Boron dichloride and its cation
Geometries, vibrational frequencies, ionization energy and excitation energies
Oliver Warschkow, Edmond P. F. Lee*¤ and Timothy G. Wright*”
Chemistry Department, T he University, HighÐeld, Southampton, UK SO17 1BJ
The geometries and harmonic vibrational frequencies of BCl and BCl ` have been calculated at various levels of ab initio theory
2
2
[MP2, MP4(SDQ), CISD and CCSD(T)] and density functional theory (BLYP and B3LYP), using a variety of basis sets. These
calculations show the neutral molecule to be bent, with a bond angle of ca. 125¡, and the cation to be linear. Calculated
vibrational frequencies were compared with experimental values, where available, including isotopic shifts. The ionization energy
of the BCl molecule was calculated to be 7.33 eV at the Gaussian-2 level of theory ; additionally, the heat of formation of the
2
cation was calculated to be 160.4 kcal mol~1. Finally, CIS and MRDCI calculations were performed, in order to ascertain the
position of excited electronic states for both the cation and the neutral molecule ; the calculated excitation energies were then
compared with reported energies for transitions in these species.
Boron trichloride is used extensively for the etching of various
semiconductor surfaces.1 In order to understand and control
the chemistry of the plasmas used in such etching procedures,
it is necessary to be able to determine the species present and
their concentrations and local temperatures, and then to
model the plasmas.2,3 Such models depend critically on the
accuracy of inputted spectroscopic and thermodynamic data,
and so it is of extreme importance to determine such data.
Spectroscopic data is useful not only from the modelling point
of view, but also with regard to detecting the species present,4
using such techniques as laser-induced Ñuorescence (LIF) and
resonance-enhanced multiphoton ionization (REMPI). In the
particular case of BCl -containing plasmas, although some
3
data are available for the parent BCl and the fragment BCl
3
species and their cations, almost nothing is known about the
other major fragment species BCl or its cation, with even the
2
ionization energy having only been estimated, even though it
has been noted that BCl is very likely present in plasmas (ref.
2
2 and other references noted below).
In this work, three areas are considered : the geometry and
vibrational frequencies of both the ground neutral and cationic states of BCl ; the ionization energy of BCl ; and the
2
2
excitation energies of excited electronic states (relative to the
respective ground state) of both the neutral molecule and cation.
1 Geometry and vibrational frequencies of BCl
2
and BCl ‘
2
Theoretical methods
Geometry optimizations were performed at various levels of
theory for the ground state of both the neutral molecule and
the cation. A number of basis sets were used to ascertain that
convergence had been obtained for the geometric parameters.
The levels of theory used were : MP2/6-31G*, MP2/cc-pVDZ,
MP2/cc-pVTZ, MP4(SDQ)/cc-pVTZ, CCSD(T)/cc-pVDZ and
CCSD(T)/6-311G(2d). In addition, CISD/cc-pVDZ and CISD/
cc-pVTZ calculations were performed for the ground-state
cation. As well as these ab initio methods, density functional
theory (DFT) was also used at various levels, to ascertain its
accuracy for these species. The levels of DFT theory used
were : BLYP/6-31G*, BLYP/cc-pVDZ, BLYP/cc-pVTZ,
¤ E-mail address : epl=soton.ac.uk
” E-mail address : tgw=soton.ac.uk
B3LYP/cc-pVDZ and B3LYP/cc-pVTZ. For the neutral
ground state, which is a doublet, unrestricted-spin HartreeÈ
Fock wavefunctions were used, but spin contamination was
found to be small (vide infra). Nevertheless, as an additional
check, ROMP2/6-31G* calculations were also performed and
compared to the UMP2/6-31G* geometries and vibrational
frequencies.
Many common acronyms have been used above : MPn is
MÔllerÈPlesset perturbation theory5 carried out to the nth
order, with SDQ indicating that single, double and quadruple
(but not triple) substitutions have been used ; ROMP2 implies
the use of a restricted open-shell HF wavefunction for the
MP2 procedure, using the method of Handy and co-workers ;6
CCSD(T)7 is the coupled cluster method, employing single
and double substitutions, but using a perturbative method for
inclusion of the triple substitutions ; BLYP stands for the
Becke88 exchange functional,8 with the Lee, Yang and Parr
(LYP) correlation functional ;9 and B3LYP is a hybrid functional which contains some HartreeÈFock exchange energy, it
is based on BeckeÏs three-parameter Ðt10 to Gaussian-1 (G1)
energies. The basis sets used are either the standard 6-31G*
and 6-311G(2d) split-valence basis sets, or the relatively recent
correlation consistent basis sets (cc-pVXZ) of Dunning et al.11
Geometry optimizations were performed using analytic gradient methods, except for the CCSD(T) calculations for which
numerical methods were employed. Similarly, analytic secondderivative methods were used to calculate harmonic vibrational frequencies, except for the MP4(SDQ), CISD and
CCSD(T) calculations for which numerical methods were utilized. All the above calculations were performed with GAUSSIAN 94,12 except for the ROMP2 calculations, which were
performed with CADPAC.13
Background
BCl is a 17-electron system, and is therefore expected to be
2
bent, on the basis of Walsh diagrams ;14 similarly, the 16-electron BCl ` species is expected to be linear. (BCl ` is valence
2
2
isoelectronic with the beryllium and magnesium diÑuorides
and dichlorides, which are known to be linear.15) The only
spectroscopic evidence for the geometry of the neutral species
comes from a matrix isolation study by Miller and Andrews16
who derived a bond angle of 125 ^ 5¡. The latter estimate is
also in agreement with an EPR study,17 where a bond angle
of ca. 122¡ was obtained. There is no experimental information available on the ground-state BCl ` geometry.
2
J. Chem. Soc., Faraday T rans., 1997, 93(1), 53È61
53
With regard to the vibrational frequencies, values for BCl
2
of 470, 240 and 990 cm~1 (apparently estimated by comparison with BCl ) were used by Dessaux et al. to assign a chemi3
luminescence spectrum obtained by reacting H atoms with
BCl ;18 however, the reference they quote in that work is an
3
early version of the JANAF Tables. Later JANAF tables19
have the following values : 720, 240 and 980 cm~1, thus there
is some doubt as to the assignment of the chemiluminescence
spectrum presented in ref. 18. Miller and Andrews obtained
IR spectra of the species present after BCl had undergone
3
proton radiolysis in an argon matrix.16 They obtained values
of 731 and 965.7 cm~1 for 11BCl , assigned to l and l ,
2
1
3
respectively, with the l frequency of the 10BCl isotopomer
3
2
being measured at 1004.3 cm~1 (note that the 731 cm~1 value
was reassigned later to HBCl 20). For the cation, there are
2
two pieces of information available : the Ðrst comes from a
synchrotron radiation study21 of the decay processes of the
BCl ` cation from excited electronic states. In that work,
3
absorption of 17.71 eV energy photons led to Ñuorescence,
which was dispersed, leading to the observation of a vibrational progression. Although the assignment of the Ñuorescence (on energetic grounds) to BCl ` was deemed to be clear,
2
it could not be unambiguously determined whether this pro-
gression was due to vibrational excitation in the upper electronically excited state or the ground state. The progression
had a frequency of 650 ^ 30 cm~1 and was thought to arise
from a progression of 2l , with the upper and lower states
2
assumed to be linear, and that the upper state had relaxed to
the vibrational ground state (leading to the observation of
only even quanta of the bend vibration) ; this assignment then
leads to a ground-state bending frequency of ca. 325 cm~1.
