SPECTRA OF DIATOMIC MOLECULES OF ELEMENTS O F THE FIFTH GROUP' G. M. ALhlY Department of Physics, University of Illinois, Urbana, Illinois Received October 8, 1936
Xlolecules formed by the union of two atoms in the same group of the periodic table should, to a first approximation, exhibit similar spectra. In each atom of the group the outermost shell of electrons is the same, except for the total quantum number, and the type of molecular binding and kind of molecular states depend largely upon these electrons. But, just as in the atomic spectra, the relative positions of the energy levels and the type of electronic coupling in the molecular spectra depend also upon the inner shells of electrons; therefore more or less gradual changes should occur in the spectra of a series of homologous molecules. The only thorough study of such a series is the one made by hlulliken (12) on the halogen molecules, in which he made use of the very extensive data on the rotational and vibrational structure of their spectra. Sufficient information concerning the spectra of the symmetrical diatomic molecules of the elements of the fifth group (nitrogen, phosphorus, arsenic, antimony, bismuth) has been accumulated to begin a correlation of the energy states and certain molecular constants of this group. It is the purpose of this paper to attempt such a correlation. I n the case of the ground states the continuity is clear. Even for the excited states the analogies run in most cases through all or a part of the group. In the case of the latter, however, many conclusions are tentative. Some states have no observed counterparts in other molecules. Except for N z and Pz,conclusions are based upon vibrational analysis alone. The rotational structure of the heavier molecules is exceedingly fine, though probably not beyond the range of the best grating spectrographs. The uncertainties in the correlations, as well as the question of the nature of the electronic coupling, could be largely settled by a rotational analysis of the various spectra. In table 1 are listed all of the known states of PZ, As*, Sbz, Biz, and the more important states of Ns. For each state is given the electronic energy, Presented a t the Symposium on Molecular Structure, held a t Princeton University, Princeton, N e v Jersey, December 31,1936 to January 2,1937, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society. 47
G. M. ALMT
48
l a
+a
9
w
s m
d II
+a
u
+a
w
E.
SPECTRA OF DIATOMIC MOLECULES
49
T , (measured from = 0 in the ground state to v' = 0), the equilibrium vibration frequency, w e , and the heat of dissociation, Do,all expressed in cm.? For the ground states a force constant, k , is also given, which is
FIG.1. Term schemes of the symmetrical diatomic molecules of the fifth group
twice the constant appearing in the approximate expression for the potential energy near equilibrium
U ( T )= T ,
+ -2k
(T-T,)'
where r e = the equilibrium distance between atoms and
where c = the velocity of light and p = the reduced mass of the molecule. Do is the depth of the potential energy curve with respect to the energy of the dissociated atoms, and k tells one something about its width. A relatively narrow, steeply rising curve has a large k . Corresponding states of the various molecules, as nearly as can be deter-
50
G. M. ALMS
mined a t present, are arranged in rows. At the left the states are giyen a letter (which seldom corresponds to previous designations of the same states) and at the right appear the most likely (certain in N z and Pz) molecular states and the best choice as to the atomic states of the products of dissociation. At the bottom of the table are given the observed transitions in the various molecules. The energy relations and the more prominent transitions are also represented in figure 1. In this diagram the energy of two normal 4Satoms is taken as the common zero for all the molecules. In figure 2 are plotted the values of D o ( X ) (heat of dissociation of ground state), k ( X ) , and r e ( X ) .
FIG.2. Constants of the ground states (X).D Ois the heat of dissociation; k is the force constant for small displacements about the equilibrium internuclear distance r.. The value of r e (1.95) for As2 is estimated from a partial rotational analysis.
