Infrared and Raman spectra, conformational stability, structural parameters, ab initio calculations and vibrational assignments of aminodifluorophosphine

Article abstract of DOI:10.1016/j.molstruc.2007.04.045

Infrared spectra (4000-50 cm^-1) have been recorded for three isotopomers of aminodifluorophosphine, H₂NPF₂, H₂¹⁵NPF₂ and D₂NPF₂, of the gases. The Raman spectra of all three molecules were recorded of the liquids. To support the vibrational assignment MP2(full) ab initio calculations with the 6-31G(d) basis set were carried out to predict the fundamental vibrational frequencies, infrared intensities, Raman activities, depolarization values and infrared band contours. Additional ab initio calculations employing a variety of basis sets with and without diffuse functions have been used to predict the conformational stability, structural parameters and centrifugal distortion constants. These predictions are compared to previously reported experimental values when available. The adjusted r₀ structural parameters have been obtained by systematically fitting the MP2(full)/6-311+G(d) predicted values with the previously reported rotational constants for five isotopomers obtained from the microwave study. The difference in the two NH distances is 0.003 ? which is much smaller than the value of 0.021 ? previously reported. The bonding around the nitrogen atom is effectively planar which is consistent with the previously reported structural information from the microwave study but differs from the reported slightly pyramidal bonding obtained in the electron diffraction investigation. The adjusted r₀ heavy atom distances and angles are: r(PF) = 1.587(3); r(NP) = 1.649(3) ?; ∠FPF = 94.7(5); ∠NPF = 100.6(5)°. Vibrational assignments are given for H₂NPF₂, H₂¹⁵NPF₂ and D₂NPF₂ which are supported by ab initio MP2/6-31G(d) calculations. These results are compared to the corresponding quantities of some similar molecules.

Full text of DOI:10.1016/j.molstruc.2007.04.045

Available online at www.sciencedirect.com
Journal of Molecular Structure 875 (2008) 406–418
www.elsevier.com/locate/molstruc
Infrared and Raman spectra, conformational stability,
structural parameters, ab initio calculations and vibrational
assignments of aminodifluorophosphine
a,
c
d,2
James R. Durig *, Pamela Tschudin b,1, Kim C. Cohn , Bryan R. Durig
,
a
a
a
Xiaohua Zhou , Chao Zheng , Ahmed M. El Defrawy
a
Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110, USA
b
Department of Chemistry, Michigan State University, East Lansing, MI 48104, USA
Department of Chemistry, California State University Bakersfield, Bakersfield, CA 93309, USA
c
d
College of Engineering, University of South Carolina, Columbia, SC 29208, USA
Received 26 March 2007; accepted 28 April 2007
Available online 18 May 2007
Abstract
Infrared spectra (4000–50 cmꢀ1) have been recorded for three isotopomers of aminodifluorophosphine, H2NPF2, H215NPF2 and
D2NPF2, of the gases. The Raman spectra of all three molecules were recorded of the liquids. To support the vibrational assignment
MP2(full) ab initio calculations with the 6-31G(d) basis set were carried out to predict the fundamental vibrational frequencies, infrared
intensities, Raman activities, depolarization values and infrared band contours. Additional ab initio calculations employing a variety of
basis sets with and without diffuse functions have been used to predict the conformational stability, structural parameters and centrifugal
distortion constants. These predictions are compared to previously reported experimental values when available. The adjusted r0 struc-
tural parameters have been obtained by systematically fitting the MP2(full)/6-311+G(d) predicted values with the previously reported
˚
rotational constants for five isotopomers obtained from the microwave study. The difference in the two NH distances is 0.003 A which
˚
is much smaller than the value of 0.021 A previously reported. The bonding around the nitrogen atom is effectively planar which is con-
sistent with the previously reported structural information from the microwave study but differs from the reported slightly pyramidal
bonding obtained in the electron diffraction investigation. The adjusted r0 heavy atom distances and angles are: r(PF) = 1.587(3);
r(NP) = 1.649(3) A; \FPF = 94.7(5); \NPF = 100.6(5)°. Vibrational assignments are given for H2NPF2, H215NPF2 and D2NPF2 which
˚
are supported by ab initio MP2/6-31G(d) calculations. These results are compared to the corresponding quantities of some similar
molecules.
Ó 2008 Published by Elsevier B.V.
Keywords: Infrared and Raman spectra; Conformational stability; Structural parameters; Ab initio calculations; Aminodifluorophosphine
1. Introduction
changes from the normal pyramidal structure found for
most organoamines to planar or quasiplanar for amino-
phosphines. We have recently investigated the conforma-
tional stability of methylaminothiophosphoryl difluoride,
CH3N(H)P(S)F2, utilizing both vibrational spectra [1]
and microwave data [2] and found the bonding around
the nitrogen atom was nearly planar. The vibrational data
could be interpreted on the basis of planar bonded substit-
uents around the nitrogen atom but the microwave data
clearly showed that the CN(H)P moiety was not planar.
Molecules containing NP bonds are structurally
interesting since the bonding around the nitrogen atom
*
Corresponding author. Tel.: +1 816 235 6038; fax: +1 816 235 2290.
E-mail address: durigj@umkc.edu (J.R. Durig).
Taken in part from the thesis of P. Tschudin which was submitted to
1
Michigan State University in partial fulfillment of the Ph.D. Degree.
2
Present address: Summit Engineering, Columbia, SC 29221, USA.
0022-2860/$ - see front matter Ó 2008 Published by Elsevier B.V.
doi:10.1016/j.molstruc.2007.04.045

