Multireference
configuration
electronic states of CIO,
interaction
calculations
of the low-lying
Kirk A. Peterson@ and Hans-Joachim Werner
Fakultiit ftir Chemie, Universitiit Bielefeld, 4800 Bielefeld, Germany
(Received 21 January 1992; accepted 10 February 1992)
Using extensive internally contracted multireference configuration interaction wave functions
and large basis sets, near-equilibrium potential energy functions for the first four doublet
electronic states (X *B, , *B,, ‘A,, and A 2A2 ) of OClO and the X ‘A ’ electronic state of Cl00
have been calculated. Electric dipole moment functions have also been computed for the
ground states of both isomers. Spectroscopic constants derived for the X and A states of OClO,
as well as for the X state of ClOO, are compared to the available experimental data, and
predictions for the other states are made. In agreement with previous assumptions about the
photodissociation of OClO, strong interactions between the first three excited electronic states
in the Franck-Condon region of the A +-X transition are indicated from cuts of the potential
energy surfaces. In particular, the experimentally observed predissociation of the A ‘A2 state is
proposed from this work to proceed initially by an interaction with the close-lying *A, state.
Additionally, the calculated asymmetric stretch potential for the A ‘A2 state of OClO does not
show evidence of a double minimum as has been previously proposed.
I. INTRODUCTION
Cl+O,
The recent increased interest in the chemistry of chlorine oxides has been due largely to the proposed role of these
species in the depletion of ozone in the Antarctic stratosphere. The most commonly accepted mechanism involves
the reaction of chlorine atoms, which are formed initially
from the photodissociation
of chloroflouromethanes
( CFCs) released into the atmosphere’ with ozone
Cl + 0, --+c10+02.
(1)
In the middle stratosphere, the chlorine monoxide molecule
can react with oxygen atom(s)
Cl0 + O-Cl
+ 0,
(2)
reform chlorine atom(s) , which can subsequently react
with another ozone molecule. Similarly, in the cold Antarctic lower stratosphere, reaction ( 1) is coupled with the formation and photolysis of the chlorine monoxide dimer
( ClO) 2, which leads to catalytic ozone 10~s.~~ At the present time, there is some doubt as to whether currently proposed reaction mechanisms can account for the entire rate of
ozone decline in the polar regions. Recently, the role of the
chlorine dioxide radical has been studied as a possible additional pathway to stratospheric polar ozone depletion.5
There are two isomeric forms of the ClO, radical and both
are believed to be formed by a coupling of Cl and Br chemistry in the upper atmosphere
to
Cl0 + BrO -+ Br + ClOO,
(3)
+Br + OClO.
(4)
Reaction (3) is the rate limiting step in a proposed ozone
catalytic loss cycle involving both Cl and Br atoms.4V6The
Cl00 isomer is also produced by the reaction of chlorine
atoms with oxygen
‘) Current address:Pacific Northwest Laboratory, Richland, WA 99352.
8948
J. Chem. Phys. 96 (12), 15 June 1992
+M-+ClOO+M.
(5)
Both of the structural isomers of ClO, have been studied by
spectroscopic techniques. The bent, symmetric OClO form
has been characterized by many high-resolution spectroscopic methods including microwave spectroscopy, while
the peroxy-like Cl00 isomer has been observed predominantly by matrix isolation methods. Unsymmetrical Cl00 is
thermodynamically more stable than OClO by about 4 kcal/
mol. The Cl00 species, however, is kinetically unstable and
attempts to study this radical by high-resolution spectroscopy in the gas phase have currently been unsuccessful, presumably due to its fast dissociation by the reverse of reaction
( 5). The bond dissociation energy Do (Cl00 -+ Cl + 0, )
has recently been measured in the gas phase to be only
4.83 + 0.05 kcal/mol.’ From the dissociation of ClOO,
chlorine atoms are formed, which are then available to react
with ozone via reaction ( 1). Therefore, the Cl00 species is
an important short-lived precursor participating in ozone
destruction. In contrast, symmetric OClO has been observed
to photodissociate primarily by
OClO + hv-+ClO + 0,
(6)
where the bond dissociation energy has been measured to be
55.2 + 2.0 kcal/mol.8 In this case, oxygen atoms are produced which can react with molecular oxygen to reform 0,
resulting in an overall null cycle for ozone loss. Recently,
however, it has been proposed5Y9that the OClO isomer may
undergo photoisomerization to ClOO, which could actively
participate in the destruction of 0, ,
OClO + hV~cloo+cl+
0,.
(7)
While photolysis of OClO in matrices and other solid media
is known to quantitatively yield CIOO,‘“~’ ’ evidence for gas
phase isomerization is limited. Recent resonant-enhanced
multiphoton ionization (REMPI) experiments,‘2~‘3 however, which have probed the products of OClO photodisso-
0021-9606/92/128948-14$06.00
@ 1992 American Institute of Physics
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K. A. Peterson and H. Werner: Configuration interaction study of CIO,
ciation, measured a quantum yield ofC1 atoms of up to 15%,
evidently confirming the existence of mechanism (7) in the
gas phase.
The main goal of the present work is the theoretical investigation of the low-lying electronic states of OClO and the
possible interactions affecting its photodissociation using extensive ab initio multireference configuration interaction
wave functions. In addition to near-equilibrium, two-dimensional potential energy functions for the first four electronic
states and an electric dipole moment function for the electronic ground state, several one-dimensional potential energy surface cuts have been computed. These results, together
with a review of the previous experimental and theoretical
work specific to OClO, are given in Sec. II. Another goal of
this study is the accurate characterization of the ground
state potential energy surface of Cl00 to facilitate high-resolution gas phase spectroscopy of this species. Three-dimensional potential energy and dipole moment functions for the
ground state of Cl00 have been calculated using nearly
identical methods as those used for OClO. These results are
given in Sec. III.
II. SYMMETRIC OCIO
A. Previous experimental
and theoretical
work
The electronic ground state of symmetric ClO, was
shown to be of *B, symmetry in the microwave studies of
Curl and co-workers.‘4 Because of its high thermodynamic
and kinetic stability, a large variety of high-resolution spectroscopic techniques have been used to obtain very precise
data (equilibrium structure, force constants, dipole moments, etc.) concerning the ground state potential energy
surface. “-26 The photochemistry of OClO is known to occur
(at least initially) on the excited A 2A2potential energy surface, which has been observed to predissociate with increasing vibrational excitation
OClO(X ‘B, ) + hv-+OClO(A 2A2)
-ClO(XYI)
+ o(3P)
-02 (X3&T or a ‘A,) + C1(2P).
(8)
The first rotational analysis of the A +Xbands in the UV was
carried out by Coon in 1946.27 Since this time, several
experimental studies of these bands have been performed.‘5*28-36Most have concentrated on the analysis of the
vibrational and rotational structure of the A-X band system, which is complicated by the diffuseness of the spectrum
at relatively low energies and the large rotational congestion.
The vibrational analyses of Richardson et al.” and Brand et
al.2s included progressions in all three vibrational modes of
the A state. One of the interesting features of these absorption spectra is the anomalously large intensity of bands involving even quanta of the asymmetric stretch (odd quanta
in Y, are not present). This was modeled by Brand et~1.~~ as
a transfer of intensity by anharmonic coupling from the
strong progressions in the Y, symmetric stretch. Previously
this effect had been ascribed by Coon et a1.29as being due to a
double minimum in the asymmetric stretch coordinate, similar to what is believed to occur in the C ‘B, state of SO, .37
More recent spectroscopic work has centered on the
8949
predissociation mechanism of the A 2A2 state. In the highresolution work of McDonald and Innes3’ and later in the
extensive work of Michielsen et aZ.,3’ the rotational structure of the symmetric stretch progressions was investigated
for u, = l-5. The results of these studies confirmed an effect
originally observed by Coon2’ that there was a greater propensity (a factor of about 2) for predissociation out of F1
spin components (J = N + l/2) than ofF, (J = N - l/2).