In the discussion of the reasons for the arrangement and assignments in table 1 and figure 1 each molecule will be taken up in order. The sources of the data and a brief description of the spectra will be given. Some recent unpublished work on As2 and Sbz is included. Assignments of the states will be made as definite as possible, considering each molecule as an independent problem. I n several cases further limitations will be imposed by making use of the fact that a considerable continuity should run through the series of molecules. NITROGEX
The molecular spectrum of nitrogen has been the subject of numerous investigations ( 5 ) . The well-established relations among the various states
51
SPECTRA O F DIATOMIC MOLECULES
are shown in table 1 and figure 1. The heat of dissociation, long in doubt, has recently been fairly definitely fixed. Diverse evidence, including the position of recently discovered 32 --$ ‘2 (Vegard-Kaplan) bands (15, 6 ) , predissociation in the upper 311 state, Lozier’s electron-impact data (8), and the interpretation by hlulliken (11) of Hopfield’s Rydberg series of N 2 absorption bands, points consistently to Da(X) = 7.3 volts. The ground state of Nz certainly dissociates into two normal 4S atoms. Although it has been assumed that a similar situation exists in the heavier molecules of this group, K2 does not fit in smoothly, as to Do(X), r e ( X ) ,or k ( X ) (figure 2) with the succeeding molecules. But, as Herzberg (4) and Nulliken (10) have pointed out, N2 approaches the “united atom,” Si, much more closely than P2 or the heavier niolecules approach the corresponding united atoms. This discontinuity between KP and PP in the behavior of the group appears also in the nature of the excited states. PHOSPHORUS
The spectrum of PP consists of a single system extending a t the least from 2000 A.U. to 3300 A.C. I t has been thoroughly studied in emission by Herzberg (4))who gives references to other work, including investigations of the absorption spectrum. Through a rotational analysis, including a consideration of the alternating intensities, he concludes that the transition is 12: f-) l2:. 12: can come reasonably only from two 4 s atoms. The excited state comes almost certainly from 2 0 P P , as indicated by its Do obtained by extrapolation and by a consideration of possible states from available atomic pairs. Predissociation in the upper state enables Herzberg to fix D o ( X ) quite precisely, the most probable value being 40,593 cm.-’ To account for the predissociation and also for perturbations occurring in the upper state he assumes the existence of a shallow state arising from 4X 2 0 which, to satisfy the rigid selection rules for perturbations, must be 32: or 3nu. Either of these states violates the rule AX = 0, which is not rigid. This transition corresponds approximately to the strong lII + ‘2 system in N2. The unobserved, perturbing triplet state may correspond to the upper state of the Vegard-Kaplan N2 bands (32:). Besides this strong system Herzberg observed a few weak bands near 4200 A.U. which may be due to another electronic transition.
+
+
PN
AND
AsN
The emission spectra of P N (2) and Ash’ (14) consist of single ‘II + ‘2 systems, corresponding presumably to the similar transitions in Nz. The constants of the ground state of P N have been interpolated between those of P2 and N2 in figure 2.
52
G. &I. ALMT ARSENC
The absorption spectrum of hsz has been found by Gibson and RIacFarlane (3) to extend from 2200 L4.V.t o 2750 A.U. and to conqist largely of a single system (Dt X ) . Some bands of another transition ( E t X) were observed. The lower state was not extended beyond v" = 9. This work established the identity of the ground state. The emission spectrum (1) consists of five systems. Two prominent systems, D -+ X and E -+ X, extend from 2200 A.U. to 5800 A.U., overlapping one another almost completely. I n the published analysis the D --+ X system was extended to v" = 44, but the extrapolation to dissociation was so great that even with the use of prediqsociation in state D we could not choose conclusively among the various possible values of D o ( X ) corresponding to the assumptions made as to the atomic states near the predissociation level. Recent work by Iiinzer ( 7 ) , using an improved quartz discharge tube operating in a furnace at about 500°C ., has extended the system to bands with v" = 72. Do(X) obtained by extrapolation of the vibrational levels to convergence is approximately 31,000 cm.