The second, less well-known predissociation of Hori and Endo is interpreted as being in all probability due to the C' 31I" state (the upper state of the Goldstein­Kaplan bands). This explanation requires that the C' state have a maximum in its potential curve at an internuclear distance of about 2.0 A. The behavior of the C and C' potential curves, which should apparently intersect at about 1.4 A, is interpreted as a noncrossing rule interaction. The vibrational structure in the region of the interaction is discussed and in particular the level reported by Pannetier et al. and that re­ported by Tanaka and Jursa are attributed to a mixture of v=5 of C and v=l of"C'. The level formerly tentatively assigned to v= 1 of C' is now considered to.be primarily v=2 of the same state. Some low­temperature afterglow mechanisms are discussed in terms of the new.interpretations of the C and C' states. The OIl" and 311" states which are to be expected in the energy range of interest are discussed theoretically by the application of both the molecular orbital and the Heitler-London methods and the conclusions are found to be consistent with the present interpretation of the experimental results.

INTRODUCTION

THE well-known predissociation in the e 3Il" state of N2 was examined in detail some years ago by

Blittenbender and Herzberg,! and their analysis forms the basis for the currently accepted value of the dis-

* This work was assisted by the Office of Aerospace Research, USAF through Electronic Systems Division, U. S. Air Force Systems Command under Contract AF19(628)-2474, and by the Office of Naval Research, Physics Branch, under Contract Nonr-2121 (01).

t Present Address: U. S. Air Force Cambridge Research Labora­tories, Laurence G. Hanscom Field, Bedford, Masschusetts.

1 G. Biittenbender and G. Herzberg, Ann. Phys. 21, 577 (1935). Earlier descriptions of the predissociation were given by E. HultMn and G. Johannson, Z. Physik 26, 308 (1924) and D. Coster, F. Brons, and A. van der Ziel, ibid. 84, 304 (1933).

sociation energy of N2• Later Hori and End02 showed that this predissociation could be suppressed by in­creasing the pressure and found that under these cir­cumstances a second predissociation was observed at higher N values. Recently the fine structure of the Goldstein-Kaplan bands was analyzed by Carroll,3 and the identification of the upper state, e', as an" raises again the question of what interactions and processes are occurring in the N2 molecule in the region around 12 eV. In this paper an attempt is made to interpret both of the predissociations in the e 3Il" state in the

2 T. Hori and T. Endo, Proc. Phys. Math. Soc. Japan 23. 834 (1941) •

3 P. K. Carroll, Proc. Roy. Soc. (London) A272, 270 (1963).

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an LEVELS AND PREDISSOCIATIONS OF N2 2171

light of the new data and to correlate the results with other experimental observations and with theoretical predictions.4

1. PREDISSOCIATION OF BUTTENBENDER AND HERZBERG

In the work of Blittenbender and Herzberg a com­plete breaking off in the rotational structure of the C 3ll .. state was observed in the four levels v= 1, 2, 3, and 4 at N=66, 56, 44, and 29, respectively. From these data a limiting curve of dissociation,6.6 which for comparison with some later results is reproduced in Fig. 1, showed conclusively that the state causing the predissociation was of moderate stability and went to the dissociation limit at 12.135 eV, i.e., the limit now identified as 4S+2D. It was shown by Schmid and Gero6 that at smaller r values also it is possible to estimate the trend of the predissociating potential curve within certain limits. (See also Coster, Van Dijk, and Lameris.7) Using this procedure and combining the result with those of Blittenbender and Herzberg for large r values, we derived the approximate form of the U(r) of the predissociating state. (See Fig. 2.) Clearly the predissociation falls into the category6 of Case b or, in the more precise nomenclature of Mulli­ken,S Case b+.

Now the predissociation had all the appearances of being very strong since a complete breaking off in the band structure was observed; furthermore, the pre­dissociating state had, apparently, a spin splitting greater than that in the C 3ll .. state. For these and for several other reasons Blittenbender and Herzberg con­cluded that the predissociating state was of Species sllu. However, there now seem to be three rather serious objections to this interpretation:

(1) As the C sll" state and the predissociating state are of the same species, one would expect a violent interaction near the crossing point of the two potential curves which would cause serious perturbations in the C state. A good example of such an interaction is found in the spectrum of NO.9 In this case, as the crossing point of the B 2II and C 2ll states is approached, large perturbations are observed in the {3 (B 2ll - X 2ll) and 5( C 2II - X 2II) systems, as a result of which bands are shifted from their predicted positions by as much

, Some of the results reported in this paper were made available to Dr. F. R. Gilmore and were used by him in preparing his very useful potential energy curves for N., 0., NO, and their ions. [Memorandum RM-4034-PR, 1964, The Rand Corporation, Santa Monica, California, and J. Quant. Spectry. Radiative Transfer 5,369 (1965).J

fi G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., New York, 1950).

• R. Schmid and L. Gera, Z. Physik 104, 725 (1937). 7 D. Coster, E. W. van Dijk, and A. T. Lameris, Physica 2,

267 (1935). 8 R. S. Mulliken, J. Chem. Phys. 33, 247 (1960). 9 A. Lagerqvist and E. Miescher, He)v. Phys. Acta 31, 221

(1958). For more recent work on this problem, see K. Dressler and E. Miescher, Astrophys. J. 141,1266 (1965).

