The Electronic Structure and Vibrational Spectrum of trans-HNOO
ABSTRACT This paper reports the theoretical results of a thorough, state-of-the-art, coupled-cluster, renormalized coupled-cluster, and vibrational study on the molecule imine peroxide, HNOO, in its trans conformation. This molecule is isoelectronic with ozone and presents many of the same difficulties for theory as ozone. We report both the theoretical geometry and the vibrational frequencies, including anharmonic corrections to the computed harmonic vibrational frequencies obtained by calculating the quartic force field at the high levels of coupled cluster theory, including CCSD(T) and its renormalized and completely renormalized extensions and methods including the combined effect of triply and quadruply excited clusters [CCSD(TQ f) and CCSDT-3(Q f)]. The motivation behind our study was the disagreement between two previous reports that appeared in the literature on HNOO, both reporting theoretical (harmonic) and experimental (matrix isolation) vibrational spectra of HNOO. Our new theoretical results and our analysis of the previous two papers strongly suggest that the correct assignment of vibrational spectra is that of Laursen, Grace, DeKock, and Spronk (J. Am. Chem. Soc. 1998, 120, 12583-12594). We also compare the electronic structure of HNOO with the isoelectronic molecules HONO and O 3 . The NO and OO bond lengths are practically identical in HNOO, in agreement with the identical OO bond lengths (by symmetry) in ozone. Correspondingly, the NO and OO stretching frequencies of trans-HNOO are in close proximity to each other, as are the symmetric and antisymmetric OO stretching frequencies in O 3 . This is in contrast to the electronic structure of HONO, which has a large difference between the two NO bond lengths, and a correspondingly large difference between the two NO vibrational frequencies. These results are readily understood in terms of simple Lewis electron dot structures.
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ABSTRACT: Recent studies show that nitrous acid, HONO, a significant precursor of the hydroxyl radical in the atmosphere, is formed during the photolysis of nitrogen dioxide in soils. The term nitrous acid is largely used interchangeably in the atmospheric literature, and the analytical methods employed do not often distinguish between the HONO structure (nitrous acid) and HNO2 (nitryl hydride or isonitrous acid). The objective of this study is to determine the thermochemistry of the HNO2 isomer, which has not been determined experimentally, and to evaluate its thermal and atmospheric stability relative to HONO. The thermochemistry of these isomers is also needed for reference and internal consistency in the calculation of larger nitrite and nitryl systems. We review, evaluate, and compare the thermochemical properties of several small nitric oxide and hydrogen nitrogen oxide molecules. The enthalpies of HONO and HNO2 are calculated using computational chemistry with the following methods of analysis for the atomization, isomerization, and work reactions using closed- and open-shell reference molecules. Three high-level composite methods G3, CBS-QB3, and CBS-APNO are used for the computation of enthalpy. The enthalpy of formation, ΔHof(298 K), for HONO is determined as −18.90 ± 0.05 kcal mol−1 (−79.08 ± 0.2 kJ mol−1) and as −10.90 ± 0.05 kcal mol−1 (−45.61 ± 0.2 kJ mol−1) for nitryl hydride (HNO2), which is significantly higher than values used in recent NOx combustion mechanisms. H-NO2 is the weakest bond in isonitrous acid; but HNO2 will isomerize to HONO with a similar barrier to the HONO bond energy; thus, it also serves as a source of OH in atmospheric chemistry. Kinetics of the isomerization is determined; a potential energy diagram of H/N/O2 system is presented, and an analysis of the triplet surface is initiated. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 378–398, 2007International Journal of Chemical Kinetics 04/2007; 39(7):378 - 398. · 1.19 Impact Factor
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ABSTRACT: Singlet carbenes exhibit a divalent carbon atom whose valence shell contains only six electrons, four involved in bonding to two other atoms and the remaining two forming a non-bonding electron pair. These features render singlet carbenes so reactive that they were long considered too short-lived for isolation and direct characterization. This view changed when it was found that attaching the divalent carbon atom to substituents that are bulky and/or able to donate electrons produces carbenes that can be isolated and storedNature 06/2008; 453(7197):906-909. · 38.60 Impact Factor
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ABSTRACT: Abstract Density functional theory methods correctly describe some properties of nitrosooxides. Electronic spectral data have been calculated for seven para-substituted aromatic nitrosooxides in different solvents using the UB3LYP/6-311+G(d,p) approximation. The calculated positions of maxima in UV spectra correlate with experimental data with high coefficient. Equations are suggested for predicting the positions of absorption maxima for the para-R-C6H4-NOO under studyJournal of Structural Chemistry 01/2006; 47(6):1051-1058. · 0.58 Impact Factor
The Electronic Structure and Vibrational Spectrum of trans-HNOO†
Roger L. DeKock,*,‡,XMichael J. McGuire,§Piotr Piecuch,*,§,@Wesley D. Allen,*,|,+
Henry F. Schaefer, III,|Karol Kowalski,§Stanisław A. Kucharski,⊥Monika Musiał,⊥
Adam R. Bonner,‡Steven A. Spronk,‡Daniel B. Lawson,#and Sandra L. LaursenI
Department of Chemistry and Biochemistry, CalVin College, Grand Rapids, Michigan 49546,
Department of Chemistry, Michigan State UniVersity, East Lansing, Michigan 48824,
Center for Computational Chemistry, UniVersity of Georgia, Athens, Georgia 30602,
Institute of Chemistry, UniVersity of Silesia, Szkolna 9, 40-006 Katowice, Poland,
Department of Natural Sciences, UniVersity of Michigan-Dearborn, Dearborn, Michigan 48128, and
CooperatiVe Institute for Research in EnVironmental Sciences, UniVersity of Colorado,
Boulder, Colorado 80309
ReceiVed: September 19, 2003; In Final Form: December 18, 2003
This paper reports the theoretical results of a thorough, state-of-the-art, coupled-cluster, renormalized coupled-
cluster, and vibrational study on the molecule imine peroxide, HNOO, in its trans conformation. This molecule
is isoelectronic with ozone and presents many of the same difficulties for theory as ozone. We report both the
theoretical geometry and the vibrational frequencies, including anharmonic corrections to the computed
harmonic vibrational frequencies obtained by calculating the quartic force field at the high levels of coupled
cluster theory, including CCSD(T) and its renormalized and completely renormalized extensions and methods
including the combined effect of triply and quadruply excited clusters [CCSD(TQf) and CCSDT-3(Qf)]. The
motivation behind our study was the disagreement between two previous reports that appeared in the literature
on HNOO, both reporting theoretical (harmonic) and experimental (matrix isolation) vibrational spectra of
HNOO. Our new theoretical results and our analysis of the previous two papers strongly suggest that the
correct assignment of vibrational spectra is that of Laursen, Grace, DeKock, and Spronk (J. Am. Chem. Soc.
1998, 120, 12583-12594). We also compare the electronic structure of HNOO with the isoelectronic molecules
HONO and O3. The NO and OO bond lengths are practically identical in HNOO, in agreement with the
identical OO bond lengths (by symmetry) in ozone. Correspondingly, the NO and OO stretching frequencies
of trans-HNOO are in close proximity to each other, as are the symmetric and antisymmetric OO stretching
frequencies in O3. This is in contrast to the electronic structure of HONO, which has a large difference
between the two NO bond lengths, and a correspondingly large difference between the two NO vibrational
frequencies. These results are readily understood in terms of simple Lewis electron dot structures.
