- Email: [email protected]
Parity assignment of Λ-doublets in NO X 2Π12
CHEMICAL PHYSICS LETTERS
Volume 187. number 5
20 December 199 I
Parity assignment of A-doublets in NO X *II1,* F.H. Geuzebroek, FOM-lnstitutr,for
M.G. Tenner, A.W. Kleyn
Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
H. Zacharias Fachbereich Physik. UniversrtiitlGHS Essen, 43 Essen 1. Germany
and
S. Stolte Laser Centrum, Vrije Universiteit, De Boelelaan 1083, 1081 HVAmsterdam,
The Netherlands
Received 9 September I99 1
By applying two separate experimental methods the parity of the two components of the n-doublet of the X 211,,zground state ofN0 is determined. In the first method the assignment is made by simultaneously measuring one- and two-photon laser induced fluorescence spectra of the A *E+ state and applying the appropriate selection rules. In the second setup hexapole focusing and resonance-enhanced multiphoton ionisation (REMPI) are combined. The upper component of the A-doublet is focused by the hexapole and the total parity of this state is assigned by detection with REMPI. again using the A’Z*tX 211,,ztransition. Both methods show that the upper component of the n-doublet of the X 2n,,2 (u=O, .I=O.S) state ofN0 has negative total parity. This assignment supports theoretical results obtained from a perturbation analysis by de Vivie and Peyerimhoff who have calculated that G ?- acts as the major contributor to the A-doublet splitting.
1. Introduction In electronic states of linear molecules with a projection of the electronic orbital angular momentum (L) onto the symmetry axis unequal to zero (n#O), the ground state is twofold degenerate. This is due to the fact that the Hamiltonian of the non-rotating molecule is invariant to reflection in a plane containing the symmetry axis. The same operation switches the sign ofn. A good basis set of eigenstates is formed by the symmetric and antisymmetric superpositions of the two projections -t/i and -4 which are degenerate in the non-rotating molecule. These states possess opposite total parity. The rotation of the molecule lifts the degeneracy of the states through the interaction with higher lying electronic states, mainly those possessing x character. The rcsult is that each rotational level with total angular momentum quantum number J splits up in two 520
closely spaced states with opposite total parity, the so-called A-doublet. Typical examples of molecules showing this behaviour in the ground state are NO and OH (both X ‘II). In processes such as gas phase bi-molecular collisions, molecule-surface scattering and photodissociation, a difference between the populations of the n-doublet levels of n-state molecular levels has been measured (see refs. [ 2-251 in ref. [ 1 ] ). These observations started a renewed interest in the spectroscopic origin of these small splittings in linear molecules. The total parity is related to the symmetry of the wavefunction by reflection of all spatial and spin coordinates in a plane containing the internuclear symmetry axis, generally defined as the z axis. The total parity of the upper and lower components of the Rdoublet alternates with J. For spectroscopic notation in a ‘l-l state the n-doublet component with total parity (- 1)J-‘/2 is assigned an “e” label, while an “f”
0009-26 14/91/S 03.50 0 199I Elsevler Science Publishers B.V. All rights reserved.
‘olume 187, number 5
is,used for states with total parity ( - I )‘+ ‘I’, hereby lifting the alternation [ 2-41. Thus these e/ parity labels are always connected to the upper or he lower component of the n-doublet. This spectrotopic notation of e and f parity makes it possible to xpress selection rules for optical transitions and lerturbations in a more transparent way. Apart from these parity-related spectroscopic asignments, geometric properties of the density disribution of the unpaired electron can be distinuished. When the coupling of the different angular nomenta can be described in a Hund’s case (b) coubling scheme, the electron spin S is coupled to the nolecular rotation vector R (or to N, the result of he coupling of R and /1 in case of a molecule with , # 0). In this case, for one of the components of the I-doublet the electron probability distribution of the mpaired electron is preferentially directed in the Ilane of rotation, while for the other component this listribution is preferentially directed perpendicular o this plane. This feature is one reason for the popclarity of determining the relative population of the wo /I-doublet levels, since it permits one to infer onclusions about the dynamics of molecular pro‘esses via the electron cloud distribution [ 5,6]. In lurid’s case (b) the e and f/i-doublet levels are ei;enstates of the operator of reflection symmetry of he electron wavefunction with respect to the plane ,f rotation, but not in a simple way [ 1 1. It depends In the spin-orbit manifold and the number of elecrons in the outer shell. To provide a new way to exness the relation between the geometrical properties )f the unpaired electron and the /l-doublet levels a lew nomenclature has recently been introduced, lamely II( A’) and II( A”) [ 11. The /i-doublet levels n which the electron wavefunction is symmetric ipon reflection of the spatial coordinates of the elecrons in the plane of rotation are defined as II evels (i.e. with the electron distribution of the un)aired electron directed preferentially parallel to the )lane of rotation). When the same operation is anisymmetric the level is assigned as a II level 1i.e. the electron distribution points preferentially jerpendicular to the plane of rotation). In Hund’s case (a) coupling, the n-doublet levels )f the rotational states are superpositions of the parlllel and perpendicular electron probability distributions, and thus the e and f levels are no longer eiibel
20 December 199 I
CHEMICAL PHYSICS LETTERS
genstates of the reflection symmetry operator. A direct correlation of a A-doublet level to an unmixed electron cloud orientation is therefore rendered impossible. As a measure of the degree of mixing of these orientations the coefficient
c:=om5+
(
4+
-112
(Y-2)2 (.I-OS)(JS1.5)
)