110

t 105

·s +"D(97940± 40 em-') 95

2000 4000 6000 8000 10000

N(N~I)-

It- FIG. 1.l/Breaking-off points from the predissociations in the C allu state. (1) Lower curve: limiting curve of Biittenbender and Herzberg. The point A with the arrow indicates that as far as the branches can be followed in the v=O level (up to N'=90) no predissociation is observed. The reason is that the minima in the effective potential curves of the predissociating state disappear at higher N values and the breaking off is determined by the crossing point of the effective potential curves for the two states which now occurs at considerably smaller r, and at correspondingly higher energy values. (See Refs. 1, 6, and 7.) (2) Full straight line: limiting curve predicted from intersection of C and C' states at r = 1.38 A (believed relevant to the Hori and Endo predissocia­tions). (3) Broken lines: proposed form of actual limiting curve. The point B with the arrow indicates that as far as the rotational levels for v = 1 of the C state can be followed (N' = 99), no Hori­Endo predissociation is observed. A similar point exists at higher energy for the v = 0 level, but is not shown as it contributes nothing further to the analysis. For full interpretation see text.

as 200 cm-1 while the rotational structure becomes very complex due to the mixing of the C and B states. No such effects are observed in the C 3ll" state of N2 near v= 2 or 3 where the perturbation should be strong­est. However, a vibrational perturbation of a different form is indeed present. Thus the !:l.G and B values decrease and the D values increase nonlinearly and more rapidly than normally as v changes from 0 to 4. These effects are illustrated graphically in Figs. 3 and 4 and they are quite typical of what would be expected as the result of a perturbation by another state of the same species which lies somewhat above the v=4level. The perturbing state has recently been identified3 as C' 3llu , the upper state of the Goldstein-Kaplan bands. (See also Sec. 3.)

(2) The 3ll .. state postulated by Blittenbender and Herzberg should have properties intermediate between those of the C and C' states, both of which combine with B 3llg • One would therefore expect the transition from the predissociating 3ll .. state to B 3llg to occur. The resulting band system should lie in the visible and near ultraviolet, but despite the extensive experimental work on N2 in recent years, it has never been observed.

(3) Hori and End02 have investigated the second positive system in an arc source at pressures of 30 cm and upwards. They made the important discovery that the breaking off observed under normal conditions is suppressed, apparently entirely, at higher pressures. This suggests that the predissociation is not of the strongest kind which one would expect if it were of

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2172 P. K. CARROLL AND R. S. MULLIKEN

,-------"'---------------------- .-- ---

110

105

\/

/'\\ , ,

N=9g(V=I) .....

.....

/7:$, ....... -...... --... -.... -~-~-~~ .. ~~~~.) .. ! ~ N=67 (11=3) •••• ,.. '.

././ •.•.............. - ....... , .... ::--... .

FIG. 2. Potential energy curves for the C and C' states. The dotted curves show the effective potentials for the levels relevant to the dis· cussion of the predissociation of Hori and Endo. The shaded areas indicate the regions within which the onset of predissociation occurs for the v=2 and 3 levels. The dot­ted line across the N = 99 curve shows the energy up to which levels are observed in the v=1 level; there is no information about the behavior of the level above this point. The horizontal lines indicate the vibrational·energy levels dis· cussed in the text. For the C state up to '11=4, the potential curve was taken from the data of J. T. Van· derslice, E. A. Mason, and E. R. Lippincott, J. Chern. Phys. 30, 129 (1959). This curve was con­structed by the Rydberg-Klein­Rees method which uses the observed t1G and B values and which consequently takes into account the effect of the perturba­tion up to v=4. For the C' state in the region of v = 0 a Morse curve going to the limit 4S+2P was used. Also shown on the figure is an approximate curve for the state, now believed to be "IIu ,

responsible for the predissociation of Biittenbender and Herzberg. Energies are plotted relative to the '/I = 0 level of the ground state, X 11:.+.

i \ "'~ : . / ".

100 "'0

; " :':' : ' .. , / -----..., , '..... ! ~'H'AMADA ..............

)0(

'E --;----:- .... F=~~~~~*==:======~~TANAKA-JURSA ....

u '-..s--PANNETIER .t 01

w

95

90~ I I

1.0

\ ....•

1.5 2.0 o

r(A)-

the homogeneous type 3Il"--"73ll,,. Further support for this interpretation is given by the fact that Hori and Endo observed a complete breaking off in the rota­tional structure at higher N values which is presum­ably due to a second and considerably stronger pre­dissociation. (See below.)

For these reasons, it seems unlikely that the pre­dissociation in the C 3Il .. state is due to the 3Il .. state arising from 4S+2D. Of the states from this limit which might be responsible, we must now consider 32;,,+, 3.1", 62;,,+, 6Ilu , and 6.1". As both A components of the C state are affected, the 32; .. + state is at once eliminated. It is highly unlikely that 3.1 .. is responsible because according to Mulliken10 molecular orbital considerations indicate that this state should be strongly bound, hav­ing a dissociation energy of about 5 eV.

10 R. S. Mulliken, The Threshold of Space (Pergamon Press Inc., New York, 1957), p. 69.

2.5

Of the quintet states the only one which could meet the requirement of moderate stability is 6Il .. as accord­ing to Mulliken,to molecular orbital theory leads one to expect that the 52; .. + and 5.1" states should be purely repulsive. It is therefore proposed that the predissoci­ation in the second positive bands is due to the OIl .. state arising from the limit 4S+2D. That the spin changes in the predissociation, which formerly would therefore have been classed "forbidden", presents no difficulty because in recent years it has become appar­ent that in a molecule like N2, due to spin-orbit inter­action, intersystem predissociation can occurS with much higher probability than had previously been thought.

