Structure and vibrational force field of methyldifluoroamine, CH3NF2. An electron-diffraction investigation augmented by microwave and infrared spectroscopic data and by Ab initio molecular orbital calculations

Article abstract of DOI:10.1021/jp980971p

The structure of methyldifluoroamine, CH₃NF₂, was determined by gas-phase electron diffraction augmented by rotational constants from microwave spectroscopy taken from the literature and by results from molecular orbital calculations. The structural results are consistent with C_s symmetry for a molecule with staggered bonds. The experimental bond distances and bond angles (r_α⁰/r_g) and 〈_α), with estimated 2σ uncertainties are C-H = 1.104/1.124(5) A? (average value), N-F = 1.406/1.408(2) A?, C-N = 1.467/1.469(6) A?, C-N-F = 104.1(2)°, F-N-F = 101.7(2)°, N-C-H_anti = 109.9(11)°, N-C-H_gauche = 106.5(10)°, H_gauche-C-H_gauche = 110.6(28)°; the subscripts indicate orientation with respect to the nitrogen lone pair. A scaled quantum-mechanical (SQM) quadratic vibrational force field was evaluated by symmetrizing the quantum-mechanical (MP2/6-311++G(d,p)) Cartesian force constants and scaling the results to fit observed infrared wavenumbers from the literature. The N-F stretching force constants for the other fluoroamines NF₃ and (CH₃)₂NF were also determined in a similar fashion. Contrary to an earlier report, the values were found to increase with decreasing bond length consistent with Badger's rule.

Full text of DOI:10.1021/jp980971p

5106
J. Phys. Chem. A 1998, 102, 5106-5110
Structure and Vibrational Force Field of Methyldifluoroamine, CH3NF2. An
Electron-Diffraction Investigation Augmented by Microwave and Infrared Spectroscopic
Data and by Ab Initio Molecular Orbital Calculations
Kolbjørn Hagen,*,†,‡ Kenneth Hedberg,*,† Earnest Obed John,§ Robert L. Kirchmeier,§ and
Jeanne M. Shreeve§
Contribution from the Department of Chemistry, Oregon State UniVersity, CorVallis, Oregon 97331-4003,
and Department of Chemistry, UniVersity of Idaho, Moscow, Idaho 83844-2343
ReceiVed: February 2, 1998
The structure of methyldifluoroamine, CH3NF2, was determined by gas-phase electron diffraction augmented
by rotational constants from microwave spectroscopy taken from the literature and by results from molecular
orbital calculations. The structural results are consistent with Cs symmetry for a molecule with staggered
0
bonds. The experimental bond distances and bond angles (rR /rg) and R), with estimated 2σ uncertainties
are C-H ) 1.104/1.124(5) Å (average value), N-F ) 1.406/1.408(2) Å, C-N ) 1.467/1.469(6) Å, C-N-F
) 104.1(2)°, F-N-F ) 101.7(2)°, N-C-Hanti ) 109.9(11)°, N-C-Hgauche ) 106.5(10)°, HgauchesC-Hgauche
) 110.6(28)°; the subscripts indicate orientation with respect to the nitrogen lone pair. A scaled quantum-
mechanical (SQM) quadratic vibrational force field was evaluated by symmetrizing the quantum-mechanical
(MP2/6-311++G(d,p)) Cartesian force constants and scaling the results to fit observed infrared wavenumbers
from the literature. The N-F stretching force constants for the other fluoroamines NF3 and (CH3)2NF were
also determined in a similar fashion. Contrary to an earlier report, the values were found to increase with
decreasing bond length consistent with Badger’s rule.
Introduction
existence of two stretching modes, a symmetric and an asym-
metric one, which have different wavenumber values. This
article is a report of our GED investigation of MeNF2 (Figure
1), which also includes a normal coordinate analysis of the
molecule, and makes auxiliary use of the earlier data from MW3
and infrared6 spectroscopy. Related to this work we also carried
out ab initio molecular orbital calculations, some at high levels
of theory, for all three MenNF(3-n) molecules. These calcula-
tions have given us important information about both their
structures and their quadratic vibrational force fields.
