Electronic transition moment of the A2∏r-X2∑+ system of TiN

Article abstract of DOI:10.1016/S0022-2860(02)00036-4

The A²∏_r-X²∑⁺ transition of TiN was observed by the dispersed laser induced fluorescence (DLIF) spectroscopy. The relative intensities of the DLIF spectra were analyzed to determine the dependence of the electronic transition moment, R_e(r), on the internuclear distance, r, as R_e(r) ∝ {1 - 0.281(26)r} (1.380 ? ≤ r ≤ 1.823 ?). This r-dependence was analyzed simultaneously with the reported values of the spin-orbit constants for A²∏_r and the hyperfine-coupling constants for X²∑⁺ to evaluate the ionic character of the Ti≡N bond, the 4s atomic character in the 9σ orbital of X²∑⁺, and the 4p atomic character in the 4π orbital of A²∏_r. These characters were confirmed to be in accordance with the reported theoretical prediction. A strong r-dependence was indicated for the 3d-4p mixing in the A²∏_r state due to the configuration mixing of the Ti(3d⁴) and Ti(3d³4p) states at a large internuclear distance.

Full text of DOI:10.1016/S0022-2860(02)00036-4

Journal of Molecular Structure 641 (2002) 7±15
www.elsevier.com/locate/molstruc
Electronic transition moment of the A2Pr±X2S1 system of TiN
*
Haruhiko Ito , Kei-ichi C. Namiki, Tsutomu Tojo, Yohji Miyamoto, Masami Ohtaka
Department of Chemistry, Nagaoka University of Technology, Kamitomioka 1603-1, Nagaoka 940-2188, Niigata, Japan
Received 23 July 2001; revised 23 January 2002; accepted 23 January 2002
Abstract
The A2Pr±X2S1 transition of TiN was observed by the dispersed laser induced ¯uorescence (DLIF) spectroscopy. The
relative intensities of the DLIF spectra were analyzed to determine the dependence of the electronic transition moment, Reꢀr†;
Ê
Ê
on the internuclear distance, r, as Reꢀr† / {1 2 0:281ꢀ26†r} (1.380 A # r # 1.823 A). This r-dependence was analyzed simul-
taneously with the reported values of the spin±orbit constants for A2Pr and the hyper®ne-coupling constants for X2S1 to
evaluate the ionic character of the TixN bond, the 4s atomic character in the 9s orbital of X2S1, and the 4p atomic character in
the 4p orbital of A2Pr. These characters were con®rmed to be in accordance with the reported theoretical prediction. A strong r-
dependence was indicated for the 3d±4p mixing in the A2Pr state due to the con®guration mixing of the Ti(3d4) and Ti(3d34p)
states at a large internuclear distance. q 2002 Published by Elsevier Science B.V.
Keywords: Radical; Electronic spectroscopy; Laser spectroscopy; TiN; Electronic state
1. Introduction
scopy of the `wavelength axis', studies on the `inten-
sity axis' have been scarce. There has been no report
on the A2Pr±X2S1 electronic transition moment of
TiN. In our series of studies on the CN [15,16], SiN
[17] and AlO [18] radicals, the dependence of the
electronic transition moment, Reꢀr†; on the internuc-
lear distance, r, has been found to be useful to discuss
the electronic structure of the relevant electronic
states. The Reꢀr† function for the A2Pr±X2S1 transi-
tion of TiN is expressed as
Since the ®rst measurement by Dunn et al. [1], a
number of studies have been made on the A2Pr and
X2S1 states of the TiN radical both experimentally
[1±10] and theoretically [11±14]. High-resolution
spectroscopy on the A2Pr±X2S1 transition has
been performed, and the precise molecular
constants for these states have been determined
up to v ˆ 2 [1±6]. Recently, the hyper®ne-coupling
constants for the X2S1, v ˆ 0 level have been
determined quite accurately, from which the elec-
tronic structure such as covalent±ionic bonding
character and the 4s atomic orbital character of
the non-bonding 9s molecular orbital for this
state has been discussed in detail [8].
D
E
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
X
R ꢀr† ˆ A2P
er X2S1
;
ꢀ1†
ꢀ
e
r
i
P
where eri is the operator of the dipole moment.