J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
407
This result appears to be in contrast to the conforma-
tional results of the corresponding molecule with two
methyl groups on the nitrogen atom where the PNC2 moi-
ety was reported to be planar [3]. Similar questionable
planarity has been reported for the (CH3)2NPF2 molecule
where the structural determinations from microwave,
infrared and Raman studies [4] along with ab initio pre-
dictions [2] gave skeletal planar PN(CH3)2 results,
whereas from the electron diffraction investigation [5], it
was reported that the bonding around N was pyramidal.
This situation is essentially similar for aminodifluorophos-
phine, H2NPF2, where the microwave data were best
interpreted [6] for a planar (Cs symmetry) PNH2 moiety
whereas the electron diffraction investigation gave a pyra-
midal nitrogen atom [5]. Also, from an X-ray determina-
tion [7] of the structure of the crystal, the space group was
cooled to ꢀ80 °C where the 1H spectrum of H2NPF2 shows
only a broad absorption which arise from the relaxation of
the proton resonance by the quadruple moment of nitro-
gen. The proton spectrum of H215NPF2 shows a doublet
(JNH = 83.2 Hz) of doublets (JPH = 19.7 Hz) of triplets
(JFH = 13.1 Hz) (which is consistent with the reported val-
ues [9] of JNH = 80.4 Hz; JPH = 18.6 Hz; JFH = 12.8 Hz).
The 19F spectrum of the normal species at ꢀ80 °C consists
of a doublet (JPF = 1186 Hz) of 1:2:1 triplets (JHF
=
12.6 Hz) that are slightly broadened by the quadruple
moment of the nitrogen (JPF = 1188 Hz; JNF = 12.6 Hz).
The nitrogen-15 sample has a 19F spectrum that consists
of a doublet (JPF = 1185 Hz) of doublets (JNF = 5.9 Hz)
split into triplets (JPF = 1180 Hz; JHF = 13.3 Hz), again,
consistent with the previously reported values [9]. No other
absorbances were observed in any of the purified samples.
If other peaks were observed, the sample was further
fractionally distilled until a pure sample was obtained. In
the 19F spectrum of H215NPF2 a small amount (<3%) of
normal H2NPF2 was observed.
Although the samples were stored at ꢀ196 °C, some dis-
proportionation to PF3 and PF(NH2)2 were expected upon
warming the sample for transfer. To avoid these impurities,
the spectral studies were made after removing the most vol-
atile fraction of the sample. An infrared spectral study per-
formed on the entire sample of H2NPF2 show a small
amount of PF3 contamination. The PF3 bands at 892,
860, 487 and 344 cmꢀ1 decreased and eventually disap-
peared as the more volatile fraction was removed. Because
of the instability of H2NPF2 it was stored at ꢀ196 °C and
manipulated in a clean dry vacuum system. All cells used
for spectroscopic studies were dried at 135 °C for 24 h
and evacuated before use.
determined to be P21=cðC5 Þ with four molecules per cell
2h
and two different PF bond distances with bonding around
the nitrogen (PNH2) being pyramidal. These results may
be quite different from the bonding in the gas phase
where there is no crystal packing or hydrogen bonding
factors operating. Because of the questionable bonding
around the nitrogen atom in aminodifluorophosphine,
we initiated a vibrational and ab initio investigation to
obtain conformational data, structural information and
a vibrational assignment which would be supported by
theoretical predictions.
We have recorded the infrared spectra of gaseous
H2NPF2 as well as two of the isotopomers, H215NPF2
and D2NPF2, and the Raman spectra of all three molecules
in the liquid phase. The optimized geometry, force con-
stants, vibrational frequencies, infrared intensities, Raman
activities and depolarization rations have been obtained
from ab initio MP2/6-31G(d) calculations to compare with
the experimental quantities when appropriate. The confor-
mational stabilities and optimized geometrical parameters
have been predicted from ab initio calculations with a vari-
ety of basis sets with and without diffuse functions up to
MP2/6-311+G(2df,2pd). Corresponding calculations have
been carried out with density functional theory with similar
basis sets by the B3LYP method. The results of these vibra-
tional spectroscopic and theoretical studies are reported
herein.
Gaseous infrared spectra from 200 to 4000 cmꢀ1 were
recorded on a Perkin–Elmer 225 Infrared Spectrophotom-
er. The gas cell used had a 10 cm path length and was
equipped with a high vacuum stopcock and O-ring seals
for the CsI windows used. Samples were either expanded
directly into the cell, or condensed into the small U-trap
attached to the cell and then allowed to expand. The
observed fundamentals for the H2NPF2, H215NPF2 and
D2NPF2 isotopomers are listed in Tables 1–3, respectively,
and some typical spectra of H2NPF2 and D2NPF2 are
shown in Figs. 1 and 2.
2. Experimental
Infrared spectra in the low frequency region (100–
225 cmꢀ1) were obtained on a Block Engineering FTS
1600 Infrared Spectrophotometer. Variation in the number
of scans from 1000 to 2000 did not appreciably improve the
signal-to-noise ratio. The samples were placed in a gas cell
with a path length of 10 cm and equipped with polyethyl-
ene windows. The samples were allowed to expand directly
into the cell.
The infrared spectra of the solutions using CCl4 as a sol-
vent were obtained on a Perkin–Elmer 457 Infrared Spec-
trophotometer. The cells were equipped with NaCl
windows. The samples were transferred by use of a syringe
in an inert atmosphere.
The aminodifluorophosphine sample was prepared by
the gas phase reaction of ammonia with chlorodifluoro-
phosphine [8]. Ammonia was dried over sodium at
ꢀ78 °C for 24 h before use. The ClPF2 sample was pre-
pared by the gaseous reaction of (CH3)2NPF2 with HCl
[8]. The H2NPF2 was purified by repeated removal of the
most volatile material and then monitoring the purity by
NMR spectra. Impurities in concentrations as low as
0.1% were detectable in the NMR spectra which made this
technique a powerful method for determining the sample
purity. The NMR spectra were recorded with the samples