Further remarks on the assignment of the dispersed Ñuorescence observed in ref. 21 will be made in Section 3 and later in
this section. The second source of information on BCl `
2
comes from the JANAF Tables,19 where values of the vibrational frequencies of 500, 120 and 800 cm~1 were estimated by
comparison with CO ; these values will be seen to be far from
2
the calculated values obtained here.
Results and Discussion
The results of the ab initio calculations are given in Tables 1
and 2. It is only possible to compare calculated results with
experimental values for the ground-state neutral (X3 2A ). It is
1
clear that, as far as the geometry is concerned, all levels of
theory predict a bond angle in the range 125 ^ 1¡, in very
Table 1 Calculated geometries and vibrational frequencies of BCl ` (X 1& `)a
2
g
method
[energy(]943)/E
MP2/6-31G*
MP2/cc-pVDZ
MP2/cc-pVTZ
MP4(SDQ)/cc-pVDZ
CISD/cc-pVDZ
CISD/cc-pVTZ
CCSD(T)/cc-pVDZ
CCSD(T)/6-311G(2d)
BLYP/6-31G*
BLYP/cc-pVDZ
BLYP/cc-pVTZ
B3LYP/cc-pVDZ
B3LYP/cc-pVTZ
0.726 463
0.782 140
0.932 252
0.807 511
0.770 285
0.908 050
0.819 007
0.877 725
1.932 216
1.977 425
2.020 834
2.017 520
2.059 340
h
bond length/Ó
bond angle/degrees
1.6112
1.6282
1.6157
1.6320
1.6265
1.6129
1.6345
1.6199
1.6319
1.6386
1.6263
1.6276
1.6163
180
180
180
180
180
180
180
180
180
180
180
180
180
l /cm~1
1
l /cm~1
2
588.4
574.2
572.8
565.1
573.8
575.9
561.3
553.4
546.4
540.3
544.2
558.1
560.6
282.8
316.4
328.4
315.7
321.9
337.1
311.6
324.3
291.0
303.4
316.6
312.5
326.1
(0)
(0)
(0)
(0)
(0)
(0)
(È)
(È)
(0)
(0)
(0)
(0)
(0)
(17)
(17)
(15)
(18)
(21)
(19)
(È)
(È)
(14)
(12)
(12)
(16)
(15)
l /cm~1
3
1504.2
1489.0
1482.1
1463.5
1480.2
1479.7
1457.6
1420.0
1415.8
1416.8
1412.7
1456.0
1449.9
(668)
(648)
(621)
(643)
(695)
(680)
(È)
(È)
(478)
(492)
(479)
(574)
(553)
a Values in parentheses in the vibrational frequencies columns are the calculated IR intensities in units of km mol~1.
Table 2 Calculated geometries and vibrational frequencies of BCl (X3 2A )a,b
2
1
method
[energy(]943)/E
UMP2/6-31G*
SS2T \ 0.754
ROMP2/6-31G*
UMP2/cc-pVDZ
SS2T \ 0.755
UMP2/cc-pVTZ
SS2T \ 0.756
UMP4(SDQ)/cc-pVDZ
SS2T \ 0.755
CCSD(T)/cc-pVDZ
SS2T \ 0.755
CCSD(T)/6-311G(2d)
SS2T \ 0.755
BLYP/6-31G*
SS2T \ 0.752
BLYP/cc-pVDZ
SS2T \ 0.752
BLYP/cc-pVTZ
SS2T \ 0.752
B3LYP/cc-pVDZ
SS2T \ 0.752
B3LYP/cc-pVTZ
SS2T \ 0.753
experimental (ref. 16)
(matrix isolation)
0.983 213
1.7225
1.007 009
1.042 754
l /cm~1
1
l /cm~1
2
l /cm~1
3
125.3
741.2 (31)
298.9 (2)
1032.2 (438)
1.7201
1.7404
125.0
125.0
744.5 (34)
731.1 (33)
296.4 (2)
290.2 (1)
1034.0 (430)
1019.0 (443)
1.195 238
1.7259
125.2
717.2 (26)
288.3 (1)
1007.2 (416)
1.070 419
1.7451
125.2
721.7 (32)
288.2 (1)
1010.7 (427)
1.080 569
1.7479
125.1
715.6 (È)
285.7 (È)
1001.9 (È)
1.143 156
1.7374
125.3
692.5 (È)
287.6 (È)
956.3 (È)
2.195 825
1.7540
125.2
667.8 (25)
277.9 (1)
925.5 (380)
2.241 713
1.7594
125.0
668.5 (23)
272.9 (1)
930.7 (378)
2.283 463
1.7439
125.7
658.7 (19)
273.6 (0)
925.9 (366)
2.291 501
1.7456
124.9
695.5 (28)
281.1 (1)
971.0 (408)
2.330 485
1.7314
125.6
684.5 (22)
281.4 (1)
964.0 (389)
È
È
125 ^ 5
731
h
bond length/Ó
bond angle/degrees
È
965.7
a Values in parentheses in the vibrational frequencies columns are the calculated IR intensities in units of km mol~1. b All calculations employ
the frozen core approximation, except for the ROMP2 calculation, which includes all orbitals.
54
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
Table 3 Calculated vibrational frequencies for the six BCl iso2
topomers at the CCSD(T)/cc-pVDZ level
isotopomer
Cl-B-Cl
35-11-35
37-11-37
35-11-37
35-10-35
37-10-37
35-10-37
l /cm~1
1
l /cm~1
2
l /cm~1
3
715.6
709.3
712.4
739.2
733.2
736.2
285.7
279.3
282.5
288.2
281.7
285.0
1001.8
997.3
999.5
1042.5
1038.2
1040.3
Ñuorescence spectrum of ref. 21 could be due to the upper or
lower state of the transition, and so two studies are made in
the present work : Ðrst, to scan the excited states of the cation
to see which states are energetically viable candidates for the
upper state of the dispersed Ñuorescence ; and secondly, to
optimize the structure and calculate the vibrational frequencies of the upper state that seems the most likely candidate. These two sets of calculations will be presented in
Section 3.
Isotopic shifts
good agreement with the experimental estimates.16,17 The
bond length has not been obtained experimentally, but the
calculations suggest that a value of 1.74 ^ 0.01 Ó should be
reliable ; a value of 1.73 Ó is quoted in the JANAF Tables,19
which is an estimated value, intermediate between those for
BCl and BCl . The vibrational frequencies seem to be a little
3
more sensitive to the level of theory used than the geometry. It
appears that, although the l frequency is close to con2
vergence, there is still some decreasing of the l and l values,
1
3
even at the highest levels of theory used here. The computed
l values are close to the experimental value, but the l value
3
1
is converging to a value signiÐcantly lower than the experimental one,16 and perhaps agrees with the fact that this
assignment was later20 changed.
