Internuclear distance and effects of Born-Oppenheimer breakdown for PtS, determined from its pure rotational spectrum

Article abstract of DOI:10.1063/1.1769365

The internuclear distance and effects of Born-Oppenheimer breakdown for platinum monosulfide (PtS) were investigated using a cavity pulsed jet Fourier-transform microwave spectrometer. The spectral analysis using a multi-isotopomer Dunham-type expression produced values for Y₀₁, Y₀₂, Y₁₁, and Y₂₁, along with large values for Born-Oppenheimer breakdown (BOB) parameters for both atoms of the molecule. The BOB parameters were rationalized in terms of the molecular electronic structure and nuclear field shift effects. The equilibrium bond length was also evaluated along with the vibrational frequency and dissociation energy.

Full text of DOI:10.1063/1.1769365

Internuclear distance and effects of Born–Oppenheimer breakdown for PtS, determined
from its pure rotational spectrum
Stephen A. Cooke and Michael C. L. Gerry
Citation: The Journal of Chemical Physics 121, 3486 (2004); doi: 10.1063/1.1769365
View online: http://dx.doi.org/10.1063/1.1769365
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 8
22 AUGUST 2004
Internuclear distance and effects of Born–Oppenheimer breakdown for PtS,
determined from its pure rotational spectrum
Stephen A. Cooke and Michael C. L. Gerrya)
Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver,
B.C. V6T 1Z1, Canada
͑
Received 12 March 2004; accepted 17 May 2004͒
ϩ
Platinum monosulfide PtS has been prepared in its X0 ground electronic state by laser ablation of
Pt in the presence of H S. The rotational spectra of eight isotopic species have been measured with
2
a cavity pulsed jet Fourier-transform microwave spectrometer. Spectral analysis using a
multi-isotopomer Dunham-type expression produced values for Y01 , Y02 , Y11 , and Y21 , along with
large values for Born–Oppenheimer breakdown ͑BOB͒ parameters for both atoms of the molecule.
The BOB parameters are rationalized in terms of the molecular electronic structure and nuclear field
shift effects. A large negative 1 Pt nuclear spin-rotation constant has been rationalized in terms of
the electron-nucleus dipole-dipole hyperfine constant. The equilibrium bond length in the
Born–Oppenheimer approximation has been evaluated. © 2004 American Institute of Physics.
95
͓
DOI: 10.1063/1.1769365͔
I. INTRODUCTION
of spectra of ZrO and ZrS ͑Ref. 10͒, HfO ͑Ref. 11͒, HfS
Ref. 12͒, PtSi ͑Ref. 13͒, and BiN ͑Ref. 14͒. All these mol-
͑
Although it is now over 70 years since Dunham first
published his model for the energy levels of diatomic
ecules have relatively large BOB terms, with the last two
showing field-shift effects for Pt and Bi, respectively.
In the recent example of PtSi ͑Ref. 13͒ initial analyses
omitting field-shift terms showed a significant difference in
magnitude between the respective Watson-type BOB param-
1
molecules, this model continues to provide the basis for the
analysis of their high resolution spectra. However, because
of the precision and accuracy of spectroscopic measure-
ments, it has had to be modified to incorporate effects of
Born–Oppenheimer breakdown ͑BOB͒. The basic procedure
Pt
Si
01
eters (⌬01 and ⌬ ). The differences were surmised to be due
1
ϩ
to field-shift effects for Pt. Fits to the experimental data
alone could not, however, separate adiabatic and nonadia-
batic effects from field-shift effects because of high correla-
tions. Because adiabatic and nonadiabatic contributions are
usually approximately the same for the two nuclei in a di-
atomic molecule, the field-shift parameters could be esti-
mated by assuming this to be the case in PtSi and refitting
the data to the Pt field-shift parameter and one ⌬01 param-
eter. Reasonable values for both were seemingly obtained.
However, since it was found that the field-shift parameter
was large in magnitude and of opposite sign to those found
for the Pb-chalcogenides and Tl-halides it was necessary to
verify it independently.
for doing this for X ⌺ molecules was published over 20
years ago by Watson2 and Bunker. This takes into account
,3
4,5
both adiabatic and nonadiabatic effects but neglects possible
effects due to the ‘‘finite size of the nuclei, the second-order
contribution of spin-orbit coupling, and other relativistic
2
effects.’’ This approach was expected, and found, to be nec-
essary for the analysis of spectra of light diatomic
2
molecules. A different formalism of Watson’s model has
been developed by LeRoy.6
Anomalies in the analysis of the millimeter wave spectra
of the lead chalcogenides and thallium halides prompted Tie-
mann et al. to include effects from the finite sizes of the
7
–9
nuclei.
Initial spectral analysis produced apparent large
8
adiabatic BOB terms for the metals. However, further study
showed that the anomalies arose because these nuclei had a
finite charge distribution. They were accounted for with a
revision of Watson’s formula which included new ‘‘field-
Schlembach and Tiemann showed that the field-shift pa-
A
A
r
e
rameter V01 for atom A is proportional to (d␳el /dr) , the
derivative of the electron density at nucleus A with respect to
the internuclear distance, evaluated at the equilibrium dis-
tance. In their early ͑1982͒ work they estimated values for Pb
and Tl using Hartree–Fock evaluations. Since that time, this
parameter has fallen into disuse. This is unfortunate, because
it can provide helpful information, verifiable experimentally,
about molecular electronic structures. Accordingly we have
recently demonstrated that density functional theory ͑DFT͒
8
shift’’ parameters.
In rotational spectroscopy effects of BOB have appeared
mostly in millimeter wave spectra, whose measurements
have always carried many significant figures. However, mea-
surements using cavity pulsed jet Fourier-transform micro-
wave ͑FTMW͒ spectrometers are now so precise that BOB
terms have been determined from spectra measured at much
lower frequencies, even for molecules containing heavy at-
oms. For example, they have been needed in recent analyses
15
may be used to estimate field-shift parameters. Application
to PtSi verified that the experimental field-shift parameter is
13
indeed reasonable.
The present paper extends this work to platinum mono-
sulfide PtS. This molecule has, however, rather different
a͒Electronic mail: mgerry@chem.ubc.ca
0021-9606/2004/121(8)/3486/9/$22.00
3486
© 2004 American Institute of Physics
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8

J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
Born–Oppenheimer breakdown for PtS
3487
Z e2
Pt
Pt
properties from those previously reported. In a Hund’s case
d␳
el
Pt
V ϭ
ͩ ͪ
͑1͒
͑
a͒ or ͑b͒ coupling scheme its electronic ground state would
01
3
⑀ k r
e e
dr
0
3
Ϫ
r
e
be X ⌺ . However, case ͑c͒ coupling actually applies, with
a large spin-orbit coupling, and the ground state is X0 .