In addition, there was no dependence of the linewidths on
the initial rotational state N within a given vibrational band.
This was analyzed in terms of a spin-orbit interaction, where
the perturbing state has either A, or B, vibronic symmetry.
Low-lying 2B2and *A1 electronic states had previously been
predicted by ab initio calculations9.38 (see below). Therefore, it was proposed that either the 2B2 state interacts
through its asymmetric stretching vibration, or the *A1 state
acts through its symmetric stretch and/or bend. In the study
of Michielsen et uZ.,~*the rotational linewidths were found
to be relatively constant for u, ~3, while the rate of predissociation was observed to increase for u, > 3. Due to the nature
of this linewidth dependence on ul, it was proposed that the
perturbing state crosses the A 2A2 state at about u, = 3. In
Ref. 3 1, an analysis of combination bands of y1 with the v2
bending mode was also included. The linewidths of these
bands were observed to be much broader than bands of similar energy in the symmetric stretch alone, indicating that the
bend promotes predissociation. Since the lower 2B2state had
been predicted to be strongly bent, it was proposed as the one
interacting with the A ‘A2 state. Michielsen et al. also investigated several mechanisms for the difference in predissociation rates between F, and F2 spin components with the conclusion that the spin-rotation interaction mixes the two
levels, causing a higher rate in F, . Recent resonance fluorescence experiments by Brockmann et ~1.~~also attributed this
effect to a strong spin-rotation interaction, specifically,
however, with the lower-lying 2A1state.
In a closely related experiment, Hamada et ~1.~~observed that all of the (u, 00) bands were perturbed by vibrational Coriolis effects within the A 2A2state. Their analysis
positioned the lowest perturbing level at 716 cm - ‘, which
was assigned to either the (011) or (021) state [a
(u, - 1,1, 1) or ( uI - 1,2,1) interaction, respectively 1. This
placed the unobserved (001) level at approximately 426 or
136 cm - ‘. Since their measured value of 2v3 was 1583 cm - ’
(see below concerning this assignment), which was much
higher than twice their estimated v3 energy, and with the
larger than expected intensities of the v3 progressions as previously mentioned, Hamada et aL3’analyzed their data by
means of a double minimum potential in Q3 as had been used
earlier by Coon et aI.
Recently the direct absorption spectrum of OClO has
been studied by Vaida and co-workers34-36 using jet-cooled
Fourier transform ultraviolet (FT-UV) spectroscopy. Their
vibrational analysis included progressions in the symmetric
stretch from u, = 4-10, which were much higher than previously analyzed. One of the results of their work was the
reassignment of the asymmetric stretch progressions, which
had earlier been misassigned by one quanta in u, , i.e., the
previously assigned (002) band was actually the ( 102). This
J. Chem. Phys., Vol. 96, No. 12.15 June 1992
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8950
K. A. Peterson and H. Werner: Configuration interaction study of C102
new assignment yielded a 2v, energy of 887 cm - ’ (previous
value-1583 cm-‘), which was in good agreement with the
v) energy of 426 cm - ’ estimated by Hamada et a1.32from
their Coriolis analysis. Richard and Vaida3’ also proposed a
double minimum potential in Q3 to explain the intensities of
the asymmetric stretch bands. Their Q3 potential utilized
the new values of 2v3 and 4v3 and resulted in a barrier height
at the C,, minimum of 1153 cm- ‘, which was surprisingly
close to the value calculated by Hamada et a1.32(1257
cm - ’), who used different values for the asymmetric stretch
energy levels. In an analysis of the rotational line broadening
present in their spectrum, Richard and Vaida36 observed
similar features at relatively high values of v, that had been
observed previously for the lower energy bands. While they
were not able to distinguish between F, and F2 spin components, the homogeneous rotational linewidth broadened
with increasing energy, and above u, = 10, the linewidths
became fairly constant until the A ‘A2 dissociation limit.
From combinations of the bend with the symmetric stretch,
they concluded that the bend is a promoting mode in the
predissociation mechanism, as the earlier studies of Michielsen et aL3’and Hamada et a1.32had also proposed. Additionally, the combinations of the asymmetric stretch with u1
were analyzed in Ref. 36 and these bands also had a greater
rotational broadening than those of similar energy involving
the symmetric stretch alone. In fact, it was observed that the
combinations of v3 with v, broadened more rapidly with
increasing energy than similar combinations of v2 with vr ,
indicating that v3 is perhaps a more efficient predissociationpromoting mode. This effect is especially interesting when
compared to the earlier data of Hamada et a1..32In their
analysis of the ( 102) band [then misassigned as the (002) 1,
the observed linewidths were qualitatively the same as those
of the (000) band, while their measurements of the (010)
showed linewidths more than twice as broad as those of the
(000) band. From the results of Richard and Vaida, however, it would be expected that the linewidths of the (102)
band would not only be wider than the (000) band, but also
broader than the (100) and (010) bands. That this is not
observed indicates that the asymmetric stretch may be a promoting mode in the predissociation only at higher energies,
whereas the bending mode affects predissociation even in the
lower energy bands.
Only afew previous theoretical calculations on OClO
have been carried out and these have not included the effects
of electron correlation. The most extensive self-consistent
field (SCF) calculations have been those of Gole and
Hayes38 and more recently by Gole.g The dependence of the
energy on the valence angle was studied in both cases, and
the more extensive work of Goleg indicated that the A *A2
state lay above both the 2B2and *A, states, with the 2B2state
being the first excited state. These SCF calculations predicted bond angles of 118”, 93”, 119”, and 105”for the first four
states (X ‘B, , 2B2, 2A,, and A 2A2, respectively). In the
work of Gole, the 2B2and ‘A, states were predicted to cross
at about 120”and the possibility for strong vibronic coupling
between these states was discussed as a mechanism for photoisomerization of OClO to ClOO.
6. Computational
details of the present study
The X 2B, ground state of OClO has the Hartree-Fock
configuration
(core)(5a, )2(3b,)2(6a, )*(7a, )2(4b2)2(2b, >’
X (% 12(8a, )‘(la,
j2(3bl I’,
(9)
and the first three excited electronic states involve single
excitations from the 5b,, 8a,, and la, orbitals into the singly
occupied 3b,. The present calculations were carried out using the MOLPRO suite of ab initio programs.3g The potential
energy functions and various cuts through the potential energy surfaces were computed using the internally contracted
multireference configuration interaction (CMRCI) methodNs4’with a restricted full valence active space. The orbitals used in the CMRCI work were taken from full valence
complete active space self-consistent field (CASSCF) calculations.42 These were carried out by distributing 13 electrons
into the nine valence orbitals corresponding to the atomic 2p
and 3p orbitals of oxygen and chlorine, respectively (in C,, :
7a, -9a,, 4b,-6b,, 2b, -3b,, and la, ). This yielded a total of
473 configuration state functions (CSFs) in C,, symmetry
and 936 CSFs in C, for the electronic ground state. All of the
valence and core orbitals were optimized in the CASSCF.
For C,, geometries, separate orbitals were calculated for
each state, while in the case of C, distortions, state-averaged
orbitals were computed. For the latter, the first two states of
‘A ’and ‘A N symmetries were averaged separately. The reference space in the CMRCI calculations consisted of the
CASSCF CSFs with the added restriction that a maximum
of two electrons could occupy the 9a, and 6b, orbitals ( 14u’
and 15a’ in C, symmetry) in any one configuration. The
resulting restricted active space (RAS) reference function
for the CMRCI totaled 149 CSFs in C,, symmetry (294
CSFs in C, ) for the ‘B, ground state ( 147 CSFs for the 2B2
and 2A, states, and 145 CSFs for the 2A2state in C2”). Test
calculations comparing the CAS and RAS references were
carried out for the bond dissociation and vertical excitation
energies. It was found that the use of the RAS reference
space in the CMRCI resulted in nearly identical values as
those obtained with the full CAS reference.
