JOURNAL OF CHEMICAL PHYSICS
VOLUME 113, NUMBER 8
22 AUGUST 2000
The pure rotational spectrum of CaNH2 and CaND2 „ X̃ 2 A 1 …:
Additional proof of planarity
M. A. Brewster and L. M. Ziurysa)
Department of Chemistry, Department of Astronomy, and Steward Observatory, 933 North Cherry Avenue,
Tucson, Arizona 85721
共Received 8 February 2000; accepted 22 May 2000兲
The pure rotational spectrum of CaNH2 in its X̃ 2 A 1 ground electronic state has been recorded using
millimeter/submillimeter direct absorption methods in the frequency range 320–537 GHz as well as
that of CaND2. The species were created by Broida-oven techniques. Eleven rotational transitions
were observed arising from the v ⫽0 and v 6 ⫽1 states of CaNH2, and eight transitions were
recorded for the v 3 ⫽1 and v 4 ⫽1 levels. For CaND2, eight transitions ( v ⫽0) were also measured.
For the majority of these transitions, K a doublets corresponding to K a ⫽0 – 5 were observed and fine
structure splittings were resolved in every component. These spectra were analyzed using an
S-reduced Hamiltonian; rotational, centrifugal distortion, and spin–rotation parameters were
determined for CaNH2, CaND2, and the three observed vibrationally excited states. An r 0 structure
has also been calculated. The data are consistent with calcium amide being a planar molecule with
C 2 v symmetry and having predominately ionic bonding, as indicated by previous optical studies.
© 2000 American Institute of Physics. 关S0021-9606共00兲00432-3兴
I. INTRODUCTION
tional transitions of CaNH2, SrNH2, and BaNH2 using laserinduced fluorescence 共LIF兲.17,18 These studies were subsequently followed by additional LIF measurements of CaNH2
and SrNH2 by Bernath and co-workers,19 who observed the
Ã→X̃ and B̃→X̃ transitions. Higher resolution electronic
spectroscopy of CaNH2 was then carried out by Whitham
and collaborators,20,21 Marr et al.,22 and, more recently,
Morbi and co-workers.23,24 These studies produced high
resolution analyses of the C̃ – X̃, B̃ – X̃, and à – X̃ systems of
CaNH2, including the determination of rotational and fine
structure constants of the ground state. Such measurements
indicated that the alkaline earth amides were planar with C 2 v
symmetry. Up to the present time, however, pure rotational
spectroscopy had not been conducted for any metal amide
species.
In this paper we present the measurement of the pure
rotational spectrum of CaNH2 in its 2 A 1 ground electronic
state, using submillimeter-wave direct absorption techniques.
Eleven rotational transitions of this free radical were recorded in its v ⫽0 state, including K a components as high as
K a ⫽7, as well as numerous lines arising from the v 4 ⫽1
state, the out-of-plane puckering motion, and the v 3 and v 6
modes. The pure rotational spectrum of CaND2 was also obtained in its ground vibrational and electronic state. No evidence of inversion was found for either molecule. These data
were analyzed using the S-reduced asymmetric top Hamiltonian and rotational, centrifugal distortion, and fine structure constants were accurately determined for CaNH2 and
CaND2. An r 0 structure has been obtained as well. Here we
present our data and its analysis, as well as an interpretation
of our findings in terms of the bonding in metal amide species.
Small, metal-containing molecules offer a unique opportunity to examine the competition between ionic and covalent bonding. Because of the generally low ionization potentials of most metals, their bonds to other elements are likely
to be ionic to a first approximation. Indeed, the properties of
many metal halide species such as CaF can be explained in
the context of ionic models, such as a ligand field approach,1
or using electrostatic polarization effects.2 However, for
some of the metals in the earlier rows of the periodic table,
strictly ionic bonding may not be able to account for molecular properties. This situation is certainly observed in the
metal monohydroxide and monocyanide molecules. The
heavier monohydroxide species such as RbOH, CsOH,
BaOH, and SrOH have strongly bound, linear structures,3–6
while large amplitude motions and quasilinear behavior are
found for KOH, NaOH, and MgOH.7–10 CuOH and AgOH
are bent with angles near 108°–110°,11 similar to covalent
H2O. An analogous trend is found in the cyanides. Here the
ionically favored structure is a T shape, as found in NaCN12
and KCN,13 where the M⫹ cation is thought to ‘‘orbit’’ the
CN⫺ anion. As covalent forces become comparable, the cyanides take on the linear, isocyanide form, observed in
MgNC14 and LiNC.15
Another interesting class of molecules where the competition between bonding types is reflected in their geometries
are metal amide species of the general formula MNH2. The
covalently bonded amide is likely to have a structure similar
to NH3, i.e., a pyramidal shape, while the ionic compounds
16
M⫹NH⫺
2 , will be planar with C 2 v symmetry. Such species
were first discovered by the Harris group, who detected opa兲
Electronic mail: [email protected]
0021-9606/2000/113(8)/3141/9/$17.00
3141
© 2000 American Institute of Physics
3142
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
II. EXPERIMENT
The data were recorded using one of the millimeter/
submillimeter direct absorption spectrometers of the Ziurys
group. The details of the construction of this spectrometer
are given elsewhere25 and will only be briefly outlined here.
The instrument consists of a phase-locked Gunn oscillator/
Schottky diode multiplier as the source of radiation, an
evacuated reaction chamber that incorporates a Broida-type
oven as a source of metal vapor, and a liquid helium-cooled
InSb bolometer as the detector. The radiation is modulated at
25 kHz to achieve phase-sensitive detection and is propagated quasioptically through the cell using a scalar feedhorn,
a polarizing grid, and a series of Teflon™ lenses. After transmission through this double-pass system the resultant radiation is recorded at 2 f , thus obtaining second derivative spectra.