Many bands have the appearance of ⌺Ϫ ⌺ transitions, and
ϩ 16
S
with an analogous equation for V0 . ZPt is the atomic num-
ber for Pt, e is the elementary charge, ⑀ is the permittivity of
1
1
1
0
1
ϩ
the ground state could easily be assigned as X ⌺ . The same
free space, k is the harmonic force constant, ␳ is the elec-
e
el
phenomenon is found for isoelectronic PtO,1
7,18
for which
tron density, and r is the equilibrium internuclear distance.
e
1
ϩ
the ground state was indeed initially thought to be ⌺ .
In conjunction with the electronic spectrum, Li et al.16
used pump-probe microwave-optical double resonance
The DFT calculation was performed using the Amster-
dam density functional program23 ͑ADF͒ and used an all-
electron basis set ͑QZ4P͒ of Slater-type orbitals ͑in prefer-
ence to Gaussian-type orbitals because the former have better
cusp behavior͒. Attempts to account for relativistic effects
͑MODR͒ to record the Jϭ5-4, 6-5, and 8-7 pure rotational
transitions of the three most abundant isotopomers of PtS.
The resolution, although high, was insufficient for measure-
were made using the zeroth-order regular approximation
1
95
4,25
ment of Pt hyperfine structure. The dataset included only
vibrational ground state transitions, and thus precluded a
Dunham-type analysis. The dipole moment of PtS has also
been measured.1
͑
ZORA͒.2
Use was also made of the statistical average of
2
6
orbital potentials ͑SAOP͒ model. Single point calculations
giving the electron densities, ␳ , at a series of different
el
9
internuclear distances were carried out. A polynomial was
then fitted to the derived densities and its derivative gave the
required quantity. These calculations also produced a poten-
tial energy curve for PtS, from which an equilibrium inter-
nuclear distance and other spectroscopic parameters could be
predicted.
In the present work the MODR measurements have been
extended by FTMW spectroscopy to further J values and
isotopomers in several vibrational states, at considerably
higher resolution. Unusual 1 Pt spin-rotation coupling has
been found. The results could be treated with the same
Dunham-type analysis as is used for closed shell molecules.
The large BOB terms found are rationalized in terms of elec-
tronic structure, and the internuclear distance has been evalu-
ated.
95
III. RESULTS AND ANALYSIS
A. Spectra and assignments
The spectroscopic constants in Ref. 16 were used to pre-
dict the corresponding transitions for those isotopomers in
the frequency range of our FTMW spectrometer. Lines re-
II. EXPERIMENTAL AND CALCULATION METHODS
A. Spectroscopic measurements
quiring the presence of both Pt and H S in the reaction mix-
2
ture were quickly found at the predicted frequencies. Some
searching then revealed transitions of previously unobserved
isotopomers and of vibrationally excited molecules. The as-
signments were confirmed by the isotopic distribution of the
lines and by the hyperfine structures of the transitions con-
taining 1 Pt (Iϭ1/2).
A pulsed Nd:YAG laser beam of wavelength 1064 nm
was focused onto a rotating glass rod wrapped with platinum
foil. The rod and foil were mounted in an ablation system
specially designed for our FTMW spectrometer.20 The result-
ing ablation produced a plasma of Pt, which then reacted
95
with a small amount ͑ϳ0.1%͒ of H S ͑Matheson у99% pu-
2
The frequencies of the measured transitions are given
with their assignments in Table I. The measurements of Ref.
rity͒ contained in Ar. This gas mixture was issued from a
reservoir held at high pressure ͑5–7 atm͒ via a solenoid
valve ͑series 9, General Valve͒. The reaction mixture then
underwent a supersonic expansion into an evacuated Fabry–
1
6 are included for completeness.
For the isotopomers containing 195Pt the coupling
2
1
scheme JϩIϭF has been employed. The Jϭ1-0 transition
Perot cavity of a Balle–Flygare type Fourier-transform mi-
1
95 32
crowave ͑FTMW͒ spectrometer.22 The microwave spectrum
of Pt S is illustrated in Fig. 1.
B. 195Pt hyperfine analysis
of PtS was recorded between 8 and 18 GHz. The gas expan-
sion occurred parallel to the central axis of the cavity mir-
rors, and parallel to the direction of propagation of the mi-
crowaves, with the result that all transitions were observed as
Doppler doublets. Linewidths with this arrangement were
typically 7–10 kHz ͑FWHM͒. Frequency measurements
were referenced to a Loran frequency standard accurate to 1
Because the program used to perform the Dunham-type
fits described below does not include hyperfine structure,
preliminary analyses were carried out for isotopic species
containing 1 Pt. Their line frequencies were fit to the con-
stants in the Hamiltonian,
95
1
0
2
4
part in 10 ; reported line frequencies are estimated to be
HϭB J ϪD J ϩC I"J
͑2͒
v
v
I
accurate to better than Ϯ1 kHz.
using Pickett’s least-squares fitting program SPFIT.27 Each
vibrational state was treated separately, giving its rotational
B. Theoretical calculations
1
95
constant B , centrifugal distortion constant D , and
Pt
v
v
Density functional theory ͑DFT͒ calculations following
nuclear spin-rotation constant C . The fits were to the data in
Table I. The resulting constants are in Table II, in comparison
with those previously reported for PtSi and PtCO.
I
1
5
the procedure outlined by Cooke et al. were used to predict
Pt
S
01
the field-shift parameters V01 and V . The calculation deter-
mined the derivative of the electron density at the given
nucleus with respect to the internuclear distance, and the
field shift parameter for Pt was estimated using
It will be noted that C for PtS is much bigger in mag-
nitude than and of opposite sign to the values for the other
two molecules. Using the constants given in Table II the
I
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3488
J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
S. A. Cooke and M. C. L. Gerry
TABLE I. Measured transition frequencies for PtS.
