Published on: Mar 4, 2016
Transcripts - PoplettOxfordJMR1981Oxonium
JOURNAL OF MAGNETIC RESONANCE u,488-507 (1981)
W2H and W/l70 Nuclear Quadrupole Double-Resonance
Study of an Oxonium Ion in H2S04-H20
IAN J. F. POPLET’I
Clarendon Laboratory, Parks Road, Oxford OX1 3PU, England
Received March 24, 1981
Using the technique of high-sensitivity double resonance with coupled multiplets
(DRCM) at 77 K, a “0-‘H dipolar fine structure was revealed for two “0 sites
in HpSO(.HzO at natural abundance. The lines are assigned to H30+ and the S-OH
group in HSO,-. To the former, the theoretical DRCM spectra fit well with the “0
maximum electric field gradient component, V,,, along a C,, axis and the sym-
metrical geometry of H30+ ion with R(O-H) = 1.03 A, R(H...H) = 1.72 A, and
H6H angle of 113.5’ indicating a slight flattening of a pyramidal ion. The I70 quad-
rupole coupling parameters obtained as e*qQ/h = +7513 kHz and n = 0.104 for the
I70 nucleus in the tetrahedral environment of a H30+ ion are shown to be consistent
with the predictions based on a Townes and Dailey model. The 2H quadrupole
double-resonance spectrum of 20% deuterated sample was measured, yielding four
inequivalent *H sites, but, for highly deuterated samples, these spectra are com-
plicated by a strong isotope effect.
Oxygen-17 nuclear quadrupole double-resonance (NQDR) spectroscopy has
proven to be a powerful technique for structural determination in solids, particularly
when used in conjunction with deuterium NQDR. Until a few years ago the experi-
ments were limited to isotropically enriched samples, with which the simple tech-
nique of double resonance with level crossing (I, 2) was employed, or else to
naturally abundant specimens, with which the technique used was that of double
resonance in the laboratory frame (3,4) with its requirement of large-amplitude
radiofrequency fields in order to satisfy the Hartmann-Hahn (5) condition.
Recently a new technique of double resonance with coupled multiplets (DRCM)
was developed (6) at Oxford, which has proved a most convenient method for
l’0 NQR spectroscopy and which is almost independent of the molar concentra-
tion of 170 nuclei. It does not require large-amplitude radiofrequency fields and
as a result it displays a fine structure on the 170 lines which gives information on
other atoms (particularly protons) that are close to the 170 nucleus. However,
the success of DRCM, which is based on the field-cycling technique, depends
ultimately on the length of the irradiation time, 7, and this in turn depends on a
sufficiently long dipolar spin-lattice relaxation time, TID. Detailed theoretical
and experimental aspects of DRCM are given elsewhere (6-8).
The deuteron quadrupole double resonance by level crossing (1) or, with more
Copyright 0 1981 by Academic F’ress, Inc.
AU rights of reproduction in any form reserved.
NQDR OF OXONIUM ION 489
sensitivity, by continuous coupling (19), has been well established as the normal
method for replacing the simple deuteron magnetic resonance technique for
routine 2H detection. It yields a wealth of information from the observed fine
structure of *H NQR lines resulting from either the isotope effect (10) or deuteron-
deuteron magnetic interaction (11).
Previously the *‘O DRCM spectrum of several hydroxy groups in carboxylic
acids and alcohols (6) was observed and well-resolved 170 multiplets were success-
fully interpreted in terms of the 170-lH dipolar interaction between an oxygen-17
nucleus and a single proton. The 170 DRCM spectrum of HZ1’O in ice Ih was also
recorded (12) but the proton fine structure is barely resolved because of the over-
1a.pof 112--+ 3/2 and 3/2 + 5/2 transition lines for 7) = 1 and also the broadening
resulting from a strong proton-proton dipolar interaction. However, the choice of
170 electric field gradient (efg) tensor configuration for the H,“O molecule with
the maximum component, V,,, normal to H,O molecular plane and the minimum
component, V,, , being the bisector of the HOH angle, gives the best fit to the
Sulfuric acid monohydrate has the monoclinic space group P2,lc with four mole-
cules per unit cell (13). One oxygen atom 0, forms three hydrogen bonds with
three different oxygens, each in one hydrogen sulfate anion. As no protons have
been located by X-ray diffraction, the structure of the assumed oxonium ion in
terms of close oxygen-oxygen contacts is illustrated in (Fig. 1) with R(O,-0,)
=: 2.566 A, R(O,-0,) = 1.649 A, and R(O,-0,) = 2.538 A and the angles,
0,-&-O, = 125.5”, 0,-8,-O, = 106.4”, and 0,-6,-O, = 100.9”. A zig-zag
chain of hydrogen sulfate groups is formed along the c axis with the hydrogen bonds
between them (R(O,-0,) = 2.657 A) parallel. These chains are held together by
FIG. 1. The bonding configuration of the oxonium ion in sulfuric acid monohydrate.
490 IAN J. F. POPLE-M
hydrogen bonds with the oxonium cations. One of the oxygen atoms, 02, in HS04-
anion forms two longer hydrogen bonds with the oxygen atoms of the oxonium ion
and that of another hydrogen sulfate anion.
