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Electric dipole moments of the MgO B1Σ+ and X1Σ+ states
139
Chemical Physics 112 (1987) 139-146 North-Holland, Amsterdam
ELECTRIC
DIPOLE MOMENTS
H. BUSENER, Instirut fir
Received
F. HEINRICH
OF THE MgO B ‘Z + AND X ‘Z + STATES
and A. HESE
Struhlungs- und Kernph_vsik, Technische Uniwrsltiit
15 July 1986; in final form 6 November
Berlin, Hurdenhergstrusse 36, D-1000
Berlin 12, Germq
1986
The electric dipole moment of the excited B’Z+ (~1’= 0) state of MgO produced in a gas-phase reaction of Mg(‘S) atoms and N,O is measured using the technique of Stark quantum-beat spectroscopy. It is shown to be 1p,.,_” 1= 5.94(24) D. The lifetime of the excited B’Z+ (a’ = 0) state is determined as 7 = 22.5(1.5) ns. Using laser excitation spectroscopy and by direct observation of the P(1) line splitting at high electric field strengths in the B ‘I: + -X ‘Z ’ (0.0) system the ground state electric dipole moment is measured yielding 1p,,_,, ) = 6.2(6) D. Furthermore an electric-field-induced Q branch is observed.
1. Introduction There has been considerable interest in reactions of alkaline earth atoms with various oxidants in recent years, both under single-collision conditions [l-6] and in flames [7-lo]. These experiments have been stimulated by the development of new spectroscopic techniques such as laser-induced fluorescence which facilitates the detection of “dark” electronic states. Furthermore the reaction of alkaline earth atoms with different oxidants shows a variety of interesting results concerning the chemiluminescence in flames and the reaction kinetics if alkaline earth atoms in different electronic states are involved [8]. The main part of the experiments, however, has been performed on the reaction of the heavier alkaline earth atoms (Ca, Sr, Ba) with molecular oxidants, most likely because many reactions with ground state Mg atoms are endothermic. On the other hand the MgO molecule is light enough to perform reliable ab initio calculations [lo-141 which should, nevertheless, be verified by experiment. Furthermore the MgO molecule plays an important role in the chemistry of the earth’s ionosphere and in astrophysical studies [15], so that it is desirable to get more information on spectroscopic parameters like electric dipole moments and transition moments.
Although a reliable analysis of the “green” ix+- lx+ system e xl‘sts since 1943 [16,17] it was not verified until 1977 that a ‘2+ state is indeed lower in energy than the neighbouring a 3II (c = 2619.86 cm-‘) and the A’Il states (T, = 3563.3 cm-‘) [18]. By deperturbation of the B’Z’-a311, and B’Z+-A’II systems accurate molecular constants for the a 311 state have been obtained [19,20]. Recently the first microwave measurements of several rotational transitions in the X ‘Z( u = 0, 1) ground state were reported [21]. Combining these microwave results with Doppler-limited laser-induced fluorescence measurements it was possible to get a new set of rotational spectroscopic parameters of the B’Z+ and the X’Z+ states [22]. However, Tiirring and Hoeft [23] showed very recently by observing the MgO microwave absorption spectrum that the optical data are of excellent quality while the results of Azuma et al. [22] suffered from systematic line shifts. The experimental determination of radiative lifetimes of several electronically excited states of MgO and an ab initio calculation of the B ‘Z + X ‘Z+ and A’II-X ‘2+ electronic transition moments was published in 1983 [24]. Moreover it was possible to assign bandheads of the d 3A-a 311 and D’A-a311, transitions in the near UV and to derive vibrational parameters for the a311 state 1251.
0301-0104/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
140
H. Biiwner et al. / Electric dipole moment of excited state MgO
In continuation of similar work on BaO [26], LiH [27,28] and NaH [29] we report here on the determination of the electric dipole moment of the MgO B’Z+( u’ = 0) state using the technique of Stark quantum-beat spectroscopy after pulsed laser excitation. Applying this method, the lifetime of the excited state could be measured simultaneously. By using electric field strengths up to 11 kV/cm the P(1) line splitting of the B’Z+X ‘Z+(O,O) system was observable by laser excitation spectroscopy and allowed the first determination of the ground state electric dipole moment of MgO by diagonalization of the Stark hamiltonian. In the excitation spectrum an electric-field-induced Q branch of the B’Z+-X’Z+ system appeared.
2. Theory In a typical Stark quantum-beat experiment after pulsed laser excitation, the short laser pulse with polarization e excites an ensemble of molecules from the ground state 1i) to the excited states { 1e)} which are split by the external electric field. Time-resolved detection of the fluorescence light with polarization u to the final states { 1f)} reveals a modulation of the decay curve corresponding to the energy splitting of the excited states. Several requirements, however, must be fulfilled if quantum beats should be observed: (a) The pulse duration of the exciting light pulse must be shorter than the decay time of the molecular state and the reciprocal of the energy splitting frequency. (b) The spectral width of the laser pulse must excite coherently all of the relevant sublevels MJt. (c) The polarization angles of the exciting light and of the fluorescence light must be chosen so that an alignment and/or orientation of the excited states is produced and detected. Evaluation of the Breit-Franken formula for pulsed excitation leads to the conclusion [26] that it is most convenient to perform the beat experiment on a R(0) line to get the simplest signal form containing only one modulation frequency and the largest modulation factor if the polarization angles are suitably chosen. Exciting the molecules and
observing the fluorescence at an angle of 90” with respect to the electric field and choosing the angle between excitation and observation as 45” and the polarization angles as 45” with respect to the electric field, the evaluation of the Breit-Franken formula leads to the following simple expression for the beat signal in the case of a R(0) line excitation and P(2) line observation [26] Z(t) = I, exp( -t/T)(l
+ 0.49 cos of),
(1)
where 7 is the population lifetime, and w the modulation frequency. For a ‘Z state the energy splitting of a rotational line with rotational quantum number J’ is given in second-order perturbation theory by [30] AE=ho 3( M;* - M;‘) _ d,E= hcB,,, 25’( J’ + 1)(25’ - 1)(2J’
+ 3) ’ (2)