can be taken [ 51. Here Y=A/B denotes the ratio of the spin-orbit splitting constant A and the rotational constant B. For the NO X state this ratio is Y= 73.6. Although the TI(A’)/II( M) symmetry labels hold rigourously only when cs = I, the labels are also used when c: < 1. To indicate the diluted preference of the electron distribution the high J limit of a certain class of levels is taken. In the case of a *II state, in the F, spin-orbit manifold (2II,,2 for NO) the II( A’) and II labels are assigned to the e and f levels, respectively [4]. In the F2 spin-orbit manifold (2113,2for NO) the situation is opposite. Because of the large value of Y in NO X ‘l-l, the mixing coefficient c: assumes a value of c: 20.9 only for J”> 50.5. Thus the coupling in the NO X *II state is intermediate between the Hund’s cases (a) and (b), and the electron cloud is a mixture with parallel and perpendicular character, especially in the lower rotational states. The total parity of then-doublet states is still well defined, which, in addition to the spectroscopic relevance, is also important for dynamic processes [ 7,8 1. Theoretically the actual parity of the /i-doublet levels can be predicted from a perturbation analysis of the major disturbing electronic state. Such an analysis was recently carried out by de Vivie and Peyerimhoff [ 9 1. They found that for NO the G ‘Cstate is the dominant disturber of the X 211state. The total parity of the lowest component of the n-doublet of the lowest rotational state (J=O.5) in X 21’1,,2is expected to be positive (+, e, II( [9-131. The n-doublet splitting has been previously determined experimentally by simultaneously measuring the fluorescence of one- and two-photon excitation of NO to the y-bands [ lo], but the parity was not assigned. On several occasions a confusion of the parity assignment of the n-doublet levels of NO has occurred. Therefore, in this Letter we report an experimental determination of this parity by two in521
Volume
187, number 5
CHEMICAL
PHYSICS LETTERS
dependent experimental approaches. The first method makes use of the opposite selection rules for one- and two-photon excitation. These processes probe transitions to the same upper state from initial states with opposite parity, i.e. the two components of the /i-doublets. By observing simultaneously the induced fluorescence from one- and two-photon excitation from the X ‘lT state to a level of the A *ZZ’ state and using the known parity of the latter [ 2 ] the parity of the components of the n-doublets can be determined. The second and most direct method makes use of the different focusing behaviour of the two components of the Ldoublets of the NO molecule in a strong electrostatic field. Again the known parity of the A ‘I&+state is used to determine the total parity of the focused state.
2. Experimental and results 2.1. One- and two-phoron spectroscopy Rotational levels of the A ‘C+ (v’=O) state are excited by a narrow band width (AP= 1.2 GHz) dye laser radiation tunable around 452 nm. The output power of about 60 kW is divided equally by a 50% beam splitter. One part is frequency doubled in a potassium pentaborate ( KB508*4H20) crystal. The generated UV beam is directed through a small glass cell equipped with quartz windows. This cell is filled with NO at a pressure of 1.3-4 ubar. At a right angle to the laser beam the excited fluorescence is monitored by a photomultiplier (RCA, 1P28 ). The other part of the blue laser beam is collimated to a parallel beam of 1.5 mm diameter and directed through a second glass cell tilled with 1.3 mbar NO. The intensity of the blue laser was sufficiently high to induce a two-photon transition to the A ‘I+ state. The corresponding fluorescence is viewed by a second photomultiplier (EMI, 6265-S). In both cases colour filter (Schott, UG5) in front of the photomultipliers discriminate against scattered visible of ultraviolet laser light. The signals of the photomultipliers are amplified and measured by gated integrators, and displayed on two identical x-t recorders. The t axis of both recorders is controlled by the output of a capacitance manometer, which monitors the pressure in the tun522
20 December
I99 1
ing chamber of the pressure-tuned dye laser oscillator [ 141. This signal and thus the t axis of the recorders is directly proportional to the dye laser frequency. Fig. 1 shows the simultaneous measurement of two rotational transitions in one- and two-photon excitation, while the dye laser is tuned to higher frequencies. The line width of about 3 GHz is limited by Doppler broadening. The right part of the figure shows transitions in the R2, and S, , branches starting from .I”= 7.5, the left part corresponding transitions in the P,, and Q,, branches starting from J”= 18.5. The two-photon transitions occur at higher laser frequencies in both cases. The schematic energy level diagrams below the spectra identify the onephoton (dashed line) and two-photon (full line) transitions. Because the spin-rotation interaction in the A ‘Z+ is weak - the coupling constant yy= - 80.35 MHz [ 151 - the spin-rotation splitting of the rotational levels in this state cannot be resolved with Doppler-limited spectroscopy at the N’ levels excited. However, as has been shown earlier [lo], Doppler-free excitation with counter propagating narrow-bandwidth laser beams will allow this spitting to be resolved. BoththeF, (N’+0.5) and theF, (N’-0.5) component of the excited rotational level N’ in the upper state have the same parity. The parity of the rotational levels in the A *Z+ state is well defined. The lowest level (N ‘= 0, J’= 0.5, F, ) has positive parity [ 21. This total parity alternates due to the alternation of the parity of the rotational wavefunction with the rotational quantum number N’. (For Z electronic state N and R are parallel because n =O. ) From the now well-known parity of the upper state [ 21 the parity of the rotational levels in the ground electronic state can easily be deduced. Because a dipole-allowed single-photon transition connects states of opposite total parity, and, correspondingly, twophoton transitions connect levels of the same parity, the parities of the n-doublets in the lower state are now also well determined. For the rotational levels shown in fig. 1 the lower Lcomponent of the J” = 7.5 level thus has negative parity and the upper n-cornponent accordingly positive parity. Similarly, in the J”= 18.5 level the lower ,4-component has positive parity and the upper &component negative parity. Also in the lower electronic state the parity alter-
Volume 187, number 5
20 December I99 I
CHEMICALPHYSICSLETTERS
250
245
2QJ
235
----
ONE PHOlUN
-
TWPHOTON
15
DYE LASER DETUNING
10
5
0
[GHzl
Fig. I. Simuhaneous measurement of the one-photon (dashed identification lines) and two-photon (full identification lines) excitation of Doppler broadened rotational lines in they (O-O) band of NO. A line identification and a level diagram are given below the transitions.