Ever since it was first observed in the case of fluorinated
methanes1 more than 60 years ago, the effect of increasing
fluorine substitution on an atom has been known to shorten the
bonds to fluorine. Thus, the length of the N-F bond is expected
to increase significantly in the series of molecules MenNF(3-n)
Me ) CH3; n ) 0-2, as fluorine atoms are successively
replaced by methyl groups. The experimental valuess1.371-
(2) Å for NF3 from microwave spectroscopy (MW),2 1.413(5)
Å for MeNF2 from MW,3 and 1.447(6) Å for Me2NF from
combined electron diffraction (GED) and MW4sare consistent
with the expected bond-length variation.
Experimental Section
As a part of the Me2NF study cited above, the relationship
between the N-F bond length and the value of the stretching
force constant in the MenNF(3-n) series of molecules was also
investigated. The results suggest that a violation of Badger’s
rule occurs. Badger’s rule5 states that the bond lengths between
atoms of a given type and the corresponding stretching force
Methyldifluoroamine was prepared by photolyzing CH3I and
N2F4 through Pyrex using a Hanovia benchtop UV lamp7 and
was purified by trap-to-trap distillation. The electron-diffraction
data were obtained with the Oregon State apparatus (nominal
accelerating voltage of 60 kV) with a nozzle-tip temperature of
295 K and with the bulk sample kept at 223 K. The nozzle-
to-plate distances were 748.16 and 299.34 mm for the long (LC)
and the middle (MC) camera distance experiments, respectively.
Exposure times were 2-3 min, beam currents were 0.39-0.45
µA, plates were Kodak projector slide, medium contrast,
developed for 10 min in D19 diluted 1 × 1. The electron
wavelength was 0.048721 Å. A voltage/distance calibration was
made with CO2 as reference (ra(C-O) ) 1.1646 Å; ra(O‚O) )
2.3244 Å). Three plates from the LC and two plates from the
MC experiments were selected for analysis. The plates were
scanned twice, making a total of 10 data sets. The ranges of
data were 2.00 e s/Å-1 e 15.50 and 8.00 e s/Å-1 e 37.00 for
the LC and MC distance experiments, respectively. The data
interval was ∆s ) 0.25 Å-1. A calculated background8 was
subtracted from each data set to yield experimental intensity
constants are inversely related; the formula is ke ) a(re - b)-1/3
,
with a and b depending on the atoms involved. For the amines
cited above, the N-F force constants were found to increase
slightly instead of decreasing as the number of fluorine atoms
changes from three to one. Because Badger’s rule has enjoyed
considerable success, this matter is puzzling. One aspect of
the problem concerns the MW results for MeNF2 which rest
on some assumptions about the hydrogen parameters. Another
concerns a possible ambiguity in the identification of the N-F
“force constant” in this molecule, which arises from the
† Oregon State University.
‡ On leave from the Deparment of Chemistry, Norwegian University of
Science and Technology, N-7034 Trondheim, Norway.
§ University of Idaho.
S1089-5639(98)00971-2 CCC: $15.00 © 1998 American Chemical Society
Published on Web 06/05/1998

Methyldifluoroamine Structure
J. Phys. Chem. A, Vol. 102, No. 26, 1998 5107
MP3, and B3LYP levels were much closer, differing by only a
few thousandths of an angstrom. Results for these calculations
are given in Table 1. Optimizations of the NF3 and Me2NF
structures were also carried out at a few theoretical levels (HF/
6-311++G(d,p), MP2/6-311++G(d,p), and B3LYP/6-311++G-
(2d,2p)), and frequencies and Cartesian force fields at these
levels were calculated for all three molecules. The calculations
for NF3 and Me2NF were for use in comparisons of force-
constant values. These comparisons are discussed in a later
section.