An interesting detail remains to be explained. In the special case of the v= 3 level of C 3Il .. , predissoci­ation starts at N = 43, but whereas the Fl component ( J = 44) is completely predissociated, the F2 compo-

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all LEVELS AND PREDISSOCIATIONS OF N2 2173

nent (J =43) is only partially predissociated while the Fa level (J=42) is apparently scarcely affected at all.ll Biittenbender and Herzberg attributed this effect to the spin splitting in the predissociating state being larger than that in the C 3IT" state. However, the rotational potential maximum in the predissociat­ing state, which determines the energy where breaking­off in the rotational structure will be observed, occurs at about 4.2 A for the v= 3 (N = 43) predissociation and one would expect the 3IT" state from'S+2D (and likewise the sIT" state from the same limit), to show only a very small spin splitting at this large inter­nuclear distance. Furthermore, the argument requires that either of the selection rules ~~=O (Case a) or ~N = 0 (Case b) applies. At N = 43 in the C 3IT" state, the separation of the Fl and the F3 components is about 6 cm-1, so that the coupling may be considered as intermediate between Case a and Case b. It is therefore unlikely that the selection rules appropriate to the pure coupling cases would apply with sufficient force to influence a strong predissociation. Instead one would expect the details of the process to be governed only by the rigorous selection rule ~J =0. However, we do not see how to explain the effect in terms of a sIT" predissociation either; but the existence of this difficulty seems clearly insufficient to override the very strong arguments against a 3IT" state, or the arguments in favor of a sIT" state as causing the predissociation.

t

em-I

2000

1900

..F;' 1800 + >

<.!)

<l

1700

1600L----L----~2~--~3----~4~---5~

v-

FIG. 3. The vibrational intervals ill the C au" state as a function of'll. The point P results from the assu~pt!on that the .level <?f Pannetier et al. is 11=5 of the estate. SlImlarly the pomt TIs obtained if one assumes that the level of Tanaka and Jursais '11=5. The dotted line shows the values of tiC calculated from the vibra­tional constants given in Ref. 5 (",,=2035.1 em-I, =.= 17.08 em-I, and y",.= -2.15 em-I). These valuesw.ere ?btained from t~e lower vibrational levels where the perturbabon IS apparently still effec­tive although to a lesser extent. It is uncertain therefore how closely the calculated values represent the intervals for the unperturbed levels and it is likely that the dotted line above curves downward rather too steeply.

11 It should be recalled that in the au state the components F I (J=N+1), F2 (J=N), ~d Fa(J=N-1) lie in the order FJ, F2, F3 with respect to increasmg energy.

1.60

'E o

;;f 1.75

1.70

o 2

v-3 4

1.2 .. 2

" 1.0 'E

0.8

0.6

o

> Cl

FIG. 4. The rotational constants Bv and Dv as a function of '/J for the C sII .. state.

2. PREDISSOCIATION OF RORI AND ENDO

As already mentioned, in studying the second posi­tive system at higher pressures, Hori and End02 found that the predissociation discussed above could be sup­pressed and the rotational structure developed in a normal way beyond the breaking-off points studied by Biittenbender and Herzberg. However, at higher ener­gies a second predissociation was observed. Thus a complete breaking off in the rotational structure at N = 80 and 67 occurred in the levels v= 2 and 3, respec­tively. The spectra published by Hori and Endo leave no doubt as to the genuineness of the effect. Due to overlapping, the level v=4 could not be studied while for v=O and 1, lines were observed up to P(112) and R(98), respectively. Again because of overlapping by other strong bands, the branches could not be followed further. To explain their results Hori and Endo assumed that the predissociation was due to a shallow potential curve which went to the limit at 12.135 eV via a poten­tial maximum.

In Fig. 1 the data of Hori and Endo are plotted in the usual way for studying a predissociation.s At first sight it might appear that a limiting curve could be drawn to correspond to Case b+, in which circumstances the curve would be convex towards the abscissa and would intersect the ordinate at right angles, like the curve for the Biittenbender-Herzberg case shown also in Fig. 1. This however, would lead to the conclusion that a dissociation limit existed at about 102 000 cm-I, which is impossible since the 'S+2D limit is at 97940 cm-I and the next limit, 4S+2P, is 9617 cm-1 higher at 107557 cm-I • In fact it does not seem possible to interpret the data shown in Fig. 1 directly in terms of any of the known cases of predissociation and one must therefore investigate how the observed effects might be understood from our present knowledge of the elec­tronic states of N2 in the relevant energy region.

With the new interpretation of Biittenbender and Herzberg'S predissociation, the noncrossing rule now requires that the C' state goes to the limit 'S+2D

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2174 P. K. CARROLL AND R. S. MULLIKEN

~\V t \ . \ ................. .

w \./

r-

B

Dissociation limit

N(N+I)-

FIG. 5. Predissociation curves for Case a+ (schematic). The U(r) curve of the predissociating state (see inset) is assumed to have no maximum at larger r values. AB: limiting curve when no penetration occurs; ACD: limiting curve when penetration occurs.

either directly or via a potential maximum. It there­fore follows that the C' state has all the properties necessary to produce a reasonably strong predissoci­ation in the C state, and indeed is the only state of the required energy which has these properties. (See Sec. 1.) If for the moment we confine our attention to smaller internuclear distances (r~ 1.6 A), inspection of Fig. 2 shows that the potential curves of the C and C' states for N = 0 should intersect at about r= 1.38 A, which we call rm. As the two states are of the same species however, an actual crossing will not take place; and if the interaction is very strong the two curves can be considered as joining together continuously over a po­tential maximum. If, on the other hand, the interaction is not so strong the effect would be to produce a rather large but essentially localized perturbation at some distance above which the two states regain their iden­tity. Initially, we inclined to the former view (d. Gilmore's paper) but for reasons which become ap­parent later we now believe the latter interpretation to be more correct.

