The shape of the ground and lowest two excited states of H2NO
A. Ricca and J. Weber
Department of Physical Chemistry, University of Geneva, 30 Quai E. Ansermet,
CH-1211 Geneva 4, Switzerland
M. Hanus and Y. Ellinger
Department of Radioastronomy, Ecole Normale Supérievre et Observatoire de Paris, 24 rue Lhomond,
75231 Paris, Cedex 05, France
~Received 1 February 1994; accepted 27 March 1995!
The structure of the ground and lowest two excited states of H2NO have been determined in large
scale configuration interaction calculations using a multiconfiguration self-consistent description of
the molecular orbitals. These treatments are based on a systematic building of the correlation
contribution which has been designed to account for the characteristics of the nitroxide group. This
approach shows that the aminoxyl functional group is more than a three electron group shared by
two atoms, but, in fact, a nine electron entity. Our best estimate of the geometry of the ground
electronic state, obtained after second-order configuration interaction using a large basis of atomic
natural orbitals, is pyramidal. However, since the potential depth between 0° and 40° is lower or of
the same order of magnitude as the estimated inversion frequency, the conclusion that this molecule
behaves like a planar system is totally justified. The structure of the excited (n2 p * ) and ~p2p*!
states have been determined and the transitions energies are in accordance with the experimental
results on the highly substituted stable nitroxide radicals. © 1995 American Institute of Physics.
I. INTRODUCTION
As a genuine radical, H2NO represents the starting point
of the nitroxide radicals, a series of compounds which has
found large variety of applications from spin labels1 to organic magnets.2 This simple species has also been shown to
be a representative model compound for the nitroxide family,
able to account for the modifications of electron paramagnetic resonance ~EPR! signatures3 and electronic
absorptions4 observed for molecules of different geometries.
As to H2NO itself, a rather unstable molecule, only a few
experimental data are available, mostly from EPR
spectroscopy.5 The EPR parameters, obtained in solution or
matrices, could not lead to precise geometrical informations.
A far infrared laser magnetic resonance ~LMR! study has
predicted a planar symmetric geometry.6 More recently, a
gas-phase microwave study7 has shown that the H2NO radical in the ground electronic state behaves like a planar system with C 2 v symmetry. However, the small but negative
inertial defect suggests a possibility that H2NO may have a
double-minimum potential function for the out-of-plane vibration ~Fig. 1!.
On the theoretical side, most of the treatments have been
performed using an unrestricted Hartree–Fock ~UHF! description for the ground state reference configuration. An exhaustive survey of such methods, from unrestricted Möller–
Plesset perturbations ~UMP2, UMP3, UMP4! to unrestricted
configuration interactions @UCISD, UCISD~T!, etc.# means
of the Gaussian package8 has been presented recently.9 The
main conclusions reached by the authors were the following.
~i! Self-consistent field ~SCF! calculations predict planar geometries when the basis set does not contain polarization functions. By contrast, all calculations involving extended basis sets give nonplanar geometries.
~ii! Perturbative calculations show the opposite general
trend, namely, that the out-of-plane deviation and inversion
barriers decrease or even vanish when polarization functions
are added to the valence representation.
~iii! Variational calculations all point to pyramidal geometries. Although the out-of-plane deviation decreases
when including polarization functions, it retains the nonplanar structure; for example, UMP3/6-3111G(d f , p) and
UMP4/6-3111G(d f ,p) yield planar structures, whereas
UCISD/6-3111G(d f ,p) and UQCISD~T!/6-3111G(d f , p)
give a511.45° and 16.90° respectively.
~iv! The other structural parameters do not exhibit significant variations upon the level of theory.
Theoretical treatments based on a restricted description
of the ground-state configuration have also been carried out.
Post restricted Hartree–Fock ~ROHF! calculations using a
perturbative approach3~a! and a DZ1P basis set gave a nonplanar structure with a517°, whereas a recent multireference single and double configuration interaction using a polarized double-zeta basis set ~MRSDCI/DZ1P! study10
concluded to a planar C 2 v structure. The general characteristic of all these calculations is that the orbitals used are
obtained in a variational treatment of a single determinant
function.