Figure 1. Diagram of the methyldifluoroamine molecule with atom
Normal Coordinate Calculations. The ab initio Cartesian
force fields were used in the program ASYM4011 to obtain
symmetry force fields or valence force fields. A set of scale
factors for the nonredundant set of symmetry force constants
was then refined to fit the observed vibrational wavenumbers6
for MeNF2, and the resulting scaled (SQM) force field used to
calculate the quantities that interconvert rR0 and ra, and Bz and
B0 needed to utilize the available rotational constants and GED
data simultaneously in the structure refinement.12 Table 2 lists
the symmetry coordinates for MeNF2 and Table 3 lists the
corresponding force constants, scale constants, and wavenum-
bers.
numbering.
Structure Analysis
Assuming Cs symmetry for the molecule, the structure of
MeNF2 can be described by four distance and five angle
parameters. These were chosen to be r(C-H) ) 1/2[r(C -H1)
+ r(C -H6)], ∆r(C-H) ) r(C -H1) - r(C -H6), r(C-N),
r(N-F), (C-N-F), (F-N-F), (N-C-H1), (N-C-H6)
)
(N-C-H7), and (H6-C-H7). There are also vibrational
amplitude parameters constructed by grouping individual am-
plitudes together; the makeup of these is seen in the table of
final results. A trial structure was constructed from the
appearance of the experimental radial distribution curve and
from the ab initio, MW, and ASYM40 results. Refinements of
this structure, based at first on the electron diffraction data alone,
were done by the method of least squares,13 adjusting a
theoretical sIm(s) curve simultaneously to the 10 experimental
data sets using a unit weight matrix. It was quickly discovered
that the parameters r(C-N) and r(N-F) were correlated strongly
with the value of the vibrational amplitudes for these distancess
their average could be determined accurately, but the difference
between them could not. Nor could the parameter ∆r(C-H)
be refined simultaneously with the vibrational amplitudes for
the C-H bonds; it was therefore held at the MP2/6-311++G-
(2d,2p) value. The refinements were next expanded by inclusion
of five sets of three rotational constants Bz derived from the
B0’s for the isotopic species CH3NF2, 13CH3NF2, CD3NF2, sym-
CDH2NF2, and asym-CDH2NF2,3 taking into account the effect
of the expected isotopic shifts r(C-D) - r(C-H); the weighting
of the rotational constant data relative to those from GED was
such as to yield a variance ratio for the final model of about
65:1 ) GED:MW. The MW data comprised a set of constraints
on the structure to be obtained from the GED analysis; their
inclusion removed the ambiguities obtained with use of GED
data alone and allowed the simultaneous refinement of eight
geometric parameters and three amplitude parameters. The
geometric parameter values resulting from this refinement are
given in Table 4 together with values from some of the ab initio
calculations and the earlier MW results. The interatomic
distances and corresponding vibrational amplitudes are given
in Table 5 and the fit to the rotational constants are given in
Table 6. Table 7 is the correlation matrix for the refined
parameters. Intensity curves for the final model are shown in
Figure 2. Intensity curves. Long camera and middle camera curves
are magnified two times relative to the backgrounds on which they are
superimposed. Average curves are in the form sIm(s). The theoretical
curve is calculated from the final model shown in Tables 4 and 5.
Difference curves are experimental minus theoretical.
data in the form sIm(s). The intensity curves with backgrounds
are shown in Figure 2. An experimental radial distribution (RD)
curve was calculated in the usual way from the modified
molecular intensity curve I′(s) ) sIm(s)ZCZF(ACAF)-1 exp(-
0.002s2), where A ) s2F and F is the absolute value of the
complex electron scattering amplitudes, using theoretical inten-
sity data for the unobserved or uncertain region s e 1.75 Å-1
.
The scattering amplitudes and phases (also used in subsequent
calculations) were taken from tables.9 The intensity data and
final backgrounds are available as Supporting Information.
