Temperature and isotope substitution effects on the structure and NMR properties of the pertechnetate ion in water

Article abstract of DOI:10.1021/ja047447i

The uniquely well-resolved ⁹⁹Tc NMR spectrum of the pertechnetate ion in liquid water poses a stringent test of the accuracy of ab initio calculations. The displacement of the ⁹⁹Tc chemical shift as a function of temperature has been measured over the range 10-45 °C for the three isotopomers Tc(¹⁶O)₄^-, Tc( ¹⁶O)₃(¹⁸O)^-, and Tc( ¹⁶O)₃(¹⁷O)^- at natural oxygen isotope abundance levels, and in addition the temperature dependence of the Tc-O scalar coupling was determined for the Tc(¹⁶O)₃( ¹⁷O)^- isotopomer. Values for these parameters were computed using relativistic spin-orbit density functional theory with an unsolvated ion approximation and with treatments of the solvated ion based on the COnductor-like Screening MOdel (COSMO) approach. The temperature and isotope dependence of ⁹⁹Tc NMR parameters inferred by these methods were in good quantitative agreement with experimental observations. The change in the Tc-O bond length associated with the changes in temperatures considered here was determined to be of the order of 10^-4 A. Vibrational energies and Tc-O bond lengths derived from these models also compare favorably with previous experimental studies.

Full text of DOI:10.1021/ja047447i

Published on Web 08/28/2004
Temperature and Isotope Substitution Effects on the
Structure and NMR Properties of the Pertechnetate Ion in
Water
Herman Cho,* Wibe A. de Jong, Bruce K. McNamara, Brian M. Rapko, and
Ingrid E. Burgeson
Contribution from the Pacific Northwest National Laboratory, P.O. Box 999,
Richland, Washington 99352
Received April 30, 2004; E-mail: hm.cho@pnl.gov
99
Abstract: The uniquely well-resolved Tc NMR spectrum of the pertechnetate ion in liquid water poses a
stringent test of the accuracy of ab initio calculations. The displacement of the 99Tc chemical shift as a
16
-
4
function of temperature has been measured over the range 10-45 °C for the three isotopomers Tc( O) ,
1
6
18
-
16
17
-
Tc( O)
3 3
( O) , and Tc( O) ( O) at natural oxygen isotope abundance levels, and in addition the
16
17
-
temperature dependence of the Tc-O scalar coupling was determined for the Tc( O)
3
( O) isotopomer.
Values for these parameters were computed using relativistic spin-orbit density functional theory with an
unsolvated ion approximation and with treatments of the solvated ion based on the COnductor-like Screening
99
MOdel (COSMO) approach. The temperature and isotope dependence of Tc NMR parameters inferred
by these methods were in good quantitative agreement with experimental observations. The change in the
Tc-O bond length associated with the changes in temperatures considered here was determined to be of
-
4
the order of 10 Å. Vibrational energies and Tc-O bond lengths derived from these models also compare
favorably with previous experimental studies.
1
. Introduction
chemical shifts due to the vanishing of both electric field
gradients and the chemical shift anisotropy. Among tetravalent
metal oxides, measurable displacements of the metal chemical
shift due to oxygen isotope substitution have been reported for
2
An unusually detailed picture of a complex ion’s structure
9
9
and environment in liquid water can be constructed from Tc
and 17O nuclear magnetic resonance (NMR) spectra of the
pertechnetate anion (TcO4 ). The Tc nuclide’s favorable NMR
5
5
- 3 95
2- 3 51
3- 4 53
2- 4
99
5
MnO4 , MoO4
,
VO4
,
CrO4 , and RuO4. The
-
99
9
9
Ru chemical shift in RuO4 has also been found to be quite
properties, which include a sizable gyromagnetic ratio (9.583
5
-
sensitive to temperature. Despite the cubic symmetry of ReO4 ,
its
6
×
10 Hz/T), moderate quadrupolar moment (Q ) -1.29 barns),
1
85
187
Re NMR line widths are too broad6 for
Re and
large spin angular momentum quantum number (I ) 9/2), and
measurement of the isotope or temperature dependence of their
chemical shifts. Both rhenium isotopes have substantially larger
1
00% isotopic abundance, combined with the cubic symmetry
-
of its environment in TcO4 , give rise to a strong, highly
resolved Tc NMR signal that is sensitive to minute perturba-
tions in the metal atom’s environment.
9
9
55
99
quadrupolar moments than Tc or Mn, and in addition Tc
9
9
1
85
has a larger spin angular momentum quantum number than Re
and Re. These factors imply that the quadrupolar broadening
of the Re and Re resonances of ReO4 in the extreme
narrowing limit will indeed be greater than that for the Tc or
187
The sensitivity of the pertechnetate ion’s NMR parameters
1
85
187
-
1
is exemplified by the findings of Tarasov et al. in their study
99
of NH4TcO4(aq) containing artificially enriched levels of the
5
5
Mn signal in the analogous species, but the magnitude of the
1
8
99
O isotope. They showed that the Tc spectrum consisted of
four resolved lines, which they assigned to four isotopomers of
difference is not completely explained by quadrupolar relaxation
6
alone.
-
18
TcO4 , corresponding to the ion with zero to three O nuclei
replacing O (the isotopomer with four O nuclei was too rare
to be detected).