The existence of the oxonium ion in H,SO, *H,O was made evident by a proton
NMR lineshape study (14) which showed a triplet pattern with a second moment
around 30 G2, characteristic of a three-spin system comprising three protons at
the corners of an equilateral triangle. Also the infrared spectroscopic studies
(15,16) of the oxonium ion show that the spectrum is similar to that of ammonia,
implying that it has an almost regular pyramidal structure. However, the informa-
tion concerning the protons in the oxonium ion obtained using spectroscopic
method has so far proved disappointing as a supplement to the X-ray structural
In this paper, the 2H and I70 NQDR spectra of the oxonium ion in sulfuric acid
monohydrate are presented. This, together with the interpretation of the 170-
three-proton dipolar fine structure, enables the accurate location of the protons by
spectroscopic means. A comparison of 170 efg tensors in HZ”0 and H,“O+ in
terms of a recent tetrahedral model based on Townes and Dailey’s theory is
Concentrated sulfuric acid was purchased in Analar form from BDH and added
to distilled water in stoichiometric amounts to form H2S04.Hz0. Five samples
with slightly different water contents (within a few percent) were prepared. The
samples were cooled slowly in cold N, gas (melting point of H,SO, .H,O = 8.5”C)
and their T,a’s were measured by a field-cycling method; a procedure made neces-
sary because the relative proportions of acid and water strongly affect Tlo, thus
determining the success of DRCM. The sample with longest T, (20 min) and TID(7
set) values had its contents titrated to give H,SO, aO.97H,O after the experiment.
Samples with higher deuterium content were prepared in a similar manner with
97% D,SO, (supplied from BDH) and various deuterium isotropic ratio of the
samples were determined by mixing weighed quantities of D20, deionized water
and either 100% H2S04 or 97% DzS04. An exact proportion of acid and water is not
critical as 2H NQDR using double resonance with level crossing (DRLC) does not
require a long TID.
Both DRCM and DRLC experiments were performed at 77 K using the double-
resonance spectrometer described elsewhere (1). As for the DRCM experiment,
the spectrum was first scanned (6) over a wide frequency range using two simul-
taneously applied rf fields separated in frequency by 2wp, where wP is the peak
frequency of the proton bath (about 50 kHz here). These fields were produced
by a double balanced mixer. When the 170 quadrupole resonance lines had been
roughly located by these means a second irradiation scheme was employed with
one fixed-frequency irradiation and a second irradiation which scanned the spec-
trum as has previously been described (6). These lines reveal fine structure.
In this way, five 170 resonance lines in the form of multiplets were detected in
undeuterated H,SO, *H,O at 77 K with the cycle time of 5 min, irradiation time of
NQDR OF OXONIUM ION 491
5 to 10 set, and linear rf field amplitude of 6 to 12 G peak to peak. Two resonances
centered at 1135 and 2232 kHz with dipolar multiplet width greater than 130 kHz
(Figs. 2a and b) were assigned to the H,O+ site because of the strong dipolar inter-
action expected between the 170 nucleus and these three protons. Three remaining
resonances, centered at 2020, 2327, and 4350 kHz with dipolar multiplet width of
100 kHz, were assigned to S-170H in HS04- anion as their dipolar multiplet
widths are typical of l’O-lH system observed in carboxylic acids (6). From these
170 frequencies, the 170 quadrupole coupling parameters were obtained as the
approximate values of e”qQ/h = 7.5 and 8.5 MHz with 7) = 0.1 and 0.8 for H,170+
and S70-H, respectively, using the I = 5/2 equations in the closed form given
elsewhere (17). These values will be refined in the next section.
Even though the strong proton-oxygen dipolar coupling favors DRCM, the
1,‘2-+ 5/2 transition expected at around 3370 kHz was not detected. This transi-
tion is known to be weak for small 7. When the l/2 + 5/2 transition is not detected
it is necessary to check that v is small and not close to unity. With 7 close to unity
the line at 1135 kHz could be assigned to both the l/2 -+ 3/2 and the 3/2 + 5/2
lines, which overlap, and the line at 2232 kHz becomes the l/2 -+ 5/2 line. How-
FIG. 2a. The experimental absorption (0) spectra of H,l’O+ ion obtained at 77 K by DRCM is com-
pared with the expected absorption (. .) spectra calculated using the data given in Table 4. The fixed
frequency of the double irradiation, (a) at 1040 kHz and (b) at 2165 kHz, is marked by the arrow and the
peak radiofrequency amplitude employed was 0.8 mT. The irradiation time was 10 sec.
492 IAN J. F. POPLETT
(b) 22go kHz
FIG. 2b. The experimental absorption spectra (0) of Hsr’O+ ion obtained at 77 K by DRCM is com-
pared with the expected absorption spectra (. .) calculated using the data given in Table 4. The fixed
frequency of the double irradiation, (a) at 1165 kHz and (b) at 2300 kHz, is marked by the arrow and the
peak radiofrequency amplitude employed was 0.8 mT.
ever, it has been shown that in this case a signal is obtained around 2232 kHz when
the fixed-frequency irradiation has a frequency around 1135 kHz. No such transi-
tions were obtained in this case so that the low 7 assignment may be assumed.
In the course of further sweeps across the HzS04.Hz0 spectrum to look for
other I70 resonances over the frequency range 400 to 4200 kHz, no resonances
were found, implying that 33Sresonances (I = 3/2, natural abundance of 0.76%),
whose quadrupole coupling constants should be as low as a few megahertz in view
of its near tetrahedral symmetry, are outside this range.