Molecular Orbital Calculations. Ab initio molecular orbital
optimizations of the MeNF2 structure were done with several
bases at different levels of theory using the program Gaussian
94.10 All calculations at the Hartree-Fock level gave a N-F
bond length much shorter (ca 0.06 Å) than the experimental
value earlier reported for this molecule.3 Values from the MP2,

5108 J. Phys. Chem. A, Vol. 102, No. 26, 1998
Hagen et al.
TABLE 1: Optimized Parameter Values for Methyldifluoroamine from Several Levels of Theorya
HF/
MP2/
MP3/
B3LYP/
6-311++ 6-311++ 6-311++
6-311++ 6-311++ 6-311++
6-311++ 6-311++ 6-311++
basis
6-31G(d)
G(d,p)
G(2d,2p) G(2df,2pd) 6-31G(d)
G(d,p)
G(2d,2p) G(2d,2p) 6-31G(d)
G(d,p)
G(2d,2p) G(2df,2pd)
r(C-H1)
r(C-H6)
r(C-N)
r(N-F)
C-N-F
F-N-F
N-C-H1 110.38
N-C-H6 107.26
H6-C-H7 110.00
1.0816
1.0797
1.4500
1.3600
105.08
102.30
1.0834
1.0807
1.4515
1.3500
105.85
102.49
110.74
107.06
109.96
1.0803
1.0780
1.4484
1.3527
1.0812
1.0783
1.4485
1.3481
1.0913
1.0899
1.4613
1.4166
1.0921
1.0834
1.4608
1.4022
104.28
102.22
110.94
106.56
110.20
1.0852
1.0835
1.4580
1.4112
1.0851
1.0832
1.4604
1.3922
1.0936
1.0919
1.4662
1.4144
1.0919
1.0898
1.4644
1.4148
104.50
101.93
111.36
106.54
109.89
1.0887
1.0871
1.4615
1.4154
1.0893
1.0874
1.4609
1.4096
105.75
105.85
103.13
103.73
104.19
103.50
104.30
104.47
102.39
110.67
107.07
109.98
102.48
110.74
107.13
109.96
101.81
110.22
106.78
110.34
101.86
110.76
106.57
110.20
101.85
110.73
106.81
110.10
102.06
110.68
106.99
109.99
101.78
111.26
106.55
109.96
101.87
111.24
106.63
109.93
a Distances in angstroms, angles in degrees.
TABLE 2: Symmetry Coordinates for Methyldifluoroaminea
groups:2,14,15 for NF3 f HNF2 f H2NF they are 0.029 and
0.033 Å. The shortening effect in X-F bonds accompanying
increasing fluorine substitution has long been known. The case
of the NF3 f MeNF2 f Me2NF series has been discussed.4
A′ species
A′′ species
S1 ) ∆r12
S10 ) 1/x2∆(r26 - r27)
S11 ) 1/x2∆(r34 - r35)
S12 ) 1/2∆(R126 - R127
S2 ) 1/x2∆(r26 + r27)
S3 ) 1/x2∆(r34 + r35)
+
-
The molecule MeNF2 is small enough to make possible tests
of the reliability of theoretical calculations for structural
predictions. As is seen in Tables 1 and 4, none of the
calculations at the HF level reproduced the correct N-F bond
length: all resulted in too small values which became still
smaller as the size of the basis set increased, diffuse functions
were added, and polarization included. For the C-N bond and
for the bond angles, the HF calculations gave results in better
agreement with the experimental results, but again larger basis
sets did not lead to improvement. When electron correlation
was included at the MP2 level, the agreement with the
experimental N-F bond length was much improved. Inclusion
of electron correlation at the MP3 level, however, did not change
the results very much and the agreement with the experimental
N-F bond length actually worsened. It is noteworthy that all
results from use of the B3LYP hybrid method, even those from
a relatively small basis set, were in good agreement with the
experimental results.
R
326 - R327
S13 ) 1/2∆(R126 - R127
326 + R327
S14 ) 1/x2∆(R234 - R234
S15 ) 1/6∆(τ1234 + τ1235
τ6234 + τ6235 + τ7234 + τ7235
)
S4 ) ∆r23
R
)
S5 ) ∆R627
)
+
S6 ) 1/2∆(R126 + R127
-
R326 - R327
)
)
S7 ) ∆R123
S8 ) ∆R435
S9 ) 1/x2∆(R234 + R235
)
a For atom numbering see Figure 1.
