Research Article Received: 29 July 2008, Revised: 10 January 2009, Accepted: 12 January 2009, Published online in Wiley InterScience: 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 Hn2nỵ (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 H525ỵ Copyright ò 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: rymaja@uni.lodz.pl 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 J Phys Org Chem 2009, 22 834–844 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 HnLnỵ (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 K, carried out for the three polyammonium ions Hn2nỵ (n ẳ 35) formed from pentamine [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 H525ỵ 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 H525ỵ(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 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 and 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 www.interscience.wiley.com/journal/poc 835 The conformation search for minima on potential-energy surfaces (PESs) of cationic species Hn2nỵ 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/6-31ỵG* 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 H525ỵ 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 H525ỵ(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 H525ỵ were initially constructed applying a solvent-box option ˚ (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 H525ỵ(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 H525ỵ(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 ỵ 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 containing extraneous ions Kỵ and OH (pH $ 13.5) On the other hand, some test GIAO DFT runs were also carried out for the free cation H525ỵ at a much more advanced B3LYP/6-311ỵG(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 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 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 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 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 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 Hn2nỵ (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 in acidic region It was obvious that assessing of the time-averaged (mean) shapes of different protonation states of the title pendant-arm Figure Selected 50.29 MHz 13C{1H} NMR-pH titration curves of ca 0.01 mol LÀ1 solution of the ligand 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 ỵ 0.72 ppm to account for the difference in diamagnetic susceptibilities of both the liquids involved) The C12 curve vertically shifted by ỵ 12 ppm, for brevity of plot 836 www.interscience.wiley.com/journal/poc Copyright ß 2009 John Wiley & Sons, Ltd J Phys Org Chem 2009, 22 834–844 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 AD of H525ỵ are listed in Table Inspection of the content revealed that a low-energy conformer B is the best single in vacuo model of the molecular shape of H525ỵ in solution [rC ẳ 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 AD is representative for single cation H525ỵ and works quite well Adequately, their 0.175:0.225:0.44:0.16 superposition was considered as a reasonable overall conformation of H525ỵ 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 H525ỵABCD).[72] The form C (as shown in Fig 2a) is perhaps the most abundant conformer of H525ỵ 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 H525ỵ in aqueous solution are given in Fig 2b The 14-membered macrocyclic units of all components A–D of H525ỵ adopt a conformation of type (3,4,3,4)-A,[73] with ring N-atoms occupying four corners of the molecular polygons and NỵH 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 H525ỵ 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 H525ỵ 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 H525ỵ was strongly Copyright ò 2009 John Wiley & Sons, Ltd www.interscience.wiley.com/journal/poc 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 Hn2nỵ 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 Hn2nỵ (n ẳ 35) 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 HnLnỵ 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 Hn2nỵ 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 Hn2nỵ (n ẳ 35) 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 H525ỵ 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 H525ỵ in solution (the spectroscopic match criterion) R B NAZARSKI Table Important energetic and regression-analysis data for the forms AD and ABCD of H525ỵ 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 Total sum S(dcorr ) [ppm2]k C dC Standard deviation [ppm]kl Estimated participation in H525ỵABCDc [%] a A B Cb D H525ỵABCDc 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 H525ỵ 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; au ¼ 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 ỵ b.