Experimental Determination of the Dipole Moments of the Degenerate States of Nh

EXPERIMENTAL DETERMINATION OF THE DIPOLE MOMENTS OF THE DEGENERATE STATES OF NH

T. A. R. IRWINAND F. W. DALBY Physics Department, University of British Columbia, Vancouver 8, B.C. Received June 2, 1965

ABSTRACT Light from the high-field region of a Lo Surdo discharge in ammonia was focused on the slit of a stigmatic spectrograph. Spectrograms of the 3 360 and 3 240 A bands of NH and the hydrogen line Hg were taken simultaneously. Froln observations of the molecular and atomic hydrogen Stark splittings and intensities the electric dipole moments of the degenerate states of NH were determined to be p(A 311) = (1.31 f 0.03), p(c lII) = (1.70 f 0.07), p (a 'A) = 1.49 f 0.06) Debye, where the signs of p(c 'II) and p(a 'A) are the same.

INTRODUCTION The electric dipole moment of a molecule is a physical quantity determined by the distribution of the electrons about the nuclei in the molecule. A kno~vl- edge of the dipole moments of a n~oleculemakes it possible to determine the electric dipole rotational transition probabilities. This information can be used to determine the concentrations of the molecules in stars, comets, etc., provided the appropriate rotational or microwave spectrum can be observed (see Weinreb et al. 1963 or Douglas and Elliot 1965). Until the present time, most of the work on the electric dipole nlonlents of molecules has been done by the techniques of capacitance ineasurements and microwave observations of the Stark effect (Townes and Schaxvlow 1955). These methods are limited to the ground states of quite stable n~olecules.

For personal use only. Since most of the n~olecules observed in extraterrestrial sources are free radicals and often in an excited state, n~easurementson the ground state of stable molecules are of little use to the astronomer. For this reason a study of the Stark effect on diatomic hydrides by optical methods was initiated. In an earlier paper (Phelps and Dalby 1965) the Stark effect on OH was presented. We present here the results of a sitnilar study on the NH nlolecule.

EXPERIMENTAL PROCEDURE The following is a brief rCsum6 of the experimental procedure. For a more detailed account see Phelps and Dalby (1965). In a Lo Surdo discharge most of the potential applied to the electrodes appears across the cathode dark space. Typical experimental parameters were: ammonia pressure between 0.2 and

Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 2 mm of Hg, applied voltage between 3.5 and 4.5 kilovolts, and aluminium cathodes between 0.5 and 1 mrn in diameter. The maximuin electric field strength achieved was 111 000 volts per cm. The light froill the discharge tube was focused on the slit of a stigmatic grating spectrograph giving spectrograms of the 3 360 and 3 240 A bands of NH in third order and the hydrogen line HBin second order. The resolving power in third order was about 100 000.

Canadian Journal of Physics. Volume -13 (October. 1965) 1766 IRWIN ASD DALBY: DIPOLE MOMENTS OF NH 1767 The electric field intensity n-as determined from the Stark splittings (corrected for second-order effects) of the Hg line (Condon and Shortley 1935).

THE 3 360 A BAND The 3 360 A% band, A 311 - X 3Z-, is the strongest and probably the best- knou-n band of NH. Accurate rotational and lambda doubling constants for these states are available from the arork of Dixon (1959). The spectrograms of this band showed Stark splittings for the lines RQD1(0)l P2(2), and ?QZ3(O).Reliable data could be taken only from the RQ21(0) line since the other two were partially overlapped. The RQ21(0) line is shown in Figs. 1 and 2. The Starlc splittings nleasured fro111 the undeviated component in ci~l-~are given in Table I. All Stark splittings are ineasured at the position of maximuill electric field.

+- INCREASING For personal use only. I.1. The Stark effect on the RQ?,(O) line of the 3 360 A band of NH. D,iscuss,ion The RQ21(0) line is the result of the transition 3111,J = 1 + 3Z-1 J = I. The theory of the Stark effect on n~olecules(Phelps and Dalby 1965; Herzberg 1950; Penny 1931) predicts that the 32-, J = 1 level is unaltered in first order and that the lanlbda doublet 3111,J = 1 is split according to the equation