Figure 2 and the corresponding radial distribution curves are
shown in Figure 3.
Discussion
Table 8 offers a comparison of the structures of several
fluoroamines. Our parameter values for MeNF2 differ somewhat
from those obtained in the MW work. We find the N-F bond
to be slightly shorter, and the C-N bond to be significantly
longer. Because our structure provides a good fit to the
rotational constants as well as the GED data, we feel it to be
the more accurate. The phenomenon of progressive bond
shortening with increasing fluorine substitution is evident. Their
values in the series NF3 f MeNF2 f Me2NF are respectively
0.035 and 0.041 Å. Similar but slightly smaller changes
are seen in the series with hydrogen replacing the methyl
We have also investigated the matter of the apparent violation
of Badger’s rule in the NF3, MeNF2, and Me2NF series of
molecules reported earlier.4 The apparent violation was based
on results of ab initio calculations at the MP2/6-311G(d,p) level
from which it seemed that the N-F stretching force constants
in the series increased with increasing bond length instead of
decreasing as predicted by the rule. As Table 3 shows, we have
been able to fit the observed frequencies of MeNF26 very well
TABLE 3: Symmetry Force Constants, Scale Factors, and Wavenumbers for Methyldifluoroaminea
scale
factorsb
F1
F2
F3
F4
F5
F6
A′
F7
F8
F9
assignments
ωobs
ωcalcd
0.903(3)
0.903(3)
0.927(11) F3
0.927(11) F4
0.935(5)
0.935(5)
0.935(5)
F1
F2
5.499
0.013
0.022 -0.030
0.109 0.079
CH str
3027.0 3039.9
2957.0 2942.7
1443.0 1444.7
1398.0 1397.5
1167.0 1166.5
1047.0 1055.3
857.5
558.0
460.0
5.622
CH sym str
NF sym str
CN str
HCH bend
CH2 wag
NCH bend
FNF bend
5.072
0.411
4.964
F5 -0.077
0.089 -0.063 -0.187
0.114 -0.025 -0.103 -0.288
0.223
0.728
0.089
0.171
F6
F7
0.660
0.063
0.041 -0.087 -0.142
0.957
848.0
558.6
461.5
0.976(21) F8 -0.038
0.976(21) F9 -0.119
0.031
0.049
0.512
0.647
0.015 -0.017
0.012 -0.035 1.863
0.524 -0.074 -0.113 -0.210 0.301 1.839 CNF sym bend
scale factorsb
F10
F11
F12
F13
F14
F15
assignments
ωobs
ωcalcd
0.887(5)
0.927(11)
0.935(5)
0.935(5)
0.976(21)
[1.0]
F10
F11
F12
F13
F14
F15
5.602
0.032
0.191
-0.003
-0.110
-0.010
CH asym str
NF asym str
NCH asym bend
NCH asym bend
CNF asym bend
CN tors
3027.0
1443.0
1134.5
836.0
3027.0
1447.1
1127.1
835.6
419.7
282.9
3.698
-0.107
0.088
0.642
0.034
0.674
-0.117
-0.135
-0.004
A′′
0.661
0.147
-0.002
1.499
-0.021
420.0
0.144
a Stretches in aJ/Å2, bends in aJ/rad2, wavenumbers in cm-1. Coordinates: see Table 2. b Identical values were refined in groups.