Comparing now the ab initio calculations and the DFT calculations (Table 2) for the neutral molecule, it can be seen that
the B3LYP/cc-pVTZ values are extremely close to the
CCSD(T)/6-311G(2d) results but, of course, the DFT calculations are signiÐcantly cheaper, computationally. This excellent performance of DFT calculations has been noted
previously by Martin et al.,22 amongst others. This good
agreement is even more pronounced for the cationic frequencies (Table 1) where the B3LYP/cc-pVTZ results are
almost exactly the same as the CCSD(T)/6-311G(2d) values.
Clearly, the DFT results in both the cationic and neutral cases
appear to be more or less converged. The close agreement of
the converged DFT and the CCSD(T)/6-311G(2d) results suggests that these values must be very close to the true experimental harmonic vibrational frequencies. These values are
also in fairly close agreement with the estimated values in the
JANAF Tables.19
Although the SS2T values for the neutral molecule are very
close to the theoretical value (0.75) for the unrestricted calculations, an additional check for lack of spin-contamination
e†ects was made by performing ROHF and ROMP2 calculations. As may be seen from Table 2, the agreement between
the geometries and vibrational frequencies for UMP2 and
ROMP2 is excellent, showing that the small amount of spin
contamination is not having a signiÐcant e†ect on any calculated properties.
For the cation, comparison of the calculated harmonic
vibrational frequencies with the estimated values from the
JANAF Tables,19 shows that there is very poor agreement
here ; only the l frequency is close to the calculated value,
1
with the other two being too small by almost a factor of two ;
this will clearly have implications for the thermodynamic data
calculated therein using these values. Considering now the dispersed Ñuorescence spectrum of Biehl et al.,21 where a progression of 650 ^ 30 cm~1 was observed and assigned to a
progression of 2l in the ground state of the cation. The com2
puted values of l , shown in Table 1, suggest that the l fre2
2
quency is ca. 310 ^ 20 cm~1, which would be in excellent
agreement with the l frequency of ca. 325 cm~1 assigned
2
from the Ñuorescence spectrum ; however, for the only-even-l
2
selection rule to hold (and assuming that the upper state is in
its ground vibrational level) there must be a linear excited
state of BCl ` energetically accessible in the synchrotron
2
studies (vide infra). The structure observed in the dispersed
Miller and Andrews16 obtained an isotopic shift for the l
3
mode : for the 11BCl and 10BCl isotopomers, the ratio was
2
2
965.7 : 1004.3(0.962 : 1.000). For completeness, the isotopic
shift was calculated for all six isotopomers at the CCSD(T)/ccpVDZ level (including the 10B and 11B, and the 35Cl and 37Cl
isotopes)Èthe results are given in Table 3. The corresponding
ratio for the 35-11-35 and 35-10-35 isotopomers is calculated
to be 0.961 : 1.000, clearly in excellent agreement with experiment, even though the absolute values are not in such good
agreement.
2 Ionization energy of BCl
2
Background
There has been no direct measurement of the ionization
energy of BCl , and there have only been three experimental
2
estimates : two based on fragmentation processes in mass
spectrometric experiments, the other based on Ñuorescence of
ions from dissociative photoionization of BCl .
3
Mass spectrometric experiments have allowed the ionisation energy (E ) to be determined, and have been performed
i
by Osberghaus in 1950,23 with follow-up studies by Marriott
and Craggs,24 Koski et al.25 and Dibeler and Walker.26 The
study of Marriot and Craggs24 gave an estimate of E
i
(BCl ) O 9 eV. The later study of Koski et al.25 gave an ion2
ization energy of 7.2 eV. Dibeler and Walker26 obtained E \
i
7.52 eV. The only other estimate of the ionization energy
comes from synchrotron studies from Tuckett and coworkers21,27 who obtained an upper limit of 7.71 eV by
assuming that the BCl ` ions they saw “ turned on Ï at their
2
thermodynamic energy.
Theoretical method and results
Although, in principle, it is possible to calculate the ionization
energy for all of these complexes at the levels of theory used in
Section 1, the cheapest way of gaining accurate ionization
energies is to use the Gaussian-2 (G2) method of Pople and
co-workers,28 which is a composite method of obtaining thermochemical data e†ectively at the QCISD(T)/6-311 ] G(3df,
2p) level, but by only doing single-point calculations at the
MP2(FULL)/6-31G* geometry (and including some empirical
corrections).
Combining the BCl G2 energy at 0 K ([944.274 558 E )
2
h
with the G2 energy (0 K) of the BCl ` cation ([944.007 954
2
E ) gives an E value of 7.25 eV. It is also possible to calculate
h
i
the ionization energy by the di†erence in the calculated Gibbs
free energies of BCl and BCl ` at 298 K (assuming a station2
2
ary electron) ; this gives an ionization energy of 7.33 eV.
Although this value is close to the value of 7.52 eV obtained
by Dibeler and Walker,26 the value of the heat of formation of
BCl obtained by them was [14.7 ^ 0.5 kcal mol~1 ; this
2
value compares extremely poorly with the G2 value calculated
by Schlegel and Harris29 of [6.79 kcal mol~1. Since G2 energies have been shown to be reliable in the vast majority of
cases, it would seen appropriate to calculate the G2 heat of
formation of the cation, using the G2 heat of formation of the
neutral species. (Note that all Gibbs free energies, enthalpies
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
55
and entropies are calculated using the simple harmonic oscillator, rigid-rotor approximation and assume ideal gas behaviour.) Doing this yields a heat of formation (298 K) of BCl `
2
of 160.4 kcal mol~1, which is fairly close to the value of
158.6 ^ 0.5 kcal mol~1, obtained by Dibeler and Walker.26 In
passing, it is worth noting that Bews and Glidewell30 performed semiempirical (MNDO) calculations to investigate the
fragmentation processes of boron trichloride, diboron tetrachloride and tetraboron tetrachloride ; in that work, they
found BCl ` to be of D symmetry, and calculated its heat
2
=h
of formation to be ca. 180 kcal mol~1, clearly in poor agreement with the G2 value ; however, this is to be expected with
the approximate MNDO method. Note also that values of
[20 ^ 15 and 148 ^ 5 kcal mol~1 are quoted in the JANAF
Tables19 for the heats of formation of the neutral molecule
and cation (298 K), respectively. These are both in rather poor
agreement with the G2 values obtained.
3 Excited states of BCl ‘ and BCl
2
2
Background
Cation. As mentioned above, there has been very little information obtained on the excited states of the cation. The only
reported work is the Ñuorescence attributed to the cation by
Biehl et al.21 This work observed Ñuorescence in the range
280È350 nm (ca. 3.5È4.4 eV), which was assigned to BCl ` on
2
the basis of energetics (these considerations led to the exclusion of the possibility that the Ñuorescence was attributable to
an excited state of the neutral molecule).
