Endothermic formation of a chemical bond by entropic stabilization: Difluoronitroxide radical in solid argon

Article abstract of DOI:10.1021/ja982222r

Difluoronitroxide radical (F₂NO) has been formed in solid argon matrices by successive addition of two diffusing F atoms to NO. This radical exists in dynamic equilibrium with a van der Waals complex (FFNO). Measurements of the equilibrium concentrations as a function of temperature show that the changes in enthalpy and the entropy associated with formation of the F₂NO radical are ΔH = 1240 ± 180 J/mol and ΔS = 62 ± 10 J/(mol K). Because both these quantities are positive, the equilibrium favors F₂NO only at elevated temperatures. This situation is a rare case in which formation of a chemical bond is stabilized only by an increase in the entropy of the system.

Full text of DOI:10.1021/ja982222r

J. Am. Chem. Soc. 1999, 121, 405-410
405
Endothermic Formation of a Chemical Bond by Entropic
Stabilization: Difluoronitroxide Radical in Solid Argon
Eugenii Ya. Misochko,† Alexander V. Akimov,† Ilya U. Goldschleger,†
Alexander I. Boldyrev,‡ and Charles A. Wight*,‡
Contribution from the Institute for Chemical Physics Research, Russian Academy of Sciences,
142432 ChernogoloVka, Moscow Region, Russia, and Department of Chemistry, UniVersity of Utah,
Salt Lake City, Utah 84112
ReceiVed June 25, 1998
Abstract: Difluoronitroxide radical (F2NO) has been formed in solid argon matrices by successive addition of
two diffusing F atoms to NO. This radical exists in dynamic equilibrium with a van der Waals complex (F-
FNO). Measurements of the equilibrium concentrations as a function of temperature show that the changes in
enthalpy and the entropy associated with formation of the F2NO radical are ∆H ) 1240 ( 180 J/mol and ∆S
) 62 ( 10 J/(mol K). Because both these quantities are positive, the equilibrium favors F2NO only at elevated
temperatures. This situation is a rare case in which formation of a chemical bond is stabilized only by an
increase in the entropy of the system.
Introduction
above 20 K (i.e., well below its melting point),2,3 thereby
forming unstable radicals and reaction intermediates that are
isolated from photolytic precursor molecules.3-7 A propitious
combination of EPR and FTIR spectroscopic detection (carried
out in separate experiments under similar conditions) allowed
us to unambiguously identify the F2NO radical and to report
its fundamental vibrational frequencies for the first time. In
addition, the infrared experiments revealed the existence of an
F-FNO complex that was observed to undergo reversible
transformation to the F2NO radical in solid argon at cryogenic
temperatures. Here, we report the details of that transformation,
When an atom and a molecule come together in the gas phase
to form a chemical bond between them, the system undergoes
a significant change in the types of degrees of freedom. Because
the product of such a reaction is a single molecule, three
translational degrees of freedom are converted to vibrational
modes. The density of translational states of gases is always
higher than that for rotations and vibrations, so the reaction
A + BC T ABC
(1)
always involves a reduction in entropy. Furthermore, the
formation of the bond itself lowers the electronic energy of the
system, so the change in enthalpy is also negative.
k+
[F-FNO]
\{ } F2NO
(3)
k-
in which formation of the second of the two N-F bonds is
favored at elevated temperatures.
∆H < 0
∆S < 0
(2)
If the reactants and products coexist in dynamic equilibrium,
then the maximum concentration of ABC will occur at the
lowest temperature; raising the temperature will invariably
enhance the probability that the bond is broken.
In this paper, we report an unusual case in which the situation
is exactly reversed. The changes in entropy and enthalpy
associated with bond formation are both positive (i.e., bond
formation is endothermic and endergonic). Nevertheless, the
process is observable because the reaction takes place within
the confines of a rare gas matrix and because the reactant
consists of a van der Waals complex of the atom and molecule,
rather than as two translationally free species.
