The interacting B 4Σ- and d 2Π states of CrN: A laser induced and dispersed fluorescence study

Article abstract of DOI:10.1063/1.474809

Chromium mononitride molecules have been produced in a laser vaporization molecular beam source using Cr metal and ammonia. The complex CrN LIF spectra between 430 and 490 nm have been examined in detail and representative bands in three new electronic subsystems, labeled B ⁴Σ^- ← X ⁴Σ^-, d ²Π_3/2←X ⁴Σ^-, and d ²Π_1/2←X ⁴Σ^-, have been rotationally analyzed. Perturbations between the B ⁴Σ^- and d ²Π states and their dependence on vibrational quantum numbers have been examined. Dispersed fluorescence (DF) spectra have been recorded which provided a measure of the state mixing. The DF spectra also reveal the presence of an electronic state of CrN with T～6000 cm^-1, identified as the a ²Σ^- state. Molecular parameters in the B ⁴Σ^-, d ²Π, and a ²Σ^- states have been established.

Full text of DOI:10.1063/1.474809

The interacting B 4 Σ − and d 2 Π states of CrN: A laser induced and dispersed
fluorescence study
Chi Zhou, Walter J. Balfour, and Charles X. W. Qian
Citation: The Journal of Chemical Physics 107, 4473 (1997); doi: 10.1063/1.474809
View online: http://dx.doi.org/10.1063/1.474809
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4
2
The interacting B ⌺؊ and d ⌸ states of CrN: A laser induced
and dispersed fluorescence study
Chi Zhou,a) Walter J. Balfour, and Charles X. W. Qian
Department of Chemistry, University of Victoria, P.O. Box 3065, Victoria, British Columbia,
Canada V8W 3P6
͑Received 24 February 1997; accepted 17 June 1997͒
Chromium mononitride molecules have been produced in a laser vaporization molecular beam
source using Cr metal and ammonia. The complex CrN LIF spectra between 430 and 490 nm have
been examined in detail and representative bands in three new electronic subsystems, labeled
4
4
2
4
2
4
B ⌺Ϫ←X ⌺Ϫ, d ⌸3/2←X ⌺Ϫ, and d ⌸1/2←X ⌺Ϫ, have been rotationally analyzed.
Perturbations between the B ⌺Ϫ and d ⌸ states and their dependence on vibrational quantum
numbers have been examined. Dispersed fluorescence ͑DF͒ spectra have been recorded which
provided a measure of the state mixing. The DF spectra also reveal the presence of an electronic
4
2
state of CrN with Tϳ6000 cmϪ1, identified as the a ⌺Ϫ state. Molecular parameters in the B ⌺Ϫ,
2
4
2
2
d ⌸, and a ⌺Ϫ states have been established. © 1997 American Institute of Physics.
͓S0021-9606͑97͒00136-0͔
I. INTRODUCTION
II. EXPERIMENT
The chromium mononitride molecules were prepared by
chemical reaction in a laser-produced plasma using chro-
mium metal and ammonia doped in helium. The basic ex-
perimental apparatus used has been described previously.1
Briefly, the setup consists of a typical laser vaporization mo-
lecular beam source, two pulsed, laser systems and the data
collecting and recording hardware and software for LIF de-
tection.
There has been considerable recent interest in the gas-
phase spectroscopic study of simple transition metal nitrides,
where important information about the bonding between a
metal atom and a nitrogen atom can be obtained.1–24 In a
recent study, we have carried out the first gas-phase spectro-
scopic investigation on CrN. The ground and the first excited
4
4
states were identified as X ⌺Ϫ and A ⌸ with electron con-
1
figurations of 1␦29␴ and 1␦24␲1, respectively. Twelve
The wavelength calibration was carried out using the
observed Cr atomic laser induced fluorescence ͑LIF͒ lines in
this region. The absolute wave numbers reported here are
believed to be accurate within 2 cmϪ1 and the relative posi-
subbands of the A←X transition were rotationally analyzed.1
Transitions involving other CrN electronic states were
also noted and, in the present paper, we report the locations
tions should be precise within 0.1 cmϪ1
.
4
and characterization of three of these, namely, the B ⌺Ϫ,
In the low-resolution dispersed fluorescence experiment,
the probe laser was fixed at selected wavelengths and the
grating of the monochromator was scanned by using a step-
ping motor. Two 0.5 mm slits were used at the entrance and
exit of the monochromator. The wavelength resolution of the
monochromator is about 5 nm. The monochromator is cali-
brated by the excitation laser wavelength. The partial laser
induced fluorescence spectra related to the quartet and dou-
blet excited states were also recorded by parking the mono-
chromator at selected wavelengths corresponding to the
doublet–doublet and quartet–quartet emissions, respectively.
To avoid power broadening and saturation in the strong
d ⌸, and a ⌺Ϫ states. Their identification is based on mo-
lecular orbital considerations, a comparison of the experi-
mental data with those of the isovalent VO molecule, and ab
initio calculations on CrN.25
2
2
4
2
The ϭ0 levels of the B ⌺Ϫ and d ⌸1/2 states lie
v
within 60 cmϪ1 of each other and, inevitably, numerous per-
turbations and interactions occur between their respective
vibration–rotation levels. One clear manifestation of this is
the observation that different bands within each of the –0
v
progressions of the B–X and d–X systems are very different
in appearance. We have used laser induced fluorescence and
4
4
B ⌺Ϫ←X ⌺Ϫ transition, the amplifier of the dye laser was
4
4
dispersed fluorescence to separate the B ⌺Ϫ←X ⌺Ϫ and
normally removed during our experiment. However, for the
d ⌸←X ⌺Ϫ components in the perturbed region of the
spectrum. Vibrational assignments have been confirmed and
rotational analyses have been carried out for three subbands,
2
4
weak d ⌸←X ⌺Ϫ bands, the amplified dye laser output
2
4
was used to enhance the signal.
one of B ⌺Ϫ←X ⌺Ϫ, one of d ⌸3/2←X ⌺Ϫ, and one
4
4
2
4
of d ⌸1/2←X ⌺Ϫ type, where perturbation is minimal.
2
4
III. RESULTS AND ANALYSES
A. Background information
Evidence is also presented for the low-lying a ⌺Ϫ state.
2
The experimental work, together with the ab initio cal-
culations, provides important information about the elec-
tronic structure of CrN.1,25 Three electron configurations are
a͒
Permanent address: Institute of Opto-Electronics, Harbin Institute of Tech-
nology, Harbin, 150001, People’s Republic of China.
J. Chem. Phys. 107 (12), 22 September 1997
0021-9606/97/107(12)/4473/10/$10.00
© 1997 American Institute of Physics
4473
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4474
FIG. 2. A survey scan of CrN LIF spectra in the 430–490 nm region.
recorded following laser excitation to the largely unperturbed
FIG. 1. Electron configurations and related states of CrN.