*H quadrupole resonance signals were detected using the DRLC technique from
three deuterated H,SO,*H,O samples, the deuterium content being 20% (Fig. 3a),
40%, and 85% (Fig. 3b), and one deuterated H,SO, sample (50% D). The cycle
time was 3 min, irradiation time was 2 set, and the linear rf field was 40 to 100 mG
peak to peak. These signals were observed to have lineshapes strongly dependent
on the deuterium content, X, of the samples which contain four different oxonium
species, H30+ (fractional abundance of (1 - x)~), H,DO+ (3x(1 - x)~), HD,O+
(3x2(1 - x)), and D,O+ (x3) (the actual ones for three samples are given in Table 1).
The assignments of these lines to Y+and V- transitions were based on the observed
NQDR OF OXONIUM ION 493
shifts upon the application of an external magnetic field of 10 G perpendicular to
the rf irradiation coil (18). Furthermore, the W/*H double quadrupole transition
spectra (19) of 40 and 85% deuterated samples, with the irradiation time of 10 set
and a linear rffield of 4 G peak to peak, were obtained to aid in the line assignments.
Since 20 and 85% deuterated samples contain large numbers of H2DO+ and D30+
species, respectively, the lines observed in these samples were simply assigned to
these partially deuterated oxonium species on the assumption that the deuteron-
deuteron dipolar interaction is absent for inequivalent deuterons. However, the
deuteron-two-proton dipolar interaction was calculated (from the diagonalization
of a 12 x 12 quadrupolar and dipolar Hamiltonian for three spins, I = 1, S = l/2,
S’ = l/2, followed by the transition probability calculation in analogy to those for
the D-H system (20)) to have a small effect on the 2H line frequencies (by about
?O. 1 kHz) in contrast to the case for the deuteron-one-proton system (+0.95 kHz
for V+ and -0.75 kHz for V-). As the 2H lines of DSO,- should be unshifted on
deuteration, the 141.4- and 129.1-kHz lines were assigned to Y+ and V- lines of that
site with e2qQ/h and q of 180.3 t 0.4 kHz and 0.136 + 0.005, slightly different
from those in H,SO, (e*qQ/h = 193.2 I 0.5 kHz and 77= 0.135 -+ 0.007). From the
spectrum of the 40% deuterated sample, it was not possible to locate 2H lines of
HD,O+ species so a frequency range for the HD,O+ band is taken for each
In double quadrupole transition (DQT) spectra (19), the *H lines with frequency
v$, 2 v&, where the indices indicate two different deuteron sites, are usually
most intense, followed by those with frequency ~3, + VA,. The lines with fre-
quencies v;, + ~6, are too weak to be observed at any rf field levels. These
lines are only observed if the ith deuteron is particularly close to thejth deuteron as
a nearest neighbor, as in HD20, and will become more complex if two nearest
deuterons are involved, as in D30+. The remaining deuterons are usually ignored
as the double quadrupole transition line intensity decreases rapidly with deuteron-
deuteron distance as a function of R(D. 1vD)-~ (19).
.: ‘. ;. *
-. :;. ., i
.. ..- -, .’ :.
.,.. ‘y ,,.L’
r :: ,,,. :*.,.-‘.
‘., “.” b.
..,....” .‘..‘.;,....,.. j -... ‘.
(b) loo 120 140
FIG. 3. ‘JWH DRLC spectra of (a) 20% and (b) 85% deuterated H,SO,.H,O at 77 K. The peak
radiofrequency amplitude employed was 0.02 mT and the irradiation time was 2 sec.
NQDR OF OXONIUM ION 495
On inspecting the X-ray structure of H2S04+H20, we have the following close
deuteron-deuteron pairs, labeled in Table 1 as
R-b; R-Q; b-D,; D,-D,; D,-D,; D,-D2,
and the less close pair, labeled as
w:here D3 and D, deuterons form hydrogen bonds with 0, of S = 0 so as to form
D,,-0,-D, with R(D* . .D) of 2.9 A. The DQT spectrum of a highly deuterated
sa.mple will exhibit all lines from all of these pairs for D30+. DSO,- and some lines
from two of the pairs in the first set, depending on two particular deuterons, and
also from the D,-D, pair in HD20+ .DSO,-. Only few lines will be seen from the
D,s-D, pair in H,DO+.DSO,-. Taking the D, deuteron frequencies to be those
with the second highest e2qQ/h value, as the D3 deuteron forms the longest
hydrogen bond with S = 02, thus formed the basis for the construction of a stick
diagram (and bands for HD,O+) spectrum to be fitted to the experimental DQT
spectrum (Fig. 4). Slight adjustment of *H V&line frequencies was necessary for
obtaining a best fit with the experiment, with the final *H line frequencies and their
quadrupole coupling parameters given in Table 1.
THE:ORY OF I’O-lH DIPOLAR INTERACTION IN AN OXONIUM ION
The oxygen-17 nucleus with a spin Z = 5/2, experiences a quadrupolar inter-
action described by its Hamiltonian,
31: - Z(Z + 1) + 4 (ii + 12)
with a non-axial-symmetrical electric field gradient. In the absence of a strong
dipolar interaction this leads to three doubly degenerate energy levels and three
a:llowed transitions v1(1/2 -+ 3/2), v2(3/2 -+ 5/2), and v3(1/2 + 5/2) in order of in-
creasing frequency; the latter transition becomes forbidden for the axial-symmetri-
cal efg (17= 0). Their quadrupole coupling constant, e’qQ/Zz, and asymmetry
parameter, n, may be derived straightforwardly using the equations in closed form
given elsewhere (17).