nates with R”, which for a Hund’s case (a) coupling is directly connected with J” according to J”=R”+SY’, with Q the sum ofA and the projection of S on the internuclear axis IL Therefore, it can easily be deduced that the lowest rotational state in X *II, ,*, J”= 0.5, has positive parity for the lower Acomponent and negative parity for the upper Acomponent. From the frequency separation of the lines in single-photon and two-photon excitation the /i-splitting can be determined. For the two lines shown in fig. 1 we measure
a separation
of 2.7 f0.3
GHz and
5.8kO.3 GHz in 5”=7.5 and J”= 18.5, respectively. The relatively large error bars are due to the Dop-
pler-limited resolution. These values are in good agreement with a theoretical calculation, which yields 2.7826 and 6.012 1 GHz, respectively, using constant p and q [ 121 from Johns et al. [ 161 and A, and B, from Engleman and Rouse [ 17 1. 2.2. Electrostatic focusing When an external electric field of several kV/cm is applied to an NO molecule in a low I state, it exhibits relatively strong linear Stark effect. Upon ap plication of the field the upper level of the A-doublet will raise its energy (i.e. show a positive Stark effect) while the lowest levels will decrease its energy (i.e. 523
Volume 187, number 5
a negative Stark effect) [ 18 1. Such an energy dependence will be used to select the upper component of the /i-doublet. The inhomogeneous electric field occurring inside a hexapole focusing device exerts a force on the molecules. States with a positive Stark effect are deflected towards the axis at the hexapole in contrast to the ones with a negative Stark effect which are deflected away from the hexapole axis. In this way a state-selected molecular beam is produced consisting mainly of the upper n-doublet state. Subsequently resonance-enhanced multiphoton ionisation (REMPI) via the A *Z+ state is used to detect the focused beam. As discussed before the well-known total parity of the intermediate state can be used to determine the total parity of the focused state, i.e. upper n-doublet. The experimental setup consists of a pulsed valve to generate a molecular beam (translational energy =O. I eV), the hexapole and a REMPI detector [ 18,19 1, The electrostatic hexapole selector consists of six polished silversteel rods with a length of 1 m and diameter of 4 mm. The rods are mounted parallel to one another in a hexapole configuration on a circle with a diameter of 12 mm. Alternating rods are grounded or held at a voltage V up to a maximum of 30 kV, producing a high field strength between any two adjacent rods (which are separated by only 2 mm). A molecular beam emerging from a pulsed valve, located on the hexapole axis about 25 cm from the hexapole entrance, is state selected by focusing the molecules with a positive Stark effect sharply onto the detector. When the distance between the detector and the exit of the hexapole is about 1 m, focusing conditions could be reached by applying a voltage on the hexapole of V= 13 kV. The molecules in the focus are detected rotational state specifically by (l+ 1) REMPI via the AZE+(v’=O, Jl)+X211,,z(u”=0, Y), with transitions in the wavelength region around 225 nm. The laser radiation of about 450 nm is generated by an excimer pumped dye laser (Lambda Physik EMG 200/FL3002). The output is frequency doubled using a BBO crystal. The system delivers a frequency doubled laser pulse of 2 mJ with a bandwidth of 0.2 cm-‘. The photoions are produced at the intersection of the molecular beam and the slightly focused ( +O.S mm diameter) laser beam and subsequently 524
20 December 199 I
CHEMICAL PHYSICS LETTERS detected
in a channeltron
electron
multiplier
(ETP,
AEM-1000). The REMPI signal obtained in a single wavelength scan of the unfocused NO beam is given in the upper part of fig. 2. The lines can be assigned to the different branches of the A2C+(u’=0, J’)+X211,,2 (v”=O, ,,I) transitions, starting at the lowest rotational levels of the 211,,2state of NO. The rotational temperature of the unfocused beam can be estimated from the relative intensities of the transitions from J”zO.5 and J”= 1.5 in the upper part of fig. 2. A temperature of T,= 5 K is found. The corresponding spectrum for the focused molecular beam is given in the lower part of fig. 2. The intensities of the Q,, (J”~0.5) and R2, (J”~0.5) lines are increased by a factor of 10, due to the focusing of the hexapole. In contrast, the R,, (J”=O.5) is decreased due to defocusing. The relative abundance of the upper /1level is more than 30 times higher than the population of the lower n-lever. From the well-known parity of the A *Z+ state it can be deduced that the total
-
et +hl
II
o 226.12
226.20
226.26
wavelength(nm) Fig. 2. Rotational state distributions of a molecular beam, with hexapole off (upper part) and with hexapole voltage at 13 kV, i.e. at the focusingcondition ofthe X 2111,2(v”=0, J”=O.S ) state (lower part).