4
B ⌺Ϫ( ϭ1) state is displayed in Fig. 3͑a͒. Two vibra-
v
Ј
tional progressions can be identified: ͑i͒ A strong progression
considered important to understanding the visible and near
UV spectra: 1␦29␴1, 1␦210␴1, and 1␦24␲1. The possible
electronic states arising from these configurations and their
relative positions ͑not to scale͒ are shown in Fig. 1.
associated with emission to the levels ϭ0–7 of the ground
v
state and, ͑ii͒ a very weak progression involving an elec-
tronic state ϳ6000 cmϪ1 above the ground state and having
a vibrational frequency of about 1000 cmϪ1. We identify
The laser induced fluorescence spectra show the allowed
2
this low-lying electronic state as the a ⌺Ϫ state. The
4
4
4
4
A ⌸←X ⌺Ϫ and B ⌺Ϫ←X ⌺Ϫ transitions, and
strong Franck–Condon activity associated with the
2
4
d ⌸←X ⌺Ϫ bands which derive their intensity through
4
4
B ⌺Ϫ←X ⌺Ϫ transition reflects a considerable difference
in geometry in the two states. This point is treated qualita-
tively in Sec. III C.
4
2
4
2
B ⌺Ϫ/d ⌸ and A ⌸/d ⌸ mixings. Spin–orbit coupling
in CrN is expected to be small and the d ⌸←X ⌺Ϫ tran-
sition ought to be quite weak. Experiments with 15NH3 have
been used to establish the vibrational numbering of the ob-
served levels. In doing so, we have assumed a vibrational
2
4
The corresponding DF spectrum obtained by excitation
2
to the d ⌸3/2( ϭ0) state is presented in Fig. 3͑b͒. Here it
v
may be seen that the d ⌸→a ⌺Ϫ emission is confined
2
2
2
4
frequency for the d ⌸ state similar to that for the A ⌸
state ͑i.e., ϳ910 cmϪ1͒, since the A and d states arise from
the same electron configuration.
It is pertinent to note here that there had been indirect
4
evidence for the presence of a 2⌸ state lying above the A ⌸
state in our study of the A–X system.1 The four ⍀ sublevels
4
of the A ⌸ state are not equally spaced and the observed
irregularity in spacing can be interpreted as being due to
2
interaction with a ⌸ state from above.
2
4
Given the closeness in energy of the d ⌸ and B ⌺Ϫ
states, it is not surprising that the spectra show the signatures
of interaction ͑perturbation͒ between these two states. What
is observed is that the appearance of the B ⌺Ϫ←X ⌺Ϫ
4
4
2
4
and d ⌸←X ⌺Ϫ bands varies dramatically with the
excited-state vibrational quantum number, whence it may be
inferred that the B ⌺Ϫ and d ⌸ states have rather different
4
2
vibrational frequencies, such that the degree of mixing is
highly -dependent. Consequently, some, but not all of the
v
2
4
d ⌸←X ⌺Ϫ bands, appear quite ‘‘bright.’’ A survey scan
of the CrN spectrum in the region of the interactions, ͑430–
490 nm͒, is shown in Fig. 2.
B. Dispersed fluorescence and LIF spectra
FIG. 3. Dispersed fluorescence ͑DF͒ spectra of CrN; ͑a͒ DF spectrum from
4
2
the B
DF spectrum from a mixed B
⌺ ⌸ ( ϭ0) state, ͑c͒
Ϫ( ϭ1) state, ͑b͒ DF spectrum from the d
v v
3/2
We have recorded dispersed fluorescence ͑DF͒ spectra
using a number of excitation wavelengths. The DF spectrum
4
2
⌺ ⌸1/2(vϭ0) state.
Ϫ(vϭ0) and d
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4475
FIG. 4. The CrN LIF spectra in the 486.5–489.5 nm region; ͑a͒ spectrum
4
2
associated with the mixed state ͓B
⌺ ⌸ ( ϭ0)], ͑b͒ the
Ϫ( ϭ0)ϩd
v v
1/2
doublet component of ͑a͒ recorded by monitoring emission to the
2
a
⌺
Ϫ( ϭ0) state, ͑c͒ the quartet component of ͑a͒ recorded by monitoring
v
4
emission to the X
⌺
Ϫ( ϭ1) state.
v
4
Ϫ
4
Ϫ
FIG. 5. Franck–Condon patterns associated with the B
⌺
→X
⌺
tran-
sitions from ϭ0 to ϭ4. Filled circles are calculated Franck–Condon
vЈ vЈ
2
2
almost entirely to the 0-0 transition. The d ⌸ and a ⌺Ϫ
states must therefore have similar bond lengths and similar
vibrational frequencies. Furthermore the intensity of the
emission is such as to imply a spin-allowed transition con-
factors.
have not been corrected for the monochromator and photo-
multiplier tube ͑PMT͒ sensitivities, show very satisfactory
agreement with experiment at the node positions. These data
are included in Fig. 5. The bond length in the ground state of
CrN has been determined from a detailed rotational analysis
of the A–X spectra and the Franck–Condon pattern simula-
tions provide a reliable estimation of the bond length in the B
state. Best agreement was found using a value for
2
4
sistent with our assignment. Where the d ⌸ and B ⌺Ϫ
levels are strongly mixed, emission occurs to the a ⌺Ϫ and
2
X ⌺Ϫ states with comparable intensities. An example of
4
such a DF spectrum is shown in Fig. 3͑c͒.
LIF spectra of CrN between 486.5 and 489.5 nm are
given in Fig. 4. The spectrum in Fig. 4͑a͒ shows the conges-
tion arising from the overlapping of the doublet and quartet
spectra. The doublet and quartet components of the spectra
can be separated to some extent by a judicial choice of moni-
toring wavelength ͓Figs. 4͑b͒ and 4͑c͔͒. We estimate the cou-
4
4
r (B ⌺Ϫ) of 0.170 nm r (X ⌺Ϫ)ϭ0.156 nm . A similar
͓
͔
0
0
treatment of the d ⌸→X ⌺Ϫ confirms that CrN in the
2
4
2
d ⌸ state has a bond length very close to its value in the
pling term between the d ⌸ and B ⌺Ϫ states to be about
2
4
ground state. Furthermore we have already noted the simi-
larity in bond length in the d ⌸ and a ⌺Ϫ states, i.e.,
2
2
30 cmϪ1 with the deperturbed d ⌸ state lying below the
2
2
4
a ⌺Ϫ and X ⌺Ϫ have essentially the same rotational and
4
B ⌺Ϫ state.
vibrational characteristics ␻(X ⌺Ϫ)Х␻(a ⌺Ϫ)Х1000
4
2
͓
cmϪ1] which lends strong support to our assertion that these
two states arise from the same electron configuration, namely
1␦29␴1.
C. The Franck–Condon patterns seen in the
dispersed fluorescence spectra from the B
4
؊
⌺
and
d
2⌸ states
Franck–Condon patterns were studied in detail in three
D. The rotational analyses of selected bands of the
B–X and d–X spectra
separate DF experiments: ͑i͒ where the excitation laser was
4
tuned to populate the ϭ0, 1, 2, 3, and 4 levels of the B ⌺Ϫ
v
4
؊
1. The (1,0) band of the B 4⌺؊—X
⌺
system
state; ͑ii͒ where the excitation laser was tuned to populate the
2
ϭ0, 1, and 2 levels of the d ⌸1/2 substate; and; ͑iii͒ where
This band is identified with a strong, relatively unper-
turbed band, centered near 473 nm. Its structure is that of a
v
the excitation laser was tuned to populate the ϭ0 and 2
v
2
4
levels of the d ⌸3/2 substate.