7
-11
Theoretical treatments have been developed
that interpret
16
18
such observations in terms of thermally- or isotope-induced13
1
2
Experimental observations of ligand isotope effects of this
magnitude have been limited mainly to those rare instances
where a diamagnetic, NMR-detectable metal center occupies a
site of high symmetry. Solution-state spin-lattice (T1) relaxation
times for metals in sites of perfect cubic symmetry are
particularly advantageous for high-resolution measurements of
(
2) Abragam, A. Principles of Nuclear Magnetism; Clarendon: Oxford, 1961.
3) Buckler, K. U.; Haase, A. R.; Lutz, O.; M u¨ ller, M.; Nolle, A. Z. Naturforsch.
(
1977, 32A, 126-130.
(
4) Tarasov, V. P.; Privalov, V. I.; Buslaev, Yu. A.; Eichhoff, U. Z. Naturforsch.
984, 39B, 1230-1235.
5) Brevard, C.; Granger, P. Inorg. Chem. 1983, 22, 532-535.
1
(
(6) Dwek, R. E.; Luz, Z.; Shporer, M. J. Phys. Chem. 1970, 74, 2232-2233.
(
7) Raynes, W. T.; Lazzeretti, P.; Zanasi, R.; Sadlej, A. J.; Fowler, P. W. Mol.
Phys. 1987, 60, 509-525.
8) Jameson, C. J.; Osten, H.-J. J. Am. Chem. Soc. 1986, 108, 2497-2503.
(
(
1) Tarasov, V. P.; Privalov, V. I.; Kirakosyan, G. A.; Gorbik, A. A.; Buslaev,
(9) Lounila, J.; Vaara, J.; Hiltunen, Y.; Pulkkinen, A.; Jokisaari, J.; Ala-Korpela,
Yu. A. Dokl. Akad. Nauk SSSR 1982, 263, 1416-1418.
M. J. Chem. Phys. 1997, 107, 1350-1361.
10.1021/ja047447i CCC: $27.50 © 2004 American Chemical Society
J. AM. CHEM. SOC. 2004, 126, 11583-11588
9
11583

A R T I C L E S
Cho et al.
changes in rotational and vibrational contributions to these NMR
properties. Because of the smallness of the energy shifts detected
in NMR experiments, a theoretical analysis that quantitatively
explains the experimental results requires consideration of
extremely subtle features of the metal complex and its interac-
tions with solvent molecules. Various solvation models have
been proposed to describe the effect of the molecular environ-
ment on NMR properties.14-22 Mikkelsen et al. demonstrated
with a dielectric continuum model that solvation effects are of
the same magnitude as rovibrational and electron correlation
effects. In this article, we account for solvation by combining
the rovibrational treatment with a similar dielectric continuum
model.
The temperature of the sample was regulated to within 0.2 K both
temporally and spatially by directing dry nitrogen gas at a high flow
rate around the NMR tube. Samples were allowed to equilibrate for at
least 30 min at the set point temperature of the experiment before the
NMR scanning was initiated. The gas temperature was controlled by a
refrigerated heat exchanger (Kinetics Thermal Systems) and the NMR
probe’s heater. The conservative temperature range of this study was
dictated at the bottom end by the reduced solubility of pertechnetate
salts at low temperatures and at the top end by considerations of
radiological safety.
14
The 99Tc NMR scans were acquired at a rate of one per second,
which ensured near-complete recovery of the magnetization between
scans for the entire temperature range investigated in this work,
24
17
according to past T
1
measurements. At natural O abundance levels
-
16
( O) isotopomer’s 99Tc sextet
17
-
and [TcO
4
] g 20 mM, the Tc( O)
3
2. Experimental Section
was readily detectable after 1000 scans.
Caution. The 99Tc isotope is a â-emitter (t1/2 ) 2.1 × 10 y). All
5
3. Computational Approach
manipulations of solids and solutions were performed in a Category 2
nuclear research facility at the Pacific Northwest National Laboratory
in Richland, WA. The NMR solutions were held in capped PTFE/FEP
copolymer sleeves (Wilmad) inserted in 10 mm glass NMR tubes, which
provided secondary containment of the radioactive liquids.
Computational studies were performed to elucidate the effects of
temperature and isotopic substitution on the NMR properties of
pertechnetate in terms of the rovibrational average structure of the
molecule. The general theory of thermal and isotope effects has been
12,13,25,26
discussed extensively.
Preparation of Aqueous 99Tc Standards. NH
by oxidative dissolution of 1 g of TcO in 150 mL of ammonium
hydroxide and 50 mL of hydrogen peroxide (30 wt % aqueous
4
4
TcO was prepared
To determine the rovibrational average value of a property, the
vibrational force constants and the property derivatives need to be
calculated. Both can be derived from calculated potential energy and
corresponding property surfaces. The surfaces were calculated on a grid
defined in the curvilinear symmetry coordinate system described by
2
2
3
solution). The solid was recrystallized three times. Ultimately, 1.28
g of NH TcO (100% theoretical yield ) 1.38 g) was collected.
KTcO was prepared by dissolution of 2.047 g of dry NH TcO
4
4
in
27
4
4
4
Gray and Robiette. Most grid points were selected as outlined by
deionized water and passage of this solution through a cation exchange
7,28,29
Raynes and co-workers
in their study of similar properties in the
+
column in the H form. The resulting HTcO
4
was titrated with 99.999%
pure 1.14 M KOH, using phenolphthalein as indicator. The solids were
washed with ethanol and ether and were then recrystallized three times.
methane molecule. These grid points allow for the determination of
the linear and quadratic force constants, as well as the cubic force
constants F111 and F222. In our pertechnetate calculations, we have
defined additional two-dimensional grids to obtain the symmetry
coordinate force constants F1SS (with S ) 2a, 3x, 4x). Other combina-
Ultimately, 1.183 g of KTcO
collected.