The new molecule imine peroxide, HNOO, appeared in the
title of two papers in back-to-back issues of the Journal of the
American Chemical Society in December, 1998. The first, by
Ling, Boldyrev, Simons, and Wight (LBSW),1was entitled
“Laser Photolysis of Matrix-Isolated Methyl Nitrate: Experi-
mental and Theoretical Characterization of the Infrared Spectrum
of Imine Peroxide (HNOO)”. The second, by Laursen, Grace,
DeKock, and Spronk (LGDS),2was entitled “Reaction of NH
(X) with Oxygen in a Solid Xenon Matrix: Formation and
Infrared Spectrum of Imine Peroxide, HNOO”. Both of these
papers relied on the same general experimental techniques
(photolysis, matrix isolation, and infrared spectroscopy) and
similar electronic structure methods (ab initio and density
functional theory). Examination of the reported infrared spectra
shows that the two papers obviously are reporting on different
molecules. The differences in the infrared spectra assigned to
HNOO are large, see Table 1. The assignment of the frequencies
according to the type of motion was done only by LGDS. These
assignments of vibrational motion are obviously only ap-
proximate, except for the torsional motion which is separated
by symmetry from the remainder of the motions. This ap-
proximate assignment of motions will be useful in our discussion
throughout this paper.
The work of LBSW was done in argon matrices and that of
LGDS in xenon matrices, but this difference is not sufficient to
account for the wide frequency disparities.3Some work using
Ar matrices is reported by LGDS, and the differences between
Xe and Ar matrices are small. Furthermore, the reported relative
intensities do not agree for the different bands. A crucial factor
in comparing these two sets of results is the assignment made
to ν3 and ν4, corresponding to the NO and OO stretching
motions. LBSW assign these at 1381.6 and 843.2 cm-1, whereas
LGDS assign them at 1092.3 and 1054.5 cm-1. For the former,
this is a ν3- ν4difference of ∼550 cm-1, whereas for the latter
it is ∼50 cm-1. According to Badger’s rule,4-6these results, in
© 2004 American Chemical Society
Published on Web 02/12/2004
†Part of the special issue “Fritz Schaefer Festschrift”.
* Corresponding authors.
§Michigan State University.
|University of Georgia.
⊥University of Silesia.
#University of Michigan-Dearborn.
IUniversity of Colorado.
J. Phys. Chem. A 2004, 108, 2893-2903
10.1021/jp036809q CCC: $27.50
turn, imply that there is a large difference between the NO and
OO bond lengths for the molecule assigned by LBSW, whereas
there is a small difference between these two bond lengths for
the molecule reported by LGDS. If HNOO has a large difference
in the NO and OO bond lengths it will behave like HONO,
whereas if there is a small difference between these two bond
lengths it will behave similarly to ozone.
There are at least three reasons why the above discrepancies
between the results of the LBSW and LGDS studies deserve a
thorough theoretical examination. First, there is an obvious need
to determine which (if any) of the two interpretations of the
observed vibrational spectra is correct. The discrepancies
between the LBSW and LGDS data are so large that only one
of these two groups can have spectroscopic evidence for the
existence of HNOO. In such a situation, a thorough theoretical
study employing state-of-the-art computational methods based
on first principles of quantum mechanics is essential. The
purported HNOO molecule contains only four atoms. For such
a “small” molecule, a thorough ab initio computational work
should be able to predict the vibrational frequencies with very
high accuracy, allowing one to distinguish between the disparate
assignments in the reported infrared spectra. In particular, the
HNOO molecule is small enough to allow for a large number
of high-level ab initio calculations based on the coupled cluster
theory7,8(cf. refs 9-12 for selected reviews) and its renormal-
ized and completely renormalized extensions.12-15The ability
of the standard coupled-cluster method with singles, doubles,
and noniterative triples [CCSD(T)]16and its higher-order
extensions accounting for the effects of singly, doubly, triply,
and quadruply excited clusters, such as CCSD(TQf),17to
accurately describe geometries, vibrational frequencies, and
other properties of molecular systems is well known.9-11,14,15
The renormalized and completely renormalized coupled cluster
approaches of Kowalski and Piecuch12-15provide further
improvements in the results of the CCSD(T), CCSD(TQf), and
similar calculations when the nondynamical correlation effects
Second, HNOO is isoelectronic with both HONO and O3.
Both of these molecules are implicated in atmospheric chem-
istry27and are therefore of interest to the chemistry community.
Since the electronic structures of HONO and O3 are quite
different, we want to determine whether HNOO mimics one of
these or the other, or if it is unique.
Third, the isoelectronic molecule O3has been the subject of
numerous theoretical studies for two reasons: (1) its multiref-
erence character28,29and significance of higher-order correlation
effetcts,30,31and (2) its importance in environmental chemistry.
Although CCSD(T), CCSD(TQf), and similar coupled cluster
methods are formally single-reference methods, they can very
accurately describe high-order correlation effects, even in
situations characterized by significant multireference character
of the many-electron wave function. In particular, the CCSD-
(T) and CCSD(TQf) methods are known to provide a very good
description of the harmonic vibrational frequencies of ozone,30-32
successfully competing with multireference methods. It is,
therefore, very likely that these and related coupled cluster
methods will provide us with a definitive, high-quality descrip-
tion of the HNOO vibrational spectrum. We might add that the
multireference character of HNOO is a consequence of its
expected diradical nature, commented upon before.33For
systems having multireference and/or diradical character, the
renormalized and completely renormalized CCSD(T) methods12-15
perform remarkably well, improving the results of the standard
CCSD(T) calculations26(cf., also, refs 12-15, 19-21, and
23-25). It is, therefore, very interesting to examine how reliable
the renormalized and completely renormalized CCSD(T) ap-
proaches are in the case of HNOO.
Two close-lying geometric isomers are possible for HNOO,
cis and trans. Both LBSW and LGDS present evidence for only
one isomer in the matrix. Although it is not certain in either
work which of the two forms was experimentally observed, both
papers state that the agreement between theory and experiment
is better for the trans isomer. Hence, this paper focuses only on
theoretical work for the trans isomer. We have completed some
preliminary theoretical work on the cis isomer, but this
information does not alter our analysis of the trans species. The
detailed ab initio study of the cis species will be discussed in a
separate paper. Further details related to a comparison of the
cis and trans isomers are presented in the Appendix.
