Physical image versus structure relation

Research Article
Received: 29 July 2008,

Revised: 10 January 2009,

Accepted: 12 January 2009,

Published online in Wiley InterScience: 9 March 2009

(www.interscience.wiley.com) DOI 10.1002/poc.1529

Physical image versus structure relation. Part
14—an attempt to rationalize some acidic
region 13C NMR-pH titration shifts for tetraaza
macrocycles throughout the conformational
GIAO DFT computational results:
a pendant-arm cyclam casey
Ryszard B. Nazarskia *
The most probable time-averaged conformations of three polyammonium cations Hn2nþ (n ¼ 3–5) formed from the
macrocyclic pentamine ligand (2, scorpiand) [derivative of 1,4,8,11-tetraazacyclotetradecane (cyclam)] were analyzed
in order to elucidate an origin of ‘wrong-way’ amine-protonation shifts found in some 13C NMR pH-profiles
determined for the acidic H2O/D2O solution. These NMR trends were reproduced quite well in dCs computed for
multicomponent shapes of related cations, which were in turn elucidated by the best fitting experimental data to
those predicted by the gauge-independent atomic orbital (GIAO) B3LYP/6-31G* method, including the IEF-PCM
approach. A consistent DFT methodology of the treatment of such equilibrated cationic mixtures is proposed.
Moreover, a few novel ONIOM2-GIAO B3LYP/6-31G*:STO-3G type supermolecular calculations were performed for a
simulated presence of bulk water molecules surrounding H525þ. Copyright ß 2009 John Wiley & Sons, Ltd.
Supporting information may be found in the online version of this article.
Keywords: multidentate ligands; scorpiand; cyclic protonated polyamines; intramolecular H-bonding; solvent effects; MMX
and OPLS-AA force fields; IEF-PCM model; supermolecular ONIOM-GIAO DFT NMR calculations

INTRODUCTION
High-resolution NMR spectroscopy is an extremely powerful tool
for the structural studies on diamagnetics, including a wide
variety of chemical entities. It enables probing the constitution,
dynamics, and conformational preference of such molecular
species, especially in the liquid phase. Nowadays, all these
possibilities have become considerably enhanced for common
spin-1/2 nuclei by an application of two supporting methods of
computational chemistry i.e., the gauge-independent atomic
orbital (GIAO)[1–11] prediction of chemical shifts, dXs, and the
DFT-based evaluation of indirect spin–spin couplings, nJABs.[12,13]
Especially, the former of these main measurable NMR parameters
is strongly sensitive to the particular molecular environment,
thereby providing an insight into the local functionality and
stereostructure.
Macrocyclic amine host ligands (azacrowns L) with the
differently pre-determined shape, size, and functionality as well
as their complexes with cationic and, more recently, anionic
species have been extensively studied for about three decades,
inter alia as small-molecule organic mimics of the enzyme
properties. A binding selectivity of these kinds of the polyionic
multidentate molecular receptors switching toward ionic substrates is commonly achieved by proton-mediated switching,
taking advantage of the protonation equilibria involving
polyamines in the aqueous solution. Polyammonium cations

formed from such macrocyclic systems were found particularly
useful in this case, owing to their ability to form the stable
host–guest (receptor–substrate) complexes with inorganic and
organic anions both in solution and in the solid state, by using
hydrogen bonds (H-bonds) in combination with the electrostatic

attractive interactions.[14–19]
Among these species, a nitrate anion is currently one of the
highest priority oxyanionic targets for the complexation studies.
In this case, new pyrrole-based and, especially, amide-type
systems with the N—H residues as strong H-bonding donors are
in common use, beside the traditional ammonium-based
macrocyclic receptors. In addition to a classical H-bond type
donation, such anionophores using also the C—H groups and/or
anion–p interactions were reported.[19]

* Correspondence to: R. B. Nazarski, Laboratory of Molecular Spectroscopy,
Faculty of Chemistry, University of Ło´dz´, Narutowicza 68, 90-136 Ło´dz´, Poland.
E-mail:
a R. B. Nazarski
Laboratory of Molecular Spectroscopy, Faculty of Chemistry, University of
Ło´dz´, Narutowicza 68, 90-136 Ło´dz´, Poland
y
For Parts 12 and 13, see References [44] and [86], respectively.

834
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Copyright ß 2009 John Wiley & Sons, Ltd.


AN ATTEMPT TO RATIONALIZE SOME NMR-PH TITRATION SHIFTS

The disruption and/or formation of the intramolecular H-bonds in
some 14-membered macromonocyclic tetraaza ligands L and related
cations HnLnþ (where L ¼ 1–3) has been preliminary considered on

the basis of approximate quantum-chemical results.[20–22] However,
the simulation for such discrete solute–solvent supermolecular
assemblies in the aqueous phase is not a trivial task, because the
species (solute) size and the number of explicit solvent molecules
(H2O) were recognized to be of crucial importance.[20,21] Fortunately,
a valuable information relevant to structures of the physically real
associates of these kinds is usually attainable, at least in part, by
means of pH-titration NMR spectroscopy.[20,22–25]
This work presents results of standard DFT-B3LYP/6-31G* study
on the equilibrium geometries fully in vacuo optimized for the
isolated species, frozen at 0 K, carried out for the three
polyammonium ions Hn2nþ (n ¼ 3–5) formed from pentamine 2
[scorpiand, the IUPAC name: 1-(20 -aminoethyl)-1,4,8,11-tetraazacyclotetradecane]. All such calculations were followed by a
prediction of 13C NMR chemical shifts, dCs, performed by the
GIAO perturbation method[1–11] at the same level of theory. The
least-squares regression analysis was used for the best fitting such
found dcalcd
s to the values dobsd
measured experimentally. In
C
C
addition, a few conformers of the macrocyclic species H525þ were
considered for testing the solvent influences, by using the standard
IEF-PCM[26–28] model. Moreover, a novel supermolecular GIAO
computational treatment involving surrounding water molecules
was used for six relatively large clusters of the type H525þÁ(H2O)n
(403 n 479) by resorting to an ONIOM[29–32] technique, in order
to investigate the expected solvent H-bonding effects.
All of these investigations were undertaken to explain some
interesting downfield-shifting (deshielding) trends in 13C NMR

pH-profiles found previously for a pentaprotic base 2 in dilute
H2O/D2O solution below pH 4.2, by using HNO3 as a titrant.[20]
Moreover, some acidic-region NMR titration data[33,34] recently
reported for the other structurally close ligands 4 and 5
possessing the 2-substituted ethylenic dangling arm at an amino
nitrogen-atom N1, were briefly discussed in view of the present
DFT calculational results. A full conformational study on
macrocycles 1–3 (including equilibria between their multiple
ring forms in the alkaline region and a deeper analysis of internal
H-bonds formed under such experimental conditions) is in
progress, and its final results will be published in the future.