According to Eq. (1), the r-dependence of the Reꢀr†
function re¯ects the properties of the electronic wave-
functions, uA2Prl and uX2S1l. In addition, the elec-
tronic parts of the spin±orbit constant, Aꢀr†; for the
A2Pr state and the hyper®ne-coupling constants, bF
(Fermi contact) and c (dipolar interaction), for the
In contrast to these extensive studies on the spectro-
* Corresponding author.
E-mail address: bu7dd8@vox.nagaokaut.ac.jp (H. Ito).
0022-2860/02/$ - see front matter q 2002 Published by Elsevier Science B.V.
PII: S0022-2860(02)00036-4

8
H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
P
In Eq. (2), aili´si is the operator of the spin±orbit
interaction. In Eqs. (3) and (4), ri and xi are the polar
coordinates of the ith electron. Hence, Aꢀr†; bF and c
also re¯ect the properties of the relevant electronic
states. Therefore, a simultaneous analysis of Reꢀr†;
Aꢀr†; bF and c will be effective to estimate the r-depen-
dence of the electronic structure.
In the early stages of the present study, the r-depen-
dence of Reꢀr† was obtained from the simulation
analysis of the intensity distribution of the
TiN(A2Pr±X2S1) emission spectrum. However, it
was found that the B2S1±A0 D transition and the
2
quasicontinuous background were overlapping with
the TiN(A2Pr±X2S1) emission spectrum. In parti-
cular, the effect of the background was so serious
for the weak transitions of the Dv ˆ 21 and 22
sequences that the precise evaluation of the intensity
distribution was dif®cult by a spectral simulation.
Therefore, the precision of the resultant Reꢀr† was
seemed to be limited. According to the recent studies
on the SiF(B2S1±X2P, C2D±X2P) [19], CF(A2S1±
X2P) [20], and CH(A2D±X2P, B2S2±X2P) [21,22]
transitions, dispersed laser induced ¯uorescence
(DLIF) spectroscopy has been found to be useful in
order to eliminate the effect of the spectral overlap.
From the above viewpoints, the present study reports
on the r-dependence of Reꢀr† of the A2Pr±X2S1 tran-
sition of TiN radical by use of DLIF spectroscopy and
on an analysis of the orbital character of the unpaired
electron centered on Ti.
Fig. 1. Detailed description of the reaction chamber. MW: micro-
wave discharge, W: quartz window.
X2S1 state have the similar forms as
D
E
ꢀ
ꢀ
ꢀ
ꢀ
X
ꢀ
Aꢀr† ˆ A2P
a l ´s A2P ;
ꢀ2†
ꢀ
r
i i
i
r
D
E
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
X
16p
bF ˆ
gIm0mN X2S1
dꢀr †s X2S1
ꢀ3†
ꢀ
i
iz
3
and
D
E
ꢀ4†
ꢀ
ꢀ
ꢀ
ꢀ
X
c ˆ 3gIm0mN X2S1ꢀ ꢀ3 cos2 xi 2 1†ri23sizꢀX2S1
:
Fig. 2. Schematic diagram of the experimental setup used in the present study. I1, I2: irises, L1, L2, L3: lenses, DP: dove prism, PMT:
photomultiplier, REC: chart recorder.

H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
9
produce the TiN radicals. They were effused into the
chamber, and were excited by the dye-laser beam
from the X2S1 state to the A2Pr state with the
A2Pr±X2S1 LIF signal being monitored. Preceding
the observation of the DLIF spectrum, the pressures
of Ar, N2 and TiCl4 were optimized so that the LIF
signal was maximum. The total pressure (predomi-
nantly Ar) was in the range of 0.6±0.8 Torr.
Fig. 2 shows a schematic diagram of the system to
observe the DLIF spectrum. A pulsed dye-laser
(Quantel TDL-60) excited by the second harmonic
of a Nd:YAG laser (Quantel YG-661-20) was used
to observe the TiN(A2Pr±X2S1) DLIF spectrum.
