The permanent electric dipole moments of chromium and vanadium mononitride: CrN and VN

Article abstract of DOI:10.1063/1.478055

The P_e(1), F = 2.5 branch feature of the (0,0) D ³Π_0e - X ³Δ₁ band system of 51 VN was recorded as a function of an applied static electric field. The resultant Stark splitting and shifts were analyzed giving values of 3.07(7) D and 6.1(4) D for the X ³Δ₁ and D ³Π_0e states, respectively, for the magnitude of the permanent electric dipole moment, <*>μ<*>. Similarly, the R_ee(0.5) branch feature of the (0,0) A ⁴Π_3/2 - X ⁴Σ^- band system of 52 CrN was recorded as a function of an applied static electric field and analyzed to produce <*>μ<*> values of 2.31(4) D and 5.42(2) D for the X ⁴Σ^- and A ⁴Π_3/2 states, respectively. In order to facilitate the dipole moment determinations for 52CrN it was necessary to record and analyze the field free spectrum of the (0,0) A ⁴Π_3/2 - X ⁴Σ^- subband system. A comparison of the dipole moments for the first row monoxides and mononitrides is made and trends are discussed with reference to a molecular orbital correlation scheme.

Full text of DOI:10.1063/1.478055

The permanent electric dipole moments of chromium and vanadium mononitride: CrN
and VN
Timothy C. Steimle, J. Scott Robinson, and Damian Goodridge
Citation: The Journal of Chemical Physics 110, 881 (1999); doi: 10.1063/1.478055
View online: http://dx.doi.org/10.1063/1.478055
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 2
8 JANUARY 1999
The permanent electric dipole moments of chromium and vanadium
mononitride: CrN and VN
Timothy C. Steimle, J. Scott Robinson, and Damian Goodridgea)
Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604
͑Received 10 August 1998; accepted 1 October 1998͒
3
3
The P (1), F ϭ2.5 branch feature of the ͑0,0͒ D ⌸0e –X ⌬1 band system of 51VN was recorded
Љ
e
as a function of an applied static electric field. The resultant Stark splitting and shifts were analyzed
3
3
giving values of 3.07͑7͒ D and 6.1͑4͒ D for the X ⌬1 and D ⌸0e states, respectively, for the
magnitude of the permanent electric dipole moment, ͉␮͉. Similarly, the Ree(0.5) branch feature of
4
4
the ͑0,0͒ A ⌸3/2–X ⌺Ϫ band system of 52CrN was recorded as a function of an applied static
electric field and analyzed to produce ͉␮͉ values of 2.31͑4͒ D and 5.42͑2͒ D for the X ⌺Ϫ and
4
A ⌸3/2 states, respectively. In order to facilitate the dipole moment determinations for 52CrN it was
4
necessary to record and analyze the field free spectrum of the ͑0,0͒ A ⌸3/2–X ⌺Ϫ subband
system. A comparison of the dipole moments for the first row monoxides and mononitrides is made
and trends are discussed with reference to a molecular orbital correlation scheme. © 1999
American Institute of Physics. ͓S0021-9606͑99͒03901-X͔
4
4
I. INTRODUCTION
metal atom and the electron affinity of the ligand. The ionic
contribution should remain fairly constant across the series
of 3-d metal containing molecules owing to the small varia-
tion in ionization potential. Insight into these complex bond-
Establishing the principles responsible for periodic
trends in transition metal bonding is germane to predicting
the chemical behavior of functional groups in organometallic
chemistry. The description of bonding between d-block at-
oms and simple ligands is complex involving simultaneous
formation of highly polar ␴ and ␲-type bonds. The
␲-orbitals can facilitate either charge transfer from the ligand
to the metal ͑␲-donor͒ or from the metal to the ligand ͑␲-
acceptor, back-bonding͒.1 The character of the resulting bond
depends upon the sensitive balance between the destabilizing
loss of exchange energy and energy expended for any pos-
sible s– p–d metal centered hybridization versus the stabi-
lizing energy gained by forming multiple covalent bonds and
the Mϩ-ligandϪ Coulomb attraction. The destabilization due
to loss of exchange energy and hybridization will be strongly
influenced by the relative energies of the (nϪ1)dx, (n
Ϫ1)dxϪ1ns1, (nϪ1)dxϪ2ns2, and (nϪ1)dxϪ2ns1np1 con-
figurations. Promotion from the (nϪ1)dx configuration to
the (nϪ1)dxϪ1ns1 or (nϪ1)dxϪ2ns1np1 configurations
may be energetically favorable since bonding with a
s-electron will result in less exchange energy loss than bond-
ing with a d-electron.2 The energy expended to form hybrid
orbitals may be recouped upon bond formation because of a
more favorable bonding overlap or as a consequence of mini-
mization of nonbonding repulsive interactions. The degree of
stabilization due to multiple covalent bond formation will be
strongly influenced by the relative radial extent of the (n
Ϫ1)d, ns, and np orbitals. The early first row transition
Ϫ
ing facets, particularly the Mϩ-͑ligand͒ charge distribution
and the polarization effects of the valence electrons, is best
surmised from an analysis of trends in experimentally deter-
mined permanent electric dipole moments, ␮.