COMPUTATIONAL DETAILS

NMR spectra prediction

Molecular modeling and frequency calculations

Single-point GIAO[1–11] empirically scaled (corrected)[5,6,9,11] DFT
B3LYP/6-31G* computations[56–60] of absolute 13C magnetic
shieldings (sCs) for the analyzed molecular entities were carried

Copyright ß 2009 John Wiley & Sons, Ltd.

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835

The conformation search for minima on potential-energy
surfaces (PESs) of cationic species Hn2nþ under this study was

J. Phys. Org. Chem. 2009, 22 834–844

performed with the MMX[35] and OPLS-AA[36–38] force field using
the Monte Carlo (MC)-type GMMX subroutine within PCMODEL.[35] A previously elaborated molecular-mechanics (MM)
searching protocol[39–44] was used with full randomization over
main macrocyclic units and all of the rotatable bonds in pendant
side-chain fragments.[45,46] Each simulation was executed for up
to approximately 150000 MC steps for each of the two methods
used; the 14.6 kJ molÀ1 energy window and a bulk value of
dielectric permittivity were used for the hydration modeling,
e ¼ 78.4. The resulting low-energy forms (typically 20–40 unique
structures for every one species embracing the energy window of
ca. 5.5 kJ molÀ1) were subjected next to a fully relaxed geometry
refinement in the gaseous phase, initially at the HF/3-21G and
then (after the first selection applying the energy criterion) at the
HF/6-31G* and B3LYP/6-31G* levels, by using the double-z quality
polarized basis set with Cartesian six-component d polarization
functions for all heavy (non-H) atoms. The Gaussian 03
package[47] was employed, with PCMODEL as a graphical
interface. A similar HF/6-31þG* level study was recently
performed for the N-bridgehead bicyclic triamines of a
comparable molecular size.[48] In addition, a few control
simulations of the influence of the surrounding bulk water
molecules were carried out for H525þ at the DFT B3LYP/6-31G*
level applying the standard polarizable continuum dielectric
method with an integral equation formalism (IEF-PCM).[26–28]
Moreover, B3LYP/6-31G* vibrational wavenumbers ni were
found for the pre-selected structures in a rigid rotor-harmonic
oscillator (RRHO) approximation according to the G-F method of

Wilson,[49] by applying the analytic second-derivatives. These
data were used to verify that all of the located stationary points
represented true energy minima on the Born–Oppenheimer PESs
(Nimag ¼ 0) and to determine the relative differences in the
standard Gibbs free energy changes, DG8298.15. Related zero-point vibrational energies (ZPVE) were evaluated from the
frequencies scaled with a uniform factor 0.96,[50] to bring them
into a better agreement with the experiment.
In addition, some new supermolecular calculations were
performed using a two-layered version of the ONIOM procedure
(ONIOM2),[29–32] for a simulation of the presence of n water
molecules in six H525þÁ(H2O)n aggregates; 403 n 479. The
GDIIS/GDPIS optimizer was applied at the B3LYP/6-31G*:
DREIDING level.[47,51] All input atomic coordinates for these
supramolecules were generated with HyperChem[52] using
the OPLS-AA force field[36–38] (final RMS gradient
˚ À1molÀ1). Six boxes with $ 445 water molecules
< 0.0042 kJ A
(as described by three-site TIP3P[53] empirical potentials)
surrounding six different B3LYP/6-31G* level structures of
H525þ were initially constructed applying a solvent-box option
˚ 3 (23.27 l 24.26 A
˚ ) and a
of this software; cell sizes of l  l  l A
˚
minimum distance of 2.2 A between the solvent and the solute
atoms were applied (see Fig. S4). The H525þÁ(H2O)n clusters
optimized in this way fulfilled all requested convergence criteria.
Geometrical calculations and molecule visualizations were
performed with PCMODEL and PLATON[54,55], respectively.
Statistical analysis was carried out by linear regression analysis

utilizing the MS Excel1 97 spreadsheet.


R. B. NAZARSKI
out at their B3LYP/6-31G* equilibrium structures[56–60] using
standard routines in Gaussian 03. In addition, several ONIOM2-GIAO
supermolecular predictions[61–63] were performed at the B3LYP/
6-31G*:STO-3G//B3LYP/6-31G*:DREIDING level, in a simulated
presence of a surrounding medium (H2O). Six ONIOM2-optimized
H525þÁ(H2O)n cluster were applied in such extremely timeconsuming predictions of sCs. The relative 13C chemical shift of
a given nucleus in all considered entities was defined as dcalcd
C
calcd
[ppm] ¼ sref
(in vacuo approach).[1–4,7,8] For the 13C NMR
C À sC
[64]
spectra, sref
as evaluated at the B3LYP/
C was of 189.7709 ppm,
*
6-31G geometry of a used external dC reference substance
[tetramethylsilane (TMS) with Td symmetry].[4]
The reliability of such a GIAO B3LYP/6-31G* approach for
aqueous-solution NMR data was verified for the lower energy
conformer of the free amine 2,[64,65] by using twelve relations of
calcd
the type sref
þ sobsd
(1 i 12).[5] As a result, an average

C ¼ dCi
Ci
value of sref
(‘in
medium’)
¼
187.61
ppm was found for the methyl
C
13
C signal of TMS ‘in a (virtual) aqueous solution,’ in good
agreement with the above gas-phase finding (189.77 ppm). A
small downfield shift computed (2.16 ppm) is attributable to
interaction effects[5] of aqueous medium as a molecular
environment i.e., strongly alkaline solution of the amine 2
containing extraneous ions Kþ and OHÀ (pH $ 13.5). On the other
hand, some test GIAO DFT runs were also carried out for the free
cation H525þ at a much more advanced B3LYP/6-311þG(2d,p)//
B3LYP/6-31G* theory level.[60]