4
(theoretical yield ) 2.284 g) was
Each solid was dried to constant weight. Stock solutions were made
in 10 mL of D O in volumetric glassware. The standard solutions were
sequentially diluted in volumetric glassware with D O to obtain a set
of standards of varying pertechnetate concentrations. Each standard was
checked by â-liquid scintillation counting (LSC) by placing a known
amount of solution into an Ultima Gold liquid scintillation cocktail.
NMR Spectroscopy. Technetium-99 NMR data were collected at
tions replacing S with the symmetric coordinates 2b, 3y, etc. are related
to the ones above by symmetry.7
,28,29
The force constants and property
2
2
derivatives (calculated on the same grid) were determined by fitting
polynomials to the grid points of the calculated potential energy and
property surfaces with Mathematica routines.30
The rovibrational average molecular structure was calculated with
the AVIBR code of Lounila et al.26 Given the force constants,
temperature, and atomic isotopes, the AVIBR code calculates the
rovibrational average molecular geometry, the deviations from the
equilibrium (zero-vibration) geometry, and the average linear and
6
1
7.565 MHz on a Tecmag Discovery spectrometer equipped with a
0-mm broadband Nalorac probe. Minor adjustments of the shims using
the deuterium lock signal were performed for every sample, but after
shimming, the field lock apparatus was put in a hold (unlocked) mode
and the Z0 shim was set to the same preselected value for all samples.
The uncompensated field drift for the 7.04 T magnet (Oxford Instru-
ments, Inc.) used in these measurements was determined to be negligible
2
quadratic symmetry coordinate values 〈S〉 and 〈S 〉. The average
symmetry coordinate values and the calculated property derivatives P
were used to calculate the rovibrational average property defined in eq
1, with P being the value of the property for the equilibrium geometry:
e
-
4
(
∼-4 × 10 ppm/h).
1
2
2
1
2
3
2
2
〈
P〉 ≈ P + P 〈S 〉 + P 〈S 〉 + P
〈S 〉 + P
〈S 〉 +
e
S
1
S S
1 1
S2aS2a 2a
S3xS3x 3x
1
(
10) Vaara, J.; Lounila, J.; Ruud, K.; Helgaker, T. J. Chem. Phys. 1998, 109,
8
388-8397.
3
2
2
P
〈S 〉 + 3P
〈S S 〉 (1)
S3xS4x 3x 4x
(11) Ruden, T. A.; Lutnæs, Z.; Helgaker, T.; Ruud, K. J. Chem. Phys. 2003,
S4xS4x 4x
1
18, 9572-9581.
(
(
(
12) Jameson, C. J. J. Chem. Phys. 1977, 66, 4977-4982.
13) Jameson, C. J. J. Chem. Phys. 1977, 66, 4983-4988.
All calculations on the pertechnetate molecule were carried out with
14) Mikkelsen, K. V.; Ruud, K.; Helgaker, T. J. Comput. Chem. 1999, 20,
31-33
the Amsterdam Density Functional (ADF 2003.01) code.
Potential
1
281-1291.
(15) Nymand, T. M.; Åstrand, P.-E.; Mikkelsen, K. V. J. Phys. Chem. B 1997,
1
01, 4105-4110.
(24) Tarasov, V. P.; Privalov, V. I.; Buslaev, Yu. A. Dokl. Akad. Nauk SSSR
1982, 262, 1433-1434.
(25) Buckingham, A. D.; Urland, W. Chem. ReV. 1975, 75, 113-117.
(26) Lounila, J.; Wasser, R.; Diehl, P. Mol. Phys. 1987, 62, 19-31.
(27) Gray, D. L.; Robiette, A. G. Mol. Phys. 1979, 37, 1901-1920.
(28) Lazzeretti, P.; Zanasi, R.; Sadlej, A. J.; Raynes, W. T. Mol. Phys. 1987,
62, 605-616.
(29) Raynes, W. T.; Fowler, P. W.; Lazzeretti, P.; Zanasi, R.; Grayson, M. Mol.
Phys. 1988, 64, 143-162.
(30) Mathematica, version 5.0; Wolfram Research: Champaign, IL, 2003.
(31) ADF 2003.01, SCM, Theoretical Chemistry, Vrije Universiteit: Amsterdam,
The Netherlands (http://www.scm.com).
(
(
(
(
16) Pecul, M.; Sadlej, J. Chem. Phys. 1998, 234, 111-119.
17) Autschbach, J.; Ziegler, T. J. Am. Chem. Soc. 2001, 123, 3341-3349.
18) B u¨ hl, M. J. Phys. Chem. A 2002, 106, 10505-10509.
19) B u¨ hl, M.; Mauschick, F. T. Phys. Chem. Chem. Phys. 2002, 4, 5508-
5
514.
(
20) Ruud, K.; Frediani, L.; Cammi, R.; Mennucci, B. Int. J. Mol. Sci. 2003, 4,
1
19-134.
(
21) Åstrand, P.-E.; Mikkelsen, K. V.; Jørgensen, P.; Ruud, K.; Helgaker, T. J.
Chem. Phys. 1998, 108, 2528-2537.
(
(
22) Cossi, M.; Crescenzi, O. J. Chem. Phys. 2003, 118, 8863-8872.
23) Cotelle, S.; Haissinsky, M. Compt. Rend. 1938, 206, 1644.