Experimental Section
Samples of nitric oxide and fluorine were prepared in an argon matrix
by vapor deposition of Ar:NO and Ar:F2 mixtures onto a CsI salt
window maintained at 16 K by a closed-cycle helium refrigerator. The
gas mixtures are prepared in separate stainless steel manifolds and the
two streams are mixed together as they exit the deposition tubes just
prior to condensation on the cold window. The sample chamber is
constructed of polished stainless steel and ultrahigh vacuum flanges.
It is pumped by a 50 L/s turbomolecular pump; the base pressure of
this apparatus is typically 5 × 10-5 Pa.
Fluorine was obtained from Spectra Gases, Inc. as a mixture of 10%
F2 in argon and was used without further purification except as noted
We recently reported1 that F2NO and F-FNO are formed in
an argon matrix containing NO and F2 when samples are
photolyzed at 355 nm and subsequently annealed at 24 K for
100 min. The method takes advantage of the ability of F atoms
to diffuse long distances through solid argon at temperatures
(2) Feld, J.; Kunti, H.; Apkarian, V. A. J. Chem. Phys. 1990, 93, 1009.
(3) Misochko, E. Ya.; Benderskii, V. A.; Goldschleger, A. U.; Akimov,
A. V.; Benderskii, A. V.; Wight, C. A. J. Chem. Phys. 1997, 106, 3146.
(4) Misochko, E. Ya.; Benderskii, V. A.; Goldschleger, A. U.; Akimov,
A. V. MendeleeV Commun. 1995, 5, 198.
(5) Goldschleger, A. U.; Misochko, E. Ya.; Akimov, A. V.; Goldschleger,
I. U.; Benderskii, V. A. Chem. Phys. Lett. 1997, 267, 288.
(6) Benderskii, V. A.; Goldschleger, A. U.; Akimov, A. V.; Misochko,
E. Ya.; Wight, C. A. MendeleeV Commun. 1995, 6, 203.
(7) Misochko, E. Ya.; Akimov, A. V.; Wight, C. A. Chem. Phys. Lett.
1998, 293, 547.
† Russian Academy of Sciences.
‡ University of Utah.
(1) Misochko, E. Ya.; Akimov, A. V.; Goldschleger, I. U.; Wight, C. A.
Infrared and EPR Spectra of the Difluoronitroxide Radical. J. Am. Chem.
Soc. 1998, 120, 11520.
10.1021/ja982222r CCC: $18.00 © 1999 American Chemical Society
Published on Web 12/29/1998

406 J. Am. Chem. Soc., Vol. 121, No. 2, 1999
Misochko et al.
below. Nitric oxide was purchased from Matheson Gases and was
purified by vacuum distillation prior to sample preparation. The argon
diluent gas (99.999%) was also purchased from Spectra Gases.
The reagent mixtures were typically prepared at mole ratios of 6.7
× 10-4, so that deposition of equal volumes from the two manifolds
produced samples that have nominal concentrations, Ar:NO:F2 ) 3000:
1:1. However, it was observed that some reaction of the fluorine
invariably occurs in the manifold and deposition line, so that its actual
concentration in the matrix is reduced by as much as 30-50% relative
to the intended concentration. A portion of the stainless steel deposition
line between the cold window and the gas-metering valve was immersed
in liquid nitrogen during sample deposition to remove any impurities
formed by reactions in the manifold.
Ultraviolet laser photolysis of the prepared matrixes was performed
with use of the third harmonic of a Nd:YAG laser (Continuum model
Surelight) at 355 nm. The laser entered the sample chamber through a
fused silica window and impinged on the sample at an incident angle
of 45°. The beam was expanded to an area of about 3.5 cm2 at the
sample to ensure uniform irradiation. The laser was operated at 10
pulses per second. Each laser pulse is nominally 7 ns in duration, and
the average light intensity at the sample was 10 mW/cm2 during
photolysis.