In this paper we focus our attention on the geometries of
H2NO, not only in its ground state but also in the lowest two
excited (n2 p * ) and ~p2p*! states commonly observed in
the electronic spectra of nitroxide species. We have used a
multiconfigurational approach necessary to properly account
for the mixing of the two valence bond structures
which determine the electronic repartition between the nitrogen and oxygen atoms. Two basis sets have been employed
which contain small exponents that allow a correct descrip-
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Ricca et al.: The shape of H2NO
275
FIG. 1. Definition of the out-of-plane deviation of the nitroxide group.
tion of the ionic valence bond ~VB! structure: a double-zeta
polarized basis from McLean et al.11 to which diffuse functions have been added following the prescriptions of Dunning and Hay,12 and the atomic natural orbital ~ANO! basis
proposed by Roos and co-workers13 in the (14s9 p4d3 f /
5s4p2d1 f ) for N and O and (8s4 p3d/4s2p1d) for H contraction pattern which proved to yield results of remarkable
accuracy. The search for systematically improved theoretical
descriptions at the multiconfiguration self-consistent field
~MCSCF! and MCSCF/CI ~configuration interaction! levels
is reported together with the structures obtained at each level
of wave function. All calculations have been performed with
the ALCHEMY II package.14
II. QUALITATIVE DESCRIPTION OF H2NO LOWEST
ELECTRONIC STATES
As the simplest system of the nitroxide series, H2NO
represents a typical H2AB molecule whose geometry has
been discussed by Walsh15 in terms of interacting symmetryadapted fragment orbitals. The qualitative behavior of the
orbitals as a function of a is shown in Fig. 2 in the form of
a correlation diagram between C s and C 2 v symmetries.
According to Walsh, the sequence of the H2AB valence
molecular orbitals by increasing energy is as follows.
~i! A low-lying s lone-pair orbital on the peripheral
atom ~O!, which is assumed to take no part in the bonding
whatever the torsion angle a.
~ii! Three s bonding orbitals, the most tightly bound
(a 8 2a 1 ) being largely localized between the heavy atoms
~N–O!. The other two main bonding orbitals are forming the
bonds between the central atom and the two hydrogens. One
of them corresponds here to the in-phase (a 8 2a 1 ) combination of two NH bonds, hereafter referred to as NH~1! , the
other one being the out-of-phase (a 9 2b 2 ) combination
NH~2! . These orbitals are increasingly binding when a goes
to zero because they acquire an increasing s character in the
process.
~iii! A bonding orbital between the heavy atoms
(a 8 2b 1 ), labeled as p considering the local symmetry. Generally localized on the peripheral atom, its bonding character
increases in the planar form.
~iv! A single lone pair orbital, labeled n in the spectroscopic notation and localized on the peripheral atom ~O!.
This orbital (a 9 2b 2 ) which is largely nonbonding, although
interacting to some extent with the NH~2! orbital, is only
weakly stabilized in the planar form.
~v! An antibonding orbital (a 8 2b 1 ) labeled as p*
which is stabilized in the bent structure due to an increasing
s character.
FIG. 2. Walsh correlation diagram for H2AB molecules.
~vi! Three antibonding orbitals (a 8 2a 1 ), (a 8 2a 1 ),
* , and NH(2)
* respec(a 9 2b 2 ) corresponding to NO*, NH(1)
tively. Only the lowest NO* orbital, strongly stabilized in the
planar form, is represented on the diagram.
H2NO is a 13 valence electron system where the extra
unpaired electron is located in the p* orbital. In the planar
form, the electronic ground state configuration of C 2 v symmetry is
~ 1a 1 ! 2 ~ 2a 1 ! 2 ~ 3a 1 ! 2 ~ 4a 1 ! 2 ~ 1b 2 ! 2 ~ 5a 1 ! 2
~ 1b 1 ! 2 ~ 2b 2 ! 2 ~ 2b 1 ! 1
which, in the pyramidal form of C s symmetry, correlates to
~ 1a 8 ! 2 ~ 2a 8 ! 2 ~ 3a 8 ! 2 ~ 4a 8 ! 2 ~ 1a 9 ! 2 ~ 5a 8 ! 2
~ 6a 8 ! 2 ~ 2a 9 ! 2 ~ 7a 8 ! 1 .