11584 J. AM. CHEM. SOC.
9
VOL. 126, NO. 37, 2004

Temperature and Isotope Substitution Effects
A R T I C L E S
energy surface and property surfaces were calculated using density
34
functional theory (DFT) within the VWN local density approach. In
3
5
36
some property calculations the Becke88 and Perdew86 (BP86)
generalized gradient approximation (GGA) were used to assess the
influence of the exchange-correlation potential on the property values.
Both scalar relativistic and spin-orbit effects were included according
to the zeroth order regular approximation (ZORA) methodology.3
For the potential energy surface and the shielding surface the standard
ADF all-electron ZORA-optimized Slater-type orbital (STO) basis sets
TZ2P, triple-ú with two polarization functions, were used for both
technetium and oxygen. The TZ2P technetium basis set was augmented
with four steep 1s functions, while the double-ú 1s function of the
oxygen TZ2P was replaced with the triple-ú taken from the standard
ZORA QZ4P basis set, as has been proposed for the calculation of
accurate scalar couplings, especially those involving heavy atoms.3
The numerical integration accuracy parameter INTEGRATION was
chosen to be 7.0 throughout. The isotropic 99Tc shielding constant
7,38
Figure 1. Temperature dependence of the 99Tc NMR spectrum of a 0.1 M
NH4TcO4(aq) solution in a 7.04 T magnetic field (νL( Tc) ) 67.565 MHz).
9-41
99
4
2,43
surface was calculated with the NMR program
with the “Best”
option selected. The JTcO spin-spin coupling surface was calculated
3
9
using the CPL program, including the diamagnetic and paramagnetic
7
-1 -1
orbital terms, and gyromagnetic ratios of 6.046 × 10 rad T
s
for
99
7
-1 -1
17
Tc and -3.628 × 10 rad T
s
for O.
The effect of the molecular environment, i.e., the solvent, on the
rovibrationally averaged properties of the pertechnetate molecule was
incorporated using the COnductor-like Screening MOdel (COSMO).4
For ꢀ a value of 78.8 was used, whereas the radii defining the cavity
surface around the pertechnetate unit were taken as 1.85 for Tc and
4-46
1
.55 for O and 1.40 for the spherical solvent radius.
4. Results and Discussion
Figure 2. Expansion of the 30 °C 99Tc spectrum from Figure 1, with vertical
scaling given on the right. The stars (top spectrum) denote the sextet of the
Variable Temperature Studies. The temperature dependence
16
17
-
Tc( O)3( O) isotopomer, and the arrow (middle spectrum) identifies the
of the 99Tc NMR chemical shift for the Tc( O)4 isotopomer
is illustrated in Figure 1. Analyses of pertechnetate solutions
made with a different concentration ([NH4TcO4] ) 0.01 M) or
a different cation ([KTcO4] ) 0.1 M) revealed no differences
of statistical significance.
16
-
16
18
-
singlet of the Tc( O) ( O) isotopomer.
3
°
C. A second factor that potentially contributes to the temper-
ature dependence of the line widths is thermal gradients in the
sample. At 67.565 MHz, a temperature spread of only a few
tenths of a degree can introduce significant inhomogeneous
broadening in these resonances, which have intrinsic line widths
of <5 Hz.
Isotope Effects. If it is assumed that a natural oxygen isotope
distribution is expressed in an ensemble of pertechnetate ions,
the probabilities of the three most common isotopomers,
The variation in peak heights reflects a broadening of the
resonance as the temperature is moved above or below ∼30
2
4
99
°
C. Tarasov et al. have found that the Tc T1 of KTcO4
measured at 18.01 MHz passes through a maximum at ap-
proximately 320 K, which suggests that the lifetime-broadened
resonance should be narrowest at a higher temperature than we
have observed. In our own inversion recovery experiments at
1
6
-
16
18
-
16
17
-
Tc( O)4 , Tc( O)3( O) , and Tc( O)3( O) , will be 99.043,
.810, and 0.159%, respectively, which implies that the
6
7.565 MHz, we observed a broad T1 plateau at temperatures
0
around 303-318 K for a range of Tc concentrations and for
both the potassium and ammonium salts. This is consistent with
the observation of a line width minimum at approximately 30
9
9
integrated intensities of the Tc NMR signals will be in the
ratio of approximately 623:5:1. The O and O isotopes have
nuclear spin quantum numbers equal to zero, and therefore, the
1
6
18
9
9
16
-
16
18
-
(
32) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor.
Chem. Acc. 1998, 99, 391-403.
Tc spectra of the Tc( O)4 and Tc( O)3( O) isotopomers
17
99
are singlets, but since I ) 5/2 for O, the Tc spectrum of
(
33) te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A.; Fonseca Guerra,
C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22,
1
6
17
-
Tc( O)3( O) consists of six lines with equal spacings and
integrated intensities. These expectations are confirmed in the
spectra of Figure 2.
9
31-967.
(
(
(
34) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1989, 58, 1200-1211.
35) Becke, A. D. Phys. ReV. A 1988, 38, 3098-3100.
36) (a) Perdew, J. P. Phys. ReV. B 1986, 33, 8822-8824. (b) Perdew, J. P.
Phys. ReV. B 1986, 34, 7406.
It may be seen from Figure 2 that 99Tc has a different isotropic
shift in the three isotopomers. The magnitude of the difference
(
37) Van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99,
4
597-4610.
