10 November 2000
Chemical Physics Letters 330 (2000) 373±382
www.elsevier.nl/locate/cplett
Rotational spectroscopy of the SrNH2 and SrND2 radicals
~ 2A1)
(X
J.M. Thompsen, P.M. Sheridan, L.M. Ziurys *
Department of Chemistry and Department of Astronomy and Steward Observatory, 933 North Cherry Avenue,
University of Arizona, Tucson, AZ 85721, USA
Received 1 August 2000; in ®nal form 15 September 2000
Abstract
~ 2 A1 state has been recorded using sub-millimeter direct
The pure rotational spectrum of the SrNH2 radical in its X
absorption techniques in the range 225±540 GHz. Measurements of SrND2 have also been conducted. Both molecules
were produced by the reaction of metal vapor and NH3 or ND3 . Fourteen and ®fteen rotational transitions were recorded for SrNH2 and SrND2 , respectively. Asymmetry doublets for Ka ˆ 0 through 5 or 6, as well as ®ne structure
splittings, were observed in every transition. From these data, spectroscopic constants have been determined, as well as
an r0 -structure. This study provides additional evidence that SrNH2 is planar with ionic bonding. Ó 2000 Elsevier
Science B.V. All rights reserved.
1. Introduction
A prime way of probing the metal±ligand bond
is through using gas-phase spectroscopy of small,
metal-containing molecules. Recent classes of
species that have been studied to examine such
bonding schemes include MOH, MX, MCH3 , and
MNH2 , using both optical and millimeter-wave
(mm-wave) techniques e.g., [1±5]. In addition to
the alkali metals, such investigations have focused
heavily on the alkaline-earth elements Mg, Ca, Sr,
and Ba. (See Bernath for a review [6].) Analysis of
the spectra of such radicals has yielded interesting
information about their electronic properties and
structure.
*
Corresponding author. Fax: +1-520-621-1532.
E-mail address: [email protected] (L.M. Ziurys).
The strontium analogs of these molecules provide an important link for understanding chemical
trends in the alkaline-earth series. Prior spectroscopic studies of the isovalent alkaline-earth
monohydroxide, monomethyl and halide species
have shown that strontium compounds have
similar properties to their calcium and barium
counterparts [6±8] and exhibit primarily ionic behavior. For example, it has been shown that
CaOH, BaOH, and SrOH are tightly bound species with a linear geometry and an M‡ OHÿ
structure [7]. It is only MgOH that does not follow these trends, being quasi-linear, and therefore
having more covalent character to the metal±OH
bond [9].
Another strontium molecule of interest is
SrNH2 , which was ®rst observed by Wormsbecher
et al. [10]. These authors detected chemiluminescence arising from the reaction of Sr metal vapor
with hydrazine or ammonia. They observed three
0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 1 1 3 - 1
374
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
distinct band spectra between 630 and 700 nm,
which they attributed to transitions from the
~ 2 B2 ; B
~ 2 A1 excited states to the ground
~ 2 B1 , and C
A
2
~
state, X A1 . However, they did not have the resolution to perform a rotational analysis of these
sub-bands. Following the work of Wormsbecher
et al., LIF spectra were recorded by Bopegedera
et al. [11], whose investigation yielded approximate
~ ÿ X;
~ ÿX
~ B
~ ÿ X,
~ and C
~
band centers for the A
electronic transitions, as well as Sr±N stretching
~ states. This study
~ and C
frequencies in the X~ ; B,
was recently superseded by the LIF work of Brazier and Bernath [12], who recorded high resolu~ 2 B2 ÿ X
~ 2 A1 and B
~ 2 B1 ÿ X
~ 2 A1
tion spectra of the A
systems. These data were of sucient quality such
that rotational analyses could be performed,
yielding the ®rst rotational constants for SrNH2 .
Up to the present time, no pure rotational
spectra had been obtained for SrNH2 . Such data
are desirable for the determination of very accurate rotational parameters. Also, structures can
usually be established through isotopic substitution. Rotational data have recently been obtained
for some of the other metal amides. For example,
following the laser spectroscopy work on CaNH2
by Marr et al. [13], Whitham et al. [3], and the
Bernath group [14,15], a mm-wave study of this
radical has been carried out by Brewster and
Ziurys [16]. This investigation included the measurement of the spectrum of CaND2 as well, and
vibrational satellite spectra of CaNH2 in its v3 ; v4 ,
and v6 modes. Very recently, Sheridan and Ziurys
[17] have recorded the pure rotational spectrum of
MgNH2 and its deuterium isotopomer [18] in their
ground electronic states ± the ®rst spectroscopic
data on this radical.