Volume 187, number 5
20 December 199I
CHEMICAL PHYSICS LETTERS
parity of the upper component of the /i-doublet of the X 9, ,z (u” = 0, J” = 0.5 ) state is negative, as can be seen in fig. 3. This means that the upper (lower) components of the li-doublets are off (e) parity and thus are lI(A’) (II( levels [1,4]. When the hexapole voltage is set to a higher value the focusing conditions of the .I”= 1.5 of the 2II,,2
state are met, where again the population of the upper level of the /l-doublet increases. Careful inspection of fig. 2 shows that this is the case even at 13 kV. Since both the total parity of the ground state as well as the intermediate state flips every step in .I” and N’ respectively, again the Q,,branch probes the higher/i-doublet which is now of positive total parity.
22+ 1;’ ,
l-
-:F’ -+Fl
l-
O’
I-
er’
k
J’
N
y2 712
3
+ F2 3t2 2 + F, 5l2 2 1
;5
:
It2
0
r;
K
Fig. 3. Schematic energy level diagram of X *rIljz state of NO with total parity ( + / - ) and e/f parity assignment of the n-doublet levels. Furthermore the relevant transitions to the intermediate A%+ state used in the REMPImeasurements are given, except for the P branches which obviously do not originate from the J= 0.5 state (see fig. 2 ).
525
Volume 187, number 5
CHEMICAL PHYSICS LETTERS
20 December 1991
3. Conclusion
References
Both experimental methods unambiguously established the total parity of the n-doublet levels in X ‘II levels of NO. The experimental result supports the recent theoretical analysis regarding the different contributions to the A splitting in the ground state of NO [9]. In the schematic energy level diagram of fig. 3 the parity assignment of the lowest rotational levels of NO is given. The two methods used show that over a range of Y from 0.5 to 18.5, the behaviour of the total parity is regular, following the expected alternation with rotational state.
[ I ] M.H. Alexander et al., J. Chem. Phys. 89 ( 1988) 1749. [2] H. Lefebvre-Brion and R.W. Field, Perturbations in the spectra of diatomic molecules (Academic Press, New York, 1986). 31 J.M. Brown, J.T. Hougen, K.P. Huber, J.W.C. Johns, 1. Kopp, H. Lefebre-Brian, A.J. Mew, D.A. Ramsay, J. Rostas and R.N. Zare, J. Mol. Spectry. 55 (1975) 500. 41 M.H. Alexander and P.J. Dagdigian, J. Chem. Phys. 80 ( 1984 ) 4325. 51 P. Andresen, G.S. Ondrey, B. Titze and E.W. Rothe, J. Chem. Phys. 80 ( 1984) 2548. [6] M.J. Bronikowski and R.N. Zare, Chem. Phys. Letters 166 (1990) 5. [ 71 L. Bigio and E.R. Grant, J. Chem. Phys. 87 (1987) 360. [ 81U. Robra, H. Zacharias and K.H. Welge, Z. Phys. D 16 (1990) 175. [ 91 R. de Vivie and S.D. Peyerimhoff, J. Chem. Phys. 90 (I 989) 3660. [IO] R. Wallenstein and H. Zacharias, Optics Commun. 25 ( 1978 ) 363. [ I I ] E. Hill and J.H. van Vleck, Phys. Rev. 32 ( 1928) 250. [ 121 R.S. Mulliken and A. Christy, Phys. Rev. 38 (193 I ) 87. [ 131 G. Herzberg, Molecular spectra and molecular structure, Vol. I. Spectra of diatomic molecules (Van Nostrand Reinhold, New York, 1950). [ 141 R. Wallenstein and H. Zacharias, Optics Commun. 32 ( 1980) 429. [ IS] A. Timmerman and R. Wallenstein, Optics Commun. 32 ( 1980) 239. [ 161J.W.C. Johns, J. Reid and D.W. Lepard, J. Mol. Spectry. 65 (1977) 155. [ 171 R. Engleman Jr. and P.E. Rouse, J. Mol. Spectry. 37 ( I971 ) 240. [ 181 M.G. Tenner, E.W. Kuipers, W.Y. La&out, A.W. Kleyn, G. Nicolasen and S. Stolte, Surface Sci. 236 ( 1990) I5 1. [ I 9 ] F.H. Geuzebroek, A.E. Wiskerke, M.G. Tenner, A.W. Kleyn, S. Stolte and A. Namiki, J. Phys. Chem., to be published.
Acknowledgement The one- and two-photon spectroscopy experiments have been performed at the University of Bielefeld. HZ thanks R. Wallenstein for his contribution in the experimental part of this work. The work using hexapole focusing has been performed at the FOM institute for Atomic and Molecular Physics in Amsterdam and is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek. SS acknowledges the EEC Grant SCI-006C for support. We like to thank Dr. J.G. Snijders for enlightening discussions. Dr. Craig Taatjes is gratefully acknowledged for his careful reading of the manuscript.