Neutral. There have been a number of studies which have
reported Ñuorescence that has been attributed to excited states
of the neutral BCl molecule. The Ðrst was the study by
2
Dessaux et al.31 who observed the Ñuorescence emanating
from the reaction region of a chemiluminescence experiment,
which reacted H with BCl ; this spectrum was later
3
assigned18 in terms of spinÈorbit splitting and vibrational
excitation of BCl . Prior to this study, emissions from BCl
2
2
had not been seen, even though they had been looked for in
Ñash photolysis experiments32 of B Cl and microwave dis2 4
charge experiments.33
There then followed two synchrotron radiation studies : one
in the range 106È190 nm34 and the other in the range 45È106
nm.35 There were a total of four bands seen in these studies,
labelled AÈD. Band A had an onset at 380 nm (ca. 3.3 eV)
with a maximum at 500 nm (ca. 2.5 eV), with no reproducible
structure ; band B consisted of two features, a broad band in
the range 280È380 nm (ca. 3.6È4.4 eV) and a sharp band at
360 nm (ca. 3.4 eV) ; band C was noted as being similar to the
chemiluminescent feature of Dessaux et al.18,31 and appeared
in the range 240È380 nm (ca. 4.4È5.2 eV) ; Ðnally, band D, only
seen in the higher energy synchrotron radiation range, and
appeared at 200È260 nm (ca. 4.8È6.2 eV).
Breitbarth and Ducke36 looked at radiofrequency discharges in BCl and observed three broad, molecular emis3
sions at 305, 350 and 480 nm from which it was deduced that
BCl was the most likely carrier.
2
Tokue et al.37 used electron impact to dissociate BCl .
3
They observed two emissions in the regions 230È380 nm (ca.
3.3È5.4 eV) and 400È580 nm (ca. 2.1È3.1 eV). The dissociation
thresholds observed Ðtted with calculated thresholds only if
the ground state was assumed to be the Ðnal state of the emission processes.
Further synchrotron studies have recently been performed
by Tuckett and co-workers.21,27 They observe two main emissions (although they noted that they may not have resolved
another emission seen in the previous synchrotron studies), in
the ranges 400È650 nm (ca. 1.9È3.1 eV) and 230È500 nm (ca.
2.5È5.4 eV) ; these were assigned to the following processes :
A3 2B ^ X3 2A and B3 2A ^ X3 2A with the higher energy
1
1
1
1
56
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
band possibly also containing some contributions from the C3
state (symmetry not noted).
Theoretical methods
Two approaches were employed :
(i) Although the CIS38 method does not, strictly speaking,
account for electron correlation, it is the cheapest method that
gives both minimum-energy geometries and harmonic vibrational frequencies for excited states. Thus it was used to give
an overview of the singlet states that were accessible in the
energy ranges indicated by the dispersed Ñuorescence spectra
of Biehl et al.21 These calculations also allowed the calculation of oscillator strengths. Single-point CIS(nstate \ 20)/631G* calculations were Ðrst performed at the linear MP2/631G* geometry of the X 1& ` state. Further optimisation and
g
frequency calculations on some selected excited states were
then made with both D and C symmetry. Finally, CIS/6=h
=v
31G* and CIS/6-311G(2df ) geometry optimisation and frequency calculations were performed for the Ðrst CIS excited
state (A3 1B ), which has a . . . (7b )1(9a )1 conÐguration in C
2
2
1
2v
symmetry. RHF/6-31G*, MP2/6-31G*, MP2/6-311G(2d),
MP4(SDQ)/cc-pVDZ and CCSD(T)/6-311G(2d) calculations
were also performed on the A3 1B state in order to obtain
2
more reliable equilibrium geometries, harmonic vibrational
frequencies, vertical excitation energies (VEE) and adiabatic
excitation energies (AEE). Similar CIS and MP2 calculations
were carried out for BCl . These calculations were performed
2
using GAUSSIAN 94.
(ii) MRDCI calculations39 (as implemented in the
GAMESS suite of programs40), with threshold selection set at
10 lE and extrapolation to zero threshold39 were performed.
h
The estimated full CI energy was then obtained by applying
the multireference variant of the Davidson correction41 which
accounts for quadruple excitations. The energies at each of
these stages are denoted E
,E
and E .
MRDCI T/0
full
An important quantity in the context of MRDCI calculations is &c2, which quantiÐes to what extent a state is repi
resented by the reference conÐgurations ; this also has an
impact on E . Strictly speaking the energies of two states,
full
calculated in this way, are only comparable if their &c2 values
i
are close and preferably above 0.9. The relative energy
between two states with signiÐcantly di†erent &c2 values coni
tains rather large di†erential contributions from the application of the Davidson correction. Therefore, the MRDCI
calculations were performed in two stages : Ðrst a relatively
small reference set was used in order to obtain a qualitative
overview of a large number of low-energy valence states. The
reference set was generated by the following approach. With
the ground-state conÐguration, all singly excited conÐgurations of the relevant symmetry within the valence space
were generated. Then all singly excited conÐgurations (again
of the relevant symmetry within the valence space) from each
conÐguration already generated were also included as reference conÐgurations. Although not all doubly excited conÐgurations were generated in this strategy, it is a simple way of
generating a reference set that is balanced for each symmetry
and geometry. For each symmetry, the four lowest CI roots
were computed. The calculations on the linear cation are performed in the D subgroup. The correlation of the sym2h
metries in each group is given in Table 4.
After this survey of states had indicated which states were
the most likely to be the source of the dispersed Ñuorescence
spectra, these few states were recalculated using a larger reference set, in order to obtain larger &c2 values and thus more
i
reliable relative energies. The reference set was extended to
include all doubly excited valence conÐgurations and all other
conÐgurations which had a contribution of c2 [ 0.005.
i
Because of the larger size of the reference set, only the lowest
few states of BCl ` were considered.
2
Table 4 Symmetry correlation tablea
C
2v
A
1
B
1
B
2
A
2
A ]B
2
2
A ]B
1
1
A ]B
1
1
A ]B
2
2
D
=h
D
&`
g
&~
g
&`
u
&~
u
%
g
%
u
*
g
*
u
2h
A
g
B
1g
B
1u
A
u
B ]B
2g
3g
B ]B
2u
3u
A ]B
g
1g
A ]B
u
1u
a The axis systems chosen are as follows : for C , the molecule lies in
2v
the yz plane, with the z axis coinciding with the C axis in a right2
handed system ; for D the z-axis lies along the molecular axis as it
2h
does in D with the molecule in the yz plane.
=h
For the cation, single-point MRDCI calculations were performed at the CCSD(T)/6-311G(2d) optimised geometries of
the X 1& ` ground state and the bent A3 1B excited state of
g
2
BCl `. For the neutral, only single-point calculations at the
2
CCSD(T)/6-311G(2d) optimised geometry of the X3 2A neutral
1
state were performed. [Bartlett and co-workers42 have recently shown that CCSD(T) methods are comparable to MRDCI
methods and so the use of a CCSD(T) optimised geometry for
the MRDCI calculations is not unreasonable. Calculations on
the second row dihalide PF led to the same conclusion.43] A
2
TZVP basis was used. The natural orbitals from a CISD calculation on the respective ground state, used as the molecular
orbital (MO) basis for the MRDCI calculations, are as follows
(BCl `)
2
. . . (5p )2(4p )2(2n )4(2n )4(6p )2(5p )2(3n )0(7p )0(6p )0
g
u
u
g
g
u
u
g
u
in D symmetry and
=h
. . . (6a )2(5b )2(7a )2(2b )2(2a )2(6b )2(8a )2
1
2
1
1
2
2
1
(7b )2(9a )0(3b )0(8b )0(10a )0
2
1
1
2
1
in C symmetry. For neutral BCl , the lowest unoccupied
2v
2
9a orbital becomes singly occupied. The lowest 11 (core)
1
MOs were kept frozen, which results in a CI space involving
12 and 13 valence electrons in 63 active orbitals for the cation
and neutral molecule respectively.