In order to provide information on chemical
trends in the alkaline-earth series, we have measured the pure rotational spectrum of both
SrNH2 and SrND2 in their ground 2 A1 states.
This study has re®ned the spectroscopic parameters for strontium amide, provided the ®rst constants for its deuterium isotopomer, and has
enabled an r0 structure to be calculated. In this
Letter, we present our data and their analysis and
compare SrNH2 to the other metal amide species
and additional small strontium-containing radicals.
2. Experimental
The spectra of SrNH2 and SrND2 were recorded via direct absorption techniques using one
of the spectrometers of the Ziurys' group. Details
of the instrumentation are provided elsewhere
[19]. Brie¯y, the instrument consists of a tunable
mm-wave radiation source, a reaction cell, and
an InSb detector cooled to 4 K. The radiation
source (which is frequency modulated to achieve
phase-sensitive detection) is a phase-locked Gunn
oscillator/Schottky diode varactor multiplier. The
reaction cell is a quasi-optical, double-pass system incorporating a Broida-type oven for metal
vaporization.
SrNH2 was synthesized by the reaction of
strontium vapor, produced by the oven, with ammonia in the presence of a d.c. discharge. Metal
was packed into an alumina crucible that was resistively heated to e€ect vapor production. This
vapor was then entrained in a mixture of about 10
mTorr of argon and 10±15 mTorr of ammonia.
This gas mixture was ¯owed into the oven from
underneath the crucible. A d.c. discharge at 30±40
V and 800 mA was applied to the reactants to
cause the formation of the monoamide. A bright
violet-blue color was noticed upon discharge,
consistent with the chemiluminescence observed
by Wormsbecher et al. [10]. SrND2 was produced
in the same manner, substituting ND3 at 20 mTorr
of pressure.
Transition frequencies for 231 lines of
SrNH2 …v ˆ 0† and 287 lines of SrND2 …v ˆ 0†
were recorded. All frequency measurements were
taken from an average of an even number of scans
at 5 MHz in width, half increasing in frequency,
half decreasing in frequency. Typical line widths
ranged from 500 to 1200 kHz over the entire frequency range.
3. Results
Table 1 contains a representative subset of the
transition frequencies measured for strontium
amide and it is deuterated analog. (The complete
data sets are available on request from the authors.) As the Brazier and Bernath [12] study has
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
375
Table 1
Selected transition frequencies of SrNH2 and SrND2 …X~ 2 A1 †a
N 0 …Ka0 ; Kc0 †J 0
N 00 …Ka00 ; Kc00 †J 00
SrNH2
mobs
mobs ÿ mcalc
17(1,17)
17(1,17)
17(3,15)
17(3,14)
17(3,14)
17(3,15)
17(1,16)
17(1,16)
16.5
17.5
16.5
16.5
17.5
17.5
16.5
17.5
16(1,16)
16(1,16)
16(3,14)
16(3,13)
16(3,13)
16(3,14)
16(1,15)
16(1,15)
15.5
16.5
15.5
15.5
16.5
16.5
15.5
16.5
227 325.149
227 407.200
228 063.034
228 063.034
228 135.067
228 135.067
229 549.898
229 616.847
)0.031
0.011
0.021
)0.028
0.089
0.136
0.071
)0.031
28(5,23)
28(5,24)
28(5,23)
28(5,24)
28(1,28)
28(1,28)
28(4,25)
28(4,24)
28(4,25)
28(4,24)
28(3,26)
28(3,25)
28(3,26)
28(3,25)
28(2,27)
28(2,27)
28(2,26)
28(2,26)
28(0,28)
28(0,28)
28(1,27)
28(1,27)
27.5
27.5
28.5
28.5
27.5
28.5
27.5
27.5
28.5
28.5
27.5
27.5
28.5
28.5
27.5
28.5
27.5
28.5
27.5
28.5
27.5
28.5
27(5,22)
27(5,23)
27(5,22)
27(5,23)
27(1,27)
27(1,27)
27(4,24)
27(4,23)
27(4,24)
27(4,23)