For the oxonium ion with three close protons, the 170 nucleus experiences
200 220 240 260 280
FIG. 4. WZH double quadrupole transition spectrum of 85% deuterated HzS04.H20 at 77 K to-
gether with the stick diagram spectrum constructed from parameters given in Table 7 and in text. The
peak radiofrequency amplitude was 0.4 mT and the irradiation time was 10 sec.
496 IAN J. F. POPLETT
some dipolar interaction with such protons (l’O- 170 dipolar interaction assumed to
be negligible in view of its low natural abundance) as a perturbation of the main
quadrupolar Hamiltonian (21). Then the total Hamiltonian of 170 nucleus in zero
field (in the principal-axis system of 170, efg asa frame of reference with I70 nucleus
at an origin) is given by
x TOT= zQ + E %:-Hi + i i jlf,“i”j + xpdbath VI
i=l i<j I=1
with X8-’ being a dipolar Hamiltonian for a pair of P and Q spins with the
proton position described in terms of polar coordinates by R(P-Q), the inter-
nuclear distance and the polar angles, 0,, and c#J~,given as (22)
c&y’ = -em@
where, in terms of Q and P spin operators, i and 5,
A = (1 - 3 cosz 6,&i,&, [41
B = - l/4(1 - 3 cos2 e,)[f+,k + i-s,], [51
c = (K + iL)[j+& + i,S+]; D = C”, [61
E = (M + iN)[f+$+]; F = E* [71
K = -312 sin 0, cos 0, cos c#J~,
L = +3/2 sin 8pe cos flpe sin c#I~,
M = -314 sin2 0, cos ~c#J,,
N = +3/4 sin2 0, sin 2+,.
Here, we have SYzmHi,X$‘-HJ B %‘pth so the effect of X$-Hi is to split each
degenerate quadrupolar energy level pair into 16 energy levels, called the multi-
plets, and hence 256 allowed intermultiplet transitions between two sets of quad-
rupolar energy levels. The effect of %!jjathis only to broaden the intermultiplet
THE MATRIX ELEMENTSOF QIJADRUP~LARHAMILTONIAN FORSPINZ = 512
I+5/2) 1+3/2) /+1/2) 1- l/2) I-312) ) -512)
(+5/21 1OY (10)“2Yr)
(+3/21 -2Y ( 18)1’2Y7j
(+1/21 (lo)“*Yq -8Y ( 18)“2Y77
(-l/21 ( 18)“2Y7j -8Y (lO)“PY?
(-3/2( (18)1’2Y1) -2Y
(-SD (lo)“*Y?j 1OY
Note. Y = e’qQl40.
498 IAN J. F. POPLETT
transition lines by a few kilohertz as well as to provide a large thermal reservoir
in the form of a proton dipolar bath as a result of a tight dipolar coupling by mutual
spin flops at a rate determined by the B term in Eq. .
Since a strong dipolar coupling in H,O+ ion is not negligible compared with 170
quadrupolar interaction (the contribution of off-diagonal matrix elements to the
170-lH dipolar splitting, X~/X,, is about 2.5 kHz), a total Hamiltonian is rewritten
in a form of a 48 x 48 matrix with the product of oxygen- 17 magnetic eigenvectors,
ImI) (ml = +5/2, ?3/2, and ? l/2) and three proton magnetic eigenvectors, 1msl) ,
[ms2), and (m&, being IJ) (J = 1to 48), instead of three 16 x 16 manifolds each
+-ml manifold represented by the I70 quadrupolar eigenvectors 1&m,) (=um (?5/2)
+ b, x /l/2) + c, I73/2)). In this way, the 48 x 48 matrix is easily constructed
from the quadrupolar Hamiltonian matrix elements (Table 2); three sets of 170-lH
dipolar Hamiltonian matrix elements, one of them tabulated in Table 3 as the lower-
left triangle only as Xg-“i is an Hermitian matrix; and three sets of ‘H- ‘H dipolar
Hamiltonian matrix elements, one of them tabulated in Table 4. It is then diag-
onalized numerically to give the energy eigenvalues, E,,j, and eigenvectors,
Im, j), as a linear combination of 48 basic states IJ) in the form of
Im,j) = $ (Z, + WJ)JJ), PI
where ZJ and W, are the real and imaginary parts of eigenvector coefficients (the
labels m andj represent thejth energy level of the mth multiplet).
The intensity of the intermultiplet transition line is obtained by calculating the
matrix elements of the rf Hamiltonian, &, which contribute to the transition
probability of each of the 256 allowed transitions between thejth energy level of
the mth multiplet and the fth energy level of the nth multiplet. The transition
probability is given as
where the radiofrequency Hamiltonian, X$ at the Kth site is
X9# = -yKhB,[2~f cos 13;+ (fK, + jK_) sin 13kcos c#&
- i(iK, - I!!) sin f3; sin I#&], [IO]
where the polar angles 13iand c#&define the direction of the rf field B, relative to
the principal-axis system of the efg at the Kth spin. However, we take the polar
angles for the protons with no defined principal-axis system to be the same as that of
170 nucleus. With the matrix elements of the angular momentum operators in the
complex form given as
A + iB = 1 (m,jl-y,j!:In, I), [Ill
C + iD = 1 (m,jly,(iLf f i!)ln, l), [=I
E + iF = 1 (m,j(y,(& - i!!)ln, I), El31
NQDR OF OXONIUM ION 499
where the index K represents any one of four nuclei in the H,O+ ion, the transition
probability, Wmj,nl, becomes
)(A + iB) cos t9I,+ (C + D) sin 6; cos $6 - i(E + iF) sin 6I, sin $I, 1’. [141
In the polycrystalline sample, the directions of the principal axes of 170 efg are
randomly oriented with respect to the directions of the rf field, &. The transition
probability is averaged over the sample to give
mutl = 4 I, (A2 + B2) + ; (C” + D2) + f (E2 + p) . [W
A list of transition frequencies and the corresponding transition probabilities are
thlen stored for the construction of a 170 multiplet spectrum. As for the 170-lH
multiplet, the procedure is similar to that above but simplified with a fewer number
of initial basis states, Iml, ms). This has been done elsewhere (6).