It is the purpose of this paper to report thorough coupled
cluster studies on trans-HNOO: geometry, harmonic vibrational
frequencies, and, above all, anharmonic corrections to the
frequencies. We then compare the calculated vibrational fre-
quencies with the experimental results of LBSW and LGDS,
and conclude that only the LGDS report is the correct assign-
ment of the spectral lines for HNOO. The calculation of
anharmonic corrections to vibrational frequencies is accom-
plished by generating several highly accurate quartic force fields
for trans-HNOO that correspond to different coupled cluster
approaches employed in this work, using the theoretical
methodology developed in refs 34-38. The reliable information
about the quartic force field and frequencies of fundamental
vibrational transitions corrected for anharmonicities, obtained
in this work, is of primary importance for our discussion, since
one of the main goals of the present study is to answer a basic
question, which of the two assignments of vibrational spectra
reported by LBSW and LGDS is correct. By having access to
“true” frequencies of fundamental vibrational transitions of the
trans-HNOO isomer, resulting from a careful anharmonic
analysis of the highly accurate ab initio electronic structure data,
we eliminate the risk of misinterpreting the spectrum by
comparing the frequencies of the fundamental vibrational
transitions observed in experiment with the approximate vibra-
tional frequencies resulting from harmonic analysis. As part of
our discussion, we critique both the theoretical and experimental
results of both LBSW and LGDS. Furthermore, we compare
our results for HNOO to those of the isoelectronic molecules
HONO and O3. We conclude that the electronic structure of
HNOO is similar to that of O3, and unlike that of HONO.
This paper is organized as follows. (1) We introduce the
computational methods that have been employed, including the
treatment of the electronic structure problem and methods used
to generate the quartic force field of trans-HNOO. (2) We
present our results for several ab initio methods, focusing on
the aforementioned high-level coupled-cluster methods and their
renormalized and completely renormalized variants. (3) We
compare these new theoretical results with the experimental
TABLE 1: Experimental Results for HNOO Reported by
LBSW and LGDSa
LBSW (ref 1)
LGDS (ref 2)
aFrequencies in cm-1, relative intensities in parentheses. See refs 1
and 2 for details regarding the relative intensities.
2894 J. Phys. Chem. A, Vol. 108, No. 15, 2004
DeKock et al.
results of LBSW and LGDS.( 4) We critique the experimental
and theoretical work of both LBSW and LGDS. (5) We compare
our work on HNOO to other experimental and theoretical work
on HONO and O3, to place the HNOO molecule in context. (6)
We summarize our findings.
Our calculations were performed in two steps. First, we
carried out the electronic structure calculations of the optimum
geometry and ground-state potential energy surface of trans-
HNOO required to generate the quartic force field for the
subsequent vibrational analysis, using a variety of coupled
cluster methods. Next, the information about the ground-state
potential energy surface of trans-HNOO was used to determine
the harmonic and anharmonic force constants, from which we
determined the final vibrational frequencies. We begin our
description of the computational procedures employed in this
study with the discussion of the electronic structure calculations.
The electronic structure calculations were initiated by opti-
mizing the geometry of trans-HNOO using the coupled cluster
CCSD(T) approach16and the cc-pVTZ basis set.39Because of
the need for high precision in the calculations of quartic force
fields, we used very tight convergence criteria for the restricted
Hartree-Fock (RHF) and CCSD (coupled cluster singles and
doubles) calculations that preceded the determination of the
CCSD(T) energies and gradients. Thus, we converged the RHF
equations to 10-12for the maximum change in the SCF density
matrix and the CCSD equations to 10-12for the maximum
change in cluster amplitudes defining the CCSD wave function.
In addition, we kept all transformed integrals in the calculations
by setting the relevant cutoff thresholds at 10-20hartree or less.
The CCSD(T) geometry optimization was carried out until the
calculated RMS energy gradient was smaller than 10-10hartree/
bohr. To facilitate the geometry optimization and maintain high
numerical precision throughout the calculations, we used the
analytic gradient capability offered for the CCSD(T) approach
by ACES II.40As in the case of the CCSD amplitude equations,
the CCSD so-called Λ equations,41,42which have to be solved
to calculate the CCSD(T) energy gradient, were converged to
10-12for the maximum change in the coefficients defining the
relevant CCSD Λ vector.
Once the equilibrium geometry of trans-HNOO was deter-
mined with the analytic CCSD(T) gradients, we generated a
common grid of 263 nuclear geometries, centered on the CCSD-
(T) optimum geometry as the reference structure, required for
the subsequent anharmonic vibrational analysis. We used this
grid to perform additional electronic structure calculations, using
a variety of coupled cluster methods, to obtain a few different
force fields for the trans-HNOO molecule. Further details related
to the grid generation procedure and subsequent anharmonic
vibrational analysis are described in a later part of this section.
The coupled cluster methods used to perform the electronic
structure calculations are discussed first.
The basic force field for the present study of the vibrational
spectrum of trans-HNOO was obtained by performing the
CCSD(T) calculations, using the grid of 263 nuclear geometries
mentioned above. We used the same cc-pVTZ basis set and
the same, very tight, convergence criteria for solving the coupled
cluster equations at each nuclear geometry from the grid as used
during the CCSD(T) geometry optimization. To test the reli-
ability of the resulting CCSD(T) vibrational frequencies, we
performed several additional calculations with state-of-the-art
coupled-cluster methods [CCSD(TQf) and CCSDT-3(Qf)17] that
account for the high-order many-electron correlation effects due
to connected quadruply excited clusters neglected in the CCSD-
(T) calculations, and with the renormalized and completely
renormalized CCSD(T) approaches [R-CCSD(T) and CR-
CCSD(T), respectively]12-15that may provide further improve-
ments in the description of diradical molecular systems, such
The need for the additional CCSD(TQf) and CCSDT-3(Qf)
calculations is justified by the fact that the HNOO molecule is
isoelectronic with ozone. It has been established that a highly
accurate description of the harmonic frequencies of ozone (errors
on the order of 10 cm-1) requires the explicit inclusion of the
connected quadruply excited clusters in the calculations.17,30,31
The CCSD(TQf) and CCSDT-3(Qf) methods allow us to
examine the effect of quadruply excited clusters without having
to deal with the prohibitive costs of the full CCSDTQ (coupled
cluster singles, doubles, triples, and quadruples)43-46calcula-
tions. Recall that the CCSD(TQf) method represents an extension
of the standard CCSD(T) approach in which, in addition to the
noniterative energy corrections to the CCSD energy due to triply
excited clusters that are already present in the CCSD(T) theory,
one considers the noniterative energy corrections due to
quadruply excited clusters.17The main advantage of the
CCSD(TQf) approximation is the relatively low cost of calculat-
ing the corrections due to quadruples. The most expensive steps
in the calculation of the noniterative quadruples (Qf) corrections
scale as no2nu5, where noand nuare the numbers of occupied
and unoccupied orbitals, respectively. This should be compared
with the usual and manageable noniterative no3nu4steps of the
CCSD(T) theory, and the prohibitively expensive no4nu6steps
of the CCSDTQ approach, which accounts for the quadruply
excited clusters in the fully iterative fashion.43-46As one can
see, the cost of calculating the noniterative (Qf) correction is
not much greater than the cost of calculating the standard triples
(T) correction of CCSD(T). To verify if the noniterative
treatment of triples in the CCSD(T) and CCSD(TQf) approaches
is sufficient to obtain the desired accuracies, we also performed
the CCSDT-3(Qf) calculations. The CCSDT-3(Qf) approach
represents an extension of the CCSD(TQf) method, in which
one adds the same type of the noniterative energy correction
due to quadruply excited clusters as used in the CCSD(TQf)
approach to the CCSDT-3 energy.47Unlike CCSD(T), the
CCSDT-3 approach, on which the CCSDT-3(Qf) method is
based, is an iterative triples method. For all practical purposes,
the CCSDT-3 approach provides results of full CCSDT (coupled
cluster singles, doubles, and triples) quality,48,49but computer
costs of the CCSDT-3 calculations are smaller than costs of
the full CCSDT calculations.47Thus, the CCSDT-3(Qf) method
can be viewed as an approach which provides results of very
high CCSDT(Qf) quality17(highly accurate results in which
noniterative corrections due to quadruples are added to the full
CCSDT energies) at a fraction of the computer cost associated
with the CCSDT(Qf) calculations.