Table 1
Observed and calculated fundamental frequencies (cmꢀ1) for H2NPF2
Symmetry
block
Vib.
No.
Approx. description
Ab
initioa
Fixed
scaledb
IR int.c Raman
act.d
dp
ratio
IR gas
IR N2 matrix Raman
PEDg
Ah
Bh
Ch
Be
liq.f
A0
m1
m2
NH2 antisymmetric
stretch
NH2 symmetric
stretch
3757
3618
3564
74.9
54.6
0.74
3519
3400
3509
3450
96S1
96S2
47
–
–
53
36
3432
55.8
119.8
0.15
3398
3370
64
m3
m4
NH2 deformation
NH2 rock
1635
980
1551
938
82.8
121.9
5.0
4.4
0.67
0.12
1547
952
1545
–
1562
979
98S3
54S4, 16S5, 16S8,
12S6
83
1
–
–
17
99
m5
m6
NP stretch
PF2 symmetric
stretch
922
833
874
791
153.7
42.6
5.6
4.9
0.58
0.12
874
794
904
784
883
780
74S5, 17S6
69S6, 24S4
100
80
–
–
20
m7
m8
PF2 deformation
PF2 rock
417
357
415
356
8.3
14.5
0.8
0.9
0.67
0.67
415
–
–
368
–
355
48S7, 38S8, 10S4
46S8, 49S7
4
99
–
–
96
1
A00
m9
PF2 antisymmetric
stretch
PF2 twist
850
469
807
455
175.6
26.6
3.6
2.7
0.75
0.75
810
440
790
438
780*
436*
98S9
–
–
100
100
–
–
m10
40S10, 40S12
18S11
60S11, 40S10
66S12, 19S11
15S10
,
,
m11
m12
NH2 wag
Torsion
225
207i
219
198i
89.6
179.6
2.9
1.1
0.75
0.75
220
175
228
–
252
190
–
–
100
100
–
–
a
MP2(full)/6-31G(d) predicted values: the letter i indicates an imaginary frequency.
b
c
d
e
f
MP2(full)/6-31G(d) fixed scaled frequencies with factors of 0.90 for all modes except PF2 bending vibrations.
Scaled infrared intensities in km/mol at MP2(full)/6-31G(d) level.
4
˚
Scaled Raman activities in A /u at MP2(full)/6-31G(d) level.
Ref. [21].
Bands marked with asterisk are obtained from Ref. [5].
Calculated at MP2(full)/6-31G(d) level and contributions of less than 10% are omitted.
A, B and C values are percentage infrared band contours.
g
h

Table 2
Observed and calculated fundamental frequencies (cmꢀ1) for H215NPF2
Symmetry
block
Vib.
No.
Approx. description
Ab
initioa
Fixed
scaledb
IR int.c
Raman
act.d
dp ratio IR gas
Raman
liq.
PEDe
Af
Bf
Cf
A0
m1
m2
m3
m4
NH2 antisymmetric stretch
NH2 symmetric stretch
NH2 deformation
NH2 rock
3746
3613
1629
973
3553
3427
1545
931
74.1
53.3
78.2
54.4
120.1
5.3
0.73
0.15
0.66
0.10
3490
3388
1538
948
3439
3345
1556
972
96S1
95S2
98S3
56S4,15S8,14S6,
12S5
47
63
84
–
–
–
–
53
37
16
120.5
3.9
–
100
m5
m6
m7
m8
NP stretch
909
830
416
355
862
787
414
354
163.3
33.3
8.2
5.5
4.9
0.8
0.9
0.60
0.11
0.67
0.67
860
790
410
331
880
–
–
75S5,19S6
64S6, 27S4
50S7, 37S8, 10S4
48S8, 47S7
100
74
3
–
–
–
–
–
PF2 symmetric stretch
PF2 deformation
PF2 rock
26
97
1
14.3
350
99
A00
m9
m10
PF2 antisymmetric stretch
PF2 twist
850
466
807
452
175.1
25.5
3.6
2.7
0.75
0.75
809
439
780
–
98S9
40S10, 41S12
18S11
60S11, 40S10
64S12, 19S11
16S10
–
–
100
100
–
–
,
,
m11
m12
NH2 wag
Torsion
225
205i
218
196i
89.9
177.6
2.8
1.1
0.75
0.75
220
174
252
190
–
–
100
100
–
–
a
MP2(full)/6-31G(d) predicted values: the letter i indicates an imaginary frequency.
b
c
d
e
f
MP2(full)/6-31G(d) fixed scaled frequencies with factors of 0.90 for all modes except those of the PF2 bending vibrations.
Scaled infrared intensities in km/mol at MP2(full)/6-31G(d) level.
4
˚
Scaled Raman activities in A /u at MP2(full)/6-31G(d) level.
Calculated at MP2(full)/6-31G(d) level and contributions of less than 10% are omitted.
A, B and C values in the last three column are percentage infrared band contours.

Table 3
Observed and calculated fundamental frequencies (cmꢀ1) for D2NPF2
f
Symmetry
block
Vib. No.
Approx. description
Ab initioa
Fixed scaledb IR int.c
Raman act.d dp ratio
IR gas
2620
Raman liq.
2594
PEDe
98S1
A
Bf
Cf
A0
m1
ND2 antisymmetric
stretch
2777
2635
43.9
28.4
0.75
30
–
70
m2
m3
m4
m5
m6
m7
m8
ND2 symmetric stretch
ND2 deformation
ND2 rock
2614
1243
721
873
899
393
339
2480
1179
689
829
859
391
336
50.8
10.4
9.6
132.0
121.8
6.3
57.3
1.0
3.0
6.6
5.5
0.6
0.8
0.14
0.51
0.32
0.61
0.01
0.74
0.64
2495
1180
741
838
860
405
325
2458
1189
744
813
862
–
98S2
84S3, 16S5
56S4, 19S6 14S8
64S5, 21S6, 13S3
59S6, 15S4, 11S8
80S7, 12S4
76
84
63
99
14
20
93
–
–
–
–
–
–
–
24
16
37
1
86
80
7
NP stretch
PF2 symmetric stretch
PF2 deformation
PF2 rock
12.6
348
65S8, 16S7
A00
m9
PF2 antisymmetric
stretch
PF2 twist
850
807
166.4
3.6
0.75
808
779
99S9
–
100
–
m10
m11
398
178
389
172
20.1
47.0
1.6
1.7
0.75
0.75
ꢁ375g
–
239
59S10, 41S12
36S11, 33S12
–
–
100
100
–
–
ND2 wag
172
,
31S10
26S12, 66S11
m12
Torsion
165i
156i
102.4
0.6
0.75
160g
184
–
100
–
a
MP2(full)/6-31G(d) predicted values: the letter i indicates an imaginary frequency.
b
c
d
e
f
MP2(full)/6-31G(d) fixed scaled frequencies with factors of 0.90 for all modes except those of the PF2 bending vibrations.
Scaled infrared intensities in km/mol at MP2(full)/6-31G(d) level.
4
˚
Scaled Raman activities in A /u at MP2(full)/6-31G(d) level.
Calculated at MP2(full)/6-31G(d) level and contributions of less than 10% are omitted.
A, B and C values in the last three column are percentage infrared band contours.
Band estimated.
g