where Z.L,, is the electric dipole moment in the vibrational level u’, E the electric field strength, B,, the rotational constant, and M[,2 are the magnetic quantum numbers of coherently excited sublevels. Using this expression and the measured beat frequency w the absolute electric dipole moment Z.L,,of the excited B’Z+ state of MgO can be determined. In order to observe directly the energy splitting in the laser excitation spectrum of MgO the electric field strength has to be enhanced considerably so that second-order perturbation theory is not applicable. In this case the determination of the electric dipole moment must be performed by diagonalization of the hamiltonian H = Ho - p E. This procedure has been applied to measure the electric dipole moment of the MgO X’Z+(u = 0) ground state. Furthermore, from the diagonalization procedure we obtain information on mixing coefficients for the rotational state under consideration. l
3. Experimental In order to perform quantum-beat spectroscopy on molecules in an electric field one has to ap-
H. Biiwner et 01. /
Electrrc chpole moment
preach single-collision conditions to eliminate quenching processes which shorten the population and coherence lifetimes and diminish the modulation factor of the quantum-beat signals. Furthermore, arcs between the Stark plates can occur at pressures larger than 10m3 mbar. However, Dagdigian [6] observed no production of MgO molecules under single-collision conditions if ground state Mg atoms were involved in the gasphase reaction with N,O. So in a first attempt, we used a radiatively heated effusive oven where Mg atoms were excited by a low-voltage dc discharge (40 V, 8 A) to produce metastable 3s3p ‘PO Mg atoms. Above the oven the oxidant (N,O) was admitted through a ring-shaped gas inlet. In this way sufficient fluorescence photons were produced to get a clearly resolved spectrum of the B ‘x+-X ‘E+(O,O) system but serious problems with arcs occurred even at low electric fields between the Stark, plates. Because these difficulties could not be overcome, a modified effusive oven without any discharge was constructed where the MgO molecules were produced by ground state Mg atoms in the following gas-phase reaction: Mg(‘S,)
+ N,O(X
+MgO(X’Z+)
lx+) +N,(X’Z,+).
This reaction is slightly exothermic ( AE = - 1.8 eV) in contrast to reactions with other oxidant gases [lo]. Seemingly contradictory results have been reported in the literature concerning this reaction because some groups observed MgO(X lx+) molecules neither in flames [8] nor under single-collision conditions in a beam-gas apparatus [6]. The non-reactivity of Mg(‘S,) atoms with N,O has been corroborated by ab initio calculations for the Mg-N,O potential surfaces, which predict an activation barrier of 0.65-0.87 eV in the entrance channel for that reaction [14]. However, taking into account the differences in experimental conditions, the abovementioned contradictory results could be shown to be consistent with one another [10,19]. In fig. 1 a diagram of the oven used in our experiment is shown. The gas inlet consisting of a stainless steel tube (inner diameter 0.5 mm, outer
ofexcitedstateMgO
141 Reaction
Zone
7
Healer
Carrier Gas (if necessary]
Heat Shields
Stainless Steel Cylinder
1
1 cm H
40
Fig. 1. Diagram of the MgO source consisting of the gas inlet and the stainless steel cylinder containing the magnesium.
diameter 1.5 mm) is fed through a 2 mm hole in the stopper of the oven where the N,O gas reacts with the Mg atoms 1 mm above the orifice. No carrier gas is used in our experiment. The temperature in the oven amounts to 1100 K corresponding to a vapor pressure of 5-10 mbar. Because the oxidant gas is led into the tube through the oven, the N,O gas is as hot as the Mg atoms. This is an important difference to the experimental conditions of Dagdigian’s apparatus [6]. Due to the rather large orifice and the high temperature, about 5 g of Mg metal were needed per hour. It should be noted that a noticeable amount of fluorescence photons could only be detected if the temperature in the oven exceeds 1000 K. Then a weak chemiluminescence is observable above the oven (approximate 3 cm high, 2 cm in diameter) which, however, could not be further analyzed because of the peculiarities of our apparatus. Aside from the oven the apparatus is essentially the same as that described in ref. [31]. After passing through a system of apertures the MgO molecules enter the interaction zone between the Stark plates (50 mm in diameter, 15 mm apart) 15 cm above the oven. Typical pressures near the interaction zone are 8 X lop4 mbar. The laser beam enters the reaction
142
H.
Biisener
et ul. /
Electric
chamber at an angle of 45” with respect to the molecular beam, the angle between excitation and observation amounts to 45”. The exciting light source is a commercial dye laser (Lambda Physik FL2002E) pumped by an excimer laser (Lambda Physik EMGSOE). A solution of coumarin 307 is used as laser dye. Because of problems with amplified spontaneous emission produced in the main amplifier stage and leading to unwanted excitation of background fluorescence, only the preamplifier cell of the dye laser is used yielding a peak laser power of 20 kW. The dye laser generates 7 ns pulses with a bandwidth of 6 GHz so that the requirements for quantum-beat spectroscopy mentioned in section 2 are fulfilled. In the experiments for the direct observation of the P(1) line splitting, an etalon is inserted into the oscillator reducing the bandwidth to 1.5 GHz. The dye laser excites the B’Z+-X ‘Z:+(O,O) band around 5000 A. The fluorescence light is transmitted through a 0.27 m monochromator (Perkin-Elmer) operated with open slits selecting the MgO B’Z+-X’Z(O,l) band to minimize stray light. The photons are collected on the cathode of a cooled RCA 31034 A photomultiplier. Using fast photon-counting electronics, the time-resolved decay signal is analyzed by the method of “de-
dipole
moment
of excited
state
MgO
layed coincidences” HP 1000 computer.
[27], stored and evaluated
in a
4. Results Fig. 2 shows a part of the MgO B’Z+-X’Z+ laser excitation spectrum (without electric field) in the vicinity of the characteristic zero gap of the (0,O) band. The lines could be unambiguously assigned using the known spectroscopic data [16]. The quantum-beat experiments have been performed on the R(0) line which is one of the weakest lines in the spectrum (at best 30 photons/s at a laser repetition rate of 180 Hz). The unassigned lines are due to isotopic species of MgO. From the excitation spectrum, the rotational temperature of the (0,O) band was determined to be T,, = 550 + 50 K. A typical Stark quantum-beat signal taken at an electric field strength of 974 V/cm is shown in fig. 3. This signal has been obtained using “crossed” polarizers in excitation (polarization angle 45” with respect to the electric field) and observation (polarization angle 135O). The beat frequency and the lifetime have been obtained by a least-squares fit revealing a frequency of v = 71.9(7) MHz and a lifetime of
P (7)
P (6) P CT) P (41 P(3)
1
SO00 wave
Fig.