The CCSD(TQf) calculations were performed on the same
grid of 263 nuclear geometries as used in the CCSD(T)
calculations. Unfortunately, we were unable to do the same for
the CCSDT-3(Qf) method. Although the CCSDT-3(Qf) method
is less expensive than the CCSDT(Qf) and CCSDTQ approaches,
the computer costs of the CCSDT-3(Qf) calculations for the cc-
pVTZ HNOO molecule make it very difficult to obtain all 263
energy values in a reasonable time (despite excellent computer
resources available to us). Because of the relatively large
computer costs, the CCSDT-3(Qf) calculations were performed
only on a subset of 32 geometries required to generate the
quadratic force field (harmonic frequencies). The CCSDT-3(Qf)
Electronic Structure and Vibrational Spectrum of trans-HNOO
J. Phys. Chem. A, Vol. 108, No. 15, 2004 2895
harmonic frequencies were subsequently corrected with anhar-
monicities resulting from the CCSD(TQf) calculations.
As mentioned earlier, we also used the renormalized and
completely renormalized CCSD(T) methods.12-15These new
methods, which are based on the recently developed formalism
of the method of moments of coupled-cluster equations,12-15,18,22,23
provide improvements in the standard CCSD(T) results when
chemical bonds are stretched or broken12-15,19-21,23-25and for
systems having diradical character.26The completely renormal-
ized CCSD(T) approach, [CR-CCSD(T)], is particularly prom-
ising in this regard. As mentioned in the Introduction, the
diradical character of HNOO has already been acknowledged.33
We can, thus, expect that the CR-CCSD(T) method provides
some improvements in the description of the vibrational
spectrum of trans-HNOO. Computationally, the R-CCSD(T)
and CR-CCSD(T) methods have essentially the same costs as
the CCSD(T) approach. They are characterized by the ease of
application of the standard CCSD(T) method. Thus, we had no
problem performing the R-CCSD(T) and CR-CCSD(T)
calculations on the entire grid of 263 geometries, required to
generate the quartic force field of HNOO, using the cc-pVTZ
basis set. As in all other coupled cluster calculations discussed
in this work, we used very tight convergence criteria in the
R-CCSD(T) and CR-CCSD(T) calculations (10-12for the
maximum change in the SCF density matrix and 10-12for the
maximum change in cluster amplitudes).
All R-CCSD(T) and CR-CCSD(T) calculations were per-
formed with the highly efficient system of coupled cluster
computer programs25which forms part of the electronic structure
package GAMESS.50We also used GAMESS, along with ACES
II, to perform the CCSD(T) calculations on the grid of 263
geometries. The CCSD(TQf) and CCSDT-3(Qf) calculations
were performed with the University of Silesia/Michigan State
University package of coupled cluster programs which is
interfaced with the ACES II Hartree-Fock and integral
The results of anharmonic vibrational analyses of various
coupled cluster data available to us are summarized in Table 2.
In addition to the aforementioned CCSD(T), R-CCSD(T), CR-
CCSD(T), CCSD(TQf), and CCSDT-3(Qf) results, we report the
results of the RHF, second-order many-body perturbation theory
(MBPT(2) or MP2), and CCSD calculations, which were
obtained during the CCSD(T) and post-CCSD(T) calculations.
Our discussion focuses on the best results available to us,
TABLE 2: Summary of Anharmonic Vibrational Analyses of trans-HNOOa
RHFMP2 CCSD CCSD(T)R-CCSD(T)CR-CCSD(T) CCSD(TQf) CCSDT- 3(Qf)b
aBond distances in Å, angles in deg, harmonic (ωi) and fundamental (νi) frequencies, and total anharmonicities (∆i) in cm-1.bQuadratic force
field combined with CCSD(TQf) cubic and quartic force constants.
2896 J. Phys. Chem. A, Vol. 108, No. 15, 2004
DeKock et al.
obtained with the higher-level CCSD(T), R-CCSD(T), CR-
CCSD(T), CCSD(TQf), and CCSDT-3(Qf) methods. The RHF,
MP2, and CCSD data are only provided for the completeness
of our presentation. It has been well established that the RHF,
MP2, and CCSD methods do not provide highly accurate
analyses of vibrational spectra. This is particularly true for
HNOO, whose electronic structure is similar to that of the
complicated ozone molecule, where the effects due to higher-
than-doubly excited clusters neglected in the RHF, MP2, and
CCSD methods are significant.
We now describe the computational procedures used to
determine the quartic force fields of trans-HNOO and the corre-
sponding anharmonic vibrational frequencies. As mentioned
earlier, all electronic structure results reported in Table 2 were
obtained on a common grid of points centered on the CCSD(T)
optimum geometry as the reference structure. The high-order
numerical differentiations for the HNOO force constants were
performed with a new computer code, INTDIF2003,51which
is capable of computing any force field through sextic order,
for any molecule and any number of coordinates, via input
information from any order of analytic derivative method,
including energy points alone. The code also uses the symmetry
of Abelian point groups to minimize the number of displace-
ments. INTDIF2003 contains explicitly programmed central-
difference formulas through order 6, does not resort to poly-
nomial fitting schemes, and implements rigorous error control
and monitoring. Regardless of the order of the input information,
the complete set of force constants in a computed field of
maximum order n will be accurate to order n + 2. With tight
convergence of ab initio wave functions described above, the
numerical errors in resulting anharmonic vibrational frequencies
can be reduced well below 0.5 cm-1. In our case, the quartic
force field of HNOO is determined directly from energy points,
and the first numerical contamination in the constants does not
appear until order 6. In total, 262 displacements (190 Cs, 72
C1) were required in addition to the CCSD(T) reference
geometry. The step sizes employed for the central-difference
computations were 0.01 Å and 0.02 rad for distances and angles,
In the first set of analyses, labeled EQ in Table 2, the quartic
force field at the reference structure was used to interpolate the
equilibrium geometry and complete cubic force field at re. In
these computations, geometric perturbations in the dominant,
diagonal stretching, quartic force constants were accounted for
by means of approximate quintic constants52given by frrrrr)
(frrrr)2(frrr)-1, while the remaining quartic constants were not
modulated. In the second set of analyses, labeled NONSTAT,
the accurate CCSD(T) reference structure was invoked as a
common equilibrium geometry, and the quadratic, cubic, and
quartic force constants at this position were used directly in
the vibrational analyses for each level of electronic structure
theory. The theoretical basis for such a vibrational treatment at
a nonstationary geometry is extensively developed by Allen and
Csa ´sza ´r.37The key principle is that at a fixed geometry the error
in electronic structure computations usually diminishes greatly
as the order of the force constant increases, yet the higher-order
force constants are very sensitive to geometric perturbations.