The Gaussian basis set used in this work consisted of the
Dunning correlation consistent polarized valence quadruple
zeta (cc-pVQZ) set for oxygen,43 which included 3d- and 2ftype polarization functions. For chlorine, a [ 6s,5p] general
contraction of the ( 17s,12~) primitive set of Partridge& was
augmented with a 3d 2fpolarization set. The Cl polarization
exponents were energy optimized for C1(2P) at the single
and double excitation configuration interaction [ CI (SD) ]
level [d exponents ( 1.64, 0.65, and 0.26) and fexponents
( 1.04 and 0.42) 1. This yielded a total of 142 contracted
Gaussian functions and is designated as basis 3d 2f: In some
cases, a g-type polarization function was also added to each
center [the optimized cc-pVQZ value for 0 and a CI(SD)
optimized exponent of 0.84 for Cl] for a total of 169 functions (denoted as basis 3d 2flg). In the internally contracted
MRCI, all single and double excitations into the external
orbitals with respect to the reference configurations were
taken (excitations from the core were not included). Config-
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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K. A. Peterson and H. Werner: Configuration interaction study of CIO,
urations with two electrons in the external orbital space were
internally contracted by applying pair excitation operators
to the reference function as a whole.40*45,46
It has been shown
that for most cases, while the internal contraction greatly
decreases the number of variational parameters, essentially
no loss in accuracy occurs in comparison to uncontracted
MRCI calculations.40V47Using the 3d 2flgbasis set, the present CMRCI calculations in C,, symmetry resulted in
1.2 X 10”variational parameters (equivalent to 75 million in
a conventional uncontracted MRCI). In C, symmetry, the
total energies for the 2A c states and lowest ‘A ’ (X2B,,
A 2A2,and *B, in C,, ) were computed in a contracted basis
specific to each states4’This method has the advantage that
the cost of the calculation scales nearly linearly with the
number of states. For the 2 ‘A ’ state, a somewhat more expensive two-state calculation was carried out, where the first
two roots of 2A ’ symmetry were computed simultaneously
in a contracted basis which consisted of the union of all contracted configurations formed from the two separate reference functions ( 1 2A ’ and 2 ‘A ‘). This method has been
shown to be very reliable in regions of narrow avoided crossings. 4* The total number of variational parameters in C,
symmetry (3d 2f basis set) was 1.9 X lo6 for the one-state
and 2.4 X lo6 for the two-state calculations. It should be noted that in a conventional uncontracted MRCI, about 140
million variational parameters would have resulted.
For the calculation of spectroscopic constants of the
first four doublet states of OClO, two-dimensional potential
energy functions (PEFs) were computed in C,, symmetry
by polynomial fits to grids of 13-14 energy values. For these
points, the large 3d 2flg basis set was used. For comparison,
the X 2B, and 2B2PEFs were also computed with the 3d 2f
basis. The computed energies were fit by polynomials of the
form
v=
c c, (6
il
)I’as2 Y,
(10)
8951
where S, = (r, f r, )/a, S, = 6&o, and the A’s indicate
displacement from the calculated equilibrium values. These
potential energy functions are expected to be valid in the
range of geometries
- 0.2a, (v’ZAr< + 0.3a, and
- 20% Ahe< + 20”. A total of 11 terms were used in the
polynomial of Eq. ( lo), which included all of the quadratic
and cubic terms and most quartic terms. The resulting PEF
coefficients Cq are shown in Table I. Asymmetric stretch
potentials (C, symmetry) were calculated using the 3d 2f
basis set by fitting five energies in the symmetry coordinate
S, = (r2 - rl )/fl, where - 0.3a, <KS’; < + 0.3a,. For
the S, potential functions, the values of S, and S, were held
fixed, hence the anharmonic coupling of the asymmetric
stretching mode to the symmetric stretch and bend was neglected in this treatment.
The electric dipole moment of the X 2B, state of OClO
was also calculated at each geometry by CMRCI. The dipole
moments were obtained as expectation values. Previous experience has shown that the CMRCI expectation values are
usually very close to the first energy derivatives with respect
to an external electric field. The computed dipole moments
in C,, symmetry (the z component, which corresponds to
the B principal axis) were fit by cubic polynomials in the
same coordinates as the potential energy function of Eq.
( 10) and expanded about the calculated (3d 2flg basis)
equilibrium geometry. For the small number of points in C,
symmetry (3d 2fbasis set), the calculated x and z components of the dipole moment were rotated into an Eckart reference frame4’ defined with respect to the calculated
CMRCI (3d2f) equilibrium geometry. The resulting acomponent dipole moments (corresponding to the A principal axis) were fit to a linear function of the displacement
coordinates Ar, and Ar, .
Spectroscopic constants have been calculated from the
fitted PEF coefficients by the usual FG matrix analysis”
and second-order perturbation theory expressions.51 All of
the fits and spectroscopic constant analyses were carried out
with the program SURFIT.'~
TABLE I. Expansion coefficientsof the two-dimensional CMRCI potential energy functions for the first four
electronic states of OClO (in atomic units).*
C,
00
20
11
02
30
21
12
03
40
22
04
X2B,
- 609.769213b
-
0.216 258
o.ooo 459
0.162 990
0.208 467
0.002 75 1
0.185 626
0.074 133
0.114 909
0.084 206
0.060 240
z4
- .609.696 498’
0.141 188
0.039 641
0.107 335
-0.116979
- 0.045 577
- 0.218 078
- 0.181 819
0.058 727
0.148 253
0.23 1 446
24
- 609.673676d
0.118 574
0.008 585
0.088 164
- 0.097 357
- 0.009 434
- 0.069 734
- 0.065 483
0.049 613
0.007 770
0.012 502
A 2A2
- 609.6728 19”
0.119 559
- 0.011 459
0.086 2 11
- 0.094 803
0.007 075
- 0.124 835
- 0.082 624
0.052 312
0.085 378
0.076 226
’Computed using the 3d 2flg basis set in the coordinates Q, = (r, + r, )/d and Q2 = 19,,,, (seethe text).
bExpanded about the calculated equilibrium geometry of r, = 2.789 Ola, and 0, = 117.860”.
‘Expanded about the calculated equilibrium geometry of r, = 3.017 33a, and 19,= 89.695’.
d Expanded about the calculated equilibrium geometry of r, = 3.046 42a,, and 0, = 120.033”.
‘Expandedaboutthe calculated equilibrium geometry of r, = 3.082 5Su,, and 0, = 106.371’.
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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K. A. Peterson and H. Werner: Configuration interaction study of C102
8952
C. Results
I. Dissociation
energies and spectroscopic
constants
Equilibrium dissociation energies for X *B, OCIO calculated by CASSCF, CMRCI, and CMRCI including Davidson’s correction for higher excitations (CMRCI + Q,
hE, = hE,,, ( 1 - 8, C ‘, >, where AEc,,, is the difference
between the reference function and the MRCI and the C,
are the coefficients of the reference configurations in the
MRCI wave function) are compared to the experimental
values in Fig. 1. An experimental dissociation energy for the
Cl + 0, asymptote was derived by use of the thermodynamic cycle
D,(Cl+O*)
=&(C1Of-O)
+&(ClO)
-&(O,)
= 55.2 + 63.4 - 118.0
= 0.6 + 2.0 kcal/mol,
(11)
where the experimental D, (Cl0 + 0) (55.2 f 2.0 kcal/
mol) was taken from the work of Fischer,* and the experimental values for DO (ClO) and DO (0, ) were taken from
Huber and Herzberg. 53 Zero point corrections to obtain experimental D, values as shown in Fig. 1 were calculated from
the available spectroscopic data. A comparison between experiment and CASSCF (Fig. 1) shows very poor agreement
for both asymptotes Cl0 + 0 and Cl + 0,. Both CASSCF
values are too low by about 44 kcal/mol, indicating a very
large dynamical electron correlation effect. Computed
CMRCI and CMRCI + Q dissociation energies are much
closer to experiment, although the CMRCI results are still
too small by about 8 kcal/mol, which is unusually large for
this level of theory and basis set. Preliminary test calculations have indicated that inclusion of the oxygen 3p orbitals
into the CMRCI active space is required to improve this
agreement. Unfortunately, this results in a total number of
variational parameters and computational cost which is exceedingly large.