Results
CIS calculations for the cation. At the linear MP2/6-31G*
geometry of the ground state of BCl `, at the
2
CIS(nstates \ 20)/6-31G* level, the Ðrst three excited singlet
states arise from a (n )3(n )1 conÐguration but have zero oscilg
u
lator strength, f. The lowest excited state with a non-zero
oscillator strength ( f \ 1.01) is the seventh excited CIS state, a
& ` state, also with a (n )3(n )1 conÐguration, and a VEE of
u
g
u
10.4 eV. Geometry optimisation in D symmetry of the latter
=h
state reduced its excitation energy from the ground state to
8.96 eV ( f \ 0.36) ; however, frequency calculations at the optimised geometry gave one imaginary frequency, which corresponded to the asymmetric stretch. Geometry optimisation in
C symmetry of this state at the CIS(nstates \ 20, root \ 7)/
=v
6-31G* level, further reduced the excitation energy to 8.45 eV,
and produced a minimum on the potential-energy surface, as
indicated by the three real frequencies [432.7 cm~1 (p), 221.8
cm~1 (n) and 1133.2 cm~1 (p)]. At the optimised geometry of
this linear asymmetric state (BCl bond lengths of 1.6505 and
1.9088 Ó), the lowest excited state is a 1% state (corresponding
to a n ] p excitation) with a VEE of 6.87 eV ( f \ 0.002).
These results make it unlikely that the dispersed Ñuorescence
spectrum of Biehl et al.21 could derive from a linear singlet
upper state, since the spectrum was seen in the energy range
3.5È4.4 eV. CIS optimisation and frequency calculations for
the Ðrst excited electronic state, employing a bent geometry,
gave a 1B state, with the computed VEEs at the
2
CIS(nstates \ 3)/6-31G* and CIS(nstates \ 20)/6-311G(2df )
level of 3.72 and 3.57 eV ( f \ 0.021 and 0.019), respectively.
These VEEs agree very well with the observed Ñuorescence
band maximum of 3.76 eV, suggesting that this 1B state is a
2
very likely candidate for the upper state of the Ñuorescence
process. Its computed minimum-energy geometries and vibrational frequencies at di†erent levels of theory are summarized
in Table 5.
MRDCI calculations for the cation. The results of the
MRDCI survey for the linear BCl ` states are shown in Table
2
6 and Fig. 1. For the bent geometry (Table 7 and Fig. 1) the
energy of the ground state is located at ca. 3.5 eV higher in
energy than the ground state of the linear cation, in qualitative agreement with the non-MRDCI calculations. An
approximate state diagram based on these survey calculations
is given in Fig. 1.
With the relatively smaller reference set, the &c 2 value for
i
the ground state is ca. 0.91 and for the excited states it is in
the range 0.77È0.85. As noted above, this a†ects the reliability
of the computed relative energies and they should be considered qualitative. The results of the calculations with the
extended reference set are shown in Tables 8 and 9, for the
linear and bent states of BCl `, respectively.
2
The computed AEEs and VEEs for the 1B state are sum2
marized in Table 10. Note that the UHF-based calculations
have considerable spin contamination (SS2T B 1, rather than
0 ; see Table 5) and so these results should be viewed with
caution. However, some deductions can be made (also the
MRDCI calculations for this state suggests that single reference methods are adequate). First, although the VEE appears
to be in excellent agreement with the experimental spectrum
for the CIS calculations, all the correlated calculations are in
Table 5 Calculated geometries and vibrational frequencies for the BCl ` (A3 1B ) state
2
2
method
[energy(]943)/E
UHF/6-31G*
SS2T \ 1.027
CIS/6-31G*
SS2T \ N/A
CIS/6-311G(2d)
SS2T \ N/A
MP2/6-31G*
SS2T \ 1.027
MP2/6-311G(2d)
SS2T \ 1.031
MP4(SDQ)/cc-pVDZ
SS2T \ 1.029
CCSD(T)/6-311G(2d)
SS2T \ 1.034
r/Ó
A/degrees
l
1
l
0.239 680
1.7534
100.0
842.0
272.5
488.8a
0.156 945
1.7316
108.1
793.9
239.2
685.5
0.225 912
1.7263
106.2
798.1
236.7
685.5
0.548 997
1.7409
101.7
834.9
264.4
170.2a
0.658 368
1.7524
99.1
803.8
259.2
240.2a
0.637 899
1.7627
102.1
809.5
249.8
498.2ia
0.708 271
1.7606
101.1
770.5
240.1
629.1
h
l
2
3
a These values may possibly be a†ected by symmetry breaking.
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
57
Table 6 MRDCI survey of states at linear BCl ` geometry (D )
2
=h
statea
relative energy/eVb
&c 2
i
main excitationc
X 1& ` (1A )
g
g
1* (1A )
u u
1* (1B )
u 1u
1& ~(1A )
u
u
1* (1A )
g g
1* (1B )
g 1g
1& `(1B )
u
1u
1& ~(1B )
g
1g
1& `(1A )
g
g
1% (1B )
g 2g
0.00
7.05
7.05
7.08
8.51
8.65
8.66
8.76
10.26
10.41
0.91
0.83
0.83
0.83
0.82
0.83
0.82
0.82
0.81
0.83
1% (1B )
g 2g
10.63
0.83
1% (1B )
2u )
1& u`(1B
u
1u
1% (1B )
u 2u
12.45
12.46
12.65
0.84
0.77
0.81
reference (0.89)
2n ] 3n (0.82)
g
u
2n ] 3n (0.80)
g
u
2n ] 3n (0.81)
g
u
2n ] 3n (0.82)
u
u
2n ] 3n (0.82)
u
u
2n ] 3n (0.70)
g
u
2n ] 3n (0.82)
u
u
2n ] 3n (0.70)
u
u
5p ] 3n (0.46)
2nu ] 7p u (0.34)
g
g
5p ] 3n (0.34)
u
u
2n ] 7p (0.45)
g
g
6p ] 3n (0.78)
5pg ] 7pu (0.68)
g
g
2n ] 7p (0.76)
u
g
a Symmetry species in the D subgroup is given in parentheses. Note
2h
that the two components of the degenerate * states were obtained in
two separate symmetries under D . b Relative energies are based on
2h
estimated full CI energies (see text) relative to the ground state at
E \ [943.835 643 E . c The c2 contribution of the main excitation
full
h
i
to the multireference wavefunction are given in parentheses.
poor agreement, except for the MRDCI calculations without
extrapolation to zero threshold and the Davidson correction.