526
Volume 187. number 5
20 December 199 I
Parity assignment of A-doublets in NO X *II1,* F.H. Geuzebroek, FOM-lnstitutr,for
M.G. Tenner, A.W. Kleyn
Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
H. Zacharias Fachbereich Physik. UniversrtiitlGHS Essen, 43 Essen 1. Germany
and
S. Stolte Laser Centrum, Vrije Universiteit, De Boelelaan 1083, 1081 HVAmsterdam,
The Netherlands
Received 9 September I99 1
By applying two separate experimental methods the parity of the two components of the n-doublet of the X 211,,zground state ofN0 is determined. In the first method the assignment is made by simultaneously measuring one- and two-photon laser induced fluorescence spectra of the A *E+ state and applying the appropriate selection rules. In the second setup hexapole focusing and resonance-enhanced multiphoton ionisation (REMPI) are combined. The upper component of the A-doublet is focused by the hexapole and the total parity of this state is assigned by detection with REMPI. again using the A’Z*tX 211,,ztransition. Both methods show that the upper component of the n-doublet of the X 2n,,2 (u=O, .I=O.S) state ofN0 has negative total parity. This assignment supports theoretical results obtained from a perturbation analysis by de Vivie and Peyerimhoff who have calculated that G ?- acts as the major contributor to the A-doublet splitting.
1. Introduction In electronic states of linear molecules with a projection of the electronic orbital angular momentum (L) onto the symmetry axis unequal to zero (n#O), the ground state is twofold degenerate. This is due to the fact that the Hamiltonian of the non-rotating molecule is invariant to reflection in a plane containing the symmetry axis. The same operation switches the sign ofn. A good basis set of eigenstates is formed by the symmetric and antisymmetric superpositions of the two projections -t/i and -4 which are degenerate in the non-rotating molecule. These states possess opposite total parity. The rotation of the molecule lifts the degeneracy of the states through the interaction with higher lying electronic states, mainly those possessing x character. The rcsult is that each rotational level with total angular momentum quantum number J splits up in two 520
closely spaced states with opposite total parity, the so-called A-doublet. Typical examples of molecules showing this behaviour in the ground state are NO and OH (both X ‘II). In processes such as gas phase bi-molecular collisions, molecule-surface scattering and photodissociation, a difference between the populations of the n-doublet levels of n-state molecular levels has been measured (see refs. [ 2-251 in ref. [ 1 ] ). These observations started a renewed interest in the spectroscopic origin of these small splittings in linear molecules. The total parity is related to the symmetry of the wavefunction by reflection of all spatial and spin coordinates in a plane containing the internuclear symmetry axis, generally defined as the z axis. The total parity of the upper and lower components of the Rdoublet alternates with J. For spectroscopic notation in a ‘l-l state the n-doublet component with total parity (- 1)J-‘/2 is assigned an “e” label, while an “f”
0009-26 14/91/S 03.50 0 199I Elsevler Science Publishers B.V. All rights reserved.
‘olume 187, number 5
is,used for states with total parity ( - I )‘+ ‘I’, hereby lifting the alternation [ 2-41. Thus these e/ parity labels are always connected to the upper or he lower component of the n-doublet. This spectrotopic notation of e and f parity makes it possible to xpress selection rules for optical transitions and lerturbations in a more transparent way. Apart from these parity-related spectroscopic asignments, geometric properties of the density disribution of the unpaired electron can be distinuished. When the coupling of the different angular nomenta can be described in a Hund’s case (b) coubling scheme, the electron spin S is coupled to the nolecular rotation vector R (or to N, the result of he coupling of R and /1 in case of a molecule with , # 0). In this case, for one of the components of the I-doublet the electron probability distribution of the mpaired electron is preferentially directed in the Ilane of rotation, while for the other component this listribution is preferentially directed perpendicular o this plane. This feature is one reason for the popclarity of determining the relative population of the wo /I-doublet levels, since it permits one to infer onclusions about the dynamics of molecular pro‘esses via the electron cloud distribution [ 5,6]. In lurid’s case (b) the e and f/i-doublet levels are ei;enstates of the operator of reflection symmetry of he electron wavefunction with respect to the plane ,f rotation, but not in a simple way [ 1 1. It depends In the spin-orbit manifold and the number of elecrons in the outer shell. To provide a new way to exness the relation between the geometrical properties )f the unpaired electron and the /l-doublet levels a lew nomenclature has recently been introduced, lamely II( A’) and II( A”) [ 11. The /i-doublet levels n which the electron wavefunction is symmetric ipon reflection of the spatial coordinates of the elecrons in the plane of rotation are defined as II evels (i.e. with the electron distribution of the un)aired electron directed preferentially parallel to the )lane of rotation). When the same operation is anisymmetric the level is assigned as a II level 1i.e. the electron distribution points preferentially jerpendicular to the plane of rotation). In Hund’s case (a) coupling, the n-doublet levels )f the rotational states are superpositions of the parlllel and perpendicular electron probability distributions, and thus the e and f levels are no longer eiibel
20 December 199 I
CHEMICAL PHYSICS LETTERS
genstates of the reflection symmetry operator. A direct correlation of a A-doublet level to an unmixed electron cloud orientation is therefore rendered impossible. As a measure of the degree of mixing of these orientations the coefficient
c:=om5+
(
4+
-112
(Y-2)2 (.I-OS)(JS1.5)
)