Spectroscopic constants calculated from the potential
energy function (PEF) coefficients of Table I are displayed
in Table II, where they are compared to the available experimental values. For all four states, the calculated CASSCF
7n
‘” : clo(x*n) + O(%?
il-
Cl0 +o
A-
50-
- +0
~Cl0
:
c
j
z
r_
~
30-
‘“,-. @)tO,(x-;)
I
4
6 -lo-
OClO
53
50
58+2
Cl0 t- 0
1 1y
+ -8
(X*8,)
s
4
-42
Cl+O*
4
cT+700,-6 -
YJ 301
-i
Cl+O*
-50 -70 .,
EXPT
CASSCF
MRCI
MRCI+Q
FIG. 1. The experimental equilibrium dissociation energiesDe of X*B,
OClO are compared to those calculated by CASSCF, CMRCI, and
CMRCI + Q. All energiesare given relative to the electronic ground state
at equilibrium.
equilibrium bond distances are much longer than those obtained by CMRCI. The dependence, however, of the calculated valence angle on dynamical electron correlation is not
very strong for the first three states, especially the ‘A, , where
13, only changes from 119.8” to 120.0” on going from
CASSCF to CMRCI. On the other hand, the A 2A2 state
demonstrates a very strong correlation effect, where the valence angle changes by - 5.7”. Good agreement between the
CMRCI results and experiment is observed for both the X
and A states. The addition of g functions to the 3d 2jbasis set
is found to decrease the bond length in the ground state by
0.0036 A and only slightly increase the value of the valence
angle ( + 0.07”). This results in a calculated CMRCI equilibrium geometry differing from the accurate microwave
values of Miyazaki et ~1.~~by just + 0.0061 A and + 0.46
for r, and 8,, respectively. The CMRCI (3d 2flg) harmonic
frequencies (w, and o, ) also show good agreement with
experiment, differing by an average of just 6 cm - ‘. The calculated value of w3, however, shows a somewhat larger error
of - 38 cm- ‘. This is presumably due to the use of the
smaller 3d 2fbasis set and evaluating w, from just a small cut
of the full potential energy surface.
For the excited electronic states, only the results for the
A 2A2 state can be compared to experiment. The CMRCI
electronic excitation energy T, is slightly too small by 0.07
eV, which is somewhat typical from our past experience in
similar calculations. The calculated CMRCI equilibrium geometry compares well with the values measured experimentally for the (000) vibrational leve1,32 with deviations between CMRCI and experiment similar to those observed for
the ground state. Our result for the asymmetric stretching
frequency, 437 cm- ‘, compares favorably with the experimental value of 404 cm - ’ estimated by combining the Ye
energy of Hamada et a1.32and the anharmonicity constants
of Richard and Vaida.35 This can also be compared to w3
calculated from the experimental inertial defect, 489 cm - *.
32 Especially interesting is the shape of the asymmetric
stretch potential, which has been previously proposed27*32*35
to have a double minimum corresponding to an asymmetric
equilibrium geometry. Our calculated A 2A2 asymmetric
stretch potential in the symmetry coordinate S, is shown in
Fig. 2. These results indicate that the equilibrium geometry
of the A 2A2state is symmetric as assumed in the earlier experimental work of Brand et ~1.~’and that there is no double
minimum. Thus, although we have not investigated the coupling between the symmetric and asymmetric stretching
modes in our calculations, anharmonic coupling now seems
to be the preferred mechanism, whereby the asymmetric
stretch borrows its intensity in the A +X UV spectrum.
In agreement with previous ab initio calculations,9’38
the 2B2state is predicted by CMRCI to be strongly bent with
a valence angle of 89.7” (Table II). Contrastingly, the ‘A,
state, which is calculated to lie just 0.02 eV below the A ‘A2
state, has a calculated equilibrium angle ( 120.0”) only slightly greater than that of the ground state ( 117.9”, cf. Fig. 3).
Both the ‘B, and ‘A1 states have calculated bending harmonic frequencies w2 (3 19 and 3 11 cm - ‘, respectively) of
similar magnitude as that of the A *A2 state (288 cm - ’) .
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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8953
K. A. Peterson and H. Werner: Configuration interaction study of CIO,
TABLE II. Calculated spectroscopicconstantscompared to experiment for OClO.
State
Method
T,
0,
@I
f%
(eV)
(deg)
(cm-‘)
(cm-‘)
@3
(cm-‘)
XZB,
CASSCF(3d2flg)
CMRCI(3dZf)
CMRCI(3d2flg)
Expt.”
1.494
1.480
1.416
1.470
119.3
117.8
117.9
117.4
865.0
944.6
955.4
963.5
432.7
452.4
455.6
451.7
1095”
52W
1133.0
“4
CASSCF( 3d 2flg)
CMRCI( 3d 2f)
CMRCI(3d2f lg)
1.80
1.95
1.98
1.630
1.601
1.597
91.1
89.7
89.7
696.8
806.0
815.0
263.3
316.5
319.5
CASSCF(3d 2f lg)
CMRCI(3d 2f)
CMRCI(3d2f lg)
2.34
1.670
119.8
532.5
273.3
2.60
1.612
120.0
696.5
311.3
CASSCF( 3d 2f lg)
2.25
1.691
112.1
567.4
190.7
2.62
2.69
1.631
1.627
106.4
106.2
737.9
288.1
287.7
24
1474d
A 2A,
CMRCI(3d2f)
CMRCI(3d2f
437’
lg)
Expt.’
713.2
404
‘Evaluated with respectto a C,, geometry of r = 1.480A and B = 117.8’.
bThe equilibrium structure was taken from Ref. 26 and the vibrational constantsfrom Ref. 15.
‘Evaluated with respectto a C,, geometry of r = 1.601A and 6 = 89.7’.
dEvaluated with respectto a C,, geometry of r = 1.616.&and 0 = 120.0”.
c Evaluated with respectto a C,, geometry of r = 1.635b; and 6 = 106.4’.
‘The structure correspondsto the valuesmeasuredby Ref. 32 in the (000) vibrational state and the vibrational constantswere obtainedfrom Refs. 35 and 15.
The value of w, was derived using an energy of 426 cm- ’ for the (001) level (Ref. 32) and the anharmonicity constantsof Ref. 35. The value of T, was
derived from the experimental To of2.61 eV (Ref. 35).
The asymmetric stretching potentials of the first two excited
states were found to be very dependent on the valence angle.
For the ‘B, state, w3 is calculated to be 520 cm- ’ at the
equilibrium
angle of 89.7”. As the angle is increased, how-
ever, to the ‘A, 19,of 120.0”, the “B, and ‘A, states become
very close or cross in C,, symmetry (see below) and, since
400
. . . . . . . . . . . . . ..‘..‘...‘.I.“.
they both have A ’symmetry upon C, bond distortions, show
an avoided crossing in their asymmetric stretch potentials.
Consequently, the *B2 S, potential is predicted to be purely
dissociative to Cl0 + 0 at these larger bond angles, while
the CMRCI value of w3 for the ‘A1 (2 2A ’ in C, ) state is
calculated to be 1474 cm - ‘, which is over 300 cm - ’ higher
than the value in the electronic ground state. Since this has
been calculated adiabatically in the region of an avoided
crossing, however, a predicted wj value for the 2A, state is
inherently ill defined.
513
2n8
4.0
5
J
.g 3.0
‘“B
ii
‘g 20
8
1.0
-0.3
-02
4.1
0
0.1
0.2
0.3
r, - r2 (bohr)
fxl
FIG. 2. The calculated CMRCI asymmetric stretch potential function for
the A ‘A, state ofOCl0 is shown in the symmetry coordinateVzs, (relative
to the equilibrium C,, geometry of r = 3.0900, and 6 = 106.4”).
a0
100
120
140
160
180
FIG. 3. The CMRCI dependenceof the potential energy on the valence
angle at r = 2.95a,, is displayed for the first five statesof OClO.