2.
Portion
of the laser excitation
spectrum
II
I
5001 1 ength
of MgO B ’ I: +-X ‘Z+ (0.0) system without line.
electric
field in the vicinity
of the R(0)
H. Biisener et al. / Electric dipole moment o/excited
01
0
,
I
20
40
143
store MgO
,
80
60
100 Time
MgO
B -
Fit
:
X
v
v’ =O.
= 71.9
J’
=l
MHz ,
E
T
=
974
= 22.1
Cnsecl
V/cm nsec
Fig. 3. Typical electric field quantum-beat signal (solid line: least-squares fit)
varying the electric field strength in the range from 0.54 to 1.15 kV/cm different modulation frequencies could be measured. The results are presented in fig. 4 in dependence on the squared electric field strength. Performing a least-squares
the R(0) line of r = 22.1(5) ns for this decay curve. The uncertainties in parentheses represent la statistical errors from the fitting procedure. The modulation amplitude was found to be 0.16 which is smaller than the theoretical value of 0.49. By
0
0 .o
.2
.4
.6
.8 E2 CkV/cmla
1. 0
1. 2
Fig. 4. Modulation frequencies Y as function of the square of the electric field strength
1. 4
H. Biixner
144
et ul. / Electric drpole moment of excited state MgO
P (5)
4996
4999 wave
Fig. 5. Laser excitation
spectrum
of MgO B’Z’-X
5000 1 ength
‘Et (0,O) system at high electric field strength
fit to a straight line, the electric dipole moment of the excited B’Z+( u’ = 0) state was determined from these measurements to be 1pftco 1 = 5.94(24) D using a rotational constant of B,,,, = 0.5799 cm-’ [17]. The B’Z+( u’ = 0, J’ = 1) state lifetime was measured to be rU,_a = 22.5(1.5) ns taking
80 El.
6. Dependence
of the P(1) line splitting
( E = 10.25 kV/cm).
into consideration all available quantum-beat signals and the time calibration errors. Increasing the electric field strength up to values of 11 kV/cm the R(0) line splitting (only caused by the excited state electric dipole moment) and the P(1) line splitting (caused by the
60
Fig.
(1,
on the squared electric field strength diagonalization of the hamiltonian).
FirId)
(solid
2
(kV/cm)’
line:
least-squares
fit obtained
by
H. Biisener et a/. / Electric dipole moment
ground state dipole moment) are directly observable in the (Doppler-limited) laser excitation spectrum. This is shown in fig. 5 where an excitation spectrum has been taken at 10.25 kV/cm. By measuring the electric field dependence of the energy splitting of the P(1) line, using pressure tuning of the dye laser, the X ‘2+( u = 0) electric dipole moment has been determined by applying a least-squares procedure including the diagonalization of the hamiltonian. For relative calibration a Fabry-Perot interferometer (11.5 GHz FSR) was used during these experiments as a frequency marker. The result is shown in fig. 6 where the measured P(1) line splittings and the fit result are depicted versus the square of the electric field strength. The electric dipole moment of the X ‘Zf( u = 0) state amounts to 1pt_,, ) = 6.2(6) D. Comparison of the spectra with and without an electric field (figs. 5 and 2) shows the appearance of an “extra line” in the zero line gap exactly between the R(0) and P(1) lines suggesting the interpretation as an electric-field-induced Q line. This “extra line” appears at electric field strengths larger than 2 kV/cm and increases in intensity with increasing field strengths. It turns out that this line represents the entire induced Q branch of the B’Z+-X’Z+(O,O) system because both electronic states possess almost identical rotational constants (Box_, = 0.5716 cm-’ [16], @_, = 0.5799 cm-’ [17]) and, as determined in our experiments, large and nearly identical electric dipole moments. By calculating the coefficients of the admixture of the rotational lines in an electric field by diagonalization of the hamiltonian, and from this the intensity of the individual Q lines, it turns out that the first three Q lines contribute noticeably to the appearance of the induced Q branch. The interpretation that no other electronic state is mixed in an electric field has been confirmed by performing lifetime measurements on this extra line versus electric field strength showing, however, no deviation from the B lE+( u’ = 0) lifetime obtained in the quantum-beat experiments within our error limits.