27(3,25)
27(3,24)
27(3,25)
27(3,24)
27(2,26)
27(2,26)
27(2,25)
27(2,25)
27(0,27)
27(0,27)
27(1,26)
27(1,26)
26.5
26.5
27.5
27.5
26.5
27.5
26.5
26.5
27.5
27.5
26.5
26.5
27.5
27.5
26.5
27.5
26.5
27.5
26.5
27.5
26.5
27.5
373 871.796
373 871.796
373 943.386
373 943.386
374 098.585
374 180.918
374 735.178
374 735.178
374 807.838
374 807.838
375 339.976
375 340.381
375 413.417
375 413.834
375 706.080
375 780.402
375 818.323
375 891.258
375 903.139
375 979.245
277 740.326
377 807.690
)0.087
)0.087
)0.084
)0.084
0.073
)0.009
0.142
0.141
0.155
0.153
)0.034
)0.229
)0.014
)0.184
0.138
0.003
0.056
0.013
)0.059
)0.130
0.066
)0.040
33(6,27)
33(6,28)
33(6,27)
33(6,28)
33(1,33)
33(1,33)
33(4,30)
33(4,29)
33(4,30)
33(4,29)
33(3,31)
33(3,30)
33(3,31)
33(3,30)
33(2,32)
33(2,32)
33(0,33)
33(2,31)
33(2,31)
33(0,33)
33(1,32)
32.5
32.5
33.5
33.5
32.5
33.5
32.5
32.5
33.5
33.5
32.5
32.5
33.5
33.5
32.5
33.5
32.5
32.5
33.5
33.5
32.5
32(6,26)
32(6,27)
32(6,26)
32(6,27)
32(1,32)
32(1,32)
32(4,29)
32(4,28)
32(4,29)
32(4,28)
32(3,30)
32(3,29)
32(3,30)
32(3,29)
32(2,31)
32(2,31)
32(0,32)
32(2,30)
32(2,30)
32(0,32)
32(1,31)
31.5
31.5
32.5
32.5
31.5
32.5
31.5
31.5
32.5
32.5
31.5
31.5
32.5
32.5
31.5
32.5
31.5
31.5
32.5
32.5
31.5
440 658.322
440 740.880
441 434.099
441 434.099
441 507.074
441 507.074
442 141.702
442 143.149
442 215.265
442 216.696
442 554.612
442 629.225
442 736.271
442 737.826
442 810.399
442 812.892
444 936.027
SrND2
0.087
0.066
)0.083
)0.088
)0.127
)0.132
)0.037
0.045
)0.061
0.032
0.053
0.011
)0.046
0.042
0.008
)0.172
0.054
mobs
mobs ÿ mcalc
374 956.416
374 956.416
375 019.356
375 019.356
)0.019
)0.019
)0.006
)0.006
376 302.617
376 302.617
376 366.004
376 366.004
0.058
)0.086
0.087
)0.054
377 607.401
377 667.436
)0.030
)0.094
376
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
Table 1 (Continued)
N 0 …Ka0 ; Kc0 †J 0
N 00 …Ka00 ; Kc00 †J 00
SrNH2
mobs
SrND2
mobs ÿ mcalc
33(1,32) 33.5
32(1,31) 32.5
445 003.655
0.036
35(1,35)
35(1,35)
35(6,29)
35(6,30)
35(6,29)
35(6,30)
35(5,30)
35(5,31)
35(5,30)
35(5,31)
35(4,32)
35(4,31)
35(4,32)
35(4,31)
35(3,33)
35(3,32)
35(3,33)
35(3,32)
35(2,34)
35(2,34)
35(0,35)
35(0,35)
35(2,33)
35(2,33)
35(1,34)
35(1,34)
34.5
35.5
34.5
34.5
35.5
35.5
34.5
34.5
35.5
35.5
34.5
34.5
35.5
35.5
34.5
34.5
35.5
35.5
34.5
35.5
34.5
35.5
34.5
35.5
34.5
35.5
34(1,34)
34(1,34)
34(6,28)
34(6,29)
33(6,28)
34(6,29)
34(5,29)
34(5,30)
35(5,29)
35(5,30)
34(4,31)
34(4,30)
34(4,31)
34(4,30)
34(3,32)
34(3,31)
34(3,32)
34(3,31)
34(2,33)
34(2,33)
34(0,34)
34(0,34)
34(2,32)
34(2,32)
34(1,33)
34(1,33)
33.5
34.5
33.5
33.5
34.5
34.5
33.5
33.5
34.5
33.5
33.5
33.5
34.5
34.5
33.5
33.5
34.5
34.5
33.5
34.5
33.5
34.5
33.5
34.5
33.5
34.5
467 248.750
467 331.414
0.061
0.080
468 083.633
468 083.633
468 156.730
468 156.730
468 831.739
468 833.549
468 905.332
468 907.106
469 260.888
469 335.598
469 429.731
469 506.753
469 479.107
469 551.571
471 779.049
471 846.813
)0.081
)0.088
)0.090
)0.096
0.064
0.043
0.040
0.017
0.025
0.011
)0.055
)0.033
0.002
0.043
0.026
0.069
37(1,37)
37(1,37)
37(4,34)
37(4,33)
37(4,34)
37(4,33)
37(3,35)
37(3,34)
37(3,35)
37(3,34)
37(2,36)
37(2,36)
37(0,37)
37(0,37)
37(2,35)
37(2,35)
37(1,36)
37(1,36)
36.5
37.5
36.5
36.5
37.5
37.5
36.5
36.5
37.5
37.5
36.5
37.5
36.5
37.5
36.5
37.5
36.5
37.5
36(1,36)
36(1,36)
36(4,33)
36(4,32)
36(4,33)
36(4,32)
36(3,34)
36(3,33)
36(3,34)
36(3,33)
36(2,35)
36(2,35)
36(0,36)
36(0,36)
36(2,34)
36(2,34)
36(1,35)