J. Chem. Phys., Vol. 96, No. 12.15 June 1992
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8954
K. A. Peterson and H. Werner: Configuration interaction study of CIO,
The existence of low-lying quartet states has also been
investigated by CMRCI with the 3d 2jbasis set. The vertical
excitation energies from the ground electronic state (at
r = 2.778~ and 0 = 117.4”) were calculated to be 6.82 eV
(4B,), 7.96 eV (4A2), 8.08 eV (4A,), and 8.27 eV (4B,),
which are much higher in energy than the A ‘A2 state (vertical excitation energy of 3.66 eV). Thus, no further investigation of these states was carried out in this work.
2. The electric dipole moment function of the X ‘B,
state
The calculated C,, (z-component) CMRCI (3d 2flg)
electric dipole moment function (EDMF) for the electronic
ground state of OClO is given in Table III. The calculated
value of ,uu, ( - 1.852 D) (negative end of dipole directed
toward terminal oxygens) is in excellent agreement with the
p0 value of 1.792 D measured by Tanaka and Tanaka” by
laser Stark spectroscopy. For the estimation of infrared intensities, it is convenient to calculate the derivatives of the
dipole moment function with respect to dimensionless normal coordinates.54 We have carried this out by way of Ltensor algebras5 using the CMRCI PEF of Table I, and the
resulting linear and quadratic terms are given in Table III for
the symmetric stretching and bending normal modes. Inspection of the relative magnitudes of these derivatives indicates that the linear terms should dominate the estimation of
infrared transition probabilities for the low-lying vibrational
TABLE III. Expansion coefficientsof thez-component CMRCI dipole moment function and derivatives with respectto dimensionlessnormal coordinates for X *B, OClO.”
Dipole moment function (a.~.)~
CC0
Cl,
Cl2
GO
CO,
CO,
CO,
C,,
- 0.728 51
- 0.205 30
0.035 25
- 0.192 56
0.123 23
- 0.376 92
0.882 73
- 0.126 86
0.373 a7
- 0.186 65
PI
- 0.0959
0.1697
0.0231
- O.colO
- o.oo60
C20
G,
Normal coordinate derivatives
I4
,,
PI1
PY2
n
PI2
8Calculated using the 3d 2flg basis set (seethe text).
“The coordinates used were Q, = (r, + r, )/fl and Q2 = e&c,. The dipole moment function was expanded about the calculated CMRCI
(3d2flg) equilibrium geometry (Table I).
‘The CMRCI ( 3d 2flg) PEF wasusedandp, correspondsto the ith normal
mode.
levels. For the asymmetric stretching mode, a fit to the Eckart frame u-component dipole moments (basis 3d 2f ) resulted in a first derivative &,/&,
equal to - 0.6276 a.u. (r, is
oriented in the positive xz quadrant). Using the CMRCI
(3d 2f) PEF, the first derivative with respect to dimensionless normal coordinates ,$ is calculated to be 0.2935 D.
While the magnitudes of the u-component quadratic terms
are not known from these calculations, they are expected to
be relatively small in comparison to those calculated for similar molecules.56 Within the double harmonic approximation (harmonic force field and linear dipole moment function), absolute infrared intensities S (at 300 K) for the
fundamental vibrational modes of X *B, OClO are calculated to be S, = 44.8 cm-‘atm-‘,
S, = 66.8 cmw2 atm-‘,
and,!& =480cm-2atm-‘{where+Si
=5.091xwi(cm-*)
x [p;(D) I’}. Past experience with similar cases has indicated that these values are probably only 5%-10% larger
than the same quantities calculated using the full anharmanic potential energy and dipole moment functions. To
our knowledge, previous calculations or measurements of
absolute infrared absorption intensities of OClO have not
been carried out and it is hoped that these results will prove
valuable in IR studies of OClO chemistry in the laboratory
and upper atmosphere.
3. One-dimensional
surfaces
cuts through the potential
energy
Although full global surfaces in C, symmetry for the
first four states of OClO would provide the most information
on the photochemistry of OClO, the extremely large computational cost of these calculations has currently prohibited
this. Therefore, for this study, we have computed several
one-dimensional cuts of the three-dimensional surfaces,
which should provide significant insight into the excited
state chemistry of this species.
a Symmetric bend.The dependence of the potential energy on the valence angle (at r = 2.95~~ ) is shown in Fig. 3
for the first five states of OClO. For the first four states, the
CASSCF orbitals used in the CMRCI were computed separately for each state. The orbitals for the 2 *A, state, however, were state averaged with the 1 *A,, and the single state
method as described previously (Sec. II B) was used in the
CMRCI. At the linear configuration, the X*B, and 1 *A,
states form a degenerate *IIu state, while the 1 *B, and A 2A2
states merge to form a degenerate 211s state at 180”. These
four states thus form two Renner-Teller pairs. The second
*A1 state forms a third Renner-Teller pair with the 2 *B,
state, which is not shown in Fig. 3 since it rises in energy
(CASSCF) upon bending. These two states have *A, symmetry at 180”. Since the orbitals of the *B, and *A1 states and
*B2 and *A2 states were not state averaged, slightly different
energies were obtained for the two *III, and two *IIs components, respectively. Hence, in Fig. 3, the energy of each degenerate state at the linear configuration is plotted only for
the lower component and the degeneracy is forced for the
second.
Several curve crossings are observed in Fig. 3 with the
most notable occurring between the 1 *B, and 1 *A, states.
J. Chem. Phys., Vol. 96, No. 12, X.5June 1992
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K. A. Peterson and H. Werner: Configuration interaction study of CIO,
As discussed earlier, these two states both have *A ’symmetry upon C, distortions, so the observed curve crossing in C,,
symmetry ( - 120”) is a conical intersection between these
two potential energy surfaces. At a somewhat wider bond
angle ( - 1357, the similar conical intersection occurs between the 1 ‘B2 and 2 *A, states. Curve crossings also occur
between the A 2A2 state and the 1 ‘B2, 1 ‘A,, and 2 *A1
states. While these are allowed crossings even in C, symmetry, they could be expected to affect the predissociation of
the A state by various nonadiabatic interactions. As discussed earlier, spin-orbit coupling is expected to be the
dominant predissociation mechanism for the A *A2 state.
Since the 1 *A, state crosses the A *A2 state at nearly the A
state equilibrium angle, it must be considered a strong candidate. Earlier experimental investigations had favored the
1 ‘B2 state, which is expected to interact strongly at wider
angles from Renner-Teller coupling, but a surface crossing
is not predicted at lower energies. The predissociation mechanism is further complicated by the strong Herzberg-Teller
interactions expected from the conical intersection of the
1 2B2and 1 2A, surfaces, which has been discussed previously by Gole’ in regards to a photoisomerization mechanism.
An initial interaction of the A 2A2state with the close-lying
1 ‘A, state could then also involve the 1 *B, surface.
As shown in Fig. 3, an avoided crossing is predicted to
occur between the first two 2A, states at a valence angle of
about 140”. This results in a fairly small barrier to linearity
(or quasilinearity) for the 1 *A, state, where the linear (quasilinear) structure is lower in energy than the bent form.