Methyldifluoroamine Structure
TABLE 4: Experimental and Theoretical Values for Structural Parameters of Difluoromethylaminea
experimental
theoreticalb
J. Phys. Chem. A, Vol. 102, No. 26, 1998 5109
ED/MWc
MWd
HF
MP2
MP3
B3LYP
e
r(C-H)
1.104(4)
[0.002]
1.091(5)
0.002
1.413(5)
1.449(5)
1.079
0.002
1.353
1.448
1.084
0.002
1.411
1.458
1.084
0.002
1.392
1.460
1.088
0.002
1.415
1.462
104.3
101.8
111.3
106.6
110.0
∆r(C-H)f
r(N-F)
1.406(2)
1.467(6)
104.1(2)
101.7(2)
109.9(11)
106.5(10)
110.6(28)
r(C-N)
C-N-F
F-N-F
N-C-H1
N-C-H6
H6-C-H7
104.6(3)
105.8
103.7
104.2
101.0(3)
110.4(3)
106.2(3)
110.3(3)
102.4
110.7
107.1
110.0
101.9
110.8
106.6
110.2
101.9
110.7
106.8
110.1
a Distances (r) in angstroms, angles ( R) in degrees. Quantities in parentheses are estimated 2σ. b Distances are re. Basis set was 6-311++G(2d,2p).
e
c This work. Distances are rR0. d Ref 3. Distances are rz. r(C-H) ) 0.5‚(r(C-H1) + r(C-H6)). f ∆r(C-H) ) r(C-H1) - r(C-H6).
TABLE 5: Distances and Vibrational Amplitudes in
Methyldifluoroaminea
0
rR
ra
rg
lexp
lcalcd
C-H1
C-H6
N-F
C-N
N‚H1
N‚H6
C‚F
1.104(5)
1.103(5)
1.406(2)
1.467(2)
2.115(12)
2.071(12)
2.265(4)
2.180(3)
2.451(16)
2.530(20)
3.217(8)
1.825(12)
1.813(35)
1.121
1.121
1.406
1.467
2.121
2.076
2.265
2.179
2.450
2.527
3.221
1.843
1.832
1.124
1.123
1.408
1.469
2.126
2.082
2.267
2.181
2.460
2.537
3.224
1.852
1.840
0.056
0.078
0.078
0.049
0.050
(5)
(3)
}
}
0.056
0.051
0.052
0.104
0.107
0.069
0.067
0.157
0.160
0.098
0.125
0.125
0.065
0.063
(4)
}
F‚F
F‚H1
F4‚H6
F5‚H6
H1‚H6
H6‚H7
a Values in angstroms. Quantities in parentheses are estimated 2σ.
Amplitudes in brackets were refined as a group.
TABLE 6: Fits to Rotational Constants for
Methyldifluoroaminea
a
isotope
CH3NF2
A0; B0; C0
Az; Bz; Cz
∆Bz
9857.186
9653.337
5463.855
9650.286
9502.218
5353.879
9096.309
8233.550
4924.541
9397.455
9288.763
5364.260
9690.035
9040.060
5218.680
9837.536
9637.387
5460.505
9634.576
9483.218
5350.649
9086.409
8220.210
4922.979
9384.855
9271.653
5361.030
9674.215
9024.770
5215.910
-2.700
-2.665
-2.721
-2.291
-0.747
-2.054
8.463
2.197
1.954
1.563
0.452
Figure 3. Radial distribution curves for methyldifluoroamine. The
experimental curve is calculated from the average intensity curve with
theoretical data for s e 1.75 Å-1 and with the convergence factor B )
0.002 Å2. Vertical bars indicate interatomic distances, lengths of bars
are proportional to the weights of the terms.
13CH3NF2
CD3NF2
for the symmetric stretch Badger’s rule is obeyed at all three
levels of calculation: the value of the force constant increases
with decreasing bond length. The same is true where symmetry
restrictions are droppedsi.e., in a valence-force fieldsfor the
HF and B3LYP calculations, although for the latter the change
between NF3 and MeNF2 is very small. It is only the valence-
force field results at the MP2 level that display the contrary
trend and hence might be considered a violation of the rule,
but here also the magnitude of the changes is very small. We
have also refined the MP2/6-311++G(d,p) force fields to fit
the observed wavenumbers for the three MenNF(3-n) molecules.