typical 4⌺Ϫ← ⌺Ϫ transition, where the combining states
The results from the first of the three experiments are
belong closely to Hund’s coupling case ͑b͒ and four R and
four P branches are expected. The band is degraded towards
the red, making the region of the R-branches somewhat con-
gested ͑Fig. 6͒. However, the P-branch region is well re-
solved and at sufficiently high rotational quantum number
displayed in Fig. 5. The data cover ϭ0–4 in the B state
v
and ϭ0–8 in the ground state. Calculated Franck–Condon
v
values have been obtained using a simple harmonic oscillator
model and, despite the fact that the experimental spectra
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4476
obtained in the A–X analysis; our Franck–Condon analysis
provided an estimate for the rotational constant B in the up-
per state; and trial values of ␥ and ␭ were used. The re-
Ј
Ј
sulting simulation produced a spectrum in qualitative agree-
ment with the observed one and permitted us to identify and
number the four P-branches at high N. These initial assign-
ments were then used as input in a least-squares fitting pro-
gram to give a set of improved spectroscopic parameters for
4
the B ⌺Ϫ state and additional line assignments. The cycle
of simulation and least-squares fitting was repeated until
eventually 116 lines with N р21 were included with a root-
Љ
mean-square deviation less than 0.08 cmϪ1. Some weak fea-
tures were not used in the fit. The transitions responsible are
believed to be associated with weak satellite branches not
4
4
allowed in pure case ͑b͒. The B ⌺Ϫ←X ⌺Ϫ(1,0) line as-
signments are given in Table I.
4
4
FIG. 6. ͑a͒ The observed CrN B
⌺ ⌺
Ϫ –X Ϫ(1,0) band near 473 nm and
its rotational assignments; ͑b͒ the computer simulation.
4
؊
2. The d 2⌸—X
⌺
bands
Two subbands belonging to the d ⌸←X ⌺Ϫ transition
2
4
2
(N Ͼ10) the four individual P branches are distinguishable.
have been rotationally analyzed, one involving the d ⌸3/2
Љ
4
4
2
A ⌺Ϫ← ⌺Ϫ simulation program was written to aid in ro-
component and one involving the d ⌸1/2 component. The
4
tational analysis. The ⌺Ϫ Hamiltonian is written using the
bands lie close to 482.0 and 466.3 nm, respectively, and
were chosen because they appeared relatively less perturbed.
following definition of parameters (NϩSϭJ),
4
Spectra of 2⌸← ⌺Ϫ transitions have been observed and
HϭTϩBN2ϩ␥N–Sϩ 2/3͒␭ 3S2ϪS2͒.
͑
͑
analyzed in several molecules.27,28 The appearance of
z
2
4
Centrifugal distortion terms were neglected since the super-
sonic jet-cooling restricted observations to Nр21. Matrix
elements for this Hamiltonian have been given by Cheung,
Taylor, and Merer.26–28
d ⌸←X ⌺Ϫ bands in CrN is very similar to that of the
A ⌸←X ⌺Ϫ transition, except only two spin–orbit com-
ponents are present. Twelve branches can be expected for
each subband. The analyses were carried out using programs
4
4
4
4
Our fitting process was similar to that used successfully
written to treat the A ⌸←X ⌺Ϫ transition, appropriately
4
4
to analyze bands in the corresponding A ⌸←X ⌺Ϫ sys-
modified with respect to ⌳-doubling in the case ͑a͒ upper
29
2
tem. Parameters for the lower state were fixed at the values
d ⌸ state.
4
Ϫ
4
Ϫ
TABLE I. Assigned lines of the CrN B
⌺
←X
⌺
͑1,0͒ band ͑values in cmϪ1͒.
R1 R2
P1
P2
P3
P4
R3
R4
N
Љ
0
1
2
3
4
5
6
7
8
21 132.37 21 130.70
21 135.93
136.64
137.18
130.93
129.41
127.71
125.75
123.65
121.37
118.87
116.15
113.21
110.22
106.97
103.58
99.93
129.63 21 131.95
128.38
127.00
125.21
123.20
120.97
118.52
115.84
112.94
110.04
106.75
103.27
99.62
130.12
128.25 21 129.41
126.19
123.96
121.55
118.87
116.15
113.21
110.04
106.75
103.27
99.62
127.00
124.45
121.82
137.31
136.91 21 136.64
119.05 21 137.00 21 136.91
9
116.15
112.94
109.95
106.48
102.91
99.17
95.26
91.16
86.89
82.44
77.82
72.98
68.05
136.55
135.80
134.86
133.83
136.29
135.57
134.59
133.56
132.27
130.70
129.23
127.35
125.21
122.98
120.61
136.29
135.57
134.59
133.43
132.13
130.70
128.92
127.00
125.03
122.62
135.93
135.04
134.05
132.85
131.42
10
11
12
13
14
15
16
17
18
19
20
21
96.15
95.83
95.74
91.69
87.47
83.07
78.53
73.78
68.80
92.14
91.87
87.96
87.69
83.64
83.33
79.07
78.80
74.35
74.09
69.47
69.25
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4477
2
4
Ϫ
TABLE II. Assigned lines of the CrN d
⌸
3/2←X
⌺
͑0,0͒ band ͑values in cmϪ1͒.
pP33 oP34
N
tR31
sR32
rR33
qR34
qQ33
pQ34
Љ
0
20 745.20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
748.08 20 740.46 20 733.11
750.93
753.98
756.96
759.89
762.91
765.88
768.82
771.79
774.77
777.71
780.64
783.58
741.45
742.79
744.29
745.89
747.57
749.16
750.79
752.61
754.33
756.01
757.73
759.41
761.14
762.81
764.50
766.18
767.86
769.54
771.14
772.78
774.42
776.06
734.05 20 733.11
20 730.96
730.49 20 730.70
730.01
729.45
728.85
734.83
735.60
736.29
736.94
737.54
738.14
738.70
739.30
739.86
740.37
740.89
741.45
741.92
742.40
733.81 20 727.39
734.05
733.80
733.54
733.11
732.55
731.94
731.35
730.70
730.01
729.33
728.51
727.78
726.96
726.36
725.67 20 726.57
729.67
728.34
726.70
725.03
723.22
721.33
719.57
717.64
715.75
723.87
721.98
720.13
718.20
716.35
714.42
712.49
710.56
708.63
706.66
704.68
702.67
700.65
698.59
723.87
721.12
718.20
715.15
712.06
708.97
705.84
702.67
699.50
711.84
709.95
707.77
705.84
2
2
2
⌸
⌸
F ͒: F J ͒ϭT ϩB J J ϩ1͒ϪD J
͓ ͑
Ј Ј Ј
J ϩ1͒
0.072 cmϪ1 ͑Fig. 8͒. Table III contains the line assignments.
͑
͑
͑
͑
͔
Ј
Ј Ј Ј
3/2
3
3/2
The effective B1/2 of this band is 0.6188 cmϪ1, which is very
ϮB q J Ϫ0.5͒ J ϩ0.5͒
͑
͑
Ј
Ј
Ј
2
close to that anticipated for the d ⌸1/2( ϭ1) level. As is
v
normally the case for 2⌸1/2 states, the ⌳ doubling was found
to be significant (pϭϪ0.0062 cmϪ1). A summary of spec-
troscopic constants for the observed states of CrN is given in
Table IV.
ϫ J ϩ1.5͒/ AϪ2B ͒,
͑1͒
͑
͑
Ј
Ј
2
F ͒: F J ͒ϭT ϩB J J ϩ1͒ϪD
J J ϩ1͒
͓ ͑
Ј Ј Ј
͑
͑
Ј Ј Ј
͔
Ј
1/2
2
1/2
Ϯ0.5 pϩ2q͒ J ϩ0.5͒.