The quantum yield for photodissociation of F2 in solid argon2 at
355 nm is 0.35-0.5. In a typical experiment, the sample was deposited
and subsequently irradiated with 355 nm light (10 mW/cm2 for 200
min at 16 K) to dissociate essentially all of the F2 to F atoms. Then the
sample was annealed at T > 20 K to allow the F atoms to diffuse
through the argon matrix and react with NO molecules. Infrared spectra
were obtained at stages during the experiment by averaging 32 scans
at 0.5 cm-1 resolution with a Mattson model RS10000 FTIR spec-
trometer. The interferometer and detector are located on opposite sides
of the sample chamber, which is equipped with two ZnSe windows to
transmit the infrared beam. This arrangement allows transmission FTIR
spectra to be obtained before, after, or during laser photolysis.
The EPR experiments were carried out in a similar manner. Details
of the apparatus and techniques were described previously.3 Samples
were deposited onto a sapphire rod at 16 K and irradiated with 337
nm light (50 mW/cm2 for 60 min at 16 K). They were then annealed
at 24 K for 100 min to allow the F atoms to diffuse and react with
NO.
Figure 1. Infrared spectra of a sample (Ar:NO:F2 ) 2000:1:1) after
deposition at 16 K (trace a), after exhaustive photolysis at 16 K and
subsequent annealing for 100 min at 26 K (trace b), and after subsequent
annealing for 1000 min at 20 K (trace c). Trace d shows difference
spectra of traces c and b. All spectra were recorded at 16 K.
Results
Infrared Spectra. Illustrated in Figure 1 are FTIR spectra
of an argon matrix containing F2 and NO. The spectrum obtained
immediately after deposition (trace a) shows bands due to NO,
(NO)2, FNO, and NOF. Exhaustive photolysis of the F2 at 16
K produced very little change in the spectrum. However,
annealing for 100 min at 26 K results in the formation of several
product bands (trace b) that were identified as FO2, F3NO, and
F2NO. The last of these is a new species whose infrared bands
were identified for the first time in a preliminary report of this
work.1 A key piece of evidence for identifying the F2NO radical
was the observation of its EPR spectrum in experiments carried
out under similar conditions (vide infra). Kinetic evidence1
shows that this species is an intermediate in the sequential
addition of F atoms to NO, forming FNO, F2NO and F3NO
provided support for the assignment. Finally, the observed
Figure 2. EPR spectrum of the F2NO radical in solid argon at 30 K.
The stick spectrum shows the characteristic triplet of triplets pattern,
as well as overlapping bands due to FO2 impurity radicals.
vibrational frequencies (1573, 813, 761, 705, and 553 cm-1
)
are in good agreement with those calculated by ab initio
quantum theory (vide infra).
observation, coupled with the fact that the pair of doublets lie
close to the frequencies of FNO and NOF, led us to assign the
doublets to the van der Waals complex F-FNO. A summary
of the infrared bands observed in this study is presented in Table
1.
EPR Spectra. Figure 2 illustrates the EPR spectra of a sample
following low-temperature UV laser photolysis followed by
annealing at 24 K. This spectrum, which was obtained at 30 K,
consists of nine narrow lines (a triplet of triplets) that are
characteristic of a radical that contains two equivalent fluorine
Also observed in the infrared spectra of the reaction products
are two doublets at 1800 (1884) and 719 (714) cm-1. Ordinarily,
these bands would not have attracted much attention. However,
we observed that by changing the temperature of the sample in
the interval 17-30 K, this product can be reversibly converted
to the F2NO radical and back again (see trace d of Figure 1).