J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
411
correlation up to the 6-311+G(2df,2pd) basis set. The den-
sity functional theory (DFT) calculations were restricted to
the B3LYP method [13,14]. The results of these calcula-
tions are listed in Table 4. These data show that the slightly
pyramidal conformer is predicted as the more stable con-
former from MP2 calculations with all basis sets investi-
gated but the energy difference with the planar nitrogen
bond is extremely small.
In order to obtain a complete description of the molec-
ular motions involved in the fundamental modes of amin-
odifluorophosphine, normal coordinate analyses have
been carried out. The force fields in Cartesian coordinates
were obtained with the Gaussian 03 program [10] from the
MP2(full)/6-31G(d) calculations. The B-matrix elements
[15] were used to convert the ab initio force field from
Cartesian coordinates into the force field in designated
internal coordinates (Table 5). These force constants were
used to reproduce the ab initio predicted vibrational fre-
quencies which are listed in tabular form for the three iso-
topomers in Tables 1–3. A scaling factor of 0.90 was
utilized for all force constants in internal coordinates
except for the PF2 bending modes where the force constant
is unscaled. The calculations were repeated to obtain the
fixed scaled force field, scaled vibrational frequencies and
potential energy distributions (PEDs) which are given for
each molecule in the vibrational tables.
Fig. 1. Infrared spectrum of gaseous H2NPF2.
The infrared spectra were predicted from the MP2(full)/
6-31G(d) calculations. Infrared intensities were calculated
based on the dipole moment derivatives with respect to
the Cartesian coordinates. The derivatives were taken from
the ab initio calculations transformed to normal coordi-
Fig. 2. Infrared spectrum of gaseous D2NPF2.
The Raman spectra were obtained from an instrument
equipped with a photomultiplier and recording device.
An Ar laser source was employed using the 5145 A excit-
+
Table 4
˚
Calculated energies (Hartree) and energy differences (cmꢀ1) for the two
possible conformers of H2NPF2
ing line. The cell construction allowed a sample to be fro-
zen into the viewing area while under vacuum. The
spectra were obtained while the sample was held at
ꢀ50 °C. Attempt to obtain Raman spectral data on gas-
eous samples at pressures up to ꢁ0.5 atm were
unsuccessful.
Nuclear magnetic resonance spectral data were obtained
by the use of a Varian Model 56/60 spectrometer. The
probe and sample were cooled to ꢀ80 °C by passing cooled
nitrogen over them. The samples were frozen into NMR
tubes under vacuum and stored at ꢀ196 °C until used.
Method/basis set
H2NP planar Slightly pyramidal DE
(Cs)
(C1)
(cmꢀ1
)
RHF/6-31G(d)
RHF/6-31+G(d)
MP2/6-31G(d)
ꢀ595.281769
ꢀ595.297095
ꢀ595.916344
ꢀ595.951058
ꢀ596.256572
ꢀ596.276471
ꢀ596.367161
ꢀ596.383264
ꢀ596.464018
ꢀ596.480183
ꢀ595.281926
ꢀ595.297179
ꢀ595.916604
ꢀ595.951092
ꢀ596.256833
ꢀ596.276536
ꢀ596.367499
ꢀ596.383483
ꢀ596.464198
ꢀ596.480246
ꢀ34
ꢀ18
ꢀ57
ꢀ7
MP2/6-31+G(d)
MP2/6-311G(d,p)
MP2/6-311+G(d,p)
MP2/6-311G(2d,2p)
MP2/6-311+G(2d,2p)
MP2/6-311G(2df,2pd)
MP2/
6-311+G(2df,2pd)
B3LYP/6-31G(d)
B3LYP/6-31+G(d)
B3LYP/6-311G(d,p)
B3LYP/6-311+G(d,p)
ꢀ57
ꢀ14
ꢀ74
ꢀ48
ꢀ40
ꢀ14
2.1. Ab initio calculations
ꢀ597.050488
ꢀ597.079673
ꢀ597.162977
ꢀ597.177157
ꢀ597.050779
ꢀ597.079742
ꢀ597.163050
ꢀ597.177172
ꢀ597.185194
ꢀ597.196925
ꢀ64
ꢀ15
ꢀ16
ꢀ3
The LCAO-MO-SCF restricted Hartree–Fock calcula-
tions were performed with the Gaussian-03 program [10]
using Gaussian-type basis functions. The energy minima
with respect to the nuclear coordinates were obtained by
the simultaneous relaxation of all the geometric parameters
using the gradient method of Pulay [11]. Calculations were
also carried out by the Møller–Plesset perturbation
method [12] to second order with valence and core electron
B3LYP/6-311G(2d,2p) ꢀ597.184870
ꢀ71
ꢀ50
B3LYP/
6-311+G(2d,2p)
B3LYP/
6-311G(2df,2pd)
B3LYP/
6-311+G(2df,2pd)
ꢀ597.196695
ꢀ597.198706
ꢀ597.211615
ꢀ597.198807
ꢀ597.211649
ꢀ22
ꢀ7

Table 5
Structural parameters (A and degree), rotational constants (MHz) and dipole moments (Debye) for H2NPF2 with planar PNH2 moiety
˚
EDa
X-rayb
MWc
Adjusted r0
d
Parameter
Internal coordinates
HF/6-31G(d)
MP2/6-311+G(d,p)
MP2/6-311+G(2d,2p)
MP2/6-
311+G(2df,2pd)
r(N–P)
r(P–F)
R1
R2, R3
1.649
1.586
1.654
1.622
1.651
1.609
1.647
1.599
1.661(7)
1.581(3)
1.581(3)
1.6394(9)
1.650(4)
1.587(4)
1.649(3)
1.587(3)
r(P–Fo) 1.5899(6)
r(P–Fi) 1.6083(11)
0.860(22)
r(N–Ho)
r(N–Hi)
\NPF
r1
0.995
0.999
100.6
1.006
1.010
100.3
1.001
1.004
100.4
1.003
1.006
100.5
0.981(5)
1.002(5)
100.6(2)
0.998(3)
1.001(3)
100.6(5)
r2
0.862(19)
c1, c2
\NPFo 99.41(4)
\NPFi 102.13(5)
93.29(4)
118.7(16)
120.7(14)
\FPF
\PNHo
\PNHi
\HNH
s(FPNH)
s(HNPH)
A
u
94.0
94.0
93.8
94.0
94.6(2)
94.7(5)
118.1(5)
123.3(5)
118.7(5)
48.4(5)
180.0
7767.1
7053.0
4596.5
a1
a2
b
120.0
124.1
115.9
48.0
180.0
7824.6
7016.2
4608.0
2.888
0.000
0.003
2.888
119.5
124.4
116.1
48.0
180.0
7488.8
6885.7
4479.6
3.345
0.000
0.360
3.364
119.3
124.5
116.2
47.9
180.0
7621.5
6935.9
4535.4
3.091
0.000
0.053
3.091
119.2
124.8
116.0
48.0
180.0
7700.4
6987.4
4567.1
2.967
0.000
0.068
2.968
119(2)
119(2)
108
119.7(4)
123.1(2)
117.2(4)
109.1(18)
180.0
7766.22(5)
7052.29(5)
4596.43(5)
2.570(7)
0.000
B
C
jlaj
jlbj
jlcj
0.18(1)
2.576(7)
jltj
a
Ref. [5].
Ref. [7].
Ref. [6].
b
c
d
Adjusted from MP2(full)/6-311+G(d,p) optimized structure, with the exception that the initial P–F distances are taken from optimized HF/6-31G(d) structure.