-I. Since the vibrational energy Go(X) is now observed to 24,574 cm.-l, only one value of D o ( X ) obtained from predissociation of state D can now be admitted, namely D o ( X ) = 31,900 cm.-l. This is obtained by assuming t h a t predissociation, observed at a total energy ( T e ( D ) Go(D)) of 42,700 cm.-', occurs into a state from ?D,10,800 cm.-' above 4S 4S. Other assumptions as t o the atomic states at predissociation give D o ( X ) equal to 42,700 em.-' (predissociation a t 4S 4S), or 24,200 cm.-l (4S "p), or smaller values, all of which are definitely excluded. Since the details (rotational structure) of predissociation have not been studied, D o ( X ) obtained by this method (31,900 cm.-l) is to be regarded as an upper limit. ]Ire will take 31,500 em.-' as the most probable value of D o ( X ) . It is probably correct within 3 per cent. The vibrational intervals of D and E are violently perturbed at low v', owing, it appears, to an interaction of the two. State D smooths out above the perturbations and is observed in absorption to V I = 17 (predissociation occurs at u' = 9). D o ( D ) obtained by extrapolation is roughly 19,000 cm.-', which makes *D 2P the most likely products of dissociation for, assuming this, D o ( D ) is 20,500 cm.-' Since D -+ X is the strongest system, D is probably lZ$ and D X corresponds to the only known PZsystem. State E does not extend beyond the region of perturbation, but appears to be converging more rapidly than state D. It is assumed t o dissociate into the next lower pair2,2D 2D,in
+
+
+
+
+
+
--+
+
2 Since this system has not been extended beyond v' = 8 it is probable that predissociation occurs in E as yell as in D. The break-off is not as definite. Our previous suggestion that dissociation by rotation occurs is probably incorrect, for the vibrational interval has dropped from 295 cm.-1 only to 210 cm.-' a t the level of 4s 2 0 , where this dissociation would occur.
+
SPECTRA O F DIATOMIC SIOI.ECl-LES
53
which case it is I I T U , or violating A S = 0, 3TI,, or 3r,. Photographh with large dispersion do not give sufficient resolution near the origin to permit> rotational analysis, but the more isolated bands appear to be of a simple two-branch type. This observation points to 38; which should give, with lS;f, only two strong branches, but this conclusion is not definitely &ablished. System C -+ X consists of a single progression extending from v ” = 21 to v” = 32, as determined by the best fit of the vibrational intervals. Assuming that it is the v’ = 0 progression of a distinct system, it arises from a state at T , = 42,003 em.-’, with r e considerably greater than r e of state X , probably shallow and dissociating into 4S 2D a t an energy of 42,700 em.-’ Thus it could account nicely for the predissociation of states D and E a t this level. Exactly such a state was assumed to exist, though not observed, by Herzberg in the case of Ps. It must be either 3Z$ or 311u to satisfy the Kronig selection rules (except A S = 0). Finally, two new systems, weaker than the three described, were obtained in the recent work on Asz. The details will be published elsewhere. One system ( B X) fits the equation,
+
--f
y
24643
=
+ I337.0 + i) - 0.83 (21’
(VI
4-$)’}
- I430.0 (d
+ 3) - 1.20 (v” + $)‘I
It consists of about thirty bands, distributed in a wide parabola, extending from v’ = 5 to V ” = 12. The upper state converges slowly; D o ( B ) w,2
--
4Xeme
-
30,000 cm.-’ (very rough ai’ld probably much too high).
+
Assuming the upper state to be from 4S 2D we find Do(B) = 17,800 ern.-’ On this assumption B must be 3TIu and C must be % ,: or vice versa. The second new system, probably due to Asz, extends from 5600 A.U. to 7000 A.U. The bands are degraded sharply to the violet (all other bands are degraded to the red). Upon analysis the bands are found t o occur in pairs, matched in intensity, with a constant interval of 162 cm.-l They can be represented by the equation:
The highest observed v‘ is 6; the highest v ” is 4. In each state the convergence is slow and w e large, indicating rather tightly bound states (2 to 3 volts). The rotational structure appears very dense and complex. I t is difficult to account for the apparent doublet structure, since neutral As2 should have only odd multiplicities. The spectrum is conceivably due to As:. KOattempt is made to fit it into the scheme of table 1.