The reversible temperature conversation of F2NO means that
this new species must be composed from the same atoms. This

Endothermic Formation of a Chemical Bond
J. Am. Chem. Soc., Vol. 121, No. 2, 1999 407
Table 1. Frequencies, Assignments, and Integrated Absorption Coefficients for Reactants and Products in Photolyzed Solid Mixtures of
Ar:F2:NO
assignment and integrated absorption cross sections (km/mol)
freq, cm-1
1884
NO
FNO
(FNO‚‚‚F)
F2NO
F3NOa
(FON)b
1880 (1884)
1877.4
1871.6
1866.5
1863.1
1862.6
1849.6 (1851)
1776.1
1754.2
1681.4
1572.7
905
ν1 (FNO)
isolated NO,b
35 ( 5 (30 ( 5)c
d
(NO)2
NO-F2
ν1, 114 ( 25 (125.0)e
d
(NO)2
2ν4, 120 ( 30
ν1
ν1, 77 ( 20
873.4
813 (808)
761
751 (746)
740.5
734.5
ν4, 370 ( 80
ν5, 65 ( 15
ν2
ν2, 95 ( 20 (92.5)e
ν2
(FON)b
719 (714)
705 (703)
552.7
529
509.8
ν2, (FNO) 62 ( 15
ν3, 48 ( 10
ν6
ν3
ν3
a Assigned in ref 13. b Assigned in ref 14. c Gas-phase value from ref 15. d Assigned in ref 16. e Ab initio calculation from ref 17.
nuclei (hyperfine constant aF ) 143 G) and one nitrogen nucleus
(aN ) 93 G), and corresponds to the F2NO radical.8,9,10,11 At
the center of the spectrum, the spectral lines are overlapped by
lines due to the FO2 radical,12 which is formed by addition of
diffusing F atoms to O2 impurity molecules. The outer lines of
the F2NO radical are well-resolved and have strongly temper-
ature-dependent line widths. In Figure 3, the measured half-
widths of two outer lines are presented as a function of the
sample temperature. The anisotropy of the fluorine hyperfine
constants is very large (∆aF ∼ 10 mT), as reported in our prior
paper,1 and the temperature dependence of the line width is
caused by incomplete averaging of the anisotropy due to
hindered molecular rotation in the matrix.
Kinetics of F2NO Formation. Figure 4 shows the relative
concentrations of NO, FNO, F2NO, F-FNO, and F3NO during
the annealing period at 24 K after 355 nm laser photolysis at
16 K. By comparing the relative intensities of the bands and
using a mass balance equation based on the assumption that all
these species contain only one NO functional group, it was
possible to determine integrated absorption coefficients for the
various bands. These values are listed in Table 1, together with
Figure 3. Plot of the natural logarithm of measured EPR line widths
some gas-phase values that were taken from the literature.13-17
of F2NO as a function of inverse absolute temperature: 1, low-field
line (mF ) -1, mN ) -1); 2, - high-field line (mF ) 1, mN ) 1).
Note that under the conditions of Figure 4, the kinetic behavior
of F-FNO is that of a precursor to F2NO, and that near the
end of the annealing period the concentration of F2NO is much
The kinetic behavior observed illustrated in Figure 4 is
consistent with an overall reaction scheme
greater than that of F-FNO.
F + NO f FNO
F + FNO f F-FNO
F-FNO f F2NO
(4)
(5)
(6)
(8) Vanderkooi, N.; Mackenzie, J. S.; Fox, W. B. J. Fluorine Chem.
1976, 7, 415.
(9) Nishikida, K.; Williams, F. J. Am. Chem. Soc. 1975, 97, 7168.
(10) Morton, J. R.; Preston, K. F. J. Chem. Phys. 1980, 73, 4914.
(11) Morton, J. R.; Preston, K. F. J. Chem. Phys. 1981, 75, 1126.
(12) Adrian, F. J. J. Chem. Phys. 1967, 46, 1543.
(13) Smardzewski, R. R.; Fox, W. B. J. Chem. Phys. 1974, 60, 2193.
(14) Smardzewski, R. R.; Fox, W. B. J. Chem. Phys. 1974, 60, 2104.
(15) Michels, H. H. J. Quantum Spectrosc. Radiat. Tranfer. 1971, 11,
1735.