The CaNH2 radical was produced by reaction of the
metal vapor with a mixture of NH3 and argon in a gas glow
discharge. The calcium vapor was generated in a Broida-type
oven, and entrained in a mixture of NH3 and argon introduced through the bottom of the oven in such a fashion as to
achieve a partial pressure of 12–15 mTorr of NH3 and 25–30
mTorr argon in the gas cell. The dc discharge was then applied from a cathode placed above the grounded oven. Depending upon the type of electrode used and the details of the
vaporizing source in the oven, a voltage range of 20–50 V
was found to result in optimum discharge conditions at a
corresponding current of 400–800 mA. It was not critical
that any particular voltage be used to produce the radical, but
rather that a rich lavender aura of atomic emission emanated
from the calcium within the crucible. CaND2 was produced
by an identical method using ND3 instead of NH3.
Transition frequencies were measured for 165 lines of
CaNH2 ( v ⫽0), 98 lines of its v 4 ⫽1 state, 114 lines of its
v 6 ⫽1 state, 58 lines of its v 3 ⫽1 state, and 142 lines of
CaND2 in the frequency range of 322–535 GHz. All measurements were made from an average of an even number of
5 MHz scans, half of which are taken in increasing frequency
and the other half in decreasing frequency. Most of these
observations required only two such scans, but weak signals,
especially the v 3 ⫽1 vibrationally excited state, required
more extensive signal averaging. Typical line widths were
800–1500 kHz over the entire frequency range.
III. RESULTS
Table I contains a subset of the data obtained for calcium
amide and its deuterium isotopomer. CaNH2 is most likely
planar with C 2 v symmetry, as will be discussed later on, and
therefore should have a 2 A 1 ground electronic state. In this
case the species is a near prolate asymmetric rotor, and the
quantum numbers which label each transition are N, K a , K c ,
and J. N designates the total angular momentum, and J indicates the spin–rotation interaction, where J⫽N⫹S. Unlike
the case of the symmetric top, however, the projection of N
onto the symmetry axis, K, is no longer a constant of the
motion. The ⫾K degeneracy present in symmetric rotors is
lifted and indices corresponding to the limiting prolate (K a )
and oblate (K c ) cases are used to label these energy levels.
M. A. Brewster and L. M. Ziurys
Moreover, for a planar, C 2 v species, the dipole moment lies
only along the symmetry axis 共in this case the â axis兲, which
means that all electric-dipole allowed transitions are a type.
Hence, as shown in Table I, only a-type transitions were
measured, meaning ⌬K a ⫽0 and ⌬K c ⫽⫾1 for ⌬N⫽⫾1
and ⌬J⫽⫾1. 共This fact is additional evidence for planarity.兲
Moreover, a general property of this notation is that K a
⫹K c ⫽N or N⫹1 and considering the above selection rules,
the K a components with K a ⫹K c ⫽N lie higher in frequency
than those with K a ⫹K c ⫽N⫹1 for a particular N.
A total of 11 rotational transitions were measured for
CaNH2 in both its v ⫽0 state and v 6 ⫽1 mode, the asymmetric (B 2 ) stretch. Individual spin–rotation doublets per K a
component were measured in each transition usually for the
K a ⫽0, 1, 2, and 3 and sometimes the K a ⫽4, 5, 6, and 7
lines, as illustrated in Table I. 共The K a ⫽1, 2, and 3 components are split as well due to asymmetry doubling, but usually these doublets are more widely separated兲. Eight transitions were additionally measured for the v 3 ⫽1 state, a
symmetric (A 1 ) stretch, and the same number for the v 4
⫽1 out-of-plane puckering motion. Again, in each transition,
components for K a ⫽0 – 5 were usually observed for these
two vibrationally excited states, all which were split into
spin–rotation doublets. Finally, eight transitions of CaND2
were recorded, for K a ⫽0 up to as high as K a ⫽7. The average spin–rotation splitting was found to be on the order of
32–39 MHz.
The transition frequencies of both molecules and all excited vibrational states were assigned using the same algorithm. For CaNH2, a range of 460–490 GHz was initially
scanned in 100 MHz increments and the frequency of all
absorptions were recorded. For CaND2 this starting range
consisted of two blocks: 467–474 and 451–458 GHz. Harmonically related spin–rotation doublets were then fit to an
effective B, D, and ␥ and additional transitions searched for,
which were incorporated into the fit. Rotational quantum
numbers were readily assigned on the basis of the optically
derived constants,22,23 as well as the magnitude of the spin–
rotation splittings. Each set of lines fit to an effective B, D,
and ␥ corresponded to a K a component. Finally, considering
differences in line intensities arising from ortho/para spin
statistics, tentative K a , K c assignments were made and a
⫾K
relationship was looked for among the B eff’s. Defining B eff a
as the effective B for the upper (⫹)K a or lower (⫺)K a
components, the following approximate relationship was
0
⫹1
⫺1
⫺(Beff
⫹Beff
)/2
then used for the assignments, namely B eff
⫹1
⫺1
⫹2
⫺2
⫹2
⫺2
⫹3
⫽(B eff ⫹Beff )/6⫺(B eff ⫹Beff )/6⫽(B eff ⫹Beff )/10⫺(B eff
⫺3
⫹Beff
)/10, and so on. This relationship is the same 1:3:5
ratio exhibited by the K structure of a prolate symmetric
rotor. In this case, we have compensated for the lifting of the
K degeneracy by averaging the effective rotational constants
of the K a doublets. In addition to the fine structure, magnetic
hyperfine and electric quadrupole interactions are also possible as both the 14N(I⫽1) and 1H(I⫽1/2) atoms have
nuclear spins. Due to the large values of N in the spectra,
such interactions were small enough to not be resolved.