RESULTS AND DISCUSSION
In the course of the determination[20,23] of a protonation sequence
for all five N atoms of the strongly alkaline pentamine 2 in the
13.4–0.2 pH range, some unexpected NMR shielding trends were
found in the resulting pH-titration curves, dC ¼ f(pH).[20] Indeed,
downfield (high-frequency) amino-protonation shifts at pH 13–11
and below pH 4.2 were observed for a few 13C nuclei (as shown in
Fig. 1). Similar tendencies were found also at pH $ 12 for two
macrocyclic tetramines 1 and 3.[20] All of these measurements

were carried out with no special attempt to control the ionic
strength I. Fortunately, very good reproduction of initial dCs was
found for numerous reverse titrations performed for the polyamine
2 in both strongly alkaline and strongly acidic solutions, most likely
owing to low concentration of this analyte ($ 0.01 mol LÀ1).
Because the protonation of any amino-N atoms is normally
associated with an upfield shift of the 13C resonance signals of
C-atoms in b-positions to a protonatable N-atom,[25,66] it was
interesting to explain the origin of all these ‘wrong-way’
(‘abnormally’ directed) 13C NMR signal shifts.
Our very preliminary ab initio STO-3G level results[20] suggested
that the foregoing non-typical NMR tendencies found in the
alkaline region are probably due to changes in H-bond bridging
i.e., disruption and subsequent formation of new intramolecular
H-bonds (between the protonated and free amino groups) and
concomitant alterations in the shape of macro-rings, occurring in
subsequent protonation steps. Because the spectacular acidicregion shifts were found only for the 13C nuclei in positions 11 and
12 (for the C12 nuclei, at pH 1.3–4.2 only) of the side arm of 2,[67]
this pentamine was generally selected for a clarification of all these
‘wrong-way’ NMR diamagnetic shielding trends observed.
On the other hand, a highly unsymmetrical nature of the
molecule of 2 bearing a 2-aminoethyl tail attached to its atom N1,
gives rise to a circumstance of the extremely complex, but
simultaneously much more informative, NMR-pH titration profiles
(Fig. 1). In the present work, such profiles were considered only in
acidic to neutral region i.e., for pH below $ 6.5, mainly due to much
larger complexity of other various physical phenomena occurring
for the system 2 in the alkaline region (changes in ring
conformations and/or numerous intramolecular H-bonds, vide
supra). Moreover, only minimal, if any, interactions of related

species Hn2nþ (n ¼ 0–2) with nitrate anions were expected for such
an aqueous medium as a surrounding environment (vide infra).
Overall conformations of the amine 2 in acidic region
It was obvious that assessing of the time-averaged (mean) shapes
of different protonation states of the title pendant-arm

Figure 1. Selected 50.29 MHz 13C{1H} NMR-pH titration curves of ca. 0.01 mol LÀ1 solution of the ligand 2 in H2O/D2O $ 90:10 v/v solution at $ 21 8C
(isotope effect for pH neglected, dCs originally[20] measured relative to an external liquid TMS were corrected[25] by þ 0.72 ppm to account for the
difference in diamagnetic susceptibilities of both the liquids involved). The C12 curve vertically shifted by þ 12 ppm, for brevity of plot.

836
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AN ATTEMPT TO RATIONALIZE SOME NMR-PH TITRATION SHIFTS

J. Phys. Org. Chem. 2009, 22 834–844

Indeed, when observing average NMR signals originating from
any rapid dynamic equilibrium, a normal procedure to estimate
the composition of a mixture is to use interpolation.
The representative calculational and statistical results found in
the above-outlined way for four geometries A–D of H525þ are
listed in Table 1. Inspection of the content revealed that a
low-energy conformer B is the best single in vacuo model of the
molecular shape of H525þ in solution [rC ¼ 0.9852, standard

deviation (SD) ¼ 0.96 ppm], for which dobsd
s measured at pH 0.24
C
were used.[25,71] But, somewhat better linear Pearson’s correlation
coefficient (r) was found with an extra contribution of three other
forms A, C, and D (rC ¼ 0.9882, SD ¼ 0.71 ppm). In particular,
obsd
‘extreme deviations’ (EDs) i.e., values (dcorr
Ci À dCi ), were
diminished in this case (from À3.04 and 2.53 ppm to À2.30
and 2.25 ppm for C2 and C11, respectively, with linear correction
used); Table S2. These values were on the order of the GIAO DFT
method used herein. An additional consideration of other forms
did not make the agreement better. Therefore, it was recognized
that such a conformer family abbreviated to entities A–D is
representative for single cation H525þ and works quite well.
Adequately, their 0.175:0.225:0.44:0.16 superposition was considered as a reasonable overall conformation of H525þ in an
aqueous medium, because related dCs both measured and
predicted are in the best way accommodated in this multicomposite shape (hereafter referred to as H525þABCD).[72]
The form C (as shown in Fig. 2a) is perhaps the most abundant
conformer of H525þ in aqueous media, in view of its higher
‘individual’ r-value of 0.9811 and about 44% contribution
estimated for the whole conformational family A–D. The
proposed fractions of these forms in equilibrium and the
GIAO-supported conformers C and D (in particular) are in
agreement with relatively small magnitude of their in vacuo
DG8298.15s (5.1–7.7 kJ molÀ1) and large similarity in the n1 values
(Table 1). On the other hand, relatively small participation of both
low-energy forms A and B in real mixture is particularly worthy of
mention. Indeed, the B3LYP/6-31G* data suggest the large