The first row transition metal monoxides are the most
thoroughly studied set3 of transition metal molecules. Ex-
perimentally derived ground state values of ͉␮͉ for many of
2
the first row monoxides now exist; ScO(X ⌺ϩ)
5
(ϭ4.55 D),4
TiO(X ⌬r)(ϭ2.96 D),
VO(X ⌺Ϫ)
3
4
7
(ϭ3.35 D),6
CrO(X ⌸r)(ϭ2.40 D),
FeO(X ⌬i)
5
5
8
9
2
(ϭ4.7 D), and CuO(X ⌸i)(ϭ4.47 D). The value of ͉␮͉
divided by the internuclear distance, r0 , ͑Ref. 3͒ ͑ScO
ϭ1.668 Å, TiOϭ1.623 Å, VOϭ1.592 Å, CrOϭ1.621 Å,
FeOϭ1.619 Å, and CuOϭ1.729 Å͒, ␮/r0 , ͑ϭ2.73 D/Å
͓ScO͔, 1.82 D/Å͓TiO͔, 2.10 D/Å͓VO͔, 2.39 D/Å͓CrO͔, 2.76
D/Å͓FeO͔, and 2.58 D/Å ͓CuO͔͒ is a more indicative reflec-
tion of the periodic change in bonding. The values of ␮/r0
for the oxides exhibit an abrupt decrease upon going from Sc
to Ti followed by a gradual increase from Ti to Fe. There is
currently insufficient information to establish analogous
trends for the first row mononitrides. Titanium mononitride
is the only first row transition metal mononitride for which
there is an experimental value of ͉␮͉
(ϭ3.56 D).10 Interest-
ingly, the observation that ␮/r0 for TiO ͑ϭ1.79 D/Å͒ is less
than ␮/r0 for TiN ͑ϭ2.25 D/Å͒ is inconsistent with the trend
in electronegativity. This observation must be due to the de-
crease in the 2s and 2p valence orbital energies of O vs
those of N and the fact that the 2s–2p energy separation is
significantly larger in O than in N. The goal of the present
study is to investigate the subtle differences in 3-d transition
metal mononitrides and monoxides as gleaned from a com-
metal elements, for which ns
͉
r
͉
ns / (nϪ1)d͉r͉(nϪ1)d
͘ ͗ ͘
͗
is closest to unity, will exhibit the greatest propensity for
multiple bond formation. The stabilization due to ionic bond
formation will depend upon the ionization potential of the
a͒
Present address: Nobeyama Radio Observatory, Nobeyama, Nagano 384-
13 Japan.
0021-9606/99/110(2)/881/9/$15.00
881
© 1999 American Institute of Physics
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882
J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
parison between the periodic trends in their permanent elec-
tric dipole moments.
Vanadium and chromium mononitrides are good candi-
dates for dipole moment determinations because their optical
spectra have been recorded. The fine and hyperfine structure
3
3
of the D ⌸–X ⌬ band system of VN was analyzed by
Balfour et al.11 The band consists of three strongly allowed
(⌬⌳ϭ⌬⍀ϭϩ1) well-separated subbands as expected for a
molecule in the case a limit. The ⌳-type doubling in the low
3
rotational levels of the D ⌸0 substate is very large ͑Ϸ19
cmϪ1͒ with the D ⌸0e levels being at lower energy than the
3
3
corresponding D ⌸0f levels. The ⌳-type doubling in the
3
3
low-rotational levels of the D ⌸1 and D ⌸2 substates is
significantly less ͑Ͻ1 cmϪ1͒ and is not detectable in the
X ⌬ state. A comparison of the spin–orbit and hyperfine
FIG. 1. A portion LIF spectrum of the ͑0,0͒ A
⌸3/2–X ⌺ band system of
4
4
Ϫ
3
a molecular beam sample of CrN. The nominal 50 MHz linewidth is due to
residual Doppler broadening and unresolved N(Iϭ1) magnetic hyperfine
splitting. The Ree(0.5) branch feature (␯ϭ13567.4305 cmϪ1) was selected
for the optical Stark measurements.
interaction parameters of VN, VO, and Vϩ suggests that VN
is more ionic than VO which is inconsistent with simple
electronegativity arguments. However, the Fermi contact
terms for VO and VN indicate that the valence orbitals of
VN are less polarized than the valence orbitals of VO, which
is in accordance with electronegativity arguments. A com-
parison of the permanent electric dipole moments in the low-
lying states of VN with those for the low-lying states of VO
should provide a more direct gauge of the ionic character and
polarizability.
newly determined values of ͉␮͉ for CrN and VN will serve as
effective tests of the predictive power of the various ab initio
techniques.
II. EXPERIMENT
Two types of measurements were performed; ͑a͒ high
resolution ͑50 MHz FWHM͒ field free laser induced fluores-
The spectroscopy of CrN is less well characterized than
that of VN. Balfour et al.12 have recently reported the first
gas-phase study of CrN. In that work 12 vibronic subbands
4
4
cence ͑LIF͒ of the ͑0,0͒ A ⌸3/2–X ⌺Ϫ band system CrN
and ͑b͒ high resolution LIF measurements for CrN and VN
recorded in the presence of a static electric field. The mo-
lecular beam spectrometer has been described previously.18
The method of molecular production was identical to that
used in the earlier studies by Balfour et al.11,12 Specifically, a
solid 1/4 in. rod of either vanadium or chromium was ablated
with the third harmonic of a Nd:YAG laser. The ablation
plume was entrained in a supersonic expansion of 5% NH3,
95% Ar mixture. The subsequent free-jet expansion was
skimmed to produce a well-collimated molecular beam,
which was crossed approximately 60 cm from the source
with the output of a cw-dye laser. The LIF signal was viewed
through a Ϯ10 nm bandpass filter centered at the excitation
wavelength and processed using gated photon counting tech-
niques. The Stark plates, which straddled the plane defined
by the molecular and laser beams, consisted of one solid
polished stainless steel plate and a metallic neutral density
filter through which the LIF was collected.
4
4
of the A ⌸–X ⌺Ϫ system for the 52Cr14N isotopomer were
recorded at moderate resolution (⌬␯ϭϮ0.2 cmϪ1) and ana-
lyzed to produce a set of fine structure parameters for the
4
4
A ⌸ and X ⌺Ϫ states. In addition, 11 other bands attrib-
uted to vibronic subbands of the B ⌺Ϫ –X ⌺Ϫ and the
4
4
2
4
d ⌸–X ⌺Ϫ systems were identified. More recently the
same authors have recorded the later band systems at mod-
erate resolution and performed a deperturbation analysis.13
They proposed dominant configurations for the X ⌺Ϫ,
4
4
4
2
A ⌸, B ⌺, and d ⌸ states based upon the observed fine
structure parameters. This assessment of the dominant con-
4
tributions predicts that
͉
␮
͉
(X ⌺Ϫ) should be significantly
4
less then ͉␮͉(A ⌸) because the electron is being promoted
from an orbital polarized away from the negatively charged
N center to an orbital that is more localized around the metal
atom.