Other tools used in the assignments were overall intensities and spin statistics. The lines that were most intense
were assigned to the ground ( v ⫽0) state, which has spin
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
Rotational spectrum of CaNH2
3143
TABLE I. Selected transition frequencies for CaNH2 and CaND2 (X̃ 2 A 1 ). a
CaNH2
v ⫽0
Transition
N ⬙ (K a⬙ ,K c⬙ )J ⬙
N ⬘ (K a⬘ ,K c⬘ )J ⬘
23共1,
23共1,
23共5,
23共5,
23共5,
23共5,
23共4,
23共4,
23共4,
23共4,
23共3,
23共3,
23共3,
23共3,
23共2,
23共2,
23共0,
23共0,
23共2,
23共2,
23共1,
23共1,
27共7,
27共7,
27共7,
27共7,
27共1,
27共1,
27共5,
27共5,
27共5,
27共5,
27共4,
27共4,
27共4,
27共4,
27共3,
27共3,
27共3,
27共3,
27共2,
27共2,
27共0,
27共0,
27共2,
27共2,
27共1,
27共1,
29共1,
29共1,
29共5,
29共5,
29共5,
29共5,
29共3,
29共3,
29共3,
29共3,
29共0,
29共0,
29共1,
24共1,
24共1,
24共5,
24共5,
24共5,
24共5,
24共4,
24共4,
24共4,
24共4,
24共3,
24共3,
24共3,
24共3,
24共2,
24共2,
24共0,
24共0,
24共2,
24共2,
24共1,
24共1,
28共7,
28共7,
28共7,
28共7,
28共1,
28共1,
28共5,
28共5,
28共5,
28共5,
28共4,
28共4,
28共4,
28共4,
28共3,
28共3,
28共3,
28共3,
28共2,
28共2,
28共0,
28共0,
28共2,
28共2,
28共1,
28共1,
30共1,
30共1,
30共5,
30共5,
30共5,
30共5,
30共3,
30共3,
30共3,
30共3,
30共0,
30共0,
30共1,
23兲
23兲
18兲
19兲
18兲
19兲
19兲
20兲
19兲
20兲
21兲
20兲
21兲
20兲
22兲
22兲
23兲
23兲
21兲
21兲
22兲
22兲
20兲
21兲
20兲
21兲
27兲
27兲
22兲
23兲
22兲
23兲
23兲
24兲
23兲
24兲
25兲
24兲
25兲
24兲
26兲
26兲
27兲
27兲
25兲
25兲
26兲
26兲
29兲
29兲
24兲
25兲
24兲
25兲
27兲
26兲
27兲
26兲
29兲
29兲
28兲
22.5
23.5
22.5
22.5
23.5
23.5
22.5
22.5
23.5
23.5
22.5
22.5
23.5
23.5
22.5
23.5
22.5
23.5
22.5
23.5
22.5
23.5
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
26.5
27.5
27.5
26.5
27.5
26.5
27.5
26.5
27.5
26.5
27.5
28.5
29.5
28.5
28.5
29.5
29.5
28.5
28.5
29.5
29.5
28.5
29.5
28.5
24兲
24兲
19兲
20兲
19兲
20兲
20兲
21兲
20兲
21兲
22兲
21兲
22兲
21兲
23兲
23兲
24兲
24兲
22兲
22兲
23兲
23兲
21兲
22兲
21兲
22兲
28兲
28兲
23兲
24兲
23兲
24兲
24兲
25兲
24兲
25兲
26兲
25兲
26兲
25兲
27兲
27兲
28兲
28兲
26兲
26兲
27兲
27兲
30兲
30兲
25兲
26兲
25兲
26兲
28兲
27兲
28兲
27兲
30兲
30兲
29兲
23.5
24.5
23.5
23.5
24.5
24.5
23.5
23.5
24.5
24.5
23.5
23.5
24.5
24.5
23.5
24.5
23.5
24.5
23.5
24.5
23.5
24.5
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
27.5
28.5
28.5
27.5
28.5
27.5
28.5
27.5
28.5
27.5
28.5
29.5
30.5
29.5
29.5
30.5
30.5
29.5
29.5
30.5
30.5
29.5
30.5
29.5
CaND2
v 3 ⫽1
v 4 ⫽1
v 6 ⫽1
v obs
v o⫺c
v obs
v o⫺c
v obs
v o⫺c
423 568.487
423 607.455
423 967.803
423 967.803
424 003.796
424 003.796
424 927.080
424 927.080
424 963.201
424 963.201
425 621.273
425 622.957
425 657.665
425 659.217
426 023.097
426 059.693
426 182.100
426 219.306
426 240.169
426 276.136
428 963.680
428 998.121
490 671.053
490 671.053
490 706.401
490 706.401
493 910.017
493 949.044
494 421.031
494 421.031
494 457.036
494 457.036
495 531.136
495 531.136
495 567.299
495 567.299
496 338.803
496 342.014
496 375.061
496 378.290
496 778.103
496 814.694
496 878.375
496 915.736
497 121.575
497 157.562
500 186.995
500 221.507
529 037.563
529 076.632
529 611.725
529 611.725
529 647.703
529 647.703
531 659.643
531 664.276
531 695.995
531 700.563
532 169.870
532 207.312
535 752.388
0.009
0.013
0.007
0.007
0.056
0.056
⫺0.074
⫺0.070
⫺0.105
⫺0.101
⫺0.100
0.075
⫺0.003
0.047
0.020
0.033
⫺0.061
⫺0.016
0.066
0.024
0.003
⫺0.003
0.021
0.021
⫺0.040
⫺0.040
0.021
0.034
⫺0.036
⫺0.036
0.008
0.008
0.093
0.106
0.102
0.114
0.030
⫺0.023
0.007
⫺0.015
⫺0.020
⫺0.051
0.039
0.035
⫺0.172
⫺0.028
0.014
0.024
⫺0.012
0.017
⫺0.060
⫺0.060
⫺0.031
⫺0.031
⫺0.071
⫺0.048
0.015
⫺0.010
0.029
⫺0.007
0.017
427 835.328
427 872.632
0.023
⫺0.016
423 299.049
423 338.169
⫺0.058
0.018
424 849.606
424 849.606
424 886.182
424 886.182
430 776.420
430 781.401
430 811.688
430 816.632
498 875.253
498 912.635
502 373.395
502 384.160
502 408.661
502 419.467
507 214.122
507 247.826
v obs
v o⫺c
⫺0.038
⫺0.034
0.029
0.032
428 216.097
428 216.097
428 251.811
428 251.811
⫺0.014
⫺0.006
0.013
0.021
425 441.575
425 478.301
425 604.249
425 641.519
425 596.643
425 632.951
428 007.746
428 042.632
0.022
⫺0.040
⫺0.044
0.047
0.089
0.001
⫺0.164
0.029
429 230.464
429 266.374
429 330.311
429 366.800
429 564.266
429 599.495
⫺0.033
⫺0.043
0.008
⫺0.006
⫺0.015
⫺0.036
493 600.479
493 639.608
⫺0.034
0.014
495 416.685