1
6
-
between the resonances of Tc( O)4 and the other two
isotopomers decreases monotonically with temperature, going
from -28.9 Hz (-0.428 ppm) to -28.1 Hz (-0.416 ppm) for
δTc(16O) (18O)- - δTc(16O) - and from -16.3 Hz (-0.241 ppm) to
-13.6 Hz (-0.201 ppm) for δTc(16O) (17O)- - δTc(16O) - as the
temperature was raised from 10 to 45 °C. In experiments
(
38) Van Lenthe, E.; Ehlers, A. E.; Baerends, E. J J. Chem. Phys. 1999, 110,
8
943-8953.
(
(
(
39) Autschbach, J. A.; Ziegler, T. J. Chem. Phys. 2000, 113, 936-947.
40) Helgaker, T.; Jaszu n´ ski, M.; Ruud, K. Chem. ReV. 1999, 99, 293-352.
41) Enevoldsen, T.; Visscher, L.; Saue, T.; Jensen, H. J. A.; Oddershede, J. J.
Chem. Phys. 2000, 112, 3493-3498.
3
4
(
(
(
42) Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1995, 99, 606-611.
43) Wolff, S. K.; Ziegler, T. J. Chem. Phys. 1998, 109, 895-905.
44) Klamt, A.; Sch u¨ u¨ rmann, G. J. Chem. Soc., Perkin Trans. 2 1993, 5, 799-
3
4
47
8
06.
1
6
( O) , the 99Tc resonance frequency was extracted
17
-
(
(
45) Klamt, A. J. Phys. Chem. 1995, 99, 2224-2235.
(47) In the case of Tc( O)
by averaging the positions of the six lines in its spectrum.
3
46) Pye, C. C.; Ziegler, T. Theor. Chem. Acc. 1999, 101, 396-408.
J. AM. CHEM. SOC.
9
VOL. 126, NO. 37, 2004 11585

A R T I C L E S
Table 1. Comparison of Experimental and Calculated Vibrational
Cho et al.
50
Table 2. Calculated 99Tc Isotropic Shielding Data (ppm)
-
1
Transition Energies (cm
)
isotopomer
temp (K)
gas phase
COSMO
scaled COSMO
mode
experiment
gas phase
COSMO
1
6
-
-
-
Tc( O)4
283
293
318
-1485.511
-1486.009
-1487.307
-1425.879
-1426.558
-1428.319
-1430.230
-1430.954
-1432.811
ν1(A1)
ν3(F2)
ν2(E)
912 ((1)
912 ((4)
325 ((2)
334 ((10)
942
940
317
341
944
903
307
319
17
Tc( O)4
283
-1484.807
-1485.315
-1486.637
-1425.086
-1425.776
-1427.565
-1429.356
-1430.092
-1432.003
ν4(F2)
2
3
93
18
1
8
Tc( O)4
283
93
318
-1484.174
-1484.691
-1486.035
-1424.373
-1425.074
-1426.889
-1428.570
-1429.318
-1431.257
99
performed at a lower field (ν( Tc) ) 18.01 MHz), Tarasov et
al. measured a displacement in the Tc chemical shift of
0.43 ppm upon each substitution of an O atom with O.
2
1
,4
99
16
18
-
They reported that this isotopic displacement did not change
with temperature, but at the lower field of their instrument the
symmetric stretch mode ν1 is unchanged. The fact that the ν1 is
not affected by the solvation model can be attributed to the
symmetry of this vibration. This mode maintains tetrahedral
symmetry and has no dipole or quadrupole moment that could
induce a polarization of the solvent. This is in contrast to the
other three modes, where the vibration distorts the molecule
and the resulting dipole and quadrupole moment induce a
polarization of the solvent. A more detailed discussion can be
small magnitude of the effect may not have been resolvable.
Franklin et al.48 have studied pertechnetate solutions that were
1
7
18
artificially enriched in both O and O and reported finding
that the 99Tc chemical shift was displaced by -0.22 ppm upon
each increment by one mass unit of one of the oxygens. The
temperature dependence of the isotropic shift or the isotopic
displacement was not discussed by them.
51
found in a review article by Tomasi and Persico and references
therein.
1
6
17
-
After Tc( O)3( O) , the next most probable natural abun-
16
18
-
dance isotopomer is Tc( O)2( O)2 . Although it represents
.0025% of the total pertechnetate ion population, or ∼1/64 of
the population of Tc( O)3( O) , the Tc resonance of
Tc( O)2( O)2 is contained in a singlet vs the sextet of
Tc( O)3( O) . The expected signal intensity of this single line
The bond lengths obtained in the calculations are 1.717 Å
for the free pertechnetate and 1.714 Å for the solvated molecule,
which are in good agreement with the value of 1.711 Å obtained
0
1
6
17
-
99
1
6
18
-
5
2,53
from single-crystal X-ray measurements.
16
17
-
Inclusion of rovibrational contributions, which include both
zero-point and finite temperature contributions, is found to
increase the computed average bond length by 0.004-0.005 Å
relative to the ground-state geometry, depending on the model.
This bond length increase is accompanied by changes in the
will therefore be ∼10% of the intensity of a single line in the
1
6
17
-
Tc( O)3( O) multiplet, well above the detection threshold.
16
18
-
However, the separation between the Tc( O)2( O)2 and
1
6
-
Tc( O)4 resonances will be only 57 Hz in a 7.04 T magnetic
16
18
-
field, which positions the Tc( O)2( O)2 line on the shoulder
9
9
16
-
Tc shielding of ∼-50 ppm (-40 ppm for the gas-phase
model) and JTcO by ∼+4 Hz, or approximately 3.5% of its total
value. The complete substitution of oxygen isotopes, going
of the much larger Tc( O)4 line. Observation of such a signal
would be problematic at 67.565 MHz, but in a higher field
magnet, the chemical shift difference should be sufficient to
detect and separate the signals of the two isotopomers.