[9,11,43,44,70] Ci ẳ 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 Hn2nỵ (n ẳ 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 H323ỵ, than those coming from OPLS-AA modelsfor H424ỵ Thus, some (usually, two or three) intramolecular H-bonds of type NỵHN, also including bifurcated systems, were found in various forms of H323ỵ (Fig 3), whereas all of the ring ỵNH bonds adopt an exodentate orientation in different conformers of H424ỵ (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 H323ỵ and H424ỵ, respectively But, somewhat poorer correlations were found for these two ions Their final individual mean shapes (with a fraction in parenthesis) H323ỵABCD (32:20:20:28) and H424ỵABC (9:33:58) were elucidated with the rCs of 0.9663 and only of 0.9533, respectively Likewise as above for H525ỵ, their gas-phase high-energy conformers were found to be abundant components, especially for H424ỵ EDs in dCs computed for such shapes of H323ỵ and H424ỵ were of 3.94/ 3.61 and 2.67/4.54 ppm, respectively For NMR data regarding www.interscience.wiley.com/journal/poc all constituents of these mean shapes see Tables S5 and S6 It seemed initially that, the deprotonation of preferred forms of H525ỵ leads to the formation of related conformers of H424ỵ possessing an inverted configuration at the secondary amino N1 site and being usually not favorable in aqueous solution, except for the equilibrium between H424ỵA and H525ỵD (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 H323ỵ 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 H424ỵ and C C 3ỵ 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 and 5a) In addition, all ions HnLnỵ (L ẳ 13) 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 in aqueous solution is given in Fig This plot, obtained with PlotPhi,[78] explicitly shows six macrospecies Hn2nỵ (n ẳ 05) 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 Copyright ß 2009 John Wiley & Sons, Ltd J Phys Org Chem 2009, 22 834–844 AN ATTEMPT TO RATIONALIZE SOME NMR-PH TITRATION SHIFTS Figure PLUTON drawings of two dominant GIAO-supported conformers of H323ỵ 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 The proposed GIAO-supported overall solution conformation of H525ỵABCD (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 H525ỵABCD are significant pH ranges over which two or even three of the considered ions Hn2nỵ 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, H323ỵ (similarly as a terminal cation H525ỵ)[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 H424ỵ 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 H323ỵ and H424ỵ, respectively.[80] In view of the foregoing, an existence of two neighboring ions (H525ỵ and, especially, of H323ỵ) had to be consider for the large ensemble of different cationic entities probed at pH 2.05 (environment formally belonging to a single ion H424ỵ) 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 H424ỵBC (37:63) with an additional 28 and 37.5% assistance of H525ỵABCD and H323ỵABCD, 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 H424ỵABC (9:33:58) were unfixed, leading to simplification of the initial three- to final two-component shape of H424ỵBC (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 2.67/4.54 ppm for initial H424ỵABC; as shown in Tables S6 and S7 Obviously, such a rationalization of the composition of a mixture of ions (and of H424ỵ, 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 H525ỵABCD Moreover, a newly evaluated amount of the cation H424ỵBC is comparable, within the uncertainty of an Figure Distribution diagram of the protonated species formed from pentamine ligand 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 839 J Phys Org Chem 2009, 22 834–844 Copyright ß 2009 John Wiley & Sons, Ltd www.interscience.wiley.com/journal/poc R B NAZARSKI Figure The proposed GIAO-supported solution conformation of the ion H424ỵ (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 H323ỵABCD ($ 37.5%), H424ỵBC ($ 34.5%) and H525ỵABCD ($ 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 ($ 34.5 vs $ 55%) The absence of the form A in final mean shape of H424ỵ 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 H323ỵABCD and H424ỵBC ($ 37.5 and $ 34.5%) Indeed, there are numerous disruptions and formations of intramolecular H-bonds of type NỵHN 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 H424ỵ and, particularly, for H323ỵ to be involved in various internal H-bonds mentioned above, with active participation of their side arm CH2CH2NHỵ 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 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 H424ỵABC (a) and for 10 forms of three different coexisting ions Hn2nỵ (final results) (b); cf also Fig 5b Hn2nỵ n ẳ 0–2 (confronted with experimental data in solution) for which internal H-bonds of the type NỵHN 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 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 H525ỵ, 