F + F2NO f F3NO
(7)
After about 100 min of annealing at 24 K, the concentrations
of all observed species reach their limiting values, and no
additional reactions are observed. This is due to the recombina-
(16) Guillory, W. A.; Hunter, C. E. J. Chem. Phys. 1969, 50, 3516.
(17) Ford, T. A.; Agnew, S. F.; Swanson, B. I. J. Mol. Struct. 1993,
297, 255.

408 J. Am. Chem. Soc., Vol. 121, No. 2, 1999
Misochko et al.
Figure 4. Kinetics of consumption of reactant molecules (∆NO) and
accumulation of reaction products during 24 K annealing of a sample
(Ar:NO:F2 ) 2000:1:1) that was exhaustively photolyzed at 16 K. All
concentrations are given relative to the initial concentration of NO
molecules in the sample.
Table 2. Relative Concentrations of NO and Fluorinated Products
in Ar:F2:NO ) 8000:3:1 after Cycles of Photolysis and Annealing
NOa FNOb F2NOb F3NOb
after 1st photolysis and 90 min
annealing at 26 K
after 2nd photolysis and annealing 0.15 0.21
after 3rd photolysis and annealing 0.10 0.19
after 4th photolysis and annealing 0.04 0.16
0.32 0.22
0.38
0.08
0.48
0.46
0.46
0.16
0.25
0.34
a Fraction of initial NO concentration remaining. b Concentration
relative to initial concentratino of NO.
Figure 5. Kinetic plot of the dissociation reaction of F2NO (open
squares) to the van der Waals complex F-FNO (open circles) following
a lowering of the sample temperature from 30 to 20 K. The curves are
tion of the diffusing F atoms with the various species, including
recombination with other F atoms to regenerate the fluorine
photolytic precursor,
single-exponential fits to the data, rate constant k ) 1.4 × 10-4 s-1
.
F + F f F2
(8)
Waals complex F-FNO in solid argon. However, the complex
F-FNO is unstable at 26 K with respect to thermally activated
conversion back to the F2NO radical. The equilibrium constant
of reaction 3 at 26 K is
Some samples were subjected to additional cycles of 16 K
photolysis and annealing at T > 20 K. In these cases, it was
observed that additional F atoms were made available for
reaction, and there was a greater extent of conversion of NO
and FNO to their more fluorinated reaction products. For
example, the relative concentrations of fluorinated products that
formed in four subsequent cycles of photolysis and annealing
are shown in Table 2. It can be seen that under these conditions
more than 96% of the NO can be converted to fluorinated
products, including a nearly 50% yield of F2NO radicals and
35% yield of F3NO molecules. The relative concentration of
F3NO is increased in each cycle, consistent with the reaction
scheme (4-7).
The sample was then cooled to 16 K and photolyzed for a
period of only 5 min. This brief photolysis resulted in the
complete destruction of F2NO and the appearance of the van
der Waals complex F-FNO in its place. Heating of the sample
to 26 K leads to a prompt recovery of the F2NO bands and
disappearance of the F-FNO bands. Similar behavior was
observed for the EPR spectra of radicals in photolyzed and
annealed Ar/F2/NO samples. Short-time photolysis at 16 K
results in complete disappearance of EPR spectra of the F2NO
radical. Subsequent annealing of the sample to 26 K causes the
EPR spectrum of F2NO to be completely recovered. No other
radical products are observed. It is worth mentioning that EPR
spectra of F-FNO complexes and F atoms in an argon matrix
are not detected due to severe anisotropic broadening of the
bands.1
[F2NO]26K
K26K
)
) 6.1 ( 1.2
(9)
[F - FNO]26K
Thermal Interconversion of F-FNO and F2NO. The
thermally activated conversion of F-FNO to F2NO in the dark
following photolysis initially led us to the conclusion that
formation of the second N-F bond in the radical is exothermic.