54
G. M. ALMY
ASTIMONY
The absorption spectrum of Sbz was first studied by Naud6 (13), who used a quartz tube in a furnace at temperatures below 1100OC. H e found two systems: one in the range 2842 to 3315 A.U., one between 2200 and 2318 A.U. From the analysis of the former he finds the constants of the ground state and of an upper d a t e at 32,027 cm.-l (D in table 1). The spectrum extends only to v ” = 7, and a reliable extrapolation to dissociation cannot be made. Rough extrapolation gives Do(X) = 32,000 cm.-’ Since the values of D o ( X ) of Biz and As2 are known much more accurately, and since w e ( X ) and k ( X ) of Sbz fit in smoothly, it will be better in arranging the states of Sbz to interpolate a value of Do(X) for Sbz. This gives D o ( X ) = 22,700 cm.-’ (figure 2), which has been used in calculating D ofor the other states of Sbz. The upper state of this system shows perturbations in its vibrational structure. Although extended to v‘ = 17, there is no indication of convergence, AG varying erratically between 207 and 228 cm.-’ If we assume that this most prominent system corresponds to the similarly perturbed, strong systems of Pzand AS^, it is lZ: + ‘Z: with l2$ from 2D *P. I n this case Do(D) = 15,800 cin-l, a reasonable value in comparison with the corresponding states of As2 and Biz. The second system of Sbz(F X) could not be analyzed with the available data. The observed intervals and its appearance at lorn temperature show that it involves the ground state. H. A. Schultz has, in this laboratory, recently photographed the absorption and thermal emission spectrum of Sbz. He used a carbon-tube furnace in an atmosphere of nitrogen, which can be heated to 2100-2200°C. He obtained in absorption the two systems photographed by Naud6 and two new weaker systems in the visible spectrum. These appear in absorption when the temperature of the molten antimony is above 1300°C. Above 1700°C. both systems are strong in thermal emission. One system extends from 4500 to 6000 A.U., the other from 6000 to 7600 A.U. Both involve the ground state. They fit the equations:
+
+-
A
B
e4 X
: 14991
+ 217.2 (v’
X: 19069 + 216.8 (v’
+ 3)z + 3) - 0.65 ( v ” + $)* + 3) - 0.40 (v’ + $)z - 269.6 (v” + 3) - 0.563 (v” + 3)’ f
3) - 0.44 (v’
- 270.1 (v”
The constants of the upper states and the distribution of intensity in the two systems are surprisingly similar. Each extends to v’ = 10, v” = 10. The analysis is supported by the isotope effect. In accounting for A and B the available states from suitably low atomic pairs are 32: from 4 s 4X and 3n, and 32: from 4X 2D. I n combining
+
+
55
SPECTRA O F DIATOMIC MOLECULES
with X(lZ$’), these violate A S = 0, not improbable in Sb2. Two interpretations are suggested: (1) A is 32; from 4S “ , B is ”$ (or 3rIu)from 4S 2 D ,311, (or 32:) (repulsive) from 4S 2D is responsible for the perturbations observed in D , as assumed in PZand Aqz. Against this interpretation is the fact that it requires Do(A) to be only 7700 cm.-’, while b y a long extrapolation it is about 27,000 cm.-l (2) The LS coupling has become so large that Hund’s case c holds. In case c, either the atomic J values are maintained in the molecule or a J is formed of L and S for the molecule as a whole, and the projection (Q) of the J’s (or J ) on the axis characterizes the state, The designations ‘IT, 32,etc., lose meaning. Now in 2D of Sb the interval is 1342 cm.?’; in 2P it is 2069 crn.-l Thus the frequency differences associated with electronic motions are several times the vibration frequencies in Sbz, and case c is therefore a possibility. The states arising from a given pair of atomic J ’ s have been discussed by Xlulliken (9). 4S3/2 2D6/2,312 would give several 1, and 0; states capable of combining with X and perturbing D . On this interpretation the similarity of states Aand B would suggest that they might form a wide “doublet” 2D3/2, B from 4S3/2 4- 2D6/2. of two similar case c states, A from 4 S 3 / 2 In this case D o ( A )is 16,200; Da(B) remains 13,500. With the available information it is hardly worth while to discuss this possibility in detail. There is some evidence for a repulsive state near the perturbed state D. Although the absorption is very strong in this region, it is difficult to photograph the bands distinctly. NaudB also reports that the system is very sensitive to the temperature and pressure of the vapor. An overlying continuum (C X) could cause these difficulties.