5
4
1
6
-
17
-
from Tc( O)4 to Tc( O)4 , leads to a decrease of the
-
5
rovibrational average bond length at 283 K of 8 × 10 Å (or
The Tc-O scalar coupling was determined from the
1
8
16
twice this value when substituting O for O). The isotope
effect is dominated by the symmetric stretch mode. A change
in temperature from 283 to 318 K results in an increase of the
1
6
17
-
Tc( O)3( O) sextet by measuring the separation between the
outermost lines and dividing by 5. The measured JTcO was found
to decline monotonically with temperature, from 132.5 Hz at
-
4
rovibrational average bond length by 1.5 × 10 Å. When the
various contributions to the temperature effect are analyzed, one
finds that all vibrational modes contribute to the same order of
magnitude.
4
9
1
0 °C to 131.9 Hz at 45 °C. Values of 131.6 Hz and 133.3
1
17
Hz have previously been obtained from the ten-line
O
O
1
17
multiplet of NH4TcO4 solutions (with ref 49 and without
enrichment), in which the 17O line widths were found to be a
Computed 99Tc isotropic shielding values for a series of
temperatures and isotopomers are presented in Table 2. Through-
out this article, the definition and sign of the shielding in relation
to the chemical shift conform to the standard convention.55 The
values in the scaled COSMO column were obtained by reducing
the COSMO F11 force constant by 8%. This scaling lowers the
vibrational mode ν1 such that it is degenerate with ν3, as
99
16
17
-
factor of 6 or greater than the Tc line widths of Tc( O)3( O) ,
while a value of 131.4 Hz was determined at 25 °C from the
9
9
17
48
Tc spectrum of O-enriched KTcO4.
Computations. The computational approach outlined in the
Computational Approach section was evaluated by calculating
vibrational frequencies and average bond lengths for comparison
with published experimental data. Table 1 shows that the
calculated vibrational results are in good agreement with
experimental data. The observed near-degeneracy of the ν1 and
ν3 modes is reproduced by the gas-phase calculations, although
overall the calculated frequencies are about 30 cm-1 too high.
When the COSMO solvation model is included in the calcula-
tion, the frequencies of the ν3, ν2, and ν4 are lowered, but the
50
observed experimentally by Weinstock et al. This scaling thus
(50) Weinstock, N.; Schulze, H.; M u¨ ller, A. J. Chem. Phys. 1973, 59, 5063-
5067.
(
51) Tomasi, J.; Persico, M. Chem. ReV. 1994, 94, 2027-2094.
(52) Krebs, B.; Hasse, K.-D. Acta Crystallogr. 1976, B32, 1334-1337.
53) Faggiani, R.; Lock, C. J. L.; Poc e´ , J. Acta Crystallogr. 1980, B36, 231-
33.
(54) The various contributions of the different terms in eq 1 for the rovibrational
(
2
1
6
-
averaged Tc( O)
4
at 283 K are P
e
) -1445.031 ppm, 〈PS1〉 ) -33.899
ppm, 〈PS S 〉 ) -3.111 ppm, 〈PS2aS2a〉 ) -3.498 ppm, 〈P
3x 3x
S S
〉 ) 5.983 ppm,
1
1
(
48) Franklin, K. J.; Lock, C. J. L.; Sayer, B. G.; Schrobilgen, G. J. J. Am.
Chem. Soc. 1982, 104, 5303-5306.
〈PS4xS4x〉 ) -6.020 ppm, and 〈PS3x 〉 ) 0.065 ppm. Force constants and
S
4x
property derivatives are provided as Supporting Information.
(55) Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Goodfellow, R.;
Granger, P. Pure Appl. Chem. 2001, 73, 1795-1818.
(49) Buckingham, M. J.; Hawkes, G. E.; Thornback, J. R. Inorg. Chim. Acta
1
981, 56, L41-L42.
11586 J. AM. CHEM. SOC.
9
VOL. 126, NO. 37, 2004

Temperature and Isotope Substitution Effects
A R T I C L E S
Table 3. Oxygen Isotope Dependence of the 99Tc Isotropic
Chemical Shift (ppm): Comparison of Calculated and
-
Experimental Results for TcO4
single atom
substitution
temp
(K)
gas
phase
scaled
COSMO
COSMO
experiment
16O f 17
O
283
-0.176 -0.198 -0.219 -0.241 ((0.012)
-0.174 -0.196 -0.216 -0.227 ((0.005)
-0.168 -0.189 -0.202 -0.201 ((0.007)
293
18
3
16O f 18
O
283
-0.334 -0.377 -0.415 -0.428 ((0.015)
-0.330 -0.371 -0.409 -0.427 ((0.006)
-0.318 -0.358 -0.389 -0.416 ((0.009)
293
18
3
1
6
-
are the differences in the chemical shifts of the Tc( O)4 and
Tc( O)3(
1
6
-
Figure 3. Measured and calculated displacements of the Tc( O)4
1
6
17,18
-
9
9
O) isotopomers, as given by the equation
isotopomer’s Tc isotropic chemical shift as a function of temperature (δ
≡
0 ppm at 283 K). The line is a least-squares fit of a second-order
-
2
exp
isotope
polynomial to the experimental data (x0 ) -19.05 ppm; x1 ) 5.36 × 10
∆
) δTc(16O)3(17,18O)-
- δTc(16O)4-
(3)
-
5
2
ppm/K; x2 ) 4.82 × 10 ppm/K (R ) 0.9999)). The sample was 0.1 M
NH4TcO4(aq).
while the theoretical data were obtained from the expression
provides insight into the effect of the symmetric stretch on the
calculated properties.
theory
isotope
1
) [δ
4
∆
Tc(17,18O)4-
- δTc(16O)4-
]
(4)
The numbers in Table 2 were obtained using LDA function-
als. To assess the influence of the exchange-correlation potential
on the property values, additional calculations were performed
using the VWN+BP86 functional. Inclusion of the BP86
functional leads to a shift of 8 ppm.