J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
413
P
nates by: (olu/oQi) =
(olu/oXj) Lij, where Qi is the ith
The Raman scattering cross sections, orj/oX, which are
proportional to Raman activities, can be calculated from
the scattering activities as well as the predicted wavenum-
bers for each normal mode, using the relationship [18,19]:
j
normal coordinate, Xj is the jth Cartesian displacement
coordinate, and Lij are elements of transformation matrix
between the Cartesian displacement coordinates and nor-
mal coordinates. The infrared intensities were then calcu-
lated with (Np)/(3c2) [(olx/oQi)2 + (oly/oQi)2 + (olz/
oQi)2]. The predicted infrared spectra were obtained and
shown for H2NPF2 and D2NPF2 in Figs. 3 and 4, respec-
tively. These data were very useful for assigning the
fundamentals.
4
4
orj ð2pÞ
ðm0 ꢀ mjÞ
h
¼
Sj
oX
45 1 ꢀ expðꢀhcmj=kTÞ 8p2cmj
where m0 is the excitation wavenumber, mj is the vibrational
wavenumber of the jth normal mode, and Sj is the corre-
sponding Raman scattering activity. To obtain the polar-
ized Raman scattering cross sections, the polarizabilities
are incorporated into Sj by multiplying Sj with (1 ꢀ qj)/
(1 + qj), where qj is the depolarization ratio of the jth nor-
mal mode. The Raman scattering cross sections and calcu-
lated wavenumbers obtained from the Gaussian 03
program [10] were used together with a Lorentzian band
shape function to obtain the simulated Raman spectra
which are also shown in Figs. 3 and 4 for the normal and
N-d2 isotopomers. This approach shows the value in hav-
ing both infrared and Raman data for making vibrational
assignments.
To further support the vibrational assignments, we have
simulated the Raman spectra from fixed scaled ab initio
MP2(full)/6-31G(d) results. The evaluation of Raman
activity by using the analytical gradient methods has been
developed [16,17]. The activity Sj can be expressed as:
Sj = gj (45a2j þ 7bj2), where gj is the degeneracy of the vibra-
tional mode j, aj is the derivative of the isotropic polariz-
ability, and bj is that of the anisotropic polarizability.
2.2. Conformational stability and structural parameters
The two previously reported [5,6] structural parameter
determinations of H2NPF2 for the vapor state and confor-
mational stability evaluation appeared nearly simulta-
neously so neither article contained significant comments
concerning the differences in the conformational stabilities
being reported by the two techniques. However, the investi-
gators in both studies concluded that there was only one con-
former present in the vapor state. A note added in proof on
the microwave study stated that the model with NH bond
distances and the PNH angles assumed to be equal were
invalid and the reported [5] HNH plane making an angle
of 146° with the NP bond was at variance with the micro-
wave results which strongly favored a planar PNH2 moiety.
However, as will be shown in this study the large difference of
Fig. 3. Simulated spectra of H2NPF2 from MP2(full)6-31G(d) calcula-
tion: (A) infrared; (B) Raman.
˚
0.021 A for the two NH bond distances as reported from the
microwave study [6] is undoubtedly in error.
In addition to the difference in the reported [5,6] stable
conformations of H2NPF2, there were major differences
in the heavy atom structural parameters. For example, a
˚
relatively short PN distance of 1.639(1) A was reported
from the X-ray study [7] whereas the microwave deter-
˚
mined value was 1.650(4) A. In contrast, one of the PF
bond distances was reported [7] to have a rather long value
˚
of 1.608(1) A from the X-ray study whereas the same PF
˚
distances have a value of 1.587(4) A from the microwave
data [6]. Thus, we have redetermined the structural param-
eters of H2NPF2 as well as provided an assessment of the
conformational stability.
We have found [20] that we can obtain good structural
parameters by systematically adjusting the structural
parameters obtained from the ab initio calculations to fit
the rotational constants obtained from the microwave
Fig. 4. Simulated spectra of D2NPF2 from MP2(full)6-31G(d) calcula-
tion: (A) infrared; (B) Raman.