According to the qualitative representation illustrated in Fig.
2, the geometry of the 2 A 8 2 2 B 1 ground state of H2NO will
result from an energetical compromise: stabilization of bent
structures due to one electron in the (a 8 2b 1 ) p* orbital vs
stabilization of the planar structure coming from all the other
doubly occupied orbitals.
The lowest two electronic transitions (n2 p * ) and
~p2p*! observed in spectroscopic studies of nitoxide radicals correspond to two excited states of H2NO.
~i! The 2 A 9 2 2 B 2 or (n2 p * ) state corresponding to the
promotion of one electron from the oxygen n O lone pair to
the hole in the p* orbital. The electronic configuration in the
planar form of this excited state of C 2 v symmetry is
~ 1a 1 ! 2 ~ 2a 1 ! 2 ~ 3a 1 ! 2 ~ 4a 1 ! 2 ~ 1b 2 ! 2 ~ 5a 1 ! 2
~ 1b 1 ! 2 ~ 2b 2 ! 1 ~ 2b 1 ! 2
which, in the pyramidal form of C s symmetry, correlates to
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1995
129.194.8.73
On:Vol.
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13 Dec
10:04:25
Ricca et al.: The shape of H2NO
276
~ 1a 8 ! 2 ~ 2a 8 ! 2 ~ 3a 8 ! 2 ~ 4a 8 ! 2 ~ 1a 9 ! 2 ~ 5a 8 ! 2
~ 6a 8 ! 2 ~ 2a 9 ! 1 ~ 7a 8 ! 2 .
With two electrons in the p* orbital, the bent structure will
be undoubtedly favored.
~ii! The 2 2 A 8 22 2 B 1 or ~p2p*! state corresponding
to an excitation within the p system from the bonding p to
the hole in the p* orbital. The electronic configuration in the
planar form of this excited state of C 2 v symmetry is
~ 1a 1 ! 2 ~ 2a 1 ! 2 ~ 3a 1 ! 2 ~ 4a 1 ! 2 ~ 1b 2 ! 2 ~ 5a 1 ! 2
~ 1b 1 ! 1 ~ 2b 2 ! 2 ~ 2b 1 ! 2
which, in the pyramidal form of C s symmetry, correlates to
~ 1a 8 ! 2 ~ 2a 8 ! 2 ~ 3a 8 ! 2 ~ 4a 8 ! 2 ~ 1a 9 ! 2 ~ 5a 8 ! 2
~ 6a 8 ! 1 ~ 2a 9 ! 2 ~ 7a 8 ! 2 .
This electronic state has two electrons in the p* orbital and
should also be pyramidal. The fact that the excited electron
comes from a p orbital which tends to stabilize the planar
structure more than the n O lets anticipate that, the ~p2p*!
state should, according to this model, be more pyramidal
than the (n2 p * ) state.
III. THE 2 A 8 2 2 B 1 GROUND STATE OF H2NO
A. MCSCF wave functions
The qualitative analysis just presented provides a guideline for the design of appropriate multiconfigurational representations of the wave functions for the ground ~GS! and
excited (n2 p * ) and ~p2p*! states.
1. MCSCF $3%
Rewriting the GS electronic configuration in terms of
symmetry-adapted fragment orbitals, the simplest MCSCF to
account for the redistribution of the three electrons inside the
p system is
2
2
1s 2O1s2N2s2ONH~1!
NH~2!
NO2 n 2O$ pp * % 3 .
If, for a planar C 2 v structure the s2p separation is automatically fulfilled, such orbitals however could not be used in
subsequent calculations. The s2p separation, indeed, cannot
be maintained for pyramidal structures where the active orbitals change and acquire a strong s character on N and O.