36(1,35)
35.5
36.5
35.5
35.5
36.5
36.5
35.5
35.5
36.5
36.5
35.5
36.5
35.5
36.5
35.5
36.5
35.5
36.5
493 818.293
493 901.044
494 714.320
494 714.320
494 787.442
494 787.442
495 502.415
495 504.861
495 576.055
495 578.469
495 946.427
496 021.227
496 098.367
496 175.713
496 203.779
496 276.066
498 600.058
498 667.955
0.029
0.065
)0.063
)0.074
)0.109
)0.119
0.036
0.064
0.044
0.083
)0.035
)0.024
)0.077
0.002
)0.062
0.003
)0.006
0.105
40(1,40)
40(1,40)
40(6,34)
40(6,35)
40(6,34)
40(6,35)
39.5
40.5
39.5
39.5
40.5
40.5
39(1,39)
39(1,39)
39(6,33)
39(6,34)
39(6,33)
39(6,34)
38.5
39.5
38.5
38.5
39.5
39.5
533 630.868
533 713.743
)0.037
0.016
mobs
mobs ÿ mcalc
396 549.787
396 621.539
397 620.540
397 620.540
397 683.510
397 683.510
398 415.019
398 415.019
398 478.235
398 478.235
)0.016
)0.016
0.019
0.019
0.006
0.006
)0.008
)0.007
)0.019
)0.018
399 609.273
399 674.171
399 082.698
399 152.159
400 496.944
400 556.495
402 857.100
402 916.305
0.054
)0.043
)0.007
)0.070
0.017
)0.090
0.086
)0.046
452 897.952
452 970.035
454 230.515
454 230.515
454 293.433
454 293.433
0.046
0.030
0.121
0.121
)0.007
)0.007
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
377
Table 1 (Continued)
N 0 …Ka0 ; Kc0 †J 0
N 00 …Ka00 ; Kc00 †J 00
SrNH2
mobs
a
40(5,35)
40(5,36)
40(5,35)
40(5,36)
40(4,36)
40(4,37)
40(4,36)
40(4,37)
40(3,38)
40(3,37)
40(3,38)
40(3,37)
40(2,39)
40(2,39)
40(0,40)
40(0,40)
40(2,38)
40(2,38)
40(1,39)
40(1,39)
39.5
39.5
40.5
40.5
39.5
39.5
40.5
40.5
39.5
39.5
40.5
40.5
39.5
40.5
39.5
40.5
39.5
40.5
39.5
40.5
39(5,34)
39(5,35)
39(5,34)
39(5,35)
39(4,35)
39(4,36)
39(4,35)
39(4,36)
39(3,37)
39(3,36)
39(3,37)
39(3,36)
39(2,38)
39(2,38)
39(0,39)
39(0,39)
39(2,37)
39(2,37)
39(1,38)
39(1,38)
38.5
38.5
39.5
39.5
38.5
38.5
39.5
39.5
38.5
38.5
39.5
39.5
38.5
39.5
38.5
39.5
38.5
39.5
38.5
39.5
46(1,46)
46(1,46)
46(6,40)
46(6,41)
46(6,40)
46(6,41)
46(0,46)
46(5,41)
46(5,42)
46(0,46)
46(5,41)
46(5,42)
46(2,45)
46(2,45)
46(2,44)
46(2,44)
46(4,43)
46(4,42)
46(4,43)
46(4,42)
45.5
46.5
45.5
45.5
46.5
46.5
45.5
45.5
45.5
46.5
46.5
46.5
45.5
46.5
45.5
46.5
45.5
45.5
46.5
46.5
45(1,45)
45(1,45)
45(6,39)
45(6,40)
45(6,39)
45(6,40)
45(0,45)
45(5,40)
45(5,41)
45(0,45)
45(5,40)
45(5,41)
45(2,44)
45(2,44)
45(2,43)
45(2,43)
45(4,42)
45(4,41)
45(4,42)
45(4,41)
44.5
45.5
44.5
44.5
45.5
45.5
44.5
44.5
44.5
45.5
45.5
45.5
44.5
45.5
44.5
45.5
44.5
44.5
45.5
45.5
534 622.704
534 622.704
534 695.931
534 695.931
535 469.938
535 473.551
535 543.825
535 547.193
535 933.301
536 008.198
536 051.892
536 129.636
536 257.468
536 329.514
538 787.509
538 855.606
SrND2
mobs ÿ mcalc
mobs
mobs ÿ mcalc
0.035
0.053
0.039
0.058
)0.040
0.002
0.214
0.069
)0.175
)0.162
)0.005
0.047
)0.256
)0.101
)0.050
0.126
455 128.800
455 128.800
455 191.965
455 191.965
455 846.180
455 846.180
455 909.407
455 909.407
456 416.111
456 460.708
456 479.328
456 523.535
456 408.744
456 473.983
455 552.165
455 623.133
457 714.563
457 773.074
460 065.916
460 125.894
0.059
0.063
)0.009
)0.006
)0.210
0.346
)0.263
0.285
)0.047
0.033
)0.073
0.032
0.016
)0.038
0.037
0.039
0.006
0.001
0.013
0.134
520 356.902
520 429.448
522 054.939
522 054.939
522 117.919
522 117.919
523 049.757
523 073.565
523 073.565
523 122.613
523 136.702
523 136.702
524 413.130
524 478.717
526 349.806
526 407.079
523 895.018
523 896.534
523 958.188
523 959.707
)0.073
)0.069
0.036
0.036
)0.010
)0.010
)0.097
0.076
0.089
0.034
0.043
0.056
0.289
0.184
)0.096
0.009