In equation (I) Av is the energy change of the level in cm-'; A is the lambda doubling in cm-I; p is the electric dipole inonlent in volts-'; E is the electric field strength in volts per cm; and J, M, and Q are quantum numbers corres- Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 ponding to the total angular n~on~entum,the component of Jin the direction of the field, and the angular momentum along the internuclear axis respectively.* In Table I Av is the displacement to the left and AV + A is the displaceinent to the right. *Equations (1) and (3) differ only in the choice of origin of energy. In eq. (1) Ar is measured from the unperturbed upper lambda doublet. In eq. (3) Ar is measured from the midpoint of the unperturbed lambda doublets. CANADIAN JOIjRNAL OF PIIYSICS. VOL. 43, IS65

/ region of 1 maximum fiy I I

energy

FIG.2. Energy level diagram showing the Starli effect of the RQZI(0) line of the 3 360 A band of NH.

For personal use only. TABLE I Starlc splittings (cm-I) of the RQsl(0) line

Right Left Exposure component component Field strength number (Av + A) (Av) in kV per cm 2 1.25f0.02 0.63f0.04 112f2 20 1.1Sf0.04 0.54f0.05 94.8f2 18 0.972~0.04 - 68.73~1 19 top 0.87f0.04 - 47.6f 2 19bottom 0.89f0.04 - 58.3f 2

By using the data from exposures 2 and 20 we get for the lambda splitting of the 3111,J = 1 state, A = (0.63 f 0.02) cm-'. This value is in good agree- Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 ment with the value 0.64 cm-l obtained by Dixon (1959). By using il = 0.63 cm-1 we can deduce a value of Av from the measured value of (Av + A). In Fig. 3 we plot the experimentally determined product, Av(Av + A), as a function of E2. Since J = 1, D = 1, and M = 1, the slope of this graph is p2/4 in volts-2. The value of p obtained by the least-squares fit is (2) p = (0.963 f 0.03) Debye. IRWIN AND DXLBY: DIPOLE b1OMESTS OF XI1 For personal use only.

FIG.3. The product of the Stark splittings of the RQ2~(0)line as a function of the electric field squared.

Corrections As a result of spin uncoupling the 3111, J = 1 state is mixed with the 3110, J = 1 state. Because of this mixing, the value of Q and hence the apparent value of p in the 3111, J = 1 state is reduced. The corrected value of Q can be calculated from the matrix elements given by Hill and Van Vleck (1928) and was found to be 0~7347.The value of p for the A 311 state of NI-I is therefore p = (1.31 0.03) Debye.* Second-order effects in the 32- state are canceled because they shift all Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 Stark components the same way. Second-order effects in the 3r11,J = 1 state are estimated to be 0.0025 cm-I and are negligible.

THE 3 240 A BAND

The 3 240 A band of NH is the result of the transition c --t a 'A. The structure of this band is much simpler than that of the 3 360 A band, but the *All errors quoted in this paper are estimates of standard deviation. 1770 ChSAD1:IN JOURNAL OF PI-IYSICS. VOL. 43, 1965 deduction of the dipole moments of the two states is complicated by the fact that both the 'I1 and 'A states exhibit first-order Starlc effects. The rotational and lambda doubling data on the band are from Pearse (1934). Most of the spectrograins of this band mere talcen with HNP' I3 Polaroid ultraviolet polarizing filrn placed before the slit of the spectrograph so that the electric vector of the transmitted light was either parallel or perpendicular to the electric field in the discharge tube. The spectrograins of parallel polarized light (AM = 0 transitions only) exhibited the folloxving Stark features: (1) the lines Q(2) and Q(3) split into symmetrical doublets; (2) the lambda doublets Q(4) and Q(5) came together and sometimes crossed over, depending on the strength of the electric field; (3) each of the lambda doublets Q(G) to Q(14) split into symmetrical doublets; (4) of the four components mentioned in (3), the inner two were the most intense; (5) the effect noted in (4) diminished as J increased; (6) the line P(2) split into a symmetrical triplet. The spectrograms talcen in perpendicularly polarized light showed the lines R(2), P(2), P(3), P(4) as synlmetrical doublets in the region of high field. The observed Stark splittings are given in Table I1 and reproductions of selected lines are shown in Fig. 4. TABLE I1 Field strengths (E) in kilovolts per cm and Stark splittings in cm-I for the lines of the 3 240 A band. I/ indicates that the line was observed in light polarized parallel to the field; 1,in light polarized perpendicular to the field

Exposure No.: P-3 P-4 P-5 P-6 P-8 P-12 E: 37.3f4 37.9f1 46.4f 6 46.9f 3 66.4f 5 65.6413 For personal use only.