Excellent agreement was obtained, but in accord with general
experience these “experimental” results differ slightly from the
theoretical ones. The values from the symmetry force fields
for NF3, MeNF2, and Me2NF are, respectively, 6.00/3.38, 4.70/
3.34, and 3.96 aJ/Å2 for the symmetric/asymmetric N-F stretch;
from a valence force field they are 4.00, 4.11, and 3.96 aJ/Å2.
The relationship between bond length and force constant value
thus depends on the symmetry coordinates chosen for the
comparison.
sym-CDH2NF2
asym-CDH2NF2
-2.603
-3.652
4.458
-0.147
a ∆Bz ) Bzobs - Bzcalc
.
by modest scaling of a symmetrized force field based on
Cartesian force constants obtained from theoretical calculations
at the slightly higher MP2/6-311++G(d,f) level. We carried
out similar force-constant calculations for the other molecules
of the series, as well as calculations at other levels for
comparison. For NF3 and MeNF2 with more than one N-F
bond the value obtained for the symmetrized N-F stretching
constant(s) from the theoretical Cartesian force field depends
on the coordinates that describe them. If the full symmetries
of these molecules are utilized in constructing the symmetry
coordinates, both a symmetric and an asymmetric N-F stretch-
ing (symmetry) constant results and will have different values.
If the symmetry restriction is dropped, only a single (valence)
N-F stretching constant occurs. We have carried out both types
of calculations with the results seen in Table 9. One notes that
The molecules studied by Badger were both limited in number
and small, and his force fields were very simpleshardly the
symmetry fields we have employed. Further, in the cases of
the polyatomic molecules (triatomic, five-atom tetrahedral, and

5110 J. Phys. Chem. A, Vol. 102, No. 26, 1998
Hagen et al.
TABLE 7: Correlation Matrix (×100) for Parameters of Methyldifluoroamine
a
sLS × 100
r1
r2
r3
l9
l10
l11
4
5
6
7
8
1
2
3
4
5
6
7
8
9
r(CsH)
r(CsN)
r(NsF)
FsNsF
CsNsF
NsCsH1
H6sCsH7
NsCsH6
l(CsH)
l(CsN)
l(C‚F)
0.16
0.20
0.05
5.94
8.08
37.7
100.0
34.8
0.51
0.27
0.40
100
-18
18
-51
42
-23
37
100
-79
-31
-71
29
100
-71
55
100
-42
-6
-47
41
1
-33
37
100
10
17
15
100
-3
-30
-2
24
42
-14
100
-69
4
-28
-62
-33
-25
5
-30
100
-3
13
-4
8
-5
69
5
-6
100
-33
37
10
11
16
-80
-27
-60
-210
100
-29
-29
14
58
100
a σLS is the standard deviation from least squares.
TABLE 8: Structures of Some Fluoroamines from Microwave Spectroscopy and Electron Diffractiona
H2NF HNF2 NF3 MeNF2
MWb MWc
Me2NF
method:
r(X-N)
r(N-F)
X-N-F
F-N-F
MWd
MWe
1.371
102.2
ED/MWf
1.467(6)
1.406(2)
104.1(2)
101.7(2)
MWg
ED/MWh
1.462(7)
1.447(6)
103.6(5)
1.0225(3)
1.4329(3)
101.08(7)
1.026(2)
1.400(2)
99.8(2)
1.449(5)
1.413(5)
104.6(3)
101.0(3)
1.365(2)
102.9(2)
102.4(1)
a Distances in angstroms, angles in degrees. Uncertainties in parentheses from different investigations have different meanings. b Ref 14. c Ref
o
15. d Ref 2b. e Ref 2a; uncertainties not given. f rR values; this work. g Ref 3. h rz values, ref 4.
TABLE 9: Calculated Values for N-F Stretch Force
Constants/AJ‚Å-2 in Fluoroamines
of computing time, and by The Research Council of Norway
(Program for Supercomputing).
force fielda
mode
NF3
MeNF2
Me2NF
Supporting Information Available: Tables of the total
scattered intensity from each plate, final backgrounds, molecular
intensities from each plate, and averaged intensities from each
camera distance (15 pages). See any current masthead page
for ordering information and Web access instructions.