)0.045
)0.014
)0.032
)0.020
In MHz.
shown, SrNH2 is a planar molecule with C2v
symmetry and a 2 A1 ground state. It also is a nearprolate asymmetric top. Consequently, the quantum numbers used to label each transition are
N ; Ka ; Kc , S, and J , in a case (b) coupling scheme.
N denotes the rotational angular momentum,
while J labels the spin±rotation interaction
^ As is the case of any asymmetric top,
(J^ ˆ N^ ‡ S).
the degeneracy with respect to the K quantum
number is removed. Ka and Kc correlate with K in
the limits of prolate and oblate symmetric tops,
respectively, and although they are not good
quantum numbers as such, they serve as labels for
the energy levels. The dipole moment for SrNH2
lies along only the ^a axis; hence, a-type dipole
transitions are only allowed. The selection rules
378
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
DN ˆ 1; DJ ˆ 1; DKa ˆ 0; and DKc ˆ 1 thus
apply.
Estimates of the rotational constants for SrNH2
were made available to this research group by
Brazier and Bernath prior to publication [12]. The
search for pure-rotational lines of this molecule
was greatly facilitated by these constants. Most
transitions were predicted to be within 100 MHz
of the actual measurements. However, no spectroscopic constants existed for SrND2 , necessitating an extensive search through frequency space.
This search was accomplished by ®rst estimating
the A; B, and C rotational parameters for SrND2 ,
scaling from those of SrNH2 by the mass di€erence. Transition frequencies were then predicted,
and data were taken in 100 MHz increments over
the entire range of 450±485 MHz. Spin±rotation
doublets were consequently identi®ed and harmonic relationships established among them. The
harmonically related doublets, which correspond
to particular Ka components, were then ®t with
e€ective B; D, and c parameters. After a series of
e€ective B values were established, a relationship
was looked for among the components by extrapolating back to the symmetric top limit. In this
way, Ka quantum numbers were assigned. Once
the asymmetric top pattern was established, transition frequencies from additional Ka components
could be readily predicted and measured. Initial
assignment of the Ka ˆ 4 components of SrND2
was also aided by its small asymmetry doubling at
high N , as expected based on prior work done on
CaND2 [16]. Asymmetry doubling of the higher Ka
components was not expected to be observed.
Spin statistics and line intensities were additionally helpful in the assignment of Ka quantum
numbers. The strongest lines were naturally attributed to the ground vibrational state. Moreover, for molecules with C2v symmetry, fermion
exchange (i.e., protons in the case of SrNH2 )
causes the odd Ka components to be statistically
favored over the even components by a 3:1 ratio.
In the case of boson exchange (i.e., deuterons of
SrND2 ), even Ka components were favored over
odd components by a 2:1 ratio. This alternating
intensity ratio was quite evident in SrNH2 , and
aided in Ka assignments. However, for SrND2 , the
2:1 alteration in intensity was less obvious and was
not as de®nitive in identifying Ka components.
Furthermore, deuterium substitution results in a
heavier molecule, and therefore lower energy levels. Consequently, components up to Ka ˆ 8 were
easily observed in SrND2 . For SrNH2 , only Ka
components up to Ka ˆ 5 were recorded.