Both the experimental and theoretical results therefore represent
9
9
the Tc chemical shift displacement caused by the substitution
1
6
17
18
of a single O atom by either O or O.
Table 3 shows that the theoretical models successfully account
for the observation that the isotopic shift displacement decreases
with increasing temperature. The predicted displacement from
the gas-phase model is between 17 and 27% less than the
experimental measurement over the temperature range consid-
ered, and inclusion of solvent effects with scaling reduces the
discrepancy between theory and experiment to less than 10%.
The effect of the changes in the property derivatives due to
the COSMO solvation model was found to be small. The
improved agreement with experiment of the COSMO and scaled
COSMO results is predominantly due to changes in the
vibrational force constants. Lowering of especially the high
frequency vibrational modes has a considerable effect on both
the temperature- and isotope-induced chemical shift displace-
ments. Hence, highly accurate vibrational force constants are
needed to calculate the temperature and isotopic trends observed
in experiment.
A discussion of chemical shifts usually begins with the
99
definition of a reference molecule, but Tc presents a number
of special difficulties in this regard. Although the pertechnetate
anion would seem to be an obvious choice, the variability of
its resonance frequency with temperature, and the sensitivity
to the molecule’s structure that this implies, makes it question-
able both experimentally and theoretically to base a chemical
-
shift scale on TcO4 . Only a limited number of technetium-
containing compounds have been studied by 99Tc, none of them
entirely satisfactory as a standard. The problem of choosing a
standard is circumvented, however, by focusing on the ther-
9
9
mally- or isotope-induced changes in the pertechnetate Tc
chemical shift rather than the shifts with respect to a fixed
reference. The temperature dependence of the 99Tc isotropic
chemical shift predicted by the theoretical models of Table 2 is
compared to experimental data in Figure 3. The dependent
variable in this plot is the displacement of the chemical shift
from the position of the resonance at 283 K, i.e.,
The overall accuracy of the calculated temperature and isotope
2
9
effects is similar to those found in earlier studies on methane,
10
9
18
water, and CSe2. B u¨ hl used molecular dynamics with a one-
dimensional symmetric stretch potential to calculate the rovi-
brational contribution in MnO4 , which is isoelectronic to
∆T ) δ(T) - δ(283 K)
(2)
-
-
TcO4 . The temperature effect observed in our article is 1 order
As this plot shows, the observed direction of the chemical shift
displacement (increasing shift with increasing temperature) is
correctly predicted by both theoretical approaches. The mag-
nitude of the displacement is underestimated by the gas-phase
model, and incorporation of solvent effects is seen to improve
the correlation of theory with experiment.56 The difference
between experimental and calculated results for the scaled
COSMO approximation, which showed the best correlation, is
less than one-third the difference for the gas-phase model.
The effect of oxygen isotope substitution on the 99Tc isotropic
chemical shift is illustrated in Table 3. The experimental results
of magnitude larger than that seen by B u¨ hl, which is not
surprising as the bending and asymmetric stretching modes have
been neglected in the latter case.
By fixing the dielectric constant in the solvation model over
the entire temperature range, the effect of temperature on the
solvent and the response of the pertechnetate ion to the changed
1
4
environment are ignored. To assess the effect of the solvent
temperature on the shielding, an additional geometry optimiza-
tion and property calculation were performed with an ꢀ value
of 67.0. This change from ꢀ ) 78.8 approximates the change
in the dielectric constant of water when heated by 35 °C.57 On
the basis of these calculations, we estimate that a 35 °C
1
6
-, going from 283 to 318 K,
4
(
56) The experimental shift measured for Tc( O)
is 2.894 ppm. The gas-phase, COSMO, and scaled COSMO shifts are 1.796,
.440, and 2.581 ppm, respectively.
2
(57) Floriano, W. B.; Nascimento, M. A. C. Braz. J. Phys. 2004, 34, 38-41.
J. AM. CHEM. SOC.
9
VOL. 126, NO. 37, 2004 11587

A R T I C L E S
Cho et al.
Table 4. Comparison of Calculated and Experimental 99Tc-17
O
have also been proposed as a cause of strong temperature and
Scalar Coupling Data (Hz)
60,61
isotope dependences.
On the other hand, among metal-
temp (K)
gas phasea
COSMOa
scaled COSMOa
experimentb,c
-
containing molecules in the solution state TcO4 is a compara-
tively rare example in which the observed sensitivity can be
mainly attributed to rovibrational corrections and effects within
the electronic ground state. Because of the need to consider the
effects of bonding and the small magnitudes of the NMR
energies, the theoretical analysis involves a demanding com-
putational effort.