Discussion

Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 The first-order Stark splitting of a state for which f2 # 0 is given by

and if ii = 0 this reduces to For personal use only.

FIG.4. (a) Thc Starlr elfect oil the I-I. lint and part of the 3 240 A band. (b) and ((.) 'The Stark elfect 011 lines of the 3 240 .\ band. Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 For personal use only. IRWIN AND DALBY: DIPOLE MOMENTS OF NH 1771 By using equations (3) and (4),we can predict the effect of the electric field on the various levels of the lTI and 'A states.* The levels of the lA state exhibit no lambda doubling (Pearse 1934). Each of these levels mill, therefore, split into 2J + 1 doubly degenerate levels for which the interlevel separation \\.ill be a constant given by 2pE/J(J+ I). Lambda doubling in the 'TI state (A = 0.0164 J(J + 1) cm-I) makes the Stark effect more complicated than that for the lA state. For the electric field strengths used in this work the lambda doubling of the J = 1, 2, 3 levels is negligible coinpared to the Stark splitting. The maximum error in the dipole moment introduced by neglecting the lambda doubling of the J = 1 and 2 levels of the 'TI state is less than 0.2%. For J > 5, the electric field will cause some mixing of the lambda components, but the energy change will be negligible. For J = 4 and 5, the Starlc energies are comparable to the lambda doubling energies. The theoretical relative intensities of the Stark components are given in Townes and Scha~vlolv(1955). The Q(10) line is typical of the lines Q(6) to Q(14) for which the Starlc splitting is due entirely to the 'A state. The expected Stark pattern for Q(10) is shown in Fig. 5. At first glance one would expect the observed components to lie at the centers of gravity of the pattern in Fig. 5. However, because of possible nonequilibrium populations in the M levels of the ITI state and the nonlinear relation between plate density and light intensity, it seems likely For personal use only.

ENERGY FIG.5. The expected Stark pattern for the Q(10) line of the 3 240 A band of KEI in parallel- polarized light. The lengths of the lines are proportional to the theoretical intensity and the Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 energy is in units of p ER/J(J + 1).

that what we are observing is a splitting intermediate between that of the centers of gravity and that of the outermost components. The calculated values of p(a 'A), assunling we see only the outermost components, are shown *Equations (I) and (3) differ only in the choice of origin of energy. In eq. (1) Av is measured from the unperturbed upper lambda doublet. In eq. (3) Av is measured from the midpoint of the unperturbed lambda doublets. 1772 C-ASXDIAS JOURS.\L 017 PIIYSICS. VOL. 43, l9G5 as a function of J in Fig. 6. The average value of p(a lA) calculated from exposures P-8 and P-12 (which appear to give the most consistent values of p(a lA)) is p(a lA) = 1.36 Debye. This provides a lower bound on the value of p(a l4). If one assumes that the observed Stark patterns correspond to the For personal use only.

FIG.6. Calculated val~lesof p(a 'A) as a function of J (6 g J < 14). The data are taken from exposures P-5, P-6, P-S, and P-12.

centers of gravity of the expected pattern, the values of p(a 'A) are higher than those given in Fig. 6 by the factor 4(J + 4)/3(J + 1). The value of p(a 'A) so obtained from plates P-8 and P-12 is p(a 'A) = 1.66 Debye. Therefore

(5) 1.36 ,< p(a ]A) 4 1.66 Debye. These limits will be used to obtain, unambiguously, accurate values for the Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 dipole n~omentsin both states from the observed splitting of low J lines. Intensities and Relative Signs of p(a ]A) and p(c 11) The relative intensities of the components of the lines Q(6) to Q(14) indicate the relative signs of p(a ]A) and p (c In). Consider two levels represented by $1 and +2, where is the upper state. In the presence of a perturbation these levels will be mixed to form the states a+] + b+2 (upper state) and a+~- b+1, where a is positive and the sign of b IR\\'IS XND D-ALBY: DIPOLE MOMEKTS OF NH 1773 is the same as the sign of the perturbatioil I-Iarniltonian. Assuining that the wave functions of the 'Astate are totally inixed and the wave functions of the state are only slightly inixed (see energy level diagram for Q(6), Fig. 7), we can predict the intensities of the various Starlc components. If b(lIt) and bl(lA) have the same signs, we expect the inner con~ponentsof the Q(6) to Q(14) lambda doublets to be the inore intense. If the b's have opposite signs, we expect the outer components to be the inore intense. Since the inner components are observed to be the illore intense, we can conclude that the perturbation k1aiiiiltonians for the two states have the same sign and thus the signs of p(a 'A) and ~(c'It) are the same. For personal use only.