Isotopomer
JЈ-JЉ
FЈ-FЉ
v
Frequency ͑MHz͒
Obs.Ϫcalc. ͑kHz͒a
1
92 32
Pt S
1-0
1-0
0
0
0
0
0
0
1
1
2
2
8844.1512
8831.1458
0.4
Ϫ0.2
0.6
3.1
5.6
1.7
0.0
Ϫ1.3
Ϫ0.2
0.2
0.1c
Ϫ0.1c
Ϫ0.1c
0.1c
Ϫ47.5d
Ϫ16.4d
Ϫ47.6d
1
94 32
Pt S
2-1
5-4
6-5
8-7
1-0
2-1
1-0
2-1
17 662.2578
44 155.0373
52 985.6640
70 646.2476
8792.9563
17 585.8765
8754.6948
17 509.3554
b
b
b
1
95 32
1
2
3
2
3
2
5
2
1
2
1
2
1
2
3
2
Pt S
1-0
Ϫ
Ϫ
Ϫ
0
0
0
0
8824.8020
8824.7016
1
2
2
-0
-1
-1
17 649.4689
17 649.4024
Ϫ
d
5
6
8
-4
-5
-7
0
0
0
44 122.9370
52 947.1850
70 594.9310
d
d
1
2
3
2
3
2
5
2
1
2
3
2
1
2
1
2
1
2
3
2
1
2
1
2
0.2c
Ϫ0.2c
Ϫ0.2c
0.2c
0.0c
0.0c
1
1
2
2
1
1
-0
-0
-1
-1
-0
-0
Ϫ
Ϫ
Ϫ
Ϫ
Ϫ
Ϫ
1
1
1
1
2
2
8786.6521
8786.5543
17 573.1726
17 573.1060
8748.4319
8748.3342
1
96 32
Pt S
1-0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
8818.4021
17 636.7694
44 091.3090
52 909.1940
70 544.3010
8780.2948
17 560.5553
8742.1168
8805.9112
17 611.7885
8767.8854
17 535.7367
8386.6878
16 733.3445
8351.3578
Ϫ0.2
2-1
5-4
6-5
8-7
1-0
2-1
1-0
0.4
6.7
3.3
0.6
b
b
b
Ϫ0.3
Ϫ0.1
0.0
Ϫ0.1
0.4
Ϫ0.3
0.0
Ϫ0.1
Ϫ1.7
1
1
98 32
Pt S
1-0
2
1
2
-1
-0
-1
94 34
Pt S
1-0
2
1
-1
-0
4.3
0.0c
0.0c
1
1
95 34
1
2
3
2
1
2
1
2
Pt S
1-0
-0
1-0
Ϫ
Ϫ
0
8380.3413
1
0
0
8380.2445
8373.9421
96 34
Pt S
Ϫ0.2
aApart from 195PtS these are the observed frequencies minus those calculated from the fitted constants of Table
III. See also footnote c below.
b
These line frequencies were taken from Ref. 16 and given a 100-fold lower weight than the other lines in the
fitting procedure.
c
These data were least-squares fit using the SPFIT program. The obs.Ϫcalc. values are the observed frequencies
minus those calculated with the constants in Table II.
d
Taken from Ref. 16. Magnetic hyperfine splitting was not observed for these transitions because of the
resolution of the experimental method. In the present work these lines were excluded from the fitting proce-
dures. The obs.Ϫcalc. values are the observed frequencies minus the hypothetical line centers obtained from
the constants in Table II.
hyperfine splitting in the MODR data of Ref. 16 was calcu-
lated. For the Jϭ8-7 transition for example the splitting is
predicted to be Ϸ60 kHz which is approximately half the
line widths obtained in the experiment. This would explain
why these splittings were not reported in Ref. 16.
vibrational state were treated separately. Enough significant
figures in the constants were retained to ensure that the cal-
culated frequencies were accurate to the experimental uncer-
tainties.
For the Dunham-type analysis hypothetical unsplit fre-
quencies for the well resolved Jϭ1-0 and Jϭ2-1 rotational
transitions were calculated from the rotational constants and
distortion constants in Table II. Again each isotopomer and
C. Dunham-type analysis
A general treatment of the rotational energy and fine
structure of a diatomic molecule following Hund’s case ͑c͒
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J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
Born–Oppenheimer breakdown for PtS
3489
ber, and (T ϪT ) is the energy difference between the
1
0
͉
⍀͉ϭ1 and ⍀ϭ0 states. Eqs. ͑4͒–͑7͒ can be reorganized, to
the precision available experimentally, as
⑀
2P2
1
2
Eϭ
ͫ
Y01
ͩ
1ϩ
Ϫ
ͪ
ϩY11
ͩ
vϩ
ͪ
Y01 Y ͑T ϪT ͒
01
ϩ¯
1
1
0
2
1
2
ϩY2
ͩ
vϩ
ͪ
ͬ
J͑Jϩ1͒
1
2
2
ϩ
ͫ
Y ϩY
ͩ
vϩ
ͪ
ϩ¯
ͬ
J ͑Jϩ1͒ ϩ¯.
͑8͒
0
2
12
2
In Eqs. ͑7͒ and ͑8͒ the effect of P is Born–Oppenheimer
breakdown, so that the term 2P /Y (T ϪT ) gives a mea-
sure of this breakdown. Kuijpers, T o¨ rring, and Dymanus
FIG. 1. Power spectrum of the Jϭ1-0 transition of 195Pt 32S, showing 195Pt
hyperfine structure. 500 averaging cycles. 4k data points were recorded, and
the power spectrum is shown as a 4k transformation.
2
0
1
1
0
31
also pointed out that when this term is very small the usual
1
ϩ
expressions for a X ⌺ molecule apply, and the physical
meanings of the Ykl are well defined.
2
,3
was published by Veseth.29,30 For a ⌺ state there are three
states for each value of J, one having ⍀ϭ0 and two of op-
posite parity having ͉⍀͉ϭ1. The ⍀ϭ0 and ͉⍀͉ϭ1 states of
the same parity interact through a perturbation operator,
3
Equation ͑8͒ should thus be compared with Watson’s
1
ϩ
expression for the rotational energy of a ⌺ molecule AB
͑see also Schlembach and Tiemann, Ref. 8͒,
k
1
Eϭ
Ykl
ͩ
vϩ
ͪ
Jl͑Jϩ1͒l
͑9͒
ˆ
͚
H ϭϪ2BJ"J ,
͑3͒
k,l
2
p
a
where B is the rotational constant, J is the operator for the
total angular momentum exclusive of nuclear spin, and Ja
ϭLϩS. Here L and S are the electronic orbital and spin
angular momentum operators, respectively. If the interacting
with
Y ϭ
Ukl
me
me
A
B
kl
1ϩ
⌬ ϩ
⌬
ͬ
,
͑10͒
kl
ͫ
kl
␮͑
kϩ2l͒/2
MA
MB
vibronic levels having ⍀ϭ0 and ͉⍀͉ϭ1 are well separated,
then Kuijpers, T o¨ rring, and Dymanus31 showed that the ro-
where the Ukl are mass-independent Dunham parameters, ␮
is the reduced mass of the molecule (ϭM M /(M
A
B
A
tational energy can be written as
ϩM )) with atomic masses M and M , and m is the
B
A
B
e
P2
P2
i
kl
2
8D
electron mass. The terms ⌬ are Born–Oppenheimer break-
down parameters, of which only the ⌬ terms are signifi-
Eϭ
ͩ
BϪ
ͪ
J͑Jϩ1͒Ϫ
ͩ
DϪ
ͪ
i
01
T1ϪT0
B T ϪT
1
0
cant. Equation ͑9͒ is thus essentially the same as Eq. ͑8͒, but
2
2
ϫJ ͑Jϩ1͒ ϩ¯.