Accordingly, in the usual vibrational analysis scheme, substantial
errors in the gradients at a given level of theory will cause
unnecessary loss of accuracy in corresponding predictions of
higher-order force constants merely by giving an insufficiently
accurate equilibrium structure. In adopting a better reference
geometry, which may be nonstationary at a given level of theory,
a first-order shift term is added to the corresponding potential
energy surface in order to cancel out spurious nonzero gradients
while leaving the more accurate higher-order force constants
unchanged. In this sense, the NONSTAT method can be
employed to approximate an equilibrium vibrational analysis
at a higher (or exact) level of theory that is devoid of errors in
its re structure. The internal coordinates for the NONSTAT
vibrational analyses were the OO, NO, and NH bond distances,
the valence ∠NOO and ∠HNO bond angles, and the ∠HNOO
We report neither NONSTAT nor EQ anharmonicities in
Table 2 for the RHF and MP2 levels of theory because these
methods are grossly deficient in their description of the
electronic structure of HNOO. In addition, anharmonic correc-
tions via the EQ scheme are omitted for the CCSD vibrational
frequencies, because the corresponding optimum geometry is
sufficiently removed from the true equilibrium region and the
CCSD(T) reference structure as to require an unreliable
extrapolation outside our grid points.
After the determination of quartic force fields in the internal
coordinate representation, analytic nonlinear transformations to
the Cartesian space were performed with the program INTDER-
2000,37,53which implements B tensor formulas54through fourth
order for all common internal variables. Upon subsequent linear
transformations of the force fields to the reduced normal
coordinate space, vibrational anharmonic constants (?ij), vibra-
tion-rotation interaction constants (Ri
centrifugal distortion constants were determined using the
formulas of vibrational second-order perturbation theory (VPT2)
as applied to the standard vibration-rotation Hamiltonian for
semirigid asymmetric top molecules.55-58This procedure has
been investigated extensively in systematic ab initio studies of
vibrational anharmonicity by Allen and co-workers.34-36,38,52,59
No resonances were excluded from the VPT2 treatment.
Although the 2ω6and ω3levels are close-lying in several cases,
the anharmonic matrix element between them is too small to
anomalously affect the perturbation treatment. Underlying data
from the vibrational analysis are presented in the Supporting
Information, which includes the quadratic, cubic, and quartic
force constants in the internal coordinate space, along with the
vibrational anharmonic constants.
B), and quartic and sextic
Discussion of the Theoretical Results on HNOO
Bond Lengths. All coupled cluster methods predict the OO
and NO bond lengths to be within about 0.01 Å. The RHF
method predicts the OO bond length to be about 0.1 Å longer
than the NO bond length, whereas the MP2 method predicts
just the opposite. This illustrates the very well-known inability
of the low-order methods to accurately model the electronic
structure of many molecular systems, including the isoelectronic
Harmonic Vibrational Frequencies. Our main interest is
in ω3and ω4, the vibrational frequencies corresponding mainly
to the NO and OO stretching motions. Just as the bond lengths
differ widely for RHF and MP2, so also there is a large
difference between these two associated vibrational frequencies,
∼500-700 cm-1. The differences between ω3and ω4from the
CCSD(T), R-CCSD(T), CR-CCSD(T), CCSD(TQf), and
CCSDT-3(Qf) methods are 128, 76, 67, 82, and 91 cm-1,
respectively, from the EQ results, and 128, 52, 50, 95, and 69
cm-1, respectively, from the NONSTAT results. In brief, our
best theoretical methods predict close proximity in NO and OO
bond lengths and in the harmonic vibrational frequencies
associated with these two bonds.
Fundamental Vibrational Frequencies. Again, our main
interest is in ν3and ν4. The difference between ν3and ν4from
Electronic Structure and Vibrational Spectrum of trans-HNOO
J. Phys. Chem. A, Vol. 108, No. 15, 2004 2897
the CCSD(T), R-CCSD(T), CR-CCSD(T), CCSD(TQf), and
CCSDT-3(Qf) methods are 105, 65, 55, 63, and 95 cm-1,
respectively, from the EQ results, and 105, 35, 38, 76, and 55
cm-1, respectively, from the NONSTAT results. As expected
from the harmonic vibrational frequencies, these fundamentals
are predicted to be close together. The anharmonic corrections
bring them into even closer proximity than they were predicted
at the harmonic level. The agreement between the theoretical
ν3 - ν4 differences (particularly those that result from the
R-CCSD(T), CR-CCSD(T), and CCSD(TQf) calculations) and
the experimental value of ν3- ν4(38 cm-1) is impressive.
Comparison of Theoretical and Experimental Results
To compare the theoretical and experimental results, we
combine some essential results from Table 2 with the experi-
mental results of Table 1 into a new Table 3. Our focus above
was on the third and fourth bands only. In Table 3, we present
all six bands predicted for trans-HNOO from our best four
theoretical methods and compare them to the experimental
results of LBSW and of LGDS.
The results presented in Table 3 strongly favor the assignment
of LGDS and disfavor the assignment of LBSW. Consider first
the highest frequency band, which is assigned to the NH stretch.
The theoretical results, in vacuo, predict this band to occur at
∼3190 cm-1in close proximity to that observed in the Xe matrix
by LGDS, 3165.5 cm-1, but far removed from the frequency
of 3287 cm-1reported in an Ar matrix by LBSW. Turning to
the second band, HNO bend, it was not observed in the
assignment of LBSW. LGDS report this band at 1485.5 cm-1
to be compared with ∼1500 cm-1from the theoretical results.
This is excellent agreement indeed. The third band, NO stretch,
is assigned by LGDS at 1092.3 cm-1, in good agreement with
the theoretical value of ∼1125 cm-1. However, LBSW assign
this band at 1381.6 cm-1, in very poor agreement with theory.
The fourth band, OO stretch, is assigned by LGDS at 1054.5
cm-1, in excellent agreement with the theoretical prediction of
∼1060 cm-1. However, LBSW assign the fourth band at 843.2
cm-1, again in very poor agreement with theory. LGDS claim
not to have observed the fifth band. LBSW assign this
fundamental at 670.1 cm-1, and the computed value is ∼650
cm-1. Finally, the sixth band is reported by LGDS at 764.0
cm-1, in excellent agreement with the theoretical value of ∼765
cm-1. The sixth band reported by LBSW is at 790.7 cm-1.
In summary, there is very good to excellent agreement
between the theoretical results and the experimental assignment
of LGDS to the HNOO molecule, but very poor agreement with
the assignment of LBSW. Further conclusive evidence for the
assignment of LGDS is provided by a comparison with the
isotopic shift data reported for HNOO by LBSW using
deuterium substitution and by LGDS using O-18 substitution.