495 416.685
495 453.226
495 453.226
0.014
0.024
⫺0.011
⫺0.001
496 109.688
496 146.428
496 232.308
496 269.644
496 354.948
496 390.988
499 080.370
499 115.279
528 708.775
528 747.973
⫺0.071
⫺0.160
⫺0.018
⫺0.001
0.062
⫺0.194
⫺0.038
0.137
⫺0.054
0.043
499 341.663
499 341.663
499 377.441
499 377.441
500 096.467
500 102.862
500 132.063
500 138.428
500 499.010
500 534.938
500 491.271
500 527.993
501 026.536
501 601.625
⫺0.057
⫺0.033
0.023
0.047
0.059
0.077
⫺0.032
⫺0.024
0.021
⫺0.018
0.007
⫺0.011
⫺0.021
0.007
531 494.257
531 531.806
534 571.750
⫺0.081
0.071
⫺0.117
0.021
0.006
0.007
⫺0.032
⫺0.027
⫺0.044
⫺0.015
⫺0.050
⫺0.002
0.030
0.030
⫺0.023
v ⫽0
536 005.608
536 042.479
⫺0.037
⫺0.036
v obs
v o⫺c
427 042.946
427 074.865
426 070.079
426 103.489
428 489.442
428 519.664
⫺0.037
⫺0.088
⫺0.052
⫺0.062
⫺0.063
⫺0.024
452 682.928
452 716.958
⫺0.016
0.026
456 186.229
456 219.952
462 226.370
⫺0.026
0.046
⫺0.011
3144
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
M. A. Brewster and L. M. Ziurys
TABLE I. 共Continued.兲
CaNH2
v ⫽0
Transition
N ⬙ (K a⬙ ,K c⬙ )J ⬙
N ⬘ (K a⬘ ,K c⬘ )J ⬘
29共1,
29共2,
29共2,
29共4,
29共4,
29共2,
29共2,
29共4,
29共4,
29共6,
29共6,
29共6,
29共6,
29共7,
29共7,
29共7,
29共7,
30共1,
30共2,
30共2,
30共4,
30共4,
30共2,
30共2,
30共4,
30共4,
30共6,
30共6,
30共6,
30共6,
30共7,
30共7,
30共7,
30共7,
a
28兲
27兲
28兲
25兲
26兲
27兲
28兲
25兲
26兲
23兲
24兲
24兲
23兲
22兲
23兲
22兲
23兲
29.5
28.5
28.5
28.5
28.5
29.5
29.5
29.5
29.5
28.5
28.5
29.5
29.5
28.5
28.5
29.5
29.5
29兲
28兲
29兲
26兲
27兲
28兲
29兲
26兲
27兲
24兲
25兲
25兲
24兲
23兲
24兲
23兲
24兲
30.5
29.5
29.5
29.5
29.5
30.5
30.5
30.5
30.5
29.5
29.5
30.5
30.5
29.5
29.5
30.5
30.5
v 3 ⫽1
v obs
v o⫺c
535 786.948
0.044
v obs
v o⫺c
CaND2
v 4 ⫽1
v 6 ⫽1
v ⫽0
v obs
v o⫺c
v obs
v o⫺c
534 606.696
531 704.131
531 403.465
530 659.461
530 659.461
531 740.213
531 440.165
530 695.844
530 695.844
0.073
0.178
0.260
0.034
0.050
0.024
0.113
⫺0.167
⫺0.150
536 734.172
536 087.199
534 862.203
534 862.203
536 769.150
536 123.197
534 897.984
534 897.984
0.023
0.012
⫺0.088
⫺0.048
0.045
0.018
⫺0.005
0.035
v obs
v o⫺c
462 256.737
459 178.142
457 413.133
⫺0.013
0.000
0.012
459 208.113
457 445.121
⫺0.019
⫺0.007
455 279.575
455 279.575
455 311.183
455 311.183
454 164.624
454 164.624
454 196.418
454 196.418
0.053
0.053
⫺0.057
⫺0.057
0.028
0.028
0.033
0.033
In megahertz. For the complete data set see Ref. 44.
statistics characteristic of A 1 symmetry. For molecules with
C 2 v geometry, particle exchange of fermions 共which applies
to protons in this case兲, results in the odd K a components
being favored statistically over even K a lines by a factor of
3:1, provided the vibrational wave function is symmetric.
The spectra assigned to the ground state had in fact stronger
odd K a lines relative to nearby even ones by about a factor of
3, as expected. The three sets of weaker lines recorded were
then attributed to vibrationally excited states. According to
optical experiments,16 the three modes lying lowest in energy
are the v 6 antisymmetric N–H bend, the v 4 puckering motion, and the v 3 Ca–N symmetric stretch, which lie approximately 320, 347, and 520 cm⫺1 above the v ⫽0 level. The
weakest lines of the three sets had K a intensities identical to
the ground state, and hence could be confidently assigned to
the v 3 symmetric stretch. The other two progressions had
spin statistics opposite to that of the ground state, namely,
the even K a lines were a factor of 3 stronger than odd K a
lines. Therefore, they had to arise from asymmetric vibrational states such as the v 4 (B 1 ) and v 6 (B 2 ) modes. The
intensity of one pattern was slightly greater than the other,
and it was identified as arising from the v 6 state, which lies
somewhat lower in energy than v 4 . However, there is some
ambiguity in this assignment, as the intensity difference between the spectra was small. On the other hand, the constants
for the lines assigned to the v 4 state are closest in value to
those of the ground state, which might be expected of the
puckering motion rather than the asymmetric stretch. Moreover, our v 4 and v 6 assignments follow the pattern found in
H2CO.