There is thus no deÐnitive agreement with the experimental
value ; however, it should be borne in mind that these VEEs
have assumed that the upper state was populated at the (000)
vibrational level (at the equilibrium geometry). Perhaps the
experimental VEE value may be a†ected by, for example,
vibrational excitation of the upper electronic state, leading to
a dramatically changed FranckÈCondon envelope. The calculated AEE values, on the other hand, are in rather good agreement for most of the methods used. In the case of the MRDCI
Table 7 MRDCI survey of states of BCl ` at the bent (C )
2
2v
geometry of the 1B state
2
state
relative energy/eVa
&c 2
i
main excitationb
1A
1B 1
1A2
1A2
1B 2
1A1
1
0.00
1.20
1.95
4.15
4.24
4.77
0.91
0.80
0.80
0.81
0.81
0.80
1B
2
5.03
0.81
1B
2
5.97
0.78
1B
1
7.14
0.80
1A
7.20
0.79
reference (0.88)
6b ] 9a (0.70)
2a 2 ] 9a 1 (0.70)
6b2 ] 3b1 (0.76)
2a 2 ] 9a 1 (0.72)
7a2 ] 9a1 (0.53)
8a1 ] 9a1 (0.13)
7b1 ] 9a1 (0.43)
2a 2 ] 3b1 (0.30)
2a2 ] 3b1 (0.41)
7b2 ] 9a1 (0.23)
7a 2 ] 3b1 (0.49)
8a1 ] 3b1 (0.29)
2b1 ] 3b1 (0.57)
1
1
1
a Relative energies are based on estimated full CI energies (see text)
relative to the ground state at E \ [943.708 419 E . b The c2 confullto the multireference
h wavefunction
i
tributions of the main excitation
are given in parentheses.
Fig. 1 Energy level diagram indicating the relative positions of the
electronic states of BCl ` in linear and non-linear geometries
2
calculations, the agreement is getting better with the extra corrections (in contrast to the VEE). Overall, on energetic
grounds, the calculated AEEs give qualitative support for the
assignment of the dispersed Ñuorescence observed by Biehl et
al.21 to the BCl ` A3 1B ] X 1& `(1A ) transition. With
2
2
g
1
regard to the vibrational frequencies, as was noted above, the
observed vibrational structure can possibly be assigned to a
progression of 2l in the ground state ; however, if the upper
2
state is bent, as seems to be the case, then the non-observation
of odd quanta is rather peculiar, especially if the upper state is
vibrationally excited. The calculated results shown in Table 5
also suggest that a progression of 2l in the upper state is
2
consistent with the observed vibrational spacings but, again,
non-observation of odd quanta is difficult to explain. The
computed values of the l asymmetric stretch [at the CIS and
3
CCSD(T) levels] in the A3 1B state appear to be consistent
2
with the observed vibrational structure, and it is at least
plausible that this vibration could be excited in some dissociative pathways, following electronic excitation upon irradiation. (The fact that the other methods give rise to vastly
Table 8 MRDCI calculation of BCl ` at the D geometry using the extended reference seta
2
=h
root
1A
1 g
1A
1 u
2
1B
1 1u
E
MRDCI
[943.795 981
[943.483 115
[943.482 505
[943.484 183
E
T/0
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
full
71 reference conÐgurations, 11 355 selected CSFs
[943.812 783
[943.834 040 (0.00)
40 reference conÐgurations, 12 235 selected CSFs
[943.530 211
[943.564 865 (7.32)
[943.529 188
[943.564 203 (7.34)
64 reference conÐgurations, 15 117 selected CSFs
[943.531 007
[943.566 003 (7.29)
a Energies (eV) relative to the ground state are given in parentheses for the E results.
full
58
E
&c2
i
0.9214
0.8982
0.8974
0.8974
Table 9 MRDCI calculation of BCl ` at the 1B C geometry using the extended reference seta
2
2 2v
E
MRDCI
root
1A
1
1
1A
2
1
2
1B
1
1
1B
2
1
E
E
T/0
108 reference conÐgurations, 15 242 selected CSFs
[943.685 824
[943.706 986 (0.00)
89 reference conÐgurations, 17 464 selected CSFs
[943.574 675
[943.614 985 (2.50)
[943.500 867
[943.539 247 (4.56)
90 reference conÐgurations, 20 450 selected CSFs
[943.508 318
[943.549 480 (4.29)
105 reference conÐgurations, 16 606 selected CSFs
[943.602 975
[943.643 767 (1.72)
[943.663 038
[943.518 709
[943.444 943
[943.454 504
[943.543 117
a Energies (eV) relative to the ground state are given in parentheses for the E
di†erent values of the l frequency, casts some doubt on the
3
reliability of these particular calculated values ; symmetry
breaking may well be a†ecting these calculations.)
Excited state calculations for neutral BCl . Although,
2
similar MRDCI calculations to those on the cation were performed on the neutral states of BCl , only the more reliable
2
results with the large reference set are shown in Table 11.
CIS(nstates \ 20)/6-311 ] G(2df ) calculations carried out at
the CCSD(T)/6-311G(2d) optimised geometry of X3 2A BCl
1
2
give results in generally good agreement with the MRDCI
results. The 1 2B and 2 2A states are 2.75 and 6.93 eV above
1
1
the X3 2A state, respectively, while the corresponding MRDCI
1
values are 2.65 and 7.37 eV. CIS geometry optimisation calculations for the Ðrst excited state, carried out in D symmetry,
=h
gave a 2& ` state (which corresponds to the X3 2A state in C
g
1
2v
symmetry) with a VEE of ca. 2.0 eV above the lowest 2%
u
state (1 2B , 2 2A in C symmetry). The optimised BCl bond
1
1
2v
length for the 2% state is ca. 1.70 Ó at the CIS level. MP2/6u
31G* calculations conÐrmed the change of the state ordering
of these two lowest states from a linear to bent strucTable 10 Calculated AEE and VEE
1B ÈX3 (1& `)1A Ñuorescence transition
2
g
1
full
(eV)
of
the
BCl `
2
method
AEE
VEE
CIS/6-31G*
CIS/6-311G(2df)
MP2/6-31G*
MP2/6-311G(2d)
MP4(SDQ)/cc-pVDZ
CCSD(T)/6-311G(2d)
E
b
EMRDCIb
ET/0b
full
experimental21
È
È
4.83 (4.43)a
5.31 (4.34)a
4.62
4.61
6.88
5.71
5.18
4.28
3.72
3.57
1.51 (1.10)a
1.23 (0.76)a
1.54
1.34
3.26
2.25
1.72
3.76
a Values in parentheses are from spin-projected energies ; all other
energies are unprojected values. b Calculated using the extended reference set, at the respective CCSD(T)/6-311G(2d) optimised geometry.
full
&c 2
i
0.9213
0.8890
0.8909
0.8869
0.8888
results.
ture. The MP2/6-31G* VEE for the 1 2B ^ X3 2A transition
1
1
was calculated to be 2.50 eV, in excellent agreement with the
corresponding MRDCI and CIS values.