Figure 4 depicts the calculated CMRCI asymmetric rclo
stretching potential for the linear 211Ustate of OClO (for
fixed roC, = 2.95~~ ), which correlates with the bent X 2B1
and 1 ‘A, states of Fig. 3. These calculations indicate that
only a small barrier exists for dissociation into ground state
Cl0 and 0 from the linear configuration and this barrier is at
or below the height of the barrier in the 1 2A1bending potential at about 140” (Fig. 3). A calculation using a full CAS
reference space in the CMRCI was also carried out for linear
211 OClO (Fig. 4) and the effect was to lower the dissociatiof; barrier by a small amount. Therefore, it appears from
these one-dimensional cuts that dissociation of the bent
1 *A1 state into Cl0 + 0 is highly favorable in the bending
coordinate.
b. Symmetricstretch. Figures 5 (a) and 5 (b) display the
calculated dependence of the potential energy on the symmetric stretch at fixed angles of 106.4” (the CMRCI A ‘A2
0, ) and 117.4” (the experimental X *B, 0, ), respectively, for
I
I
I
I
8=106.40
8= 106.40
1
s.!3
\
-I
3.5
$
%
*iI 1.5
::
w
a’
L
-1
~,,,,,,,,,,,,,,,,,,,,,,‘1
3.75
3.35
2.95
2.55
r (Bohr)
(a)
5.5
ss
. ..‘...‘...‘...‘...I...
cl =117.40
\
3.5
B
Ls
&
‘2
3 ljj&I
4.0
2
B
t
6
”6
$
B
1
I
I
5.5
I
-.TX
8955
“.““r^“;-
l.OI
25
3.0
3.5
4.0
4.5
5.0
55
6.0
RCIO (Bohr)
FIG. 4. The calculated CMRCI asymmetric ‘cl0 stretching potential is
shown (for fixed rot, =
2.95a,) for the ‘II,, groundstate of linearOCIO.
2.55
(b)
I
2.95
I
f
3.35
I
3.75
r (Bohr)
FIG. 5. The dependenceofthe potential energyon rfor C,, geometrieswith
valenceanglesof (a) 106.4’and (b) 117.4”is shown for the first four elec-
tronic states of OCIO.
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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K. A. Peterson and H. Werner: Configuration interaction study of CIO,
8958
the first four states of OClO. In the experiments of Michielsen et al.,31 a crossing of another electronic state with the
A *A2 potential energy surface in the symmetric stretch at
u, = 3 was predicted due to the observed behavior of the
rotational linewidth broadening. As previously observed in
Figs. 3,5(a), and 5(b), the 1 ‘A1 state does cross the A *A2
state, and the crossing point is very sensitive to the valence
angle. Changing 8 from 106.4” to 117.4”varies the point of
the curve crossing from about 7000 cm- * above the A state
minimum (ui - 10) to just 800 cm - ’ ( u1 - 1). In addition,
the *A, state is close to the A *A2 state at nearly all values of
r. This is in contrast to the ‘B, state which, while it comes
close to the A *A2 state at 117X, is predicted to cross the A
state only with higher bending excitation. Figures 5 (a) and
5(b) also indicate how the conical intersection of the ‘B,
and 1 *A, states shown initially in Fig. 3 for fixed r varies
with r and 8. While these two states do not appear to cross at
the A *A2 equilibrium valence angle, the intersection is predicted to occur close to the ground state equilibrium geometry. Therefore as the crossing point of the 1 ‘A, and A *A2
states decreases in energy, which increases the expected
spin-orbit mixing, the vibronic coupling of the 1 *Al and *B2
states also increases. These strong dependencies on the valence angle [Figs. 3, 5 (a), and 5 (b) ] agree well with the
experimental observations that the bending mode promotes
predissociation.
c. Asymmetricbondstretching.The effect of asymmetric
bond distortions on the first four electronic states of OClO is
shown in Fig. 6 for ro,, = 2.95a, and 19= 117.4”. For these
cuts, the two-state method was used in the CMRCI. The
avoided crossing between the first two *A ’ states, which is a
consequence of the C,, crossing of the *B, and 1 *A1 states
4.0~
22A’
(*A,)
1
3.05
2%
3
b
l-z 2.0g
.H
2
.z
::
WI
ocl
(X2rI) + 0 @)
LO-
2.5
I
I
I
1
I
3.0
35
4.0
4.5
5.0
5.5
R,to (Bohr)
FIG. 6. The effect of asymmetric bond length distortion is displayed for
rot, = 2.95a,, and Oo,, = 117.4”.
shown in Figs. 3 and 5(b), is seen clearly as well as the
barriers to dissociation to Cl0 + 0. Because of the avoided
crossing of the two *A ’states, the lower state (‘B, in C,, ) is
unbound, while the barrier to dissociation for the upper ‘A ’
state is relatively high. The asymmetric stretch is expected to
promote predissociation of the A ‘A2 state by way of the
following three-step mechanism:
A *A2(2 ‘A “) j 1 ‘A1 (2 ‘A’) (spin-orbit coupling),
1 ‘A, (2 2A ‘) j 1 2B2( 1 ‘A ‘) (vibronic coupling
via asymmetric stretch),
1 2B2( 1 *A ‘) -Cl0
+ 0 (via asymmetric stretch).
( 12)
This process is especially expected to be favored for angles
wider than the A state 13,and when the symmetric stretch is
excited, which also brings the *A, and 2B2states into closer
proximity to one another [cf. Figs. 5 (a) and 5 (b) 1. Since
the asymmetric stretch is the dissociating mode in the A *A2
state, direct predissociation is also expected to occur at higher vibrational energies. As shown in the one-dimensional cut
in Fig. 6, the height of the dissociation barrier may not be
that high in the v3 mode. These results are in good agreement with the experimental trends, though full C, potential
energy surfaces will be required for a complete mechanism in
these regions of the potential energy surfaces.
Ill. THE Cl00 ISOMER
A. Previous experimental
and theoretical
work
As previously mentioned, the experimental characterization of the Cl00 isomer is far from complete, even for the
electronic ground state. The first tentative identification of
this short-lived species was made by Rochkind and Pimentel” by IR spectroscopy in rare gas matrices. Definitive IR
matrix experiments were carried out soon after by Arkell
and Schwager,” who measured all three vibrational modes
and carried out isotopic labeling studies, which confirmed
the unsymmetrical structure of this species. Since this time,
ESR spectra have also been observed in various matrix and
crystalline media,58959which indicated that the electronic
ground state has 2A ’ symmetry. The only gas phase spectroscopic observation has been carried out by Johnston et a1.,60
who used a molecular modulation technique to observe the
UV spectrum between 2300 and 2600 A and the IR spectrum
from 1430 to 1460 cm- ‘. A detailed vibrational analysis,
however, was not possible from their spectra. Due to its proposed role in the chemistry of Cl in the upper atmosphere
and in laboratory environments, the gas phase kinetics of
Cl00 have also been of increased interest.7*6’ One of the
results of these studies has been an accurate value of the bond
dissociation energy for this species.’
Previous theoretical studies on Cl00 have also been
limited. Early restricted SCF calculations were carried out
by Gole and Hayes3’ and by Gale.’ The study of Gole and
Hayes indicated that the Cl00 isomer was lower in energy
than symmetrical OClO. The work of Gole included the dependence of the potential energy on the Cl00 valence angle
for both the X 2A ” and 1 *A ’states. Both were found to have
J. Chem. Phys., Vol. 96, No. I.?,15 June 1992
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8957
K. A. Peterson and H. Werner: Configuration interaction study of C102
equilibrium angles of about 110”. The most extensive ab initio study has been carried out by Jafri et a1.62using a doublezeta plus polarization basis set and MCSCF-CI wave functions. They calculated potential energy surface cuts of eight
doublet and eight quartet states. Qualitative excitation energies and binding characteristics were obtained for all 16
states. From this study, it was predicted that all of the excited doublet electronic states of Cl00 are dissociative in the
Cl + 0, coordinate. In contrast to some earlier assumptions, their calculations also indicated that the 1 ‘A ’ state
dissociates to ground state products.
B. Computational
bond, the potential energy surface is very flat in the R,,,
coordinate. At shorter Cl0 bond lengths, increased anharmanic coupling to the 0, bond occurs [Fig. 7(a) 1. In Fig.
7(b), which depicts the angular dependence of the Cl0
stretch, it is observed that as the Cl0 bond is stretched, the
dependence of the potential energy on the Cl00 angle is very
small. Spectroscopic constants calculated from the CMRCI
PEF are displayed in Table V, where they are compared to
details for Cl00
Using the 3d 2jbasis set and the RAS reference function
for the CMRCI as described previously for OClO (Sec.