Another possible interpretation of the CaNH2 spectrum
is for the ground state to be undergoing inversion. A molecule that possesses an average structure that is orthorhombic, but has achieved such a configuration by inversion, also
will exhibit the same statistical weighting as observed in the
v ⫽0 state. The spin statistics observed in optical spectra
could be interpreted as planarity or possible inversion.20,22
共In the lower resolution spectra the two inversion states
could be blended兲. Moreover, the proton statistics in the upper inversion state are identical to that in the v 4 mode.
Hence, the spectra identified as arising from the v 4 state
could be actually coming from the upper inversion level.
Indeed, the rotational constants for the v ⫽0 and the proposed v 4 states are quite similar, as expected for two inversion levels.26,27 For example, B varies by 28 MHz and C by
1 MHz between the two sets of spectra. On the other hand,
inversion levels are usually close in energy and hence one
would expect quite similar line intensities. In this case, the
ground state spectra were about a factor of 2.5 stronger than
those of the other state. Furthermore, molecules undergoing
inversion develop a small but non-negligible c-type dipole
moment and hence exhibit c-type transitions. Such transitions have been readily detected for such inverting molecules
as NH2CN and NH2NC. 26,27 In contrast, no obvious c-type
lines were observed in the spectra of CaNH2. Overall, the
evidence supports a planar, C 2 v geometry for calcium amide.
For CaND2, the proton spin statistics change again. Substituting bosons (D:I⫽1) for fermions (H:I⫽1/2) alters the
weighting scheme to 3:6, odd K a to even K a . This pattern
was observed in the spectra of CaND2. Also, deuterium substitution created a heavier molecule. K a components up to
K a ⫽8 were observed in this species, although only lines
through K a ⫽7 were included in the fit. For CaNH2, only
components with K a as large as 5 were recorded, with the
exception of a few K a ⫽7 lines. The K a ⫽6 features were
usually too weak to be measured.
The complexity of the CaNH2 spectrum is illustrated in
Fig. 1, which is a stick diagram of the N⫽25→26 rotational
transitions covering 458–469 GHz. The heights of the stick
figures show the approximate relative intensities of the various spectral features. Spin–rotation splittings are neglected.
The lines assigned to the v ⫽0 state clearly dominate the
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
FIG. 1. A stick spectrum of the N⫽25→26 rotational transition of CaNH2
(X̃ 2 A 1 ) showing the lines observed over a 10 GHz region and their approximate relative intensities, as a function of vibrational and K a quantum number. The transitions originating in the ground vibrational state ( v ⫽0) are
clearly the strongest, with spin statistics favoring the odd K a lines over the
even K a components. The v 3 ⫽1 satellite lines, which arise from the Ca–N
stretch, are the weakest, with identical spin statistics as the ground state.
Features with intermediate intensities are attributed to the v 4 ⫽1 out-ofplane puckering motion and the v 6 ⫽1 asymmetric bend. Both these states
exhibit opposite spin statistics from the ground state.
spectrum, especially for odd K a transitions. Features assigned to the v 4 and v 6 modes are clearly weaker, with even
K a transitions being stronger in this case. Finally, the v 3
spectral lines have the lowest intensity.
Representative spectra of CaNH2 are shown in Figs. 2
and 3. Figure 2 presents spectra of the N⫽26→27 rotational
Rotational spectrum of CaNH2
3145
FIG. 3. Vibrational satellite spectra arising from the N⫽26→27 transition
of the v 6 ⫽1 state of CaNH2 near 483 GHz. Again the K a ⫽0, 2 ⫹ , 2 ⫺ , 3 ⫹
and 3 ⫺ components are visible in the spectrum, as well as one of the K a
⫽1 components of the v ⫽0 state. The spin–rotation doublets are clearly
resolved for each K a component, and the even K a lines are stronger than the
odd K a features. The spectrum covers over 1 GHz in frequency and is a
composite of ten scans, each 100 MHz in coverage and about 1 min in
duration.
transition of the ground vibrational state near 479 GHz. Only
the K a ⫽0, 2 ⫹ , 2 ⫺ , 3 ⫹ , and 3 ⫺ components are present in
this spectrum, which covers about 800 MHz. The spin–
rotation doublets are resolved in every K a component. While
the two K a ⫽2 transitions 关N(K a ,K c )⫽26(2,25) – 27(2,26)
and 26共2, 24兲–27共2, 25兲兴 are substantially separated in frequency, the K a ⫽3 transitions 关26共3, 24兲–27共3, 25兲 and 26共3,
23兲–27共3, 24兲兴 are virtually collapsed. The K a ⫽3 components are also clearly the strongest. Additionally present in
this spectrum is a very weak line corresponding to the 26共1,
26兲–27共1, 27兲 transition of the v 6 ⫽1 state of CaNH2.
In Fig. 3, several lines arising from the N⫽26→27 transition of CaNH2 in its v 6 ⫽1 state are presented near 482
GHz. In contrast to the v ⫽0 spectrum, here the even K a
lines 共K a ⫽0, and 2兲 are stronger than the odd K a features
(K a ⫽3). Again, the spin–rotation splittings are resolved in
every component. A doublet arising from the 26共1, 25兲–
27共1, 26兲 transition in the ground state is also visible in this
spectrum, which covers 1 GHz in frequency. The intensity of
this line relative to the v 6 features is considerably larger.
IV. ANALYSIS
FIG. 2. Spectra arising from the N⫽26→27 transition in the ground vibrational state of CaNH2 near 479 GHz. The quantum number labeling is N
(K a ,K c ). The K a ⫽0, 2 ⫹ , 2 ⫺ , 3 ⫹ and 3 ⫺ components of this transition are
shown, as well as one K a ⫽1 component of the v 6 ⫽1 state. Each component is split into doublets as a result of fine structure interactions, and the
K a ⫽3 lines are about a factor of 3 stronger in intensity than the other
components, as predicted by spin statistics for C 2 v symmetry species. This
spectrum is a composite created from eight separate 100 MHz scans, each
⬃1 min in duration.