The energy Em at which the "crossing" of the poten­tial curves occurs is about 98 200 cm-1 and as this is very close to the dissociation limit 4S+2D at 97 940±40 em-I, the predissociation, referred to this limit, would fall into Case a+. In this situation, if for the moment it is assumed that the C' state has no maximum at larger values and that it goes smoothly to the limit 4S+2D, the limiting curve should be a straight line of relatively steep slopeD and it can immediately be drawn from the rm and Em values given above. The limiting curve determined in this way is shown by the full straight line in Fig. 1. It is seen at once that the ob­served energies at which the actual predissociations for the different vibrational levels occur, lie below the values predicted from the calculated limiting curve. The logical explanation of this effect is that tunneling must be occurring through the intersection maxima near r= 1.4 A on the effective potential curves. (See Fig. 2). The probability for penetration in any given case can be estimated by determining the area en­closed by the ma:ximum and the energy at which the

breaking off of the rotational structure is observed. The values obtained are such that penetration of the barrier to the extent required by the experimental observations seems likely.

Now because of the similarity in the shape of the maxima, tunneling, at least for higher N values, should be effective, for different v values, over approximately the same range below the sharp maxima of the effec­tive curves. One would therefore expect the points where predissociation sets in to lie on a curve similar to that represented by the broken lines in Fig. 5. The sloping part should lie below the calculated limiting curve (full line, Fig. 5) by an approximately constant amount as shown, while the region AC represents the behavior at lower N values where the breaking off is controlled by the rounded rotational maxima at larger r values and where it is assumed that, because of the broadness of these maxima, no penetration occurs. Now the data of Hori and Endo are not exactly consistent with such a scheme, since a curve similar to that in Fig. 5 cannot be drawn through the observed breaking off points so as to pass through a known dissociation limit.

The most likely explanation seems to be that at larger r values a potential hump (maximum) exists on the C' curve whose effect first becomes noticeable at higher v, and hence smaller N, values. Now from Fig. 1 it can be noted that the predissociation in v=3 (N = 67) occurs at a higher energy than would be expected from that in v= 2 (N = 80). Between these two points therefore a changeover may occur from the case where the predissociation is determined by the inner sharp maximum, with some penetration, to that where it is controlled by the outer flat maximum, through which, because of its relatively larger width, penetration is substantially less so that it can be ne­glected for our present purposes.

The limiting curve for the outer maximum should also be straight or almost straight and its slope and intercept should give the position and magnitude, re­spectively, of the maximum on the U(r) curve. Un­fortunately, in the present case the data are insufficient to permit us to make a reliable extrapolation back to N=O. However, the dashed straight line shown in Fig. 1 extending to the left through the point marked v= 3, and from which subsequent calculations were made, represents a reasonable informed guess. (Its loca­tion was influenced to some extent by indirect infer­ences from other sources as to the likely shape of the C' curve: see following sections.) On the basis of the intercept of this line at N = 0, the outer maximum should lie at an internuclear distance of about 2.0 A and at an energy of about 99850 em-I. The potential curve for the C' state was therefore drawn in Fig. 2 so that it passes through a maximum at this point and then drops to the limit 4S+2D at larger inter­nuclear distances.

The resulting C' curve is of a form such as one ex­pects when a crossing between two states of the same

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an LEVELS AND PREDISSOCIATIONS OF N2 2175

species is avoided. One may suppose that, for increasing internuclear distance starting with its equilibrium dis­tance, the C' state curve tends toward some higher dissociation limit, here taken as 4S+2P, while the sec­ond state involved in the avoided crossing must be the one repulsive 3llu state predicted from 4S+2D (See below).

3. INTERPRETATION OF VIBRATIONAL STRUCTURE

The above interpretations of the predissociations in the C 3llu state, and the form inferred for the C' poten­tial curve, were essentially based only on the observed predissociation phenomena and on our knowledge of the electronic states of N2 in the energy region con­cerned. It is of interest now to consider if these results can be supported by, or used to explain, other related experimental observations.

Before discussing the vibrational structure of the C and C' states, which is the main topic of this section, a related observation is mentioned briefly. In the rota­tional analysis of the Goldstein-Kaplan bands3 it was found that in some branches a few lines were present at higher N values than would be observed if the C' potential curve went without a hump to the limit 4S+2D. In short, the expected pre dissociation by rota­tion was not observed, and indeed it was inferred from that evidence alone that a maximum must exist on the C' potential curve. This result is certainly in keep­ing with the form now suggested for the U(r) curve. (As already pointed out,a the 5llu state which causes the predissociation of Biittenbender and Herzberg is unlikely to affect the C' state strongly. This can be seen at once by inspection of Fig. 2 and by application of the Franck-Condon principle.)

To begin our discussion of the vibrational structure we shall first summarize the experimental data on levels, other than those already mentioned, which have been assigned to either the C or C' states. Three such levels have been reported:

(1) Pannetier et al.p in studying flame spectra with aliphatic amines in active nitrogen, observed, together with other structure, bands of the N2 second positive system. The 0-0 sequence was the most clearly defined and towards its short wavelength end an extra band with a head at 3259.2 A was observed. It was inter­preted as the 5-5 vibrational transition of the system on the ground that it lay in the position expected by a smooth extrapolation and that it had the general appearance of the other bands of the system.13 On this assignment the energy of the v= 5 level of C would be 98 224 cm-I, or about 280 cm-I above the dissociation limit at 4S+2D.