Kunze and Harrison14,15 have performed detailed ab ini-
tio calculations from which predictions of the properties for
ScN, TiN, VN, and CrN were made. The predicted values for
␮/re are 3.58 D/Å, 2.05 D/Å, 1.80 D/Å, and 1.24 D/Å, re-
spectively. Like the oxides, ␮/re values for the nitrides are
predicted to decrease significantly in going from Sc to Ti.
Unlike the oxides, ␮/re values for the nitrides are predicted
to gradually decrease in going from Ti to Cr rather than
III. OBSERVATIONS
A. Field free LIF of CrN
A prerequisite for the analysis of the optical Stark effect
is a precise determination of the field free energy level pat-
tern. The rerecording and reanalysis of the ͑0,0͒
A ⌸3/2–X ⌺Ϫ subband system of CrN was required be-
cause the previous spectra were recorded at a significantly
lower resolution12 ͑5 GHz FWHM vs 50 MHz FWHM͒. A
portion of the field free LIF spectrum in the region of the
origin is given in Fig. 1. The spectrum is dominated by the
52Cr14N isotopomer, but weak features that exhibit 53Cr (I
ϭ3/2) magnetic hyperfine structure are also evident. Note
2
4
4
increase. The predicted values of ␮/re for TiN(X ⌺ϩ),
which is the most thoroughly studied mononitride, vary con-
siderably depending upon the method of calculation. Mattar
predicted a value of ␮/re of 2.33 D/Å using local density
functional theory.16 Some time ago Bauschlicher predicted a
value of ␮/re of 1.87 D/Å at the complete active space mul-
tireference self-consistent field ͑CASSCF͒ level.17 The
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J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
883
The optical Stark spectrum of the P (1), F ϭ2.5
Љ
that the N(Iϭ1) magnetic hyperfine splitting is not resolved.
As noted in the previous analysis,12 the branch structure is
relatively complex because the rotational levels of the
ee
branch feature, recorded in the presence of an 894.0 V/cm
static field is presented in Fig. 5. The applied static electric
field was oriented parallel to the linearly polarized laser ra-
diation resulting in ⌬MFϭ0 selection rules, where MF is the
projection quantum number of the total angular momentum.
In the presence of the applied electric field the spectral fea-
4
X ⌺Ϫ state are rapidly switching from a case a pattern at
low rotational excitation to a case b limit at intermediate
excitation. This occurs because the spin–spin interaction pa-
rameter, ␭, is only a factor of 4 larger than the rotational
parameter, B. Even so, the low rotational levels, which are
the primary interest here, can be grouped according to the
magnitude of the approximately good quantum number ⍀.
ture splits into six components. ͑One of the ͉MF͉ϭ1.5 fea-
tures is obscured by the field free spectrum in Fig. 5.͒ The
spectra were recorded by momentarily turning the electric
field off while the laser frequency was swept across the field
free spectral region to facilitate an accurate determination of
the splittings and shifts. The predicted energy level pattern
͑see below͒ as a function of applied electric field is given in
Fig. 6. Note that the spectral feature splits into six compo-
4
4
Accordingly, the A ⌸3/2–X ⌺Ϫ subband consist of 6
strongly allowed (⌬⍀ϭ⌬⌳ϭϩ1) branches originating
from the
͉
⍀
͉
ϭ1/2 set of levels and 6 weaker (⌬⍀Þ⌬⌳)
ϭ3/2 set of levels of the
branches originating from the
͉⍀͉
X ⌺Ϫ state. The entire spectral region from 13 549.0 cmϪ1
to 13 578.0 cmϪ1 was recorded in which a total of 98 tran-
sitions, with contributions from all possible 12 branch fea-
tures, were assigned. The observed and calculated transition
frequencies are given in Table I.
4
3
nents due to a first order shift in the X ⌬1 state and the
centroid of this pattern moves to lower frequency due to a
3
second order shift in the D ⌸0 state. The measured posi-
tions relative to the field free feature and the quantum num-
ber assignment are given in Table III.
B. Optical Stark spectra of CrN
In order to achieve the best possible signal to noise ratio,
IV. ANALYSIS
the Ree(0.5) branch feature of the ͑0,0͒ A ⌸3/2–X ⌺Ϫ
band system of 52CrN (␯ϭ13 567.4305 cmϪ1) was selected
for the optical Stark measurements. This is because it is as-
sociated with the levels involving the lowest total angular
momentum quantum numbers. This spectral feature, re-
corded in the presence of a 2042 V/cm static electric field, is
presented in Fig. 2. The applied static electric field was ori-
ented parallel to the linearly polarized laser radiation result-
ing in ⌬MJϭ0 selection rules, where MJ is the projection
quantum number. The predicted energy level pattern ͑see
below͒ as a function of applied electric field is given in Fig.
3. The spectral feature rapidly splits into two components
due to a first order splitting of the degenerate ⌳-doublet in
4
4
A. The field free LIF spectrum of CrN
The analysis of the field free spectrum of the ͑0,0͒
4
4
A ⌸3/2–X ⌺Ϫ band system of 52CrN was identical to that
used for the analogous transition in the isovalent radical
MoN.19 There was no indication of magnetic hyperfine split-
ting, or of ⌳-type doubling in the spectrum. Accordingly, the
4
effective Hamiltonian operator for the X ⌺Ϫ state was taken
as
HeffϭBR2ϪDR4ϩ␥R•Sϩ 2␭ 3S2ϪS2͒
͑1͒
͑2͒
͑
3
z
4
and that for the A ⌸3/2 state as
HeffϭT3/2ϩBR2ϪDR4.