It should be noted, as well, that magnetic and
quadrupole hyper®ne structure is possible for these
molecules due to the interactions concerning the
14
N…I ˆ 1†; 1 H…I ˆ 1=2† and D(I ˆ 1) nuclei. In the
frequency ranges investigated, the principal rotational levels examined for both molecules were
quite high in N . Hyper®ne splitting is not expected
to be observed at these levels. In addition, signals
arising from the other strontium isotopomers,
namely the 86 Sr and 87 Sr analogs, are probably
present. However, the spectra of these species were
too weak to be realistically studied. (The strontium
isotope ratio is 88 Sr : 87 Sr : 86 Sr  83 : 7 : 10.)
Sample spectra of SrNH2 are presented in Figs.
1 and 2. Fig. 1 shows a section of the N ˆ 36 ! 37
rotational transition of the ground electronic and
vibrational state near 496 GHz. The spectrum is a
composite of 10 successive 100 MHz scans, totaling 1 GHz of frequency space. Evident in the scan
are the Ka ˆ 0; 2, and 3 components for this
Fig. 1. Spectrum of a section of the N ˆ 36 ! 37 rotational
~ 2 A1 † near 496 GHz. Asymmetry doutransition of SrNH2 …X
bling is resolved in the Ka ˆ 2 and 3 transitions, and the spin±
rotation splitting is apparent in every Ka component. Asterisks
mark unidenti®ed lines, some which arise from vibrationally
excited SrNH2 . This spectrum is a composite of 10 scans, each
covering 100 MHz in frequency with a duration of about 60 s.
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
379
basis, with the additional incorporation of a spin±
rotation term, i.e.,
H^eff ˆ H^rot ‡ H^sr :
…1†
The ®rst term concerns molecular frame rotation
and a considerable number of centrifugal distortion corrections:
H^rot ˆ AN 2x ‡ BN 2y ‡ CN 2z ÿ DN N 4
ÿ DNK N 2 N 2z ‡ d1 N 2 …N 2‡ ‡ N 2ÿ † ‡ d2
…N 4‡ ‡ N 4ÿ † ‡ HN N 6 ‡ HNK N 4 N 2z
‡ HKN N 2 N 4z ‡ LNK N 4 N 4z ‡ LNNK N 6 N 2z
‡ LKKN N 2 N 6z ‡ PNKK N 4 N 6z
Fig. 2. Spectrum of a section of the N ˆ 40 ! 41 transition of
~ 2 A1 † near 467 GHz. Spin±rotation interactions are
SrND2 …X
observed in every Ka component present (Ka ˆ 0; 2; 3, and 4),
some of which exhibit asymmetry doubling as well. Twelve 100
MHz scans were required to produce this spectrum, each 60 s
in duration.
transition. In each case, spin±rotation doublets are
readily resolved and asymmetry doubling is apparent in the Ka ˆ 2 and 3 lines. It should be noted
that the intensity of the Ka ˆ 3 components is
clearly greater than that of the 0 or 2 components,
as predicted for fermion exchange. Asterisks mark
vibrational satellite transitions or unknown lines.
In Fig. 2 a typical spectrum of SrND2 is displayed. These data show a part of the
N ˆ 40 ! 41 transition near 467 GHz, which includes most of the Ka ˆ 0; 2; 3, and 4 components.
(One set of Ka ˆ 2 doublets is not present as it
occurs higher in frequency.) Here the 2:1 even Ka
:odd Ka boson ratio is apparent. Also, the asymmetry doubling in the Ka ˆ 3 components is on the
same order of magnitude as the spin±rotation
splittings, while it is totally collapsed for the
Ka ˆ 4 lines. This spectrum is a composite of 12,
100 MHz scans.
4. Analysis
The SrNH2 and SrND2 spectra were analyzed
using a slightly modi®ed form of the S-reduced
rotational Hamiltonian of Watson [20] in the I r
‡ PNNK N 6 N 4z ‡ PKN N 2 N 8z ‡ PNK N 8 N 2z :
…2†
The second term involves only the diagonal terms
in the spin±rotation tensor (as appropriate for C2v
symmetry), and one centrifugal distortion correction to the spin±rotation:
X
eaa N a S a ‡ DSNK …N S†N 2 N 2z :
…3†
H^sr ˆ
a
This Hamiltonian was used to model the data,
employing the least-squares ®tting routine SPFIT,
developed by Pickett and co-workers at JPL. To ®t
the data, only lower-order centrifugal distortion
corrections to the rotation were initially employed.
To achieve a better rms, higher-order terms were
then added successively. A centrifugal distortion
correction to the spin±rotation interaction was
found necessary in the analysis of both SrNH2 and
SrND2 . Altogether, 14 centrifugal distortion terms
were used to model SrNH2 ; an almost identical set
was needed to analyze SrND2 . Only components
up to Ka ˆ 6 were included in the SrND2 ®t.