of excitedstate
MgO
145
5. Discussion To date few experimental data concerning the electric dipole moments of the alkaline earth oxides exist. For the excited ‘Z+ state measurements have been performed only on BaO [26,32] yielding a value of 1p 1 = 3.0 D for u’ = 0. For the X ‘2+ ground state, the electric dipole moment was determined for the heavier alkaline earth oxides BaO [33], 1~ I = 7.954(3) D, and SrO [34], 1~ I = 8.900(3) D, in the vibrational state u = 0. Concerning the lighter alkaline earth oxides, there exist only theoretical predictions for the permanent electric dipole moment whose values vary depending on the calculation method used. From ab initio calculations, an electric dipole moment of I_L = 7.6 D was deduced for the X ‘2+ state of BaO [35] while similar calculations for CaO yielded values of II.= 8.64 D and p = 8.72 D for the X’Z+ and A’Z+ states, respectively [36]. Pouilly et al. [37] predict an electric dipole moment of p= 4.7 D for the MgO X ‘Z+ state and /J= 5.9 D for the excited B’Z+ level at an internuclear distance of R = 3.3 a,, i.e. near the equilibrium distance. Better agreement of our experimental results with theoretical work is obtained if our data are compared to the (single-point) values of Diffenderfer and Yarkony [13] who obtained p= 5.7 D and 1_1=6.15 D for the X’Zf and B ‘Z+ states, respectively. Concerning the lifetime of the alkaline earth oxide first excited ‘2+ states, almost identical statements can be made as above regarding the available experimental data. So far, the lifetime of the excited ‘Z+ state was measured only for the BaO A’Z+ state [26,38] yielding a value of T = 328(15) ns for u’ = 3. Furthermore a preliminary lifetime measurement of 7 = 155(60) ns was reported for the A’Z+( u’ = 6) level of CaO [4]. In the case of the MgO molecule, our result of T = 22.5(1.5) ns for the B ‘Z+( u’ = 0, J’ = 1) state can be compared with an experimental value of T = 32.7(1.7) ns measured at the (0,O) bandhead [24]. The striking difference between our result and the value of Dagdigian [24] remains unexplained. To confirm our result we measured the B’Z+ (u’ = 0) lifetime separately by varying the chamber
146
H. Biiwner et al. / Electnc dipole moment of exerted state MgO
pressure in the range of 1 x 1O-4 mbar and 3 X 10-3 mbar. However, we found no deviation (within the error limits) from the value obtained in the beat experiments. Furthermore, the fact that a beating phenomenon occurs in the electric field indicates that no pressure influence was present during our experiments. At pressures higher than 10e3 mbar the quantum beats disappeared. To check our electronic equipment we determined the lifetime of the Na 3p 2Pr,z state to be r = 16.0(6) ns in agreement with the most exact value of 7 = 16.40(3) ns reported in the literature [39]. Ab initio calculations of the lifetime yield values of r = 21 ns [13] and r= 24 ns [24] for the B’Z+ state. So our experimental result is in excellent agreement with the theoretical predictions. 6. Conclusion We have determined the permanent electric dipole moment of MgO both in the excited B ‘Z + (u’ = 0) state and in the X ‘E+( u = 0) ground state. Within the error limits, the measurements yield identical and large values of 1p 1 for both states. This fact favours the appearance of an extra line at high electric field strengths which is identified as an electric-field-induced Q branch. The measured lifetime of the B ‘2+( u’ = 0) level is in excellent agreement with ab initio calculations. Acknowledgement We would like to thank Dr. M. &-ieger for valuable help and advice during the early stage of the experiments. This work was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 161 “Hyperfeinwechselwirkungen”.
References [l] CD. Jonah, R.N. Zare and C. Ottinger, J. Chem. Phys. 56 (1972) 263. [2] P.J. Dagdigian, H.W. Cruse, A. Schultz and R.N. Zare, J. Chem. Phys. 61 (1974) 4450. [3] J.P. Irvin and P.J. Dagdigian, J. Chem. Phys. 73 (1980) 176. [4] J.P. Irvin and P.J. Dagdigian, J. Chem. Phys. 74 (1981) 6178. [5] J.W. Cox and P.J. Dagdigian, J. Phys. Chem. 86 (1982) 3738.
(61 P.J. Dagdigian, J. Chem. Phys. 76 (1982) 5375. [71 D.J. Benard, W.D. Slafer and J. Hecht, J. Chem. Phys. 66 (1977) 1012. J. Rostas and G. Taieb, J. Chem. Phys. WI B. Bourguignon, 77 (1982) 2979. 191 H.H. Michels and R.A. Meinzer, Chem. Phys. Letters 98 (1983) 6. and H. Umemoto, J. Phys. Chem. 87 WV W.H. Breckenridge (1983) 1804. J. Chem. Phys. 56 [111 J. Schamps and H. Lefebvre-Brion, (1972) 573. Jr., D.M. Silver and D.R. Yarkony, J. WI C.W. Bauschlicher Chem. Phys. 73 (1980) 2867. and D.R. Yarkony, J. Phys. Chem. 86 1131 R.N. Diffenderfer (1982) 5098. [I41 D.R. Yarkony, J. Chem. Phys. 78 (1983) 6763. 1151 W.W. Duley and T.J. Millar, Astrophys. J. 220 (1978) 124. WI A. Lagerqvist, Arkiv Mat. Astron. Fys. A29 (1943) 1. P71 A. Lagerqvist and U. Uhler, Arkiv Fysik 1 (1949) 459. WI T. Ikeda, N.B. Wong, D.O. Harris and R.W. Field, J. Mol. Spectry. 68 (1977) 452. of Chemistry, MIT, P91 P.C.F. Ip, Ph.D. thesis, Department Cambridge MA, USA (1983). WI R.W. Field, private communication. J. 1211 T.C. Steimle, Y. Azuma and P.G. Carrick, Astrophys. 227 (1984) L21. WI Y. Azuma, T.R. Dyke, G.K. Gerke and T.C. Steimle, J. Mol. Spectry. 108 (1984) 137. ~231 T. Tiirring and J. Hoeft, Chem. Phys. Letters 126 (1986) 477. D.R. Yarkony and P.J. Dagdigian, J. v41 R.N. Diffenderfer, Quant. Spectry. Radiative Transfer 29 (1983) 329. J. McCombie and J. Rostas, Chem. Phys. v51 B. Bourguignon, Letters 113 (1985) 323. WI H.S. Schweda, A. Renn, H. Btisener and A. Hese, Chem. Phys. 98 (1985) 157. ~271 M. Brieger, A. Hese, A. Renn and A. Sodeik, Chem. Phys. Letters 76 (1980) 465. WI M. Brieger, A. Renn, A. Sodeik and A. Hese, Chem. Phys. 75 (1983) 1. 1291 M. Brieger, A. Hese, A. Renn and A. Sodeik, Chem. Phys. Letters 78 (1981) 153. 1301 H.W. Kroto, Molecular rotation spectra (Wiley, New York, 1975). [31] G. Dohnt, A. Hese, A. Renn and H.S. Schweda, Chem. Phys. 42 (1979) 183. [32] R.F. Wormsbecher, S.L. Lane and D.O. Harris, J. Chem. Phys. 66 (1977) 2745. [33] L. Wharton and W. Klemperer, J. Chem. Phys. 38 (1963) 2705. [34] M. Kaufmann, L. Wharton and W. Klemperer, J. Chem. Phys. 43 (1965) 943. [35] Y. Yoshioka and K.D. Jordan, Chem. Phys. 56 (1981) 303. [36] W.B. England, Chem. Phys. 53 (1980) 1. [37] B. Pouilly, J.-M. Robbe and M.H. Alexander, J. Phys. Chem. 88 (1984) 140. [38] S.D. Darrah and S.J. Silvers, Chem. Phys. Letters 121 (1985) 377. [39] A. Gaupp, P. Kuske and H.J. Andr& Phys. Rev. A 26 (1982) 3351.
