Spectroscopy and MRCI calculations on CrF and CrCl

Article abstract of DOI:10.1063/1.1367395

A study of the spectroscopic and MRCI calculations on CrF and CrCl was performed. The thermal emission with FTS techniques were used to record the band system of the CrCl radical. The data from the MRCI calculations were used to analyze the dispersed fluo

Full text of DOI:10.1063/1.1367395

Spectroscopy and MRCI calculations on CrF and CrCl
R. Koivisto, O. Launila, B. Schimmelpfennig, B. Simard, and U. Wahlgren
Citation: The Journal of Chemical Physics 114, 8855 (2001); doi: 10.1063/1.1367395
View online: http://dx.doi.org/10.1063/1.1367395
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 114, NUMBER 20
22 MAY 2001
Spectroscopy and MRCI calculations on CrF and CrCl
R. Koivisto
Department of Physics, Stockholm University, Box 6730, S-11385, Stockholm, Sweden
O. Launila
FOA 2, Defence Research Establishment, Department of Energetic Materials, S-14725 Tumba, Sweden
B. Schimmelpfennig
Department of Physics, Stockholm University, Box 6730, S-11385, Stockholm, Sweden
B. Simarda)
Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Drive, Ottawa,
Ontario, K1A 0R6, Canada
U. Wahlgren
Department of Physics, Stockholm University, Box 6730, S-11385, Stockholm, Sweden
͑Received 12 January 2001; accepted 5 March 2001͒
The B 6⌸–X 6⌺ϩ band system of the CrCl radical has been recorded in thermal emission with FTS
techniques in the region 6900–11 700 cmϪ1, using a resolution of 0.025 cmϪ1. An analysis of the
͑0,0͒ band of this system has been carried out. A rotational constant of B0ϭ0.1615 cmϪ1 and a
spin–orbit parameter of A0ϭ51 cmϪ1 have been estimated for the B 6⌸ state. Improved values for
the ␥ and ␭ parameters of the X 6⌺ϩ ground state have been obtained. MRCI calculations have been
performed on CrF and CrCl and comparisons have been made with both experiments and DFT
calculations ͓Bencheikh et al., J. Chem. Phys. 106, 6231 ͑1997͔͒. The calculations on CrF have
provided valuable aids in the interpretations of the fluorescence excitation and dispersed
fluorescence spectra of a state observed at 31 700 cmϪ1. This state has now been assigned as D 6⌸.
A number of transitions in the dispersed fluorescence spectra are believed to involve the hitherto
unknown C 6⌬ state. Spin–orbit-configuration-interaction ͑SO-CI͒ calculations have been carried
out on both CrF and CrCl. It is shown that the second-order spin–orbit parameters ␭ of the X 6⌺ϩ
e
ground states are due mainly to interactions with the B 6⌸ states. © 2001 American Institute of
Physics. ͓DOI: 10.1063/1.1367395͔
form spectrophotometer. The analysis of the A 6⌺ϩ –X 6⌺ϩ
transition has been presented earlier.4 In the present study we
are concerned with the more intense and more complicated
B 6⌸–X 6⌺ϩ system. There are also some additional bands
which are absent in the otherwise similar spectrum of CrF.
These bands are not easy to understand from the recorded
spectrum alone. Some time ago, the CrF molecule was stud-
ied by laser-induced fluorescence techniques ͑LIF͒ through
excitation of an electronic state at 31 700 cmϪ1, tentatively
I. INTRODUCTION
The large number of low-lying states, often of high mul-
tiplicity, in transition metal containing diatomic molecules
presents difficulties for both spectroscopists and theoretical
chemists. This has brought a number of improvements in the
methods of analyzing complicated spectra, such as
Loomis–Wood1-based techniques in the analyses of dense
high-temperature spectra. Different experimental techniques,
e.g., laser excitation techniques and/or molecular beams, are
also used to obtain experimental spectra that are easier to
interpret and, new sophisticated software and, faster and less
expensive computers extend the use of accurate quantum
chemical methods. Methods to treat scalar relativistic effects
have been available for a decade, and lately efficient methods
to compute spin–orbit effects have been developed.2,3 Ab
initio calculations can now be used as guidance when plan-
ning experiments or analyzing experimental results for quite
complicated spectra.4–7
6
assigned as a ⌸ state. Both dispersed and fluorescence ex-
citation experiments were performed. The dispersed fluores-
cence spectra were not rotationally resolved, but contained at
least three vibrational progressions. The strongest one con-
sists of transitions to the already known A 6⌺ϩ state, while
the other two progressions may yield information on two
hitherto unknown states. There are thus at least three primary
reasons to study the CrCl and CrF molecules by theoretical
methods. First, it is important to obtain additional informa-
tion on the not fully analyzed B 6⌸–X 6⌺ϩ transition of
CrCl. Second, it is important to find the origin of the addi-
tional bands in the spectrum of CrCl, and third, it is of inter-
est to identify the two observed but uncharacterized states
of CrF.
In the present work, we deal mainly with information
extracted from two different experiments. A thermal emis-
sion spectrum of CrCl was recorded using a Fourier trans-
a͒
Electronic mail: benoit.simard@nrc.ca
0021-9606/2001/114(20)/8855/12/$18.00
8855
© 2001 American Institute of Physics
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8856
J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Koivisto et al.
6
ϩ
FIG. 1. An overview spectrum of the B 6⌸–X
⌺ transition of CrCl. Also,
6
ϩ
FIG. 2. The F1 subband of the B 6⌸–X
⌺
transition of CrCl. As can be
6
6
ϩ
the ͑0, 0͒ band of the A
⌺
ϩ –X
⌺
transition can be clearly seen in this
6
ϩ
seen, most spin components of the X
⌺
state are connected with the F1e
view. The F6 subband of the B–X transition is severely overlapped by the
͑0,1͒ band of the A–X transition. The Loomis–Wood method is important in
these situations.
and F1f levels of the B 6⌸. These connections are often essential if the
spin-splitting parameters of the ground state are to be accurately determined.
II. EXPERIMENTAL METHODS AND ANALYSES
of the upper state were well represented with several possible
branches down to the X 6⌺ϩ ground state. Because of large
values of some interaction parameters in combination with
the severe congestion, it has not been possible to obtain a
global fit of the B 6⌸ state. The only identified levels in CrCl
are both ⌳-doubling components of F1 and F6 and the
e-parity levels belonging to the F2 spin component. A spec-
trum showing the assigned branches of the F1-subband can
be seen in Fig. 2. The identified levels of the B 6⌸ state can
be seen in the term value plot of Fig. 3, while the observed ⌳
doublings are presented in Fig. 4. A list of the identified term
values of the B 6⌸ state is shown in Appendix A. The as-
signed branches are, for clarity, listed in Table I. The relative
sizes between the ⌳ doublings of the F1 and F6 components
and the obtained spin–orbit constant are both reasonable in
comparison with CrF10 and our relativistic calculations,
A. The Fourier transform „FT… experiment
The experiment has been described elsewhere4 and only
a short description will be given here. The CrCl molecules
were produced when a mixture of chromium powder and
CrCl3 was heated to a temperature of 1500 K. The CrCl
spectra were recorded in thermal emission between 6900 and
11 500 cmϪ1 with a BOMEM DA3.002 Fourier transform
spectrophotometer with a resolution of 0.025 cmϪ1. The
pressure was kept below 100 Torr during the experiment. In
total, 960 scans were recorded in two separate regions, cor-
responding to an effective scanning time of 9 h. Appropriate
filtering was used. Light from an Fe–Ne hollow cathode
lamp was recorded together with the spectrum and neon lines
8
´
from Kaufman and Edlen were used as internal references.
The spectrum consists of the already analyzed
A 6⌺ϩ –X 6⌺ϩ transition, the B 6⌸–X 6⌺ϩ system, and a
third uncharacterized band system without a counterpart in
the otherwise similar spectrum of CrF. Overviews of the
spectra can be seen in Figs. 1 and 2.
B. Analysis of the FT spectrum of CrCl
The analysis of the B 6⌸–X 6⌺ϩ transition, and the
analysis of the A 6⌺ϩ –X 6⌺ϩ transition described in
Bencheikh et al.4 relies to a large extent on the microwave
work by Oike et al.9 First, a number of branches were picked
out using an interactive Loomis–Wood program.1 These
were then matched against combination differences of the
ground state, obtained from the microwave work.9 Data ob-
tained in Ref. 9 were important in order to overcome the
inadequacy of the spin-splitting parameters of the ground
state obtained from the analysis of the A 6⌺ϩ –X 6⌺ϩ tran-
sition. This problem is common in ⌺–⌺ transitions because
there is a correlation between upper and lower state spin
splitting constants. In a 6⌸–6⌺ϩ transition there are 108
possible branches and the spin components F1 , F2 , and F6
FIG. 3. The identified rotational levels of B 6⌸( ϭ0) of CrCl. The ⌳
doubling of the F6 component is too small to be seen in this picture.
v
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J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Spectroscopy of CrF and CrCl
8857
6
ϩ
TABLE II. Improved parameters of the X
⌺
ground state of CrCl. In the
microwave work by Oike et al., they obtained ␭0ϭ0.266 849 06 cmϪ1
,
107␭D0ϭϪ4.455 415 cmϪ1
,
and ␥0ϭ0.002 190 151 cmϪ1
.