͑4͒
A
B
with U01 /␮(1ϩ(m /M )⌬ ϩ(m /M )⌬ ) replacing
e
A
01
e
B
01
2
Y (1ϩ⑀/Y Ϫ2P /Y (T ϪT )). The ⌬ terms may be
In this expression,
01
01
01
1
0
01
2
,3,8
expanded,
1
2
1
2
Bϭ͑Y ϩ⑀͒ϩY ͑vϩ ͒ϩY ͑vϩ ͒ ϩ¯,
͑5͒
͑6͒
͑7͒
0
1
11
12
2
͑
D͒
͑
␮gJ͒
␮⌬Y
01
1
1
2
A
A
ad
B
DϭϪY ϪY ͑vϩ ͒ϪY ͑vϩ ͒ ϩ¯,
⌬ ϭ͑⌬ ͒ ϩ
ϩ
,
͑11͒
0
2
12
2
22
2
01
01
mp
m B
e e
Pϭ
͗
v,J ,⍀ϭ1
͉
͘
B͑J ͒ ͉vЈ,J ,⍀ϭ0 .
a ϩ a
a
where (␮gJ)B is the isotopically independent value of ␮g
referred to nucleus B as the origin,2
J
In these expressions Ykl are the Dunham coefficients, ⑀ is the
Dunham correction to Y01 , v is a vibrational quantum num-
͑
␮g ͒ ϭ␮g ϩ2c m M /͑M ϩM ͒
͑12͒
J
B
J
A
p
A
A
B
(
D)
and c is the formal charge on atom A, ⌬Y
is the Dunham
01
A
correction. The mass of the proton is represented as m , and
TABLE II. Molecular constants in MHz for 195Pt S and Pt S.
32
195 34
p
A
ad
A
(
⌬ ) represents the adiabatic contribution to ⌬ . There is
01 01
B
3
(195Pt) CI
Isotope
v
B
10 D
a corresponding expression for ⌬ . The rotational g factor
in a nonrelativistic approximation is given by
J
01
3
2
1
95 32
4412.370 43͑99͒a
4393.296 25͑99͒
4374.186 24͑75͒
4190.141 26͑75͒
4851.219 96͑99͒
3322.833 56͑31͒
Pt S
0
1
2
0
0
0
1.440͑136͒
1.429͑136͒
Ϫ0.066 80͑157͒
Ϫ0.065 63͑157͒
Ϫ0.065 13͑189͒
Ϫ0.064 53͑189͒
ϩ0.030 98͑157͒
ϩ0.024 20͑87͒
2
mp
Ie
2
͗ ͘
͉ k͉Lx͉0 ͉
b
2
1.429
1.440
gJϭ
Z z Ϫ
,
͑13͒
ͩ
͚i
i
i
͚
ͪ
1
1
1
95 34
b
me kÞ0 TkϪT0
Pt S
95 28
c
Pt Si
PtCO
1.693͑136͒
0.450͑20͒
95
d
where Z and z are, respectively, the atomic number and
position of atom i. L is an orbital angular momentum op-
erator, and the sum over k is over all excited ⌸ states.
i
i
x
aNumbers in parentheses are one standard deviation in units of the last
1
significant figure.
When the terms of Eqs. ͑11͒, ͑12͒, and ͑13͒ are inserted
into the expression for Y01 ͓Eq. ͑10͔͒ and the result is sim-
plified we obtain
b
Constrained to this value.
c
Reference 13.
d
Reference 28.
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8

3490
J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
S. A. Cooke and M. C. L. Gerry
in which
͗ ͗
r2͘A and r2͘B are mean-square charge radii of
nuclei A and B, respectively, in the reference isotopic spe-
cies.
͑
01
D͒
U01
⌬Y
me
Ie
ad
2
Y ϭ
1ϩ⌬ ϩ
ϩ
͚i Zizi
0
1
ͫ
01
␮
Be
2
L
The method of analysis of the spectrum of PtS was thus
the following. An initial fit to the experimental data in Table
2
P
Ϫ
,
͑14͒
ͬ
Y ͑T ϪT ͒
0
1
k
0
Pt
S
01
I used Eqs. ͑9͒ and ͑10͒, including ⌬01 and ⌬ , but ignoring
ad
where ⌬01 is the total adiabatic correction to Y . In the final
possible field-shift effects. The other fitted constants were
U01 , U02 , U11 , and U21 . The results are in Table III. In this
01
term,
table are given also values for the constants Y01 , Y02 , Y11
,
ˆ
P ϭ
L
͗
v,L,⌳ϭ1
͉
B Lϩ͉vЈ,L,⌳ϭ0
͘
.
͑15͒
e
and Y21 for each isotopomer. The r.m.s. deviation was 1.1
kHz, an entirely acceptable value in light of the measurement
accuracies of the transition frequencies.
1
Also, it is assumed that only one excited ⌸ electronic state
contributes. In this term the distinction between B , Y
,
01
e
and U01 /␮ is insignificant. If the adiabatic contribution and
the small fourth term are ignored ͑or considered assimilated
into the Dunham correction͒, and Eq. ͑14͒ is inserted into Eq.
Several interesting features of the parameters in Table III
are ͑a͒ the high precision of the fitted constants, especially
Pt
S
U01 and U11 ; ͑b͒ the very large values of ⌬ and ⌬ and
01
01
S
Pt
͑9͒, then Eqs. ͑9͒ and ͑8͒ are found to be phenomenologi-
the fact that ⌬ Ϫ⌬ ϷϪ20; and ͑c͒ the isotopic variations
01 01
cally the same, albeit with P replacing P. However, in terms
of angular momentum operators the L, ⌳ dependence of PL
of the re values calculated directly from the Y01 values.