Attempts to assign the various observed emission/
Ñuorescence spectra of the neutral molecule are fraught with
uncertainty ; however, some comments will be made. First, as
noted above, the assignment18 of the chemiluminescence spectrum (in the energy range 3.4È4.2 eV) of Dessaux et al.31 in
terms of a l frequency of 470 cm~1 seems uncertain, con1
sidering the JANAF estimated value19 of 720 cm~1, the
matrix isolation value of 731 cm~1 and the values calculated
here (Table 1). Similar bands in this energy region (3.4È5.2 eV)
have been seen by Suto et al.34 (labelled bands B and C
therein), Lee et al.35, Creasey et al.27 and Biehl et al.21 in their
synchrotron experiments. Additionally, the same bands
appear to have been seen in electron impact studies by Tokue
et al.37 and in the plasma emission studies of Breitbarth and
Ducke36 (labelled bands X and Y in the latter work). This
feature has been tentatively assigned by Creasey et al.27 to the
B3 2A state, with perhaps contributions from the (unassigned)
1
C3 state. A broader, lower energy emission is also observed in
all the above experiments (labelled band A in the synchrotron
studies, unlabelled in the electron impact studies, and labelled
band Z in the plasma emission study) ; this band is assigned
(again tentatively) to the A3 2B state by Creasey et al.27 The
1
results of the MRDCI and CIS scans show that there is indeed
a 2B state at a VEE energy (from the ground state) of 2.65 eV
1
(Table 11) (this is the energy separation at the ground-state
optimised geometry), which is the most accurate value here.
This is entirely consistent with the experimental observations
for band A (1.9È3.1 eV). The higher energy band, which is
assigned to the A3 2A state by Creasey et al.,27 is at an energy
1
of between 2.5 and 5.4 eV ; however, the calculated VEE (from
the ground state) is 7.37 eV for the Ðrst excited 2A state
1
(Table 11), and so this is only a plausible assignment for that
band. More possible is an assignment to the Ðrst excited 2B
2
state, which has a calculated VEE of 6.4 eV ; the AEE will be
to lower energy, giving rise to a band similar to that observed.
It appears that the B3 and C3 states are the Ðrst excited 2A and
1
Table 11 MRDCI calculation of BCl at the C geometry of the X3 2A state using the extended reference seta
2
2v
1
root
2A
1 1
2
2A
1 2
2
2B
1 1
2B
1 2
E
MRDCI
[944.038 654
[943.731 749
[943.761 941
[943.723 522
[943.911 202
[943.772 653c
E
T/0
E
full
98 reference conÐgurations, 18 459 selected CSFsb
[944.066 512
[944.095 471 (0.00)
[943.780 235
[943.824 571 (7.37)
64 reference conÐgurations, 17 871 selected CSFs
[943.813 792
[943.850 690 (6.66)
[943.806 941
[943.849 865 (6.68)
72 reference conÐgurations, 18 946 selected CSFs
[943.963 908
[943.998 222 (2.65)
74 reference conÐgurations, 17 984 selected CSFsc
[943.818643c
[943.861 971c (6.35c)
&c2
i
0.9075
0.8780
0.8936
0.8839
0.8993
0.8795c
a Energies (eV) relative to the ground state are given in parentheses for the E results. b The reference set for the 2A states is just the full doubly
fullas these states did not require further1 non-valence conÐgurations.
excited valence conÐgurational space. No further conÐgurations were added,
c The MRDCI calculation on the 2B state using a fully doubly excited valence reference set failed. The energies quoted here are taken from the
2
survey calculations using a small reference
set.
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
59
2B states, but the ordering of these is unclear ; the MRDCI
2
calculations suggest the A3 state is the 2B state, in disagree2
ment with the CIS results. Note that the two low-lying 2A
2
states are also in this energy region, but that transitions to the
ground state from these states should not be allowed under
dipole selection rules ; however, if there are any coupling
mechanisms, such as vibronic coupling, then these states may
become allowed, and indeed may be contributing to this
region. Clearly, only qualitative conclusions can be drawn
from the calculations as they stand at the moment.
2
3
4
5
6
Conclusions
The geometry and vibrational frequencies of the ground electronic neutral and cationic states of boron dichloride have
been calculated. Both ab initio and density functional theory
approaches were used, and gave similar results at the highest
levels used. The calculated parameters were in very good
agreement with experiment, where such values are available.
An attempt was then made to assign the dispersed Ñuorescence spectrum obtained by Biehl et al.,21 attributed to the
cation. CIS and MRDCI calculations were performed on the
cation, in order to ascertain the energy positions of such
states. These calculations appeared to exclude any linear
singlet cationic states in the energy region of interest. Calculations under C symmetry, however, showed that the Ðrst
2v
excited, bent 1B state was probably the most likely candidate
2
for the source of the emission. The assignment of the vibrational structure seen in the dispersed Ñuorescence is not
straightforward. In order to clarify the assignment, sophisticated FranckÈCondon factor calculations would have to be
performed.
Finally, a scan of the excited states of the neutral molecule
was performed using MRDCI calculations, and some CIS calculations were also carried out ; the two sets of calculations
were in very good agreement. Some preliminary assignments
of Ñuorescent transitions seen in a variety of di†erent experiments were made on the basis of these results.
7
8
9
10
11
12
13
14
15
Note added
After this work was submitted, a paper appeared by Jacox et
al., who studied the results of the interaction of excited neon
atoms with BCl .44 Species observed in the matrix were,
3
amongst others, BCl and BCl `. The former had measured
2
2
l values which were in excellent agreement with those of
3
Andrews and co-workers.16,20 An IR absorption of ca. 1436
cm~1 was attributed to the l mode of BCl `. This assign3
2
ment was aided by ab initio calculation of the harmonic frequencies of this molecule. Calculations were performed at
various levels, with the highest being CCSD(T)/6-311G(2df ).
These calculations give very similar values to those reported
in Table 1. The calculated geometry of ref. 44 is also in good
agreement with the calculated values presented in Table 1.
We gratefully acknowledge the EPSRC for provision of computer time at ULCC. Dr. Julie Altmann (ULCC) is thanked
for valuable advice during this work. T.G.W. thanks the
LloydÏs Tercentenary Foundation for the award of a two-year
fellowship. E.P.F.L. thanks the Hong Kong Polytechnic University for support.
16
17
18
19
20
21
22
23
24
25
26
27
28
References
1
60
S. Matsumoto, N. Nishida, K. Akashi and K. Sugai, J. Mater.
Sci., 1996, 31, 713 ; A. Salok, O. O. Awadelkarim, F. Preuniger
and Y. D. Chan, Appl. Phys. L ett., 1996, 68, 1690 ; M. W. Cole,
W. Y. Han, R. L. Pfe†er, D. W. Eckhart, F. Ren, W-S. Hobson, J.
R. Lothian, J. Lopata, J. A. Caballers and S. J. Pearton, J. Appl.
Phys., 1996, 79, 3286 ; C. Chou, K. Saravanan, J. Kava and M.
Siegel, J. V ac. Sci. T echnol. B, 1996, 14, 474 ; G. Franz, C. Hoyler
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
29
30
31
32
33
and J. Kaindel, J. V ac. Sci. T echnol. B, 1996, 14, 126 ; I. W.
Rangelow, F. Shi, P. Hudek, I. Kostic, E. Hammel, H. Loschner,
G. Stengl and E. Cekan, Microelectron. Eng., 1996, 30, 257.
G. R. Scheller, R. A. Gottscho, T. Intrator and D. B. Graves, J.
Appl. Phys., 1988, 64, 4384.
R. Gottscho, Phys. Rev. A, 1987, 36, 2233 ; C. E. Gaebe, T. R.
Hayes and R. A. Gottscho, Phys. Rev. A, 1987, 35, 2993.