Information
6
ϩ
from the B 6⌸–X
⌺
transition is crucial for the values of these param-
eters, obtained from the infrared data.
6
ϩ
X
⌺
Te
Ϫ197.513
⌬G1/2
396.6622͑15͒
0.266 04͑36͒
Ϫ2.80͑42͒
0.167 581 8͑23͒
0.000 971 74͑56͒
1.1798͑11͒
1.02͑41͒
␭
e
107␭
D
Be
␣
e
107De
1010␤e
␥
0.002 164 8͑62͒
2.194
e
Re ͑Å͒
rms err.
0.013
FIG. 4. The ⌳-type doublings of the F1 and F6 spin components of CrCl.
The ⌳ doubling of the F6 spin component is actually smaller than the wave
number accuracy for small J values. The rotational levels for the two parities
could still be observed. The reason is the different set of observable sub-
bands for the two parities.
number of uncharacterized branches found with the Loomis–
Wood procedure is large in comparison with the number of
missing ⌳-doubling components, which indicates the pres-
ence of hot bands. Even if a global fit of the B state has not
been possible, some estimates have been made in the follow-
ing way. First the term values of the two parities were aver-
aged for the F1 and F6 spin component separately. Thereaf-
ter T and B parameters were fitted for each one of the two
spin components according to the known formula TϭBJ(J
ϩ1). Note that the e-parity levels of the F2 spin component
have not been taken into account and that only levels with J
values р50.5 have been included. The value of the Ae pa-
rameter was estimated as (T7/2ϪTϪ3/2)/5 and the B and T
values as the averages of the B and T values of the two spin
components. The results of this procedure are presented in
Table III. The results of MRCI calculations are also pre-
sented for comparison. Reliability of the procedure has been
tested with the better known B 6⌸ state of CrF, which gave a
B value of 0.361 cmϪ1 and an A value of 46.4 cmϪ1, which
compare very well with the experimental values of Be
ϭ0.3628 cmϪ1 and Aeϭ47.04 cmϪ1 obtained in Ref. 10.
Both experimental and theoretical ͑vide infra͒ electronic en-
ergies are presented in Fig. 5 and Fig. 6 for CrF and CrCl,
respectively.
which support these assignments. There would otherwise be
additional possible assignments with the fragmentary set of
data. During the analysis an integrated graphical environ-
ment, containing Loomis–Wood and other graphical display
modules, has been used together with different numerical
programs.11
A new improved fit of the ground state was obtained
combining data from the A–X transition and the new
branches of the B 6⌸–X 6⌺ϩ transition. The results of this
new fit are presented in Table II. The calculated term values
of the X 6⌺ϩ state are shown in Appendix B. This fit has
been done using a Hamiltonian written in the case ͑a͒ basis
according to Brown et al.,12 using the following definitions
of parameters: NϭJϪS:
2
HϭTeϩ␻ ϩ1/2͒Ϫ␻ x ϩ1/2͒
͑v ͑v
e
e e
ϩ B Ϫ␣ ϩ1/2͒ N2Ϫ D ϩ␤ ϩ1/2͒ N4
͑v ͑v
͓
͔
͓
͔
e
e
e
e
ϩ1/3 ␭ ϩ␭ ϩ1/2͒ϩ␭ N2,3S ϪS2
͑v
͓
͔
ϩ
e
v
D
z
ϩ ␥ ϩ␥ ϩ1/2͒ϩ␥ N2 N•S.
͑1͒
͓
͑v
͔
e
v
D
A more complete Hamiltonian, given in Ref. 10, was used
for the orbitally degenerate states of this work. Note that the
difference between our ␭ value and the ␭ value of Ref. 8
C. The LIF experiment on the CrF radical performed
through excitation of the D 6⌸ state at 31 700
cmÀ1
D
D
exceeds our statistical uncertainty. These kinds of deviations
between microwave and near-infrared data are not unusual
and one reason is often the shorter J-number9,13 range of
microwave works. In CrF there were also a number of stron-
ger branches belonging to the ͑1,1͒ band, whose presence
also was expected in CrCl. These hot bands would then
cause even larger problems due to the larger congestion. The
The CrF molecules were formed in an ablation source,
where a rotating Cr metal rod was evaporated by the third
TABLE III. Estimated parameters for the B 6⌸ state of CrCl. The two e/f
parities of the F1 and F6 spin components were averaged and rotational
levels of the F2 spin components were disregarded. A global fit was not
possible to obtain partly because of large ⌳-doubling and SO-interaction
parameters.
6
ϩ
TABLE I. The identified branches of the B 6⌸–X
⌺
transition of CrCl.
Estimated values
Calculated values
R
N
F1e
F1f
F2e
F6e
F6f
R1 Q12 R13
Q1 R12 P12 Q13 P14
T0 ͑cmϪ1
͒
͒
͒
8870
0.162
51
8412
0.1615
51
Q
O
O
M
SR21 Q2 R23 Q24 P25
B0 ͑cmϪ1
A0 ͑cmϪ1
R0 ͑Å͒
Q
O
M
SQ64 P65 Q6
Q
TQ63 P64 Q65
2.23
2.235
R
R
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8858
J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Koivisto et al.
6
6
ϩ
FIG. 7. The fluorescence excitation spectrum of the D
⌸
X
⌺
transi-
tion at 31 700 cmϪ1. The arrows indicate the excitation wavelengths used
when recording the dispersed fluorescence spectra.
shown in Figs. 8 and 9, the dispersed spectra obtained at the
first two excitation frequencies contained mainly two vibra-
tional progressions, in which transitions down to the already
known A 6⌺ϩ state dominate. The second structure is as-
signed as D 6⌸–C 6⌬ ͑vide infra͒. In these two first spectra
there are some additional features that do not form any ap-
parent structure. In the spectrum obtained at the third exci-
tation frequency and shown in Fig. 10, there is a third struc-
ture comparable in intensity with the progression assigned as
the D 6⌸–C 6⌬ transition. Interestingly, transitions to the
already known B 6⌸ state are weak in comparison to the
D 6⌸–A 6⌺ϩ and D 6⌸–C 6⌬ transitions. Most of this
analysis is intimately linked to the ab initio calculations and
is therefore presented in Sec. III B.
FIG. 5. An experimental and calculated MRCI energy level diagram of CrF;
term values in cmϪ1
.
harmonic ͑355 nm͒ of a pulsed YAG laser. The chromium
vapor was expanded in a supersonic beam of helium contain-
ing a small mixture of SF6 as a reactive gas. The produced
CrF molecules were then excited by a frequency doubled
excimer pumped LUMONICS HD500 dye laser operated
with KR620 dye. The fluorescence excitation spectrum was
then recorded in the region 31 500–31 900 cmϪ1. The spec-
trum contained a number of subbands attributed to a
6⌸–X 6⌺ϩ transition and is presented in Fig. 7. Subse-
quently, the excitation laser was fixed to three different
wavelengths and one dispersed fluorescence spectrum was
recorded for each one of these excitation wavelengths. As
The assignment of the 31 700 cmϪ1 band as D 6⌸
X 6⌺ϩ was further verified by generating a synthetic spec-
trum of the ͑0,0͒ band of this transition using the ground
state parameters ͑with Teϭ0) from Ref. 10, and the follow-
ing upper state parameters ͑cmϪ1͒: Teϭ31 695, ␻eϭ695 ͑ab
initio, Table XI͒, A0ϭ31.3, Beϭ0.3855 ͑ab initio, Table
FIG. 8. Excitation at 31 638 cmϪ1. The intensities of the D 6⌸–A
⌺
6
ϩ
bands agree well with the calculated Franck–Condon factors. The situation
is slightly different for the D 6⌸–C 6⌬ transition, where the agreement is
less prominent.
FIG. 6. An experimental and calculated MRCI energy level diagram of
CrCl; term values in cmϪ1
.
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J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Spectroscopy of CrF and CrCl
8859
rine were taken from Wachters15 and the contraction coeffi-
cients were obtained from atomic SCF calculations using the
Raffenetti16 scheme.
The molecular orbitals used in the MRCI calculations
were obtained from restrictive–active-space-self-consistent-
field ͑RASSCF͒ calculations for each state. Exceptions were
6
the two low-lying ⌺ϩ states for which we used a common
set of orbitals for both CrF and CrCl, obtained from an av-
erage RASSCF calculation with equal weights for the A and
X states. These averaged orbitals, in fact, gave rise to a lower
MRCI energy for the ground state than the ground state or-
bitals, and more accurate transition energies. A smaller basis
set was used for chlorine than for fluorine (10s6p4d3f con-
tracted to 5s4p3d2 f on fluorine and 17s12p2d contracted
to 5s5p2d on chlorine͒, and this fact should be kept in mind
when the theoretical results for CrCl and CrF are compared.