4
the Jϭ1.5 level of the A ⌸3/2 state. The centroid of the
spectrum which moves to higher frequency due to a second
In Eq. ͑1͒ ␥ and ␭ are the spin–rotation and spin–spin inter-
4
order shift of the Jϭ0.5 level in the X ⌺Ϫ state. The mea-
action parameters, respectively. The energy levels of the
4
X ⌺Ϫ state were obtained by numerical diagonalization of a
sured positions relative to the field free feature and the quan-
tum number assignments are given in Table II.
4ϫ4 case a (⌿(case a)ϭ͉n⌳;S⌺;J⍀MJ ) matrix repre-
͘
4
sentation. The energies of the A ⌸3/2 state were obtained by
numerical diagonalization of an 8ϫ8 case a matrix represen-
tation. The origin parameters T5/2 , T1/2 , and TϪ1/2 were held
fixed to their previously determined values12 of 13 639.98
cmϪ1, 13 559.61 cmϪ1, and 13 419.52 cmϪ1, respectively.
The unequal spacing of the sub-states precluded modeling
the origin splittings as a simple spin–orbit interaction. The
transition frequencies were obtained by taking the appropri-
ate combination of eigenvalues. The nonlinear least squares
optimized parameters, associated errors and correlation ma-
trix are given in Table IV. The standard deviation of the fit
(␴ϭ0.0036 cmϪ1) is commensurate with the measurement
uncertainty.
C. Optical Stark spectra of VN
The field free LIF spectrum of the Pee(1) branch feature
3
3
of the ͑0,0͒ D ⌸0 –X ⌬1 band system of 51VN is presented
in Fig. 4. Identification and assignment was readily made
using the results of Balfour et al.11 The branch feature con-
sists of three components due to the 51V (Iϭ7/2) magnetic
3
hyperfine interaction. Specifically, in the X ⌬1 state the J
ϭ1 level is coupled with the nuclear spin to produce three
levels characterized by the total angular momentum quantum
number, F, of 5/2, 7/2, and 9/2. The coupling of the Jϭ0
3
level of the D ⌸0e state with the nuclear spin produces a
single level characterized by Fϭ7/2. The P (1), F ϭ2.5
Љ
ee
branch feature (␯ϭ16 117.8444 cmϪ1) was selected for op-
tical Stark measurements because it arises from levels asso-
ciated with the lowest total angular momentum quantum
numbers and thus will split into the fewest number of com-
ponents upon application of an electric field.
B. The optical Stark spectrum of 52CrN
4
The energies of the Jϭ1.5 rotational level of the A ⌸3/2
state and the Jϭ0.5 rotational level of the X ⌺Ϫ state, in
4
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884
J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
band system of CrN
4
4
Ϫ
TABLE I. The observed and calculated transition energies for the ͑0,0͒ A
͑in cmϪ1͒.
⌸3/2–X ⌺
Branch
J
Observed
Obs.Ϫcalc.
Branch
J
Observed
Obs.Ϫcalc.
Љ
Љ
͉
⍀
͉
ϭ3/2–1/2
Qef
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
13 562.3991
562.1188
562.1306
562.3088
562.5837
562.8842
563.2152
563.5436
563.8706
564.1778
564.4740
564.7513
565.0018
565.2408
565.0456
Ϫ0.0050
0.0033
0.0033
Ϫ0.0010
0.0043
Ϫ0.0059
Ϫ0.0016
Ϫ0.0015
0.0039
0.0018
0.0043
0.0060
0.0008
Rff
7.5
8.5
9.5
573.6131
575.1486
576.6984
0.0028
Ϫ0.0083
Ϫ0.0068
Rce
0.5
1.5
2.5
3.5
13 567.4305
570.1735
573.0026
575.8569
0.0057
0.0003
0.0059
0.0020
͉
⍀
͉
ϭ3/2–3/2
Qef
10.5
11.5
12.5
13.5
14.5
15.5
1.5
2.5
3.5
4.5
13 555.7834
554.7042
553.2844
551.6393
0.0007
Ϫ0.0018
0.0028
0.0021
0.0052
0.0020
Qfe
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
13 556.0338
555.5561
554.9803
554.3550
553.6747
552.9572
552.2004
551.4079
550.5925
0.0002
Ϫ0.0022
Ϫ0.0014
0.0018
Ϫ0.0009
0.0007
Ϫ0.0002
Ϫ0.0032
0.0025
Qfe
1.5
2.5
3.5
4.5
5.5
6.5
7.5
13 567.1192
568.7134
570.3548
572.0035
573.6523
575.2813
576.9143
0.0032
Ϫ0.0033
0.0027
0.0035
0.0047
Ϫ0.0060
0.0001
Pce
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
13 559.0560
557.8450
556.8133
555.8509
554.9389
554.0458
553.1525
552.2480
551.3334
550.4086
Ϫ0.0023
Ϫ0.0022
0.0063
Ϫ0.0029
Ϫ0.0029
0.0000
Rff
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
13 558.8381
558.9830
558.7867
558.3637
557.8038
557.1545
556.4428
555.6798
554.8637
554.0180
553.1367
552.2191
0.0001
Ϫ0.0030
0.0022
0.0009
Ϫ0.0009
Ϫ0.0016
0.0009
0.0010
Ϫ0.0026
Ϫ0.0041
Ϫ0.0002
0.0036
Ϫ0.0037
Ϫ0.0027
Ϫ0.0027
Ϫ0.0067
10.5
11.5
12.5
Pce
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
0.5
1.5
2.5
3.5
4.5
13 565.6560
566.0711
566.4931
566.9288
567.3414
567.7381
568.1284
568.5020
568.8575
569.1809
569.4844
569.7783
570.0384
13 564.9453
565.4613
566.3937
567.6254
569.0402
570.5244
572.0588
Ϫ0.0035
Ϫ0.0010
Ϫ0.0040
0.0068
Rce
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
13 559.0852
559.8303
560.4881
561.0820
561.6203
562.1188
562.5989
563.0272
563.4320
563.7983
564.1465
Ϫ0.0034
Ϫ0.0018
0.0035
0.0024
Ϫ0.0052
Ϫ0.0032
0.0002
0.0032
Ϫ0.0037
Ϫ0.0087
0.0047
Ϫ0.0022
0.0035
0.0053
Ϫ0.0008
Ϫ0.0049
0.0038
0.0019
0.0017
Ϫ0.0015
Ϫ0.0018
Ϫ0.0047
0.0048
Ϫ0.0033
Ϫ0.0023
10.5
11.5
Ϫ0.0058
0.0052
Rff
Pce
Pff
2.5
3.5
13 552.4906
550.6984
Ϫ0.0007
Ϫ0.0033
2.5
13 551.6488
Ϫ0.0001
5.5
6.5
␴ϭ0.0036
the presence of the static electric field, were modeled by
adding to the field free Hamiltonian operators given in Eqs.