͑2͒
͑
͑
Ј
2
2
The notations for ⌸3/2(F3) and ⌸1/2(F2) are the same as
IV. DISCUSSION
those used by Merer.27
A. Equilibrium constants and the bonding of the
The d ⌸3/2←X ⌺Ϫ(0,0) band was analyzed first. Its
observed line positions and assignments are shown in Fig. 9
and listed in Table II. No significant ⌳-doubling was found
͑i.e., qϭ0͒, and 117 lines with Jр25.5 were fitted ͑r.m.s.
deviation Ͻ0.058 cmϪ1͒ to yield a value for the effective
rotational constant B3/2ϭ0.6210 cmϪ1. For a 2⌸ state the
Beff is approximately given by B 1ϮB/A , where A is the
2
4
4
؊
d
2⌸ and B
⌺
states
Rotational analysis establishes the equilibrium bond
4
length in the B ⌺Ϫ state as 0.1694 nm. We note that the
estimate obtained from a consideration of the Franck–
Condon activity in the B–X DF spectra is in excellent agree-
ment with this. The bond length in B ⌺Ϫ is considerably
4
͓
͖
2
4
spin–orbit coupling constant. In the d ⌸ state of CrN, we
estimate A to be about 250(Ϯ20) cmϪ1. It follows, allowing
for a slight variation of B with vibrational quantum numbers
longer than that in either the ground state or A ⌸ state ͑an
increase of ϳ6%͒. The A state arises from a 4␲←9␴ elec-
tron promotion, the B state from a 10␴←9␴ electron pro-
motion. The CrN 4␲ orbital comes predominantly from Cr
4p orbitals and is essentially nonbonding; the 10␴ orbital has
mixed s– p character. In the isoelectronic molecule VO, the
s– p mixing in the 10␴ orbital is sufficiently large that the
(␣e of the order of 0.003 cmϪ1), that B1/2 , the effective
2
value in the d ⌸1/2( ϭ0) level, should be about
v
0.619 cmϪ1. However, attempts to fit the ͑0,0͒ band of the
d ⌸1/2←X ⌺Ϫ system gave
a
B
value of about
Ј
2
4
4
0.568 cmϪ1 and a large deviation for the fit ͑r.m.s.
X ⌺Ϫ(␦2␴1) state has a sizable Fermi contact parameter
ϳ0.1 cmϪ1͒. Clearly the ϭ0 level of the d state is strongly
bF. The observation of a greater bond length for the B state
is an indication of a significant degree of anti-bonding char-
acter in the 10␴ orbital. This is as expected, for the result of
the s– p mixing is that the 10␴ orbital is slightly polarized,
pointing towards the negative nitrogen ligand and the repul-
sive ligand field interaction will act to raise the 10␴ orbital
v
v
perturbed by the nearby ϭ0 level of the B state, such that
its observed B value is a rough average of the values asso-
Ј
ciated with the parent, unperturbed B ⌺Ϫ and d ⌸ states.
4
2
In contrast no such difficulty was encountered in treat-
ment of the d ⌸1/2←X ⌺Ϫ(1,0) band, where a fit of 101
2
4
2
1
lines with Jр21.5 yielded a root-mean-squares deviation of
energy. The d ⌸ state is derived from the same 1␦24␲
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4478
2
4
Ϫ
TABLE III. Assigned lines of the CrN d
⌸
1/2←X
⌺
͑1,0͒ band ͑values in cmϪ1͒.
N
sR21
rR22
qR23
pR24
qP21
pP22
oP23
nP24
Љ
0
21 440.58
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
443.43 21 435.43
21 436.08
436.58 21 429.42
446.33
449.28
452.22
455.17
458.12
461.02
464.01
466.92
469.82
472.68
475.59
478.45
435.99
436.95 21 430.24 21 429.23
436.95
437.50
437.96
438.47
438.93
439.34
439.80
440.22
440.58
441.04
441.46
441.96
442.28
442.70
428.22 21 422.71
438.24
439.66
441.23
442.88
444.49
446.15
447.76
449.28
451.03
452.68
454.34
430.89
431.57
432.22
432.77
433.41
429.42
429.23
428.82
428.36
427.76
427.21
426.43
425.74
425.01
424.23
423.54
427.21
426.29
425.42
424.59
423.77
422.94
422.11
421.29
420.46
419.59
421.06 21 421.98
419.22
417.39
415.51
413.58
411.65
409.68
407.71
405.65
419.36
416.52
413.58
410.51
407.39
404.27
401.11
397.95
394.75
391.50
388.20
384.95
381.66
378.41
375.03
434.33
4
configuration as the A ⌸ state and this is reflected in almost
significantly different is evident from the markedly different
A values for the A ⌸ and d ⌸ states. This difference de-
4
2
identical bond lengths for these two states. A similar state-
ment applies to the related a ⌺Ϫ and X ⌺Ϫ states.
serves further comment.
2
4
2
1
Two states of ⌸ symmetry arise from the 1␦24␲ con-
figuration ͑see Fig. 1͒. The wave functions of these two
states can be constructed in the form of Slater determinants
using the following basis sets:31
B. Spin–orbit coupling and the d 2⌸ state
The doublet and quartet components of the LIF spectrum
of the B ⌺Ϫ( ϭ0)ϩd ⌸
(
ϭ0)←X ⌺Ϫ transitions
4
2
4
v
v
Ј
Ј
1/2
2
Ϫ1/2
͉
⌸
1͒ ϭ 2͒
͉
␦ϩ␣␦Ϫ␣␲ϩ␤
͉
Ϫ
͉
␦ϩ␣␦Ϫ␤␲ϩ␣
͉
,
͑
3/2
͑
͓
͔
͘
can be separated by careful monitoring of emissions to dif-
͑3a͒
2
ferent lower levels. Such experiments place the d ⌸1/2
(
v
Ј
ϭ0)←X ⌺Ϫ subband at 488.5 nm. Another weak band is
͉
⌸
1͒ ϭ 2͒
͉
␦ϩ␤␦Ϫ␣␲ϩ␤
͉
Ϫ
͉
␦ϩ␤␦Ϫ␤␲ϩ␣
͉
,
4
2
Ϫ1/2
͑
1/2
͑
͓
͔
͘
͑3b͒
observed near 482.0 nm, which it is natural to assume is the
2
4
related d ⌸3/2
(
ϭ0)←X ⌺Ϫ transition. These transition
v
Ј
and
assignments give an estimate for the spin–orbit constant A in
2
Ϫ1/2
͉
͉
⌸
⌸
2͒ ϭ 6͒
2͉ ͉
␦ϩ␤␦Ϫ␣␲ϩ␣
the d ⌸ state of 250(Ϯ20) cmϪ1. It may be noted that this
2
͑
͑
͓
͘
3/2
4
value is considerably larger than that observed for the A ⌸
Ϫ
͉
␦ϩ␣␦Ϫ␣␲ϩ␤
͉
Ϫ
͉
␦ϩ␣␦Ϫ␤␲ϩ␣
͉
͉
, ͑4a͒
͔
͔
state (73.5 cmϪ1) which arises from the same electron con-
2
Ϫ1/2
2͒ ϭ 6͒
Ϫ2
͓
͉
␦ϩ␣␦Ϫ␤␲ϩ␤
␦ϩ␤␦Ϫ␤␲ϩ␣
͉
figuration (1␦24␲1) as the d ⌸ state. As was pointed out in
͑
1/2
͑
2
͘
discussion of the A–X system,1 the spin–orbit coupling con-
ϩ
͉
␦ϩ␤␦Ϫ␣␲ϩ␤
͉
ϩ
͉
.