FIG. 7. Energy level diagram for the Stark effect on the Q(6) line of the 3 240 A band of NH.

Evaluation of p (a l A) and p (c 'It) The Starlc effect on lines Q(2) and P(2) which involve transitions between Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 two states exhibiting first-order Stark effects can be determined from expression (4) together with the limits (5) and the Itnowledge that the two dipole moments have the same sign. The lines Q(2) and P(2) in parallel-polarized light then split as shown in Figs. 8 and 9, where the total theoretical splittings are given by

and 1774 CAWADIAN JOURNAL OF PIIYSICS. VOL. 43, 1965

By using the measured values of Av[Q(2)] and Av[P(2)] and assuming that the inner components of Q(2) do not affect the measurements, we calculate from (6) and (7) the values of ,U(CIn) and ,U(U'A) :

,U(CIn) = (1.70 f 0.07 )Debye, ,U(UlA) = (1.49 f 0.06) Debye.

I 0 1 ENERGY FIG. 8. The expected Stark pattern for the Q(2)line of the 3 240 band of SH in parallel- polarized light. The lengths of the lines are proportional to the intensities and the energy is in units of -jl(e'A)E - $p(clII)E. For personal use only.

ENERGY

Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14 FIG. 9. Theexpected Stark pattern for the P(2) line of the 3 240 A band of NH in parallel- polarized light. The lengths of the lines are proportional to the intensities and the energy is in units of &(c 'n)E - &(a 'A)E.

The Stark effect on the other lines of low J is more colnplicated and it is not clear which of the several conlponents correspond to the observed lines. The data froin these lines are, however, in agreement with the values of ,U(Cln) and ,U(UlA) just given. IRWIN AND D.4LBY: DIPOLE MOMENTS OF NH

SUMMARY The dipole monlents of the degenerate states of NI-I were found to be

Ip(A 311)1 = (1.31 f 0.03) Debye, Ip(c 'II)l = (1.70 f 0.07) Debye, Ip(a IA) I = (1.49 & 0.06) Debye, where p(c 'II) and p(a IA) have the same sign. Calculated values of the electric dipole moment for the ground state, X 32-, are listed by Krauss and Wehner (1958). They range between 0.58 and 1.94 Debye. It is unfortunate that no theoretical values are available for the excited states and that no experimental value is available for the ground state. It would be nlost useful to remove both these deficiencies.

ACKNOWLEDGMENTS We wish to acknowledge the aid given on all phases of this work by D. H. Phelps. This work was supported by the National Research Council of Canada and the President's Fund of the University of British Colun~bia.

REFERENCES CONDON,E. U. and SHORTLEY,G. H. 1935. The theory of atomic spectra (Cambridge University Press). DIXON,R. N. 1959. Can. J. Phys. 37, 1171. DOUGLAS,A. E. and ELLIOT,G. A. 1965. Can. J. Phys. 43, 496. HERZBERG,G. 1950. Molecular spectra and molec~~larstructure. I. Spectra of diatomic n~olecules(Van Nostrand. New York). HILL.E. L. and VAN VLBCK.1. H. 1928. Phvs. Rev. 32. 250. KRAUSS, M. aid WEI-INER,J'."F. 1958. hem'. Phys. 29,'1287.

For personal use only. PEARSE,R. 141. B. 1934. Proc. Roy. Soc. (London), Ser. A, 143, 112. PENNY,W. G. 1931. Phil. Mag. 11, 602. PHELPS,D. H. and DALBY,F. W. 1965. Can. J. Phys. 43, 144. TOWNBS,C. H. and SCHAWLOW,A. L. 1955. Microwave spectroscopy (McGraw-Hill, New York). WEINREB,S., BARRBTT,A. H., MEEKS,M. L., and HENRY,J. C. 1963. Nature, 200, 829. Can. J. Phys. Downloaded from www.nrcresearchpress.com by UNIV MONCTON on 06/17/14