Therefore, it took us by surprise that when the sample was
cooled to lower temperatures, the F2NO began to disappear and
was replaced by a corresponding growth of the infrared bands
corresponding to the F-FNO complex, as illustrated in Figure
1 (traces c and d). The kinetics of this conversion at 20 K (see
Figure 5) are exponential with a characteristic rate constant of
1.4 × 10-4 s-1. The relative concentration of product and
reactant at equilibrium is
[F2NO]20K
K20K
)
) 0.60 ( 0.12
(10)
[F - FNO]20K
Subsequent heating of the sample to 26 K resulted in the
complete recovery of the F2NO radical in less than 5 min, as
was described in the previous section for the dark reaction
following photolysis.
Because K20 < K26 the N-F bond formation in reaction 3
must be endothermic! To determine the enthalpy of reaction 3,
several measurements of the equilibrium concentrations of F2-
These observations demonstrate unambiguously that the F2NO
radical is dissociated by 355 nm light to the open-shall van der

Endothermic Formation of a Chemical Bond
J. Am. Chem. Soc., Vol. 121, No. 2, 1999 409
Table 4. Structure, Energy, and Vibrational Frequencies of F2NO
QCISD/
cc-pvdz
QCISD(T)/
cc-pvdz
QCISD/
6-311++G**
experiment
(ref 1)
property
R(N-O), nm 0.1183
R(N-F), nm 0.1435
FNO, deg 116.88
0.1176
0.1475
117.11
101.82
0.1179
0.1423
116.74
102.24
FNF, deg
102.11
E
tot, hartrees -328.708229 -328.730038 -328.845002
ω1(a′), cm-1 1580
ω2(a′), cm-1 747
ω3(a′), cm-1 598
ω4(a′′), cm-1 422
ω5(a′′), cm-1 863
ω6(a′′), cm-1 450
1659
710
533
354
806
393
1557
761
613
438
877
472
1573
761
705
813
553
Table 5. Calculated N-F Bond Dissociation Energies of F2NO
BDE,b
kJ/mol
BDE+ZPE,c
total energy
(au)
method/basis seta
kJ/mol
CCSD/cc-pvdz
CCSD(T)/cc-pvdz
CCSD/aug-cc-pvdz
CCSD(T)/aug-cc-pvdz
QCISD/6-311++G**
CCSD/cc-pvtz
CCSD(T)/cc-pvtz
G1
-15.52
-12.38
-0.25
5.15
12.64
9.87
17.24
15.48
19.12
-23.97
-20.17
-8.70
-2.64
3.68
1.42
9.46
6.53
10.17
-328.703 403
-328.726 615
-328.788 109
-328.817 714
-328.845 002
-329.016 388
-329.055 703
-329.105 201
-329.107 558
Figure 6. Logarithmic plot of the equilibrium constant for reaction 3
as a function of inverse absolute temperature.
Table 3. Structure, Energy, and Vibrational Frequencies of FNO
QCISD/
cc-pvdz
QCISD(T)/
cc-pvdz
QCISD/
6-311+G* experiment
property
R(N-O), nm 0.1148
R(N-F), nm 0.1496
FNO, deg 110.04
0.1151
0.1524
110.23
0.1138
0.1501
110.01
0.1136
0.1512
110.08
G2
a All energy calculations were performed at the optimal QCISD/6-
311++/G** geometry. b Classical value, De, not including zero-point
energy corrections. c Zero-point energy corrections were calculated at
the QCISD/6-311++/G** level of theory.
E
tot, hartrees -229.187727 -229.206242 -229.280062
ω1(a′), cm-1 1889
ω2(a′), cm-1 810
ω3(a′), cm-1 546
1861
783
1901
789
1843.5
765.8
515.9
513
525
tational results strongly support the assignment of these five bands to
the F2NO radical. The experimentally observed frequencies were
reported for the first time in a preliminary account of this work.1
We next turned to calculating the strength of the NF bond in the
F2NO radical. The fact that the experiments show reversible intercon-
version of F-FNO and F2NO indicate that this bond is exceptionally
weak, or perhaps metastable; the calculations bear this out. Table 5
lists the bond dissociation energies calculated by using several different
combinations of methods and basis set in order of increasing accuracy.