4
stant for the A ⌸ state can be attributed largely to a p
electron of Cr. That the situation in the d ⌸ state must be
2
͑4b͒
4
2
Ϫ
TABLE IV. Spectroscopic constants for the CrN: B
⌺
Ϫ, d 2⌸, and a
(106)D
⌺
states ͑values in cmϪ1͒.
States
T
B
␭
␥
Deviation
0.080
4
Ϫ
B
a
X
⌺
( ϭ1)
21 133.99͑7͒
ϳ6000
0.5333͑4͒
Ϫ0.69(40)
2.715͑60͒
0.0341͑60͒
v
2
Ϫ
⌺
( ϭ0)
v
⌺
( ϭ0)a
0
T
0.6259͑8͒
B
•••
(106)D
•••
•••
•••
•••
•••
2.0͑60͒
2.628͑82͒
p
•••
Ϫ0.006(15)
•••
0.005͑30͒
0.042͑10͒
Ϫ0.035(25)
0.005͑8͒
4
Ϫ
v
q
•••
•••
Deviation
0.058
0.072
2
2
d
d
A
A
A
A
⌸
⌸
( ϭ0)
20 737.17͑5͒
21 431.33͑7͒
13 639.98͑9͒
13 559.61͑15͒
13 485.37͑5͒
13 419.52͑9͒
0.6210͑3͒
0.6188͑6͒
0.6216͑6͒
0.6123͑10͒
0.6040͑4͒
0.5924͑11͒
v
3/2
1/2
5/2
3/2
1/2
( ϭ1)
v
⌸
⌸
⌸
⌸
( ϭ0)a
4
v
( ϭ0)a
4
v
( ϭ0)a
4
4
v
( ϭ0)a
v
Ϫ1/2
aValues are quoted from Ref. 1 for comparison. Numbers in parentheses are one standard deviation.
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4479
2
2
2
The observed ⌸ states ͓we label them ⌸(A) and ⌸(B)͔
are the linear combination or mixing of the two sets of eigen-
functions. They can be written as
2
2
2
͉
⌸
A͒ ϭC
͉
⌸
1͒ ϩC
͘
͉
⌸
2͒
͑
͑
͑
͘
͘
⍀
1A
⍀
2A
⍀
⍀ϭ1/2,3/2͒
͑5a͒
͑
and
2
2
2
͉
⌸
B͒ ϭC
͉
⌸
1͒ ϩC
͑
͘
⍀
͉
⌸
2͒
͑
͑
͘
͘
⍀
1B
2B
⍀
⍀ϭ1/2,3/2͒.
͑5b͒
͑
2
If we assign one of them, 2⌸(A), as the d ⌸ state, then, we
can write
2
1
2
2
͉
d ⌸⍀ 1␦24␲ ͒ ϭC
͉
⌸
1͒ ϩC
͘
͉
⌸
2͒
͑
͘
⍀
͑
͑
͘
1
⍀
2
⍀ϭ1/2,3/2͒.
͑6͒
͑
FIG. 7. Perturbations between vibronic levels in the A 4⌸, d 2⌸, and
4
Ϫ
The mixing coefficients C1 and C2 can be estimated from the
magnitude of the d ⌸ state spin–orbit splitting.
B
⌺
states.
2
The spin–orbital coupling operator is
Hsoϭ⌺ a l s ϩ 1/2͒⌺ a lϩsϪϩlϪsϩ͒.
͑7͒
4
tion pushes down the A ⌸3/2 substate by 6.88 cmϪ1 and the
͑
͑
i
i
i iz iz
i i
i
i
i
A ⌸1/2 substate by 7.63 cmϪ1 from their unperturbed posi-
4
2
For the d ⌸ state
d2⌸ Hso d2⌸3/2
tions ͑Fig. 7͒.
͉
͉
͗
͘
3/2
The diagonal elements and eigenvalues of the Hamil-
tonian matrix for A ⌸ are
4
ϭC21 d2⌸ 1͒
͉
Hso
͉
d2⌸3/2 1͒
͑
͑
͗
͘
3/2
AH3/2,3/2ϭ13 566.5 cmϪ1
AH1/2,1/2ϭ13 493.0 cmϪ1 unperturbed positions͒,
,
ϩC22 d2⌸ 2͒
͉
Hso
͉
͉
d2⌸3/2 2͒
͑
3/2
͑
͗
͘
͑
ϩ2C1C2 d2⌸ 1͒
Hso d2⌸3/2 2͒
͉
͑
͘
͑
͗
A
3/2
␭
␭
3/2ϭ13 559.6 cmϪ1
1/2ϭ13 485.4 cmϪ1
,
ϭA d2⌸͒/2,
͑8͒
A
͑
observed positions͒.
͑
2
2
which, with the following substitutions:
If we assume that d ⌸3/2 and d ⌸1/2 are pushed up from
their unperturbed positions by the same amounts, respec-
tively, we can also find the diagonal elements and eigenval-
d2⌸ 1͒
͉
͉
͉
Hso
Hso
Hso
͉
͉
͉
d2⌸3/2 1͒ ϭa ,
͑9a͒
͑9b͒
͑
͑
͗
͗
͗
͘
3/2
␦
d2⌸ 2͒
d2⌸3/2 2͒ ϭϪa ϩa /3,
͑
͘
␦ ␲
2
͑
3/2
ues of the Hamiltonian matrix for d ⌸ to be
dH3/2,3/2ϭ20 730.3 cmϪ1
,
d2⌸ 1͒
d2⌸3/2 2͒ ϭ 12͒
2a ϩa ͒, ͑9c͒
͑
␦ ␲
Ϫ1/2
͑
3/2
͑
͑
͘
dH1/2,1/2ϭ20 457.5 cmϪ1 unperturbed positions͒,
͑
gives
d
␭
␭
3/2ϭ20 737.2 cmϪ1
1/2ϭ20 465.1 cmϪ1
,
2
1
2
2
Ϫ1/2
a C ϩ Ϫa ϩa /3͒C ϩ 3͒
2a ϩa ͒C C
␦ ␲ 1 2
͑
͑
͑
␦
␦
␲
d
observed positions͒.
͑
ϭA d2⌸,1␦24␲ ͒/2.
͑10͒
1
͑
Because the spin–orbit interaction is diagonal in the 2ϫ2
matrix for each ⍀ value, we may use the diagonal matrix
elements and eigenvalues above to calculate the off-diagonal
elements as
We know, from a study of the A–X system that the spin–
4
orbit coupling in the A ⌸ state comes mainly from a of
␲
the Cr atom and hence30 A(A ⌸,1␦24␲1)ϭa /3
4
␲
ϭ73.5 cmϪ1, i.e., a ϭ220.5 cmϪ1. Also, since the CrN 1␦
␲
2
4
d ⌸
͉
3/2
HSO
͉
A ⌸3/2
͗
͘
orbital is predominately a 3d atomic orbital in Cr, we can
take the ␨ Cr(3d) ϭ243 cmϪ1 as the value31 of a␦ . These
͓
͔
2
2
d
2
ϭ
␭
3/2ϪA␭ ͒2Ϫ dH32/2,3/2ϪAH32/2,3/2
͒
1/2/2
͓͑
͑
͔
3/2
considerations give two solutions ͑assuming the larger coef-
ficient to be positive͒:
ϭϮ220 cmϪ1
,
͑11a͒
C1ϭ0.9718, C2ϭϪ0.2358 or
C1ϭ0.5225, C2ϭ0.8523.