12 G. Pannetier, L. Marsigny, and H. Guenebaut, Compt. Rend. 252, 1753 (1961).

13 Hori and Endo (Ref. 2) did not observe higher vibrational levels (v>4) in the C state. The reason may well be that although the rotational temperature in their source was high, the vibra­tional temperature was low so that the intensity of the bands fell off very markedly in going from 11'=0 to 11'=4.

(2) While studying the spectra of nitrogen after­glows at pressures up to 10 cm of Hg at the tempera­ture of liquid nitrogen, Tanaka and Jursa14 observed, together with the second positive and the Goldstein­Kaplan bands and other nitrogen molecule features, a new progression of three bands ending on three vibra­tional levels of the B 3llo state. The bands were triple­headed and degraded to the red. Tanaka and Jursa, unaware of the work of Pannetier et al. which had appeared only a short time previously, also considered their new bands to be part of the v' = 5 progression of the second positive system. The upper level, whose energy as determined from the central heads of the bands is 98365 cm-I , is certainly not the same as that of Pannetier et al. and lies at about 420 cm-I above the limit 4S+2D.

(3) HamadaI5 also investigated the spectrum of afterglows at liquid-air temperatures and at relatively high pressures (up to several centimeters of mercury). His results were in a number of ways very similar to those of Tanaka and Jursa and apart from observing the v' = 0 progression of the Goldstein-Kaplan bands from 0-2 through 0-12 he also assigned two much weaker bands to the vibrational transitions 1-4 and 1-5. The existence of these bands was confirmed by Tanaka and Jursa who adopted the same vibrational assignments. However, as pointed out elsewhere,3 the resulting value of ~Ga), 1396 cm-I, as determined from the measurements of Tanaka and Jursa, yields a value of we~1420 cm-I, which is much too large for a state of the properties of C'. Thus from the rotational constants3 one gets we~651 cm-I while the isotope shift16 in the v= 0 level gives approximately we~850 cm-I • Some alternative interpretation of the level there­fore seems necessary and such an interpretation is given in subsequent paragraphs.

From the available data summarized above we can now suggest a reasonably coherent picture of the vibra­tional structure in the C and C' states. Thus in the region of the C state we have the five vibrational levels, v=O through 4, which are normally associated with the second positive bands, and as already pointed out, these show a vibrational-type perturbation which in­creases with increasing v. The trend of the ~G, B~, and D~ values as shown in Figs. 3 and 4 is just what would be expected if a perturbing state of the same species, but smaller B and We values, is being approached as the energy increases. In short the C state acquires some C' character.

Conversely the C' state should acquire some C char­acter. However, this cannot be demonstrated clearly from the limited data available as the expected trend of the unperturbed vibrational levels in the C' state cannot be determined and because rotational data are available only for the v=O level. There is, however,

14 Y. Tanaka and A. S. Jursa, J. Opt. Soc. Am. 51, 1239 (1961). 1~ H. Hamada, Phil. Mag. 23, 25 (1937). 16 D .• Mahon-Smith and P. K. Carroll, J. Chem. Phys. 41, 1377

(1964).

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2176 P. K. CARROLL AND R. S. MULLIKEN

good evidence that v= 0 of C' retains its identity in large measure and shows little contamination by C aIT". Thus the C' state has essentially pure Case b coupling3

whereas the C state is in Case a at lower N values. Again, isotopic workl6 on the Goldstein-Kaplan bands shows only a very small shift in their common upper level, a behavior expected for the v= 0 level of a sepa­rate state rather than that for a higher vibrational level of the C state. For this reason the level is shown in Fig. 2 as a full line in that part of the U(r) curve which corresponds to the C' state, although it is con­tinued as a broken line into the C region to show that it very probably has at least some small amount of C character. (It may be noted that if the molecule in this level spends part of its time at smaller r values, that is in the region of the C state, the B value for the level would need some reinterpretation and would yield a larger r value. There is no way of estimating the necessary correction, although the arguments just given suggests that it is very small.)

Next we consider the level of Pannetier et al. Here the experimental evidence is very limited and the iden­tification of the level must be treated with some re­serve. From the appearance of the band on the pub­lished reproduction of the low-resolution spectrogram it looks like a second positive band and it seems to degrade in the correct direction, i.e., toward shorter wavelengths. If the identification is accepted the posi­tion of the upper level as illustrated by the IlG curve in Fig. 3 is such that the perturbation present in aIT" for v= 0 through 4 has now reached a considerable magnitude. Furthermore, the energy of the level is very close to the "crossing point" of the C and C' potential curves and also lies near the expected posi­tion of the v= 1 level of the C' state. We therefore, propose that the level of Pannetier et al. is not a pure vibrational level but is mainly a mixture of v=5 of C and v= 1 of C', with the C character predominating, and for this reason it is represented by a full line ex­tending across the interacting C and C' potential curves.

At slightly higher energy we reach the Tanaka-Jursa level. Again this lies very close to the "crossing point" of the two potential curves and apparently must be interpreted as a mixture of the two states and not simply v= 5 of C aIT" as originally proposed by Tanaka and Jursa. Three observations make this quite evident: (1) the level is considerably displaced from the posi­tion where v=5 might reasonably be expected (See Fig. 3); (2) the bands in the progression to the B aITD

state are degraded to the red unlike the usual second positive bands and (3) the coupling constant of the level as determined by the head spacings is about 19 cm-1 which is only about half that of the other vibra­tionallevels of the C state. It would therefore, appear that the Tanaka-Jursa level, because of its intermedi­ate properties, should be considered as arising from a mixture of the C and C' states with the C' character predominating. In Fig. 2 therefore the level is shown .as a full line extending from the left-hand side of the

C curve to the right-hand side of the C' curve. On these interpretations we see that the mixing of the two states near v= 5 of C and v= 1 of C' generates two levels, both displaced from their unperturbed positions, which latter unfortunately cannot be predicted accu­rately from the available data. (See Fig. 3 for the C state.)