The wavelength of the dye-laser was 610±670 nm
(DCM) for the observation of the Dv ˆ 0 and 21
sequences and 580±589 nm (Rhodamine 610) for
the Dv ˆ 11 sequence. The power of the dye-laser
beam was typically < 10 mJ/pulse. The dye-laser
beam was introduced into the center of the chamber
through two irises, I1 and I2, and a lens, L1, to mini-
mize undesired stray light due to the laser scattering.
The LIF generated right angle to the laser beam was
introduced into a monochromator (Shimadzu UV-
360) through two lenses, L2 and L3. Between L3 and
the entrance slit of the monochromator, a dove prism,
DP, was set so as the image of LIF generated horizon-
tally along the dye-laser beam was rotated vertically
to coincide with the entrance slit of the monochro-
mator. The band-pass of the monochromator was set
at 8 nm. The DLIF signal was processed by a photo-
multiplier (Hamamatsu R955), two boxcar integrators
(Stanford SR250), and a recorder. The wavelength
dependence of the sensitivity of the detection system
was calibrated using a standard halogen lamp (Ushio
Electric Co.). In the present experiment, the pulsed
DLIF signal was overlapped by a strong plasma emis-
sion which was modulated sinusoidally at 50 Hz due
to the ripple of the microwave generator. In order to
cancel the effect of this background emission, two
boxcar integrators, A and B in Fig. 2, were used.
The sampling gate widths of A and B were set equally
at 15 ms, and the delay of the sampling gate of B to
that of A was set to be 100 ms where the LIF signal
was not detected. The other conditions such as sensi-
tivity and integration time, etc. were set equally for A
and B. Then, the difference, A 2 B, of the integrated
signals was recorded. By use of the above process, the
background signal could be completely eliminated.
Fig. 3. Observed dispersed ¯uorescence spectrum of the TiN(A2Pr±
X2S1) transition. The bandhead of the Q2 ꢀV ˆ 3=2† branch of the
1±0 band was excited by the laser as indicated by an arrow.
2. Experimental
Fig. 1 shows a schematic description of the experi-
mental apparatus to produce the TiN radicals. It
consists of a stainless steel chamber (o.d. 4 in.) and
a glass tubing system (o.d. 15±25 mmB) which are
evacuated by a combination of a mechanical booster
(110 m3/h) and an oil rotary (600 l/min) pumps. A
trace amount of N2 diluted by an excess amount of
Ar was excited by a microwave discharge (2.45 GHz,
100 W) in a quartz tube. Just under the discharge
section, a trace amount of TiCl4 was introduced
through a stainless-steel nozzle (i.d. 1 mmB) to
Table 1
Observed transitions of the DLIF spectrum
Excitationa
DLIFb
Intensity ratioc
1±0
1±1
2±1
2±2
1±1, 1±2
1±0, 1±2
2±2, 2±3
2±1, 2±3
0.04376(34)
0.2769(53)
0.06454(25)
0.2692(39)
a
The vibrational quantum numbers of the bands used for the laser
excitation.
b
The vibrational quantum numbers of the dispersed ¯uorescence
spectrum used for the analysis.
c
The observed intensity ratio of the dispersed ¯uorescence spec-
trum which is the average of intensity ratios of the V ˆ 1=2 and V ˆ
3=2 subbands. Values in parentheses denote the standard errors.

10
H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
0
00
is expressed as
3. Results and analysis
Then, Reꢀr†
v v
0
00
Reꢀr†
/ ‰1 1 a1kv0uruv00l=kv0uv00l
v v
Fig. 3 shows the example of the observed DLIF
spectrum, where the 1±0 bandhead of the Q2 ꢀV ˆ
3=2† branch is excited by the dye-laser. Since the
intensity of the 1±0 band was observed to be affected
by the laser scattering, the intensities of the 1±1 and
1±2 bands were adopted for the analysis. Similar
observations were made for the excitation of the Q1
ꢀV ˆ 1=2† bandhead and for the other combinations of
the vibrational quantum numbers. Table 1 lists the
combinations of the bands excited and analyzed.
Both the Q1 and Q2 excitation spectra were observed
for each combination. The average was taken as listed
in the last column of Table 1 for the intensity ratios for
the Q1 and Q2 excitation spectra which were observed
several times to check the reproducibility. The source
of the errors listed in Table 1 is predominantly the
difference of the intensity ratios between the Q1 and
Q2 excitation.