These variations are an order of magnitude bigger than those
of many other molecules, of which PtSi is a good example.13
Both the large ⌬01 values and these variations suggest that
the limit of the Born–Oppenheimer approximation i.e.,
Born–Oppenheimer breakdown, BOE͒ is reached more eas-
ily than for many stable molecules.
L
is the same as the J , ⍀ dependence of P. Accordingly Wat-
a
ϩ
son’s formalism can be meaningfully used to fit 0 states in
Hund’s case ͑c͒.
The problem with Eq. ͑14͒ for spectral fitting is that all
four correction terms are mass ͑isotope͒ dependent. It must
be returned to the form in Eq. ͑10͒ which includes the mass-
To give some indication of the relative size of the ⌬01
terms, they are compared with those of other diatomic mol-
ecules studied to date in Table IV. With a few exceptions,
both constants are an order of magnitude larger than those of
all the other molecules. Given the case ͑c͒ coupling of PtS, it
A
B
01
independent terms ⌬01 and ⌬ . These are easily shown to
become
͑
0
D͒
␮
⌬Y
2c M
A
␮
1
A
A
A
ad
2
⌬
ϭ ͑⌬ ͒ ϩ
ϩ
ϩ
͚i Zizi
0
1
ͫ
01
ϩ
ϩ
m B
͑M ϩM ͒
Ie
e
e
A
B
is likely that the interaction between close-lying 1 and 0
states is the cause of these large values.
2
L
␮
2P
Pt
S
The difference between ⌬ and ⌬ was now addressed.
Ϫ
͑16͒
01
01
Pt
ͬ
S
m Y ͑T ϪT ͒
e
01
1
0
Values for the field-shift parameters V01 and V were esti-
01
B
mated theoretically, as described in Sec. 2.2 above, and ap-
with a corresponding expression for ⌬ . It will be noted
that the term Ϫ␮/m (2P /Y (T ϪT )) appears in the ex-
pressions for both ⌬01 and ⌬ . If this term contributes much
more than the others its effects will dominate both ⌬0 and
0
1
2
L
plied to Eq. ͑17͒. They were calculated to be Ϫ83.99
e
01
1
0
Ϫ7
Ϫ2
Ϫ7
Ϫ2
A
B
01
ϫ10 fm
͗ ͘
only the term in V01 was significant. Values of ␦ r
Pt,PtЈ
and 0.02ϫ10 fm , respectively. Clearly,
Pt
2
A
1
39
B
were obtained from tables. The basis molecule was
⌬
.
0
1
194 32
Pt S. It was found to have the correct sign and magnitude
While Eq. ͑10͒ is valid when the molecules contain light
to account for the difference found in the ⌬01 values.
atoms alone, it must be modified when at least one of the
atoms is heavy. In this case the nuclei can no longer be
considered point charges: their charges are distributed over a
A new Dunham-type fit was then carried out using Eqs.
Pt
Pt
01
͑
9͒ and ͑17͒. Because ⌬01 and V could not be separated
with the experimental data alone, the fit instead assumed that
finite volume to produce a so-called field-shift contribution.
Pt
S
This can be accounted for by modifying Eq. ͑10͒ to8
⌬ ϭ⌬ Ϯ1 ͑recall that Watson has shown that these two
01 01
2
terms should be approximately, but not exactly, equal ͒; the
¯
U
me
me
values in Table IV indicate that this approximation is reason-
0
1
A
B
01
A
r2͘AAЈ
Y ϭ
ͫ
1ϩ
⌬ ϩ
⌬ ϩV ␦
͗
S
Pt
0
1
01
01
¯
␮
MA
MB
able. The fit was thus to U , U02 , U11 , U21 , ⌬ and V
01
01
01
,
S
¯
S
with V0 set to zero. The resulting values of U , ⌬ , and
1
01
01
Pt
01
B
r2
V
are given in Table IV. The remaining terms (U02 , U11
,
ϩV ␦
͗
͘
ͬ
,
͑17͒
0
1
BBЈ
and U ) were found to agree with the values given in Table
2
1
A
B
III within the experimental uncertainties. The agreement be-
where V0 and V are isotopically independent field-shift
1
01
Pt
01
tween V determined in this way and using DFT is very
parameters as defined in Eq. ͑1͒. To apply Eq. ͑17͒ one iso-
topic species is chosen as a reference ͑e.g., Pt S), so that
1
94 32
good.
2
2
͗ ͗
␦ r ͘AAЈ and ␦ r ͘BBЈ are the changes in mean square
nuclear charge radius on the isotopic substitutions A→AЈ
¯
and B→BЈ, respectively. The constant U applies to the
IV. DISCUSSION
0
1
reference isotopic species. It is related to the mass-
A. Internuclear distance
independent parameter U01 by
Enough data have been obtained to evaluate the equilib-
¯
A
01
r2͘AϩVB
r2͘B͒.
U ϭU ͑1ϩV
͗
͗
͑18͒
0
1
01
01
rium internuclear distance r of PtS. This can be done using
e
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8

J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
Born–Oppenheimer breakdown for PtS
3491
TABLE III. Mass-independent and -dependent Dunham parameters for nine isotopomers of PtS.
2
U11 (u3/2MHz)
Ϫ2740.693͑47͒
2
Pt
S
U01 (uMHz)
U02 (u MHz)
U21 (u MHz)
⌬
⌬
01
01
PtS
121 604.07͑30͒a
Ϫ1.092͑3͒
Ϫ13.48͑8͒
Ϫ42.69͑74͒
Ϫ62.47͑5͒
Y01 (MHz)b
103Y02 (MHz)
Ϫ10 De
Y11 (MHz)
Ϫ␣e
103Y21 (MHz)
Parameterd
Be
3
10 ␥e
3
r (Å)c
e
1
1
1
1
1
1
1
1
94 32
Pt S
4425.109 88
4421.893 99
4418.717 15
4412.451 64
4431.633 44
4202.168 71
4198.952 48
4195.775 30
Ϫ1.449
Ϫ1.447
Ϫ1.445
Ϫ1.441
Ϫ1.454
Ϫ1.307
Ϫ1.305
Ϫ1.303
Ϫ19.059 06
Ϫ19.038 27
Ϫ19.017 74
Ϫ18.977 27
Ϫ19.101 26
Ϫ17.635 37
Ϫ17.615 11
Ϫ17.595 10
Ϫ17.89
Ϫ17.87
Ϫ17.84
Ϫ17.79
Ϫ17.95
Ϫ16.13
Ϫ16.11
Ϫ17.60
2.039 828 30
2.039 827 71
2.039 827 05
2.039 825 82
2.039 829 69
2.039 763 90
2.039 763 30
2.039 762 67
95 32
Pt S
96 32
Pt S
98 32
Pt S
92 32
Pt S
94 34
Pt S
95 34
Pt S
96 34
Pt S
Covariances from least squares fite
U01
U02
U11
1
0.000
Ϫ0.001
0.003
Ϫ0.208
Ϫ0.008
1
0.000
0.000
0.000
0.000
1
U2
Ϫ0.003
0.004
0.000
1
1
Pt
⌬0
Ϫ0.010
0.000
1
1
S
⌬0
0.010
1
1
a
Numbers in parentheses are one standard deviation in units of the last significant figure.
b
The mass-dependent Dunham parameters Ykl have been obtained from the mass-independent parameters, Ukl
by Eq. ͑10͒.