contribution of B (DEel ¼ 0.43 kJ molÀ1 and DG8298.15 ¼
2.17 kJ molÀ1). But, it must be kept in mind that all these
thermodynamics were computed for an idealized (hypothetical)
case of isolated entities in the gaseous phase. The scatter diagram
with least-squares line and statistic data for the four composite
model of H525þ in aqueous solution are given in Fig. 2b.
The 14-membered macrocyclic units of all components A–D of
H525þ adopt a conformation of type (3,4,3,4)-A,[73] with ring
N-atoms occupying four corners of the molecular polygons and
NþÀH bonds situated outward a macrocycle cavity. Similar
rectangular shape of macro-rings was also determined crystallographically, for the fully protonated states of per-protonated (or
partially deuterated) cyclic fragments of the parent cyclam itself
(1)[74,75] and its mono N-substituted pendant-arm derivatives.[73,76]
Above satisfactory results on H525þ were intended to compare
with related structural data and subsequent GIAO predictions
made in the presence of bulk water simulated using the PCM
dielectric continuum model. Unexpectedly, very bad convergence was found for these efforts. Only three of the six promising
forms of H525þ were successfully examined. The large terms
(polarized solute–solvent) were evaluated e.g., of À3705.48 and
À3713.93 kJ molÀ1 for Chydr and Dhydr, respectively. Interestingly,
very similar values of DEel and identical DG298s were found for
both these conformers (Table 1). Strictly, the contribution of the
form D in a mean shape of the hydrated ion H525þ was strongly

Copyright ß 2009 John Wiley & Sons, Ltd.

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837

macrocyclic amine ligand was essential in developing a
comprehensive understanding of the ‘wrong-way’ NMR trends
mentioned above. The information necessary for elucidating
chemical structures of the formed ions Hn2nþ was previously
derived in the NMR spectra analysis,[25] by using the aminoprotonation shifts plus other techniques of the qualitative
(pH-dependent dXs) or quantitative (line-width effects) nature. In
this pentamine the N2 atom is protonated first, then N4, N5, N3,
and N1.[20,23,25] All of the experimental dC data related to the
present work are given in Table S1. Thus, an advanced
molecular-modeling study was performed to determine the
overall conformations of the cations Hn2nþ (n ¼ 3–5) existing in
the acidic solution,[25] especially taking into account a great
mobility of these 14-membered macrocycles. Really, a large
structure averaging owing to very fast (on the NMR time scale)
flexing between different forms of HnLnþ was previously found
for all macrocyclic systems 1–3.[24,25]
Accordingly, the GMMX randomization program was used to
search for pertinent conformation hyperspaces; as shown in
Computational Details. The MMX[35] method was initially applied,
but with the passage of time another force field (OPLS-AA)[36–38]
was unexpectedly recognized as a much better MM method for
modeling the conformers of penta and tetraprotonated forms of
amine 2, but not for related triprotonated species. A relatively
large molecular size of ions Hn2nþ forced to make all these
calculational efforts without explicit considering the solvent
influences (free-molecule approach). However, dielectric permittivity of 78.4 was always applied for a rough modeling of the
aqueous medium. The resulting geometries were verified, initially
with the HF/3-21G energies and then with NMR spectra predicted
for all low-energy structures pre-selected in this way, by using the
GIAO method at the B3LYP/6-31G* level.[56–60] Adequate

statistical evaluation of the agreement (experiment vs. theory)
was applied to draw relevant conclusions. Finally, linear
regression was employed to correct the systematic errors
associated with smaller basis sets and/or an inaccurate density
functional and gas-phase approximation used in the computational treatment.[11]
An examination of such in vacuo designed models of three
polyammonium ions Hn2nþ (n ¼ 3–5) with respect to their
structural goodness for NMR parameters measured in aqueous
solution was of crucial importance. Indeed, many initially good
geometrical candidates were recognized as reflecting local
gas-phase energy minima only. Generally, a ‘solution (i.e.,
environmental) match criterion’ revealed to be the strongest
determinant for such goodness, besides the principal ‘minimumenergy criterion.’ A similar situation was previously found in an
elucidation of some conformation of flexible 3,4’-diquinolinyl
sulfides.[43] As a result, usually recommended[10,11,68,69] calculations
weighted with respect to Boltzmann population statistics of
various lowest-energy structures of entities under this study were
practically not applicable (vide infra).
Thus, single conformers of ions H525þ were found by fitting the
experimental dobsd
s[20,25] to those predicted in an experimentally
C
scaled GIAO approach, dcorr
C s (Table S2). A full complement of nine
B3LYP/6-31G* forms similar in energy were examined. These
forms were obtained after selection of related HF/3-21G
geometries computed, starting from 21 initial OPLS-AA models.
An agreement of the measured and predicted dCs was used in
statistical testing[70] of such obtained promising models and in
final searching for correct representation of the mean shape

adopted by H525þ in solution (the spectroscopic match criterion).


R. B. NAZARSKI

Table 1. Important energetic and regression-analysis data for the forms A–D and ABCD of H525þ
Calculational result\species
DEel [kJ molÀ1]d
DG8298.15 [kJ molÀ1]h
First harmonic vibrational mode n1 [cmÀ1]
Slope a jk [unitless]
Intercept b jk [ppm]
Coefficient r(dC) jk
obsd 2
Total sum S(dcorr
) [ppm2]k
C À dC
Standard deviation [ppm]kl
Estimated participation in H525þABCDc [%]

a

A

B

Cb

D

H525þABCDc

0.00e
0.00i
30.10
0.7457
7.855
0.9767
50.09
0.99
17.5

0.43
2.17
29.12
0.7740
6.805
0.9852
31.98
0.96
22.5

4.30f
5.08f
36.64
0.7691 (0.8426)
5.305 (4.7286)
0.9811 (0.9800)
40.75 (43.23)
0.90 (1.00)

44

7.60g
7.71g
37.54
0.7163 (0.8009)
6.970 (5.679)
0.9630 (0.9689)
79.17 (66.62)
1.18 (0.93)
16

—
—
—
0.7726
5.698
0.9882
25.64
0.71
—

a

Mainly for in vacuo B3LYP/6-31G* optimized geometries.
As shown in Fig. 2a.
c
The composite, four-component structure of H525þ found as ca. 0.175: 0.225: 0.44: 0.16 ‘superposition’ of its forms A–D, as also has
been shown in Fig. 2b.
d