0
2
00
0
00
¼
1 a2kv ur uv l=kv uv l 1 Š:
ꢀ8†
The vibrational matrix elements, kv0uv00l; kv0uruv00l;
kv0ur2uv00l; ¼ were evaluated by use of the Rydberg±
Klein±Rees (RKR) potentials for the A2Pr and X2S1
states of TiN based on the reported molecular
constants for these states [5]. The coef®cients
a1; a2; ¼ were adjusted. The observed intensity ratios
can be fully reproduced by only one parameter a1 as
ꢀ21
a1 ˆ 20:281ꢀ26† A
;
ꢀ9†
where the value in parenthesis is the standard error.
The effective region of r for Reꢀr† was evaluated on
the basis of the minimum and maximum values of the
r-centroid,
rc ˆ kv0uruv00l=kv0uv00l
ꢀ10†
Analysis of the intensity ratios was made as
described below. The intensity of the DLIF spectrum
for the ꢀn0; v0; J0† ! ꢀn00; v00; J00† transition is expressed
as [23]
as
ꢀ
1:380 A # r # 1:823 A:
ꢀ
ꢀ11†
Our preliminary analysis of the TiN(A2Pr±X2S1)
emission spectrum has provided the a1 value as
h
i
ꢁ
ꢂ
n0v000J0
n000v00J0 0
2
J000
4
0 0 0
In00v J00 / nn v J00 qv v ‰Reꢀr† Š SJ Se nn00v 0J0 ; ꢀ5†
0
00
v0v00
n v J00
ꢀ21
a1ꢀemission† ˆ 20:216ꢀ56† A
;
ꢀ12†
where n, v, J are, respectively, the electronic, 0vibra-
tional, and spin-rotational quantum numbers, nn v J00 is
00
the transition wavenumber, qv v is the Franck±
n00v00J0 0
which is in accordance with the present evaluation
(see Eq. (9)). Furthermore, the error of the a1 value
in Eq. (9) is about half of that in Eq. (12). Thus, the
evaluation of Reꢀr† from the analysis of the DLIF
spectrum is con®rmed to be more precise than that
from the simulation analysis of the emission spec-
trum.
0
0
00
is the vibrational matrix
Condon factor, Reꢀr†
v v
0
element of the electronic transition0 moment, SJJ00 is
n000v 0J0 0
È
the Honl±London factor, and Seꢀnn v J00 † is the sensi-
tivity of the detection system. Since the Q1 and Q2
band heads consisted of several rotational lines were
excited by the laser, the intensit0y ratio of 00the DLIF
spectrum for the transitions ꢀn ; v0† ! ꢀn ; v00† and
ꢀn0; v0† ! ꢀn00; u00† (v00 ± u00) was approximated as
4. Discussion
In this section, Reꢀr†; Aꢀr†; bF and c are analyzed
simultaneously to discuss the electronic structure of
the X2S1 and A2Pr states of TiN. According to Refs.
[11,14], the dominant electronic con®gurations for the
X2S1 and A2Pr states are, respectively,
ꢁ
0 ꢂ
"
#
0
0
4
v00
ꢃ
ꢄ
Ivv00
nvv00
qv v Reꢀr†
2
Se nv
ꢁ
0
00
0
00
00
v v
ꢂ
ˆ
:
ꢀ6†
v0
v0
0
Se nvu00
0
00
0
qv u Reꢀr†
I
n
u00
u00
v u
On the basis of Eq. (6), the dependence of Reꢀr† on r
was determined as follows: Reꢀr† was represented by a
polynomial of r as
ꢀcore†3p48s29s
and
2
ꢀcore†3p48s24p;
¼
Reꢀr† / 1 1 a1r 1 a2r 1
ꢀ7†

H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
11
where
tively, these states are partially ionic. This ionic
nature is caused by the overlap of the contributions
from Eq. (1) the strongly polarized 8s and 3p inner
shell electrons causing the ionic Ti1yN2 bond and
from Eq. (2) strongly back-polarized 9s or 4p valence
electrons [14]. Thus, the radial distribution of the 9s
and 4p electrons are affected by this ionic nature. This
ionic effect was taken account into the modeling of
Reꢀr† by modifying the atomic matrix elements
appearing at the right-hand side of Eq. (18) to the
mixture of the atomic and ionic matrix elements as
ꢀcore† ˆ 1s22s21p43s24s25s26s22p47s2:
Hence, the A2Pr±X2S1 transition of TiN can be
represented essentially as that between the 4p and
9s molecular orbitals. Then, Reꢀr† de®ned by Eq.