Since CaNH2 is a near prolate asymmetric rotor, an appropriately modified S-reduced Hamiltonian of Watson28 in
the I r basis was used to model the spectra. This extended
Hamiltonian accounts for rotation, its centrifugal distortion
correction, electron spin–rotation interaction, and in one
case, centrifugal distortion correction to the spin–rotation
coupling, and can be expressed as
H eff⫽H rot⫹H cd⫹H sr⫹H srcd .
共1兲
Watson’s S-reduced Hamiltonian plus several additional
higher order terms was used for the H rot⫹H cd contribution,
which has the general form
3146
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
M. A. Brewster and L. M. Ziurys
TABLE II. Rotational constants of CaNH2 and CaND2. a
CaND2
CaNH2
a
Constant
v ⫽0
v 6 ⫽1
v 3 ⫽1
v 4 ⫽1
v ⫽0
A
B
C
⑀ aa
⑀ bb
⑀ cc
S
⌬ NK
DN
D NK
d1
d2
h1
h2
h3
HN
H NK
H KN
L NNK
L NK
L KKN
P NNK
P NKK
P KN
392 127共89兲
9009.0649共47兲
8782.7559共49兲
45.7共1.8兲
32.063共99兲
41.110共96兲
⫺5.1(1.4)⫻10⫺6
0.010 383 3共14兲
1.874 04共78兲
⫺0.000 335 0共15兲
⫺0.000 112 1共23兲
¯
3.3(2.1)⫻10⫺9
7.8(2.9)⫻10⫺10
¯
3.917(48)⫻10⫺5
⫺0.006 701共75兲
¯
⫺9.4(3.5)⫻10⫺8
⫺5.28(26)⫻10⫺5
⫺6.27(73)⫻10⫺11
2.012(45)⫻10⫺8
⫺1.637(31)⫻10⫺6
360 362共204兲
9098.572共10兲
8830.5110共94兲
39.5共1.9兲
31.73共13兲
39.94共13兲
¯
0.010 871 6共84兲
2.1677共17兲
⫺0.000 543 1共32兲
⫺0.000 144 1共27兲
¯
6.6(1.8)⫻10⫺9
¯
9.3(4.6)⫻10⫺9
1.97(16)⫻10⫺5
0.020 19共42兲
¯
⫺1.14(12)⫻10⫺6
⫺5.06(28)⫻10⫺4
⫺3.42(36)⫻10⫺10
¯
1.010(45)⫻10 ⫺5
354 053共1431兲
9154.777共50兲
8854.055共49兲
34.1共2.8兲
31.68共13兲
39.01共12兲
¯
0.009 872共29兲
2.410共44兲
⫺0.000 304共24兲
0.000 088共17兲
⫺8.5(1.2)⫻10⫺8
¯
⫺7.77(57)⫻10⫺9
⫺1.54(14)⫻10⫺7
9.63(81)⫻10⫺5
0.0755共96兲
⫺1.30(38)⫻10⫺8
¯
⫺0.006 11共60兲
¯
¯
¯
479 141共1509兲
8981.1407共92兲
8783.7724共86兲
45.7共2.1兲
32.43共13兲
41.14共13兲
¯
0.010 727 3共71兲
1.4242共71兲
⫺0.000 263 3共26兲
0.000 122 8共49兲
¯
⫺6.3(2.2)⫻10⫺9
¯
¯
2.839(35)⫻10⫺4
⫺0.0906共20兲
4.51(53)⫻10⫺9
⫺0.000 018 07共18兲
6.618(99)⫻10⫺3
¯
¯
¯
195 668.8共6.6兲
7807.6329共74兲
7484.6850共64兲
22.5共2.3兲
27.886共88兲
35.376共76兲
⫺2.24(80)⫻10⫺6
0.007 053 6共12兲
1.251 64共43兲
⫺0.000 396 2共15兲
⫺0.000 192 6共18兲
¯
5.8(1.1)⫻10⫺9
1.76(15)⫻10⫺9
¯
2.520(15)⫻10⫺5
⫺0.002 130共29兲
¯
1.93(12)⫻10⫺7
⫺2.80(83)⫻10⫺6
⫺2.82(37)⫻10⫺11
¯
⫺1.015共82兲⫻10⫺7
rms of fit
0.069
0.037
0.036
0.088
0.038
In megahertz; errors quoted are 3␴ and apply to the last quoted decimal place.
H rot⫹H cd⫽AN2x ⫹BN2y ⫹CNz2 ⫺D N 共 N2 兲 2 ⫺D NK N2 Nz2
2
2
4
4
⫹d 1 N2 共 N⫹
⫹N⫺
⫹N⫺
兲 ⫹d 2 共 N⫹
兲 ⫹H N 共 N2 兲 3
⫹H NK 共 N2 兲 2 Nz2 ⫹H KN N2 Nz4 ⫹L NK 共 N2 兲 2 Nz4
⫹L KKN N2 Nz6 ⫹L NNK 共 N2 兲 3 Nz2 ⫹ P NNK 共 N2 兲 3 Nz4
⫹ P NKK 共 N2 兲 2 Nz6 ⫹ P KN N2 Nz8 ,
共2兲
where N⫾ ⫽Nx ⫾iNy . Watson’s D K and H K parameters were
not employed because no transitions were recorded that depended on K a , K c alone. The one unpaired electron in
CaNH2 gives rise to fine structure doublets that are accounted for by the third term in Eq. 共1兲. Owing to the molecules’ orthorhombic symmetry, the only components of the
spin–rotation matrix that are nonzero are the diagonal terms
and are included in H eff as
H sr⫽1/2
兺␣ ⑀ ␣␣共 N␣ S␣ ⫹S␣ N␣ 兲 .
共3兲
In many cases it was found that inclusion of a centrifugal
distortion correction to the spin–rotation improved the fit.