At the highest level of theory, the results indicate that gas-phase F2NO
is stable with respect to dissociation of one N-F bond, but only by
about 10 kJ/mol.
NO and F-FNO as a function of temperature were made. From
a linear least-squares fit of these data, which are plotted in Figure
6, the changes in enthalpy and entropy for the interconversion,
reaction 3, were determined to be
∆H ) 1240 ( 180 J/mol
(11)
∆S ) 62 ( 10 J/mol K
The uncertainties are limited by the accuracy of the relative
concentration measurements rather than the linear fits to the
experimental data. This result shows that formation of the second
N-F bond in the F2NO radical is endothermic. Furthermore,
the reaction is accompanied by a significant increase in entropy,
more than six times the universal gas constant, R.
Discussion
The measurements of equilibrium relative concentrations of
F-FNO and F2NO as a function of temperature clearly show
that low temperatures favor dissociation of the N-F bond, and
the highest concentrations of F2NO are observed at elevated
temperatures. This result shows that formation of the second
N-F bond in the F2NO radical is endothermic by 1240 ( 180
J/mol and that the reaction is accompanied by an increase in
entropy of 62 ( 10 J/(mol K).
Theoretical Calculations
We carried out several quantum chemical calculations to provide
support for our assignments of the infrared spectra and to provide
additional insight to the energetics of bond formation between F and
FNO.
A direct comparison of these values with ab initio quantum
calculations is not possible because the calculations are strictly
for gas-phase species. At the highest level of theory, the
calculations predict that in the gas phase, N-F bond formation
is very slightly exothermic (bond dissociation energy of 10 kJ/
mol). In solid argon, the initial state is a van der Waals complex,
F-FNO, not the free species F + FNO. Therefore, the binding
energy of the complex and differential solvent effects must be
considered to make a direct comparison between theory and
experiment. We attempted to calculate the energy of the F-FNO
complex, but were unable to locate the equilibrium geometry
due to difficulty in SCF and QCI convergences. Future
experiments in other matrices (krypton and xenon) will be
performed to clarify the influence of solid environment on the
The first series of calculations was performed for FNO. This was
done in part to determine the reliability of the different computational
methods used. These results are presented in Table 3. The QCISD
method, when used with the larger 6-311++G** basis set, yields
structural parameters that are in nearly perfect agreement with the
experimental values. The calculated harmonic vibrational frequencies
differ by only 3% from the experimentally observed fundamental
frequencies.
The same methods were then used to calculate the properties of F2-
NO radical, and these results are presented in Table 4. All three
combinations of method and basis set gave similar bond lengths and
bond angles. The agreement with the frequencies of the five infrared
bands assigned to F2NO in this work is good. At the highest level of
theory (QCISD/6-311++G**), the maximum relative error is 17% and
the root-mean-square relative error is only 8%. Therefore, the compu-

410 J. Am. Chem. Soc., Vol. 121, No. 2, 1999
Misochko et al.
reaction exothermicity. However, for purposes of qualitative
comparison, the ab initio calculations show that the experimental
result presented here is a reasonable one.
Over the experimental range of temperatures (17-26 K) this
function spans the range 6.4-7.1 R.