2
4
d ⌸
͉
HSO
͉
A ⌸1/2
͗
͘
1/2
2
2
1/2
1/2ϪA␭ ͒2Ϫ dH12/2,1/2ϪAH12/2,1/2
͒
1/2/2
d
2
ϭ
␭
͓͑
͑
͔
4
2
We next consider the perturbation between A ⌸ and d ⌸
ϭϮ230 cmϪ1
.
͑11b͒
4
4
states. The A ⌸1/2 and A ⌸3/2 substates are perturbed by
remote states,1 most likely through spin–orbit coupling to
the d ⌸ state. Careful inspection shows that this perturba-
These two matrix elements should be the same.32 Agreement
between the two experimental estimates is most satisfactory.
2
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4480
4
Ϫ
TABLE V. Hamiltonian matrix elements of B
⌺
and d 2⌸ in a case ͑a͒ basis. Note: xϭ(Jϩ1/2)2Ϫ1. ϯ signs refer to the Wang sum and difference
functions; they give the e and f levels, respectively.
Ϫ
3/2
Ϫ
1/2
2
2
4
4
d
⌸
d
⌸
B
⌺
B
⌺
3/2
1/2
Ϫ
3/2
so
4
4
1
2
TBϩ2␭ϩBBx
0
B
B
⌺
⌺
H
(B,d)
3/2
Ϫͱ3x B Ϫ ␥
͕
B
1
Ϫ DB(x2 ϩ 3x)
1
2
Ϫ 2DB x ϯ (J ϩ
)
͔
͖
͓
Ϫ
1/2
Hs1o/2(B,d)
TBϪ2␭ϩBB(xϩ4)ϯ2(BBϪ 1␥2)
0
2
(J ϩ 1) Ϫ DB (x ϩ 4)2 ϩ 3x
͓
2
1
2
2
ϩ 4(J ϩ
)
ϯ 4(x ϩ 4)(J ϩ 12)]
Tdϩ 1Aϩ(Bdϩ 1q)(xϪ1)
Ϫ Dd (x ϩ 1)(x Ϫ 2) ϩ 3
1
4
1
2
1
2
2
2
d
d
⌸
⌸
Ϫͱx B ϩ pϯ q(Jϩ )Ϫ2D x
͓
͔
3/2
1/2
d
d
2
͓
2
͔
SYMMETRIC
TdϪ 1Aϩ(Bdϩ 1q)(xϩ1)ϯ 1p(Jϩ 1)
2
2
2
2
Ϫ Dd (x ϩ 1)(x ϩ 2) Ϫ 1
͓
͔
2
1
2
2
The above result permits a second, independent determi-
nation of the mixing coefficients C1 and C2 of Eq. ͑6͒. There
are two solutions for
͉
d ⌸⍀ 1␦24␲ ͒ ϭ C
͉
⌸
1͒ ϩC
͉
⌸
2͒ ]͉
͑ v
͘ ͘
⍀
͑
͓
͑
͘
͘
1
⍀
2
⍀ϭ1/2,3/2͒.
͑14c͒
͑
SO
3/2
The Hamiltonian matrix elements, mainly from Ref. 28, are
given in Table V.
2
4
H
d,A͒ϭ d ⌸
͉
HSO
͉
A ⌸3/2
͑
͗
͘
3/2
Ϫ1/2
Ϫ1/2
ϭϪ 6͒
2a ϩa ͒C ϩ 18͒
The case ͑a͒ basis functions satisfy the selection rule of
⌬⌳ϭϮ1, ⌬⌺ϭϯ1, ⌬Sϭ1, and ⌬⍀ϭ0. The perturbation
between them is homogeneous and mainly caused by the
spin–orbital coupling. The off-diagonal matrix elements be-
͑
͑
͑
␦
␲
1
ϫ Ϫ6a ϩa ͒C
2
͑
␦
␲
ϭϮ220.
͑12͒
2
4
tween the d ⌸ and B ⌺Ϫ states are
They are C1ϭ0.9774, C2ϭϪ0.2115 and C1ϭϪ0.2231,
C2ϭ0.9748, where the negative sign for H3/2 SO(d,A) has
been chosen to make the larger coefficient positive. The first
set of these coefficients is in good agreement with the values
calculated solely from the observed spin–orbit splitting. We
Ϫ
Ϫ
2
4
2
4
d ⌸
͉
HSO
͉
B ⌺1/2 ϭ d ⌸
͉
HSO
͉
B ⌺3/2 ϭ0,
͗
͘
͗
͘
3/2
1/2
SO
3/2
Ϫ
2
4
H
B,d͒ϭ d ⌸
͒
͉
HSO
͉
B ⌺3/2
͒
͑
͑v
3/2
͑v
Ј
Љ
͗
͘
1
1
2
take an average for the wave functions of d ⌸ states:
ϭ
a
C1Ϫ
C2
͉
ϭ122
͉ ,
v v
Ј Љ
͘
v v
Ј Љ
͗
͘
͗
␲
ͩ
ͪ
2
)
2
1
2
͉
d ⌸⍀ 1␦24␲ ͒ ϭ0.975
͉
⌸
1͒
͑
͑
͘
͘
⍀
͑15a͒
͑15b͒
2
Ϫ0.222
͉
⌸
2͒
⍀ϭ1/2,3/2͒,
͑
͑
͘
⍀
SO
1/2
Ϫ
2
4
H
B,d͒ϭ d ⌸
͒
͉
HSO
͉
B ⌺1/2
͑v
͒
͑
͑v
1/2
Ј
Љ
͗
͘
͑13͒
1
1
1
2
2
which means that d ⌸ is basically from the ⌸(1) part.
ϭ
a
C1Ϫ C2
͉
v v
Ј Љ
͗
͘
␲
ͩ
ͪ
2
2
3
Although only the perturbation from d ⌸ state is consid-
)
ered, and the Franck–Condon factor is not included in the
above calculation, the good agreement in the result obtained
from two different mechanisms shows that the deviation
caused by other perturbations must be minor.
1
SO
3/2
ϭ
H
ϭ70
͉ ,
v v
Ј Љ
͘
͗
)
2
where
͉
͉
͉
is the Franck–Condon factor, which has
been calculated in the harmonic approximation assuming
v v
Ј Љ
͗
͘
␻(d ⌸)ϭ950 cmϪ1
,
␻(B ⌺)ϭ640 cmϪ1
,
B(d ⌸)
2
4
2
C. Perturbation between the d 2⌸ and B 4⌺ states
4
ϭ0.619 cmϪ1, and B(B ⌺)ϭ0.5333 cmϪ1. The results are
given in Table VI. Values for the corresponding perturbation
We have considered the B and d states together in an
attempt to fit the B–X and d–X spectra. The B and d state
wave functions in case ͑a͒ basis can be written as
SO
terms HS3/O2(B,d) and H (B,d) are also listed in Table VI.