can be taken [ 51. Here Y=A/B denotes the ratio of the spin-orbit splitting constant A and the rotational constant B. For the NO X state this ratio is Y= 73.6. Although the TI(A’)/II( M) symmetry labels hold rigourously only when cs = I, the labels are also used when c: < 1. To indicate the diluted preference of the electron distribution the high J limit of a certain class of levels is taken. In the case of a *II state, in the F, spin-orbit manifold (2II,,2 for NO) the II( A’) and II labels are assigned to the e and f levels, respectively [4]. In the F2 spin-orbit manifold (2113,2for NO) the situation is opposite. Because of the large value of Y in NO X ‘l-l, the mixing coefficient c: assumes a value of c: 20.9 only for J”> 50.5. Thus the coupling in the NO X *II state is intermediate between the Hund’s cases (a) and (b), and the electron cloud is a mixture with parallel and perpendicular character, especially in the lower rotational states. The total parity of then-doublet states is still well defined, which, in addition to the spectroscopic relevance, is also important for dynamic processes [ 7,8 1. Theoretically the actual parity of the /i-doublet levels can be predicted from a perturbation analysis of the major disturbing electronic state. Such an analysis was recently carried out by de Vivie and Peyerimhoff [ 9 1. They found that for NO the G ‘Cstate is the dominant disturber of the X 211state. The total parity of the lowest component of the n-doublet of the lowest rotational state (J=O.5) in X 21’1,,2is expected to be positive (+, e, II( [9-131. The n-doublet splitting has been previously determined experimentally by simultaneously measuring the fluorescence of one- and two-photon excitation of NO to the y-bands [ lo], but the parity was not assigned. On several occasions a confusion of the parity assignment of the n-doublet levels of NO has occurred. Therefore, in this Letter we report an experimental determination of this parity by two in521
Volume
187, number 5
CHEMICAL
PHYSICS LETTERS
dependent experimental approaches. The first method makes use of the opposite selection rules for one- and two-photon excitation. These processes probe transitions to the same upper state from initial states with opposite parity, i.e. the two components of the /i-doublets. By observing simultaneously the induced fluorescence from one- and two-photon excitation from the X ‘lT state to a level of the A *ZZ’ state and using the known parity of the latter [ 2 ] the parity of the components of the n-doublets can be determined. The second and most direct method makes use of the different focusing behaviour of the two components of the Ldoublets of the NO molecule in a strong electrostatic field. Again the known parity of the A ‘I&+state is used to determine the total parity of the focused state.
2. Experimental and results 2.1. One- and two-phoron spectroscopy Rotational levels of the A ‘C+ (v’=O) state are excited by a narrow band width (AP= 1.2 GHz) dye laser radiation tunable around 452 nm. The output power of about 60 kW is divided equally by a 50% beam splitter. One part is frequency doubled in a potassium pentaborate ( KB508*4H20) crystal. The generated UV beam is directed through a small glass cell equipped with quartz windows. This cell is filled with NO at a pressure of 1.3-4 ubar. At a right angle to the laser beam the excited fluorescence is monitored by a photomultiplier (RCA, 1P28 ). The other part of the blue laser beam is collimated to a parallel beam of 1.5 mm diameter and directed through a second glass cell tilled with 1.3 mbar NO. The intensity of the blue laser was sufficiently high to induce a two-photon transition to the A ‘I+ state. The corresponding fluorescence is viewed by a second photomultiplier (EMI, 6265-S). In both cases colour filter (Schott, UG5) in front of the photomultipliers discriminate against scattered visible of ultraviolet laser light. The signals of the photomultipliers are amplified and measured by gated integrators, and displayed on two identical x-t recorders. The t axis of both recorders is controlled by the output of a capacitance manometer, which monitors the pressure in the tun522
20 December
I99 1
ing chamber of the pressure-tuned dye laser oscillator [ 141. This signal and thus the t axis of the recorders is directly proportional to the dye laser frequency. Fig. 1 shows the simultaneous measurement of two rotational transitions in one- and two-photon excitation, while the dye laser is tuned to higher frequencies. The line width of about 3 GHz is limited by Doppler broadening. The right part of the figure shows transitions in the R2, and S, , branches starting from .I”= 7.5, the left part corresponding transitions in the P,, and Q,, branches starting from J”= 18.5. The two-photon transitions occur at higher laser frequencies in both cases. The schematic energy level diagrams below the spectra identify the onephoton (dashed line) and two-photon (full line) transitions. Because the spin-rotation interaction in the A ‘Z+ is weak - the coupling constant yy= - 80.35 MHz [ 151 - the spin-rotation splitting of the rotational levels in this state cannot be resolved with Doppler-limited spectroscopy at the N’ levels excited. However, as has been shown earlier [lo], Doppler-free excitation with counter propagating narrow-bandwidth laser beams will allow this spitting to be resolved. BoththeF, (N’+0.5) and theF, (N’-0.5) component of the excited rotational level N’ in the upper state have the same parity. The parity of the rotational levels in the A *Z+ state is well defined. The lowest level (N ‘= 0, J’= 0.5, F, ) has positive parity [ 21. This total parity alternates due to the alternation of the parity of the rotational wavefunction with the rotational quantum number N’. (For Z electronic state N and R are parallel because n =O. ) From the now well-known parity of the upper state [ 21 the parity of the rotational levels in the ground electronic state can easily be deduced. Because a dipole-allowed single-photon transition connects states of opposite total parity, and, correspondingly, twophoton transitions connect levels of the same parity, the parities of the n-doublets in the lower state are now also well determined. For the rotational levels shown in fig. 1 the lower Lcomponent of the J” = 7.5 level thus has negative parity and the upper n-cornponent accordingly positive parity. Similarly, in the J”= 18.5 level the lower ,4-component has positive parity and the upper &component negative parity. Also in the lower electronic state the parity alter-
Volume 187, number 5
20 December I99 I
CHEMICALPHYSICSLETTERS
250
245
2QJ
235
----
ONE PHOlUN
-
TWPHOTON
15
DYE LASER DETUNING
10
5
0
[GHzl
Fig. I. Simuhaneous measurement of the one-photon (dashed identification lines) and two-photon (full identification lines) excitation of Doppler broadened rotational lines in they (O-O) band of NO. A line identification and a level diagram are given below the transitions.