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 H525ỵ (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] 840 www.interscience.wiley.com/journal/poc Copyright ß 2009 John Wiley & Sons, Ltd J Phys Org Chem 2009, 22 834–844 AN ATTEMPT TO RATIONALIZE SOME NMR-PH TITRATION SHIFTS The simulated hydrated states of six pre-selected forms of H525ỵ 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 H525ỵDhydr (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 H525ỵBhydr 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 H525ỵ (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 H525ỵ Generally, the present structural and spectroscopic predictions concerning in the acidic region were in good agreement with the analogous results on amines 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 Hn2nỵ 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 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 H525ỵD 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 CaH2CbHỵ NH3 unit was found outside the 14-membered ring cavities in all acidic-region cations Hn2nỵ (n ẳ 35); 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 H525ỵ were in a close neighborhood of the axially oriented ỵN1H 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 H525ỵ 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 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 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 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 seem to fully confirm the correctness of the DFT GIAO-supported conformational approach used here for But, additional considerations on the influence of an ionic medium, mainly of NOÀ 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 Indeed, some literature reports indicate for the ion pairing of simple diammonium cation ỵ [85] H3NCH2CH2NHỵ So, with NO3 or Cl in aqueous solutions ỵ 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 to (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- 841 J Phys Org Chem 2009, 22 834–844 Copyright ß 2009 John Wiley & Sons, Ltd www.interscience.wiley.com/journal/poc 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 Hn2nỵ (n ẳ 35) 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 H323ỵ, whereas the latterfor cations H424ỵ and H525ỵ 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 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 Hn2nỵ 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 anion located in the close vicinity of atoms C11/C12 i.e., residing outside the macrocyclic cavities of related ions Hn2nỵ Undoubtedly, this problem demands additional studies It is likely that a more advanced Boltzmann-weighted consideration of different conformers of the species Hn2nỵ, 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 Hn2nỵ (nẳ35, with the spectrum at pH 2.05), GIAO DFT computational results [including those for the ‘hydrated’ states (IEF-PCM and/or ONIOM2 approach, also H525ỵBhydr 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´ REFERENCES [1] K Wolinski, J F Hilton, P Pulay, J Am Chem Soc 1990, 112, 8251–8260 and references therein [2] G Rauhut, S Puyear, K Wolinski, P Pulay, J Phys Chem 1996, 100, 6310–6316 [3] J R Cheeseman, G W Trucks, T A Keith, M J Frisch, J Chem Phys 1996, 104, 5497–5509 [4] J B Foresman, Ỉ Frisch, Exploring Chemistry with Electronic Structure Methods, 2nd edn., Gaussian, Inc Pittsburgh, PA 15106, USA, 1996, Chapter ỵ Errata [5] D A Forsyth, A B Sebag, J Am Chem Soc 1997, 119, 9483–9494 [6] I Alkorta, J Elguero, Struct Chem 1998, 9, 187–202 [7] K B Wiberg, J Comput Chem 1999, 20, 1299–1303 [8] R M Aminova, G A Schamov, A V Aganov, J Mol Struct Theochem 2000, 498, 233–246 and references therein [9] R M Claramunt, C Lo´pez, D Sanz, I Alkorta, J Elguero, Heterocycles 2001, 55, 2109–2121 [10] K W Wiitala, T R Hoye, C J Cramer, J Chem Theory Comput 2006, 2, 1085–1092 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Goddard, III, J Phys Chem 1990, 94, 8897–8909 [52] HyperChem Molecular Modeling System Release 7.0 for Windows Hypercube Inc., Gainesville, FL 32601, USA, January 2002 [53] W L Jorgensen, J Chandrasekhar, J D Madura, R W Impey, M L Klein, J Chem Phys 1983, 79, 926–935 [54] A L Spek, J Appl Cryst 2003, 36, 7–13 [55] A L Spek, PLATON, A Multipurpose Crystallographic Tool, Version 230203, Utrecht University, Utrecht, The Netherlands, 2003, http:// www.cryst.chem.uu.nl/platon [56] This is a standard DFT GIAO methodology applied for mediumsized low-polar molecules analyzed in apolar solutions, see e.g References 8, and 57–59 [57] G Barone, L Gomez-Paloma, D Duca, A Silvestri, R Riccio, G Bifulco, Chem Eur J 2002, 8, 3233–3239 [58] D Colombo, P Ferraboschi, F Ronchetti, L Toma, Magn Reson Chem 2002, 40, 581–588 [59] P Cimino, L Gomez-Paloma, D Duca, R Riccio, G Bifulco, Magn Reson Chem 2004, 42, S26–S33 [60] Indeed, some reports (e.g., References 3,6,10,11) suggested that