THE FITTING OF THE H,O+ THEORETICAL AND EXPERIMENTAL SPECTRA
The next stage of the theory of 170-lH dipolar interaction is to construct the
theoretical 170 DRCM spectra using the structure of the oxonium ion as input
piarameters so as to obtain a fit with the experimental DRCM spectra.
First of all, the approximate 170 quadrupolar frequencies are taken as the centers
of the l’0 quadrupolar transition multiplets and from them, using the closed form
equations, the 170 quadrupole coupling constants and asymmetry parameter are
obtained as 7500 kHz and 0.1, respectively. From the symmetry consideration and
theoretical evidence (23), the maximum efg component, V,,, is assumed to lie along
the Csl; axis and the minimum efg component, V,,, in the plane containing the C,,
and one of the three O-H bands. Then, for the reason that the 170 DRCM spectra
are insufficiently resolved to detect any deviations from the geometrical sym-
metry, we will only take the symmetrical H,O+ structure with equal O-H and
H. . .H internuclear distances (R(O-H) = 1.0 A and R(H(* *.Hj> = 1.70 A) and
identical polar angles, B(O-Hi) = llO”, in view of the tetrahedral symmetry of
the H,O+ ion, and also 8(Hi. *.Hj) = 90” for proton pairs, as an initial basis for the
dipolar interaction calculation, together with the other polar angles, 4, as follows:
O-HI, & = 0”; H,-H2, $4 = 150”;
0-H2, +2 = 120”; Hz-H3, & = 270”;
0-Hs, & = 240”; H,-H,, & = 30”.
IJsing the input parameters given above, the frequencies vi and relative intensities
Pti of the 256 allowed intermultiplet transitions for each of three quadrupolar
transitions are obtained by the procedure described in a previous section to give the
stick diagram spectra (the examples for best-fit parameters are given in Fig. 5 for
2,),(1/2+ 3/2) and ~,(3/2 -+ 5/2) transitions). In view of strong dipolar interaction
between the protons, the individual line corresponding to one intermultiplet
transition is broadened into the assumed lineshape g(ui - Q), which is a truncated
Lorentzian lineshape, being the product of Gaussian (linewidth at half-intensity
500 IAN J. F. POPLETT
THE MATRIX ELEMENTSOFTHE DIPOLAR~NTERACTION HAMILTONIAN
FOR Two SPINS,S = 112 AND s' = 112
1l/2, l/2) (l/2, -l/2) )- 112, l/2) [-l/2, -112)
(l/2, l/21 (ll4)A’ (1/2)(K’ + X’) (1/2)(K’ + iL’) (M’ + iN’)
(l/2, -l/21 (1/2)(K’ - Z’) -(1/4)A’ B’ -(1/2)(K’ + 2’)
(-l/2, l/21 (1/2)(K’ - Z’) B’ -( 1/4)A ’ -(1/2)(K’ + X’)
(-112, -l/21 (M’ - iN’) -(1/2)(K’ - iL’) -(1/2)(K’ - Z’) ( 1/4)A ’
= 2.36~) and Lorentzian (linewidth at half-intensity = 26) lineshapes (24). So the
H3170+ quadrupolar multiplet spectrum is constructed by the convolution of the
individual lines and the truncated Lorentzian lineshapes.
As no 170 signals in the form of doublets were detected by single irradiation
over two regions of vl and u2 transitions, the quadrupolar spin-lattice relaxation
time, TIQ, is presumably longer than a few seconds (7) so the quadrupolar relaxa-
tion contribution (in the form of thermal mixing effect) to the spin dynamics in-
volved in DRCM is negligible. Thus by omitting the T;Q’part in the double-reso-
nance rate equations (7) we have the change in proton magnetization, AM, for
DRCM signal detection as
AM = M,(l - exp(-&I)), Ml
(a) 1’. . ” 1 ” ” ” ” ” ” ”
2 i? N
FIG. 5. Stick diagram spectra of (a) l/2 + 3/2 and (b) 3/2 + 5/2 transitions of “O-3(‘H) quad-
rupolar and dipolar system in the oxonium ion. For the parameters used, refer to Table 5.
NQDR OF OXONIUM ION 501
where Rij is the rate of rf heating given (7,8) as
wlnere the indices label the rf field and Wi = Ci?!lAKg(Vi - vK). This forms the
required equation for theoretical fitting of the 170 DRCM spectrum. A number of
theoretical I70 DRCM spectra are plotted using a computer for some increments
in each input parameter until a best fit is achieved for the parameters given in
Table 5 (Figs. 2a and b).