͑1͒ and ͑2͒ the operator,
lected case a basis set is block-diagonal in the projection
quantum number MJ but of infinite dimension. The represen-
tation was truncated to include only the Jϭ0.5, 1.5, and 2.5
contributions. The dimension of the representations for the
HStarkϭϪ␮•E.
͑3͒
4
4
͉
MJ
͉
ϭ0.5 levels of the A ⌸3/2 and X ⌺Ϫ states are 20 and
The representation of the Hamiltonian operator in the se-
16, respectively. Stark effect shifts and splittings in the op-
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J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
885
4
4
Ϫ
FIG. 2. The Ree(0.5) branch feature of the ͑0,0͒ A
⌸
3/2–X
⌺
band
system of 52CrN recorded in the presence of a 2042 V/cm static electric
field. The electric field was orientated parallel to that of the linearly polar-
ized laser radiation resulting in ⌬MJϭ0 selection rules.
FIG. 3. The energy levels associated with the Ree(0.5) branch feature of the
4
4
Ϫ
͑0,0͒ A
⌸3/2–X ⌺
band system of 52CrN as a function of applied electric
field. The N(Iϭ1) hyperfine splitting was not resolved at the highest reso-
lution ͑50 MHz͒ and is therefore not indicated. The field free energy level
pattern was predicted using the parameters of derived from the analysis of
the field free spectrum ͑see text͒.
tical spectra, calculated from combinations of predicted en-
4
4
ergy shifts for the A ⌸3/2 and X ⌺Ϫ states were used as
input into a nonlinear least squares fitting routine. The opti-
mized ͉␮͉ values were determined to be 2.31͑4͒ D and
3
ϭ
͉
n⌳;S⌺;J⍀IFMF ) matrix representations for the X ⌬
͘
1
4
4
5.42͑2͒ D and for the X ⌺Ϫ and A ⌸3/2 , respectively.
These results are given, along with the correlation coeffi-
cient, in Table II. The numbers in parentheses represent a
purely statistical 2␴ random error estimate. The systematic
error, which is primarily due to the calibration of the Stark
plate spacing, is estimated to be approximately 3%.
state with ͉MF͉ϭ0.5, 1.5, and 2.5 were 54, 44, and 42, re-
spectively. At low electric field strengths the Jϭ1, Fϭ2.5
3
level of the X ⌬1 state exhibits a linear first order Stark shift
due to the ⌳-doublets degeneracy. At higher fields there is a
TABLE II. Measured and calculated Stark shifts for the Rce(0.5) branch
4
4
Ϫ
band system of 52CrN ͑in MHz͒.
C. The optical Stark spectrum of 51VN
feature of the ͑0,0͒ A
⌸
3/2–X
⌺
3
3
The energies of the X ⌬1 and D ⌸0 states of 51VN in
the presence of a static electric field were modeled by aug-
menting the previously employed effective Hamiltonian
operator11 by that Stark operator of Eq. ͑3͒. The matrix rep-
resentation of the Stark operator is diagonal in MF but of
infinite dimension. The matrix was truncated at a size com-
mensurate with the estimated precision of the measurement
͑Ϸ10 MHz͒. The lower level associated with the Pee(1),
Shifta
Shifta
Field
Field
͑V/cm͒ Observed Obs.Ϫcalc. ͑V/cm͒ Observed Obs.Ϫcalc.
1190.3
1488.4
1786.3
Ϫ575.6
710.1
Ϫ707.5
914.4
Ϫ827.4
1118.2
8.6
Ϫ2.3
3.1
3.6
1.6
1934.7
2042.4
Ϫ884.4
1123.1
Ϫ932.3
1298.1
0.6
0.9
Ϫ7.7
Ϫ1.8
1.5
F ϭ2.5 feature selected for the optical Stark studies is the
Jϭ1 level of the X ⌬1 state ͑see Fig. 6͒. The energies in
Љ
Dipole momentsb
3
4
͉
͉
␮
␮
͉
͉
(X
(A
⌺
⌸
Ϫ)ϭ2.31(4) D
3/2)ϭ5.42(2) D
this state were modeled by considering the electric field in-
duced interaction amongst all the field free levels within the
4
Correlation coefficientϭϪ0.08
3
X ⌬1 substate having Fϭ0.5 through Fϭ4.5. This ac-
aThe first and second entries for a given voltage are associated with the ‘‘A’’
and ‘‘B’’ spectral features of Fig. 2. The shifts are relative to the field free
transition frequency.
counted for interaction amongst the two ⌳-doublets of the
Jϭ1 and Jϭ2 rotational levels and the majority of the con-
tribution from the ⌳-doublets of the Jϭ3 rotational level.
bThe numbers in parentheses represent a 2␴ statistical error estimate. The
systematic errors are estimated to be approximately 3%.
The dimension of the required case a␤ (⌿(case a␤J
)
J
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886
J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
FIG. 4. The field free LIF spectrum of the Pe(1) branch feature of the ͑0,0͒
3
D
3⌸0 –X band system of 51VN. The splitting into three components
⌬
1
characterized by the total angular momentum, F , of 9/2, 7/2, and 5/2, arises
Љ
from the coupling of the 51V(Iϭ7/2) nuclear spin with the J ϭ1 angular
Љ
3
momentum of the X
⌬ state. The spectral feature associated with F
Љ
1
ϭ5/2 was selected for optical Stark measurements.
departure from the linear field dependence because the Stark
shift becomes comparable to the magnetic hyperfine splitting
in the Jϭ1 rotational level ͑see Fig. 6͒.