,
c
2
2
e
Calculated from Y01 using Y01ϭh/8␲ ␮r , where ␮ is the atomic reduced mass.
d
Spectroscopic parameters to which Y is approximately equal, where Ev,JϭJ(Jϩ1)͓B ϪD J(Jϩ1)Ϫ␣ (v
kl
e
e
e
2
3
ϩ1/2)ϩ␥ (vϩ1/2) Ϫ⑀ (vϩ1/2) ͔.
e
e
e
r.m.s.ϭ1.95 kHz; no. of data pointsϭ33; no. of isotopomersϭ8.
several methods, which each give slightly different results,
and considerable care must be taken in their interpretation.
h
v
r ϭ
ͱ
.
01
͑21͒
e
2
¯
8
␲ U
The first method used the Y values for each isotopomer
0
1
4
0
in the equation,
C2
Y ͑MHz͒␮͑u͒
reϭ
,
͑19͒
The result, which is given in Table V, applies to the reference
isotopomer, Pt S.
ͱ
194 32
0
1
where ␮ is the reduced mass of the isotopomer, and
The isotopically independent Born–Oppenheimer bond
length re , in which field-shift effects have been accounted
BO
1
7
1
0 hN
¯
A
for, was obtained using U01 from U in Eq. ͑17͒. For this
01
C ϭ
ͱ
2
␲2
2
8
purpose the value V from Table IV was used, with
for 1 Pt as 28.90͑10͒ fm from Ref. 44. Although
͗
r
͘Pt
Pt
95
2
2
͗
r ͘S is
͘Pt ; given that in
ϭ710.900 137 9͑25͒ Å MHzϪ1/2uϪ1/2
.
͑20͒
2
unknown, it is undoubtedly smaller than
͗
r
addition V is calculated to be 0.02ϫ10 fmϪ2, i.e., three
Ϫ7
C has been evaluated using the fundamental constants rec-
2
S
ommended by CODATA in 1998 in the paper by Mohr and
Pt
2
orders of magnitude smaller than V01 , the term VS
͗
r ͘S was
4
1
Taylor. The values for each isotopomer, which are in Table
III, were obtained using the 1993 atomic masses published
ignored. The resulting value of U01 is in Table IV. A value
BO
¯
for re was then calculated using Eq. ͑20͒ with U replaced
4
2
01
by Audi and Wapstra. There is a variation with isotopomer
Ϫ5
by U01 ; it is given in Table V. Its uncertainty is set by the
over 6ϫ10 Å, which is nearly two orders of magnitude
Pt
assumed uncertainty in ⌬01 , which ultimately affects that
bigger than the uncertainties, indicating clearly the onset of
Born–Oppenheimer breakdown at this point. It is also an
order of magnitude bigger than the corresponding variation
of U01
.
The analysis started with the assumption that if the ⌬
01
1
ϩ
1
3
values were small enough then the formalism of X ⌺ mol-
ecules would apply, and the Y (U ) constants would have
in PtSi, though the variation found in ZnO ͑Ref. 10͒ is
comparable.
kl
kl
¯
clear physical interpretation. This is the basis on which the re
The parameter U01 , obtained in the fit including Pt
nuclear field-shift effects, which is given in Table IV, was
values were calculated. It should thus be expected that they
should agree well with the ab initio values. The comparison
in Table V shows that this is indeed the case.
v
used to obtain r . This is an equilibrium distance in which
e
4
volume effects are included, and was determined with
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3492
J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
S. A. Cooke and M. C. L. Gerry
TABLE IV. Watson-type ⌬01 terms, field-shift terms VA ͑where known͒, and mass reduced Dunham-type
coefficient U01 for several diatomic molecules.
A
B
10Ϫ7
A
(fmϪ2
AB
⌬0
⌬
V
)
U01 (uMHz)
Reference
This work
1
01
01
a
121 604.07͑30͒b
¯
U ϭ121 610.91(50)
01
PtS
Ϫ42.60͑74͒
Ϫ62.5͑10͒
Ϫ62.466͑49͒
Ϫ62.46͑5͒
c
Ϫ104͑9͒
Ϫ84e
U01ϭ121 647.1(20)d
PtSi
BiN
10.75͑68͒
Ϫ2.99͑4͒
Ϫ2.99͑4͒
118 923.32͑33͒b
13
14
c
¯
Ϫ3͑1͒
Ϫ72͑12͒
Ϫ110e
32e
U
ϭ118 927.94(54)
1
0
U01ϭ118 952.7(47)d
¯
Ϫ2.788͑19͒
Ϫ2.788͑19͒
135 003.18͑10͒b
c
¯
Ϫ2.8͑10͒
U
1ϭ135 004.17(10)
0
U01ϭ134 991.08(45)d
172 480.086͑98͒
108 670.07͑19͒
170 239.68͑18͒f
108 708.38͑27͒
111 378.117͑49͒
128 210.086͑10͒
110 913.1͑82͒
ZrO
ZrS
Ϫ4.872͑39͒
Ϫ5.325͑82͒
Ϫ3.40͑57͒
Ϫ4.18͑53͒
¯
Ϫ6.1888͑25͒
Ϫ6.523͑39͒
Ϫ5.656͑23͒
Ϫ5.820͑49͒
Ϫ1.4427͑287͒
¯
10
10
11
12
33
34
35
36
37
38
7
HfO
HfS
AlCl
g
h
InF
¯
Ϫ1.505͑87͒i
Ϫ2.62͑35͒
Ϫ2.0545͑12͒
Ϫ0.26͑20͒
Ϫ12.94͑141͒
Ϫ1.86͑14͒
i
GeSe
GaH
CO
Ϫ4.2181͑13͒
Ϫ2.0982͑13͒
0.1262͑8͒
Ϫ1.997͑71͒
Ϫ1.988͑70͒
Ϫ1.243͑49͒
Ϫ1.257͑73͒
183 363.95͑42͒
397 029.003͑24͒
311 077.90͑96͒
96 642.20͑50͒f
ClH
PbS
j
k
PbS
Ϫ1.333
26.38͑51͒
40.9͑55͒
9
7
9
TlCl
TlCl
Ϫ18.96͑200͒
81857.0͑1͒f
j
k
Ϫ0.500
a
The numbers in parentheses are one standard deviation in units of the last significant figure.