Relative changes in classical (raw) total electronic energies Eel.
e
Absolute energy of À749.32775 hartrees; 1 au ¼ 1 Ha ¼ 2625.50 kJ molÀ1.
f
PCM(H2O) data: Eel and total DG298 (in solution, with all non-electrostatic terms) of À750.71948 and À750.70471 Ha, respectively.
g
PCM(H2O) data: Eel and total DG298 of À750.71937 and À750.70471 Ha, respectively.
h
Relative changes in the standard Gibbs free energy.
i
Absolute energy of À748.89355 Ha.
j
calcd
For the best-fit regression line of type dcorr
þ b.[9,11,43,44,70]
Ci ¼ a  dCi
k
The PCM(H2O) results in parenthesis.
l
obsd
For all deviations in dcorr
Ci s versus dCi s.
b

838

supported. Moreover, such incomplete GIAO NMR data were
found as very similar to standard in vacuo results. Therefore, only
structural (and GIAO predictive) findings for the gaseous phase
were mainly used in further part of this work, as results are

sufficiently reliable.
Adequately, two remaining ions Hn2nþ (n ¼ 3 and 4)[25] were
analogously in vacuo investigated. Both types of pre-selected
geometries were used i.e., generated with two different force
fields. Unexpectedly, the initial HF/3-21G structures originated
from the MMX models were found as more appropriate for H323þ,
than those coming from OPLS-AA models—for H424þ. Thus,
some (usually, two or three) intramolecular H-bonds of type
Nþ—HÁÁÁN, also including bifurcated systems, were found in
various forms of H323þ (Fig. 3), whereas all of the ring þN—H
bonds adopt an exodentate orientation in different conformers of
H424þ (Fig. 5a). The latter arrangement is much better for the
stronger interactions with aqueous medium. As a matter of fact,
the OPLS-AA approach was especially optimized for liquid
simulations. One of the important differences among these MM
methods is that in the OPLS-AA force field there are no ‘lone pairs’
at N atoms.
Generally, eleven and nine pre-selected low-energy B3LYP/
6-31G* level structures were subsequently GIAO NMR examined
for H323þ and H424þ, respectively. But, somewhat poorer
correlations were found for these two ions. Their final individual
mean shapes (with a fraction in parenthesis) H323þABCD
(32:20:20:28) and H424þABC (9:33:58) were elucidated with the
rCs of 0.9663 and only of 0.9533, respectively. Likewise as above
for H525þ, their gas-phase high-energy conformers were found to
be abundant components, especially for H424þ. EDs in dCs
computed for such shapes of H323þ and H424þ were of À3.94/
3.61 and À2.67/4.54 ppm, respectively. For NMR data regarding

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all constituents of these mean shapes see Tables S5 and S6. It
seemed initially that, the deprotonation of preferred forms of
H525þ leads to the formation of related conformers of H424þ
possessing an inverted configuration at the secondary amino N1
site and being usually not favorable in aqueous solution, except
for the equilibrium between H424þA and H525þD (as shown
however, below).
On the whole, identical HF/3-21G structures of two aforementioned ions were often found starting from different initial
force-field-based models, especially for H323þ. This finding can be
easily explained with a considerable macrocycle flexibility
observed for all of the amines 1–3 in solution (vide supra).[24,25]
So, weaker correlations dcalcd
versus dobsd
found for H424þ and
C
C
3þ
H32 can partially result from their mobility (and, so, from the
need to consider a considerable variety of conformers). The
aforementioned inversion of the configuration at N1 leading to
two series of diastereomers (or enantiomers) is also important
(Figs 3 and 5a). In addition, all ions HnLnþ (L ¼ 1–3) exist in fast
dynamic equilibria with other species on neighboring protonated
states.[24] Without any doubt, observed worsening of the dC
agreement is due in part to all these phenomena. On the other
hand, any two processes of the protonation overlap measurably
unless associated pKa values differ by more than about four
logarithm units.[77]
A distribution diagram of different molecular species coexisting for pentamine 2 in aqueous solution is given in Fig. 4. This

plot, obtained with PlotPhi,[78] explicitly shows six macrospecies
Hn2nþ (n ¼ 0–5) characterized by their mean shapes. It was
obvious, that the real situation regarding individual components
of these superimposed states (i.e., particular conformers
considered as physically distinct microspecies) is much more
complicated.[79] According to the potentiometric data,[20,21] there

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AN ATTEMPT TO RATIONALIZE SOME NMR-PH TITRATION SHIFTS

Figure 3. PLUTON drawings of two dominant GIAO-supported conformers of H323þ found at the B3LYP/6-31G*//B3LYP/6-31G* level;
(1S,8R)-form A ($ 32%) (a) and (1S,8R)-form D ($ 28%) (b). Dashed lines
indicate intramolecular H-bonds; only NH hydrogen atoms are shown.
Figure 2. The proposed GIAO-supported overall solution conformation
of H525þABCD (a): PLUTON view of its B3LYP/6-31G*-optimized major
component C ($ 44%); only the (1R)-enantiomer is depicted. (b): Scatter
plots of isotropic dobsd
versus dcalcd
for the B3LYP/6-31G* level overall
C
C
four-component conformation of H525þABCD.

are significant pH ranges over which two or even three of the
considered ions Hn2nþ coexist in reasonable amounts. Such
ranges were not the same in 13C NMR pH-titrations, but were

rather similar.[20]
The coexistence of different ions was a very important issue in
elucidating the overall shapes of such species. Indeed, H323þ
(similarly as a ‘terminal’ cation H525þ)[71] was rather well
characterized spectroscopically, because very broad plateau
observed for all dC profiles in the pH region of 4–7 (Fig. 1) can be
safely attributed to this trication. In sharp contrast, an
intermediate ion H424þ reaches the maximum concentration
of only $ 55% (according to Fig. 4) and, so, its direct NMR
observation was practically impossible. Thus, dCs found at pH
5.77/6.18 and 2.05 were assumed as related to H323þ and H424þ,
respectively.[80] In view of the foregoing, an existence of two
neighboring ions (H525þ and, especially, of H323þ) had to be
consider for the large ensemble of different cationic entities
probed at pH 2.05 (environment formally belonging to a single
ion H424þ).
Indeed, the best agreement dcalcd
s versus dobsd
s at pH 2.05 was
C
C
found (rC ¼ 0.9896) for 34.5% of shape of H424þBC (37:63) with an
additional 28 and 37.5% assistance of H525þABCD and
H323þABCD, respectively (Fig. 5). Initially, the original contributions of coexisting forms A, B, etc. were used in mean shapes of
all these ions. At the end of the analysis, however, fractions

concerning H424þABC (9:33:58) were ‘unfixed,’ leading to
simplification of the initial three- to final two-component shape
of H424þBC (37:63), in a ‘self-consistent’ manner. It must be kept
in mind, that this single cation was rather badly characterized

spectroscopically (vide supra). The EDs in dCs found for such a
computed ensemble of 10 forms was diminished to À2.65/2.08
versus À2.67/4.54 ppm for initial H424þABC; as shown in Tables S6
and S7.
Obviously, such a rationalization of the composition of a
mixture of ions (and of H424þ, in particular) at pH 2.05 is slightly
arbitrary. However, very good agreement in dCs strongly suggests
that used computational methodology is correct (as shown in
Figs 5b and 6). Indeed, observed agreement in dCs is similar to
that found for H525þABCD. Moreover, a newly evaluated amount
of the cation H424þBC is comparable, within the uncertainty of an