1/2
Figure 7 is an energy level diagram showing the relative
positioning of the interacting d and B vibronic states. Similar
interactions are also anticipated for higher vibrational levels.
Ϫ
4
1
͉
͉
B ⌺3/2 1␦210␴ ͒ ϭ
͉
͉
␦ϩ␣␦Ϫ␣␴␣͉ ͉
,
v
͘
͑14a͒
͑
͘
͘
2
4
As may be seen, the d ⌸1/2( ϭ0) and B ⌺Ϫ( ϭ0) levels
v
v
Ϫ
4
1
Ϫ1/2
B ⌺1/2 1␦210␴ ͒ ϭ 3͒
͉
͉
␦ϩ␤␦Ϫ␣␴␣
͉
lie close together, as do the d ⌸3/2( ϭ1) and B ⌺Ϫ(
2
4
͑
͑
͑
͘
͘
v
v
ϭ2) levels. This accounts for the difficulties in the analysis
ϩ
ϩ
͉
͉
͉
͉
␦ϩ␣␦Ϫ␤␴␣
͉
͉
͘
͘
encountered in efforts to treat individual bands associated
4
␦ϩ␣␦Ϫ␣␴␤
)
͉
,
͑14b͒
with these levels. On the other hand, the B ⌺Ϫ( ϭ1),
v
v
͘
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4481
4
Ϫ
TABLE VI. Calculated Franck–Condon factors and the perturbation terms between the B
⌺
and d 2⌸ states.
4
Ϫ
B
⌺
ϭ0
ϭ1
ϭ2
ϭ3
ϭ4
v
v
v
v
v
2
d
⌸
Franck–Condon factors:
ϭ0
ϭ1
ϭ2
0.1518
0.2281
0.2186
0.3386
0.1094
0.0013
0.3142
0.0145
0.1234
0.1525
0.2244
0.0450
0.0387
0.2754
0.0527
v
v
v
Perturbation terms ͓H3/2so(B,d); H1/2so(B,d)͔:
48;27
58;33
57;33
71;41
40;23
4.4;2.5
68;39
15;8.0
43;25
48;27
58;33
26;15
24;14
64;37
28;16
ϭ0
ϭ1
ϭ2
v
v
v
2
2
2
d ⌸3/2( ϭ0), and d ⌸ ( ϭ1) levels, since they lie
ϪX 4⌺Ϫ( ϭ0)͔ and 466.4 nm ͓predominantly d ⌸
(
v
v
v
v
)
1/2
1/2
4
somewhat separated from each other and neighboring levels,
suffer from perturbation to a much lesser degree.
ϭ1)ϪX ⌺Ϫ( ϭ0)͔. The molecular constants (cmϪ1
v
found are, for the B ⌺Ϫ( ϭ1) level: Tϭ21 136.27(10),
4
v
A global fit requires data from the whole range of vibra-
tional levels associated with the d and B states, which is
impractical. Instead we have proceeded by treating together
Bϭ0.5329(6), DϭϪ9(10)ϫ10Ϫ7, ␭ϭ2.911(80), and ␥
2
ϭ␥ ϭ␥ ϭ0.030(8), and for the d ⌸( ϭ1) state: T
v
1
2
ϭ21 554.47(11),
Aϭ250(fixed),
Bϭ0.6201(9),
D
the B ⌺Ϫ and d ⌸ levels of a given as a group, diago-
ϭϪ2.7(1.0)ϫ10Ϫ6, and pϭϪ0.0058(250).
4
2
v
nalizing the appropriate e and f upper level 4ϫ4 matrix, or
where necessary, 6ϫ6 matrix. The eigenfunctions corre-
sponding to the set of fitted parameters were obtained from
the eigenvectors of the matrix and, were used in a simulation
program, assuming that the transition to the ground state
Attempts to achieve a similar fit to the corresponding
v
ϭ0 data have met with less success: A fit to 213 lines gave
an rms deviation of 0.15 cmϪ1. Expansion of the data set to
4
include the B ⌺Ϫ( ϭ1) level gave no significant improve-
v
ment. However, agreement between theory and experiment is
2
2
from the d2⌸ state is totally forbidden. The d ⌸ state bor-
good for the band near 482 nm ͓predominantly d ⌸3/2
4
4
rows intensity from the B ⌺Ϫ state, which involves the
( ϭ0)←X ⌺Ϫ( ϭ0)͔, as may be seen in Fig. 9.
v
v
Ϫ
1/2
33
4
¨
⌺
Honl–London factors between basis functions
⌺
and
The source of the difficulty in the fit of the vϭ0 bands
Ϫ
4
may be traced to interaction from a third state. A system is
observed whose ͑0,0͒ sub-bands lie at 531.6, 533.6, 535.2,
and 536.8 nm. The system is very weak and we have been
unable to record spectra with quality good enough to char-
acterize it. The ͑1,0͒ bands are seen at 507.5, 509.3, 510.8,
and 512.2 nm, and by extrapolation the ͑2,0͒ bands should
fall near 485.4, 487.1, 488.5, and 489.7 nm, precisely the
of the B and ground states, and the Franck–Condon
3/2
factors between the B and X states ͑Fig. 5͒.
4
A very satisfactory fit was obtained for the B ⌺Ϫ(
v
2
ϭ1) and d ⌸( ϭ1) group with 217 lines fitted, with a
v
root-mean-square deviation of 0.076 cmϪ1
. Values for
HS1/O2(B,d) and H (B,d) of 38.0 and 23.8 cmϪ1 were ob-
SO
3/2
tained. Figures 6 and 8 show the assigned experimental spec-
2
4
region covered by the d ⌸1/2( ϭ0)/B ⌺Ϫ( ϭ0)
v
v
tra and the comparison with the calculated profiles for the
4
ϪX ⌺Ϫ( ϭ0) spectra.
4
bands at 473.0 nm ͓predominantly B ⌺Ϫ( ϭ1)
v
v
2
4
2
4
FIG. 8. ͑a͒ The CrN d
⌸
1/2–X
⌺
Ϫ(1,0) band near 482 nm and its rota-
FIG. 9. ͑a͒ The CrN d
⌸
3/2–X
⌺
Ϫ(0,0) band near 482 nm and its rota-
tional assignments; ͑b͒ the computer simulation.
tional assignments; ͑b͒ the computer simulation.
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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Zhou, Balfour, and Qian: B 4⌺ and d 2⌸ states of CrN
4482
ACKNOWLEDGMENTS
We are unable to assign the weak quartet system with
confidence. Its sub-band locations give approximately values
for the spin–orbit splitting and vibrational frequency of 60
and 900 cmϪ1, respectively. No quartet state of suitable en-
Financial support for this research was provided through
operating grants to W.J.B. and C.Q. from the Natural Sci-
ences & Engineering Research Council of Canada and the
University of Victoria. The authors wish to thank Jianying
Cao for helpful discussions and a referee for constructive
comments.
4
4
ergy in CrN other than the A ⌸ and B ⌺Ϫ states is pre-
dicted from the electronic configurations 1␦29␴1,
1␦210␴1, and 1␦24␲1. However, Merer and co-workers
4
have identified three low-lying quartet states, 4⌸ and
⌽
derived from 9␴11␦14␲1, and ⌬ from 9␴11␦110␴ elec-
tronic configurations in the spectra of VO.34 If the weak CrN
system has as its upper state the corresponding 4⌸(␴1␦1␲1),
a question remains as to why the observed transition from
the ground state is so weak.