+
+
+
+
+
BISMUTH
The absorption spectrum of Biz (16) consists principally of four systems of bands with discrete structure and a region (near 3100 A.U.) of strong continuous absorption. The four systems are: (1) A system in the visible extending from 4500 to 7900 A.U. ( B X). (2) A system between 2600 and 2900 A.U., in which the absorption is more intense than in the visible system but which could not be extended to high v in either state. The upper state is perturbed. The system is probably D + X and has its counterpart in every molecule of the group. (3) A far ultra-violet system ( < 2250 A.U.) corresponding in general appearance to the F X system of Sb2. (4) A violet system (4000 to 4200 A.U.), appearing only with dense rapor at temperatures greater than 1000°C., which is a transition between excited states, probably E t - B . The heat of dissociation D a ( X )is obtained most reliably from extrapolation of the upper state ( B ) of the visible system. The atomic states are so widely spaced and the extrapolation sufficiently short that there can be no question that B dissociates into 4S ‘D6/2,if, as assumed throughout, +-
+-
+
56
G . M. ALMT
X dissociates into 4S+ 4S.
This interpretation leads to D o ( X ) = 13,735 cm.-' In the bismuth atom the doubiet intervals (4019 cm.-* in 2 0 , 10,505 cm.-' in "p) are of the same order of magnitude as the molecular binding energies. It is therefore quite probable that case c obtains in the molecule and the term designations of table 1 have little meaning. The absence of state A , observed in Sbz, may well be due to the fact that it lies beyond 8000 A.U., the limit of t h e region photographed. The continuum near 3100 A.U. is due, presumably, to a repulsive state C arising from 4Sand one component of zD. It would thus correspond to the repulsive or shallow states perturbing state D in Pz, Asz, and Sbz. On the present assignment C lies below D in Biz and the perturbations in D must be ascribed to other states. REFERENCES (1) ALMY,G. bf., AND KrSzER, G. D.: Phys. Rev. 47, 721 (1935). J., HERZBERG, L., AXD HERZBEHG, G.: Z. Physik 86,348 (1933). (2) CURRY, (3) GIBSON,G. E., AND MACFARLANE, A , : Phys. Rev. 46, 1059 (1934). (4) HERZBERG, G.: Ann. Physik 151 16, 677 (1932). (5) HERZBERG, G . , AND SPONER, H.: Z. physik. Chem. 26B, 1 (1934). This article contains references to many papers on the spectrum of Nn, especially those bearing on the heat of dissociation of the ground state. (6) KAPLAN, J.: Phys. Rev. 44, 947 (1933). (7) KIXZER,G. D.: Thesis, University of Illinois, 1936. (8) LOZIER,W. W.: Phys. Rev. 44, 575 (1933); 46, 840 (1934). R. S.: Phys. Rev. 36, 1440 (1930). (9) MULLIKEN, (10) MULLIKEN, R. S.: Rev. hlodern Phys. 4, 15 (1932). (11) MULLIKEN, R. S.: Phys. Rev. 46, 144 (1934). (12) MULLIKEN, R. S.: Phye. Rev. 46, 549 (1934). (13) N A U D S. ~ , M . : Phys. Rev. 46, 820 (1934); South African Journal of Science 32, 103 (1935). (14) SPINKS,J . W. T.: Z. Physik 88, 511 (1934). (15) VEGARD, L . : Z. Physik 76, 30 (1932). (16) SPARKS, F. hI., A N D ALMY, G. M.: Phys. Rev. 44, 365 (1933).