Chemical Physics 112 (1987) 139-146 North-Holland, Amsterdam
ELECTRIC
DIPOLE MOMENTS
H. BUSENER, Instirut fir
Received
F. HEINRICH
OF THE MgO B ‘Z + AND X ‘Z + STATES
and A. HESE
Struhlungs- und Kernph_vsik, Technische Uniwrsltiit
15 July 1986; in final form 6 November
Berlin, Hurdenhergstrusse 36, D-1000
Berlin 12, Germq
1986
The electric dipole moment of the excited B’Z+ (~1’= 0) state of MgO produced in a gas-phase reaction of Mg(‘S) atoms and N,O is measured using the technique of Stark quantum-beat spectroscopy. It is shown to be 1p,.,_” 1= 5.94(24) D. The lifetime of the excited B’Z+ (a’ = 0) state is determined as 7 = 22.5(1.5) ns. Using laser excitation spectroscopy and by direct observation of the P(1) line splitting at high electric field strengths in the B ‘I: + -X ‘Z ’ (0.0) system the ground state electric dipole moment is measured yielding 1p,,_,, ) = 6.2(6) D. Furthermore an electric-field-induced Q branch is observed.
1. Introduction There has been considerable interest in reactions of alkaline earth atoms with various oxidants in recent years, both under single-collision conditions [l-6] and in flames [7-lo]. These experiments have been stimulated by the development of new spectroscopic techniques such as laser-induced fluorescence which facilitates the detection of “dark” electronic states. Furthermore the reaction of alkaline earth atoms with different oxidants shows a variety of interesting results concerning the chemiluminescence in flames and the reaction kinetics if alkaline earth atoms in different electronic states are involved [8]. The main part of the experiments, however, has been performed on the reaction of the heavier alkaline earth atoms (Ca, Sr, Ba) with molecular oxidants, most likely because many reactions with ground state Mg atoms are endothermic. On the other hand the MgO molecule is light enough to perform reliable ab initio calculations [lo-141 which should, nevertheless, be verified by experiment. Furthermore the MgO molecule plays an important role in the chemistry of the earth’s ionosphere and in astrophysical studies [15], so that it is desirable to get more information on spectroscopic parameters like electric dipole moments and transition moments.
Although a reliable analysis of the “green” ix+- lx+ system e xl‘sts since 1943 [16,17] it was not verified until 1977 that a ‘2+ state is indeed lower in energy than the neighbouring a 3II (c = 2619.86 cm-‘) and the A’Il states (T, = 3563.3 cm-‘) [18]. By deperturbation of the B’Z’-a311, and B’Z+-A’II systems accurate molecular constants for the a 311 state have been obtained [19,20]. Recently the first microwave measurements of several rotational transitions in the X ‘Z( u = 0, 1) ground state were reported [21]. Combining these microwave results with Doppler-limited laser-induced fluorescence measurements it was possible to get a new set of rotational spectroscopic parameters of the B’Z+ and the X’Z+ states [22]. However, Tiirring and Hoeft [23] showed very recently by observing the MgO microwave absorption spectrum that the optical data are of excellent quality while the results of Azuma et al. [22] suffered from systematic line shifts. The experimental determination of radiative lifetimes of several electronically excited states of MgO and an ab initio calculation of the B ‘Z + X ‘Z+ and A’II-X ‘2+ electronic transition moments was published in 1983 [24]. Moreover it was possible to assign bandheads of the d 3A-a 311 and D’A-a311, transitions in the near UV and to derive vibrational parameters for the a311 state 1251.
0301-0104/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
140
H. Biiwner et al. / Electric dipole moment of excited state MgO
In continuation of similar work on BaO [26], LiH [27,28] and NaH [29] we report here on the determination of the electric dipole moment of the MgO B’Z+( u’ = 0) state using the technique of Stark quantum-beat spectroscopy after pulsed laser excitation. Applying this method, the lifetime of the excited state could be measured simultaneously. By using electric field strengths up to 11 kV/cm the P(1) line splitting of the B’Z+X ‘Z+(O,O) system was observable by laser excitation spectroscopy and allowed the first determination of the ground state electric dipole moment of MgO by diagonalization of the Stark hamiltonian. In the excitation spectrum an electric-field-induced Q branch of the B’Z+-X’Z+ system appeared.
2. Theory In a typical Stark quantum-beat experiment after pulsed laser excitation, the short laser pulse with polarization e excites an ensemble of molecules from the ground state 1i) to the excited states { 1e)} which are split by the external electric field. Time-resolved detection of the fluorescence light with polarization u to the final states { 1f)} reveals a modulation of the decay curve corresponding to the energy splitting of the excited states. Several requirements, however, must be fulfilled if quantum beats should be observed: (a) The pulse duration of the exciting light pulse must be shorter than the decay time of the molecular state and the reciprocal of the energy splitting frequency. (b) The spectral width of the laser pulse must excite coherently all of the relevant sublevels MJt. (c) The polarization angles of the exciting light and of the fluorescence light must be chosen so that an alignment and/or orientation of the excited states is produced and detected. Evaluation of the Breit-Franken formula for pulsed excitation leads to the conclusion [26] that it is most convenient to perform the beat experiment on a R(0) line to get the simplest signal form containing only one modulation frequency and the largest modulation factor if the polarization angles are suitably chosen. Exciting the molecules and
observing the fluorescence at an angle of 90” with respect to the electric field and choosing the angle between excitation and observation as 45” and the polarization angles as 45” with respect to the electric field, the evaluation of the Breit-Franken formula leads to the following simple expression for the beat signal in the case of a R(0) line excitation and P(2) line observation [26] Z(t) = I, exp( -t/T)(l
+ 0.49 cos of),
(1)
where 7 is the population lifetime, and w the modulation frequency. For a ‘Z state the energy splitting of a rotational line with rotational quantum number J’ is given in second-order perturbation theory by [30] AE=ho 3( M;* - M;‘) _ d,E= hcB,,, 25’( J’ + 1)(25’ - 1)(2J’
+ 3) ’ (2)