414
J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
experimental data (computer program A&M, Ab initio and
Microwave, developed in our laboratory). In order to
reduce the number of independent variables, the structural
parameters are separated into sets according to their types.
Bond lengths in the same set keep their relative ratio, and
bond angles and torsional angles in the same set keep their
differences in degrees. This assumption is based on the well-
accepted assumption that the errors from ab initio calcula-
tions are largely systematic. Therefore, it should be possible
to obtain ‘‘adjusted r0’’ structural parameters for aminodi-
fluorophosphine from the 15 previously determined rota-
tional constants, particularly, since for this method there
are now only eight parameters to be determined. These
parameters are expected to be more accurate than those
that could be obtained from a re-investigation of the elec-
tron diffraction data or additional microwave studies with
more isotopic species.
differences are within the reported uncertainties. Neverthe-
less, to fit the experimental rotational constants the pre-
dicted differences of 0.007 A between the two PF bond
distances had to be ignored. The error in using the mole-
cule with the pyramidal nitrogen arose from not investigat-
ing the energy differences between the two forms (Cs and
C1) which would have showed that the well depth was
not sufficient to accommodate a ground state energy level.
˚
2.3. Vibrational assignment
The frequencies chosen for the fundamental vibrations
are significantly different from many of those previously
proposed [7,21]. However, in neither of these studies were
complete assignment proposed or (potential energy distri-
bution) PED given. In addition to the predicted frequen-
cies, the PEDs were also obtained from the ab initio
calculations. A set of symmetry coordinates which were
The results of this structural determination (Table 5)
show excellent agreement with the parameters reported
from the earlier microwave study [6] except for those asso-
˚
Table 7
ciated with the N–H bond. The distance of 0.981(5) A is
Symmetry coordinates of H2NPF2
unrealistically too short and the angle PNHo is too large
by maybe as much as a degree. Part of the problem may
arise from the assumption that the corresponding NH
and ND distances have the same values, i.e., neglecting
the shorter ND distance. The fit of the fifteen rotational
constants is excellent with all but two of the A constants
fit to better than 1 MHz and only the A constant for the
D2NPF2 isotopomers has a significant difference of
1.59 MHz (Table 6). We believe the uncertainties on the
Species
A0
Description
Symmetry coordinatea
NH2 antisymmetric stretch
NH2 symmetric stretch
NH2 deformation
NH2 rock
S1 = r1 ꢀ r2
S2 = r1 + r2
S3 = 2b ꢀ a1 ꢀ a2
S4 = a1 ꢀ a2
S5 = R1
S6 = R2 + R3
S7 = u
S8 = c1 + c2
NP stretch
PF2 symmetric stretch
PF2 deformation
PF2 rock
˚
A00
PF2 antisymmetric stretch
PF2 twist
NH2 wag
S9 = R2 ꢀ R3
S10 = c1 ꢀ c2
S11 = s1
distances are 0.003 A with those for the angle of 0.5°.
The parameters reported herein are slightly different
from those given earlier [2] from ab initio predictions where
the molecule with the slightly pyramidal nitrogen atom was
utilized. However, for the NP and NF bond distances the
Torsion
S12 = s2
a
Not normalized.
Table 6
Comparison of rotational constants (MHz) obtained from modified ab initio MP2(full)/6-311+G(d,p) predictions, experimental values from microwave
spectra and the adjusted r0 structural parameters for aminodifluorophosphine
Isotopomer
H2NPF2
Rotational constant
MP2(full)/6-311+G(d,p)
Experimentala
Adjusted r0
jDj
1.06
0.90
0.14
A
B
C
7488.8
6885.7
4479.6
7766.2
7052.3
4596.4
7767.3
7053.2
4596.6
H215NPF2
A
B
C
7477.8
6674.6
4392.9
7756.0
6833.0
4505.7
7756.8
6833.5
4505.8
0.77
0.52
0.08
HDNPF2 (cis)
HDNPF2 (trans)
D2NPF2
A
B
C
7308.7
6511.0
4380.0
7580.9
6667.5
4493.1
7580.6
6667.6
4492.7
0.28
0.09
0.39
A
B
C
7485.1
6396.1
4268.1
7761.5
6552.4
4380.0
7761.5
6551.6
4380.0
0.01
0.83
0.07
A
B
C
7299.7
6077.3
4182.2
7569.6
6224.1
4290.4
7568.0
6223.5
4290.6
1.59
0.64
0.27
a
Ref. [6].

J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
415
used are list in Table 7 with the internal coordinate listed in
Table 5 for determining the PEDs. In addition to these
listed symmetry coordinates, we also utilized comparable
ones for a slightly pyramidal bonded nitrogen atom.
This assignment then requires the spectral data from the
matrix of the species B which was obtained from raising
the temperature of the matrix to the 32–40 K range to be
compared to the spectrum of the gas.
Of the two previous investigations [7,21] of the vibra-
tional modes of H2NPF2 the more complete study [7] uti-
lized the infrared spectra of the gas, amorphous and
crystalline solids, and Raman spectra of the liquid and
crystalline solid for making the vibrational assignment.
For the amorphous solid there was a reasonable correspon-
dence of bands observed in the gas with those in the spec-
trum of solid except for a fundamental assigned at
315 cmꢀ1 in the gas which was assigned at 355 in the liquid
and 358 cmꢀ1 in the solid. In the other study [21], the infra-
red spectra of H214NPF2 was investigated in N2 matrix at
10 K which was then warmed to 32–40 K where a complete
conversion was observed from a form A to form B in about
20 min. Shorter periods of time resulted in the observation
of both forms with neither being perturbed by the presence
of the other. Also, these observations did not appear to be
effected by the concentrations of the sample in the matrix
which was varied from 1000:1 to 100:1 by using the
pulsed-deposition technique. In both of these studies there
is essential agreement for the assignments of the two NH2
stretches, the NH2 deformation, and the NH2 rock (A0) but
most of the other assignments differ significantly. There-
fore, our emphases are on the skeletal modes although
there is some difficulty in the choice of the band centers
for the NH2 (also ND2) modes (Figs. 1 and 2) where the
A0 modes for the planar PNH2 moiety give rise to A, C
or A/C-type hybrid contours, all of which should have very
distinct Q-branches. However, as can be seen from the
spectra, there are a multitude of Q-branches on both
NH2 as well as ND2 stretches and we have chosen the
strongest Q-branch in each case as the fundamental.
There are four fundamentals predicted (Table 1) in the
790–940 cmꢀ1 region with only the PF2 antisymmetric
stretch (A00) giving rise to the B-type band contour with
an expected distinctive minimum. As can be seen from
the predicted (Fig. 3) intensities for both of the infrared
bands and Raman lines there is little information from
these predictions for choosing the band centers for three
of these fundamentals (Fig. 1). In the infrared spectrum
of the gas (Fig. 1), there are two relatively strong maxima
but it is difficult to pick out the third band center (mini-
mum). From the infrared spectrum of the matrix isolated
sample (species A), only one weak band is reported [21]
at 797 cmꢀ1 where two fundamentals are expected. The
breadth of the 794 cmꢀ1 gas phase band could contain
two fundamentals particularly since the predicted differ-
ence in the frequencies of the two PF2 stretching vibrations
is only 16 cmꢀ1. By comparing the frequencies for this
group of bands observed in the spectra of the H215NPF2
and D2NPF2 (Fig. 4), we have made the following assign-
ments for the normal species in the gas phase: NH2 rock
(952 cmꢀ1), NP stretch (874 cmꢀ1), PF2 symmetric stretch
(794 cmꢀ1) and the PF2 antisymmetric stretch (810 cmꢀ1).
The assignment of the skeletal bending modes required
mainly reliance on the ab initio predicted values since no
depolarization data from the Raman spectrum were avail-
able and the infrared band contours in the far infrared
spectrum were non-descript. Also, it is expected that data
from the liquid may be significantly different from that
for the vapor because of the presence of hydrogen-bonded
dimers. Similar problems will also be present from the
infrared and Raman spectra of the crystalline solid where
crystal packing factors may also cause changes in the spec-
tra. Thus, the exact frequencies for these low frequency
bends will require much higher resolution and better qual-
ity spectral data with relatively small uncertainties.
3. Discussion
In the earlier microwave study the evidence for a planar
nitrogen configuration was well documented. For example,
the out-of-plane second moments, Pbb = Rmib2i , are nearly
2
˚
the same with a value of 51.6810 u A for H2NPF2 with the
2
˚
differences of ꢀ0.0001, ꢀ0.0081, 0.0025 and ꢀ0.0006 u A
for the 15N, NHD(cis), NHD(trans) and ND2 isotopomers,
respectively. The fact that the changes are very small and
in two cases negative is strong evidence for planar bonded
nitrogen. The experimentally determined dipole moment
components also support a planar PNH2 group since
assuming a pyramidal nitrogen led to lb = ꢀ0.009
0.031D whereas the assumption of only two components
led to realistic values of la = 2.570 0.007 and
lc = 0.18 0.01D. Other evidence is the relatively short
PN distance which is more consistent with values for a dou-
ble bond than a single bond and the proton NMR coupling
constant for 15NH value of 83.2 Hz which is consistent with
sp2 hybridization which requires 33% s-character compared
to the predicted value of 30% from the coupling constant.
Further support for the planar PNH2 moiety is obtained
from the ab initio calculations where the depth of the
‘‘well’’ for the C1 form (pyramidal nitrogen bonding) is
predicted with values ranging from a high value of
74 cmꢀ1 (MP2/6-311G(2d,2p)) to a low value of 14 cmꢀ1
(MP2/6-311+G(2df,2pd)) compared to the Cs form. These
values are sufficiently small that based on the vibrational
zero-point energies none of the predicted wells could
accommodate an energy level. However, there was one pos-
sible indication of a small hump in the potential function
from the value for the rotational constants of the 2m12
vibrational excited state which do not vary in a harmonic
manner. It was previously proposed [6] that it could be
due to a vibrational–rotational interaction of 2m12 with m8
which have similar frequencies. Therefore, we have con-
cluded that the effective symmetry for the interpretation
of the vibrational and rotational spectra is Cs but there is
a small hump at the planar conformation of the H2NP moi-