the use of triple-z basis sets is necessary in the GIAO DFT calculations to 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 Hn2nỵ 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 one of referees) empirically scaled GIAO predictions at a much more advanced B3LYP/6-311ỵG(2d,p)//B3LYP/6-31G* level3,10,11 were also carried out for the forms A-D of H525ỵ These GIAO results and their comparison with the B3LYP/6-31G*//B3LYP/6-31G* data are presented in Table S4 and Fig S2 In general, rather similar statistics 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 conformation H525ỵBCD (57:32:11) differs from the standard shape H525ỵABCD (17.5:22.5:44:16) The latter finding suggests that the uncertainty of such a GIAO-supported valuation of the compositions of these kinds of complex cationic mixtures in an aqueous medium is about 10–15% [61] For ONIOM-GIAO calculations, see e.g., A Zheng, M Yang, Y Yue, C Ye, F Deng, Chem Phys Lett 2004, 399, 172–176 and references therein [62] A Zheng, L Chen, J Yang, Y Yue, C Ye, F Deng, Chem Commun 2005, 2474–2476 [63] V Vailikhit, W Treesuwan, S Hannongbua, J Mol Struct Theochem 2007, 806, 99–104 [64] R B Nazarski, unpublished results classically GIAO predicted for the lowest[65] Analysis of data dcalcd C energy conformer of free amine at the HF/6–31G** and DFT B3LYP/6–31G* levels suggests that in the former case about ỵ3 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 [66] See also literature cited in Reference [25] [67] An arbitrary atom labeling used throughout this work (Fig 1) was forced by software applied for final visualization of the computed structures [68] G Barone, D Duca, A Silvestri, L Gomez-Paloma, R Riccio, G Bifulco, Chem Eur J 2002, 8, 3240–3245 [69] P Taăhtinen, A Bagno, K D Klika, K Pihlaja, J Am Chem Soc 2003, 125, 4609–4618 and references therein [70] The Pearson correlation coefficient value r was used to measure a calcd=corr ¼ f (dCi ), and the linear strength of relationships dobsd Ci regression equation of the type yi ẳ a xi ỵ b to mathematically define these relations For details see note 16 in Reference [43] [71] The pentaprotonated (full protonation) state of pentamine at pH 0.24 was assumed [72] In the used notation, conformers from A to D of H525ỵ were ordered according to their classical (gas-phase) total electronic energies Eel The same convention was applied in further part of this work [73] M Meyer, V Dahaoui-Gindrey, C Lecomte, R Guilard, Coord Chem Rev 1998, 178–180, 1313–1405 and references therein 843 J Phys Org Chem 2009, 22 834–844 Copyright ß 2009 John Wiley & Sons, Ltd www.interscience.wiley.com/journal/poc R B NAZARSKI [74] J M Harrowfield, H Miyamae, T M Shand, B W Skelton, A A Soudi, A H White, Aust J Chem 1996, 49, 1051–1066 [75] M Domagała, R B Nazarski, in preparation [76] S Fuăzerova, J Kotek, I Csarova, P Hermann, K Binnemans, I Lukesˇ, Dalton Trans 2005, 2908–2915 [77] K A Hunter, Acid-base Chemistry of Aquatic Systems, University of Otago, Dunedin, New Zealand, 1998 [78] D Sroczyn´ski, unpublished work.21 PlotPhi, The C computer program generating distribution plots of the species HnBnỵ (where B ¼ any n-protic base) according to the stepwise macroscopic protonation constants KHi,iỵ1 ẳ [HiBiỵ]/[Hi1B(i-1)ỵ][Hỵ], i ẳ 1$n, by using general formulas given in J Incze´dy, Analytical Applications of Complex Equilibria, E Horwood, Ltd., Chichester, 1976, Chapter [79] See, e.g., Z Szaka´cs, M Kraszni, B Nosza´l, Anal Bional Chem 2004, 378, 1428–1448 and references therein [80] Previously,25 the dCs measured at pH 5.31 were assumed for H323ỵ; however, the averages from two titration points (pH 5.77 and 6.18) [81] [82] [83] [84] [85] [86] used in this work are more appropriate As to H424ỵ, 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 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 Hn2nỵ (0 n 2) See Reference [64] G Ambrosi, P Dapporto, M Formica, V Fusi, L Giorgi, A Guerri, M Micheloni, P Paoli, R Pontellini, P Rossi, Chem Eur J 2003, 9, 800–810 F Bernardi, E Gaggelli, E Molteni, E Porciatti, D Valensin, G Valensin, Biophys J 2006, 90, 1350–1361 S Xiang, G Yu, Y Liang, L Wu, J Mol Struct 2006, 789, 43– 51 S Cascio, A De Roberts, C Foti, Fluid Phase Equilib 2000, 170, 167–181 and references therein R B Nazarski, Phosphorus, Sulfur, and Silicon 2009, 18, issue 844 www.interscience.wiley.com/journal/poc Copyright ß 2009 John Wiley & Sons, Ltd J Phys Org Chem 2009, 22 834–844 ... 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... pre-selected low-energy B3LYP/ 6-31G* level structures were subsequently GIAO NMR examined for H323ỵ and H424ỵ, respectively But, somewhat poorer correlations were found for these two ions Their... flexibility observed for all of the amines 1–3 in solution (vide supra).[24,25] So, weaker correlations dcalcd versus dobsd found for H424ỵ and C C 3ỵ H32 can partially result from their mobility (and,