The calculated potential energy curves were used as in-
put to the VIBROT module of the MOLCAS package. The VI-
BROT program fits a polynomial to a number of points of the
FIG. 9. The dispersed fluorescence spectrum obtained through excitation at
31 662 cmϪ1 is similar to that shown in Fig. 8. The main difference is the
number and positions of the uncharacterized features marked by arrows.
6
ϩ
These additional features cannot be attributed to either the D 6⌸–A
⌺
or
6⌸–C 6⌬ transitions. These uncharacterized features are believed to ap-
pear because of mixing between the sextets and low-lying quartets. Accord-
D
4
ϩ
ing to the ab initio calculations the a
⌺
and b 4⌸ states may be of interest
here.
¨
potential curve and solves the vibrational Schrodinger equa-
tion. The calculated values of both vibrational frequencies
and bonding distances compare well with experiments. The
spin-free results are presented in Tables IV and V and com-
pared with previous DFT4 results and experiments.4,10,17,18
The computed anharmonicity and distortion parameters are
satisfactory considering the size of the calculations. Some of
these results are presented in Table VI.
XI͒, and ␣ϭ0.002. The agreement with the observed spec-
trum was qualitatively good. However, a full rotational
analysis of this system was not possible, since the resolution
of the fluorescence excitation spectrum was not good
enough. As is evident from Fig. 7, the subbands of the
D 6⌸ X 6⌺ϩ system are not equidistant. Attempts were
therefore made to include higher-order diagonal spin–orbit
parameters ͑␭, ␩, ␪͒, to the description of the D 6⌸ state, but
the results were not conclusive.
Bond distances obtained by Bencheikh et al.4 using DFT
deviate up to 5% for the quartets but less than 1% for the
sextets from our results, and the differences in computed
vibrational frequencies are also larger for the quartets. It
should be emphasized that since both CrCl and CrF have five
open shells, the quartets must be described by several deter-
minants. Since DFT is a one determinant method, the values
obtained for the quartets are inaccurate. A proper description
III. THEORETICAL CALCULATIONS
A. Technical details and the spin-free calculations
of the low-lying states
The calculations were done using the commercially
available MOLCAS package.14 For Cr and F we used the
ANO-S basis sets by Pierloot et al. provided with the MOL-
CAS package, extended with the chromium f- and g-orbital
basis from the ANO-L basis. The primitive basis set for chlo-
TABLE IV. The MRCI results of CrF compared with experiment ͑Refs. 10,
17, and 18͒ results of Bencheikh et al. ͑Ref. 4͒. The estimated DFT results
of the quartets are satisfactory.
Expt.
DFT
MRCI
6
6
6
6
ϩ
X
B
A
C
a
⌺
Te
Re
͑cmϪ1
͑Å͒
͒
0
0
0
1.784
664
8134
1.828
629
9953
1.892
581
1.788
720
10 136
1.818
699
1.785
677
7689
1.836
635
9973
1.915
579
11 854
1.890
615
9748
1.788
631
11 903
1.823
637
16 693
1.813
608
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
⌸
Te
Re
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
ϩ
⌺
⌬
Te
Re
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
Te
Re
16 635
1.875
662
8160
1.761
755
11 957
1.744
782
17 187
1.781
723
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
4
4
4
ϩ
⌺
⌸
⌬
Te
Re
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
b
Te
Re
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
FIG. 10. When the excitation frequency was moved to 31 788 cmϪ1, the
c
Te
Re
intensities of the D–C bands became much weaker compared to those of the
6
ϩ
͑cmϪ1
͒
D
6⌸–A
⌺
transition. The uncharacterized transitions appeared as a com-
␻
e
plete progression at this excitation wavelength.
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8860
J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Koivisto et al.
TABLE V. The MRCI results of CrF compared with experiment and DFT
results of Bencheikh et al. ͑Ref. 4͒. The estimated DFT results of the quar-
tets are satisfactory for both bonding distances and vibrational frequencies,
but deviate slightly from the MRCI values for the transition energies.
TABLE VII. Compositions of the molecular orbitals for CrF. These are the
orbitals optimized for the B 6⌸ state, the weights given for the different
configurations in Table X have been obtained using these orbitals. The ͑5␲͒
orbital has a larger contribution from (Cr 3dϩ1) than (Cr 4pϩ1), but
(Cr 4pϩ1) will form a larger overlap with the (F 3pϩ1). See Fig. 11.
Expt.
DFT
MRCI
Comments
6
6
6
6
ϩ
X
B
A
C
a
⌺
Te
Re
͑cmϪ1
͑Å͒
͒
0
0
0
2.194
397
8870
2.206
390
9998
2.272
356
2.203
398
8412
2.235
396
9190
2.286
389
10 128
2.275
380
12 356
2.204
431
12 724
2.171
401
13 914
2.196
391
1␦ 1.00(Cr 3d2ϩ
4␲ 0.98(Cr 3dϩ1)Ϫ0.17(F 2pϩ1
)
Nonbonding
Nonbonding
Nonbonding
Back-polarized
Nonbonding
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
)
e
⌸
Te
Re
9␴ 0.95(Cr 4s)Ϫ0.25(Cr 4p0)Ϫ0.18(Cr 3d0)
10␴ 0.96(Cr 3d0)ϩ0.19(Cr 4s)Ϫ0.18(Cr 4p0)
5␲ 0.70(Cr 3dϩ1)Ϫ0.47(Cr 4pϩ1)Ϫ0.54(F 3pϩ1
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
ϩ
⌺
⌬
Te
Re
9469
2.270
379
Forward-polarized
)
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
Te
Re
15 309
2.293
379
9269
2.284
425
11 879
2.100
400
16 056
2.109
410
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
energy curves CrCl were well described by a Morse poten-
tial, but this was not the case for CrF. The higher electrone-
gativity and shorter bond distance in CrF are believed to be
the reasons for this difference. The orbitals are ionic in na-
ture for both CrCl and CrF, as can be seen in Tables VII,
VIII, and Fig. 11. The corresponding configurations are pre-
sented in Tables IX and X.
4
4
4
ϩ
⌺
⌸
⌬
Te
Re
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
b
Te
Re
␻
͑cmϪ1
͑cmϪ1
͑Å͒
͒
͒
e
c
Te
Re
␻
͑cmϪ1
͒
e
6
B. Spin-free calculations on CrF concerning the ⌸
state at 31 700 cmÀ1
6
Calculations have been performed on a high-lying ⌸
must take into account all of the determinantal wave func-
tions and their interactions. The DFT values listed here for
the quartets are estimates obtained using methods derived by
Raftery et al.7 and more recently by Daul.19 The potential
state of CrF at 31 700 cmϪ1. Our aim was to study a number
of features in dispersed and fluorescence excitation spectra
͑vide supra͒.
6
In order to calculate the transition energies to the ⌸
states in CrF, we used the following procedure. The two
lowest-lying 6⌸ states of CrF were calculated simulta-
neously in a common basis set. The calculated energy differ-
ence between the two 6⌸ states, 23 863 cmϪ1, was then
TABLE VI. Anharmonicity and distortion parameters for some states of CrF
and CrCl. There are no comparisons for the B 6⌸ state of CrCl because of
6
ϩ
the absence of a complete rotational fit. The A
⌺
states of both CrF and
CrCl are too perturbed for comparisons to be meaningful.
6
added to the total energy of the lower ⌸ state, shown in
Table IV. This procedure gave an excitation energy of
MRCI
Expt.
MRCI/Expt.
31 900 cmϪ1, relative the ground state, for the upper
⌸
6
6
ϩ
CrF X
⌺
state. The bond distance of the lower 6⌸ state, obtained with
the common orbital basis, is about 1% too long compared to
experiment ͑see Table IV͒. From this result we deduced a
correction factor of Ϫ1%, which we considered valid for
both 6⌸ states. The calculated vibrational frequencies for the
two states are shown in Table XI.
␻
676.8
5.33
0.3803
0.002 85
4.87
664.1058
4.220 96
0.380 812 8
0.003 096 11
5.0481
1.02
1.26
0.999
1.09
0.965
1.0006
e
␻exe
Be
␣
e
107De
Re ͑Å͒
1.7850
1.7839
6
B
⌸
Calculated Franck–Condon factors for the D 6⌸–A 6⌺ϩ
and D 6⌸–C 6⌬ transitions are compared with the intensi-
ties of dispersed fluorescence spectra in Fig. 8. In order to
calculate the FC factors for the D 6⌸–A 6⌺ϩ transition, we
␻
634.7
1.49
0.3594
0.002 29
4.498
629.2830
e
␻exe
Be
0.362 787 6
0.002 672 3
4.7423
0.99
0.86
0.95
1.005
␣
e
107De
Re ͑Å͒
1.8361
1.8277
6
ϩ
CrCl X
⌺
TABLE VIII. Compositions of the molecular orbitals for CrCl. These are
the orbitals optimized for the B 6⌸ state, the weights given for the different
configurations in Table IX have been obtained using these orbitals.