nates with R”, which for a Hund’s case (a) coupling is directly connected with J” according to J”=R”+SY’, with Q the sum ofA and the projection of S on the internuclear axis IL Therefore, it can easily be deduced that the lowest rotational state in X *II, ,*, J”= 0.5, has positive parity for the lower Acomponent and negative parity for the upper Acomponent. From the frequency separation of the lines in single-photon and two-photon excitation the /i-splitting can be determined. For the two lines shown in fig. 1 we measure
a separation
of 2.7 f0.3
GHz and
5.8kO.3 GHz in 5”=7.5 and J”= 18.5, respectively. The relatively large error bars are due to the Dop-
pler-limited resolution. These values are in good agreement with a theoretical calculation, which yields 2.7826 and 6.012 1 GHz, respectively, using constant p and q [ 121 from Johns et al. [ 161 and A, and B, from Engleman and Rouse [ 17 1. 2.2. Electrostatic focusing When an external electric field of several kV/cm is applied to an NO molecule in a low I state, it exhibits relatively strong linear Stark effect. Upon ap plication of the field the upper level of the A-doublet will raise its energy (i.e. show a positive Stark effect) while the lowest levels will decrease its energy (i.e. 523
Volume 187, number 5
a negative Stark effect) [ 18 1. Such an energy dependence will be used to select the upper component of the /i-doublet. The inhomogeneous electric field occurring inside a hexapole focusing device exerts a force on the molecules. States with a positive Stark effect are deflected towards the axis at the hexapole in contrast to the ones with a negative Stark effect which are deflected away from the hexapole axis. In this way a state-selected molecular beam is produced consisting mainly of the upper n-doublet state. Subsequently resonance-enhanced multiphoton ionisation (REMPI) via the A *Z+ state is used to detect the focused beam. As discussed before the well-known total parity of the intermediate state can be used to determine the total parity of the focused state, i.e. upper n-doublet. The experimental setup consists of a pulsed valve to generate a molecular beam (translational energy =O. I eV), the hexapole and a REMPI detector [ 18,19 1, The electrostatic hexapole selector consists of six polished silversteel rods with a length of 1 m and diameter of 4 mm. The rods are mounted parallel to one another in a hexapole configuration on a circle with a diameter of 12 mm. Alternating rods are grounded or held at a voltage V up to a maximum of 30 kV, producing a high field strength between any two adjacent rods (which are separated by only 2 mm). A molecular beam emerging from a pulsed valve, located on the hexapole axis about 25 cm from the hexapole entrance, is state selected by focusing the molecules with a positive Stark effect sharply onto the detector. When the distance between the detector and the exit of the hexapole is about 1 m, focusing conditions could be reached by applying a voltage on the hexapole of V= 13 kV. The molecules in the focus are detected rotational state specifically by (l+ 1) REMPI via the AZE+(v’=O, Jl)+X211,,z(u”=0, Y), with transitions in the wavelength region around 225 nm. The laser radiation of about 450 nm is generated by an excimer pumped dye laser (Lambda Physik EMG 200/FL3002). The output is frequency doubled using a BBO crystal. The system delivers a frequency doubled laser pulse of 2 mJ with a bandwidth of 0.2 cm-‘. The photoions are produced at the intersection of the molecular beam and the slightly focused ( +O.S mm diameter) laser beam and subsequently 524
20 December 199 I
CHEMICAL PHYSICS LETTERS detected
in a channeltron
electron
multiplier
(ETP,
AEM-1000). The REMPI signal obtained in a single wavelength scan of the unfocused NO beam is given in the upper part of fig. 2. The lines can be assigned to the different branches of the A2C+(u’=0, J’)+X211,,2 (v”=O, ,,I) transitions, starting at the lowest rotational levels of the 211,,2state of NO. The rotational temperature of the unfocused beam can be estimated from the relative intensities of the transitions from J”zO.5 and J”= 1.5 in the upper part of fig. 2. A temperature of T,= 5 K is found. The corresponding spectrum for the focused molecular beam is given in the lower part of fig. 2. The intensities of the Q,, (J”~0.5) and R2, (J”~0.5) lines are increased by a factor of 10, due to the focusing of the hexapole. In contrast, the R,, (J”=O.5) is decreased due to defocusing. The relative abundance of the upper /1level is more than 30 times higher than the population of the lower n-lever. From the well-known parity of the A *Z+ state it can be deduced that the total
-
et +hl
II
o 226.12
226.20
226.26
wavelength(nm) Fig. 2. Rotational state distributions of a molecular beam, with hexapole off (upper part) and with hexapole voltage at 13 kV, i.e. at the focusingcondition ofthe X 2111,2(v”=0, J”=O.S ) state (lower part).