where Z.L,, is the electric dipole moment in the vibrational level u’, E the electric field strength, B,, the rotational constant, and M[,2 are the magnetic quantum numbers of coherently excited sublevels. Using this expression and the measured beat frequency w the absolute electric dipole moment Z.L,,of the excited B’Z+ state of MgO can be determined. In order to observe directly the energy splitting in the laser excitation spectrum of MgO the electric field strength has to be enhanced considerably so that second-order perturbation theory is not applicable. In this case the determination of the electric dipole moment must be performed by diagonalization of the hamiltonian H = Ho - p E. This procedure has been applied to measure the electric dipole moment of the MgO X’Z+(u = 0) ground state. Furthermore, from the diagonalization procedure we obtain information on mixing coefficients for the rotational state under consideration. l
3. Experimental In order to perform quantum-beat spectroscopy on molecules in an electric field one has to ap-
H. Biiwner et 01. /
Electrrc chpole moment
preach single-collision conditions to eliminate quenching processes which shorten the population and coherence lifetimes and diminish the modulation factor of the quantum-beat signals. Furthermore, arcs between the Stark plates can occur at pressures larger than 10m3 mbar. However, Dagdigian [6] observed no production of MgO molecules under single-collision conditions if ground state Mg atoms were involved in the gasphase reaction with N,O. So in a first attempt, we used a radiatively heated effusive oven where Mg atoms were excited by a low-voltage dc discharge (40 V, 8 A) to produce metastable 3s3p ‘PO Mg atoms. Above the oven the oxidant (N,O) was admitted through a ring-shaped gas inlet. In this way sufficient fluorescence photons were produced to get a clearly resolved spectrum of the B ‘x+-X ‘E+(O,O) system but serious problems with arcs occurred even at low electric fields between the Stark, plates. Because these difficulties could not be overcome, a modified effusive oven without any discharge was constructed where the MgO molecules were produced by ground state Mg atoms in the following gas-phase reaction: Mg(‘S,)
+ N,O(X
+MgO(X’Z+)
lx+) +N,(X’Z,+).
This reaction is slightly exothermic ( AE = - 1.8 eV) in contrast to reactions with other oxidant gases [lo]. Seemingly contradictory results have been reported in the literature concerning this reaction because some groups observed MgO(X lx+) molecules neither in flames [8] nor under single-collision conditions in a beam-gas apparatus [6]. The non-reactivity of Mg(‘S,) atoms with N,O has been corroborated by ab initio calculations for the Mg-N,O potential surfaces, which predict an activation barrier of 0.65-0.87 eV in the entrance channel for that reaction [14]. However, taking into account the differences in experimental conditions, the abovementioned contradictory results could be shown to be consistent with one another [10,19]. In fig. 1 a diagram of the oven used in our experiment is shown. The gas inlet consisting of a stainless steel tube (inner diameter 0.5 mm, outer
ofexcitedstateMgO
141 Reaction
Zone
7
Healer
Carrier Gas (if necessary]
Heat Shields
Stainless Steel Cylinder
1
1 cm H
40
Fig. 1. Diagram of the MgO source consisting of the gas inlet and the stainless steel cylinder containing the magnesium.
diameter 1.5 mm) is fed through a 2 mm hole in the stopper of the oven where the N,O gas reacts with the Mg atoms 1 mm above the orifice. No carrier gas is used in our experiment. The temperature in the oven amounts to 1100 K corresponding to a vapor pressure of 5-10 mbar. Because the oxidant gas is led into the tube through the oven, the N,O gas is as hot as the Mg atoms. This is an important difference to the experimental conditions of Dagdigian’s apparatus [6]. Due to the rather large orifice and the high temperature, about 5 g of Mg metal were needed per hour. It should be noted that a noticeable amount of fluorescence photons could only be detected if the temperature in the oven exceeds 1000 K. Then a weak chemiluminescence is observable above the oven (approximate 3 cm high, 2 cm in diameter) which, however, could not be further analyzed because of the peculiarities of our apparatus. Aside from the oven the apparatus is essentially the same as that described in ref. [31]. After passing through a system of apertures the MgO molecules enter the interaction zone between the Stark plates (50 mm in diameter, 15 mm apart) 15 cm above the oven. Typical pressures near the interaction zone are 8 X lop4 mbar. The laser beam enters the reaction
142
H.
Biisener
et ul. /
Electric
chamber at an angle of 45” with respect to the molecular beam, the angle between excitation and observation amounts to 45”. The exciting light source is a commercial dye laser (Lambda Physik FL2002E) pumped by an excimer laser (Lambda Physik EMGSOE). A solution of coumarin 307 is used as laser dye. Because of problems with amplified spontaneous emission produced in the main amplifier stage and leading to unwanted excitation of background fluorescence, only the preamplifier cell of the dye laser is used yielding a peak laser power of 20 kW. The dye laser generates 7 ns pulses with a bandwidth of 6 GHz so that the requirements for quantum-beat spectroscopy mentioned in section 2 are fulfilled. In the experiments for the direct observation of the P(1) line splitting, an etalon is inserted into the oscillator reducing the bandwidth to 1.5 GHz. The dye laser excites the B’Z+-X ‘Z:+(O,O) band around 5000 A. The fluorescence light is transmitted through a 0.27 m monochromator (Perkin-Elmer) operated with open slits selecting the MgO B’Z+-X’Z(O,l) band to minimize stray light. The photons are collected on the cathode of a cooled RCA 31034 A photomultiplier. Using fast photon-counting electronics, the time-resolved decay signal is analyzed by the method of “de-
dipole
moment
of excited
state
MgO
layed coincidences” HP 1000 computer.
[27], stored and evaluated
in a
4. Results Fig. 2 shows a part of the MgO B’Z+-X’Z+ laser excitation spectrum (without electric field) in the vicinity of the characteristic zero gap of the (0,O) band. The lines could be unambiguously assigned using the known spectroscopic data [16]. The quantum-beat experiments have been performed on the R(0) line which is one of the weakest lines in the spectrum (at best 30 photons/s at a laser repetition rate of 180 Hz). The unassigned lines are due to isotopic species of MgO. From the excitation spectrum, the rotational temperature of the (0,O) band was determined to be T,, = 550 + 50 K. A typical Stark quantum-beat signal taken at an electric field strength of 974 V/cm is shown in fig. 3. This signal has been obtained using “crossed” polarizers in excitation (polarization angle 45” with respect to the electric field) and observation (polarization angle 135O). The beat frequency and the lifetime have been obtained by a least-squares fit revealing a frequency of v = 71.9(7) MHz and a lifetime of
P (7)
P (6) P CT) P (41 P(3)
1
SO00 wave
Fig.
