Energy Pooling by Triplet Nitrogen (A 3 Σ u + ) MoleculesD. H. Stedman and D. W. Setser Citation: The Journal of Chemical Physics 50, 2256 (1969); doi: 10.1063/1.1671359 View online: http://dx.doi.org/10.1063/1.1671359 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/50/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Energy transfer models in nitrogen plasmas: Analysis of N 2 ( X Σ g + 1 ) – N ( 4 S u ) – e − interaction J. Chem. Phys. 141, 184302 (2014); 10.1063/1.4900508 Studies of energy transfer processes in triplet states of N2. I. Energy pooling by vibrationally selected N2(A 3Σ+ u ,v) molecules J. Chem. Phys. 83, 3932 (1985); 10.1063/1.449105 Triplet–triplet energypooling processes in magnesium vapor J. Chem. Phys. 74, 2073 (1981); 10.1063/1.441254 Erratum: A Measurement of the Diffusion Coefficient and Radiative Lifetime of Nitrogen Molecules in theA 3Σ u + State J. Chem. Phys. 39, 3534 (1963); 10.1063/1.1734228 Measurement of the Diffusion Coefficient and Radiative Lifetime of Nitrogen Molecules in the A 3Σ u +State J. Chem. Phys. 38, 2034 (1963); 10.1063/1.1733921

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2256 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 50, 1969

Based on the heat of atomization of UC(s),

AHOat•298[UC(s)]=319±7 kcal/mole,

that was calculated from pertinent literature data, one obtains for the dimensionless parameterS

a=0.5AHOat.298[UC(S) ]/Do29S[UC(g)]

a value of 1.44.~With this a value and the known heats of atomization of the corresponding solid monocarbides the dissociation energies D029S of the diatomic carbides of some electropositive transition metals have been calculated. The values, in kilocalories per mole, are: ThC, 116; PuC, 89; CeC, 98; TiC, 113; ZrC, 126; HfC, 130; and VC, 111.

The recent determination of the dissociation energy of DO o( Ce2) = 41.8±6 kcal/mole9 also permits the test of the applicability of the Pauling method10 to the bond energy of CeC (g) . With a single· bond energy D(C-C) = 83.1 kcaljmole 10 and the electronegativities Xc= 2.5 and XCe= 1.2, one calculates by using the geometric mean methodlO a value of DOo(CeC) = 110 kcal/mole. In a similar calculation for DOo(UC), using an estimated value for DOO(U2)11~40 kcal/mole and an estimated electronegativity of 1.3 for tetravalent uranium,12 one obtains DOo(UC) = 101 kcal/mole. On the basis of the rather good agreement between calculated and experi­mental values for CeC and UC, both compounds may be described in terms of the Pauling model as having a sizable ionic contribution to their bonding. Accordingly one may explain the higher M-C2 bond energies of dicarbides13 and tetracarbides14 in terms of a further, additional ionic contribution to the bonding, that may be expressed by assignment of a Pauling electronega­tivity of approximately 3.3 to the C2 radical. The disso­ciation energies of the diatomic scandium-subgroup carbides which are predicted after the Pauling model are, in kilocalories per mole: SeC, 93; YC, 99; and LaC, 120.

The dissociation energies predicted by either method are estimated to be correct within 15 kcal/mole.

1 E. K. Storms, Thermodynamics (International Atomic Energy Agency, Vienna, 1966), Vol. 1, p. 309.

2 G. DeMaria, M. Guido, L. Malaspina, and P. Pesce, J. Chern. Phys. 43, 4449 (1965).

8 K. A. Gingerich, J. Chern. Phys. 49, 14 (1968). • J. B. Mann, J. Chern. Phys. 40,1632 (1964). 6 G. Balducci, A. Capalbi, G. DeMaria, and M. Guido, "Mass­

Spectrometric Study of Rare Earth-Carbon Systems," Wright­Patterson Air Force Base, Ohio, Tech. Rept. AFML-TR-67-335, October 1967.

6 R. C. Feber and C. C. Herrick, "Ideal Gas Thermodynamic Functions of Lanthanide and Actinide Elements," Los Alamos Scientific Laboratory, Los Alamos, N.M., LA-3184, 1965.

7 J. M. Leitnaker and T. G. Godfrey, J. Nucl. Mater. 21, 175 (1967) .

8 R. Colin and P. Goldfinger, in Condensation and Evaporation of Solids, E. Rutner, P. Goldfinger, and J. P. Hirth, Eds. (Gordon and Breach, Science Publishers, Inc., New York, 1964), p. 165.