2. MCSCF $2,5%
The next step in building the multiconfigurational space
and anticipating on the (n2 p * ) calculations is to introduce
the explicit correlation of the NO bond in
2
2
1s 2O1s 2N2s 2ONH~1!
NH~2!
$NONO* % 2 $ n Opp * % 5 ,
where the most active electrons are separated from the s
support. Correlating the two electrons in the sNO bond is
intended to provide a better description of the NO bond
length and, at the same time, to prevent this orbital from
mixing with the p system since it is given its own correlating
function. As MCSCF $3%, this configuration space does not
preserve the nature of the orbitals as p orbitals get a strong s
character when increasing the out-of-plane deviation, with a
large participation of oxygen centered functions.
3. MCSCF $4,9% and $2,2,9%
The results of these small size calculations together with
several attempts to isolate the 2s O orbital pointed out the
necessity of treating the aminoxyl functional group as a
whole entity leading to configuration spaces
* NH~2!
* %4$NOsp On Opp*NO* % 9
1s 2O1s 2N$NH~1!NH~2!NH~1!
or
1s 2O1s 2N$NH~1!NH~1!*%2$NH~2!NH~2!%2
3$NOsp On Opp*NO* % 9 .
The nine electrons of the aminoxyl group, including those of
the oxygen lone pair which has more sp O than 2s O character,
are treated on an equal footing in this description. The remaining four valence electrons which link the substituents to
the aminoxyl group are treated as a unique, although separate, entity in MCSCF$4,9% or as two different groups in
MSCSF$2,2,9% anticipating the treatment of possible nonequivalent substituents. The two wave functions thus defined
retain their chemical meaning with the variation of a.
4. MCSCF $13%
The final step in this systematic build-up of a chemically
meaningful configuration space to generate the orbitals to be
used in subsequent CI calculations is the full valence complete active space self-consistent-field ~CASSCF! function
* NH~*2 ! % 13 .
1s 2O1s 2N$NH~1!NH~2!NOsp On Opp*NO*NH~1!
Such configuration space meets all the desired requirements,
giving well-behaved orbitals as anticipated.
Before turning to the computational aspect of this work,
several points should be outlined. The most important one is
that the aminoxyl functional group is a nine electron entity. It
cannot be reduced any further in a variational multiconfiguration treatment that covers geometrical deformations. Any
partitioning of this $9 electrons in 6 orbitals% space, which is
certainly possible using arbitrary projection techniques, for
example, may result in a nonstable wave function which
could lead to erroneous conclusions; there is no guarantee
that a CI calculation based on these orbitals will give qualitatively correct potential surfaces.
The necessity for including the sp O lone pair and not
only the p O orbital on oxygen in the active space is dictated
by energy considerations linked to hybridization. The MCSCF procedure is indeed telling us that the 2s and 2p orbitals here are too close in energy for the hybridization space to
be split and the 2s/2sp orbital to be frozen as postulated in
the Walsh qualitative description.
The last point is just another confirmation that MCSCF
procedures are numerical methods which do not care about
chemistry, the nature of the orbitals being governed by immediate profit in terms of correlation energy gain. It is then
logical that s components, which bring more correlation energy, are systematically introduced in the orbitals even to the
point of changing the chemical nature of the wavefunction.
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1995
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13 Dec
10:04:25
Ricca et al.: The shape of H2NO
TABLE I. MCSCF optimized geometries and total energies for the ground
state of H2NO. Distances in Å; angles in degrees; energies in a.u.
277
TABLE III. SOCI optimized geometries and total energies of H2NO ground
state. Distances in Å; angles in degree; energies in a.u.
Wave function
r~NO!
r~NH!
/HNH
a
Energy
Orbitals
r~NO!
r~NH!