Figure 4. Distribution diagram of the protonated species formed from
pentamine ligand 2 in water, as a function of pH. The plot was calculated
from related protonation constants evaluated potentiometrically
(I ¼ 0.1 mol LÀ1 KNO3, 25 8C),[20,21] by using the PlotPhi[78] program

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R. B. NAZARSKI

Figure 5. The proposed GIAO-supported solution conformation of the
ion H424þ (a): PLUTON view of the B3LYP/6-31G* structure of the major

component C ($ 63%); only the (1S)-enantiomer is depicted. (b): Scatter
plots of isotropic dobsd
versus dcalcd
found for a multicomponent mixture of
C
C
cations H323þABCD ($ 37.5%), H424þBC ($ 34.5%) and H525þABCD
($ 28%) at pH 2.05; 10 equilibrating conformers were considered. This
figure is available in color online at www.interscience.wiley.com/journal/
poc

applied GIAO DFT treatment,[60] with its concentration estimated
from Fig. 4 ($ 34.5 vs. $ 55%). The absence of the form A in final
mean shape of H424þ is also consistent with the foregoing finding
on a configuration inversion at the N1 site in the last protonation
step. Finally, the strongest broadening of 13C signals of the five
consecutive carbon atoms C4–C8 of 2, observed at pH 2.05 (Fig.
S1), found ultimately its rational theoretical explanation as being
due to dynamic equilibria mostly between entities H323þABCD
and H424þBC ($ 37.5 and $ 34.5%). Indeed, there are numerous
disruptions and formations of intramolecular H-bonds of type
Nþ—HÁÁÁN in such processes (as shown in e.g., Fig. 3). As a result,
the 13C lines of five macro-ring carbon atoms surrounding both of
the involved amino N3/N4 sites are substantially broadened.
On the other hand, there was possibility for H424þ and,
particularly, for H323þ to be involved in various internal H-bonds
mentioned above, with active participation of their side arm
CH2CH2NHþ
3 . This H-bonding is usually quite well modeled in
gas-phase calculations, especially using the MMX force field.[81]

Such interactions disappear in polar solvents when solutes lose
their rigidity arising from intramolecular H-bonds, leading to a
coexistence of new forms stabilized by a specific solvation.[82–84]
This is especially the case in aqueous medium, where hydration
effects often overpower intrinsic properties e.g., selective abilities
of protonated polyamines as anion receptors.[17] Similar
conclusion results also from in vacuo findings on the systems

Figure 6. Bar graphs of the dC differences between data in vacuo
calculated/predicted and measured at pH 2.05, for two different
approaches used. Related data from GIAO results for three forms
contributing to an initial time-average shape of H424þABC (a) and for
10 forms of three different coexisting ions Hn2nþ (final results) (b); cf. also
Fig. 5b

Hn2nþ n ¼ 0–2 (confronted with experimental data in solution) for
which internal H-bonds of the type Nþ—HÁÁÁN seem to be
strongly overestimated.[64]
So, when solvation plays a major role in short-range
interactions further computational treatment should be basically
used like e.g., the IEF-PCM[26–28] or ONIOM[29–32] technique. In
particular, the latter is a conceptually simple approach whereby
both long-range and local environmental effects on the properties of the molecules (studied in an explicit solvent) can be
captured. Hence, this approach was used for parallel prediction of
NMR spectra of six pre-selected conformers of a fully protonated
form of pentamine 2.

An ONIOM study of the clusters H525RÁ(H2O)n
The foregoing failures encountered in the IEF-PCM/H2O structure
predictions for a per-protonated and, therefore, strongly hydrophilic ion H525þ, prompted us to carry out some time-consuming

GIAO NMR ONIOM2 (B3LYP/6-31G*:STO-3G) runs for a simulated
presence of medium [(H2O)n, n $ 445], departing from six
pre-selected low-energy gas-phase B3LYP/6-31G* geometries of
H525þ (Computational Details). Similar HF calculations carried out
with the AM1 hamiltonian, instead of a STO-3G base, were recently
applied for the outer low-layer regions of supermolecular models
of some supramolecules in the ONIOM2-structure optimizations
made at more advanced levels.[61]

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AN ATTEMPT TO RATIONALIZE SOME NMR-PH TITRATION SHIFTS
The simulated ‘hydrated states’ of six pre-selected forms of
H525þ were computed as structures slightly stabilized by a
complex three-dimensional network of intermolecular H-bonds
(Fig. S4). These systems were initially compressed from equilibrium (in the OPLS-AA force field) and then relaxed at the
ONIOM2 B3LYP/6-31G*:DREIDING level. On the whole, such
‘hydrated’ forms were found as being comparable to the initial
gas-phase species. Generally, similar dCs were predicted for all
these structures in relation to in vacuo results, with only the
exception of H525þDhydr (however, affording an excellent
shielding of C11); as shown in Tables S2 and S3. In fact,
somewhat weakened agreement dcalcd
s versus dobsd