2.
Portion
of the laser excitation
spectrum
II
I
5001 1 ength
of MgO B ’ I: +-X ‘Z+ (0.0) system without line.
electric
field in the vicinity
of the R(0)
H. Biisener et al. / Electric dipole moment o/excited
01
0
,
I
20
40
143
store MgO
,
80
60
100 Time
MgO
B -
Fit
:
X
v
v’ =O.
= 71.9
J’
=l
MHz ,
E
T
=
974
= 22.1
Cnsecl
V/cm nsec
Fig. 3. Typical electric field quantum-beat signal (solid line: least-squares fit)
varying the electric field strength in the range from 0.54 to 1.15 kV/cm different modulation frequencies could be measured. The results are presented in fig. 4 in dependence on the squared electric field strength. Performing a least-squares
the R(0) line of r = 22.1(5) ns for this decay curve. The uncertainties in parentheses represent la statistical errors from the fitting procedure. The modulation amplitude was found to be 0.16 which is smaller than the theoretical value of 0.49. By
0
0 .o
.2
.4
.6
.8 E2 CkV/cmla
1. 0
1. 2
Fig. 4. Modulation frequencies Y as function of the square of the electric field strength
1. 4
H. Biixner
144
et ul. / Electric drpole moment of excited state MgO
P (5)
4996
4999 wave
Fig. 5. Laser excitation
spectrum
of MgO B’Z’-X
5000 1 ength
‘Et (0,O) system at high electric field strength
fit to a straight line, the electric dipole moment of the excited B’Z+( u’ = 0) state was determined from these measurements to be 1pftco 1 = 5.94(24) D using a rotational constant of B,,,, = 0.5799 cm-’ [17]. The B’Z+( u’ = 0, J’ = 1) state lifetime was measured to be rU,_a = 22.5(1.5) ns taking
80 El.
6. Dependence
of the P(1) line splitting
( E = 10.25 kV/cm).
into consideration all available quantum-beat signals and the time calibration errors. Increasing the electric field strength up to values of 11 kV/cm the R(0) line splitting (only caused by the excited state electric dipole moment) and the P(1) line splitting (caused by the
60
Fig.
(1,
on the squared electric field strength diagonalization of the hamiltonian).
FirId)
(solid
2
(kV/cm)’
line:
least-squares
fit obtained
by
H. Biisener et a/. / Electric dipole moment
ground state dipole moment) are directly observable in the (Doppler-limited) laser excitation spectrum. This is shown in fig. 5 where an excitation spectrum has been taken at 10.25 kV/cm. By measuring the electric field dependence of the energy splitting of the P(1) line, using pressure tuning of the dye laser, the X ‘2+( u = 0) electric dipole moment has been determined by applying a least-squares procedure including the diagonalization of the hamiltonian. For relative calibration a Fabry-Perot interferometer (11.5 GHz FSR) was used during these experiments as a frequency marker. The result is shown in fig. 6 where the measured P(1) line splittings and the fit result are depicted versus the square of the electric field strength. The electric dipole moment of the X ‘Zf( u = 0) state amounts to 1pt_,, ) = 6.2(6) D. Comparison of the spectra with and without an electric field (figs. 5 and 2) shows the appearance of an “extra line” in the zero line gap exactly between the R(0) and P(1) lines suggesting the interpretation as an electric-field-induced Q line. This “extra line” appears at electric field strengths larger than 2 kV/cm and increases in intensity with increasing field strengths. It turns out that this line represents the entire induced Q branch of the B’Z+-X’Z+(O,O) system because both electronic states possess almost identical rotational constants (Box_, = 0.5716 cm-’ [16], @_, = 0.5799 cm-’ [17]) and, as determined in our experiments, large and nearly identical electric dipole moments. By calculating the coefficients of the admixture of the rotational lines in an electric field by diagonalization of the hamiltonian, and from this the intensity of the individual Q lines, it turns out that the first three Q lines contribute noticeably to the appearance of the induced Q branch. The interpretation that no other electronic state is mixed in an electric field has been confirmed by performing lifetime measurements on this extra line versus electric field strength showing, however, no deviation from the B lE+( u’ = 0) lifetime obtained in the quantum-beat experiments within our error limits.