The ®nal results of this data analysis are given
in Table 2. The rms of the data ®tting was 92 kHz
(SrNH2 ) and 87 kHz (SrND2 ), smaller than the
estimated experimental accuracy of 100 kHz.
Constants obtained from the optical study of
Brazier and Bernath [12] are also shown in the
table. (Only those centrifugal distortion parameters that can be meaningfully compared are listed.)
The constants for SrNH2 from two data sets are in
good agreement. The only exception is eaa , which is
about a factor of two larger in the mm-wave ®t
than in the optical work. A subsequent reanalysis
380
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
Table 2
Rotational constants for SrNH2 and SrND2 …X~ 2 A1 †a
Constant
SrNH2
SrND2
SrNH2 b optical
A
B
C
eaa
ebb
ecc
DSNK
DN
DNK
d1
d2
h2
h3
HNK
HKN
LNK
LKKN
LNNK
PNNK
PNKK
PKN
PNK
394 340(140)
6790.2961(27)
6659.5159(26)
160.4(2.3)
59.740(86)
89.657(81)
ÿ5:5…1:2† 10ÿ6
0.00607534(75)
1.3595(14)
)0.00015394(46)
ÿ4:943…83† 10ÿ5
ÿ1:31…38† 10ÿ9
ÿ2:93…62† 10ÿ10
2:31…13† 10ÿ5
)0.00620(18)
1:6…1:3† 10ÿ6
ÿ1:383…45† 10ÿ4
ÿ8:9…6:0† 10ÿ10
ÿ1:00…22† 10ÿ10
2:26…29† 10ÿ8
)
3:3…1:5† 10ÿ13
196 565(12)
5815.9704(49)
5633.5686(36)
91.3(2.3)
51.526(79)
76.841(69)
ÿ1:84…42† 10ÿ6
0.00410838(60)
0.91401(90)
)0.00017665(60)
ÿ8:025…56† 10ÿ5
1:52…20† 10ÿ9
4:62…53† 10ÿ10
1:641…42† 10ÿ5
)0.002087(63)
8:5…1:8† 10ÿ8
ÿ5:5…2:2† 10ÿ6
ÿ2:82…79† 10ÿ10
ÿ5:1…2:5† 10ÿ12
ÿ7:3…2:5† 10ÿ10
ÿ1:24…31† 10ÿ7
)
394 001(7)
6791.67(69)
6656.15(69)
88(33)
54.1(2.5)
86.4(2.5)
Rms of ®t:
0.092
0.087
0.00580(23)
1.3583(69)
3:64…28† 10ÿ5
)0.00901(19)
a
In MHz; all errors are quoted to 3r and apply to the last quoted decimal place.
b
Ref. [12].
by C.R. Brazier of their data (private communication) indicates that the value of eaa is relatively
insensitive to their overall ®t. Fixing eaa to the mmwave value near 160 MHz leads to virtually identical results in the optical analysis.
5. Discussion
This mm-wave study has resulted in re®ned
spectroscopic constants for SrNH2 and the ®rst
such parameters for SrND2 . These data indicate
that both species are planar, as concluded by the
previous optical investigations [10±12]. Evidence
for planarity is found in the line intensities, which
follow the pattern expected for C2v symmetry and
fermion or boson particle exchange. Other evidence for planar geometry is found in the inertial
defects …D0 †, as shown in Table 3.
The inertial defect found for SrNH2 is
2 . Although this value is not as
D0 ˆ 0:180 amu A
small as that of some known planar species such as
Table 3
Inertial defects for SrNH2 and related species
Molecule
D0
2 )
(amu A
Ref.
SrNH2
SrND2
CaNH2
CaND2
MgNH2
MgND2
LiNH2
LiND2
NaNH2
NH2 CN
ND2 CN
NH2 NC
0.180
0.242
0.157
0.210
0.078
0.096
0.115
0.150
0.079
)0.285
)0.746
)0.756
This work
This work
[16]
[16]
[18]
[18]
[22]
[22]
[5]
[23]
[23]
[24]
H2 CO (0.0577; Ref. [21]), it is very close to those
found for other planar amides. For example, the
inertial defects for CaNH2 ; NaNH2 and LiNH2 are
2 [5], and 0.115
2 [16], 0.079 amu A
0.157 amu A
2 [22], respectively (see Table 3). The defect
amu A
for SrNH2 is also positive. Other amide-type species such as NH2 CN that show inversion have
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
large, negative values [23,24]. In fact, that of
deuterated cyanamide is quite large and negative
2 . The inertial defect inat D0 ˆ ÿ0:746 amu A
creases somewhat on deuteration for strontium
2 ), but this trend
amide (SrND2 : D0 ˆ 0:242 amu A
2 ),
is also observed for CaND2 …D0 ˆ 0:210 amu A
2
and LiND2 …D0 ˆ 0:150 amu A ), both planar
species. Moreover, the value of D0 does not change
sign with deuteration, as found for non-planar
formamide [25]. In this molecule, the inertial defect
2 ), but changes
is small and positive (0.008 amu A
sign on deuteration ± an unusual property that
indicates a non-planar structure.