FIG. 6. The energy levels associated with the Pe(1) branch feature of the
3
͑0,0͒ D 3⌸0 –X
⌬
band system of 51VN as a function of applied electric
1
3
The Stark effect in the D ⌸0 state was treated in a
field. The N(Iϭ1) hyperfine splitting was not resolved at the highest reso-
lution ͑50 MHz͒ and is therefore not indicated. The field free energy level
pattern was predicted using the parameters of Ref. 11.
similar fashion. The upper terminus of the P (1), F ϭ2.5
Љ
e
branch feature is the Fϭ3.5 hyperfine component of the J
3
ϭ0 rotational level of the D ⌸0 state. The associated
͉
MF͉ϭ0.5–3.5 energy levels were modeled by considering
field dependence because of an interaction with the Jϭ1
level of the D ⌸0e stack of levels ͑see Fig. 6͒.
the electric field induced interaction amongst the Fϭ0.5
through Fϭ4.5 field free levels. This resulted in the con-
struction and diagonalization of matrices of dimension 56,
3
The predicted shifts and splittings in the optical Stark
spectra, calculated using the appropriate combination of en-
48, 44, and 32 for the ͉MF͉ϭ0.5, 1.5, 2.5, and 3.5 levels,
3
3
ergy shifts for the X ⌬1 and D ⌸0 states, were used as
respectively. The ⌳-doubling in the Jϭ0 rotational level of
the D ⌸0 state is approximately 19.35 cmϪ1. Thus at low
3
input into a nonlinear least squares fitting. The optimized
3
3
values of ͉␮͉ for the X ⌬1 ͑ϭ3.07͑7͒ D͒ and D ⌸0
͑ϭ6.1͑4͒ D͒ states and the correlation coefficient is given in
the Table III. The numbers in parentheses represent a purely
statistical 2␴ random error estimate. The systematic error,
which is primarily due to the calibration of the Stark plate
spacing, is estimated to be approximately 3%.
electric field strengths the energy levels exhibit a quadratic
V. DISCUSSION
4
A. The fine structure parameters of the A
⌸
and
3/2
4
؊
X
⌺
states of 52CrN
4
The determined field free parameters for the X ⌺Ϫ state
of 52CrN are consistent with the previously determined
values12 but have an uncertainty that is an orders of magni-
tude smaller ͑see Table IV͒. The newly determined field free
4
parameters for the A ⌸3/2 state are not within the error es-
timates of the previous values. This is due to the different
approaches used in modeling the energy levels and is not an
error in the quantum number assignments. Balfour et al. used
a simple analytical formula to calculate the energies, whereas
the present work employed a diagonalized of a matrix repre-
sentation of the Hamiltonian operator.
FIG. 5. The optical Stark spectrum of the P (1), F ϭ2.5 branch feature of
Љ
e
3
the ͑0,0͒ D 3⌸0 –X
⌬
band system of 51VN was recorded in the presence
1
of a 894.0 V/cm static electric field. The electric field was orientated parallel
to that of the linearly polarized laser radiation resulting in ⌬MFϭ0 selec-
tion rules.
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J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
887
TABLE III. Measured and calculated Stark shifts for the Pc(1), Fϭ2.5 branch feature of the ͑0,0͒
3
D
3⌸0 –X band system of 51VN ͑in MHz͒.
⌬
1
Assignment
Shifta
Assignment
Shifta
Field
Obs.Ϫ
Field
͑V/cm͒
MF
MFЈ
Obs.
calc.
͑V/cm͒
MF
MЈ
Obs.
Obs.Ϫcalc.
F
357.7
Ϫ2.5
Ϫ1.5
Ϫ0.5
1.5
Ϫ2.5
Ϫ1.5
Ϫ0.5
1.5
Ϫ229.8
162.2
Ϫ99.1
63.0
Ϫ5.2
Ϫ3.6
Ϫ10.8
Ϫ6.3
Ϫ11.9
Ϫ6.0
24.4
8.3
3.8
Ϫ28.8
894.0
Ϫ2.5
Ϫ1.5
Ϫ0.5
0.5
2.5
0.5
Ϫ2.5
Ϫ1.5
Ϫ0.5
0.5
2.5
0.5
635.8
Ϫ518.2
Ϫ383.2
Ϫ207.3
202.8
1.0
Ϫ7.6
Ϫ12.8
6.2
2.5
2.5
148.7
5.9
2.6
4.0
596.9
Ϫ2.5
Ϫ1.5
Ϫ0.5
1.5
Ϫ2.5
Ϫ1.5
Ϫ0.5
1.5
Ϫ405.5
Ϫ277.1
Ϫ187.0
58.6
1013.4
1191.9
Ϫ284.8
167.6
2.5
2.5
Ϫ1.5
Ϫ0.5
0.5
1.5
2.5
Ϫ1.5
Ϫ0.5
0.5
1.5
2.5
Ϫ768.2
Ϫ587.0
Ϫ406.5
Ϫ174.5
104.1
Ϫ19.6
Ϫ3.7
Ϫ8.6
7.5
2.5
2.5
184.7
715.6
Ϫ0.5
0.5
Ϫ238.8
Ϫ103.6
21.5
22.1
15.2
␴ϭ12.5 MHz
Dipole momentsb
͉
͉
␮
␮
͉
͉
(X 3⌬1)ϭ3.07(7) D;
3
(D
⌸0e)ϭ6.1(4) D
Correlation coefficientϭϪ0.872
aThe shifts are relative to the field free spectral feature ͑see Fig. 3͒.
bThe numbers in parentheses represent a 2␴ statistical error estimate. The systematic errors are estimated to be
approximately 3%.