(1) can be reduced to be the one-electron integral as
Reꢀr† ˆ k4pum^u9sl;
ꢀ13†
where m^ is the perpendicular component of the
operator of the dipole moment. According to the theo-
retical prediction of Ref. [12], the 4p and 9s orbitals
are essentially the non-bonding and centered on the Ti
nucleus. The squares of the coef®cients of the atomic
orbitals in these molecular orbitals have been calcu-
4p
4p
9s
4s
Reꢀr† < C ꢀr†C ꢀr†{‰1
2 Cionꢀr†Šk4ppꢀTi†um^u4ssꢀTi†l
1 Cionꢀr†k4ppꢀTi1†um^u4ssꢀTi1†l}
2
2
2
lated to be uC49ssu ˆ 0:82; uC u ˆ 0:16; uC44ppu ˆ
9s
4p
0:81 and uC34dpu2 ˆ 0:18 at the equilibrium internuclear
distance of the individual state, where the contribution
of the 3ds(Ti) atomic orbital in the 9s molecular
orbital has been predicted to be negligibly small,
uC39dsu2 ˆ 0:03: Thus, the observed r-dependence of
4p
9s
1 C ꢀr†C ꢀr†{‰1
3d
4p
2 Cionꢀr†Šk3dpꢀTi†um^u4psꢀTi†l
1 Cionꢀr†k3dpꢀTi1†um^u4psꢀTi1†l};
ꢀ19†
9s
4s
9s
4p
Reꢀr† can be interpreted in terms of C ꢀr†; C ꢀr†;
4p
4p
4p
C
ꢀr† and C ꢀr†: Accordingly, the 4p and 9s mole-
3d
where Cion(r) denoted the ionicity of the TiN bonding.
Evaluation of the matrix elements appearing on the
right-hand side of Eq. (19) was made by use of Slater-
type atomic orbitals and orbital exponents for the rele-
vant atomic orbitals of Ti and Ti1 reported in Ref.
[24]. They were found to be
cular orbitals are expressed approximately as
4p
4p
4p
3d
u4pꢀr†l < C ꢀr†u4ppꢀTi†l 1 C ꢀr†u3dpꢀTi†l
and
ꢀ14†
ꢀ15†
9s
4s
9s
4p
u9sꢀr†l < C ꢀr†4ssꢀTi†l 1 C ꢀr†u4psꢀTi†l;
k4ppꢀTi†um^u4ssꢀTi†l ˆ 72:255 a:u:;
k3dpꢀTi†um^u4psꢀTi†l ˆ 70:171 a:u:;
ꢀ20†
ꢀ21†
ꢀ22†
where
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
2
2
ꢀ
and
4p
4p
3d
ꢀC ꢀr†ꢀ 1ꢀC ꢀr†ꢀ ˆ 1
ꢀ16†
4p
k4ppꢀTi1†um^u4ssꢀTi1†l ˆ 72:083 a:u:
and
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
2
2
ꢀ
9s
4s
9s
4p
ꢀC ꢀr†ꢀ 1ꢀC ꢀr†ꢀ ˆ 1;
ꢀ17†
k3dpꢀTi1†um^u4psꢀTi1†l ˆ 70:274 a:u:
ꢀ23†
according to the normalization condition. Based on
the above assumptions, Reꢀr† can be reduced approxi-
mately as
The spin±orbit constant, Av, for A2Pr was analyzed as
described below. The observed values of Av were
taken from Ref. [5]. Using these values, Aꢀr† was
obtained according to the procedure as in Ref. [27].