/HNH
a
Energy
$13%/DZP dif
$4,9%/DZP dif
$2,2,9%/DZP dif
$13%/ANO
1.297
1.307
1.309
1.290
1.028
1.016
1.014
1.000
115.0
118.4
117.1
119.8
33.2
32.1
34.4
20.0
2130.530 78
2130.521 62
2130.517 81
2130.555 27
$2,2,9%/DZP dif
1.310
1.298
1.300
1.291
1.015
1.012
1.016
1.010
117.6
121.5
117.5
120.9
28.3
0.0
30.0
0.0
2130.6949
2130.6946
2130.7963
2130.7053
A. Results of MCSCF optimizations. The optimized geometrical parameters are shown in Table I. It is clear that all
MCSCF calculations indicate a nonplanar structure. The general trends shown in UCI variational calculations9 as a function of the basis extension are reproduced at the MCSCF
level, namely, a shortening of the bonds, an opening of the
HNH angle, and a decrease in the out-of-plane deviation.
B. 2 CI wave functions
While MCSCF theory retrieves only about one-third of
the electronic correlation, it provides well-behaved orbitals
for subsequent CI treatments. Two such treatments of increasing quality have been performed.
1. First-order CI
The first-order corrections to the full valence space are
calculated using the orbitals obtained at the and MCSCF $13%
and $2,2,9% levels. In each case, the first order CI ~FOCI!
n-particle space is composed of the complete valence space
generated by distributing the 13 valence electrons in the 10
valence orbitals ~which is equivalent to the CASSCF space
when MCSCF $13% orbitals are used! to which are added all
the configurations coming from the distribution of 12 electrons in the valence space and one electron in the external
orbitals. The results presented in Table II show the pyramidal
structure of H2NO whatever the orbitals used.
2. Second-order CI
The final plateau in this systematic progression is obtained by adding second-order corrections. The wave functions are expanded in n-particle spaces generated from the
following classes of configurations and using the MCSCF
$2,2,9% orbitals: ~a! the full valence space; ~b! the full first
order space of the aminoxyl functional group; ~c! the full
second order space of the aminoxyl functional group; ~d! all
single excitations from the NH bonds to the external orbitals;
~e! all double excitations from the NH bonds to the external
orbitals.
CI calculations including classes ~a!, ~b!, and ~c! with
the DZP dif basis set give practically no energy difference
between the planar and pyramidal forms ~Table III!. Adding
TABLE II. FOCI optimized geometries and total energies of the H2NO
ground state. Distances in Å; angles in degrees; energies in a.u.
Orbitals
r~NO!
r~NH!
/HNH
a
Energy
$13%/DZP dif
$2,2,9%/DZP dif
1.288
1.318
1.033
1.014
115.2
116.3
24.6
33.5
2130.647 26
2130.592 30
$2,2,9%/ANO
classes ~d! and ~e! ~limited to single excitations within this
CAS space! has the only effect of increasing the out of plane
deviation to a530°; limiting classes to double excitations
with respect to the ground state configuration has no significant effect on the geometry. The same configuration space
used in connection with the ANO basis set leads to very
similar geometrical parameters ~Table III!.
The present results confirm the bent structure obtained in
variational calculations9 with a slightly increased value for
the a angle. The energy difference between the planar and
the bent conformations is, at most, 0.6 kcal in our best
second-order CI calculation ~SOCI!, which is in the range
~0.0–0.9 kcal! of the values reported in the extensive compilation by Komaromi and Tronchet.9 Since the same value is
found for the energy at the top of the barrier ~a50°! and at a
strongly bent structure ~a540°!, it is clear that H2NO is a
very flexible molecule whose properties cannot be accounted
for by a static description, as stated previously in vibronic
studies of its EPR spectrum.16
IV. THE 2 A 9 2 2 B 2 STATE OF H2NO
This state, more often referred to as the (n2 p * ) state in
the nitroxide series, as been optimized at the MCSCF, FOCI,
and SOCI levels of wave functions using the DZP dif basis
set. The results are presented in Table IV.
These values are confirmed by SOCI calculations using,
as previously, the MCSCF$2,2,9%/ANO orbitals and the same
definition for the n-particle space. The final geometrical parameters are
r ~NO!51.470 Å,
r ~NH!51.031 Å,
/HNH5102.2°,
a 573.9.