Volume 187, number 5
20 December 199I
CHEMICAL PHYSICS LETTERS
parity of the upper component of the /i-doublet of the X 9, ,z (u” = 0, J” = 0.5 ) state is negative, as can be seen in fig. 3. This means that the upper (lower) components of the li-doublets are off (e) parity and thus are lI(A’) (II( levels [1,4]. When the hexapole voltage is set to a higher value the focusing conditions of the .I”= 1.5 of the 2II,,2
state are met, where again the population of the upper level of the /l-doublet increases. Careful inspection of fig. 2 shows that this is the case even at 13 kV. Since both the total parity of the ground state as well as the intermediate state flips every step in .I” and N’ respectively, again the Q,,branch probes the higher/i-doublet which is now of positive total parity.
22+ 1;’ ,
l-
-:F’ -+Fl
l-
O’
I-
er’
k
J’
N
y2 712
3
+ F2 3t2 2 + F, 5l2 2 1
;5
:
It2
0
r;
K
Fig. 3. Schematic energy level diagram of X *rIljz state of NO with total parity ( + / - ) and e/f parity assignment of the n-doublet levels. Furthermore the relevant transitions to the intermediate A%+ state used in the REMPImeasurements are given, except for the P branches which obviously do not originate from the J= 0.5 state (see fig. 2 ).
525
Volume 187, number 5
CHEMICAL PHYSICS LETTERS
20 December 1991
3. Conclusion
References
Both experimental methods unambiguously established the total parity of the n-doublet levels in X ‘II levels of NO. The experimental result supports the recent theoretical analysis regarding the different contributions to the A splitting in the ground state of NO [9]. In the schematic energy level diagram of fig. 3 the parity assignment of the lowest rotational levels of NO is given. The two methods used show that over a range of Y from 0.5 to 18.5, the behaviour of the total parity is regular, following the expected alternation with rotational state.
[ I ] M.H. Alexander et al., J. Chem. Phys. 89 ( 1988) 1749. [2] H. Lefebvre-Brion and R.W. Field, Perturbations in the spectra of diatomic molecules (Academic Press, New York, 1986). 31 J.M. Brown, J.T. Hougen, K.P. Huber, J.W.C. Johns, 1. Kopp, H. Lefebre-Brian, A.J. Mew, D.A. Ramsay, J. Rostas and R.N. Zare, J. Mol. Spectry. 55 (1975) 500. 41 M.H. Alexander and P.J. Dagdigian, J. Chem. Phys. 80 ( 1984 ) 4325. 51 P. Andresen, G.S. Ondrey, B. Titze and E.W. Rothe, J. Chem. Phys. 80 ( 1984) 2548. [6] M.J. Bronikowski and R.N. Zare, Chem. Phys. Letters 166 (1990) 5. [ 71 L. Bigio and E.R. Grant, J. Chem. Phys. 87 (1987) 360. [ 81U. Robra, H. Zacharias and K.H. Welge, Z. Phys. D 16 (1990) 175. [ 91 R. de Vivie and S.D. Peyerimhoff, J. Chem. Phys. 90 (I 989) 3660. [IO] R. Wallenstein and H. Zacharias, Optics Commun. 25 ( 1978 ) 363. [ I I ] E. Hill and J.H. van Vleck, Phys. Rev. 32 ( 1928) 250. [ 121 R.S. Mulliken and A. Christy, Phys. Rev. 38 (193 I ) 87. [ 131 G. Herzberg, Molecular spectra and molecular structure, Vol. I. Spectra of diatomic molecules (Van Nostrand Reinhold, New York, 1950). [ 141 R. Wallenstein and H. Zacharias, Optics Commun. 32 ( 1980) 429. [ IS] A. Timmerman and R. Wallenstein, Optics Commun. 32 ( 1980) 239. [ 161J.W.C. Johns, J. Reid and D.W. Lepard, J. Mol. Spectry. 65 (1977) 155. [ 171 R. Engleman Jr. and P.E. Rouse, J. Mol. Spectry. 37 ( I971 ) 240. [ 181 M.G. Tenner, E.W. Kuipers, W.Y. La&out, A.W. Kleyn, G. Nicolasen and S. Stolte, Surface Sci. 236 ( 1990) I5 1. [ I 9 ] F.H. Geuzebroek, A.E. Wiskerke, M.G. Tenner, A.W. Kleyn, S. Stolte and A. Namiki, J. Phys. Chem., to be published.
Acknowledgement The one- and two-photon spectroscopy experiments have been performed at the University of Bielefeld. HZ thanks R. Wallenstein for his contribution in the experimental part of this work. The work using hexapole focusing has been performed at the FOM institute for Atomic and Molecular Physics in Amsterdam and is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek. SS acknowledges the EEC Grant SCI-006C for support. We like to thank Dr. J.G. Snijders for enlightening discussions. Dr. Craig Taatjes is gratefully acknowledged for his careful reading of the manuscript.
526