From the spectrum-fitting analysis, the relative position of the fine-structure
peaks and the overall width of the DRCM multiplet line are observed to be strongly
affected by R(O-H) and to a lesser extent by the angle between V,, and O-H
bonds 8, while 4 is assumed to be unchanged. As the dipolar interaction Hamil-
tonian is symmetrical about 13= 0 and 90”, the 170 DRCM spectrum is identical for
two values of 8,70 and 1IO“, the former value implying the direction of V,, inward
from the apex of a pyramidal H,O+ ion and the latter one, outward. The remaining
parameter, R(H. * *H), which depends on R(O-H), 8, and c#~exclusively, falls
within the range 1.65 to 1.75 A, giving a similar spectrum; the geometrical value
from the three parameters mentioned above gives R(H+ *+H) of 1.65 A and the
proton NMR lineshape analysis for an isolated H,O+ ion (as in HN03. Hz0 (14))
gives R (H ** *H) of 1.72 A, corrected for thermal motion, indicating the general
agreement with the experiment. The structural information from the 170 DRCM
spectrum gives the HbH angle of 113.5”, close to a tetrahedral angle of lOY28’ in
agreement with an average of three angles of 110.9” obtained from an X-ray dif-
fraction study of H,SO,*H,O (13). Finally the sign of the quadrupolar coupling
constant is obvious from the asymmetry of the 170 multiplet spectrum for the
vl( l/2 + 3/2) transition with the high-frequency sidebands having their intensities
In spite of low resolution of the 170 DRCM spectra, the error margin for struc-
tural parameters of ? 15%, assessed by a line-fitting procedure, is a conservative
estimate for the symmetrical H,O+ ion, or even more for an unsymmetrical ion,
as long as two of three efg components lie on the planes of CBcsymmetry. For this
THE BEST-FIT PARAMETERS FROM “O/‘H DRCM EXPERIMENT FOR
THE OXONIUM ION IN H,SO,~H,O AT 77 K
I?0 quadrupole coupling constant, e*qQ/h
“0 asymmetry parameter, r)
O--H bond length (average of three O-H bonds), R(O-H)
H . .H internuclear distance (average of three H. H distances), R(H. . .H)
Angle between V,, and O-H bonds, 0
Deduced H-6-H angle
Gaussian linewidth parameter, v
Lclrentzian linewidth parameter, 8
7490.6 2 10 kHz
0.117 2 0.010
1.03 + 0.02 A
1.72 ? 0.07 A
105 + 10
113.2 + 5”
502 IAN J. F. POPLETT
reason the 170 DRCM technique will not detect any deviations from symmetry
in proton position in the 170 efg tensor framework, let alone the average of inter-
nuclear distances and polar angles for three protons configurations under CIV
I70 Quadrupole Resonance of the Oxonium Ion
The l’0 electric field gradient tensor deduced for the oxonium ion (Table 5) is in
reasonable agreement with the symmetry consideration of the ion. The magni-
tudes of the tensor components are quite close to that obtained by an ab initio
LCAO-MO SCF calculation for an isolated oxonium ion with an optimum geom-
etry (e2QVzz/h = -10 MHz) (23), only if the crystal lattice effect and hydrogen
bonding effect (resulting in the reduction of about 10 to 40% on consideration to
a solid state of the 170 efg (25,26)) are taken into account. However, the sign of
the maximum component of the l’0 efg is in disagreement; this point will be taken
Both the oxonium ion and the water molecule are embodied in the form of a tetra-
hedron with four sp3 hybrid orbitals radiating toward the vertices from the oxygen
atom at center. This fact enables the trends in the 170 efg tensor to be predicted
using the simple theory proposed by Edmonds et al. for the nitrogen-14 efg in a
tetrahedral environment (27). This is based on a Townes and Dailey’s model with
the assumption that the electric field gradient is entirely attributable to the 2p
orbitals centered on the oxygen atom.
Here, in order to reduce the number of variables involved, we assume (27) that
two of four sp3 hybrid orbitals, +3 and $Qin Fig. 6, of the oxygen atom are equivalent
with same electron occupancy number, a. The oxygen site then has a plane of
symmetry passing through the remaining two orbitals, $r and I&, with their respec-
tive electron occupancy numbers, b and c. Then using a simple procedure given
in Ref. (27) we have the following electron occupancy number equations in terms
FIG. 6. A diagram showing the idealized tetrahedral orbitals of the oxygen atom with the XZ plane
of symmetry between two O-H (T orbitals.
of 170 quadrupole coupling constants:
(b + c - 2a) = --3v (l+rl) [181
(b - c) = 21’2 1 - 1( 3 )(J$) sin 29”,
Thie constant, e2QVo/h, is the maximum efg component resulting from a single
electron in a single 2p atomic orbital and for 170 is equal to 420.9 MHz (28), but
for the oxygen atom with a positive charge on it causing the contraction of the elec-
tron cloud, V. should be increased by a factor of 1.20 (29). The angle, B’, is the
rotation angle around the y axis in Fig. 6; it may be between V,, and the z axis.
‘Taking two identical O-H u bonds in H20 and H30+ as c&and & orbitals, we see
that for an idealized H,O molecule with two lone-pair orbitals, & and &, c = b;
then 13”= 0 and q = 1. However, from electronegativity consideration, a < b
= c; then V,, is positive from Eq. [l] with the maximum efg principal axis along the
OZ axis in Fig. 6 or in other words, perpendicular to the H,O molecular plane,
in agreement with a recent DRCM work on ice Ih (12).
As for the idealized H30+ ion, we take the third O-H u orbital to be a <bzhybrid
orbital with c = a and one lone-pair orbital to be a + hybrid orbital with b > c = a ;
then 77= 0 and an axial symmetry about OZ’ exists in the direction of & (0” = 35.3”).