These results show that the (n2 p * ) state has a highly bent
structure reminiscent of hydroxylamine H2NOH17
~ r ~NO!51.453 Å;
r ~NH!51.016 Å;
TABLE IV. Optimized geometries and total energies for the (n2 p * ) state
of H2NO. Distances in Å; angles in degrees; energies in a.u.
Wave function
MCSCF wave functions
@13#/DZP dif
@4,9#/DZP dif
@2,2,9#/DZP dif
FOCI wave function
@2,2,9#/DZP dif
SOCI wave function
@2,2,9#/DZP dif
r~NO!
r~NH!
/HNH
a
Energy
1.451
1.468
1.457
1.040
1.034
1.030
100.3
102.1
103.7
72.5
72.1
71.0
2130.489 47
2130.483 25
2130.480 45
1.477
1.035
101.4
73.4
2130.547 80
1.470
1.030
102.6
73.3
2130.636 46
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Chem. Phys.,
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1995
129.194.8.73
On:Vol.
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10:04:25
Ricca et al.: The shape of H2NO
278
TABLE V. Optimized geometries and total energies for the ~p2p*! state of
H2NO. Distances in Å; angles in degrees; energies in a.u.
Wave function
r~NO!
r~NH!
/HNH
a
Energy
1.72
1.74
1.033
1.025
110.7
111.5
46.5
45.2
2130.369 28
2130.361 58
1.67
1.02
114.7
43.6
2130.531 63
MCSCF wave functions
@13#/DZP dif
@4,9#/DZP dif
SOCI wave function
@2,2,9#/DZP dif
a 567.4°).
/HNH5107.1°;
10
Previous calculations, assuming C 2 v symmetry in total
contradiction with qualitative models, led to a geometry:
r ~NO!51.413 Å,
/HNH5128.6°;
r ~NH!50.997 Å,
a 50°
which has nothing in common with the real molecule.
V. THE 2 2 A 8 22 2 B 1 STATE OF H2NO
This state, generally referred to as the ~p2p*! state in
the nitroxide series is the second state in the symmetry of the
ground state. It has been optimized as the second root of
(A 8 2B 1 ) symmetry at the MCSCF and SOCI levels of wave
functions using the DZP dif basis set. The results are presented in Table V.
In order to confirm these values in the ANO basis set,
and especially the unusual length of the NO bond, this bond
was reoptimized in a SOCI treatment using the
MCSCF$2,2,9%/ANO orbitals of the second root. A slightly
shorter bond length was obtained: r ~NO!51.642 Å. In the
final calculations, and to limit the size of the external space
generated by the ANO basis set with a minimum loss of
accuracy, we used the natural orbitals of the first order CI on
the aminoxyl group ~with a cutoff of 1025 in the occupation
numbers!. The best estimate of the geometry of this excited
~p2p*! state is then
r ~NO!51.642 Å,
r ~NH!51.029 Å,
/HNH5110.0
a 556.0°
which, with a somewhat longer NO bond, is also a nonplanar
structure resembling the hydroxylamine parent.
VI. QUANTITATIVE DESCRIPTION OF THE LOWEST
ELECTRONIC STATES OF H2NO
A. The shape of the system
The qualitative model presented at the beginning of this
report can now be revisited in the light of the numerical
results obtained in the MCSCF/CI calculations. Three very
different structures are obtained for the three electronic states
considered whose orbital occupation are given in Fig. 3. All
three are bent, but with different torsion angles and NO bond
lengths.
The first point concerns the out-of-plane deviation. We
have found that the ground state is slightly more stable in the
pyramidal than in the planar structure, and that the (n2 p * )
state is more pyramidal than the ~p2p*! state contrary to the
FIG. 3. Orbital occupations of the nitroxide group.
qualitative model. This contradiction is only apparent since it
is based on the assumption that the p orbital is more localized on the peripheral atom which, by consequence means
that the p* antibonding orbital is more localized on the central atom. This is well known of the CO bond in the carbonyl
system, but not true of the NO bond in the aminoxyl group.
A cursory examination of the orbitals reveals just the opposite behavior. In fact, the p and p* (a 8 2b 1 ) orbitals will
both favour the Cs form while the n O (a 9 2b 2 ) still favors
C 2 v symmetry.