The most significant form of this correction was found to be
S
H srcd⫽⌬ NK
共 N"S兲 N2 Nz2
terms including a minimal set of centrifugal distortion parameters, while fixing A to previously reported values of
Marr et al.22 Typically, D N and D NK were sufficient initially,
but d 1 and d 2 were used in some cases. After this crude fit
had been refined, subsequent K a components and higher order centrifugal distortion constants were included until the
total rms of the fit was below 100 kHz, the estimated experimental accuracy. During the addition of the higher order
terms, A was allowed to float in the fit. Higher order centrifugal distortion corrections outside of the set in Eq. 共2兲 were
necessary to model the highest K a doublets (h 1 ,h 2 ,h 3 ).
During the final stage of this process, the centrifugal distortion to the spin–rotation was included in the Hamiltonian
and refined to produce the constants presented in Table II. It
should be noted that collapsed K a doublets 共in particular,
K a ⫽4兲 were given as separate lines of input to the fitting
routine.
共4兲
and was the only correction retained in the final analysis.
The data were analyzed using the least-squares fitting
routine, SPFIT, developed by Pickett and co-workers at JPL.
To achieve a minimum set of parameters that accurately reproduced the data, it was found best to fit the K a ⫽0, 1, and
2 components only with the pure rotation and spin–rotation
V. DISCUSSION
One of the most interesting questions concerning metal
amide species is their geometry, which is a reflection of their
bonding. One test for a planar geometry concerns the inertial
defect. To a first approximation, a small, positive value for
this quantity, defined as ⌬⫽I c ⫺I a ⫺I b , indicates a planar
molecule. However, as discussed in a series of papers by Oka
and Morino,29,30 the interpretation of the inertial defect is not
always this simple. The inertial defect is composed of three
contributions: vibrational, electronic, and centrifugal distortion components, i.e.,
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
Rotational spectrum of CaNH2
TABLE III. Inertial defects of CaNH2 and related species.a
CaNH2
CaND2
NaNH2
SrNH2
H2CO
NH2CN
ND2CN
NH2NC
NH2CHO
ND2CHO
3147
TABLE IV. Structural parameters of CaNH2.
⌬0
⌬6
⌬4
⌬3
⌬ elec
Reference
0.157
0.210
0.079
0.177
0.0577
⫺0.285
⫺0.746
⫺0.756
0.008
⫺0.015
0.127
¯
¯
0.053
¯
¯
0.291
¯
¯
⫺0.000 15
⫺0.000 21
¯
This work
This work
34
33
31
26
26
27
31
31
r0
共millimeter
wave兲
r CaN (Å) 2.126 共3兲
r NH (Å) 1.018共3兲
␪ HNH
105.8° 共5兲
r 0 共optical兲a
Ab initiob
2.122 共6兲
2.13
¯
1.02
105.5–106.0 共4.6兲 105.6°
NH2c
NH⫺d
2
¯
¯
1.025 1.041共15兲
103.1° 102.1° 共3.1兲
a
Reference 22.
Reference 16.
c
Reference 36.
d
Reference 37.
b
a兲
In amu Å2.
⌬ 0 ⫽⌬ vib⫹⌬ elec⫹⌬ cent .
共5兲
These three contributions can add together for a given molecule in a way that the inertial defect is small, yet the species
is not planar. This effect is seen in formamide, for
example.31 The only certain way to access the meaning of
the inertial defect is to examine each of the three terms, and
establish whether there is some unusual cancellation in their
summation.
The inertial defect for CaNH2 was found to be ⌬ 0
⫽0.157, as shown in Table III. This value is relatively small
and positive. For CaND2, the inertial defect is ⌬ 0 ⫽0.210,
and hence there is no sign change with deuterium substitution. Several of the terms contributing to ⌬ 0 can be evaluated
for CaNH2. From the spin–rotation constants, the g tensor
can be calculated,29 which results in ⌬ elec⫽⫺0.000 15.
Hence, this contribution is not large and has not significantly
reduced the value of ⌬ 0 . Part of ⌬ vib can also be derived,
because rotational constants for the v 3 , v 4 , and v 6 modes
have been measured. These three vibrational states make a
contribution of 1/2(⌬ 3 ⫹⌬ 4 ⫹⌬ 6 )⫽0.236 共see Table III兲 to
⌬ vib . Because ⌬ cent is always small and positive,30 its contribution to ⌬ 0 is negligible; therefore, the major remaining
contribution is from the inertial defects of the v 1 , v 2 , and v 5
modes. We did not observe these states. Considering the
other numbers, 1/2(⌬ 1 ⫹⌬ 2 ⫹⌬ 5 ) must equal approximately
⫺0.079, which does not appear particularly unusual.
The inertial defect determined for CaNH2 is also comparable to what has been observed for other planar metal
amides, such as SrNH2, 32,33 and NaNH2, 34 which have ⌬ 0
⫽0.177 and ⌬ 0 ⫽0.079. In contrast, the inertial defects observed for similar pyramidal species that undergo inversion
are much larger and negative. As shown in Table III, ⌬ 0 for
cyanamide and its deuterium isotopomer are ⌬ 0 ⫽⫺0.285
and ⌬ 0 ⫽⫺0.746; the value for isocyanamide is ⌬ 0
⫽⫺0.756. Moreover, although the inertial defect is small
and positive for formamide 共0.008兲, it changes sign 共⫺0.015兲
on deuterium substitution of the NH2 group. The inertial defects for CaNH2 and CaND2 are thus consistent with a planar
geometry.