␻
420.7
396.7
1.06
0.9993
0.72
0.88
1.004
e
Be
0.167 467
0.000 698 5
1.0410
0.167 581 8
0.000 971 74
1.1798
␣
e
107De
Comments
Re ͑Å͒
2.203
2.194
6
B
⌸
1␦
1.00(Cr 3d2ϩ
)
Nonbonding
␻
399
5␲
0.99(Cr 3dϩ1)Ϫ0.13(F 2pϩ1
)
Nonbonding
e
Be
0.158 72
0.000 995 6
1.05
11␴ 0.98(Cr 4s)Ϫ0.14(Cr 4p0)Ϫ0.11(Cr 3d0)
Nonbonding
Back-polarized
Nonbonding
␣
e
107De
12␴ 0.98(Cr 3d0)ϩ0.16(Cr 4s)Ϫ0.10(Cr 4p0)
Re ͑Å͒
2.2565
Forward-polarized
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J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Spectroscopy of CrF and CrCl
8861
TABLE X. The dominating configurations for different states of CrCl.
Weights
Occupations
6
ϩ
X
⌺
0.70
0.20
0.90
0.22
0.67
0.92
0.91
0.88
0.03
0.03
0.88
(11␴)(5␲)2(1␦)2
(12␴)(5␲)2(1␦)2
6
6
B
A
⌸
ϩ
(11␴)(12␴)(5␲)(1␦)2
(12␴)(5␲)2(1␦)2
⌺
(11␴)(5␲)2(1␦)2
6
C
a
b
⌬
(11␴)(12␴)(5␲)2(1␦)
(12␴)(5␲)2(1␦)2
4
4
ϩ
⌺
⌸
(11␴)(12␴)(5␲)(1␦)2
(11␴)(2(5␲)(1␦)2)
(11␴)2(5␲)2(1␦)
4
c
⌬
(11␴)(12␴)(5␲)2(1␦)
FIG. 11. Amplitude plots for the orbitals of CrF presented in Table VII.
C. Spin–orbit „SO… calculations
The spin–orbit calculations were done using the
Douglas–Kroll20 form of the microscopic spin–orbit Hamil-
tonian. Spin–orbit effects were calculated at the quasidegen-
used the experimental bond distance for the A 6⌺ϩ state,
while the theoretical value, corrected by Ϫ1% as described
above, was used for the D 6⌸ state. The agreement between
the calculated FC factors and the measured intensities for the
D 6⌸–A 6⌺ϩ transition is indeed satisfactory; see Fig. 8.
The good agreement for the D 6⌸–A 6⌺ϩ transition made it
reasonable to keep the bond distance of the D 6⌸ state fixed
for the D 6⌸–C 6⌬ transition. Then, the Franck–Condon
factors for the D 6⌸–C 6⌬ system were calculated for vari-
ous bond lengths of the C 6⌬ state until the best agreement
with the experimental dispersed fluorescence was obtained.
Despite some deviations, a satisfactory agreement was also
obtained in this case. A closer look shows that there remain
features that do not belong to either the D 6⌸–A 6⌺ϩ or
D 6⌸–C 6⌬ transitions, and a full account of these extra
transitions is important if the small deviations in the calcu-
lated intensities are to be understood. It should be noted that
the presence of these extra features depends strongly on the
excitation considered, and this indicates that the origin of
these features is a perturbation with an unknown state. A
strong candidate could be the b 4⌸ state, which may interact
with the C 6⌬ state through spin–orbit ͑SO͒ interactions.
This hypothesis has some support in the theoretical results
presented in Table IV or Table XIII.
21
erate perturbation level using the LUCIA code in combina-
tion with atomic spin–orbit mean-field integrals.3 In the
spin–orbit calculations an orbital basis common for all states
involved has to be used, and it frequently happens that the
diagonal matrix elements in the spin–orbit Hamiltonian are
too large, in particular, for higher excited states. This prob-
lem can be handled by using an effective Hamiltonian where
the diagonal matrix elements are shifted to reproduce large
spin-free CI results.22,23 In the effective Hamiltonian both
orbital relaxation and dynamic correlation is mimicked by a
simple shift in the diagonal matrix elements. The results of
the spin–orbit calculations are presented in Table XII for
CrF and in Table XIII for CrCl.
The transition energies shown in Tables XII and XIII
can be used to calculate the spectroscopic parameter ␭e ,
which is used to express the total second-order SO interac-
tion on a specific state. The exact definition of the ␭ param-
e
eter can be extracted from Eq. ͑1͒ in Sec. II.
The parameter ␭ is fairly large for the ground states in
e
both CrF and CrCl, 0.54 and 0.266 cmϪ1, respectively. Oka-
bayashi et al.13 have proposed that the large ␭ parameter of
e
the ground state is due to spin–orbit mixing with a low-lying
4
Ϫ
4
Ϫ
⌺
state. Okabayashi estimated the position of the ⌺
state to 11 000 cmϪ1 above the ground state. In Ref. 13, they
have analyzed the pure rotational spectrum of CrF, and their
treatment is limited to that specific molecule. The position of
the lowest-lying ⌺Ϫ state was also estimated using DFT in
4
TABLE IX. The dominating configurations for different states of CrF.
the work of Bencheikh et al.4 to 12 000 cmϪ1. It should be
emphasized that the DFT calculations cannot handle elec-
tronic states with mixed character properly due to the multi-
reference character of the wave function. Thus, the transition
Weights
Occupations
6
6
ϩ
ϩ
X
A
⌺
⌺
0.90
0.03
0.03
0.87
0.92
0.94
0.90
0.92
0.90
0.03
0.03
0.89
(9␴)(4␲)2(1␦)2
(10␴)(4␲)2(1␦)2
(9␴)(4␲)2(1␦)2
(10␴)(4␲)2(1␦)2
(9␴)(10␴)(4␲)(1␦)2
(9␴)(10␴)(4␲)2(1␦)
(4␲)2(1␦)2(5␲)
TABLE XI. The two 6⌸ states of CrF calculated in a common orbital basis.
The transition energy of the B state is the same as in Table IV. The experi-
mental values are within parentheses.
6
6
B
C
D
a
⌸
⌬
⌸
ϩ
6
4
⌺
(10␴)(4␲)2(1␦)2
(9␴)(10␴)(4␲)(1␦)2
(9␴)2(4␲)2(1␦)2
(9␴)2(4␲)2(1␦)
6
6
B
⌸
D ⌸
4
b
⌸
⌬
Te ͑cmϪ1
Re ͑Å͒
͒
7800 ͑8134͒
1.8485 ͑1.828͒
625 ͑629͒
31 900 ͑31 700͒
1.773
695
4
c
(9␴)(10␴)(4␲)2(1␦)
␻
͑cmϪ1
͒
e
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141.218.1.105 On: Sun, 21 Dec 2014 22:48:05

8862
J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Koivisto et al.
TABLE XII. The SO-CI results of CrCl. A satisfactory agreement between
TABLE XIII. The CO-CI results of CrF. A satisfactory agreement between
6
ϩ
6
ϩ
calculated and experimental SO splitting of the X
⌺
state has been ob-
calculated and experimental SO splittings of the X
⌺
state has been ob-
tained. The calculated positions of the different spin components of both
tained. The situation is also satisfactory for the B 6⌸ state. When it comes to
6
ϩ
6
ϩ
A
⌺
and B 6⌸ states show rather irregular behavior in comparison with
the A
⌺
state there is no agreement, partly because of the severely per-
CrF.
turbed nature of the A state. It should be noted that the calculated spin–orbit
6
ϩ
splittings of the A state show a regular pattern similar to that of the X
⌺
⌬Ecalc ͑cmϪ1
͒
⌬Eexpt ͑cmϪ1
͒
Multiplet states
⍀
state, even if a ␭ value estimated from this pattern is incorrect.