It follows that the compromise between the trends to
planar or pyramidal geometries for the ground state is more
fragile than ever expected. The geometry of the nitroxide
group will actually be determined by the perturbation induced by the substituents, which rationalizes the geometrical
changes with the electronegativity of the substituents found
in recent theoretical calculations,18 as well as the large variety of structures, planar19 or pyramidal20 observed in x-ray
diffraction experiments ~see Fig. 4 for selected examples!.
This specific behavior of the p system also explains that
the out-of-plane deviation is larger in the (n2 p * ) than in
the ~p2p*! state. Both states have two electrons in the p*
orbitals which also favors the bent structure. Since the electrons in the n O lone pair have no influence on the geometry,
it follows that the ~p2p*! state which has one electron left
in the p orbital will be less distorded ~a556°! than the
(n2 p * ) state ~a573°! which has kept its two electrons. At
the same time the HNH angle closes from 117.5° to 114.7°
and 102.6° to accomodate pyramidality.
The second point concerns the NO bond length. It can
also be rationalized from Fig. 3 and the so-called ‘‘chemist
bond order.’’21 This bond order, b, is a measure of the number of effective bonds between a specific pair of atoms. It is
defined as
b5 21 ~ p2 p * ! ,
where p and p * are the numbers of electrons in bonding and
antibonding orbitals ~s or p!. A complete view of the various
NO bonds can be obtained from
b
r ~NO!
HNO
H2NO
~GS!
H2NO
(n2 p * )
H2NOH
H2NO
~p2p*!
2
1.14
1.5
1.30
1
1.47
1
1.45
0.5
1.64
which shows that the fractional bond orders fall at the right
place in the sequence.
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Chem. Phys.,
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1995
129.194.8.73
On:Vol.
Fri,103,
13 Dec
10:04:25
Ricca et al.: The shape of H2NO
279
TABLE VI. Computed dipole moment for ground state of H2NO.
Wave function
Method
m xa
m ya
m za
umub
MCSCF $13%
CASSCF
FOCI
SOCI
0.0
0.0
0.0
20.2957
20.3123
20.3495
21.1233
21.1578
21.2359
2.95
3.05
3.26
MCSCF $4,9%
FVCI
FOCI
SOCI
0.0
0.0
0.0
20.3054
20.2999
20.3591
21.1706
21.1576
21.2474
3.07
3.04
3.30
MCSCF $2,2,9%
FVCI
FOCI
SOCI
0.0
0.0
0.0
20.3044
20.3077
20.3642
21.1697
21.1582
21.2412
3.07
3.04
3.29
a
Atomic units.
Debyes.
b
FIG. 4. Selected examples of planar and pyramidal nitroxide radicals.
At the end of this discussion on the shape of the electronic states of H2NO, it should be mentioned that the 2 A 1
structure reported in a recent publication10 ~r ~NO!51.212 Å;
r ~NH!51.308 Å; /HNH5150.6; a50.0°! is only a saddle
point on the potential surface leading to H1HNO when the
C 2 v constraints are released ~r ~NO!51.187 Å; r ~NH!51.520 Å;
/HNH5139.4; a50.0°! as verified at the MCSCF$13%/ANO
level of theory.
B. The electronic properties
The values given in Tables VI and VII show the dipole
moment, transition energies, and transition moments calculated at the various theoretical plateaus presented in this
study. These tables are intended to illustrate how the properties vary as a function of the choice of orbitals and level of
wave function. It can be seen that the values at the full va-
lence level ~CASSCF or FVCI! calculated using the orbitals
obtained in three different MCSCF calculations, i.e.,
MCSCF$13%, $4,9%, and $2,2,9% are slightly different but that
this difference almost vanishes when the configuration space
is extended to second order, justifying the present strategy.
The dipole moment is calculated to be 3.26 D at our best
SOCI level of wave function. It is consistent with the value
of 3.14 D found ~Ref. 22! for tetramethyl-2,2,6,6 piperidine
oxyde ~TANANE @Ref. 20~b!#!.