Aꢀr† was represented by a polynomial of r 2 re as
4p
4p
9s
Reꢀr† < C ꢀr†C ꢀr†k4ppꢀTi†um^u4ssꢀTi†l
4s
4p
3d
9s
4p
1 C ꢀr†C ꢀr†k3dpꢀTi†um^u4psꢀTi†l; ꢀ18†
where k4ppꢀTi†um^u4psꢀTi†l and k3dpꢀTi†um^u4ssꢀTi†l
2
¼
Aꢀr† ˆ a0 1 a1ꢀr 2 re† 1 a2ꢀr 2 re† 1
;
ꢀ24†
vanish due to symmetry.
Since the X2S1 and A2Pr states of TiN have large
dipole moments, 3.56(5) and 4.63(4) D [6], respec-
where re was the equilibrium internuclear distance of
A2Pr. Then, Av was expressed as the vibrational

12
H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
Table 2
Analysis of the spin±orbit constant for TiN(A2Pr)
matrix element of Aꢀr† as
Av ˆ a0
Obs.a
o. 2 c.b
h
i
1 a1 kvuruvl 2 reŠ 1 a1‰kvur2uvk 2 2rekvuruvl 1 re2
156.7666(24)
155.9421(15)
153.0250(20)
2 0.3150
0.5739
¼
2 0.2589
1
;
(25)
a
Observed values taken from Ref. [5].
Differences between the observed and calculated values.
b
where the vibrational matrix elements, kvuruvl etc.
were evaluated by use of the RKR potential of
A2Pr. The observed values of Av were ®tted to Eq.
(25) by a non-linear least-squares analysis with
a0; a1; ¼ as parameters. In the present analysis, they
are ®tted satisfactorily with Aꢀr† being the ®rst-order
polynomial of r as
because the angular expectations for 4ss and 4ps are
0 and 4/5, respectively. The c constant was approxi-
mated according to the extended free-atomic compar-
ison method [25] as
o
ꢀ
ꢀ2
ꢀ
c ˆ 12 C 9sꢀr†
6
5 f
j
4s
Aꢀr† ˆ 157:8ꢀ8† 2 177ꢀ46†ꢀr 2 re†:
ꢀ26†
n
o
 ꢀ1 2 Cionꢀr††a ꢀTi† 1 Cionꢀr†a ꢀTi1† ; ꢀ29†
12
4p
12
4p
The result of the above analysis is listed in Table 2. As
indicated in Table 2, the differences between the
observed and calculated values far exceed the errors
of the observed Av values. However, these differences
are within 0.4% of the observed values, which is
considered to be small enough for the present
analysis.
Since the spin±orbit interaction in the A2Pr state is
caused by the unpaired electron in the 4p orbital, Aꢀr†
can be reduced to the one-electron integral as
where a ꢀTi† and a ꢀTi1† were the hyper®ne-
12
4p
12
4p
coupling constants for the 4p orbital of Ti and Ti1,
respectively. They were evaluated as follows. First,
they were predicted by an ab initio calculation at the
Hartree±Fock level according to Ref. [30]. Second,
they were scaled by use of experimental [29] and ab
initio [30] z4p(Ti) and z4p(Ti1) values because both
the znl and a constants are proportional to kr23l.
12
nl
12
These evaluations result in a ꢀTi† ˆ 228:6 MHz
4p
and a ꢀTi1† ˆ 285:1 MHz:
12
4p
Aꢀr† ˆ k4pꢀr†uau4pꢀr†l:
ꢀ27†
Since the Fermi-contact interaction is proportional
to the density of the unpaired electron on the nuclei, bF
re¯ects mainly the 4s character in the unpaired 9s
electron. Therefore bF was approximated according
to the extended free-atomic comparison method [25]
as
According to a similar discussion as in the case of
Reꢀr† described above, Aꢀr† was approximated
according to the extension of the method outlined in
Ref. [28] to include the ionic nature of the bond as
h
i
2
4p
4p
Aꢀr† < C ꢀr† {‰1 2 Cionꢀr†Šz4pꢀTi†
n
o
ꢀ30†
ꢀ
ꢀ
2
ꢀ
ꢀ
b ˆ C9sꢀr† ‰1 2 Cionꢀr†Ša10ꢀTi† 1 Cionꢀr†a10ꢀTi1† ;
ꢀ
ꢀ
F
4s
4s
4s
h
i
2
1 Cionꢀr†z4pꢀTi1†} 1 C ꢀr† {‰1
4p
3d
where a ꢀTi† ꢀˆ 2487 MHz† and a ꢀTi1† ꢀˆ
10
4s
10
4s
2 Cionꢀr†Šz3dꢀTi† 1 Cionꢀr†z3dꢀTi1†};
ꢀ28†
2822 MHz† were the Fermi contact terms for the 4s
orbital of Ti and Ti1, respectively [26]. The bF and c
constants were taken from Ref. [8]. Since these
constants were determined only for v ˆ 0 level of
X2S1, the r appearing in the right-hand sides of
Eqs. (29) and (30) was substituted by re.