e
6
6
ϩ
⌬Eexpt ͑cmϪ1
͒
1/2
3/2
5/2
Ϫ3/2
Ϫ1/2
1/2
3/2
5/2
7/2
5/2
3/2
1/2
Ϫ1/2
1/2
3/2
5/2
7/2
9/2
1/2
3/2
Ϫ1/2
1/2
3/2
5/2
1/2
3/2
5/2
7/2
0
0.99
2.95
8710
8731
8794
8835
8892
8966
9419
9439
9447
0
X
B
⌺
Multiplet states
⍀
⌬Ecalc ͑cmϪ1
͒
1.07
3.20
8750
8790
6
6
ϩ
1/2
3/2
5/2
Ϫ3/2
Ϫ1/2
1/2
3/2
5/2
7/2
1/2
0
2.19
6.55
7565
7613
7662
7712
7765
0
X
⌺
2.17
6.51
7676
7719
7767
7814
7863
7912
⌸
B
⌸
9010
9468
9482
9490
6
6
ϩ
A
C
⌺
7818
4
ϩ
a
⌺
9757.92
9759.16
9951
9970
9980
3/2
5/2
3/2
1/2
⌬
9900
6
ϩ
A
⌺
9953
9955
9959
10 002
10 098
10 190
10 278
10 363
12 236
12 311
12 633
12 764
12 788
12 825
13 725
13 865
13 996
14 118
4
6
C
6⌬ and b
⌸
C
C
C
b
⌬
⌬
⌬
⌸
⌸
⌬
⌸
⌬
⌸
11 600
11 707
11 809
11 817
11 890
11 909
11 958
12 005
12 025
12 097
16 491
16 632
16 769
16 903
Ϫ1/2
1/2
6
6
4
4
ϩ
a
b
⌺
3/2
4
Ϫ1/2
1/2
4
4
4
b
C
b
C
b
C
⌸
6
5/2
3/2
6
7/2
4
c
⌬
5/2
6
⌬
9/2
4
c
⌬
1/2
3/2
5/2
7/2
energy has to be estimated somewhat indirectly. In our cal-
culations we do not find a ⌺Ϫ state in the appropriate en-
ergy region.
4
bution to the ground state is to a substantial degree caused by
interactions with the b 4⌸ and B 6⌸ states. For the ground
Our calculated ␭ values for the ground states of CrF
e
states of CrF and CrCl, we have used the fact that the ␭
e
and CrCl are, in fact, in good agreement with the experi-
parameter is dominated by a rather remote perturber with a
potential energy curve similar to that of the ground states.
This makes it possible to disregard the vibrational structure
of the electronic states involved. For the B states the main
perturbers are the closer-lying A states, and in this case it
may be important to take the effects of the vibronic levels
into account. However, despite this problem we have applied
a similar fitting procedure to the B 6⌸ state of CrF.
ment; see Table XIV. The most important contribution to ␭
e
comes from the interaction with the B 6⌸ state at 8134 cmϪ1
for CrF and at 8870 cmϪ1 for CrCl. The ␭ parameter will be
e
meaningful only if the B 6⌸ state is sufficiently remote to
prevent the inclusion of higher-order corrections and to make
it possible to disregard the vibrational structure of the states
involved. In this case, we only have to use the SO-CI term
values of the ground state spin components to estimate the
␭e . The results for CrCl and CrF are presented in Table
XIV. It is now obvious that the main part of this parameter
originates from interactions with the b 4⌸ and B 6⌸ states. A
similar treatment of the A 6⌺ϩ state would produce an incor-
rect result, since the levels are locally perturbed by vibra-
tional levels of the close-lying B 6⌸ state.
The Ae and ␭ parameters are often insufficient to com-
e
pletely account for the SO interaction. One can in these cases
include the third- and fourth-order corrections defined using
the parameters ␩ and ␪ defined according to Cheung et al.25
as
TABLE XIV. A comparison between calculated and experimental ␭ values
It should be noted here that no account is taken to spin–
e
6
ϩ
in the X
⌺
ground states of both CrF and CrCl. The calculated values
spin interactions, the effective ␭ parameter being defined as
e
have been obtained by fitting the ␭ parameter to the SO-CI energies of the
24
e
␭effϭ␭SOϩ␭
.
However, the spin–spin part is in most
SS
6
ϩ
X
⌺
states, given in Table XIII and Table XIV.
cases small compared to the second-order spin–orbit part.
The electronic wave function obtained for the ground state
Experiment ͑cmϪ1
͒
SO-CI ͑cmϪ1
͒
6
6
consists of ⌺ϩ with an admixture of about 1% of ⌸, in-
dependent of the orbital basis, and very little of anything
else. It is thus clear that the second-order spin–orbit contri-
6
ϩ
CrF X
⌺
0.54
0.266
0.528
0.248
6
ϩ
CrCl X
⌺
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J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Spectroscopy of CrF and CrCl
8863
TABLE XV. A comparison between calculated and experimental values of
SO parameters of the B 6⌸ state of CrF. The electronic states involved have
not been treated as separate vibronic levels and one common orbital basis
has been used. The results must therefore be considered as satisfactory. A
rms error of 0.02 cmϪ1 was obtained when fitting these parameters to the
SO-CI energies given in Table X.
TABLE XVII. The calculated Franck–Condon factors ͑ϫ100͒ between the
6
ϩ
A
⌺
and B 6⌸ states. As can be seen the ⌬ ϭ0 sequence ͑boldface͒ is
v
6
ϩ
clearly dominating. FC factors between the A
4⌸ state are similar in this regard.
⌺
state and the calculated
b
6
6
A
⌺
ϩگB
⌸
0
1
2
3
4
5
0
1
2
3
4
5
92
6
6
79
12
SO-CI ͑cmϪ1
͒
Expt. ͑cmϪ1
͒
13
68
16
Te
Ae
7689.007
50.57
0.365
Ϫ0.0291
Ϫ0.003 28
18
58
19
3
47.04
0.41
Ϫ0.0264
23
49
21
1
27
41
␭
e
␩
␪
0.001 39
D. An attempt to explain the ‘‘the additional bands’’
in the spectrum of CrCl as resulting from
spin–orbit coupling between the A 6⌺¿ state and
higher vibrational levels of B 6⌸
3rd
SO
S,⌺,⍀
S,⌺,⍀
͉
͉
H
H
͉
S,⌺,⍀ ϭ␩⌳⌺ ⌺2Ϫ 1 3S Sϩ1͒Ϫ1
,
͑2͒
͓
͑
͔
͗
͗
͘
͕
͖
5
␪
From the beginning this additional band system ͑Fig. 1͒
was considered as a pure quartet transition, but this could be
ruled out when several branches were successfully matched
with second combination differences of the ground state. Its
absence in the otherwise similar spectra of CrF indicates that
this system could appear through intensity borrowing and
one hypothesis would then be a state interacting with the
near-lying A 6⌺ϩ state through the spin–orbit operator. One
possible perturber that was considered previously was the
4th
SO
͉
S,⌺,⍀ ϭ
35⌺4Ϫ30S Sϩ1͒⌺2
͓ ͑
͘
12
ϩ25⌺2Ϫ6S Sϩ1͒ϩ3S2 Sϩ1͒
.
2
͑
͑
͔
͑3͒
As can be seen in the work by Wallin et al.,10 all four
SO parameters Ae , ␭e , ␩, and ␪ had to be used in order to
describe the total SO interaction in the B 6⌸ state of CrF.
These parameters have been estimated from the calculated
term values obtained through SO-CI for CrF and the results
are presented in Table XV.
⌺
state suggested by Okabayashi et al.13 The positions of
4
Ϫ
4
Ϫ
two low-lying
⌺
states were estimated in the work
Bencheikh et al.4 However, the energies
⌺
states pro-
4
Ϫ
An attempt to do the same estimate for CrCl shows that
the SO-CI values of the B 6⌸ state form an irregular pattern
and that a fifth-order SO parameter would be necessary. This
could also be the case for the experimental data. The reason
may be the smaller energy difference between the A 6⌺ϩ and
B 6⌸ states. Of interest would also be a comparison of the
SO-CI values of the Ae parameters of the different states and
values obtained according to the atom-in-molecule approxi-
mation. This comparison is presented in Table XVI.
As can be seen the atom-in-molecule26 approximation
seems to be consistent with the SO-CI results. The spin-free
energies are much more sensitive to the exact composition of
the different electronic states than are the spin–orbit split-
tings. This is a probable explanation for the differences be-
tween the spin-free energies of the quartets of CrF and those
of CrCl.
duced with MRCI calculations were considerably higher than
10 000–12 000 cmϪ1, proposed in Ref. 4. Our spin–orbit cal-
culations show that the nondiagonal spin–orbit interaction
with the ground state is attributed mainly to the B 6⌸ and not
4
to a ⌺Ϫ state, which was the original idea in Ref. 13. The
remaining states are those presented in Table V. All these
states except B 6⌸ and b 4⌸ could be ruled out because of
selection rules. The MRCI calculations place the b 4⌸ state
3000 cmϪ1 above the level obtained from the extra bands, so
there remains only the B 6⌸ state as the most probable ex-
planation. It is then necessary that there are large FC factors
between suitable levels of the B 6⌸ state and vibrational lev-
els of the A 6⌺ϩ state that possess large transition moments
to the ground state. The intensity of such extra bands will
depend on the factor
2
␯
͉
␯
␯
͉␯
͔
͘
X
.