At the same level, we obtain two vertical transition energies of 6.18 and 2.52 eV for the (n→ p * ) and ~p→p*!
transitions, respectively, to be compared with the transition
energies obtained experimentally for stable nitroxide
radicals,23 namely, the intense absorption ~e'3000! attributed to the ~p→p*! transition at lmax5234 –240 nm ~5.39–
5.17 eV! for all dialkyl aminoxyl radicals and the weak absorption ~e'5! attributed to a forbidden (n→ p * ) transition
in the visible region at lmax5420– 480 nm ~2.95–2.58 eV!.
The shifts in the lmax values come naturally from the large
effects arising from the substituents whose presence is necessary to the stabilization of the nitroxide group.
TABLE VII. Computed transition moments and energies of H2NO.
Transition
Wave function
Method
m xa
m ya
m za
DE b
GS2p→p*
$13%
GS2p→p*
$4,9%
GS2p→p*
$2,2,9%
GS2n→ p *
$13%
GS2n→ p *
$4,9%
GS2n→ p *
$2,2,9%
CASSCF
FOCI
SOCI
FVCI
FOCI
SOCI
FVCI
FOCI
SOCI
CASSCF
FOCI
SOCI
FVCI
FOCI
SOCI
FVCI
FOCI
SOCI
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0475
20.0440
20.0410
20.0325
0.0416
0.0384
20.0331
20.0418
0.0387
0.4531
20.5025
20.5087
0.4650
20.5220
20.5256
0.4644
0.5180
0.5227
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.5782
20.6240
20.6395
0.6283
20.6621
20.6669
0.6300
0.6612
0.6638
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6.61
6.24
6.18
6.72
6.33
6.22
6.72
6.35
6.23
2.33
2.56
2.52
2.29
2.39
2.59
2.29
2.38
2.55
m in a.u.
DE in eV.
a
b
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280
Ricca et al.: The shape of H2NO
V. CONCLUDING REMARKS
In this paper we have reported the results of extensive
calculations on the structures and relative energies of the
H2NO radical in its ground and lowest two excited states.
From a theoretical and computational point of view, there are
several interesting points to this paper.
One is the use of a constructive approach of the electronic correlation whose contribution to the wave function is
systematically improved at each theoretical plateau. This approach which permits to restrict the treatment of correlation
effects to those regions of a molecule where they make important contributions has shown that the nitroxide functional
group is a nine electron entity which cannot be partitioned
without loss of generality on the bending surface. Satisfying
this requirement makes H2NO a well suited model for this
class of radicals which can be used in systematic investigations of the electronic properties of the nitroxide series as a
function of the out-of-plane deviation.4
Another point concerns the pyramidal structure found
for the H2NO ground state. Contrary to H2CO which is a
rigid planar molecule in its ground state, H2NO is a flexible
system with high amplitude motion. However, it has such a
shallow potential well, that it behaves like a planar molecule.
This conclusion, already reached at lower levels of wave
functions in systematic studies of EPR parameters taking
into account the motional averaging,23 is reinforced by the
present calculations. It is also in agreement with the general
finding that the lowest energy vibrational wagging of the NO
bond is larger than the corresponding energy barriers.9 Finally, it is consistent with the suggestion of a possible nonplanar geometry derived from the microwave studies. In general, planar molecules have a small and positive inertial
defect, whereas molecules having large amplitude out-ofplane motion have small but negative inertial defects, and
this is effectively what is observed.7
The last point is the structure found for H2NO excited
(n2 p * ) and ~p2p*! states. The present study shows unambiguously that they are pyramidal, resembling the H2NOH
parent in agreement with the qualitative models of structural
chemistry.
ACKNOWLEDGMENTS
Part of the calculations reported in this paper were supported by the ‘‘Institut du Développement et des Ressources
en Informatique Scientifique ~IDRIS!’’ which is gratefully
acknowledged. This work has also been partially supported
by the Swiss National Science Foundation.
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J.
Chem. Phys.,
No. 2013
1, 1 July
1995
129.194.8.73
On:Vol.
Fri,103,
13 Dec
10:04:25