HF/6-311++G(d,p)
symmetry
valence
sym str
asym str
9.17
6.15
7.16
7.50
5.68
6.59
5.89
5.89
MP2/6-311++G(d,p)
symmetry
valence
sym str
asym str
6.14
3.51
4.38
5.07
3.70
4.39
4.43
4.43
References and Notes
(1) Brockway, L. O. J. Phys. Chem. 1937, 41, 185.
(2) (a) Sheridan, J.; Gordy, W. Phys. ReV. 1950, 79, 513. (b) Otake,
M.; Matsumura, C.; Morino, Y. J. Mol. Spectrosc. 1968, 28, 316.
(3) Pierce, L.; Hayes, R. G.; Beecher, J. F. J. Chem. Phys. 1967, 45,
4352.
(4) Christen, D.; Gupta, O. D.; Kadel, J.; Kirchmeier, R. L.; Mack, H.
G.; Oberhammer, O.; Shreeve, J. M. J. Am. Chem. Soc. 1991, 113, 9131.
(5) Badger, R. M. J. Chem. Phys. 1934, 2, 128; 1935, 3, 710.
(6) Atalla, R. H.; Craig, A. D.; Gailey, J. A. J. Chem. Phys. 1966, 45,
423.
B3LYP/6-311++G(2d,2p)
symmetry
valence
sym str
5.84
3.15
4.05
4.78
3.24
4.01
3.86
3.86
asym str
a The symmetry and valence force fields were obtained from the
same Cartesian force fields.
(7) Frazer, J. W. J. Inorg. Nucl. Chem. 1960, 16, 63.
(8) Hedberg, L. Abstracts, Fifth Austin Symposium on Gas-Phase
Molecular Structure, Austin, TX, 1974; p 37.
(9) Ross, A. W.; Fink, M.; Hilderbrandt, R. International Tables of
Crystallography, Kluwer Academic Publishers: Dordrecht, 1992, Vol. 4,
p 245.
(10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, ReVision C.2 and
D.4; Gaussian, Inc.: Pittsburgh, PA, 1995.
seven-atom octahedral) it is not clear what wavenumbers or
masses were used to derive the force constants. If one assumes
the wavenumbers were from the symmetric stretches, then our
results show that the rule applies qualitatiVely as well to NF3,
MeNF2, and Me2NF as it does to Badger’s original examples.
However, the rule defines a quantitative link between bond
distances and bond stretching force constants, and it is clear
from the range of force-constant values (Table 9) that the results
will vary widely for the different sets. To the extent that there
is any value at all in attempting to use Badger’s rule in modern
applications, it is worth noting that, scaled by the factor 0.927,
the symmetry force constants for the symmetric N-F stretches
obtained from MP2/6-311++G(d,p) calculations predict dis-
tances in excellent agreement with those observed: NF3, 1.369
Å; MeNF2, 1.414 Å; and Me2NF, 1.448 Å.
(11) Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 1993, 160, 117.
(ASYM20). The later ASYM40 version presented in: Hedberg, L. Abstracts,
15th Austin Symposium on Molecular Structure, Austin, TX, March 1994.
(12) Because the ra type of distance required for fitting GED data is
not consistent with the fitting of B0 rotational constants, these are brought
0
to a common basis by use of rR type distances and Bz type rotational
constants.
(13) Hedberg, K.; Iwasaki, M. Acta Crystallogr. 1964, 17, 529.
(14) Christen, D.; Minkwitz, R.; Nass, R. J. Am. Chem. Soc. 1987, 109,
Acknowledgment. This work was supported by the National
Science Foundation under grants CHE88-10070 and CHE95-
23581 to Oregon State University and CHE87-03790 to the
University of Idaho, by Oregon State University through grants
7020.
†
(15) Lide, D. R. J. Chem. Phys. 1963, 38, 456.
University.
Oregon State