9 K. A. Gingerich, Chern. Commun. 1969, 9. 10 L. Pauling, The Nature of the Chemical Bond (Cornell Uni­

versity Press, Ithaca, N.Y., 1960), 3rd ed., Chap. 3. 11 K. A. Gingerich and G. D. Blue, J. Chern. Phys. 47,5447

(1967).

12 W. Gordy and W. J. O. Thomas, J. Chern. Phys. 24, 439 (1956) .

13 W. A. Chupka, J. Berkowitz, C. F. Giese, and M. G. Inghram, J. Phys. Chern. 62, 611 (1958).

14 G. Balducci, A. Capalhi, G. DeMaria, and M. Guido, J. Chern. Phys. 43, 2136 (1965).

Energy Pooling by Triplet Nitrogen (A 82:,. +) Molecules

D. H. STEDMAN AND D. W. SETSER*

Chemistry Department, Kansas State University, Manhattan, Kansas 66502

(Received 13 December 1968)

Energy pooling by triplet aromatic hydrocarbon molecules by a process known as triplet-triplet annihila­tion gives delayed fluorescence in solid and liquid phases.1 Examples of energy pooling by long-lived, excited-electronic-state molecules in the gas phase is limited to singlet oxygen 02(IAg) studied particularly by Ogryzlo and co-workers.2-4 We report here the first conclusive evidence for gas-phase energy pooling by triplet molecules shown by the metastable nitrogen (A 32:u +) state and give an estimate of its rate constant.

Our discharge flow apparatus for producing N 2(A 32:u+) in the absence of other active species by the reaction Ar*(3 PO,2) + N2~N2*( C)~N2*(B) +hv-+ N2*(A 32:,.+) +hv has been described in previous papers.6 Refinement in observation techniques and further purification of the gases resulted not only in stronger N 2(A-X) Vegard-Kaplan band (V-K) emission, but also in the appearance of weak second positive (C-B) emission downstream of the mixing zone of Ar* and N2. That this was not scattered light from the intense Ar*+ N2 flame zone was shown by four separate experi­ments: (a) The addition of quenchers for N 2(A), such as S02, between the flame zone and the reaction results in the complete removal of both V-K and second

rN2 A(3r :,J" relative units

FIG. L The variation of second positive intensity with concen­tration of N2 (A 32:u +) at 298°K, Points shown are over a pressure range between 1 and 6 torr, without discernable pressure dependence.

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J. CHEM. PHYS., VOL. 50, 1969 LETTERS TO THE EDITOR 2257

positive emission, although leaving the Ar*+N2 flame unchanged; (b) the relative vibrational populations in the C state from the Ar*+N2 flame for v'=O, 1, 2, 3 are 100, 21, 5, 1.7, whereas the downstream second positive emission shows a much more excited population 100, 100, 66, ,.....,50; (c) The Ar*+N2 flame shows ex­treme rotational enhancement of the v' = 0 level, such that the (1, 2) and (2, 3) bands are overlapped by (0, 1) rotational emission.6 A comparison of band contours at low resolution showed that this rotational enhancement was definitely absent in the (C-B) emis­sion accompanying the N 2(A); (d) The use of xenon metastables6b for the generation of N 2 (A) eliminates the second positive flame zone emission, but maintains V-K and concurrent second positive emission identical to the argon system.

A kinetic study of the variation of second positive intensity (12+) with V-K intensity and pressure was undertaken. The intensity of V-K emission which is a measure of [N 2 (A) ] could be varied by adding chemical quenchers upstream of the observation region or alter­ing the hollow cathode discharge power. Pressure and V-K intensity could both be altered by closing a down­stream valve or by changing the total flows of added N2 and Ar. For these purposes the 2+ (0, 1) band was measured for various [N2(A)] using repeated mono­chromator scans. The V-K intensity was measured using the unblended (1, 9) band or using a Cs/Te cathode photomultiplier (H.T.V. R166) with a 2800± 50-A interference filter, which detects the (0, 7) V-K band. For all the methods of varying [N2(A)], a direct dependence of 12+ on (lV-K) 2 was found. Figure 1 shows a typical plot of 12+ against (lV_K)2. The points shown were taken at pressures ranging from 1 to 6 mm Hg and show no trend with pressure. This behavior is direct confirmation of triplet-triplet disproportionation energy pooling:

N2(A 81;,,+) + N2(A 31;,,+)~N2(X l1;g+) + N2 ( C 3II,,).