II B), a three-dimensional potential energy function for the
X ‘A ” ground state of the unsymmetrical Cl00 isomer was
calculated at 44 geometries in C, symmetry, which covered
the following geometry ranges [where AR,,o = R,,,
- R,,, (e), etc. ] :
-0.6
a.u.(AR,,,<
-0.2
a.u.<Ar,<
+0.6
f0.3
a.u.,
a.u.,
-2o"<Ae,,,<+20".
The energy points were fit by polynomials of fourth degree
(22 terms) in R,,, , roof and Sc,,, , where the Simons-ParrFinlan coordinate (r - re )/r was chosen for the stretches
(Q, and Q2 ), and the bend ( Q3 ) was expressed in terms of
the Carter-Handy coordinate,63 which consists of a cubic
expansion in A&-,, as Q3 =A,,AO+A,A02+A2Af93.
The value of A, was roughly optimized, and the A, and A,
coefficients were obtained from the normalization and
conditions
boundary
Q,(e= 180”) = 1
and
aQ3 (0 = 180”)/&9 = 0, respectively. The resulting fit, the
coefficients of which are shown in Table IV, reproduced all
of the calculated energy values to within 6 cm - 1 (rms = 2.8
cm - ’). Fits to a smaller number of points close to the minimum, while decreasing the size of the residuals, did not significantly affect the resulting spectroscopic constants.
The electric dipole moment of Cl00 was also calculated
as CMRCI expectation values at each geometry. For these
calculations, the molecule was oriented in the xz plane and
the Cl atom was on the positive z axis. The computedpu, and
pZ dipole moment components were rotated to an Eckart
reference frame fixed with respect to the CMRCI equilibrium geometry and the principal axes of inertia A, B, and C.
The electric dipole moment function (EDMF) of Table IV
was subsequently obtained by fitting the resulting,u= andpu,
components to cubic polynomials in displacement coordinates of R,,, , r,, and 0c,,, .
C. Results
1. Pofenfial energy function and spectroscopic
consfanfs
Contour plots of the/Y 2A ” Cl00 potential energy function of Table IV are shown in Figs. 7(a) and 7 (b) for R,,, vs
r, and &loo, respectively. As expected for such a weak
TABLE IV. Expansion coefficientsof the three-dimensionalCMRCI potential energy and dipole moment functions for X ‘A ” Cl00 (in atomic
units).’
Potential energy functionb
GO
c ?.M)
c I IO
c 020
C 101
C 0’1
C002
C 3x3
C 210
C ‘20
C030
C 201
C III
C021
C ‘02
Con*
C003
GW
GW
GM
C 201
C022
- 609.770 160
0.217 027
0.256 956
1.876 656
0.001 301
.
0.029 264
0.040 204
- 0.454 550
- 1.604 649
1.220 424
- 1.923 976
- 0.013 018
- 0.292 441
0.083 115
- 0.202 038
-0.042812
- 0.014 329
- 0.989 550
- 1.114200
0.015 535
0.329 780
0.077 640
Dipole moment function’
a component
C loo
C0’0
CMl
C 200
C 110
C 020
C 101
C011
Ca32
C 300
C 210
C I20
C030
C 20’
C Ill
C02’
C 102
C012
C 003
- 0.433 8 1
0.014 08
0.828 71
- 0.021 00
0.594 34
- 0.632 84
- 1.022 51
0.103 85
- 0.080 52
0.10004
- 0.356 CO
-0.18070
0.207 95
1.394 20
- 0.204 20
0.833 86
- 0.315 89
0.798 88
- 0.726 92
0.108 32
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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K. A. Peterson and H. Werner: Configuration interaction study of C102
8958
TALBE IV. (Continued.)
26
,
I
2.5
b component
Gx
c ml
c 010
CM,
Cz m
C t 10
C010
C 101
C01I
Cc m
C 300
C 210
C 120
C030
C 201
C III
C021
C 102
C012
C033
- 0.058 52
0.080 63
0.079 48
0.040 00
o.ooo 95
- 0.066 2 1
- 0.049 87
- 0.123 71
- 0.025 16
0.068 82
- 0.038 48
0.057 89
- 0.205 89
0.109 65
0.037 48
0.030 73
0.066 57
- O.ooO18
- 0.093 7 1
- 0.135 17
2.4
2
g
2.3
8
L
2.2
2.1
3.4
3.7
4.3
4.0
4.6
(al
c .---~~~~~~~~_--:~:2%
s8 ntfc
‘)I ,
,\\
\ j\‘1\c’
‘.._
.-__-~---’
’
:<:,:;:-:‘
q;..
2 hs@$$s&~>
-~~---r___:~
._
.‘~~~~~+t
- -=z
---m_.-p-bzm
140
130
120
110
“Computed using the 3d 2fbasis set (seethe text).
bThe coordinates are Q, = 1 - R,(ClO)/R(ClO), Q2 = 1 - r,(OO)/
r(OO), and Q, =A,A6’+A,A6’2fA,A83,
where A8 =B(ClOO)
- f?,(ClOO),A, = 1.4O,A, = -O.l136Orad-‘,andA,
= -0.30287
rad - *. The potential has beenexpandedabout the calculatedequilibrium
geometryof&,, = 4.0419Ou,, roe = 2.269 75a,, and &k,o = 115.658”.
‘ThecoordinatesareQ, =R(ClO) -R,(ClO),Q,
=r(OO) -r,(OO),
and Q, = B(C100) - 6, (CIOO), and the dipole moments (rotated into
an Eckart frame) have been expandedabout the CMRCI equilibrium geometry. The a and b componentscorrespondto the A and B principal axes,
respectively(seethe text).
the available experimental data. The ground state of Cl00 is
calculated by CMRCI (3d 2f) to lie 12.7 kcal/mol below
that of OClO. This can be compared to the experimental
value of 4 + 2 kcal/mol, which has been derived from the
energies
dissociation
two
the
in
difference
D,(OClO-Cl+
0,) and D,(ClOO-+Cl+
0,). The discrepancy between CMRCI and experiment for the isomerization energy is mainly due to the error ( - 8 kcal/mol) in
the calculated OClO + Cl + O2 dissociation energy (Sec.
II C). The CMRCI equilibrium geometry differs slightly
from the structure assumed in the matrix experiments of
Arkell and Schwager. lo In particular, the CMRCI values of
R, (ClO) and 19,(ClOO) are larger by 0.3 1 A and 5.7”, respectively. Our result for r, ( 1.201 A) is particularly interesting since it is shorter than the value calculated for molecular 0, with the same basis set and active space ( 1.204 A).
This is indicative of significant charge transfer from 0, to
Cl, resulting in the polarity - Cl-O>, which is confirmed by
the calculated dipole moments (cf. the next section). The
vibrational frequencies have been calculated using secondorder perturbation theory. The calculated or stretching vibrational frequency ( 181.2 cm- ’) is smaller than the IR
matrix value by 45%. The cause for this discrepancy could
be threefold. On the one hand, our CMRCI surface is too
100
901
,
3.4
(b)
3.7
*
I
4.0
”
!
4.3
”
I
I
4.6
R,,&bohr)
FIG. 7. Contour plots of the CMRCI potential energy function for the
X *A * ground state of CIOO. The first contours and the intervals between
successivecontours are 250 cm - ‘. (a) The stretching displacementsare
depicted for f?,,, = 115”.(b) The dependenceof the potential energy on
R cIo and bm is plotted for r, = 2.25an.
shallow, as evidenced by our small calculated value of De
(2.46 kcal/mol) compared to experiment’ ( 5.61 kcal/mol) .
This is not unexpected for a van der Waals-like bond, where
diffuse polarization functions would be needed to reproduce
the dispersion energy. Since the dissociation occurs in the
Cl0 bond stretch, the small calculated binding energy could
lead to a predicted stretching frequency which is too small.