of excitedstate
MgO
145
5. Discussion To date few experimental data concerning the electric dipole moments of the alkaline earth oxides exist. For the excited ‘Z+ state measurements have been performed only on BaO [26,32] yielding a value of 1p 1 = 3.0 D for u’ = 0. For the X ‘2+ ground state, the electric dipole moment was determined for the heavier alkaline earth oxides BaO [33], 1~ I = 7.954(3) D, and SrO [34], 1~ I = 8.900(3) D, in the vibrational state u = 0. Concerning the lighter alkaline earth oxides, there exist only theoretical predictions for the permanent electric dipole moment whose values vary depending on the calculation method used. From ab initio calculations, an electric dipole moment of I_L = 7.6 D was deduced for the X ‘2+ state of BaO [35] while similar calculations for CaO yielded values of II.= 8.64 D and p = 8.72 D for the X’Z+ and A’Z+ states, respectively [36]. Pouilly et al. [37] predict an electric dipole moment of p= 4.7 D for the MgO X ‘Z+ state and /J= 5.9 D for the excited B’Z+ level at an internuclear distance of R = 3.3 a,, i.e. near the equilibrium distance. Better agreement of our experimental results with theoretical work is obtained if our data are compared to the (single-point) values of Diffenderfer and Yarkony [13] who obtained p= 5.7 D and 1_1=6.15 D for the X’Zf and B ‘Z+ states, respectively. Concerning the lifetime of the alkaline earth oxide first excited ‘2+ states, almost identical statements can be made as above regarding the available experimental data. So far, the lifetime of the excited ‘Z+ state was measured only for the BaO A’Z+ state [26,38] yielding a value of T = 328(15) ns for u’ = 3. Furthermore a preliminary lifetime measurement of 7 = 155(60) ns was reported for the A’Z+( u’ = 6) level of CaO [4]. In the case of the MgO molecule, our result of T = 22.5(1.5) ns for the B ‘Z+( u’ = 0, J’ = 1) state can be compared with an experimental value of T = 32.7(1.7) ns measured at the (0,O) bandhead [24]. The striking difference between our result and the value of Dagdigian [24] remains unexplained. To confirm our result we measured the B’Z+ (u’ = 0) lifetime separately by varying the chamber
146
H. Biiwner et al. / Electnc dipole moment of exerted state MgO
pressure in the range of 1 x 1O-4 mbar and 3 X 10-3 mbar. However, we found no deviation (within the error limits) from the value obtained in the beat experiments. Furthermore, the fact that a beating phenomenon occurs in the electric field indicates that no pressure influence was present during our experiments. At pressures higher than 10e3 mbar the quantum beats disappeared. To check our electronic equipment we determined the lifetime of the Na 3p 2Pr,z state to be r = 16.0(6) ns in agreement with the most exact value of 7 = 16.40(3) ns reported in the literature [39]. Ab initio calculations of the lifetime yield values of r = 21 ns [13] and r= 24 ns [24] for the B’Z+ state. So our experimental result is in excellent agreement with the theoretical predictions. 6. Conclusion We have determined the permanent electric dipole moment of MgO both in the excited B ‘Z + (u’ = 0) state and in the X ‘E+( u = 0) ground state. Within the error limits, the measurements yield identical and large values of 1p 1 for both states. This fact favours the appearance of an extra line at high electric field strengths which is identified as an electric-field-induced Q branch. The measured lifetime of the B ‘2+( u’ = 0) level is in excellent agreement with ab initio calculations. Acknowledgement We would like to thank Dr. M. &-ieger for valuable help and advice during the early stage of the experiments. This work was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 161 “Hyperfeinwechselwirkungen”.
References [l] CD. Jonah, R.N. Zare and C. Ottinger, J. Chem. Phys. 56 (1972) 263. [2] P.J. Dagdigian, H.W. Cruse, A. Schultz and R.N. Zare, J. Chem. Phys. 61 (1974) 4450. [3] J.P. Irvin and P.J. Dagdigian, J. Chem. Phys. 73 (1980) 176. [4] J.P. Irvin and P.J. Dagdigian, J. Chem. Phys. 74 (1981) 6178. [5] J.W. Cox and P.J. Dagdigian, J. Phys. Chem. 86 (1982) 3738.
(61 P.J. Dagdigian, J. Chem. Phys. 76 (1982) 5375. [71 D.J. Benard, W.D. Slafer and J. Hecht, J. Chem. Phys. 66 (1977) 1012. J. Rostas and G. Taieb, J. Chem. Phys. WI B. Bourguignon, 77 (1982) 2979. 191 H.H. Michels and R.A. Meinzer, Chem. Phys. Letters 98 (1983) 6. and H. Umemoto, J. Phys. Chem. 87 WV W.H. Breckenridge (1983) 1804. J. Chem. Phys. 56 [111 J. Schamps and H. Lefebvre-Brion, (1972) 573. Jr., D.M. Silver and D.R. Yarkony, J. WI C.W. Bauschlicher Chem. Phys. 73 (1980) 2867. and D.R. Yarkony, J. Phys. Chem. 86 1131 R.N. Diffenderfer (1982) 5098. [I41 D.R. Yarkony, J. Chem. Phys. 78 (1983) 6763. 1151 W.W. Duley and T.J. Millar, Astrophys. J. 220 (1978) 124. WI A. Lagerqvist, Arkiv Mat. Astron. Fys. A29 (1943) 1. P71 A. Lagerqvist and U. Uhler, Arkiv Fysik 1 (1949) 459. WI T. Ikeda, N.B. Wong, D.O. Harris and R.W. Field, J. Mol. Spectry. 68 (1977) 452. of Chemistry, MIT, P91 P.C.F. Ip, Ph.D. thesis, Department Cambridge MA, USA (1983). WI R.W. Field, private communication. J. 1211 T.C. Steimle, Y. Azuma and P.G. Carrick, Astrophys. 227 (1984) L21. WI Y. Azuma, T.R. Dyke, G.K. Gerke and T.C. Steimle, J. Mol. Spectry. 108 (1984) 137. ~231 T. Tiirring and J. Hoeft, Chem. Phys. Letters 126 (1986) 477. D.R. Yarkony and P.J. Dagdigian, J. v41 R.N. Diffenderfer, Quant. Spectry. Radiative Transfer 29 (1983) 329. J. McCombie and J. Rostas, Chem. Phys. v51 B. Bourguignon, Letters 113 (1985) 323. WI H.S. Schweda, A. Renn, H. Btisener and A. Hese, Chem. Phys. 98 (1985) 157. ~271 M. Brieger, A. Hese, A. Renn and A. Sodeik, Chem. Phys. Letters 76 (1980) 465. WI M. Brieger, A. Renn, A. Sodeik and A. Hese, Chem. Phys. 75 (1983) 1. 1291 M. Brieger, A. Hese, A. Renn and A. Sodeik, Chem. Phys. Letters 78 (1981) 153. 1301 H.W. Kroto, Molecular rotation spectra (Wiley, New York, 1975). [31] G. Dohnt, A. Hese, A. Renn and H.S. Schweda, Chem. Phys. 42 (1979) 183. [32] R.F. Wormsbecher, S.L. Lane and D.O. Harris, J. Chem. Phys. 66 (1977) 2745. [33] L. Wharton and W. Klemperer, J. Chem. Phys. 38 (1963) 2705. [34] M. Kaufmann, L. Wharton and W. Klemperer, J. Chem. Phys. 43 (1965) 943. [35] Y. Yoshioka and K.D. Jordan, Chem. Phys. 56 (1981) 303. [36] W.B. England, Chem. Phys. 53 (1980) 1. [37] B. Pouilly, J.-M. Robbe and M.H. Alexander, J. Phys. Chem. 88 (1984) 140. [38] S.D. Darrah and S.J. Silvers, Chem. Phys. Letters 121 (1985) 377. [39] A. Gaupp, P. Kuske and H.J. Andr& Phys. Rev. A 26 (1982) 3351.