416
J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
ety. The determination of the rotational constants for 3m12
state could possibly provide information on the presence of
the hump along with estimates of its magnitude.
The two major differences in the values determined in this
study compared to those previously reported is the adjusted
˚
˚
r(NH0) distance of 0.998(3) A versus the 0.981(5) A value
from the microwave study where no restriction was used
for its determination and the conformation of the short
˚
adjusted r(NP) distance of 1.649(3) A, compared to 1.650
(4) A from microwave study [6] but a long value of
1.661(7) A from the electron diffraction study [5]. However,
˚
˚
the larger uncertainty from the ED study made the values
to be in near agreement. Nevertheless, the shorter distance
is in much better accord with the near planar arrangement
of the H2NP moiety. Thus, the shorter distance is consistent
with significant double bonding of the NP bond compared to
a longer single bond with sp2 hybridization for the bonding
around the nitrogen atom.
Fig. 6. Infrared spectrum of nitrogen–deuterium stretching vibrations of
D2NPF2.
‘‘hot bands’’ and we have arbitrarily chosen the highest fre-
quency band for both the NH (Fig. 5) and ND (Fig. 6)
stretches. The Q-branches between the two ND stretches
are possibly due to the NHD isotopomer which is an impu-
rity in the N-d2 sample. Thus, an investigation of a very
dilute krypton or xenon solution would probably help to
identify the band centers since the spectral data of the
liquid (Raman) or that of the amorphous solid probably
have some significant frequency shifts from those for the
gas due to hydrogen bonding resulting in the presence of
dimers or association forms.
There is very limited data on NP bond distance for com-
parison. In our recent microwave study [2] of (methylami-
no)thiophosphoryl difluoride, CH3NHP(@S)F2, an NP
˚
distance of 1.621(5) A was reported which is much shorter
than the value obtained for this bond in H2NPF2. The
˚
adjusted r0 NP bond distance [2] of 1.652(4) A in
˚
(CH3)2NPF2 is in agreement with values of 1.648(8) A
reported from an electron diffraction study [5] and
˚
There is some significant mixing where the NH2 rock has
contributions from the PF2 rock (16%), PF2 symmetric
stretch (12%) and NP stretch (16%) which is somewhat sur-
prising. There is also extensive mixing of the PF2 deforma-
tion and rock in the A0 species and major mixing of three of
the four fundamentals (except for the PF2 antisymmetric
stretch) of the A00 species. Similar mixing is also found in
the corresponding vibrations for the D2NPF2 isotopomer.
As can be seen the calculations with diffusion functions
(Table 4) result in significantly lower values of the energy
differences between the slightly pyramidal and planar
H2NP moiety. This difference is mainly due to the predicted
1.657(1) A reported from a microwave study [4]. This small
difference is expected due to the substitution of the methyl
groups for the hydrogen atoms. These limited results indi-
cate that a relatively large range can be expected for the NP
bond distance among compounds and they will be signifi-
cantly effected by the substituents on the phosphorous
atom.
In general, the frequencies for the normal modes are well
determined but there is an unusual uncertainty in their
band centers even for the A0 mode with a Q-branch indicat-
ing the center. For example, the two NH stretches have a
large number of Q-branches which are probably due to
˚
very large elongation (0.018 A) of the PF bond distance
with diffuse functions which is already predicted much
too long from MP2/6-311G(d,p) calculations. The pre-
dicted NP distances are not significantly effected by using
diffuse function so the main differences in the predicted
vibrational frequencies are for the two PF stretches. How-
ever, these changes in the PF stretches result in a large
change in the PED for m5 where this mode was predicted
to be only 50% NP stretch with 33% NH2 rock and
14% PF stretch compared to 74% NP stretch (Table 1)
without the diffuse functions. Therefore, the ab initio pre-
dictions without diffuse functions appear to be in better
agreement with the experimentally determined values
where available.
The significant difference in the reported assignments for
the fundamentals compared tothose given earlier may be due
in part to decomposition of the samples depending on how
they were handled. It is clear from the studies reported herein
that decomposition was a significant factor affecting
Fig. 5. Infrared spectra of nitrogen–hydrogen stretching vibrations: (A)
H2NPF2; (B) H215NPF2.