͓
͗
͗͘
B
A
A
Here, the matrix elements of the spin–orbit and the di-
pole operators have been approximated as independent of the
internuclear distance. Calculated Franck–Condon factors be-
tween the A and B states are presented in Table XVII and as
TABLE XVI. The atom-in-molecule results have been calculated according
the assumption that the sextets and quartets belong to a 6D and 4D complex,
respectively. Each one of these complexes arises when one considers a Crϩ
ion in the d4 s(6D) or d4 s(4D) state perturbed by a negative closed shell
can be seen the ⌬ ϭ0 sequence dominates. The FC factors
v
ion. All units are in cmϪ1
.
between A 6⌺ϩ and B 6⌸ states should now be combined
with the dominating bands of the A 6⌺ϩ –X 6⌺ϩ transition,
which are the first bands of the upper state progression. The
outcome of this procedure is presented in Table XVIII.
Attempts were made to assign the identified levels of the
extra bands as higher vibrational levels of the B 6⌸ state by
SO-CI CrF
SO-CI CrCl
Atom-in-molecule
Expt. CrF
47.04
6
B
C
b
⌸
51.2
46.3
64.1
65.5
50.6
49.7
69.3
68.5
48.6
48.6
72.9
72.9
6
⌬
⌸
⌬
4
4
c
extrapolating from the known energies of B 6⌸( ϭ0).
v
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8864
J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Koivisto et al.
ACKNOWLEDGMENTS
Some of these extra branches, matching with the second
combination differences of the ground state, may share the
The authors want to thank Professor Mats Larsson for
reading the manuscript. This paper was issued as NRCC
43880.
( ϭ3) levels of the F and F spin components as the upper
v
1
2
state. These branches would then belong to the ͑3,0͒ band of
the B 6⌸–X 6⌺ϩ transition. Even if the extrapolated levels
appear close to the observed ones, it is not possible to make
a definite identification. However, it should be pointed out
that the extra bands indeed appear, where bands of the
B 6⌸–X 6⌺ϩ transition should be expected. Especially some
of the stronger extra bands appear at correct vibrational spac-
ings from the strong F1 subband of the ͑0, 0͒ band of the
B 6⌸–X 6⌺ϩ transition.
APPENDIX A: Experimental term values of the B6⌸
state „vÄ0…
J
F1f
F2e
F6e
F6f
F1e
6.5
7.5
9021.4723
9023.9895
9026.7652
9029.8401
9033.3053
9037.0605
9041.1558
9045.4988
9050.2351
9055.3011
9060.7530
9066.4321
9072.4451
9078.7919
9085.5546
9092.5688
9099.8343
9107.5156
9115.5303
9123.8784
9132.4532
9141.4650
9150.7646
9160.3819
9170.3930
9180.5939
9191.2438
9202.1309
9213.3326
9224.8728
9236.7988
9248.9863
9261.5163
9274.3716
9287.5536
9301.0812
9314.8999
9329.0451
9343.5220
9358.3133
9373.4331
9388.8681
9404.6568
9420.7604
9437.1618
9483.8998
9470.9550
9488.3247
9506.0370
9524.0577
9542.3981
9561.0667
9580.0564
9599.3685
9618.9923
9638.9451
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
21.5
22.5
23.5
24.5
25.5
26.5
27.5
28.5
29.5
30.5
31.5
32.5
33.5
34.5
35.5
36.5
37.5
38.5
39.5
40.5
41.5
42.5
43.5
44.5
45.5
46.5
47.5
48.5
49.5
50.5
51.5
52.5
53.5
54.5
55.5
56.5
57.5
58.5
59.5
60.5
61.5
IV. CONCLUSION
8804.4157
8808.1662
8812.2724
8816.6940
8821.4522
8826.5929
8832.0327
8837.7755
8843.8957
8850.3199
8857.1265
8864.1892
8871.6412
8879.4142
8887.4866
8895.9362
8904.6716
8913.7430
8923.1731
8932.8892
8942.9698
8953.3497
8964.0541
8975.0999
8986.5005
8998.1790
9010.2026
9022.5430
9035.2949
9048.2217
9061.5944
9075.2281
9089.2307
9103.4881
9118.1340
9133.0986
9148.3699
9163.9796
9179.8918
9196.1519
9212.7275
9229.6298
9246.8451
9264.3804
9282.2592
9300.4450
9318.9450
9337.7674
9356.9416
9376.4105
9396.2089
The limited set of identified levels of the B 6⌸ state of
CrCl in combination with the large ⌳ doubling and nondi-
agonal SO coupling have prevented a complete analysis of
the B 6⌸–X 6⌺ϩ transition. However, approximate rota-
tional and first-order spin–orbit constants have been obtained
for the B state, and improved spin–rotation and spin–spin
constants have been derived for the X 6⌺ϩ state.
8814.6775
8821.1755
8828.0226
8835.1804
8842.6692
8850.4903
8858.6136
8867.0904
8875.8859
8884.9353
8894.3353
8904.0769
8914.1266
8924.5009
8935.1823
8946.1980
8957.5299
8969.1764
8981.1508
8993.4352
9006.0567
9018.9704
9032.2178
9045.7450
9059.6536
9073.8558
9088.3665
9103.2197
9118.3647
9133.8385
9149.6291
9165.7359
9182.1704
9198.9230
9215.9828
9233.3669
9251.0684
9269.1023
9287.4278
9306.0758
9325.0551
9344.3345
9363.9440
9078.8765
9085.5623
9092.5584
9099.9121
9017.5738
9115.5639
9123.8718
9132.5086
9141.4814
9150.7472
9160.3818
9170.3142
9180.5641
9191.1692
9202.0846
9213.3317
9224.8899
9236.7932
9248.9950
9261.5089
9274.3501
9287.5534
9301.0636
9314.8883
9329.0594
9343.5551
9358.3155
9373.4474
9388.8920
9404.6485
9420.7381
9437.1740
9453.8958
9470.9542
9488.3141
9506.0239
9524.0614
9542.4045
9561.0802
9580.0598
9599.3714
9618.9977
9638.9506
MRCI calculations have been carried out on several low-
lying states of CrF and CrCl. The data have been used to
analyze the dispersed fluorescence spectra of CrF, excited at
31 700 cmϪ1. This high-lying state has been confirmed to be
6
a ⌸ state and is assigned as D 6⌸. The dispersed fluores-
cence spectra are essentially due to D 6⌸→C 6⌬ and D 6⌸
→A 6⌺ϩ.
Spin–orbit–configuration–interaction ͑SO-CI͒ calcula-
tions have been carried out on both CrF and CrCl. It has been
shown that the second-order spin–orbit parameters ␭ of the
e
X 6⌺ϩ ground states are caused, to a major extent, by inter-
8933.8937
8944.8079
8956.0157
8967.5671
8979.4138
8991.5695
9004.0519
9016.8418
9029.9711
9043.3821
9057.1390
9071.1948
9085.5739
9100.2653
9115.2797
9130.5928
9146.2142
9162.1840
9178.4380
9195.0282
9211.9365
9229.1335
9246.6607
9264.5103
9282.6470
9301.1422
9319.9074
9339.0203
9358.3967
actions with the B 6⌸ states.
It is apparent in this work that the present state-of-the-art
ab initio calculations have been accurate enough to give a
profound support for difficult spectroscopic problems. This
is probably transferable to the analysis of other kinds of ex-
perimental data.
TABLE XVIII. Some possible extra bands of the B 6⌸–X
that might appear because of an interaction between the A
⌺
transition
and B ⌸
6
ϩ
6
ϩ
6
⌺
states. Note that some of the ‘‘possible extra bands’’ listed in the rightmost
column would have large intensity even without an interaction with the
6
ϩ
A
⌺
state.