s was found
C
C
for such a modeled form D (gas-phase rC value of 0.9630
diminished to 0.9523). On the other hand, rC ¼ 0.9689 was
evaluated for a form of this kind in the IEF-PCM treatment (vide
supra). Hence, about 17.5:45.5:21:16 superposition of such
hydrated forms A–D was estimated, respectively; rC ¼ 0.9874,
EDs ¼ À2.34/2.50 ppm, and SD of 0.72 ppm (ONIOM2-GIAO
results). The substantial (45.5%) contribution of H525þBhydr
relative to in vacuo result (only 22.5%) is worth mentioning.
However, such a difference is roughly within an estimated
uncertainty of the GIAO-based methodology used here.[60]
As far as we are aware, there are the first simulations of
supermolecular assemblies of this sort, which were carried out
using the hybrid approach mentioned above. It should also be
noted that, in sharp contrast to large but finite chemical systems
usually treated by the ONIOM method, only H-bond stabilizing
interactions exist between the solution environment and H525þ
(as a center region of the supramolecules under study). Indeed,
an ‘infinite’ space of the aqueous bulk was arbitrarily cut off to
about 445 water molecules in the calculations, mainly due to
HyperChem limitations. It was obvious that more advanced
treatment [involving molecular dynamics (MD) simulations, as
shown in e.g., Reference [16] could be used for mimicking the
environmental effects and to make GIAO predictions.[31,61]
However, in the used approach we only wanted to tentatively
estimate an overall influence of these effects for NMR shieldings
of the 13C nuclei in the pentacation H525þ.
Generally, the present structural and spectroscopic predictions

concerning 2 in the acidic region were in good agreement with
the analogous results on amines 1 and 3.[22,24,,64] Moreover, all
previous 13C NMR signals assignments[20,25] were fully confirmed
calculationally. But, it is realized that spectral data for the
scorpionate-like cations Hn2nþ were interpreted mainly in terms
of their non-solvated composite molecular shapes mimicking the
total conformational populations existing in a strongly polar
aqueous solution. Furthermore, the presence of the anions as
accompanied counterions was fully neglected above for the
cations under study.
Seeking for another explanations of non-typical
shifts observed

13

C NMR

The rationalization of the low-pH 13C NMR deshielding trends
experienced by pendant-arm atoms C11/C12 of 2 below pH 4.2 is
rather unambiguous. As a matter of fact, they were generally
quite well reproduced in the above NMR computations; nevertheless some doubts remain. Indeed, the used methodology of an
elucidation of the GIAO-supported mean multicomponent
molecular shapes is not a standard method. Moreover, the
crucial form H525þD gave a little weaker correlation among dCs at
its ONIOM2-modeled hydrated state.

On the other hand, it was possible to decline some other
explanations of the non-typical 13C NMR tendencies in
considering their sources. First, the CaH2CbHþ
2 NH3 unit was

found outside the 14-membered ring cavities in all acidic-region
cations Hn2nþ (n ¼ 3–5); as shown in Figs 2a, 3, and 5a.
Simultaneously, all four backbone N-atoms adopted an exodentate configuration in the last protonation step. In consequence,
13
C nuclei at the position 11 of H525þ were in a close
neighborhood of the axially oriented þN1—H bonds. But, similar
structural situation existing also for ring atoms C1 and C10
eliminates this ‘spatial suggestion.’ Therefore, a close proximity of
C11/C12 to both adjacent ammonium centers in H525þ was
finally considered as a second likely important cause, giving rise
to some specific short-range NMR effects with active participation of the nitrate anion (as shown in the Introduction). Indeed, it
was possible to postulate that such an arrangement enables the
electrostatic and/or ionic H-bonding interactions of two cationic
sites at N1 and N5 with a surrounding NOÀ
3 anion persisting in
outer spheres of these C atoms under strongly acidic conditions.
Unexpectedly, comparable low-pH 13C NMR trends were
reported recently for the CaH2CbH2SH side-chain of
2-(1,4,7,10-tetraazacyclododecan-1-yl)-ethanethiol (5).[34] In fact,
a down- and up-field protonation shift of carbon signals were
observed, respectively, for Ca and Cb of this non aminoN-containing unit below pD $ 2.5 using HClaq as a titrant. This
finding for the nucleus Cb was tentatively explained[34] by the
b-upfield 13C-shift criterion[25,66] as an indicative of protonation at
an adjacent basic N1 center. Accordingly, two different pH ranges
would also be taken into account for C11/C12 in a structurally
similar amine 2 i.e., below and above pH $ 1.3. Indeed, the
protonation of its tertiary amino N1 site occurs in very strongly
acidic solution.[20,23,25] In view of the foregoing, such a process
would be also reflected in similar NMR signal shifts for the vicinal
Ca and more remote Cb atoms, below pH 1.3. Consequently,

$ 2.4 ppm deshielding effect observed for two pendant-arm
carbons of 2 on going from pH 4.2 to 1.3 seemed to be really the
‘wrong-way’ one. However, it was quite well reproduced in
present GIAO predictions.
Above results on the ligand 5 seem to fully confirm the
correctness of the DFT GIAO-supported conformational approach
used here for 2. But, additional considerations on the influence of
an ionic medium, mainly of NOÀ
3 ions, appear to infer that the
latterly proposed ‘supermolecular explanation’ is also one of the
possibilities. Certainly, a lot of the nitrate anions were present in
strongly acidic solution of 2. Indeed, some literature reports
indicate for the ion pairing of simple diammonium cation
þ
À
[85]
À
H3NCH2CH2NHþ
So,
3 with NO3 or Cl in aqueous solutions.
þ
À
the interactions N —HÁÁÁO —N seem to be rational, at least as
coexistent occurrences. Moreover, such a proposal is consistent
with a reasonable supposition that the discussed nuclei C11/C12
were in similar chemical environments under the experimental
conditions used. The latter assumption results, in turn, from a
striking similarity in the 13C NMR titration profiles observed for
both these C-atoms, from pH 2 to 8 (resemblance criterion).[25]

CONCLUSIONS
The importance of using appropriate types of molecularmodeling methods supported with the GIAO DFT predictions
of experimental 13C NMR chemical shifts was demonstrated for
an elucidation of presumably preferred time-averaged multi-