(1)

The energies are N 2(A)v' =0(6.2 eV)v' = 1 (6.4 eV) which are present in equal populations, and N2 ( C) v' = 0(11.0 eV)v' = 1(11.3 eV)v' = 2(11.5 eV)v' =3(11.7 eV). This reaction is orbital-angular-momentum forbidden in the case of a linear transition state.7 Bromer and Spieweck's observations of "about-equal-intensity" V-K and 2+ bands in their very pure discharge system may have been a consequence of Reaction (1), espe­cially since the vibrational populations in their 2+ bands are very similar to ours.

No other nitrogen emission could be detected in our system excluding, of course, V-K emission and that arising upstream from argon-metastable impact with N2, although a careful search for possible Kaplan IT

bands (E-A) or first positive bands (B-A) was under­taken. (It should be noted that B-A emission arising from C-B cascade would have been too weak for detection. )

The rate constant kl can be estimated from the total absolute intensities of the two emissions, 1v-Ko and 12+°. These intensities were obtained by calibration with a standardized quartz/iodine tungsten filament lamp and comparison with the known absolute intensity of the air afterglow (O+NO) emission.9 Using the best available estimate for the radiative lifetime T of N 2(A) of 10 sec,s Iv-Ko gives [N2(A)]. Since there IS no quenching of N2 ( C),

d[N2( C) ]/dt{ = kl [N2(A) ]2},

therefore kl = 12+° X (lV-KOT )-2. The value obtained from the slope of the line shown in Fig. 1 is 5Xl011 cc mole-l·secl. In view of the uncertainty in the present knowledge of the value for T, and the errors inherent in absolute intensity calibrations, this must be considered as an order-of-magnitude estimate. The rate constant for the disproportionation energy pooling of 02(1Ag )

was reported as 1.2X 106 cc mole-I. sec-I, which has since been confirmed.lO The low value may result from the fact that this reaction is spin forbidden.

Two other forms of energy pooling were discussed by Ogryzl05 for O2 singlet species. The first is radiative pooling in which a colliding pair combine to produce a single photon at approximately twice the energy. The other is termolecular pooling in which the excitation of two molecules is transferred to a third. In our system, radiative pooling would presumably give rise to a photon around 1400 A, for which our detection equip­ment is unsuitable. Termolecular pooling in which two N2(A) molecules excited a third N2 would be pressure dependent and can, therefore, be ruled out in our sys­tem. It should perhaps be noted that energy pooling by N2* and NO* leading to ionization of NO has been suggested.ll One possibility for N2* was N2(A 31;,,+); our results may be taken as tentative support for such a reaction.

We thank J. Meyer for helpful discussions. This work was supported by the National Air Pollution Control Administration, Consumer Protection and Environ­mental Health Service, Public Health Service, Grant AP-00391.

Note added in proof: We thank Shemansky for permission to quote his latest average value of the N 2(A) ratiative lifetime of 2.0 sec.12 Use of this value would give kl = 1.25 X 1013 cm3 mole-l·see-l.

* Alfred P. Sloan Foundation Fellow. 1 (a) C. A. Parker, Advan. Photochem. 2, 305 (1964). (b)

F. Wilkinson, Quart. Rev. (London) 20, 403 (1966). (c) A. B. Zahlan, S. Z. Weisz, R. C. Jarnagin, and M. Silver, J. Chern. Phys. 42, 4244 (1965).

2 R. J. Browne and E. A. Ogryzlo, Proc. Chern. Soc. 1964, 117. 3 S. J. Arnold and E. A. Ogryzlo, Can. J. Phys. 45, 2053 (1967). 4 E. A. Ogryzlo and A. E. Pearson, J. Phys. Chern. 72, 2913

(1968) . 6 (a) D. H. Stedman, J. A. Meyer, and D. W. Setser, J. Chern.

Phys. 48, 4320 (1968); (b) D. W. Setser and D. H. Stedman, "Chemical Applications of Metastable Argon Atoms. II. A Clean System for the Formation of N.(A 32:,,+)," Chern. Phys. Letters (to be published). (c) D. H. Stedman, J. A. Meyer, and D. W. Setser, J. Am. Chern. Soc. 90, 6856 (1968).

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2258 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 50, 1969

6 (a) E. S. Fishburne, J. Chern. Phys. 47, 58 (1967); (b) D. W. Setser and D. H. Stedman (unpublished data).

7 G. Herzberg, Electronic Spectra of Polyatomic Molecules (D. Van Nostrand Co., Inc., New York, 1966).

8 H. H. Brorner and F. Spieweck, Planetary Space Sci. 15, 689 (1967) .

9 A. Fontijn, C. B. Meyer, and H. 1. Schiff, J. Chern. Phys. 40, 64 (1964).

10 A. M. Falick and B. H. Mahan, J. Chern. Phys. 47, 4778 (1967) .

11 (a) A. Fontijn and P. H. Vree, J. Phys. Chern. 70, 2071 (1966); (b) A. Fontijn and R. Ellison, ibid. 72, 3701 (1968).