B. L. Preppernau and T. A. Miller, in Glow Discharge Spectroscopies, ed. R. K. Marcus, Plenum Press, New York, 1993.
C. MÔller and M. S. Plesset, Phys. Rev. A, 1934, 46, 618.
J. S. Andrews, D. Jayatilaka, R. G. A. Bone, N. C. Handy and R.
D. Amos, Chem. Phys. L ett., 1991, 183, 423 ; R. D. Amos, J. S.
Andrews, N. C. Handy and P. J. Knowles, Chem. Phys. L ett.,
1991, 185, 256 ; P. J. Knowles, J. S. Andrews, R. D. Amos, N. C.
Handy and J. A. Pople, Chem. Phys. L ett., 1991, 186, 130 ; D. J.
Tozer, N. C. Handy, R. D. Amos, J. A. Pople, R. H. Nobes, Y. Xie
and H. F. Schaefer, Mol. Phys., 1993, 79, 777.
J. Cizek, Adv. Chem. Phys., 1969, 14, 35 ; G. D. Purvis and R. J.
Bartlett, J. Chem. Phys., 1982, 76, 1910 ; G. E. Scuseria, C. L.
Janssen and H. F. Schaefer III, J. Chem. Phys., 1988, 89, 7382 ; G.
E. Scuseria, J. Chem. Phys., 1989, 90, 3700.
A. D. Becke, Phys. Rev. A, 1988, 38, 3098.
C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785.
A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
D. E. Woon and T. H. Dunning Jr., J. Chem. Phys., 1993, 98,
1358 ; T. H. Dunning Jr., J. Chem. Phys., 1989, 90, 1007.
GAUSSIAN 94 (Revision C.3), M. J. Frisch, G. W. Trucks, H. B.
Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheesemans, T. W. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B.
Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M.
Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J.
L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox,
J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. HeadGordon, C. Gonzalez and J. A. Pople, Gaussian Inc., Pittsburgh
PA, 1995.
CADPAC : The Cambridge Analytic Derivatives Package, Issues
5.0 and 5.2, Cambridge, 1992. A suite of programs developed by
R. D. Amos with contributions from : I. L. Alberts, J. S. Andrews,
S. M. Colwell, N. C. Handy, D. Jayatilaka, P. J. Knowles, R.
Kobayashi, N. Koga, K. E. Laidig, P. E. Maslen, C. W. Murray,
J. E. Rice, J. Sanz, E. D. Simandiras, A. J. Stone and M-D. Su.
A. D. Walsh, J. Chem. Soc., 1953, 2266.
J. M. Dyke and T. G. Wright, Chem. Phys. L ett., 1990, 169, 138 ;
C. I. Frum, R. Englemann Jr. and P. F. Bernath, J. Chem. Phys.,
1991, 95, 1435 ; Yu. A. Buslaev and Klyagina, Coord. Chem Rev.,
1993, 126, 149 ; J. M. Dyke, D. Haggerston, M. P. Hastings and
T. G. Wright, Chem. Phys., 1994, 81, 355 ; D. M. Hassett and C. J.
Marsden, J. Mol. Struct., 1995, 346, 249 ; N. Vogt, G. V. Girichev,
J. Vogt and A. G. Girichev, J. Mol. Struct., 1995, 352/353, 175.
J. H. Miller and L. Andrews, J. Am. Chem. Soc., 1980, 102, 4900.
R. Franzi, M. Geo†rey, E. A. C. Lucken and N. Leray, J. Chem.
Phys., 1983, 78, 708.
O. Dessaux, P. Goudmand and G. Pannetier, Bull. Soc. Chim. Fr.,
1969, 447.
JANAF T hermochemical T ables, ed. D. R. Stull and H. Prophet,
National Bureau of Standards, US (NSRDS-NBS 37), 2nd edn.,
1971.
P. Hassanzadeh and L. Andrews, J. Phys. Chem., 1993, 97, 4910.
H. Biehl, J. C. Creasey, D. M. Smith, R. P. Tuckett, K. R. Yoxall,
H. Baumgartel, H. W. Jochims and U. Rockland, J. Chem. Soc.,
Faraday T rans., 1993, 91, 3073.
J. M. L. Martin, J. El-Yazal and J. P. FrancÓois, Mol. Phys., 1995,
86, 1437.
O. Osberghaus, Z. Phys., 1950, 128, 366.
J. Marriot and J. D. Craggs, J. Electron. Control, 1957, 3, 194.
W. S. Koski, J. J. Kaufman and C. F. Puchucki, J. Am. Chem.
Soc., 1959, 81, 1326.
V. H. Dibeler and J. A. Walker, Inorg. Chem., 1969, 8, 50.
J. C. Creasey, P. A. Hatherley, I. R. Lambert and R. P. Tuckett,
Mol. Phys., 1993, 79, 413.
L. A. Curtiss, K. Raghavachari, G. W. Trucks and J. A. Pople, J.
Chem. Phys., 1993, 98, 1293.
H. B. Schlegel and S. J. Harris, J. Phys. Chem., 1994, 98, 11178.
J. R. Bews and C. Glidewell, J. Mol. Struct. (T HEOCHEM), 1982,
89, 333.
O. Dessaux, P. Goumand and G. Pannetier, C. R. Acad. Sci.
Paris (Se r. C), 1965, 265, 480.
A. G. Massey and J. J. Zwolenik, J. Chem. Soc., 1963, 5354.
R. T. Holzmann and W. F. Morris, J. Chem. Phys., 1958, 29, 677 ;
A. G. Briggs, M. S. Reason and A. G. Massey, J. Inorg. Nucl.
Chem., 1975, 37, 313.
34
35
36
37
38
39
40
M. Suto, C. Ye, J. C. Han and L. C. Lee, J. Chem. Phys., 1988, 89,
6653.
L. C. Lee, J. C. Han and M. Suto, J. Chem. Phys., 1989, 91, 2036.
F.-W. Breitbarth and E. Ducke, Contrib. Plasma Phys., 1990, 30,
691.
I. Tokue, M. Kudo, M. Kasakabe, T. Honda and Y. Ito, J. Chem.
Phys., 1992, 96, 8889.
J. B. Foresman, M. Head-Gordon and J. A. Pople, J. Phys.
Chem., 1992, 96, 135.
R. J. Buenker and S. D. Peyerimho†, T heor. Chim. Acta, 1974, 35,
33 ; 1975, 39, 217 ; R. J. Buenker and S. D. Peyerimho†, Mol.
Phys., 1978, 35, 771.
M. F. Guest and J. Kendrick, GAMESS User Manual, SERC
Daresbury Laboratory, CCP1/86/1.
41
The single-reference correction is described in : E. R. Davidson in
T he W orld of Quantum Chemistry, ed. R. Daudel and B. Pullman,
Reidel, Dordrecht, 1974, p. 17. The multireference extension is in :
G. Hirsch, P. J. Bruma, S. D. Peyerimho† and R. J. Buenker,
Chem. Phys. L ett., 1977, 52, 442.
42 J. Olsen, P. JÔrgensen, H. Koch, A. Balkova and R. J. Bartlett, J.
Chem. Phys., 1996, 104, 8007.
43 E. P. F. Lee, D. C. Wang and F. T. Chau, J. Phys. Chem., in the
press.
44 M. E. Jacox, K. K. Irikura and W. E. Thompson, J. Chem. Phys.,
1996, 104, 8871.
Paper 6/03342C ; Received 13th May, 1996
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
61