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R. B. NAZARSKI
component conformations of the three neighboring protonated
states of a polyamine scorpionate-like ligand 2, existing in an
aqueous medium at a pH below $ 6.5. To the best of our
knowledge, this is the first application of such a jointed approach
to recognizing the mean shapes of variously protonated polyaza
macrocycles in the aqueous solution.
It was found that a subtle balance between the crucial
energetic criterion (gas-phase or liquid/solution results) and the
environmental match criterion (solution NMR data) must be
taken into account in making all such structural choices. However
(in our opinion), the best fitting of the experimental dobsd
s was the
C
most verificative statistical criterion of these choices i.e.,
calcd=corr

magnitudes of coefficients r and sums S(dC
À dobsd
)2.
C
Especially, the latter one (absolute error squared) is the best
match criterion of this kind when coefficients of linear correlation
are close.
It is apparent that, due to large structural flexibility of the
species Hn2nþ (n ¼ 3–5) their composite computational models
represent whole families of closely related multiple conformational states, rather than single entities. Moreover these
‘superimposed’ structures elucidated in a three-stage ‘NMR data
analysis/modeling and spectra prediction/statistical treatment of
results’ protocol correspond, more or less, to local and not to
global energy minima (in the sense of assessing the equilibrium
forms). Without any doubt, a jointed procedure used here can
also be useful for analogous structural purposes concerning the
other heteromacrocycles with the N-ring atoms.
An interesting observation was accomplished about the utility
of the MMX versus OPLS-AA force field for modeling different
protonated states of the macrocyclic polyamines. The former MM
method was found as more appropriate for intramolecularly
H-bonded forms of H323þ, whereas the latter—for cations H424þ
and H525þ adopting an exodentate ring configuration much
more favorable for hydration. Furthermore, a two-step computational treatment (initial compressing of the molecular system in
the OPLS-AA force field followed by its relaxation at the
ONIOM2 B3LYP/6-31G*:DREIDING level) is also worth mentioning.
The proposed conformational explanation of downfield
amine-protonation shifts found for two pendant-arm atoms
C11 and C12 of 2 below pH 4.2 is rather unambiguous, because
they were reproduced quite well in dCs, predicted for pertinent

GIAO-supported overall conformations of the coexisting polyammonium cations Hn2nþ. In particular, the successful reproduction of the 13C NMR spectrum of the complex ionic mixture at pH
2.05 strongly points out the correctness of such an interpretation.
Moreover, the strongest broadening observed under these
conditions for 13C signals due to the nuclei C4–C8, found its
theoretical rationalization. On the other hand, it was suggested
only, that the ‘wrong-way’ NMR tendency can also partially result
from an influence of the NOÀ
3 anion located in the close vicinity of
atoms C11/C12 i.e., residing outside the macrocyclic cavities of
related ions Hn2nþ. Undoubtedly, this problem demands
additional studies.
It is likely that a more advanced Boltzmann-weighted
consideration of different conformers of the species Hn2nþ,
especially supported with suitable MD simulations (taking into
account both hydration effects and specific structural influences
due to the presence of counteranions), would give still better
results on their mean composite shapes in aqueous solution and,
so, subtle NMR effects could be observed. However, the molecular
size of these heteromacrocyclic systems efficiently prevents such
a type of supermolecular calculation at the current time.

SUPPLEMENTARY INFORMATION
AVAILABLE
Relevant 13C NMR data for Hn2nþ (n¼3–5, with the spectrum at
pH 2.05), GIAO DFT computational results [including those for the
‘hydrated’ states (IEF-PCM and/or ONIOM2 approach, also
H525þBhydr view)], their statistical analysis, Cartesian coordinates,
and energetics for all crucial forms investigated (Tables S1-S24,
Figs S1-S4) (24 pages, PDF).

Acknowledgements
The author thanks Dr. Dariusz Sroczyn´ski (Department of General
and Inorganic Chemistry, University of Ło´dz´) for kindly providing
the program for generating the species distribution. The author
also thanks two anonymous reviewers for their very helpful
comments on an earlier draft of this article. Financial support
for present work was partially provided by Grants Nos. 505/671/
2005 and 505/0707/2008 from the University of Ło´dz´.

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obtain accurate dCs, but (in our opinion) an applied herein 6-31G*

basis set is sufficient, particularly taking into account a large mobility
of the cations Hn2nþ existing in a strongly polar aqueous solution,
which were in vacuo analyzed as isolated entities. However, it was
reported that, as a rule, medium-sized molecules may be well
accounted for by a low-level structure optimization followed by a
higher level GIAO dC calculation.59 Accordingly, related (suggested by
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were found at this higher level, except for a substantial value of
À dobsd
)2. Also EDs and SDs were worse; À2.50/2.59 and
S(dcalcd
C
C
0.87 ppm versus À2.30/2.25 and 0.71 ppm. As a consequence, only
initial (more cost-effective) B3LYP/6-31G* level scaled results were
used in the whole work. On the other hand, a newly found overall
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C
energy conformer of free amine 2 at the HF/6–31G** and DFT
B3LYP/6–31G* levels suggests that in the former case about
þ3 ppm correction should be used for all C atoms adjacent to
the amino-N atoms, to bring original GIAO HF level predictions into
a better agreement with experiment.64 An analogous ‘oxygencorrection’ term (DdCÀO of þ7 ppm per one ether-type oxygen
atom) was previously proposed for the O-bearing carbon atoms
at the same HF/6–31G** level.42 The magnitude of these dC corrections seems to be very well in agreement with an electronegativity of
both heteroatoms considered.
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calcd=corr
¼ f (dCi
), and the linear
strength of relationships dobsd
Ci
regression equation of the type yi ¼ a  xi þ b to mathematically
define these relations. For details see note 16 in Reference [43].
[71] The pentaprotonated (full protonation) state of pentamine 2 at pH
0.24 was assumed.

[72] In the used notation, conformers from A to D of H525þ were ordered
according to their classical (gas-phase) total electronic energies Eel.
The same convention was applied in further part of this work.
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843

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R. B. NAZARSKI
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[81]
[82]
[83]
[84]
[85]
[86]

used in this work are more appropriate. As to H424þ, an inflexion
point in the pH titration profile of C12 at pH $2.05 and the strongest
broadening of some 13C lines found under such experimental
conditions (see Figs 1 and S1) were tentatively assumed as an
indicative of its high concentration.
This kind of interaction was found in gross forms of the alkalineregion scorpiand systems Hn2nþ (0 n 2). See Reference [64].
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R. B. Nazarski, Phosphorus, Sulfur, and Silicon 2009, 18, issue 4.

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