In fact, for 7 = 0.104 for H2S04*H20, we have V,, tilted by 1.5” away from the
C:,, axis. Since (b + c - 2~) is positive, the 170 quadrupole coupling constant must
be: positive, in agreement with our DRCM results but not with LCAO-MO SCF
Assuming that q = 1 for Hz0 and 7) = 0 for H,O+, we have b - a = 0.41 and
0.40 for Hz0 and H30+, respectively, implying that the O-H (+ orbitals and lone-
pair orbitals have their electron occupancy decreased proportionally from H,O+
with oxygen atom with no hydrogen bond to H20 with two hydrogen bonds. This
may be justified by the following arguments. For the H30f ion the positive charge
on the oxygen atom enhances the hydrogen bond strength with a corresponding
increase in electron occupancy number of the O-H (T orbital while the lone-pair
orbitals are not affected. For H,O with longer hydrogen bonds (R(0 *. *0) = 2.76 A)
the formation of two hydrogen bonds toward the oxygen atom results in a decrease
in electron occupancy number of both lone-pair orbitals with a corresponding
equal decrease in that of the O-H c orbitals on hydrogen bond weakening.
The deviation in the 170 asymmetry parameter from the ideal value (7 = 0 for
H30+ and 7) ==1 for H20) may be caused by two factors (30): first, the imbalance
in the electronic distribution resulting from the presence of external charges, the
hydrogen bond being the main contribution, and second, the deviation of the H6H
angle from the tetrahedral angle resulting from the small admixture of sp* and p3
504 IAN J. F. POPLETT
orbitals into the sp3 orbital (31). At present it is not possible to quantify these con-
tributions to our 170 asymmetry parameter but the former seems to be important
for a H30+ ion involving three nonidentical hydrogen bonds.
It is concluded that the simple theory based on the Townes and Dailey model
for a tetrahedral environment holds well for 170 NQR work as well as for 14NNQR.
It predicts that with increasing hydrogen bond strength, 170 quadrupole coupling
constants (if 7 = 0 for H,O+) will decrease as a result of the polarization of O-H (+
orbitals only. Such decrease will be faster for HZ0 because of the charge depolariza-
tion of two lone-pair orbitals and hence smaller (b - a) value.
Other I70 Quadrupole Resonances
In addition to the 170 efg tensor for the S-“OH site in HzS04.H20 obtained by
the DRCM spectral line-fitting procedure given elsewhere (Table 6), the other 170
quadrupole coupling constants and dipolar parameters given in Table 6 were
obtained in a similar way for frozen H,SO, at 77 K from the unpublished work of
Davidson and Edmonds (32). The single S-“OH site is in agreement with X-ray
structure data (33) which show the twofold rotation axis through the sulfuric atom.
If we assume that HSO,- anions are similar for both oxonium and potassium salts,
then 170 quadrupole coupling constant is given in Table 6 from the uncompleted
work on KHSO, at room temperature (34); one 170 quadrupole parameter is
taken to be an average although the X-ray symmetry for KHS04 predicts two
S-170H sites (35).
With an important assumption that two of efg components lie on the S-O-H
molecular plane, the 170 efg tensor (with the maximum efg component, V,,, at an
angle of around 50 or 130” anticlockwise from the O-H bond and the minimum efg
component, V,,, being the bisector of SdH angle for both H,SO, and H,SO, .H,O)
is similar to that for C-170H in phenols and alcohols (6). The implication is that
the exchange of carbon and sulfur atoms with similar electronegativity does not
affect the electronic environment around the oxygen nuclei.
The remaining three 170 sites in HSO,- of H,SO,*H,O have remained unde-
tected in the DRCM experiment although they form hydrogen bonds with the
oxonium ion so as to give sufficient sensitivity for 170 DRCM detection. How-
ever, the single S=170 site has been detected (32) in H,SO, with I70 frequencies
1105 and 2200 kHz; with 170 quadrupole coupling constant, e*qQ/h, of 7338 + 5
LIST OF “0 QUADRUPOLAR PARAMETERS FOR HYDROGEN SULFATE GROUP IN SEVERAL COMPOUNDS
Temperature SqQlh R(O-H)
Sample WI “0 site WW ? (A) 0 $ Reference
H,O+HSO,- 77 S-“OH -8561.1 + 8 0.832 + 0.01 1.03 * 0.02 45 * 5” (P -
HzSO. 77 S-“OH -&m.l * 5 0.74 i- 0.01 1.01 c 0.01 51 f 5” W Unpublished data of
S=‘Q 7340 f 5 0.06 f 0.05 - - - Davidson and Edmonds
K+HSO,- 293 S-“OH 8380 -t 2F 0.69 c 0.05” - - (33)
’ Average of 1.7% and 1.79~MHz l/2 + 3/2 lines and of 2.31- and 2.36MHz 3/2 - 5/2 lines.
NQDR OF OXONIUM ION 505
kHz; and n = 0.059 + 0.007. Because of the similarity of S-“OH 170 quadrupole
coupling constants in H,SO, and H2S04 *HzO, we take the S=“O frequencies of
HSOI- in HzS04.Hz0 to be at around 1100 and 2200 kHz so as to fall within the
strong H,“O+ multiplets at 1135 and 2232 kHz and are consequently unobserved.
Deuterium Quadrupole Resonance
The general relationship between 2H quadrupole coupling constants and the
hydrogen bond lengths, R (0. +.0), was proposed by Soda and Chiba (36) on the
fact that the deuteron efg is sensitive to the positions of near neighboring nuclei
to an extent that depends on the effective screening of those nuclei by electrons
as viewed from the deuteron. The correlation equation has since been revised by
drawing on the 2H quadrupole resonance results, with the latest one, based on 2H
DRLC work (18) on inorganic hydroxy compounds, given as
e2qQlh = 442.7 - R3(0 kHz.