B. The permanent electric dipole moments
tion of the net metal charges for the ground state TiN, VN,
and CrN are 0.50, 0.47, 0.51, respectively.15 Interestingly,
the values of c for the nitrides are only slightly smaller than
those of the oxides, despite the greater electronegativity of
the O ligand. The experimentally determined energy separa-
tions between the average of the states arising from the (n
Ϫ1)dxϪ1ns1 and the (nϪ1)dxϪ2ns2 configuration ͑Ti: 0.81
eV; V: 0.25 eV; and Cr: Ϫ1.1 eV͒23,24 were used to establish
the relative position of the 4s and 3d orbitals. The 2p orbital
energies for O and N were taken as the Hartree–Fock calcu-
lated orbital energies24 plus the scaled electron affinity ͑EA͒:
Although the experiment determines only the magnitude
of the dipole moment, ͉␮͉, it is reasonable to expect that the
ground and low-lying excited state charge distribution is
M␦ϩN␦Ϫ. The experimental values of ␮/r0 for the ground
state of the 3d-oxides and 3d-nitrides are graphically dis-
played in Fig. 7 along with the theoretical values of Kunze
and Harrison.14,15 The three major conclusions are ͑a͒ the
periodic trend in ␮/r0 for the nitrides does not show the
inflection observed in the corresponding oxides on going
from Ti to V, ͑b͒ the ab initio values are in fairly good
agreement with the experimental values but are consistently
10
2
lower; ͑c͒ the excited state values ͑TiN (A ⌸)(ϭ4.63 D),
4
4
Ϫ
3
4
TABLE IV. Field free parameters for the ͑0,0͒ A
⌸
3/2–X
⌺
band sys-
VN(D ⌸0e)(ϭ6.2 D), and CrN (A ⌸3/2) ͑ϭ5.42 D͒͒ are
significantly larger than the those for ground state.
tem of CrN.
The simple molecular orbital correlation diagram illus-
trated in Fig. 8, which is drawn specifically for CrN, is useful
in understanding the observed trends in dipole moments for
the mononitrides and monoxides. This diagram is similar to
that used by Balfour et al.12 and Merer.3 A comment on the
how the atomic orbital energies of Fig. 8 were estimated is
warranted. The chemical bonding in the oxides22 and also, by
analogy, the nitrides, can be thought of as arising from inter-
action of two species with characters intermediate between
neutral atoms and singly charged ions. Therefore, the highest
occupied orbital of the metal was assigned an energy which
is the weighted mean of the first and second ionization po-
tentials; energyϭcϫ(IP2)ϩ(1Ϫc)ϫ(IP1). The values for c
were taken from ab initio estimates for the net metal charge
in the molecules. In the case of the monoxides, the predicted
net metal charges in the ground states of TiO, VO, and CrO
are 0.55, 0.52, 0.49, respectively.20–22 The ab initio predic-
Parameter
T3/2 ͑Origin͒
This worka
Ref. 12
13 560.3447͑16͒
13 559.61͑15͒
0.6259͑8͒
2.628͑82͒
0.005͑8͒
4
4
Ϫ
X
A
⌺
B
␭
␥
B
p
0.62372͑12͒
2.6102͑9͒
0.0067͑2͒
0.60605͑12͒
¯
⌸
0.6123͑10͒
0.005͑30͒
Correlation matrixb
1.000
Ϫ0.313
Ϫ0.152
Ϫ0.210
Ϫ0.301
0.397
1.000
0.020
0.989
1.000
Ϫ0.011
0.309
1.000
0.487
0.056
0.502
1.000
Ϫ0.551
Ϫ0.634
Ϫ0.050
Ϫ0.032
Ϫ0.312
Ϫ0.308
1.000
0.948
0.229
Ϫ0.245
1.000
aFit using data in Table I. The numbers in parentheses represent a 1␴ error
estimate.
bGiven in order as the parameter appears.
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888
J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
energy configurations based upon the correlation diagram is
complicated by two major considerations. First, the 3d–3d
exchange energy is larger than the atomic orbital energy
separation. Thus, it may be more advantageous for an elec-
tron to occupy a more energetic orbital prior to filling mo-
lecular orbitals that have significant 3d contribution. Second,
there can be significant changes in the nature and energy of
the molecular orbitals upon excitation. For example, the 4␲
3
molecular orbital in D ⌸0 state is predicted to have signifi-
1
cantly less 4p character ͑Ϸ77%͒ than it does in the e ⌸
state even though the states arise from the same dominant
configuration. Recognition of these aspects makes it pos-
sible, as was done by Simard et al.10 and Balfour et al.,12,13
to assign primary configurations to the low-lying states of
TiN, CrN, and VN which are consistent both with the previ-
ously observed fine and magnetic hyperfine structure param-
eters and with Fig. 8. This assignment is
FIG. 7. A plot of the experimental values for ␮/r0 for the first row transition
metal monoxides and mononitrides. Also shown are the ab initio predicted
values for the mononitrides from Refs. 14 and 15.
energyϭHartree–Fock orbital energyϩ¯cϫ(EA), where ¯c is
1
2
TiN: ...8␴23␲49␴ →X ⌺ϩ
the mean of the net metal charge for the mononitrides
͑ϭ0.48͒ or monoxides ͑ϭ0.53͒. The 2s orbitals of N and O
will not participate significantly in bonding because they lie
approximately 10 eV and 17 eV, respectively, lower in en-
ergy than the 2p orbitals and are therefore not included.
A plausible ordering of the molecular orbitals for CrN is
illustrated in Fig. 8. A similar ordering for the molecular
orbitals of TiN and VN can be deduced based upon the rela-
tive values of the metal atomic orbital energies which are
also given in Fig. 8. The ab initio results of Harrision15 pre-
dict that there is significant mixing of the 4s, 4p, and 3d
orbitals which is initiated at long internuclear distances ͑Ͼ3
Å͒. This ligand induced hybridization of the Cr centered or-
bitals is indicated in Fig. 8. The determination of the lowest
1
2
...8␴23␲44␲ →A ⌸
VN: ...8␴23␲49␴11␦1→X ⌬
3
...8␴23␲41␦14␲ →D ⌬
1
3
CrN: ...8␴23␲41␦29␴ →X ⌺Ϫ
1
4
...8␴23␲41␦24␲ →A ⌸.