b
In this fit field-shift effects were neglected.
c
A
B
This is an estimated value and uncertainty based on the assumption that ⌬01ϭ⌬ Ϯ1. This allows field-shift
01
effects to be considered in the fitting procedure, see text for details.
d
¯
Value calculated from U using Eq. ͑18͒; see text.
01
e
14
This value was obtained using DFT following the methods outlined in Ref. 15. In the case of BiN, the
¯
calculated value was used in the determination of U01 and U01
This value for U01 has been calculated from the data given in the appropriate reference.
.
f
g
h
i
Cl
1
Because of the occurrence of only one naturally occurring isotope of Al only ⌬0 terms could be determined.
i
0
⌬
terms were not determined.
1
B
These numbers are actually ⌬ terms determined from a fit to Dunham potential parameters, but differ from
B
1
⌬0
terms only in that they do not contain a contribution from the Dunham correction, which is expected to be
small.
j
A
In this fit allowance was made for nuclear field-shift effects resulting in a reduction in magnitude for the ⌬01
terms.
k
This value was held fixed during this fitting procedure, Ref. 8 should be consulted for the specific details of the
fitting procedure used.
B. General topics
TABLE V. Internuclear distances of PtS and related compounds.
Kratzer45 and Pekeris46 have presented equations
whereby the vibration frequency, anharmonicity constant,
and dissociation energy of a diatomic molecule can be esti-
mated. These are
Molecule
Bond length ͑Å͒
Remarks ͑Ref.͒
ϩ
a,b
PtS (X0 )
r ϭ2.039 828 30(70)
Expt. ͑this work͒
Expt. ͑this work͒
Expt. ͑this work͒
e
v
b
r ϭ2.038 553(4)
e
BO
r
r
ϭ2.038 250(13)
reϭ2.0376
e
DFT calculation ͑this work͒
SAOPϩHCTH͑93͒/QZ4P ͑Ref. 43͒
Expt. ͑Ref. 13͒
3
1
ϩ
BO
PtSi (X ⌺ )
ϭ2.061 206(42)
4Y0
1
e
1
ϩ
Y Ϸ␻ Ϸ
ͱ
,
͑22͒
PtC (X ⌺ )
reϭ1.679
reϭ1.682
reϭ1.727
Expt. ͑Ref. 19͒
Expt. ͑Ref. 19͒
Expt. ͑Ref. 19͒
10
e
ϪY02
2
PtN (X ⌸)
3
Ϫ
PtO (X ⌺ )
2
aNumbers in parentheses are one standard deviation in units of the last
significant figure.
ϪY Y
11 10
Y Ϸ␻ x ϷY
ϩ1
,
͑23͒
2
0
e
e
01
ͩ
ͪ
2
b
Value obtained for the reference isotopomer 194Pt S.
32
6Y
01
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J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
Born–Oppenheimer breakdown for PtS
3493
TABLE VI. Estimated and DFT calculated spectroscopic parameters for
Pt S.
surprising. On the other hand, our results do suggest that
T ϪT ) decreases on going from PtO to PtS. Although this
194 32
(
1
0
trend is not intuitive, a similar result has been observed for
Parameter
Value
Remarks ͑Ref.͒
the Bi-monohalides, where (T ϪT ) decreases in the order
BiFϾBiCϾBiBrϾBiI.
1
0
Ϫ1a
␻e
511͑5͒ cm
This work using Eq. ͑22͒
This work, DFT calc.b
Ref. 16
49
Ϫ1
5
5
32.1 cm
Ϫ1
Table II shows that the nuclear spin-rotation constant,
49.45 cm
CI(195Pt) is large, and of opposite sign compared to those
Ϫ1
␻exe
1.79͑3͒ cm
This work using Eq. ͑23͒
This work, DFT calc.b
This work
Ϫ1
1
2
.75 cm
found for PtSi and PtCO. In the case of X ⌺ molecules nega-
Ϫ1
50
␣e
0.000 635 7͑1͒ cm
.000 69 cm
tive values for C are unusual ͑see also, for example, Ref.
I
Ϫ1
This work, DFT calc.b
0
5
1͒. It was thus reasonable to anticipate that this value has
Ϫ1
De
407͑11͒ kJ mol
This work using Eq. ͑24͒
Ϫ1
This work, DFT calc.b
arisen in PtS because of the case ͑c͒ coupling. To our knowl-
4
68 kJ mol
edge C values for only two comparable molecules have
I
aNumbers in parentheses are one standard deviation error in units of the last
significant figure.
This result has been obtained using a potential energy curve for PtS pre-
pared using the SAOPϩHCTH͑93͒/QZ4P ͑Ref. 43͒ method. Spectroscopic
constants were then obtained from the potential energy curve using Dun-
ning’s VIBROT program ͑Ref. 47͒.
been measured. These are BiF ͑Ref. 52͒ and BiCl ͑Ref. 53͒.
ϩ
b
Both have X0 ground electronic states, and in both cases
C (Bi) is negative. For BiF and BiCl, Tischer, M u¨ ller, and
I
5
0
T o¨ rring rationalized the negative C (Bi) constants in the
I
bismuth halides in the following way. Initially the micro-
3
scopic hyperfine structure Hamiltonian for a ⌺ state taken
from Frosch and Foley54 was used to derive an expression
for the effective nuclear spin-rotation constant, (CI)eff . The
constant (CI)eff is the experimental nuclear spin-rotation
constant obtained from the frequency measurements using a
2
1
Y
0
D Ϸ
e
.
͑24͒
4
Y20
The values for 194Pt S have been estimated from its Y
32
kl
hyperfine structure energy formula, generally applicable to a
constants in Table III and are given together with the spec-
troscopic constants obtained from the DFT potential energy
1
⌺
-state molecule ͑as has been done here͒. The expression
5
0
obtained by Tischer, M u¨ ller, and T o¨ rring, is
curve in Table VI. The agreement between ␻ obtained using
e
Eq. ͑22͒ and the value obtained using isotope shifts in Ref.