12 D. E. Shernansky and N. P. Carleton, J. Chern. Phys. (to be published) .

Notes

Calculation of the Principal Components of an Asymmetric g Tensor from

Paramagnetic Resonance Studies. Application to Cu(NH 3)4(SCN)2

D. E. BILLING AND B. J. HATHAWAY

Department of Chemistry, University of Essex Colchester, Essex, England

(Received 20 June 1968)

We have usedl the method of Geusic and Brown2 for the calculation of the principal g factors of copper(II) complexes from data on single crystals. The method involves measuring the effective g values (g.) at orien­tations provided by rotating the crystal successively about each of three arbitrary orthogonal axes (X, Y, Z). A Fourier, or a regression, analysis of the values of g.2 as a function of rotation angle yields the elements of the matrix [gi.rJ, which is then diagonalized.

The rotation angles are not arbitrary and must be defined by the convention of Geusic and Brown. The experimental technique may be simplified if slight mis­alignments (expressed as angles a." all, and a.) can be tolerated in mounting the crystal. This Note describes a correction for such misalignments.

The experiment is designed so that this correction for azimuthal errors is the only important one. For this purpose, a prominent crystal face is attached, in turn, to two mutually perpendicular faces ground on to a perspex rod. One face is parallel to the rod axis, and the field is rotated about this axis, the rod being located between cone bearings. The angles of rotation, in the measurements, are taken from an origin where the parallel face of the rod is approximately aligned to contain the field direction. The only important errors may be combined with the azimuthal corrections, if the two reorientations of the crystal (between measure-

ments) involve exactly 90° rotations. The orthogonality of the two rod faces guarantees this for one reorienta­tion, while the other may be accurately performed using a microscope.

The three rotations allow g=2, g1l1l2, and g.i to be determined twice, and if the angles a are zero, three equations are redundant. If the angles a are not zero, then the two sets of values of gii2 are no longer identical. The three, previously redundant, equations may then be used in the following manner to determine, and hence to correct for, the angles of misalignment.

The Eqs. (12)-(14) of Geusic and Brown become (introducing subscripts x, y, and z to refer to the rota­tions about X, Y, and Z, respectively, and replacing gill, gzi, and g7li by A"" B"" and Cr, respectively)

X",= g.2=A" cos2 (a,,+4>,,) +B" sin2(a:!+4>,,)

+2C", cos(a",+4>",) sin (a",+4>",) . (1)

A least-squares analysis of the dependence of X on 24> allows the determination of a, b, and c for each rotation. These Fourier parameters are defined as: a= A+B, b=!(A-B) cos2a+C sin2a, and c=C cos2a­HA-B) sin2a, from which, A=!a+bcos2a-csin2a, B=!a-b cos2a+c sin2a, andC=bsin2a+c cos2a. They must be obtained by solving the simultaneous equa­tions: P-!na-Qb-Rc=O, S-!Qa-Tb-Uc=O, and V -tRa-Ub-Wc=O, where P=~X, Q=~ cos24>, R=~ sin2q" S=~X cos24>, T=!n+!~ cos#, U= ! ~ sin#, V = ~X sin2q" and W =!n -! ~ cos#. Sum­mations are taken over the n measurements in each rotation.

On identifying the A's and B's with the gii2 elements in Eqs. (1) and rearranging, we have

g=2=BII =A.=!(a.+all -a",) ,

glli=A.,=B.=!(a",+a.-all ) ,

g .. 2=B",=A II =!(a",+ay -a.). (2)

Further, the gi.r elements are

gll.2 = Cx = [b",2+cx2_i( a.-au) 2]112,

gzi =CII = [b ll+ci-i(a",-a.)2]I/2,

g,i =C.= [b.2+c.2-l-(all -ax )2]I/2. (3)

Since C=c if a=O, the sign of c may be taken for that of C when a is small. The equations allow the angles a to be determined.

The usefulness of Eqs. (2) and (3) may be illus­trated by an example from our room-temperature meas­urements at 9150 GHz with a Varian V 4502-12 EPR spectrometer using a standard V-4S33 rotating cavity. The complex Cu(NHs)4(SCNh contains tetragonal CU(NHS)42+ species.s The crystal shows only one reso­nance line at all orientations. This is characterized by principal g factors of gl = 2.044, g2 = 2.056, and gs =

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