1
4
As pointed out by Harrison,15 the trend in the ground
state dipole moments on going from TiN to CrN is the result
of three competing effects associated with the changes in the
9␴, 8␴, and 3␲ orbitals. The 8␴ and 3␲ orbitals are polarized
towards the N-center, tending to increase ͉␮͉, whereas the 9␴
orbital is pointed away and has an opposing effect. As indi-
cated in Fig. 8, on going from Ti to Cr the 3d orbital rapidly
drops in energy, and thus there is a shift of excess N-centered
charge back to the metal ͑i.e., enhanced back-bonding in Cr
vs Ti͒. This effect contributes to a decrease in ͉␮͉ on going
from Ti to Cr. In contrast to the 3d orbital, the energy of the
4s orbital remains much more constant in going from Ti to
Cr ͑see Fig. 8͒ and therefore will not, to a first approxima-
tion, contribute to the observed decrease of ͉␮͉ on going from
Ti to Cr. The larger the hybridization of the back-polarized
9␴ orbital the greater the reduction of ␮. The propensity for
4s–4p hybridization will depend upon the energy separation
between the ground (nϪ1)dxϪ2ns2 ͑Ti and V͒ or (n
Ϫ1)dxϪ1ns1 ͑Cr͒ configurations and the excited (n
Ϫ1)dxϪ2ns1np1 configuration. This spacing increases on
going from Ti to Cr,23 thus tending to decrease the propen-
sity 4s–4p hybridization and increase ͉␮͉. Evidently, this
increase is not enough to counteract the opposing effect of
the 3␲ polarization. This is basically the same conclusion
that Harrison made from a detailed charge distribution
analysis.15
The correlation diagram of Fig. 8 implies that the ground
state values of ␮/r0 for the oxides should be significantly
larger than the corresponding values for the nitrides because
the 8␴ and 3␲ orbitals in the oxides will have less 3d metal
contribution. However, while ␮/r0(CrN) is less than
␮/r0(CrN), as expected, ␮/r0(VN)Ϸ␮/r0(VO) and
FIG. 8. A molecular orbital correlation diagram for CrN.
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J. Chem. Phys., Vol. 110, No. 2, 8 January 1999
Steimle, Robinson, and Goodridge
889
culated dipole moments shows that, while the most advanced
calculations can predict trends in such physical properties,
there is still a significant discrepancy in the absolute values.
␮/r0(TiN) is significantly greater than ␮/r0(TiO). Experi-
mental evidence suggests that this inconsistency for the Ti
molecules does not result from a difference in the nature of
the 9␴ orbital. Specifically, the magnetic hyperfine interac-
tions in TiN ͑Ref. 10͒ and TiO ͑Ref. 25͒ show that the 9␴
orbital consists of 72% and 69% 4s character, respectively.
Evidently the 1␴ orbital, which is occupied in TiO and va-
cant in TiN, is polarized away from the N-center.
ACKNOWLEDGMENTS
This work was supported by a grant from the Fundamen-
tal Interaction Branch, Division of Basic Energy Sciences,
Department of Energy ͑DE-FG03-94ER14468-004͒. The au-
thors would like to thank Dr. John Dickinson and Dr. Kei-
ichi Namiki for their assistance in the laboratory measure-
ments and helpful comments.
The experimentally determined ͉␮͉ values for the excited
10
2
3
states of TiN (A ⌸)(ϭ4.63 D), VN(D ⌸0e) ͑ϭ6.2 D͒,
4
and CrN (A ⌸3/2) ͑ϭ5.42 D͒ are in reasonable agreement
with those predicted by Harrison;15 TiN (A ⌸)(ϭ4.43 D),
2
1 M. J. Winter, d-Block Chemistry ͑Oxford Science, Oxford, 1994͒.
2 R. A. Carter and W. A. Goddard, III, J. Phys. Chem. 92, 5679 ͑1988͒.
3 A. J. Merer, Annu. Rev. Phys. Chem. 40, 407 ͑1989͒.
4 J. Shirley, C. Scurlock, and T. Steimle, J. Chem. Phys. 93, 1568 ͑1990͒.
5 T. C. Steimle and J. E. Shirley, J. Chem. Phys. 91, 8000 ͑1989͒.
6 R. Suenram, G. T. Fraser, F. J. Lovas, and C. W. Gillies, J. Mol. Spec-
trosc. 148, 114 ͑1991͒.
3
4
VN(D ⌸0e) ͑ϭ4.51 D͒, and CrN (A ⌸3/2) ͑ϭ5.73 D͒. ␮
3
4
values for the D ⌸0e state of VN and the A ⌸3/2 state of
CrN are 3.84 D/Å and 3.43 D/Å, respectively. All of the
excited states represent excitation from the singly occupied
metal centered 9␴ orbital which is polarized away from the
ligand, to a slightly antibonding metal centered orbital that is
less polarized, thereby reducing the dipole moment.
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VI. CONCLUSION
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The permanent electric dipole moments in the ground
and excited electronic states of VN and CrN have been mea-
sured experimentally for the first time. During the course of
the spectroscopic analysis, the accuracy of the CrN fine
structure parameters has also been improved. The measure-
ments have enabled a preliminary investigation into the pe-
riodic trends exhibited by early transition metal nitrides and
provide a basis for comparison with the bonding character-
istics of the corresponding oxides. The smooth decrease in
ground state dipole moments on going from TiN to CrN and
the increase in the magnitude of the dipole moment upon
electronic excitation, have been reconciled with a simple mo-
lecular orbital description of the molecules. This approach
can also provide some insight into the observation that the
dipole moments of the nitrides are, in general, only slightly
smaller than the dipole moments of the oxides, a fact that
runs contrary to simple electronegativity arguments. In this
manner, the results also serve as a benchmark, against which
the currently available theoretical bonding models can be
tested. A comparison of experimentally measured versus cal-
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