Finally, the Hamada level must be considered. We now suggest that this is in fact the v= 2 level of the C' state. On this interpretation the value of w. is about 710 cm-I, in reasonably good agreement with the val­ues determined from the rotational constants (~651 cm-1) and from the isotopic shifts (~850 cm-1) , espe­cially when the uncertainties in making these estimates are taken into account. Again the head separations in the bands from the Hamada level are approximately the same as those of the Goldstein-Kaplan (v=O) bands, and both groups degrade to longer wavelengths. The character of the level is therefore primarily that of the C' state, although it should be contaminated slightly by the C state. In this respect it is rather analo­gous to Vi = 0 of C' and v' = 4 of C, which although they presumably interact to some small extent, do not lose their fundamental character. We may therefore con­clude that the C' state regains its identity rather rapidly after the "crossing point" of the two curves is passed. Presumably the same is true of the C state, although in this case we have no observed higher vi­brationallevels to verify the effect. That higher levels of either Cor C' have not been reported can be attrib­uted to the fact that they would be very close to, or above, the potential maximum on our C' curve (Fig. 2) at r~2.0 A. Indeed, as previously noted, the height of this maximum can be determined only approximately and it may well be somewhat lower than shown in Fig. 2, and thus all difficulty created by the non­appearance of higher levels is removed.

To summarize, we may therefore characterize the various levels near the crossing point as being mixtures of the C and C' states in proportions for which we offer the following as very uncertain guesses:

v=4 of C: 95% C+5% C',

V=O of C' : 5% C+95% C',

Pannetier et at.: 70% C+30% C',

Tanaka-Jursa:

Hamada:

30% C+70% C',

5% C+95% C'.

The most detailed study of a noncrossing rule inter­action has been given by Lagerqvist and Miescher9 for the case of the B 2IT and C 2IT states of NO. Here it was possible to follow the vibrational and rotational structure right through the region of maximum inter­action to the stage where the states began to regain their identity. Our knowledge of the C and C' states of N2 at and above the region of interaction is by comparison very incomplete. Nevertheless, the inter­pretation given above is, at least qualitatively, analo-

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3ll LEVELS AND PREDISSOCIATIONS OF N2 2177

gous to that given by Lagerqvist and Miescher in the case of NO.

It should now he emphasized that the identification of higher levels of both the C and C' states gives very strong and independent support to the result deter­mined from our analysis of the predissociation of Hori and Endo, namely that at larger r values a maximum must exist on the C' potential curve. Without such a maximum the observation of these levels would be quite impossible. Furthermore, the highest level (v= 2 of C') provides the quantitative information that the maximum must lie at a height of at least 1000 cm-I

above the 4S+2D limit.

4. AFTERGLOW MECHANISMS

One can now make some reasonable speculations on the mechanisms by which, in certain types of after­glow, molecules are produced in levels near 12.1 eV. Spectral studies of afterglows strongly suggest that the loss of both ground-state (4S) and metastable (2D) nitrogen atoms due to wall processes is markedly reduced in cooled systems, thus leaving increased densi­ties of these species for reactions in the volume of the gas. Now the temperature in the discharge and after­glow region in the experiments of Tanaka and Jursa and of Hamada must be considerably higher than that at the walls and might conservatively be estimated as room temperature, 300oK, at which kT has the value 0.025 eV corresponding to about 200 cm-I • If now we consider collisions between a 4S and a 2D nitrogen atom and a third body (which will usually be a ground­state nitrogen molecule) sufficient kinetic energy will be available in many of these collisions to surmount the potential barrier at 2.0 A. Again the collision fre­quency should be quite high because of the relatively high pressures used in the experiments. If the third body, M, is responsible for stabilizing the nitrogen atoms into an N2 molecule in the triple collision, then the following processes can be expected:

or

~N2 (Tanaka-Jursa level) + M

(2) or

(3)

Such reactions, although probably to a lesser degree, could produce molecules in the v=O through 4 levels of the C state but scarcely to a sufficient extent to account for the high intensity of the second positive bands observed in the high-pressure low-temperature afterglows and it is therefore very likely that some other mechanism or mechanisms are also operative. [It must be remembered that the bands from the Hamada level, the Tanaka-Jursa level and, although to a lesser extent, the C' (v=O) level are much weaker

than the second positive bands.] However, the reac­tions given above explain in a satisfactory manner the distinctive features of high-pressure low-temperature afterglows which provide the only source so far known of the Tanaka-Jursa and the Hamada bands and in which the Goldstein-Kaplan bands (v'=O) appear with greater relative intensity than in other sources.

A closely related phenomenon has been observedI7 ,18

when the ordinary Lewis-Rayleigh afterglow, where the pressure is approximately one or two orders of magnitude less than in the afterglows just described, is studied at low temperature (the walls of the after­glow tube cooled with liquid nitrogen). In these cir­cumstances the second positive system, which ordi­narily is absent, appears but with a pronounced en­hancement of bands from the levels v=3 and more particularly v=4. This has been explained by the Her­mans17 and Tanaka et al. I8 as a recombination of nitrogen atoms so as to give selective excitation at v= 4 and 3. In particular the effect was explained by Tanaka et al. as an inverse predissociation into C aITu through the state postulated by Biittenbender and Herzberg. The inverse predissociation must now be considered to occur via the 5IT" state. Basically the in­terpretation of inverse predissociation seems extremely likely but the details of the process would appear to require some further explanation. In particular for a pure two-body inverse predissociation, only the rota­tional levels above the critical energy should be popu­lated. Thus in the present case rotational states should be populated only for N>28, N>43, N>55, andN>65 in the levels v=4, 3, 2, and 1, respectively. As the temperature was low in the experiments it is evident why the bands from the v= 4 level should be particularly enhanced. However, in the low-resolution spectrograms of Tanaka et al., these bands appear to have sharp heads in their usual positions, which would not be expected if the structure began at N = 28. It would therefore seem that some form of rotational-relaxation process, possibly due to low-energy collisions, may be occurring during or after the act of inverse predissoci­ation.