The theoretical and experimental isotopic shifts are sum-
marized in Table 4. We examine first the deuterium substitution
work of LBSW. There was an observed shift of 844 cm-1in
the first band and 301 cm-1in the “third” band. (The ν2band
was assumed undetected.) These shifts are in very poor
agreement with the computed shifts of approximately 800 and
10 cm-1, respectively. If we assume that the second observed
band is in fact the ν2band, then the agreement between theory
and experiment is better, ∼260 vs 301 cm-1, although still not
acceptable. In any case, there is very poor agreement between
theory and LBSW’s experiment for both band shifts. The last
three bands assigned by LBSW to HNOO also show extremely
poor agreement with the computed isotopic shifts, as seen in
Table 4. The fourth theoretical band is predicted to exhibit a
shift of ∼80 cm-1, whereas the LBSW’s experimental assign-
ment places the shift at 20 cm-1. The fifth theoretical band is
TABLE 3: Comparison of Experimental and Theoretical Vibrational Frequencies, cm-1
TABLE 4: Isotopic Vibrational Frequency Shifts (cm-1) for trans-HNOO
-11 (or -82)
-203 (or -132)
aExcluding ω3- 2ω6resonance.
2898 J. Phys. Chem. A, Vol. 108, No. 15, 2004
DeKock et al.
predicted to exhibit a shift of ∼20 cm-1, whereas the LBSW’s
experimental assignment places the shift at 11 cm-1. Finally,
the sixth theoretical band is predicted to exhibit a shift of ∼180
cm-1, whereas the LBSW’s experimental assignment places the
shift at ∼200 cm-1. All in all, there is very poor agreement
between the results of our high-level coupled-cluster calculations
including anharmonicities and LBSW’s experiment for all of
We turn now to the O-18 isotopic shift work of LGDS. The
experimental work reported isotopic shifts for HN18OO, HNO18O,
and HN18O18O. Since five bands were observed for each
molecule and we have three isotopic variants, there are fifteen
bands for which we can compare theory and experiment, Table
4. These fifteen numbers show an astonishing agreement
between theory and experiment, usually within 1 cm-1. This
very close agreement between theory and experiment provides
further evidence for the assignment of LGDS.
Critique of Previous Experimental Results on HNOO, O3,
Comparison of Photolytic Precursor. Both the LBSW and
LGDS papers utilized the experimental techniques of photolysis,
matrix isolation, and infrared spectroscopy. The starting mol-
ecule for LBSW was methyl nitrate, CH3ONO2, whereas that
for LGDS was hydrazoic acid, HN3, followed by reaction with
In the work of LGDS, hydrazoic acid is photolyzed to HN
and N2. Generation of the HN precursor from HN3has been
reported in two other publications.60,61So the purported reaction
HN + O2f HNOO is very simple and “clean”. Nonetheless,
there are numerous bands reported in the matrix isolation
experiment that are assigned to “impurity” molecules by LGDS.
These include cis-HONO, trans-HONO, NH2OH, N2H2, H2O,
and CO2. These impurity molecules could be identified on the
basis of other matrix isolation experiments, and upon the
behavior of the bands to further annealing and photolysis. Hence,
although there were six impurity molecules, the behavior of the
various bands due to these molecules was fairly well understood.
The assignment of the new bands to HNOO was based upon
the simple chemistry of the system and the photolytic behavior
of these bands to form both cis-HONO and trans-HONO
molecules in the matrix.
In contrast to the relatively simple system described above,
the photolysis of methyl nitrate results in a plethora of bands.
LBSW propose that methyl nitrate decomposes via two channels.
One channel forms formaldehyde (H2CO) and hydrogen nitryl
(HNO2), and another forms formaldehyde and HNOO. We count
23 bands in Table 1 of LBSW, due to photoproducts of methyl
nitrate after 20 min of photolysis, and 41 bands after 520 min
of photolysis. Out of the first 23 bands, five bands were labeled
as C, which were eventually assigned to HNOO. A strong factor
in the assignment of these bands to HNOO was the excellent
agreement between the QCISD62(quadratic configuration
interaction with singles and doubles) harmonic frequencies for
HNOO and the bands labeled as C. The inability of the QCISD
theoretical method to accurately model the electronic structure
of HNOO will be discussed below.
Comparison to O3. Given that HNOO is isoelectronic to O3,
it is worthwhile to compare the symmetric and antisymmetric
stretching frequencies of ozone to the corresponding bands of
HNOO. LGDS stated that “It may be reasonable to think of
HNOO as an ‘isotopically substituted’ ozone molecule, since
the NH group is of similar mass to an oxygen atom and is poorly
coupled to the lower-frequency modes.” The assignment of
LGDS of the NO and OO stretching motions is to bands at
1092.3 cm-1and 1054.5 cm-1. These “...frequencies are
remarkably close to the ozone stretching frequencies at 1103
cm-1and 1042 cm-1(gas phase).” These two bands are
separated by 37.8 cm-1for HNOO and 61 cm-1for O3. LBSW
assigns these two stretching modes at 1382 cm-1and 843 cm-1
for HNOO, separated by 539 cm-1, and far removed from the
corresponding bands in ozone. In this respect the assignment
of LBSW shows substantial similarity to HONO.
Comparison to HONO. Given that HNOO also is isoelec-
tronic with HONO, it is worthwhile to compare the NO and
OO stretching frequencies of HNOO with the two NO stretching
frequencies of HONO. For purposes of comparison, we will
quote our results from LGDS corresponding to the Xe matrix.
The results quoted by LBSW in an Ar matrix are very similar.
For trans-HONO in a Xe matrix, the NO stretching frequen-
cies occur at 1680 and 794 cm-1; the equivalent modes in cis-
HONO absorb at 1626 and 842 cm-1. These bands are separated
by 886 cm-1and 784 cm-1; this splitting is in reasonable
agreement with the 539 cm-1splitting as assigned by LBSW
to HNOO. This is completely different from the splitting of the
two stretching modes in ozone (∼60 cm-1). The NO-OO
splitting results of LGDS suggest a molecule with an electronic
structure similar to ozone, whereas the results of LBSW suggest
an electronic structure closer to HONO than ozone.
On the basis of the coupled cluster results reported above,
the electronic structure of HNOO is much more like that of
ozone than of HONO. Hence, we expect the vibrational
frequencies to be similar to those of ozone and not of HONO,
as argued by LGDS and as summarized above. But this bald
statement can be further justified by presenting theoretical results
on HNOO, HONO, and O3.
Theoretical Results on Isoelectronic Molecules
HONO. We write three Lewis electron dot structures for
We expect the first structure to dominate; it shows a single
bond between the central N and O atoms and a double bond on
the terminal pair. The second structure, in which the single and
double bonds are interchanged is less important, as there are
nonzero formal charges on the two oxygen atoms. The third
structure, meant to depict diradical character, also is unimportant
for reasons of formal charge. Both the experimental and
theoretical work reported in the next paragraph support the
assertion that the first resonance structure is dominant.