283
293
318
-120.286
-120.235
-120.102
-131.242
-131.183
-131.028
-130.836
-130.772
-130.615
132.5 ((0.2)
132.1 ((0.1)
131.9 ((0.1)
a
Theoretical results for the Tc( O)4 isotopomer. b Experimental results
17
-
16
17
-
c
for the Tc( O)3( O) isotopomer. The sign of JTcO cannot be determined
from the experimental spectra.
Although temperature changes of as little as 1 °C can cause
temperature increase of the solvent will increase the temperature-
induced shift displacement by 0.1 ppm, which improves the
correspondence with experiment.
9
9
the pertechnetate Tc peak to shift by an amount exceeding its
line width, to our knowledge the observation of temperature-
induced displacements of the chemical shift and scalar coupling
has never been reported. While oxygen isotope effects have been
studied in the past with isotopically enriched samples, we have
shown that it is feasible to detect and resolve three, and perhaps
four, pertechnetate isotopomers with oxygen isotope populations
at natural abundance levels and to discern differences in their
Calculated and experimental values for the Tc-O scalar
coupling are compared in Table 4. In contrast to the chemical
shift, not only the temperature and isotope displacements but
also the scalar coupling constant itself can be compared to
experimental data. The scalar coupling values for the (COSMO)
solvated pertechnetate ion seem to be in good agreement with
those observed in experiment. This agreement might be
somewhat fortuitous as the value of JTcO depends on the
exchange-correlation functional chosen. For example, for the
VWN+BP86 functional the scalar coupling is reduced by 5 Hz.
The theoretical models correctly predict the trend that the
absolute value of the scalar coupling decreases with increasing
temperature. The predicted changes due to temperature are
smaller than those observed in experiment.58 A solvation model
involving explicit water molecules could improve the overall
accuracy of both the scalar coupling value and the predicted
trend, since the direct interaction of the oxygen with the water
molecules will affect its electronic density and thereby JTcO.
Although not presented here, the calculations predict the
isotopic displacements to be in the order of 0.01 Hz. This change
is 1 order of magnitude smaller than the displacement due to
temperature changes and is smaller than the experimental
uncertainty in the measurement of JTcO.
16
17
-
response to changes in temperature. For the Tc( O)3( O)
isotopomer, an added interest is the possibility of measuring
the Tc-O scalar coupling from the multiplet pattern of its 99Tc
spectrum. The scalar coupling has been determined from the
1
7
17
O NMR spectrum, but the O lines are significantly broader
than the Tc peaks, and hence the 99Tc-derived value can be
considered more accurate. These findings suggest that the
pertechnetate ion, in addition to being a useful test case for ab
initio calculations, can serve as a sensitive model probe for
solvent-ion interactions.
99
Acknowledgment. We thank Prof. D. A. Dixon (University
of Alabama) for insightful discussions, Prof. J. Lounila (Uni-
versity of Oulu, Finland) for providing the AVIBR software
and some test cases, and an anonymous reviewer for helpful
advice on computing scalar couplings of heavy atoms. This
research was performed in part using the Molecular Science
Computing Facility (MSCF) in the William R. Wiley Environ-
mental Molecular Sciences Laboratory (EMSL) at the Pacific
Northwest National Laboratory. Portions of this work were
supported by the Laboratory Directed Research and Develop-
ment Program at the Pacific Northwest National Laboratory.
EMSL operations and the MSCF are funded by the Office of
Biological and Environmental Research in the U.S. Department
of Energy. The Pacific Northwest National Laboratory is
operated for the U.S. Department of Energy by the Battelle
Memorial Institute under Contract DE-AC06-76RLO-1830.
5. Conclusion
The theoretical analysis presented suggests that most of the
temperature and oxygen isotope dependence of the pertechnetate
molecule’s 99Tc NMR parameters can be accounted for by
9
9
accurate thermal averaging over rovibrational states. The Tc
resonance remained narrow over the entire temperature range,
which implies that the ion maintained its tetrahedral symmetry
despite changes in temperature. The primary modification in
structure was thus in the Tc-O bond length, which can be
-
4
4 4
Supporting Information Available: NH TcO solubility in
calculated to be on the order of 10 Å. Inclusion of solvent
effects in the theoretical treatment lowers the calculated
vibrational frequencies and thereby improves the correspondence
of the calculated and experimental values.
water as a function of temperature (0-70 °C), temperature
9
9
dependence of the Tc chemical shift of 0.01 M NH4TcO4 and
9
9
0
0
.10 M KTcO4, Tc inversion recovery T1 measurements of
.01 M NH4TcO4 and 0.10 M KTcO4 at 10, 30, and 45 °C, and
Strong sensitivity of a metal’s solution state NMR parameters
to temperature or surrounding isotope has been noted in a large
calculated force constants and property gradients from gas-phase
and COSMO solvation calculations. This material is available
free of charge via the Internet at http://pubs.acs.org.
5
9
number of cases. Past explanations have identified thermally
activated exchange phenomena as a common source of this
sensitivity. In systems with low-lying electronic excited states,
changes in the splitting of the ground state and the excited states
JA047447I
(
60) Freeman, R.; Murray, G. R.; Richards, R. E. Proc. R. Soc. London, Ser. A
(
58) The effect of a change in solvent temperature is estimated to be only 0.03
1957, 242, 455-466.
Hz.
(61) Benedek, G. B.; Englman, R.; Armstrong, J. A. J. Chem. Phys. 1963, 39,
3349-3363.
(59) Multinuclear NMR; Mason, J., Ed.; Plenum: New York, 1987.
11588 J. AM. CHEM. SOC.
9
VOL. 126, NO. 37, 2004