Brazier and Bernath [12] estimated the geometry of SrNH2 by ®xing the N±H bond length to
± that of NHÿ . Because the spectrum of
1.041 A
2
SrND2 has been measured, a true r0 structure can
be calculated for SrNH2 using the pure rotational
data. The results of this calculation are presented
in Table 4, along with the structure of CaNH2
from Brewster and Ziurys [16], obtained by an
identical method. As the table shows, the N±H
bond lengths and H±N±H angles for SrNH2 and
CaNH2 are virtually identical. The only di€erence
between these two species is the metal±nitrogen
bond length, which increases for SrNH2 . This
lengthening is expected, since the strontium atom
is larger than that of calcium. These geometric
similarities suggest that the M‡ NHÿ
2 structure is
381
dominant for both species. Otherwise, more differences might be expected, for example, in the H±
N±H bond angle. The H±N±H bond angle of
about 105°, found for both calcium and strontium
amide, is a little larger than the 100° value estimated by Brazier and Bernath [12]; however, these
authors ®xed the H±N bond distance to be 0.02
larger than found in the r0 calculation.
A
Additional evidence for ionic bonding can be
found in the spin±rotation constants for SrNH2 .
Although the unpaired electron in SrNH2 is to a
®rst-order approximation located in an s-type orbital on the strontium atom, some degree of p,d,f
. . . character mixes into this orbital from nearby
excited electronic states. The mixing occurs because of second-order spin±orbit coupling to the
ground state from these excited states [26]. The
result is that the spin±rotation constants are no
longer merely mass-dependent terms. They re¯ect
the magnitude of the spin±orbit coupling and
consequently the anisotropic character of the
orbital of the unpaired electron. Therefore, massnormalized spin±rotation constants can be a diagnostic of non-symmetric orbital character, and
consequently, the deviation from ionic (spherical stype distribution) to covalent (non-spherical p,d
. . . distribution). This interpretation is especially
useful for simple single valence electron systems,
like SrNH2 .
Table 4
Structures for SrNH2 and CaNH2
Molecule
rN±H
(A)
rM±N
(A)
hH±N±H
(degrees)
Ref.
SrNH2
1.021
1.041a
1.018
2.256
2.247
2.126
105.4
100.0
105.8
This work
[12]
[16]
CaNH2
a
Fixed bond length.
Table 5
Normalized spin±rotation constants for strontium radicals
Molecule
Ground state
c=B
1=2…ebb ‡ ecc †=B
1=2…ebb =B ‡ ecc =C†
Ref.
SrF
SrOH
SrNH2
SrCCH
SrCH3
SrH
2
0.010
0.010
)
0.020
)
0.034
)
)
)
)
0.021
)
)
)
0.011
)
)
)
[27]
[28]
This work
[30]
[8]
[29]
R
R
2
A1
2
R
2
A1
2
R
2
382
J.M. Thompsen et al. / Chemical Physics Letters 330 (2000) 373±382
A list of normalized spin±rotation constants for
simple strontium-containing radicals is presented
in Table 5. The molecules involved have either
2
R or 2 A ground electronic states, and hence there
is a direct comparison. Also, it should be noted
that ebb and ecc are the important spin±rotation
components for symmetric and asymmetric tops,
since the second-order spin±orbit coupling occurs
through the L^x operator. The species in Table 5
range from very ionic species (SrF, SrOH) to a
primarily covalent one (SrH). The normalized
spin±rotation parameters have values of 0.010 for
SrF [27] and SrOH [28] while that of SrH is larger:
0.034 [29]. Those of SrCH3 [8] and SrCCH [30] fall
in between, about 0.02. Curiously, the normalized
constant for SrNH is 0.011 ± very close to that of
SrF and SrOH. A similar trend has been found for
CaNH2 in comparison with other calcium radicals
[16]. Consequently, the nature of the orbital of the
unpaired electron in SrNH2 is very close to that of
the hydroxide and the ¯uoride, and the Sr‡ NHÿ
2
con®guration is probably a very good approximation of the structure of this radical.
Acknowledgements
This research is supported by NSF Grant CHE98-17707.
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