Table 5 presents experimental and theoretical data related to
the NO bond lengths and their associated vibrational frequencies
for trans-HONO. The experimental difference in the two bond
lengths is approximately 0.25 Å; the corresponding computed
difference is approximately 0.20 Å at the Hartree-Fock level
and 0.24 Å at levels that include correlation [MP4, QCISD,
CCSD(T)]. The difference in the frequencies assigned to the
NdO and N-O stretching motions is near 900 cm-1, whether
by experiment, Hartree-Fock, or one of the more advanced
theoretical methods. In particular, the QCISD approach, used
by LBSW in their study of HNOO, works reasonably well for
HONO. The problem is that the electronic structure of trans-
Electronic Structure and Vibrational Spectrum of trans-HNOO
J. Phys. Chem. A, Vol. 108, No. 15, 2004 2899
HNOO has little in common with HONO and a lot in common
with ozone, for which QCISD fails (see below). A reasonable
performance of QCISD for HONO does not guarantee that the
same is true for ozone and HNOO.
O3. By contrast to the above description of HONO, the
electronic structure of ozone is murky indeed. For ozone, three
Lewis electron dot structures are needed.
The first two structures show a positive charge on the central
atom and are analogous to those for HONO. The last structure
has diradical character; it exhibits weakly paired π electrons
on the terminal heavy atoms, and zero formal charge on all the
atoms. No single resonance structure is predicted to be dominant.
From the point of view of theory, the diradical character means
that we expect multireference character in the ground state of
ozone or the significant role of the connected triply and
quadruply excited clusters if we want to retain a single reference
It has been known for at least thirty years that a minimum of
two electronic configurations is needed to describe the ground
state of ozone.28In one configuration, two of the four π electrons
are in the bonding π molecular orbital, depiction + + +, and
two in the nonbonding π molecular orbital, depiction + ‚ -.
(The symbols represent the signs of the π lobes from above,
and the dot represents a node at that atom.) In another, the two
occupied π molecular orbitals are depicted as + + + and
+ - +.29This multireference character has made it difficult to
compute vibrational frequencies that are close to the observed
frequencies for ozone, see Table 6. A total of 10 theoretical
results are presented, and compared to experiment.
The results for the symmetric stretching frequency lie in the
range 1133-1278 cm-1, except for those of the HF and CISD
methods, which are much higher. All of these results are
reasonably close to the harmonic frequency derived from
experiment, 1135 cm-1. The bending frequency results all occur
in the range 707-762 cm-1, except for those of HF and CISD,
which are much higher. This also is in close agreement with
(harmonic) experiment, 716 cm-1. The results for the antisym-
metric stretch are much worse. The experimental (harmonic)
value is 1089 cm-1, and the computed values range from a high
of 2241 (MP2) to a low of 968 cm-1[QCISD(T); for a
description of the QCISD(T) approach, which is a QCI analogue
of CCSD(T), see ref 16]. The range is so large that the MP2
and CISD methods predict the antisymmetric stretching fre-
quency to be higher than the symmetric stretching frequency.
Of the results presented in Table 6, the methods70,71that show
the closest agreement with experiment are CCSD(TQf) (used
in this work) and CCSDT(Qf) [approximated in this work by
CCSDT-3(Qf)]. In these two cases, the splitting between the
stretching harmonic frequencies is 50 and 21 cm-1, respectively.
The CCSD(T) and CCSDT results also are in good agreement
with experiment, with splittings of 99 and 46 cm-1, respectively.
The QCISD and QCISD(T) results show a splitting between
the symmetric and antisymmetric stretching frequencies of 258
and 176 cm-1, respectively, compared to an experimental
splitting of 46 cm-1. It is our contention that, just as the QCISD
method overestimates the splitting between the symmetric and
antisymmetric stretches in ozone, it does the same for the
splitting between the NO and OO stretches in imine peroxide.
We will substantiate this point with new theoretical results
reported in the next subsection.
HNOO. In Table 7 we gather the bond lengths and frequen-
cies primarily associated with the NO and OO stretching motions
for trans-HNOO. Included are the QCISD results from LBSW,
and new results that we have obtained using the QCISD(T)
theoretical method. The QCISD and QCISD(T) data are
compared to a selection of our best coupled-cluster results,
obtained with the CR-CCSD(T), CCSD(TQf), and CCSDT-
The results in Table 7 show that Hartree-Fock theory is
incapable of describing the competition between the NO and
OO bonds for electron density, as we have discussed previously.
The second column shows the QCISD result from LBSW.
Compared to the Hartree-Fock result, the QCISD method
predicts a lengthening of both the NO bond (0.07 Å) and the
OO bond (0.04 Å); the NO distance is still 0.07 Å shorter than
the OO bond. This has substantial implications for the corre-
sponding frequencies. The NO stretch is predicted at 1391 cm-1
and the OO stretch at 841 cm-1, for a separation of 550 cm-1,
when the QCISD method is employed. This is not as large as
the 719 cm-1separation predicted by the Hartree-Fock method,
but it is substantially greater than the values predicted by our
best coupled cluster results, as shown in Tables 2, 3, and 7.
The QCI formalism is unable to produce the very small, ca. 50
cm-1difference between ν3and ν4observed in our calculations
and experiment, since even the better QCISD(T) approach
produces a difference of ∼200 cm-1between these two
TABLE 5: Experimental and Theoretical Data Associated with the NdO and N-O Stretching Motions of trans-HONOa
r(NdO) (Å) 1.1701.1531.144
r(N-O) (Å)1.432 1.3451.342
ν2(NdO) 1700 18202032
δ (ν2- ν4)910 850953
aThe theoretical frequencies are unscaled and harmonic, cm-1. The results from this work were obtained with Gaussian 98.67
TABLE 6: Experimental and Computed Harmonic
Stretching Frequencies (cm-1) for O3a
aAll of the results are with the cc-pVTZ basis set. The QCISD results
are from this work, using Gaussian 98.67The others are taken from the
monograph by Jensen,69except as noted.
2900 J. Phys. Chem. A, Vol. 108, No. 15, 2004
DeKock et al.
Our best theoretical calculations, including the calculations
performed with the state-of-the-art CR-CCSD(T), CCSD(TQf),
and CCSDT-3(Qf) methods, predict the NO and OO bond
lengths to be practically identical. In consequence, the corre-
sponding vibrational frequencies are predicted to be much closer
together. Clearly, our best theoretical methods reproduce the
observed ca. 38 cm-1difference between ν3and ν4extremely
well. The QCISD and QCISD(T) methods cannot do it.
The three Lewis electron dot structures for HNOO are
analogous to those for ozone.
Our theoretical structure and frequency results for HNOO predict
it to be similar to that of ozone, and not similar to HONO. This
fits with simple predictions based upon Lewis electron dot
In summary, these results on HONO, O3, and HNOO show
that the RHF and QCISD methods cannot adequately describe
the electronic structure of the latter two molecules. This forces
us to question the assignment reported by LBSW, who used
the QCISD methodology to support their findings. By contrast,
the more advanced of the coupled cluster results on ozone,
employing methods used in this work, are excellent, and so we
expect that they also describe the essential features of HNOO.
The trans-HNOO molecule has OO and NO bond lengths
and vibrational stretching frequencies close together from theory
and experiment. According to the results of LGDS, the stretching
frequencies appear at 1092 and 1055 cm-1in a Xe matrix.
Computed stretching frequencies using advanced coupled cluster
methodologies, particularly CR-CCSD(T), CCSD(TQf), and
CCSDT-3(Qf), corrected for anharmonicities, are in excellent
agreement with this result for the trans isomer.