Strong bands
of the
Large FC factors
Possible extra bands
of the
6
6
ϩ
A
⌺
ϩ –X
⌺
between the
6
ϩ
6
ϩ
transition
A
⌺
and B 6⌸ states
B
6⌸–X
⌺
transition
͑0,1͒
͑0,0͒
͑1,0͒
͑2,0͒
͑3,0͒
͑3,1͒
͑4,1͒
͑0,0͒
͑0,0͒
͑1,1͒
͑2,2͒
͑3,3͒
͑3,3͒
͑4,4͒
͑0,1͒
͑0,0͒
͑1,0͒
͑2,0͒
͑3,0͒
͑3,1͒
͑4,1͒
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J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Spectroscopy of CrF and CrCl
8865
J
F1f
F2e
F6e
F6f
J
F1f
F2e
F6e
F6f
F1e
F1e
62.5 9378.1695 9383.8420 9416.3149 9659.2139 9659.2096
63.5 9398.2358 9404.0972 9436.7460 9679.7918 9679.8008
64.5 9418.5840 9424.6442 9457.5121 9700.7118 9700.7242
65.5 9439.2760 9445.5197 9478.5778 9721.9407 9721.9297
66.5 9460.2628 9466.7119 9499.9692 9743.4907 9743.4897
67.5 9481.5731 9488.2122 9521.6777 9765.3523 9765.3681
68.5 9503.1942 9510.0222 9543.7064 9787.5545 9787.5533
69.5 9525.1272 9532.1612 9566.0565 9810.0761 9810.0356
70.5 9547.3538 9554.6030 9588.7201 9832.8785 9832.8727
71.5 9569.9418 9577.3683 9611.7184 9856.0247 9855.9977
72.5 9592.8222 9600.4543 9635.0227 9879.4896 9879.4561
73.5 9616.0233 9623.8538 9658.6398 9903.2701 9903.2484
74.5 9639.5325 9647.5563 9682.5882 9927.3649 9927.3521
75.5 9663.3363 9671.5858 9706.8408 9951.7824 9951.7826
76.5 9687.4735 9695.9211 9731.4182 9976.4944 9976.4822
77.5 9711.9303 9720.5714 9756.2838 10 001.5625 10 001.5359
78.5 9736.6861 9745.5394 9781.4835 10 026.9250 10 026.9317
79.5 9761.7426 9770.8215 9807.0229 10 052.6092 10 052.5971
80.5 9787.1645 9796.4007 9832.8457 10 078.6004 10 078.5997
81.5 9812.8539 9822.3125 9859.0212 10 104.9517 10 104.9253
82.5 9838.8679 9848.5337 9885.4704 10 131.5725 10 131.5329
83.5 9865.1946 9875.0661 9912.2540 10 158.5118 10 158.4836
84.5 9891.8304 9901.9107 9939.3448 10 185.7769 10 185.7411
85.5 9918.7937 9929.0551 9966.7742 10 213.3484 10 213.3171
86.5 9946.0450 9956.5324 9994.4734 10 241.2746 10 241.2201
87.5 9973.6189 9984.3177 10 022.5072 10 269.4546 10 269.4113
88.5 10 001.5048 10 012.4130 10 050.8793 10 297.9803 10 297.9471
89.5 10 029.7304 10 040.8094 10 079.5447 10 326.8159 10 326.7775
90.5 10 058.2146 10 069.5371 10 108.5149 10 355.9703 10 355.9269
91.5 10 087.0380 10 098.5751 10 137.8131 10 385.4384 10 385.3825
92.5 10 116.1746 10 127.8948 10 167.4187 10 415.1985 10 415.1514
93.5 10 145.6140 10 157.5430 10 197.3236 10 445.2868 10 445.2335
94.5 10 175.3919 10 187.5031 10 227.5739 10 475.6988 10 475.6330
95.5 10 205.4252 10 217.7718 10 258.0785 10 506.4167 10 506.3588
96.5 10 235.8081 10 248.3602 10 288.9528 10 537.4368 10 537.3677
97.5 10 266.4879 10 279.2304 10 320.1034 10 568.7946 10 568.7016
98.5 10 297.4594 10 310.4416 10 351.5827 10 600.4273 10 500.3517
99.5 10 328.8046 10 341.9540 10 383.3468 10 632.3941 10 532.2989
100.5 10 360.3990 10 373.7785 10 415.4458 10 664.6479 10 664.5485
101.5 10 392.3182 10 405.9007 10 447.8447 10 697.2274 10 697.1444
102.5 10 424.5502 10 438.3233 10 480.5440 10 730.1505 10 730.0542
103.5 10 457.0832 10 471.0769 10 513.5692 10 763.3541 10 763.2229
104.5 10 489.9462 10 504.1093 10 546.8993 10 796.8478 10 796.7327
105.5 10 523.1010 10 537.4751 10 580.5324 10 830.6520 10 830.5363
106.5 10 556.5585 10 571.1478 10 614.4729 10 864.7792 10 864.6749
107.5 10 590.3267 10 605.1338 10 648.7355 10 899.2319 10 899.1190
108.5 10 624.4126 10 639.3993 10 683.2924 10 933.9892 10 933.8195
109.5 10 658.7943 10 673.9683 10 718.1544 10 969.0509 10 968.8827
110.5 10 693.4934 10 708.8743 10 753.3252 11 004.4003 11 004.2278
111.5 10 728.4802 10 744.0837 10 788.8173 11 040.0668 11 039.9059
112.5 10 763.7845 10 779.5645 10 824.6170 11 076.0526 11 075.8702
113.5 10 799.4053 10 815.3963 10 860.6973 11 112.3243 11 112.1402
114.5 10 835.3050 10 851.5026 10 897.0910 11 148.9210 11 148.7128
115.5 10 871.5267 10 887.8901 10 933.7982 11 185.8040 11 185.6141
116.5 10 908.0659 10 924.6562 10 970.8004 11 222.9972 11 222.8297
129.5
130.5
131.5
132.5
133.5
134.5
135.5
136.5
137.5
138.5
139.5
140.5
141.5
142.5
143.5
144.5
145.5
146.5
147.5
148.5
149.5
150.5
11 410.5698
11 451.3363
11 492.3756
11 533.7556
11 575.4221
11 617.4000
11 659.6517
11 702.2319
11 745.0978
11 788.2481
11 831.7211
11 875.4694
11 919.5422
11 963.9127
12 008.5471
12 053.4951
12 098.8287
12 144.3056
12 190.2837
12 236.4690
12 283.0024
12 329.8058
11 479.5409
11 520.7753
11 562.3351
11 604.1477
11 646.2938
11 688.7252
11 731.4732
11 774.5098
11 817.8478
11 861.4691
11 905.3822
11 949.6112
11 994.1291
12 038.9584
12 084.0991
12 129.4714
12 175.1504
12 221.1615
12 267.4682
12 314.0234
12 360.8989
12 408.065
11 733.8284
11 775.2248
11 816.9648
11 858.9705
11 901.2500
11 943.8806
11 943.8806
12 030.0023
12 073.5006
12 117.2730
APPENDIX B: CALCULATED TERM VALUES
X 6⌺¿ STATE „vÄ0…
J
F2
F3
F4
F5
F6
F1
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
0.3890
2.1583
1.3851
2.9511
0.0177
2.6431
1.2172
3.4902
0.0000
0.3257
1.4762
2.1099
4.1162
4.7810
3.6017
4.8202
5.8428
6.8243
0.9902
3.0930
4.9180
6.4912
7.8754
9.1796
1.9916
4.4179
6.5773
8.4973
10.2305
12.9138
15.9275
19.2731
22.9512
26.9621
31.3062
35.9836
40.9945
46.3388
52.0166
58.0279
64.3727
71.0509
78.0626
85.4078
93.0863
11.8604
14.8711
18.2133
21.8881
25.8958
30.2368
34.9112
39.9191
45.2605
50.9356
56.9441
63.2863
69.9619
76.9711
84.3137
91.9897
99.9990
3.3288
6.0812
8.5752
10.8376
13.5117
16.5197
19.8616
23.5372
27.5467
31.8901
36.5672
41.5782
46.9229
52.6014
58.6135
64.9593
71.6387
78.6517
85.9981
5.0013
8.0813
10.9096
13.5797
16.5848
19.9246
23.5990
27.6078
31.9508
36.6280
41.6392
46.9845
52.6636
58.6766
65.0234
71.7039
78.7181
86.0658
7.0088
9.3509
10.4174
13.0888
16.0952
19.4364
23.1122
27.1223
31.4668
36.1455
41.1583
46.5051
52.1859
58.2007
64.5492
71.2315
78.2474
85.5970
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
21.5
22.5
23.5
24.5
25.5
12.0275
15.0386
18.3840
22.0636
26.0774
30.4253
35.1072
40.1232
45.4730
51.1568
57.1743
63.5256
70.2107
77.2293
84.5815
117.5 10 944.8933 10 961.6633 11 008.1202
118.5 10 982.0355 10 998.9830 11 045.7294
119.5 11 019.4569 11 036.6402 11 083.6650
120.5 11 057.2286 11 074.5552 11 121.8977
121.5 11 095.2704 11 112.7976 11 160.4283
122.5 11 133.6365 11 151.3570 11 199.2499
11 260.2779
11 298.0673
11 336.2109
11 374.6097
11 413.2918
11 452.2745
11 491.6141
11 531.2097
93.6781 101.0981 108.3416
93.7471 101.6913 109.4431 117.0175
93.2801 101.7618 110.0380 118.1214 126.0265
92.2673 101.2967 110.1099 118.7178 127.1328 135.3686
123.5 11 172.2885
124.5 11 211.2463
125.5 11 250.5008
126.5 11 290.0689
127.5 11 329.9299
128.5 11 370.0882
11 238.3805
11 277.8229
11 317.5308
11 357.6207
11 397.9423
11 438.5756
26.5 100.2865 109.6467 118.7913 127.7308 136.4772 145.0437
27.5 108.6390 118.3300 127.8059 137.0770 146.1547 155.0517
28.5 117.3248 127.3465 137.1536 146.7561 156.1650 165.3926
29.5 126.3439 136.6962 146.8345 156.7682 166.5082 176.0663
30.5 135.6961 146.3790 156.8482 167.1132 177.1842 187.0726
31.5 145.3814 156.3948 167.1949 177.7909 188.1928 198.4115
11 611.3692
11 651.8480
11 692.7115
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8866
J. Chem. Phys., Vol. 114, No. 20, 22 May 2001
Koivisto et al.