where znl(Ti) and znl(Ti1) (nl ˆ 4p or 3d) were the
spin±orbit coupling constants for the nlth orbital of Ti
and Ti1, respectively, as z4pꢀTi† ˆ 130:0 cm21
;
;
z4pꢀTi1† ˆ 389:1 cm21
The hyper®ne-coupling constants for X2S1 were
analyzed as described below. The dipolar interaction
re¯ects the 4p character in the unpaired 9s electron
;
z3dꢀTi† ˆ 82:2 cm21
z3dꢀTi1† ˆ 112:5 cm21 [29].
Based on the formulations outlined above, the
observed values of Reꢀr†; Aꢀr†; bF and c were simul-
taneously analyzed as described below. According to

H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
13
Table 3
Result of the simultaneous analysis of Reꢀr†; A(r), bF and c
and
Cionꢀr† ˆ 0:5505ꢀ23†;
ꢀ33†
a
Reꢀr† (a.u.)b
o. 2 c.c
Ê
r (A)
where values in parentheses are the standard errors.
These errors are considered to be underestimated
because the errors in the orbital exponents, znl values
and the atomic hyper®ne-coupling constants were not
taken into account. The result of the analysis is
summarized in Table 3.
Reꢀr†
1.3796
1.4094
1.6001
1.6087
1.8157
1.8234
1.114
2 0.010
2 0.009
0.001
1.098
0.996
0.990
0.880
0.876
0.001
0.012
0.013
The essential feature of the r-dependence of these
values are summarized in (1)±(3) below.
A(r)
d
Ê
e
r (A)
A(r) (cm21
)
o. 2 c.c
(1) The 4s atomic character in the 9s orbital,
9s
2
uC ꢀr†u ; is estimated to be < 0.83, which is inde-
1.5992
1.6089
1.6207
157.08
155.36
153.28
0.15
0.01
4s
pendent of r. This estimation is in good correspon-
dence with the theoretical prediction, 0.79, with
quite small positive dependence on r [14].
2 0.17
bF and c
(2) The ionic character of the TixN bond is esti-
mated to be < 55%, being in accordance with the
theoretical prediction, 46% [14].
f
Ê
r (A)
bF (MHz)g
2 558.80
o. 2 c.c c (MHz)g o. 2 c.c
0.00 2 15.0 0.0
1.5852
4p
(3) According to Eq. (31), the C ꢀr† value has a
4p
a
The Ti±N inernuclear distance, where the r-centroids of the
TiN(A2Pr±X2S1) transition observed in the present study are taken.
Ê
Normalized at the r-centroid of the 0±0 band, 1.5919 A, of the
TiN(A2Pr±X2S1) transition.
strongly-negative dependence on r, suggesting that
the 3d±4p mixing in the A2Pr state is found to
increase as r increases. A discrepancy has been
found in the 4p atomic character in the 4p orbital
b
c
Difference of the observed and calculated values.
The Ti±N internuclear distance, where the vibrational average
d
2
4p
4p
at r ˆ re: From Eq. (31), the uC ꢀre†u value is
of r at the A2Pr, v ˆ 0; 1 and 2 levels are taken.
estimated to be < 0.34, which is found to be
much smaller than the theoretical prediction, 0.80
[14] (see below).
e
See Eq. (26).
The vibrational average of r at the X2S1, v ˆ 0 level.
f
g
Taken from Ref. [7].
The above results are discussed as described below.