An r 0 structure for CaNH2 was calculated on the basis of
the rotational data and the results presented in Table IV. The
bonds lengths and H–N–H bond angle were established
from a nonlinear least-squares fit to the moment of inertia
equations,35 using the A, B, and C rotational constants of
CaNH2 and CaND2. The calculation results in r Ca–N
⫽2.126 Å and r N–H⫽1.018 Å, with ␪ H–N–H⫽105.8°. These
values are in excellent agreement with ab initio calculations,
which suggest r Ca–N⫽2.13 Å, r N–H⫽1.02 Å, and ␪ H–N–H
⫽105.6°, as well as estimates from the optical study of Marr
et al.22 At face value the N–H bond length and H–N–H
bond angle of CaNH2 are closer to those of the NH2 radical,
which has r N–H⫽1.025 Å and ␪ H–N–H⫽103.1°, 36 than those
of NH⫺
2 . This ion has a N–H bond distance of 1.041 共15兲 Å
and an H–N–H angle near 102.1° 共3.1兲.37 Such geometric
similarities suggest that CaNH2 has a large degree of covalent character, as opposed to only a Ca⫹ NH⫺
2 structure. Considering the uncertainties, however, the geometries of the
NH2 radical and NH⫺
2 are very similar, so a detailed comparison cannot be done.
The Ca–NH2 bond length can be compared with other
calcium–ligand bond distances. In Table V, these distances
are presented for CaCH3, 38 CaNH2, CaOH,39 and CaF.40 The
Ca–F and Ca–OH bond distances are quite similar 共1.955
and 1.985 Å兲, and scale approximately as the atomic radii.
The Ca–CH3 and Ca–NH2 bond lengths, on the other hand,
are appreciably longer 共2.326 and 2.126 Å兲. The lengthening
of the calcium–ligand bond in these cases does not scale as
atomic radii, and likely arises in both molecules from steric
hindrance induced by the hydrogen atoms, and/or a change
in bonding character.
Another insight into the bonding in CaNH2 can be
gained from examining the spin–rotation constants. Because
the main contribution to this parameter is second-order spin–
orbit coupling, the magnitude of the spin–rotation constant is
a reflection of the p, d, f,... character of the orbital of the
unpaired electron, when normalized by the rotational
constant.41 The second-order contribution to ␥, the spin–
rotation constant, can be expressed mathematically as
TABLE V. Calcium–ligand bond lengths.a
Species
CaCH3
CaNH2
CaOH
CaF
a
r Ca–L (Å)
b
2.326
2.126
1.985
1.955 共1.952兲c
From an r 0 structure unless stated otherwise.
Assumes r C–H⫽1.1 Å.
c
R e structure in parentheses.
b
Reference
38
This work
39
40
3148
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
M. A. Brewster and L. M. Ziurys
TABLE VI. Normalized spin–rotation constants for calcium radicals.
Species
Ground state
␥ /B
Reference
CaOH
CaF
CaNH2
CaCCH
CaCH3
CaH
⌺
⌺
2
A1
2
⌺
2
A
2
⌺
0.0035
0.0038
0.0041a
0.0064
0.0073b
0.010
39
40
This work
42
38
43
2
2
scheme. Comparison of the spin–rotation parameters determined in this work with other small calcium-bearing species
additionally suggests primarily ionic bonding. Other studies
are now in progress for metal amides to establish when, and
if, more covalent species of this type exist.
ACKNOWLEDGMENTS
This research is supported by NASA Grant No. NAGW
5-3785 and NSF Grant Nos. CHE-98-17707 and AST-9820576.
1
Actually 2 关 ⑀ bb /B⫹ ⑀ cc /C 兴 .
b
Actually ( ⑀ bb ⫹ ⑀ cc )/2B.
a
␥ /B⯝⫺2
⫻
2
兺
␣
具 ␣ 兩 Lx 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 aLx 兩 ␣ 典 ⫹ 具 ␣ 兩 aLx 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 Lx 兩 ␣ 典
E ␣ ⫺E ␣ ⬘
⬘
,
共6兲
where ␣ represents the ground electronic state and ␣⬘ indicates near-by excited states; a is the spin–orbit constant of
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1/2( ⑀ bb ⫹ ⑀ cc )/B, and for an asymmetric top,
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1
冊
1 ⑀ bb ⑀ cc
.
⫹
2 B
C
Clearly the value of the spin–rotation constant increases proportionally as the coupling between the ground and excited
states via the Lx operator.
Normalized spin–rotation constants for calcium-bearing
radicals in doublet electronic ground states are shown in
Table VI. The trend from ionic to covalent bonding is illustrated in the spin–rotation constants. The smallest values are
for the most ionic compounds, CaF and CaOH, with ␥ /B
⫽0.0038 and 0.0035. The species with the more covalent
bonds such as CaH have higher values near 0.01. The normalized spin–rotation parameter for CaNH2 is 0.0041—
closer to those determined for ionic molecules than covalent
species. 共An identical number is found for CaND2, as expected兲. Therefore, the spin–rotation constants suggest primarily ionic bonding in CaNH2, similar in degree to that
found in halides and hydroxides. This property is consistent
with the planar geometry, as well. In contrast, molecules like
CaCCH and CaCH3 appear to have larger normalized constants and greater covalent character.
VI. CONCLUSION
Analysis of the pure rotational spectrum of CaNH2 in its
ground vibrational and v 3 ⫽1, v 4 ⫽1, and v 6 ⫽1 excited
states indicates that this metal amide is planar with C 2 v symmetry, as suggested by previous optical studies. There is no
evidence in the spectra of an inverting molecule. Although
the inertial defect for CaNH2 of ⌬ 0 ⫽0.157 is not as small as
other planar species like H2CO, the value is consistent with
other planar metal amides, and does not change sign on deuterium substitution. Measurements of the deuterium isotopomer, CaND2, have allowed for an r 0 structure determination that is consistent with an Ca⫹NH⫺
2 -type bonding
J. Chem. Phys., Vol. 113, No. 8, 22 August 2000
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44
See EPAPS Document No. E-JCPSA6-113-004032 for a complete list of
measured transition frequencies for CaNH2 ( v ⫽0, v 3 ⫽1, v 4 ⫽1, v 6
⫽1) and CaND2 ( v ⫽0). This document may be retrieved via the EPAPS
homepage 共http://www.aip.org/pubservs/epaps.html兲 or from ftp.aip.org in
the directory /epaps/. See the EPAPS homepage for more information.
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43