J
F2
F3
F4
F5
F6
F1
J
F2
F3
F4
F5
F6
F1
100.5 1610.5274 1643.9909 1677.2432 1710.2874 1743.1267 1775.7642
101.5 1643.1598 1676.9411 1710.5110 1743.8727 1777.0293 1809.9839
102.5 1676.1125 1710.2112 1744.0985 1777.7774 1811.2509 1844.5223
103.5 1709.3850 1743.8009 1778.0052 1812.0010 1845.7913 1879.3792
104.5 1742.9771 1777.7099 1812.2310 1846.5434 1880.6501 1914.5542
105.5 1776.8885 1811.9379 1846.7755 1881.4042 1915.8270 1950.0470
106.5 1811.1189 1846.4847 1881.6384 1916.5831 1951.3217 1985.8573
107.5 1845.6681 1881.3498 1916.8195 1952.0799 1987.1340 2021.9848
108.5 1880.5357 1916.5331 1952.3183 1987.8941 2023.2635 2058.4293
109.5 1915.7214 1952.0343 1988.1347 2024.0256 2059.7098 2095.1903
110.5 1951.2249 1987.8529 2024.2683 2060.4740 2096.4728 2132.2676
111.5 1987.0460 2023.9888 2060.7188 2097.2389 2133.5520 2169.6608
112.5 2023.1843 2060.4415 2097.4859 2134.3202 2170.9471 2207.3697
113.5 2059.6395 2097.2109 2134.5692 2171.7173 2208.6579 2245.3938
114.5 2096.4412 2134.2965 2171.9685 2209.4301 2246.6840 2283.7329
115.5 2133.4993 2171.6980 2209.6834 2247.4582 2285.0250 2322.3867
116.5 2170.9032 2209.4152 2247.7136 2285.8012 2323.6807 2361.3548
117.5 2208.6228 2247.4476 2286.0588 2324.4589 2362.6506 2400.6368
118.5 2246.6577 2285.7951 2324.7186 2363.4309 2401.9346 2440.2325
119.5 2285.0076 2324.4571 2363.6927 2402.7168 2441.5321 2480.1414
120.5 2323.6721 2363.4335 2402.9807 2442.3164 2481.4430 2520.3633
121.5 2362.6509 2402.7239 2442.5824 2482.2292 2521.6668 2560.8978
122.5 2401.9437 2442.3278 2482.4974 2522.4550 2562.2031 2601.7445
123.5 2441.5501 2482.2451 2522.7253 2562.9934 2603.0517 2642.9031
124.5 2481.4698 2522.4752 2563.2658 2603.8440 2644.2122 2684.3732
125.5 2521.7024 2563.0180 2604.1185 2645.0064 2685.6842 2726.1545
32.5 155.3996 166.7434 177.8744 188.8013 199.5340 210.0829
33.5 165.7507 177.4249 188.8866 200.1443 211.2076 222.0867
34.5 176.4346 188.4391 200.2314 211.8198 223.2136 234.4228
35.5 187.4513 199.7859 211.9087 233.8277 235.5520 247.0910
36.5 198.8005 211.4653 223.9184 236.1679 248.2225 260.0914
37.5 210.4823 223.4771 236.2605 248.8403 261.2250 273.4237
38.5 222.4965 235.8212 248.9347 261.8448 274.5595 287.0879
39.5 234.8430 248.4975 261.9411 275.1812 288.2259 301.0838
40.5 247.5217 261.5059 275.2794 288.8495 302.2240 315.4114
41.5
26.5325 274.8463 288.9496 302.8496 316.5538 330.0704
42.5 273.8753 288.5186 302.9516 317.1812 331.2150 345.0609
43.5 287.5500 302.5226 317.2852 331.8444 346.2076 360.3826
44.5 301.5564 316.8583 331.9503 346.8390 361.5315 376.0354
45.5 315.8945 331.5256 346.9468 362.1648 377.1865 392.0192
46.5 330.5641 346.5245 362.2746 377.8217 393.1724 408.3339
47.5 345.5651 361.8541 377.9335 393.8097 409.4892 424.9793
48.5 360.8973 377.5151 393.9234 410.1285 426.1367 441.9552
49.5 376.5607 393.5071 410.2442 426.7780 443.1148 459.2616
50.5 392.5551 409.8300 426.8957 443.7580 460.4234 476.8983
51.5 408.8804 426.4836 443.8778 461.0686 478.0622 494.8651
52.5 425.5363 443.4679 461.1903 478.7093 496.0311 513.1619
53.5 442.5229 460.7825 478.8331 496.6803 514.3300 531.7885
54.5 459.8399 478.4274 496.8060 514.9812 532.9587 550.7448
55.5 447.4872 496.4025 515.1090 533.6119 551.9171 570.0306
56.5 495.4647 514.7076 533.7417 552.5723 571.2050 589.6458
57.5 513.7721 533.3425 552.7041 571.8622 590.8223 609.5901
58.5 532.4094 552.3071 571.9961 591.4815 610.7687 629.8634
59.5 551.3763 571.6012 591.6174 611.4299 631.0441 650.4656
60.5 570.6728 591.2246 611.5678 631.7073 651.6483 671.3964
61.5 590.2986 611.1773 631.8473 652.3136 672.5812 692.6557
62.5 610.2536 631.4589 652.4556 673.2485 693.8426 714.2433
63.5 630.5376 652.0694 673.3926 694.5119 715.4323 736.1590
64.5 651.1504 673.0085 694.6580 716.1035 737.3500 758.4027
65.5 672.0919 674.2761 716.2517 738.0233 759.5957 780.9741
66.5 693.3619 715.8721 738.1736 760.2711 782.1692 803.8730
67.5 714.9601 737.7961 760.4234 782.8465 805.0702 827.0993
68.5 736.8865 760.0481 783.0009 805.7495 828.2985 850.6527
69.5 759.1409 782.3628 805.9060 828.9799 851.8540 874.5331
70.5 781.7229 805.5350 829.1384 852.5374 875.7364 898.7402
71.5 804.6326 828.7697 852.6980 876.4218 899.9455 923.2739
72.5 827.8695 852.3314 876.8545 900.6330 924.4813 948.1339
73.5 851.4337 876.2201 900.7978 925.1707 949.3433 973.3200
74.5 875.3248 900.4356 925.3376 950.0348 974.5314 998.8320
75.5 899.5426 924.9776 950.2037 975.2249 1000.0455 1024.6697
76.5 924.0870 949.8460 975.3960 1000.7410 1025.8852 1050.8329
77.5 948.9577 975.0404 1000.9141 1026.5828 1052.0504 1077.3213
78.5 974.1545 1000.5608 1026.7580 1052.7500 1078.5408 1104.1347
79.5 999.6772 1026.4068 1052.9273 1079.2424 1105.3563 1131.2729
80.5 1025.5257 1052.5784 1079.4218 1106.0599 1132.4965 1158.7357
81.5 1051.6996 1079.0751 1106.2414 1133.2021 1159.9612 1186.5228
82.5 1078.1987 1105.8969 1133.3857 1160.6689 1187.7503 1214.6339
83.5 1105.0228 1133.0434 1160.8546 1188.4600 1215.8635 1243.0689
84.5 1132.1718 1160.5146 1188.6478 1216.5752 1244.3005 1271.8275
85.5 1159.6453 1188.3100 1216.7651 1245.0142 1273.0611 1300.9095
86.5 1187.4431 1216.4295 1245.2062 1273.7768 1302.1450 1330.3145
87.5 1215.5650 1244.8728 1273.9709 1302.8628 1331.5520 1360.0424
88.5 1244.0107 1273.6398 1303.0590 1332.2719 1361.2819 1390.0929
89.5 1272.7800 1302.7301 1332.4702 1362.0038 1391.3344 1420.4657
90.5 1301.8727 1332.1434 1362.2042 1392.0582 1421.7092 1451.1606
91.5 1331.2885 1361.8797 1392.2608 1422.4351 1452.4060 1482.1773
92.5 1361.0271 1391.9385 1422.6397 1453.1339 1483.4247 1513.5155
93.5 1391.0883 1422.3197 1453.3407 1484.1546 1514.7649 1545.1751
94.5 1421.4718 1453.0229 1484.3635 1515.4969 1546.4264 1577.1556
95.5 1452.1775 1484.0479 1515.7078 1547.1604 1578.4089 1609.4568
96.5 1483.2049 1515.3945 1547.3735 1579.1449 1610.7121 1642.0785
97.5 1514.5539 1547.0624 1579.3601 1611.4501 1643.3358 1675.0204
98.5 1546.2241 1579.0512 1611.6674 1644.0758 1676.2796 1708.2822
99.5 1578.2154 1611.3608 1644.2952 1677.0217 1709.5433 1741.8635
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