It has been pointed out that the 4s±4p mixing in the 9s
orbital originates in the polarization effect due to the
electrostatic repulsion between the unpaired electron
in the 9s orbital and the negatively-charged N atom
[12±14], being consistent with the ionic nature of the
TixN bond. Hence the results (1) and (2) suggest that
the polarization effect is almost independent of r in the
the normalization conditions in Eqs. (16) and (17), the
9s
4p
adjustable parameters were C ꢀr†; C ꢀr† and Cion(r);
4s
4p
these parameters were expressed as polynomials of
(r 2 re), where re was the equilibrium internuclear
2
ꢀ
distance of A Pr ꢀre ˆ 1:596 A†: Thus, the coef®-
cients of (r 2 re)n ꢀn ˆ 0; 1; 2; ¼† were adjusted by a
non-linear least-squares analysis of the observed
values of Reꢀr†; Aꢀr†; bF and c according to Eqs.
Ê
Ê
range of 1.380 A # r # 1.621 A. Since the TixN
bond in A2Pr is essentially the same as that in X2S1
[14], the polarization effect in the 4p orbital is also
expected to be almost independent of r. This expecta-
(19), (28)±(30). They were satisfactorily ®tted when
4p
4p
C
ꢀr† was assumed to be a ®rst-order polynomial of
(r 2 re) with C49ssꢀr† and Cion(r) being independent of r
as
tion suggests that the origin of the negative depen-
4p
dence of C ꢀr† is not a polarization effect but
4p
4p
4p
C
ꢀr† ˆ 0:582ꢀ1† 2 0:820ꢀ28†ꢀr 2 re†;
ꢀ31†
ꢀ32†
con®guration mixing. The increase in con®guration
mixing in the A2Pr state at large internuclear distance
can be explained along the lines of discussion in Ref.
[12] as follows: The dissociation limit of A2Pr is
9s
C ꢀr† ˆ 0:9123ꢀ5†
4s

14
H. Ito et al. / Journal of Molecular Structure 641 (2002) 7±15
predicted to be either Ti(3d4) 1 N(2p3) or
Ti(3d34p) 1 N(2p3). Since the energy separation
between these limits is quite small ( < 2000 cm21),
a large 3d±4p con®guration mixing is indicated near
the dissociation limit. On the other hand, the energy
separation between the corresponding ionic states,
Ti1(3d3) 1 N2(2p4) and Ti1(3d24p) 1 N2(2p4), is
quite large, < 20,000 cm21. Hence, the 3d±4p
con®guration mixing near the equilibrium internuc-
lear distance is predicted to be quite small because
of the contribution of the ionic (Ti1yN2) bond.
According to the above discussion on the atomic
is evaluated to be strongly-negative r-dependent,
being attributed, according to the reported theoretical
prediction, to the strongly-positive r-dependence of
the 3d±4p mixing in the A2Pr state due to the con®g-
uration mixing between the Ti(3d4) and Ti(3d34p)
states at a large internuclear distance. Thus, the
present method of analysis provides an effective
method to evaluate the polarization and con®guration
mixing effects in the X2S1 and A2Pr states of TiN. A
more quantitative evaluation of these effects will be
possible if more accurate values of the atomic and
ionic spin±orbit constants become available.
con®guration in A2Pr, it is suggested strongly that
4p
the negative r-dependence of C ꢀr† is due to the
4p
Acknowledgements
increase of the 3d±4p con®guration mixing in the
neutral state of the Ti atom as r increases. The
4p
4p
The authors are grateful to Professor Kozo
Kuchitsu for his support and fruitful discussions in
the early stage of the present study. This work was
supported by the Grant-in-Aids for Scienti®c
Research, The Ministry of Education, Science, Sports
and Culture, Japan.
disagreement in the observed and theoretical C ꢀr†
value pointed out in (3) can be ascribed to the over-
estimate of the z4p(Ti1) ( ˆ 389.1 cm21). This value is
much larger than the other znl values (82±130 cm21).
Since this value has been predicted by a single-con®g-
uration Hartree±Fock level calculation [29], the accu-
racy of this value is considered to be limited. If a
smaller value of z4p(Ti1) ( ˆ 200 cm21) is assumed,
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4p
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