Note that the dominating mechanisms in the two types of low-temperature afterglow are quite different. At low pressures the important process must approxi­mate fairly closely to an inverse predissociation through the 5ITu state:

(4)

where the reaction should be considered as going from left to right. At higher pressures, the characteristic processes (1)-(3) do not involve the 5IT" state but describe three-body recombinations over the potential maximum of the C' aIT" state. Reaction (4) must still occur to a greater or lesser extent but because of the increased pressure it is likely to be modified by the

17 L. Herman and R. Herman, Nature 161, 1018 (1948). 18 Y. Tanaka, F. LeBlanc, and A. Jursa, J. Chern. Phys. 30,

1624 (1959).

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2178 P. K. CARROLL AND R. S. MULLIKEN

presence of a third body. If this is so, an additional mechanism is available which might populate the v=O through 4 levels of the C 31l,. state and which might therefore contribute to the high intensity of the second positive bands, which has been referred to above.

The experiments of Pannetier et al. involve more complicated systems than those found in the nitrogen afterglow discussed above and no attempt is made here to explain the observed spectra. Suffice it to say that if the excitation of the second positive bands, whatever it may be, occurs at smaller internuclear distances, the Pannetier et al. level, if approximately a 70-30 mixture of C and C' as suggested, would be favored in the excitation. In contrast the Tanaka-J ursa level, according to the mechanism proposed above, is populated by atoms recombining from larger inter­nuclear distances and hence if it is a 70-30 mixture of C' and C would be favored over the level of Pan­netier et al.

5. 6Ilu_6~g+ TRANSITION

Since the fillu state from 4S+2D and the 6~g+ state from 4S+4S both have minima in their potential curves (the fi~g+ only a very shallow one), the transition fill,,~6~g should, in principle at least, be observable. An examination of the curve for the fill" state given in Fig. 2 and that of the 5~q+ state proposed elsewhere19

suggests that the corresponding spectrum should lie in the region of the red or near infrared. Furthermore, application of the Franck-Condon principle suggests that the emission may, in part at least, be continuous. Because of the considerable uncertainty in the forms proposed for both curves, these estimates must be treated as being quite speCUlative. Failure to observe the transition in ordinary emission sources, where exci­tation is primarily due to electron impact, can readily be understood because to excite 61l" from the ground state, X l~g+, would require a double change in electron spin. Furthermore, even if such excitation did occur, application of the Franck-Condon principle suggests that only the higher vibrational levels of fill" close to the dissociation limit would be excited. The most likely source of the 51l,,~6~g+ transition would therefore ap­pear to be some form of afterglow such as those referred to in the present paper. It might also be noted that the fill,,~6~g + transition would compete against the process of inverse predissociation mentioned in the previous section. However, this does not make the interpreta­tion of the selective excitation of the v=4 level of C 31l" untenable because one would expect the prob­ability of an intersystem predissociation to be of about the same order of magnitude as that of an allowed radiative transition.

6. THEORETICAL CONSIDERATIONS ON ELECTRON CONFIGURATIONS

It is of interest to examine the electron configura­tions of N2 to see if theory can predict states of the

19 P. K. Carroll, J. Chern. Phys.37, 805 (1962).

properties, i.e., energy and species, required by the foregoing interpretation. The MO configurations which should be considered, and their states, include:

(I) * KK(20"g) 2(20",,) 2 (1'lT,,) 3 (30"g) (1'lTg)2, 1,1,1,3,3,3,3,61l,,; 1,3<1>",

(II) **

(III) ** KK (20"g) 2(20",,) 2( l'lT,J 2 (30"g) 2( 1'lT g) (30"u) 1,1,1,3,3,3,3,61l,,;

1,3<1>", (IV) ** KK (20"g) 2(20",,) 2( 1'lT,,) (30"g) 2( l'lTg) 2( 30",,), 1,1,1,3,3,3,3,61l,,;

1,3<1>,., (V) *** KK (20"g) 2(20",,) 2( 1?T,,) 2( 1?T g) 3 (30",,), 1,1,1,3,3,3,a,61l,.; 1,3<1>".

(VI) **** (The number of asterisks attached to the configuration numeral is the number of excited electrons.) Of the above configurations, (I) gives the well-known C 31l"

state. It is now important to establish the energy order and the properties of the states resulting from the other configurations. The excitation energies of various orbitals can be estimated at various r values from the potential curves of known states of known configurations.20 From such considerations it is found that the molecular orbitals in any configuration are in the order given above, and that Configurations (III) to (VI) lie sufficiently above (II) at r values in the range of interest to be eliminated from the discussion although probably to an appreciable extent some of their states should help by configuration interaction to stabilize the states of (II).