For the other limit, that of a rotational harmonic oscillator,
we can estimate the characteristic frequency of each of the three
librational oscillators from the barrier height and the corre-
sponding rotational constant
What makes this system particularly interesting is the
observation that the entropy of the F2NO radical is greater than
that of the van der Waals complex F-FNO. An important clue
for why this might be so comes from the EPR data. In our
preliminary report,1 we noted that the F-FNO complex was
not observed at all by EPR because the anisotropy of the g tensor
and the hyperfine constants causes the lines to be severely
broadened. For this reason, neither F atoms nor any complexes
of F with closed-shell molecules have ever been observed in
rare gas matrices by EPR. The fact that the isotropic EPR
spectrum of the F2NO radical is observed at T > 20 K provides
strong evidence that the radical undergoes hindered rotational
motion in solid argon on a time scale that is comparable with
the characteristic time of the EPR measurement. We have
estimated the rotational correlation time from the spectral line
widths in the limit that the radicals undergo rapid incoherent
rotation to be18,19
ν˜B ≈ n(V0B)1/2 ) n(0.695‚V0TB)1/2 ) 13 cm-1 (16)
where we have estimated n ) 4 to be the number of equivalent
configurations of F2NO in an argon lattice site. The librational
entropy is
xi
i
Slib
)
R
- ln(1 - e-x
)
(17)
∑
[
]
exi - 1
i
where
xi ) hcν˜i/kT
To this must be added a term to account for the configurational
entropy
τc ∼ 18H0∆H/ω0∆aF2 ) 10-9
s
(12)
Sconf ) R ln n ) 1.4R
(18)
The entropy in this limit spans the range 4.3-5.5 R over the
experimental range of temperatures.
If we assume that the van der Waals complex F-FNO has a
large barrier to rotation (>100 cm-1) then its rotational entropy
will be negligible at T < 30 K, and the measured ∆S ) 7.5R
for the reaction is therefore quite reasonable in magnitude.
at 25 K. The temperature dependence of the line widths allows
us to estimate the barrier to hindered rotation from the slope of
the plot shown in Figure 3. The result is an estimated barrier
V0 ∼ 35 cm-1
.
The rotational entropy of F2NO can be estimated in two
limits: a librator (rotational harmonic oscillator) or a free rotor.
The actual situation lies somewhere between these limits. For
the free rotor, we have calculated the rotational constants and
characteristic temperatures
Conclusions
We have detected and characterized the F2NO radical and a
van der Waals complex F-FNO in a solid argon matrix. The
two species undergo reversible interconversion at temperatures
in the range 17-30 K. Measurements of the equilibrium
concentrations as a function of temperature show that formation
of F2NO in this reaction is endothermic and involves a
substantial increase in entropy. The structure and weak N-F
bond energy of F2NO has been verified by ab initio quantum
chemical calculations.
A ) 0.38 cm-1
B ) 0.33 cm-1
C ) 0.18 cm-1
TA ) 0.54 K
TB ) 0.47 K
TC ) 0.26 K
(13)
This rare case of entropic stabilization of a chemical bond is
realized only as a consequence of two effects of the solid-state
environment. First, the reactant, F-FNO, is stabilized at low
temperature as a van der Waals complex that does not have
free translational or rotational motion, as it would in the gas
phase. Second, the entropy of the product, F2NO, is greatly
enhanced by its ability to undergo rapid hindered rotation in
the argon matrix. Because of this, the radical can occupy a
relatively large density of states at T > 20 K, thereby reducing
the rate of N-F bond dissociation relative to the bond formation
rate.
from the moments of inertia of F2NO obtained in the ab initio
calculations. Note that the corresponding rotational frequencies
(∼1010 s-1) are only 1 order of magnitude greater than the
observed hindered rotational correlation frequency (∼τc-1) at
25 K. The free rotational partition function in the classical limit
(T . TA) is
T3/2
2(TATBTC)1/2
Zrot
)
(14)
and the rotational entropy is
d(RT ln Zrot)
Acknowledgment. This research is supported by the U.S.
National Science Foundation (Grants CHE-9526277 and CHE-
9618904) and by the Russian Foundation for Basic Research
(Grant 98-03-33175).
3
2
Srot
)
) R + R ln Zrot
(15)
dT
(18) Freed, J. H.; Fraenkel, J. K. J. Chem. Phys. 1963, 39, 326.
(19) Fraenkel, J. K. J. Phys. Chem. 1967, 71, 139.
JA982222R