J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
417
˚
3000
2500
2000
1500
1000
500
cantly larger than the values of 1.595 and 1.602 A predicted
from MP2/6-311+(2df,2pd) ab initio calculations for a pyra-
midal H2NP moiety which is a strong indication of the dis-
tortion of the molecule in the condensed phases. Thus,
analyses of higher resolution infrared spectrum of the gas
or very dilute solutions in rare gases are needed to obtain
more accurate values for the fundamental band centers.
The twofold barrier to internal rotation has been pre-
dicted from the MP2/6-31G(d) calculations with a value
of 2485 cmꢀ1 (7.1 kcal/mol) (Fig. 7) which is considerably
higher than most threefold barriers. This probably reflects
the short NP distance with some partial double bond char-
acter of the nitrogen–phosphorus bond. The potential
function governing the internal rotation is predicted to
have V2 and V4 terms of 2387 and 101 cmꢀ1, respectively.
Based on the good agreement found between the predicted
threefold barriers from ab initio MP2/6-31G(d) calcula-
tions with experimentally determined values, we expect
the predicted ones for this twofold barrier to be reasonably
close to the actual values for the H2NPF2 molecule. We did
not obtain the barrier from the torsional frequency since
the band assigned to this mode has a predicted PED of
only 66% contribution for this motion.
0
0
100
200
300
DIHEDRAL ANGLE (τ)
Fig. 7. Torsional potential function governing the PF2 rotation calculated
at the MP2(full)/6-31G(d) level.
Table 8
Calculated and observed microwave frequencies (MHz) of H2NPF2
Transition
Observeda
Da,b
Calculatedc
Dd
000–101
101–202
01–220
110–211
111–212
413–432
11648.76
21421.15
32941.17
25753.19
20841.47
14583.47
12703.83
15510.66
11444.93
24940.83
17230.21
18353.18
9798.84
0.04
ꢀ0.05
0.05
11648.76
21421.14
32941.18
25753.23
20841.43
14583.43
12703.84
15510.66
11444.96
24940.82
17230.22
18353.20
9798.81
0.00
ꢀ0.01
0.01
1
ꢀ0.09
ꢀ0.09
ꢀ0.98
ꢀ0.01
ꢀ2.51
0.02
ꢀ2.13
ꢀ5.25
ꢀ0.83
0.46
ꢀ6.07
ꢀ9.39
1.18
1.09
3.27
0.04
In the microwave study [6], the authors did not deter-
mine the centrifugal distortion constants but the difference
between the observed and predicted frequencies for the
higher J values indicate that there was sufficient data to
determine the five usually determined centrifugal distortion
constants, i.e., DJ, DJK, DK, dJ and dK. Therefore, we have
used the previously reported frequencies (Table 8) and
obtained values for these constants with their statistical
uncertainties (Table 9). All but DJ have very small uncer-
tainties. These distortion constants have been predicted
from MP2/6-31G(d) and MP2/6-31+G(d) calculations for
both the C1 (slightly pyramidal N bond) and the Cs forms
(planar PNH2) and the difference between the C1 and Cs
predictions is relatively small. However, there is a signifi-
cant difference between the values obtained with and with-
out diffuse functions with the small basis sets where those
with diffuse function are in much better agreement with
the experimental values. We have also obtained the centrif-
ugal distortion constants from MP2/6-311+G(d,p) calcula-
tions. These values are in excellent agreement with the
experimentally determined values. Nevertheless, it should
be noted that very good predicted values are obtained from
even a very small basis set, i.e., 6-31+G(d) from the values
ꢀ0.04
ꢀ0.04
0.01
0.00
0.03
4
23–422
523–542
5
6
33–532
15–634
633–652
634–633
643–642
734–753
43–762
753–752
854–853
ꢀ0.01
0.01
0.02
ꢀ0.03
19995.52
20016.76
7903.54
15404.52
13195.68
19995.54
20016.75
7903.51
15404.51
13195.69
0.02
7
ꢀ0.01
ꢀ0.03
ꢀ0.01
0.01
9
64–963
a
Ref. [6].
Without distortion constants.
Calculated utilizing five distortion constant (Table 9) with data listed
b
c
in Ref. [6].
d
Difference between observed and calculated frequencies.
consistent vibrational data. Also the spectra from different
physical states show the effect of association of the molecules
in the condensed phases. The single crystal X-ray data [7]
show this effect where the two PF distance have values (Table
˚
5) of 1.590(1) and 1.608(1) A. These differences are signifi-
Table 9
Calculated (method/basis set) and experimental centrifugal distortion constants (kHz) of aminodiflourophosphine
Distortion constants
MP2(full)/6-31G(d)
MP2(full)/6-31+G(d)
MP2(full)/6-311+G(d,p)
Pyramidal C1
Experimental valuea
Cs
Planar Cs
Pyramidal C1
Planar Cs
Pyramidal C1
DJ
DK
DJK
dJ
2.93
ꢀ2.28
6.46
0.81
4.61
3.17
ꢀ3.00
7.52
0.92
5.49
2.94
ꢀ9.41
13.67
0.82
3.08
ꢀ10.06
14.58
0.88
3.14
ꢀ6.39
10.71
0.90
6.02(2.50)
ꢀ6.42(0.27)
11.19(0.24)
0.96(0.03)
6.23(0.10)
dK
a
7.66
8.21
6.52
Calculated from the reported frequencies of the assigned transitions from microwave spectrum, Ref. [6].

418
J.R. Durig et al. / Journal of Molecular Structure 875 (2008) 406–418
[9] D.W.H. Rankin, J. Chem. Soc. A (1971) 783.
of the force constants relative to values needed to obtain
the fundamental frequencies. Therefore, we believe the cen-
trifugal distortion constants obtained from the previously
reported microwave frequencies [6] have been well deter-
mined except for DJ which has a relatively large uncer-
tainty, but considering the lower limit of its value it also
is in reasonably good agreement.
[10] Gaussian 03, Revision B.04, M.J. Frisch, G.W. Trucks, H.B. Schlegel,
G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T.
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Acknowledgment
J.R.D. acknowledges the University of Missouri-Kansas
City for a Faculty Research Grant for partial financial sup-
port of this research.
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