Second, for such a weak bond, large amplitude motions may
also be expected and perturbation theory is often inaccurate
in these cases.In addition, there could be large matrix effects
for the Cl0 stretch in the experimental IR study, which
would increase the measured matrix stretching frequency
over the actual gas phase value. In contrast, our result for vZ
(Cl00 bend) is in very good agreement with the IR matrix
value, differing by just 18 cm - ‘. The CMRCI value for Ye,
which is predominantly the oxygen stretch, is larger than
that of Arkell and Schwager” by about 4.5%. Identical calculations on 0, (at R,,, = 50a, and I$,, = 115”) yielded
an harmonic frequency larger than experiment by 2.4%. The
larger discrepancy for Cl00 is not unexpected, since this
force constant (and the Cl0 stretch as well) is very sensitive
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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K. A. Peterson and H. Werner: Configuration interaction study of CIO,
TABLE V. Spectroscopicconstants of X 2A Cl00 calculated from the
CMRCI PEF compared to experiment.
2.6
l
Constant
R,(CIO)(A,
r,wN (A)
e,cCDO) (deg)
0, (cm-‘)
co1(cm-‘)
0, (cm-‘)
X,, (cm-')
X2, (cm-')
X3, (cm-')
X,, (cm-')
X,, (cm-‘)
X2, (cm --‘)
v, (cm-‘)
v, (cm-‘)
v3 (cm-‘)
D, (kcal/mol)
CMRCI
2.5
Expt.
2.139
1.201
115.7
1.83”
1.23”
110”
193.6
403.2
1538.3
- 4.28b
- 5.67
- 20.2
- 12.5”
4.87
10.4
181.2
390.8
1505.6
2.46
2.4
F
g
23
8
L
2.2
317
4.0
413
4.6
4.3
4.6
R,,,(bohd
407’
373’
144lC
5.61*
L Assumed structure in the analysis of the IR matrix spectrum taken by Arkell and Schwager (Ref. 10).
bPossibly perturbed in thesecalculations by a 20, - o2 Fermi resonance.
c v, correspondsto the Cl0 stretch, v, to the bend, and v, is predominantly
the 00 stretch. The experimental values were obtained from the IR spectrum in an Ar matrix (Ref. IO).
d The gas phaseresult of Ref. 7 corrected for zero point vibrations using the
CMRCI vibrational constants.
-z
-5
8
120
cr?8
110
100
90
3.4
3.7
(b)
to the amount of charge transfer from 0 to Cl, i.e., the Cl-O,
bond distance.
4.0
R,,,(bohr)
FIG. 8. Contour plots of the a-component CMRCI electric dipole moment
function (in Debye) of Cl00 for (a) R,,, vs r, at ec,, = 11s”and (b)
R c,o vs .9,,,, at roe = 2.25ae.
2. Dipole moments and infrared intensities
The total dipole moment of Cl00 is calculated (Table
IV)tobe1.113D(pU,=
-l.103Dandpu,=
-0.149D)
at the CMRCI equilibrium geometry. The negative sign of
pa, which is the major dipole moment component, is consistent with the polarity mentioned above. (The A principal
axis lies nearly along the Cl0 bond.) The CMRCI ,u, is
much larger than the value of 0.3 D previously calculated by
Jafri ei aZ.62The dipole moment function, however, is very
sensitive to the reference geometry used in the expansion due
to the strongly changing charge transfer. At the equilibrium
Jafri
et al.
[R(ClO) = 3.75ao,
geometry
of
R(O0) = 2.48ao, 0(ClOO) = 113.6”], the dipole moment
is calculated to be 0.53 D. The equilibrium dipole moment
calculated in this work, while dependent on the assumed
equilibrium geometry, is still encouraging for future pure
rotational spectroscopy of this important transient species.
Contour plots of the a-component dipole moment function
of Table IV are shown in Figs. 8 (a) and 8 (b) for R,,, vs roe
and &,, , respectively. The charge transfer between Cl and
0, is evidenced by the very nonlinear nature of the dipole
moment function in the R,,, coordinate. In particular, the
a-component dipole moment function exhibits extrema close
to the calculated value of R, (ClO) of 4.04ao, reflecting the
minimum energy configuration of Cl with respect to 0,.
Dipole moment derivatives with respect to dimensionless
normal coordinates have been calculated using the CMRCI
PEF and EDMF, and the linear and quadratic terms for
both the a and b dipole moment components are shown in
Table VI. From inspection of the first derivatives, the vS
mode (0, stretch) is predicted to be much stronger than
either the Y, or v2 (I+ 9 vi > v2 >. In view of Figs. 8 (a) and
8 (b), it is not surprising that the quadratic terms for the vi
mode (Cl0 stretch) are of the same magnitude or larger
than the linear ones. In contrast, for the vs vibration, the first
derivatives are very dominant (Table VI) and the intensities
of the lower vibrational states of this mode should be well
approximated by the linear terms. Using the double harmonic approximation, the absolute infrared intensity of the v3
band is calculated to be 340 cm - 2 atm - ’ at 300 K.
V. CONCLUSIONS
Near-equilibrium
two-dimensional potential energy
functions and several potential energy surface cuts have been
calculated for the first four electronic states of the OClO
radical using large basis sets and multireference configuration interaction wave functions. While large-scale potential
energy surfaces in C, symmetry have not been carried out at
J. Chem. Phys., Vol. 96, No. 12,15 June 1992
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8960
K. A. Peterson and H. Werner: Configuration interaction study of CIO,
TABLE VI. First and secondderivatives with respectto dimensionlessnormal coordinatesfor the X *A *, Cl00 E&art frame” dipole moments (in
Debye).
a component
I4
P2
P4
,,
PII
w
P22
PY3
I,
PI2
PY3
f&
- 0.0068
- 0.0017
0.2082
0.0944
0.0670
- 0.0429
- 0.0467
- 0.0359
0.0192
b component
PI
P2
P3
PY,
Pee;;
R
P33
,,
PI2
I,
PI3
*
P23
-
0.0368
0.0117
0.0148
0.0023
0.0136
0.0017
0.0026
0.0024
o.OcO3
“The Eckart frame is definedwith respectto the calculated CMRCI equilibrium geometry and the principal axesof inertia A, B, and C, and /I, correspondsto the ith normal mode (seethe text).
this time due to the exceedingly large computational cost,
the present results have indicated that the predissociation
mechanism of the A ‘A2 state is a complicated function of the
bending and asymmetric stretching modes in the first two
excited electronic states ( 1 ‘B, and 1 ‘A, ), which couple via
nonadiabatic interactions to the A *A2 state. From predicted
surface crossings of the 1 *A1 state with that of the A *A2
state, we conclude that it is the 1 ‘A1 state which predissociates the A ‘A2 state through spin-orbit coupling. After this
initial crossing to the 1 2A1 surface, it is predicted that the
molecule may dissociate through the linear configuration
(to Cl0 + 0) by excitation of the bending mode, or cross
onto the 1 *B2 surface by strong vibronic Herzberg-Teller
interactions in the asymmetric stretching coordinate. Dissociation to Cl0 + 0 from the 1 *B, state would then proceed
through the asymmetric stretch, which is purely dissociative
at valence angles larger than the 19,of the A 2A2 state. The
possibility for photoisomerization from OClO to Cl00 has
not been dealt with in this study. These calculations, however, are currently underway and initial results are in agreement with current assumptions that the isomerization occurs through the bending mode of the 1 2B2 state.
Three-dimensional potential energy and dipole moment
functions for the electronic ground state of Cl00 have also
been calculated by internally contracted MRCI. Strong
charge transfer between Cl and 0, is observed. The calculated structure and force constants are in generally good agreement with previous matrix isolation experiments, although
some of the calculated spectroscopic constants are found to
be very dependent on the depth of the computed surface. The
predicted microwave and infrared intensities calculated
from the CMRCI electric dipole moment function appear to
be large enough for the high-resolution, gas phase study of
this species.
ACKNOWLEDGMENTS
This work was supported by the Deutsche Forschungsgemeinschaft (SFB 2 16) and the German Fonds der Chemischen Industrie. The calculations were made possible by
generous grants of supercomputing time on the CRAYYMP at the HLRZ Jiilich and NEC SX-3 at the RRZ Koln.
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