We believe that the experimental results of LBSW do not
provide strong evidence for the formation of HNOO from
photolysis of CH3ONO. There are too many photoproducts in
the matrix and the reaction is too complex to identify HNOO
as a primary product. Furthermore, the QCISD theoretical
method, used by LBSW to argue in favor of their assignment
of the observed spectrum, is not to be trusted for the HNOO
molecule as indicated by results in Table 7; the QCISD approach
and its QCISD(T) extension to account for the effect of triples
do not provide good results for the isoelectronic ozone, Table
Contrary to the poor results obtained from QCISD and
QCISD(T), we believe that the results provided by the CCSD(T)
approach and the more advanced coupled cluster methods used
in this work are trustworthy on the basis of their ability to
provide Very good results for ozone. The CCSD(T) method
utilizing a basis set such as cc-pVTZ has been shown to provide
high-quality results for a wide range of molecules.72Nonethe-
less, we do recognize that excellent theoretical vibrational
frequencies for molecules such as ozone may require a higher
level of theory than CCSD(T). Hence, we have included in our
study the results of some of these more advanced methods
accounting, in particular, for the combined effect of triply and
quadruply excited clusters. Kucharski and Bartlett31have shown
that connected quadruple excitations are needed for quantitative
structure and frequency predictions of ozone.
In the work reported here we must decide whether the NO
and OO stretching frequencies occur at 1382 and 843 cm-1as
reported by LBSW, or at 1092 and 1055 cm-1as reported by
LGDS. For such a large difference, the CCSD(T) method with
the cc-pVTZ basis set seems more than adequate, although we
decided to be very critical and tested the reliability of the
CCSD(T) approach in the calculations for HNOO by performing
a large number of additional calculations with the R-CCSD(T),
CR-CCSD(T), CCSD(TQf), and CCSDT-3(Qf) approaches. Our
studies indicate that the CCSD(T) results are improved upon
by the R-CCSD(T), CR-CCSD(T), CCSD(TQf), and CCSDT-
3(Qf) methods, although CCSD(T) is capable of providing a
reasonable description of the HNOO geometry and spectrum.
Our excellent agreement between the experimental and theoreti-
cal CCSD(TQf) and CCSDT-3(Qf) vibrational frequencies of
HNOO is in accord with the similar agreement observed by
Kucharski and Bartlett for ozone.31It is very interesting to
observe that the recently proposed CR-CCSD(T) method of
Kowalski and Piecuch,12,13which is not much more expensive
than CCSD(T), provides an excellent description of the vibra-
tional spectrum of trans-HNOO. The CR-CCSD(T) results are
better than those obtained with the standard CCSD(T) ap-
proximation when the NO and OO stretches are considered. This
is probably related to a partially multireference or diradical
character of HNOO, which should be well described by the CR-
Acknowledgment. This work was partially supported by the
National Center for Supercomputing Applications under grant
number CHE990012N and utilized the Exempler X-Class
machine billie.ncsa.uiuc.edu at the National Center for Super-
computing Applications, University of Illinois at Urbana-
Champaign. The majority of the coupled cluster calculations
were performed on a 32-processor Origin 3400 system at
Michigan State University obtained through a grant from the
National Science Foundation, Chemical Instrumentation #9974834.
Some of our work was performed on a Beowulf cluster at Calvin
College, obtained through a grant from the National Science
Foundation, NSF-MRI Grant 0079739. The Dreyfus Foundation
provided financial support to A.R.B. and S.A.S. through a
Camille and Henry Dreyfus Scholar/Fellow Program for Un-
dergraduate Institutions grant to RDK. The latter acknowledges
TABLE 7: Pertinent Theoretical Data Associated with the NO and OO Stretching Motions of trans-HNOOa
δ (ω3- ω4)
aThe QCISD and QCISD(T) results employ the 6-311+G* basis set. The QCISD(T) values were obtained with Gaussian 98.67
of comparing frequencies, ω3and ω4EQ values are given with corresponding NONSTAT results in parentheses.
Electronic Structure and Vibrational Spectrum of trans-HNOO
J. Phys. Chem. A, Vol. 108, No. 15, 2004 2901
Calvin College for a Calvin Research Fellowship and a
sabbatical leave that supported this work. Acknowledgment is
made to the Donors of the American Chemical Society
Petroleum Research Fund, for partial support of this research
through the Undergraduate Faculty Sabbatical program. The
work at the University of Georgia was supported by the U.S.
Department of Energy, Office of Basic Energy Sciences,
Combustion Program (Grant DE-FG02-97ER14748) and Sci-
DAC Computational Chemistry Program (Grant DE-FG02-
01ER15226). The work at Michigan State University was
supported by the Department of Energy, Office of Basic Energy
Sciences, SciDAC Computational Chemistry Program (Grant
DE-FG02-01ER15228) and by the Alfred P. Sloan Foundation
(awards provided to P.P.).
We mention pertinent data related to the cis and trans isomers
of HNOO. In our previous paper, ref 2, we presented CCSD(T)
harmonic vibrational frequencies for both the cis and the trans
isomers. The six frequencies for the cis are 3268, 1502, 1215,
1062, 656, and 874 cm-1. The corresponding values for the trans
are 3379, 1553, 1193, 1068, 670, and 770 cm-1. (These
harmonic values are very close to those reported in this work,
using a different basis set.) In each case, the first vibrational
frequency corresponds mainly to the NH stretch, and the last
to the torsional motion.
The main differences between the two molecules are in the
first and the last frequency, as we would expect from qualitative
arguments about the two molecules. For example, in the cis
molecule there can be intramolecular hydrogen bonding, leading
to a lower NH stretching frequency, exactly as we observe
computationally. The NH stretching frequency for the cis isomer
is about 100 cm-1lower than that of the trans. Conversely, such
intramolecular interaction should cause the torsional frequency
to be higher for the cis as compared to the trans isomer. Again,
this is exactly what we observe computationally, and by about
Now, our unpublished work shows that the anharmonic
corrections are about the same for both the cis and the trans
isomers. This correction is about -175 cm-1for the NH stretch,
and -20 cm-1for the torsional motion. Therefore, our expected
theoretical placement of the NH stretch for the cis isomer is
3268 - 175 ) 3093 cm-1. But LGDS report their first band at
3165.5 cm-1, for a difference of 73 cm-1. Likewise, the expected
theoretical placement of the torsional frequency is 874 - 20 )
854 cm-1. But LGDS report the lowest frequency band at 764
cm-1, for a difference of 90 cm-1. The comparison between
theory and experiment is even worse if we use the experimental
data of LBSW.
Looking now at the close agreement between theory (trans)
and experiment for all observed bands presented in Table 3,
we see that such differences as 73 and 90 cm-1are untenable.
It is mainly for this reason that we reject the assignment of the
experimental bands to the cis isomer.
Supporting Information Available: Additional tables of
theoretical results on trans-HNOO. These tables include
quadratic, cubic, and quartic force constants, as well as
anharmonic constants. This material is available free of charge
via the Internet at http://pubs.acs.org.
References and Notes
(1) Ling, P.; Boldyrev, A. I.; Simons, J.; Wight, C. A. J. Am. Chem.
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Electronic Structure and Vibrational Spectrum of trans-HNOO
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