Th.en from 2H line frequencies given in Table 1 for D,O+ species only, the 2H site
assignments are made with the predicted R(O. -0) bond distances given in Table 7
together with those from X-ray structure studies (13); they correlate well, with
the exception of the 0,. . ‘0, hydrogen bond, a disparity that cannot be accounted
for. From the correlation graph of R(O-H) and R(O*.*O) obtained from the
neutron diffraction work on hydrogen bonds (37) the O-H bond distances are
extrapolated giving the average R(O-H) distance, [( l/r3)]-1’3, of 1.01 A, close to
the R(O-H) value of 1.03 A from l’0 DRCM work if the proton thermal motional
effect is allowed for. Obviously the 2H quadrupole coupling constants for the
oxonium ion are not unique, as they depend on hydrogen bond lengths; this value
of 212 kHz for perchloric acid monohydrate obtained from the deuteron magnetic
re:sonance (38) is explained by much longer 0-H. . .0, hydrogen bonds.
The *H asymmetry parameter measures the symmetry of the electric field
around the hydrogen bond or, in other words, it depends on the relative con-
figuration of the oxygen orbitals at both ends of the hydrogen bond through
V,.,43x2 - rZ) and V,,a(3y2 - r2). For the H30+ case the differences in asym-
metry parameters must be attributed to a different configuration of the orbitals of
DEDUCED BOND LENGTHS FROM *H QUADRUPOLE RESONANCE DATA,
COMPARED WITH X-RAY STRUCTURE WORK
ZH sites NO-H)
Hydrogen bond in H,O+ *H(DsO+ ) extrapolated
(lat&d by X-ray assigned e*qQlh R(O,..O) R(O..,O) fromR(O,,.O) 05..i),. .s
dfiaction study) (9 CkHz) from X-ray predicted in Ref. (13) ‘H 7 (“I
(J.-H.. ‘0, 1 140.5 2.538 2.53 1.04 0.154 118
OS--H.. .O, 2 166.0 2.566 2.60 1.00 0.125 148
‘&..H.. _. .O, 3 177.2 2.649 2.64 0.99 0.153 107
0,.-H.. .02 DSO,- 180.4 2.657 2.65 0.99 0.135 126
506 IAN J. F. POPLETT
the oxygen acceptors in S=O of HS04- anion. Inspection of the last two columns
of Table 7 shows a decrease of the 2H asymmetry parameter with increasing bond
angle, O5*f *02=S, as a result of oxygen u and rr orbitals in the S=O bond being
further away from the deuteron but as the proton position has not yet been deter-
mined by X-ray diffraction, this argument has not yet been made quantitatively.
An isotope effect, being the shift in 2H quadrupole coupling constant upon
deuteration, may originate (39) from (1) different zero-point amplitudes of the
torsional modes of several partially deuterated oxonium species or (2) the replace-
ment of the proton by the deuteron, which is an electron-donating substituent,
leading to further screening of the oxygen nucleus with the consequent decrease of
the zH quadrupole coupling constant of the other deuteron in the same oxonium ion.
For a light molecule such as Hz0 and H,O+, the deuteration will largely affect
the moment of inertia and hence the torsional librational amplitude, (P). But
the actual magnitude is complicated by two opposing contributions, one being the
effect of (9) on the 2H e”qQ/h value as predicted by the Bayer model (positive
isotope effect) and other being the fact that the reduction of (eZ) causes 2H to
spend more of its time in the mean position (i.e., further from the bonding oxygen
atom) and if it is hydrogen bonded, this will reduce 2H e’qQ/h (negative isotope
effect). The latter will become important for shorter hydrogen bonds. This is
further compounded by the negative isotope effect contribution resulting from the
replacement of the proton by the deuteron mentioned above to give the observed
negative isotope effect of around -3 kHz for the oxonium species, D,O+ and
H2DO+, comparable to those reported for potassium oxalate monohydrate
(- 1.6 kHz) (39) and barium chlorate monohydrate (- 2.4 kHz) (40). The value of
2H NQR experiments for the isotope effect study is limited by the requirement
of the presence of the deuteron to measure the isotope effect.
Nuclear quadrupole double-resonance spectroscopy proves to be a versatile
spectroscopic method for the study of the oxonium ion; it gives interesting insight
into two most important characteristics. The first is the electronic structure deter-
mined by 170 NQR parameters, of which the trends are understood by the con-
sideration of a Townes and Dailey model for a oxygen nucleus in a tetrahedral
environment. The other is the geometrical structure of the H,O+ ion allowing for
the thermal motion effects determined by the fine structure observed in 170 quad-
rupole resonance spectrum, assuming that the structure is almost symmetrical,
thus confirming the established structure of the oxonium ion. In addition 2H quad-
rupole double-resonance spectroscopy gives indirect information on the hydrogen
bond structure, even surpassing that from established infrared spectroscopy in
terms of the resolution. This spectroscopic technique will be applied to other
hydrated proton species, which will be the subject of future papers on acid hydrates.
The apparatus was built with the help of a capital grant from the Chemistry Committee of the SRC.
I am the holder of an SRC Postdoctoral Research Fellowship. I am grateful to Mr. S. G. P. Brosnan and
NQDR OF OXONIUM ION 507
Dr. D. T. Edmonds for their helpful discussions and to the latter for supplying the data on anhydrous
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