4
1
1 W. J. Balfour, C. X. W. Qian, and C. Zhou, J. Chem. Phys. 106, 4383
͑1997͒.
2 H. Li, C. M-T. Chan, and A. S-C. Cheung, J. Mol. Spectrosc. 176, 219
͑1996͒.
3 A. J. Marr, M. E. Flores, and T. C. Steimle, J. Chem. Phys. 104, 8183
͑1996͒.
A larger spin–rotation coupling constant ␥ was found for
4
4
the B ⌺Ϫ state than for the ground-state X ⌺Ϫ in the fit-
ting, either when bands were treated individually or together
as a group. The ␥ parameter is actually an effective one since
it includes not only the first order contribution from spin–
rotation interaction HSR, but also second-order contributions
principally from coupling to 4⌸ states (HSOϫHROT).27,31
4 K. Y. Jung, T. C. Steimle, D. Dai, and K. Balasubramanian, J. Chem.
Phys. 102, 643 ͑1995͒.
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6 Y. Azuma, G. Huang, M. P. J. Lyne, A. J. Merer, and V. I. Srdanov, J.
Chem. Phys. 100, 4138 ͑1994͒.
7 K. J. Jung, D. A. Fletcher, and T. C. Steimle, J. Mol. Spectrosc. 165, 448
͑1994͒.
4
4
The A ⌸ state lies much closer to the B ⌺Ϫ state than it
8 R. S. Ram and P. F. Bernath, J. Opt. Soc. Am. 11B, 225 ͑1994͒.
9 R. S. Ram, P. F. Bernath, W. J. Balfour, J. Cao, C. X. W. Qian, and S. J.
Rixon, J. Mol. Spectrosc. 168, 350 ͑1994͒.
does to the X ⌺Ϫ state and a greater second-order contribu-
4
tion to ␥(B ⌺Ϫ) is to be expected. The contribution from
4
10 R. S. Ram and P. F. Bernath, J. Mol. Spectrosc. 165, 97 ͑1994͒.
11 E. J. Friedman-Hill and R. W. Field, J. Chem. Phys. 100, 6141 ͑1994͒.
12 D. A. Fletcher, K. J. Jung, and T. C. Steimle, J. Chem. Phys. 99, 4288
͑1993͒.
͑second order͒ spin–orbit coupling to 2⌺ is not significant at
our experimental resolution and the parameters ␥1 and ␥2 in
Table V were then taken to be identical.
13 W. J. Balfour, A. J. Merer, H. Niki, B. Simard, and P. A. Hackett, J.
Chem. Phys. 99, 3288 ͑1993͒.
A matrix-based fit was also performed for the previously
4
4
analyzed A ⌸←X ⌺Ϫ transition. The procedure gave a
14 D. A. Fletcher, K. J. Jung, and T. C. Steimle, J. Chem. Phys. 99, 901
͑1993͒.
satisfactory fit in terms of standard deviation, yielding the
following ⌳-doubling parameters ͑in cmϪ1͒ for the A ⌸
4
15 R. S. Ram and P. F. Bernath, J. Chem. Phys. 96, 6344 ͑1992͒.
16 B. Simard, H. Niki, and P. A. Hackett, J. Chem. Phys. 92, 7012 ͑1990͒.
17 B. Simard, C. Masoni, and P. A. Hackett, J. Mol. Spectrosc. 136, 44
state: oϩpϩqϭ0.418(30), pϩqϭ9.38(10)ϫ10Ϫ5, and q
ϭ6.78(8)ϫ10Ϫ5. However, as may be observed, these val-
ues do not satisfy the relations p/qϭA/B and p2ϭ4oq, ex-
pected from the ‘‘pure precession’’ approximation, which
assumes the ⌳-doubling to arise from the interaction with a
͑1989͒.
18
¨
Y. Azuma, J. A. Barry, M. P. J. Lyne, A. J. Merer, J. O. Schroder, and J.
´
´
L. Femenias, J. Chem. Phys. 91, 1 ͑1989͒.
19 S. L. Peter and T. M. Dunn, J. Chem. Phys. 90, 5333 ͑1989͒.
20
´
´
´
J. L. Femenias, C. Athenour, K. M. Rao, and T. M. Dunn, J. Mol. Spec-
trosc. 130, 269 ͑1988͒.
4
4
single ⌺ state with an identical potential curve. The A ⌸
state in CrN is influenced by its proximity to both the B ⌺Ϫ
4
21 R. C. Carlson, J. K. Bates, and T. M. Dunn, J. Mol. Spectrosc. 110, 215
͑1985͒.
2
and d ⌸ states. Hence the ⌳-doubling in the A state is not
22 K. Brabaharan, J. A. Coxon, and A. B. Yamashita, Can. J. Phys. 63, 997
simply related to the spin–rotation constant of the B-state.
In conclusion, three new bands in the electronic spec-
trum of CrN have been rotationally analyzed. The upper
͑1985͒.
23
´
´ ´
C. Athenour, J. L. Femenias, and T. M. Dunn, Can. J. Phys. 60, 109
͑1982͒.
4
2
2
states are representatives of ⌺Ϫ, ⌸1/2 , and ⌸3/2 symme-
24 A. E. Douglas and P. M. Veillette, J. Chem. Phys. 72, 5378 ͑1980͒.
25 J. F. Harrison, J. Phys. Chem. 100, 3513 ͑1996͒.
26 A. S-C. Cheung, A. W. Taylor, and A. J. Merer, J. Mol. Spectrosc. 92, 391
͑1982͒.
2
tries. The wave function of the d ⌸ state has been charac-
terized through an analysis of the spin–orbit interactions in-
2
4
27 R. W. Martin and A. J. Merer, Can. J. Phys. 51, 125 ͑1973͒.
28 R. W. Martin and A. J. Merer, Can. J. Phys. 51, 634 ͑1973͒.
29 J. M. Brown and A. J. Merer, J. Mol. Spectrosc. 74, 488 ͑1979͒.
volving the d ⌸ and A ⌸ states. Analysis shows that the
2
spin–orbit coupling in the d ⌸ must involve ␦ and ␲ elec-
trons associated with the Cr atom. The interaction between
30 The a value is slightly different from that used in Ref. 1. This new value
␲
4
2
B ⌺Ϫ and d ⌸ states, and its dependence on the vibra-
is deduced with the effect of 2⌸ and 4⌸ perturbation removed.
31 H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Di-
atomic Molecules ͑Academic, Orlando, 1986͒.
tional quanta can be qualitatively understood from the nature
4
of the spin–orbit coupling and from the fact that the B ⌺Ϫ
32 A. G. Adam, Y. Azuma, J. A. Barry, A. J. Merer, U. Sassenberg, J. O.
2
and d ⌸ states have very different bond lengths. A quanti-
¨
´ ´
Schroder, G. Cheval, and J. L. Femenias, J. Chem. Phys. 100, 6240
͑1994͒.
tative deperturbation analysis was also attempted, but with
limited success due to interactions with a nearby, uncharac-
terized, dark quartet state.
33 R. N. Zare, Angular Momentum ͑Wiley, New York, 1988͒.
34 A. J. Merer, Annu. Rev. Phys. Chem. 40, 407 ͑1989͒.
J. Chem. Phys., Vol. 107, No. 12, 22 September 1997
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