1/2
͑
C ͒ ϭfϩ͑bϪf ͒sin ␹ /͓J͑Jϩ1͔͒
I eff J
1
6 is poor; the value obtained from the DFT calculation is
intermediate between the two numbers.
It is clear from Tables IV and V that the values of ⌬0
ϩ͑bϩcϪf ͒sin2 ␹ /J͑Jϩ1͒,
1
2
͑27͒
J
Pt
1
S
where f is the nuclear spin-rotation interaction constant, the
angle ␹J is the angle representing the unitary transformation
required to diagonalize the energy matrix for a molecule with
a ground state ⍀ϭ0 which is coupled by a weak Coriolis
interaction to the 1 state. This angle may be approximated
and ⌬0 are unusually large. It is not unreasonable that the
cause is a low-lying 1 excited state. A brief inspection of
1
ϩ
Eqs. ͑14͒ and ͑10͒ shows that
ϩ
2
2P2
ϩ
me
me
2P
L
Pt
S
⌬
1ϩ
⌬ ϷϪ
ϵϪ
.
0
01
by
MPt
MS
Y ͑T ϪT ͒
Y ͑T ϪT ͒
01
1
0
01
1
0
͑
25͒
P
Pt
S
01
ͱ
tan ␹ Ϸ2 2
͓J͑Jϩ1͔͒1/2
.
͑28͒
If we assume ⌬ ϭ⌬ ϭϪ62.5 ͑as in Table V͒, the spin-
orbit energy gap 1 Ϫ0 ͓ϵ(T ϪT )͔ can in principle be
estimated. However, the value of P is a problem: In the ide-
alized ‘‘pure precession’’ approximation it is given roughly
J
0
1
T1ϪT0
ϩ
ϩ
1
0
To a good approximation the remaining constants in Eq. ͑27͒
5
5
are
2
9,31
by
2
1
6␲
3 cos ␪Ϫ1
bϭg ␮ ␮
͉
␺͑0͒ 2
͉
Ϫ
͑29͒
͑30͒
PϳB
but the value of Ja is unknown. For Bi ͑Ref. 31͒ it was
assumed that J ϭ1 is reasonable, making PϭB 2. For PtS
this approximation gives (T ϪT )ϳ471 cm . This value is
ͱ
J ͑J ϩ1͒,
͑26͒
N
B
N
ͫ
ͩ
r3
ͪ
ͬ
a
a
3
av
2
ͱ
3 cos ␪Ϫ1
a
Ϫ1
cϭ3gN␮B␮N
ͩ
ͪ
r3
1
0
av
not far from ␻ ͑Table VI͒. However, there were no hints of
perturbations in the spectra of vibrationally excited mol-
ecules. In addition, there is no mention of a low-lying ex-
e
͉
␺(0) 2
͉
is the probability of finding unpaired electron den-
sity at the nucleus in question, g is its nuclear g factor, ␮
N
B
cited electronic state in the literature. Furthermore, (T
and ␮N are the Bohr and nuclear magnetons, respectively, r
is the distance between the nucleus and electron, and ␪ is the
angle between the internuclear axis and the radius vector
from nucleus to electron.
1
Ϫ1
ϪT )ϳ471 cm seems low. We may make a comparison to
0
the related molecule PtO, for which (T ϪT ) is reported
1
0
Ϫ1 17
from its electronic spectrum as 946 cm
.
From its micro-
4
8
wave spectrum we have recently obtained, assuming P
Tischer et al. show that owing to a small rotation angle
Ϫ1
ϭB
ͱ
2 a value of ϳ612 cm , which is significantly lower.
␹ in the case of the Bi-halides the terms in Eq. ͑27͒ involv-
J
2
Evidently the approximation that J ϭ1 is poor for PtO; this
ing sin (1/2)␹ /J(Jϩ1) may be neglected. The negative
a
J
is likely also the case for PtS. Given that the unpaired elec-
trons are in ␲-molecular orbitals with a significant contribu-
tion from 5d on Pt (lϭ2!) ͑see below͒, this is perhaps un-
sign of (C ) (Bi) is therefore shown to arise in Eq. ͑27͒
from a large and negative rotational hyperfine structure con-
stant b.
I
eff
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3494
J. Chem. Phys., Vol. 121, No. 8, 22 August 2004
S. A. Cooke and M. C. L. Gerry
8
9
A very similar situation applies for PtS. Its T ϪT gap
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13 ͑2004͒.
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0
has been estimated in the BOB analysis given above to be
smaller than the corresponding gap for the Bi halides. How-
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͑
10
11
Eq. ͑28͒ shows that ␹ is small, Ϸ0.1° for the highest J
J
1
1
2
3
observed (Jϭ2). Accordingly the ground state is nearly a
ϩ
pure X0 state, and the terms in Eq. ͑27͒ involving
2
sin (1/2)␹ /J(Jϩ1) may again be neglected. Just as with
14
J
1
95
the Bi halides, a negative CI( Pt) requires b also to be
negative. Population analysis from our DFT calculation
shows that the unpaired electrons in PtS ͑which are in a ␲
orbital͒ have contributions of Ϸ0.6 3p from S and Ϸ0.4 5d
1
1
5
6
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18
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͑
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͉
␺(0)
͉
in Eq. ͑26͒ essentially zero, so that b is again nega-
19
2
3
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20
21
22
av
A crude estimate for f might be the value of C (195Pt)
I
Ϸ30 kHz, recently found for 1 PtSi. This would permit a
95
13
23
2
similarly crude estimate of b͓ϷϪg ␮ ␮ ((3 cos ␪
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B
N
3
Ϫ1)/r ) ͔ of the order of Ϫ20 MHz. Such a value is not
24
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2
2
7
8
29
3
3
3
0
1
2
ϩ
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⌺
ϩ
33
34
states. This procedure has been shown to be valid. The
Pt
S
01
Born–Oppenheimer breakdown parameters ⌬01 and ⌬
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35
36
ϩ
Pt
S
01
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37
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39
length r has been evaluated, along with the vibration fre-
e
40
quency and dissociation energy.
4
4
4
1
2
3
ACKNOWLEDGMENTS
This research has been supported by the Natural Sci-
ences and Engineering Research Council ͑NSERC͒ of
Canada and by the Petroleum Research Fund, administered
by the American Chemical Society.
44
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4.88.136.149 On: Tue, 25 Nov 2014 13:52:49
8