Let us therefore consider the states arising from 'lT~30"g'lT~2 in the configuration (II). The 'lTg2 group would gIve nse to states 3~g-, l;lg and l~g+. In O2 the a~­and l~g+ states lie, respectively, about 1.0 eV bel;w and 0.7 eV above the l;lg state, although the spacing may be somewhat closer in N2• The inclusion of the 0" g electron will leave the energies of the 1 ~ + and 1 A • 0 I..J.g

states essentIally unchanged and convert the states from singlets to doublets. The 3~g- state, on the other hand, splits into 2~g-, with an estimated increase in energy of about 1.0 eV, and 4~g-, with a decrease of about the same amount. The effect of now including the 3'lT" group can be estimated at about 1 eV on the

20 F~r eX<l;mple the 1,.-,,-:-1,.-u energy difference can be estimated at vanous mternuclear distances from the differences between the ground state, X '2:.+[KK(2uu)2(2uu)2(1,.-,,)'(3u )2J and the A '2:" +, a' '2:,,-, and w 'D." states which all have the ~onfiguration KK(20'u) 2 (20',,).2 (1,.-u) 3 (30'a) 2 (1,.-0)' (See Ref. 10.) The 1"-u-30'" en~rgy was.estl~ated from the O2 molecule where the 'II" state, which predlssoClates B 32:"- (the upper state of the Schumann­Runge bands),.has the configuration KK(20'u)2(2O',,)2(30'g)2(1,.-,,)' (1,.-0) (30',,) while the ground state, X 32:.-, arises from KK(20')2 (20',,) 2 (30'u) 2 (1,.-,,) 4 (1'11'0) 2. [See P. G. Wilkinson and R. S. Mullik.:n, Astro{lhys J. 125, 594 (1957) and P. K. Carroll ibid 129 794 (1959).J ' . ,

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311 LEVELS AND PREDISSOCIATIONS OF N2 2179

basis of the known separation of the a lIlo and B 3Ilo states of N2 and one now has an idea of the order of the electronic states arising from the complete con­figuration.

As a result of this procedure it is found that the lowest state of (II) should be an inverted 6Ilu state. One to a few electron volts above this there should be four 3Il" states, perhaps rather close together, two of them inverted and two regular, if each is built up from one of the 7ri states 3l;g-, lLlg and ll;g+ (two from 3l;g-). However, mixing among these 3Il" states of varied an­cestry is expected, and the simplest interpretation of the C' 3Il" state is that it is a mixture of two or more of these states in an appropriate proportion to give an almost pure Case b state as observed. If, as seems fairly certain from the discussion in the previous sec­tions, the predissociation of Blittenbender and Herz­berg is not due to a sIl" state, the C' state must go to the limit 4S+2D. Similarly the 5Il" state from Con­figuration (II) must go to the same limit and the above discussion indicates that it should lie somewhat below the lowest sIlu state. This is in good agreement with the position of the predissociating state as in­ferred from the experimental results of Blittenbender and Herzberg.

It should be noted that on this analysis the C and C' states differ strongly in electron configuration [see (I) and (II)]. This provides a plausible explanation of why the interaction of the two states can be inter­preted as a fairly localized perturbation as discussed in Secs. 2 and 3, rather than as a strongly avoided crossing.

At larger r values, molecular orbital configurations, such as (I)-(IV) no longer correspond to good ap­proximations for actual states and mixtures of these are needed. Alternatively, the Heitler-London ap­proach, which is valid as r-too, may be used. Apply­ing the Heitler-London method to the 3Il" and 5Ilu states from 4S+2D, one may start by assigning A and A values to the two atoms. Both states have the elec­tron configuration ls22s22p3 and it is sufficient to con­sider only the p group of electrons and the 2Il part of 2D. Thus 4S is 0"7r+7r-, 4l;-, while 2D II has to be a mixture of 0"27r, 2Il and r, 2Il. (Here 0" and 7r mean pO"

and p7r, of course). Applying the A conservation rule,21 one finds that 0"27r from 2D II, plus 4Sl;-, correlates with 7r" 20"0 27rgO"", 6,3,lII" (where the sIl" state is regular) while r, 2D II, plus 4S~, correlates with 7r" 30"g7rg2,

6,3,lIl" (where the sIlu state is the lowest expected and, as we have seen, inverted) or with 7ru 47rgO"", 3Il". Whereas from a direct consideration of MO's, the lowest energy 3Il" and 5Il" states would be attributed to the one con­figuration, the Heitler-London approach leads to an interpretation of the states in terms of a mixture of MO configurations. With respect to the 3Ilu state from 4S+2D atoms, the fact that the Heitler-London con­figuration corresponds at larger r values to a mixture including the higher MO configurations (III)-(VI) which contain one electron in the powerfully anti­bonding 30"" orbital, makes it plausible that the energy at first rises as the 4S and 2D atoms approach. At smaller r values, where the more bonding configura­tions, (I) and (II), should increase in importance, the energy can be expected to decrease again, thus yielding a maximum in the potential curve followed by a mini­mum at smaller r.

7. CONCLUSION

It is evident from the present work that the energy scheme and the processes occurring in N2 in the 12-eV region are very complex. It is realized that the inter­pretations presented here, while providing a reasonable and consistent explanation of the predissociations and the afterglow phenomena, may have to be modified to some extent in the light of further evidence. More in­formation on the levels of Tanaka and Jursa, Hamada, and, in particular, of Pannetier et al. would be very desirable. Again, the predissociation of Hori and Endo should be reinvestigated at the highest feasible resolu­tion to determine if possible the breaking-off points for other vibrational levels and to investigate such phenomena as line broadening and pressure dependence. The nature of the equilibrium existing in the different types of discharge, which could have a significant effect on the observed spectra, might also prove a profitable subject for study.

21 R. S. Mulliken, Phys. Rev. 32, 186 (1928).

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