Silver(I) affinities of amides: a combined ab initio and experimental study

Abstract

The interaction of Ag⁺ with amides was studied through prototypical systems mimicking the binding of Ag⁺ to the peptide bond. The Ag⁺ binding affinities (energies) of formamide, N-methylformamide, N,N-dimethylformamide, acetamide, N-methylacetamide and N,N-dimethylacetamide were determined by the mass spectrometric kinetic method to be 162, 179, 193, 181, 198 and 208 kJ mol⁻¹, respectively, with an estimated uncertainty of ±11 kJ mol⁻¹. The relative stability of different possible Ag⁺ binding modes was investigated effectively at the ab initio CCSD(T)/[HW(f),6-31+G(d)] level of theory. The absolute theoretical affinities are in good general agreement with the experimental values, even though calculated values tend to be too high by an average of 10 kJ mol⁻¹. The theoretical results show that Ag⁺ binds preferentially to the amide carbonyl oxygen, whereas monodentate binding to the amino nitrogen, or bidentate binding to both oxygen and nitrogen, are about 40 to 60 kJ mol⁻¹ less stable. Methyl substitution at the amide carbon and amino nitrogen enhances the Ag⁺ affinity by increasing the molecular polarizability of the amide. The effects of C-methyl and N-methyl substitution on Ag⁺ binding at the amide carbon and amino nitrogen are found to be significantly different and this difference is discussed.

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1. Introduction

The medical application of the silver ion and its coordinated complexes has long been known and well documented.^1–4 The silver ion shows remarkable toxicity to lower forms of life, but minimal adverse effects on humans and higher animals. This differential behaviour allows some of its complexes to be used as bactericides and germicides to inhibit the growth of fungi and bacteria, and as active ingredients in eye drops for newborns.³ Much of the biological action is believed to be initiated by Ag⁺ binding to functional group of proteins in microorganisms.^3,4 For example, a recent study of cystein-mutated potassium ion channel in Murine Kir 2.1 showed that the H5 pore region of the channel could be blocked by the silver ion.⁵

Silver ion is found to bind strongly to amino acids^6–8 and peptides.^9–11 In peptides, the amide carbonyl oxygen of the peptide bond is one of the most common and preferred binding sites for Ag⁺.¹⁰ A recent theoretical study has shown that, for the Ag⁺-triglycine complex, Ag⁺ is preferentially tetracoordinated to the terminal amino nitrogen and the three amide carbonyl oxygens of the peptide backbone.¹¹ Mass spectral fragmentation of Ag⁺-peptide complexes has been demonstrated to be useful in peptide sequencing.^12,13 The competition among the different fragmentation pathways are determined, to a large extent, by the energetics of Ag⁺ binding to the different binding sites of the peptide.^6–8,10

The Ag⁺ binding affinity of a ligand, L, is the enthalpy change, ΔH, of the dissociation reaction (1) at temperature T, typically at 0 K.

Ag⁺–L → Ag⁺ + L (1)

Knowledge of metal cation binding affinities of model ligands bearing the O/N heteroatom function groups (binding sites) of amino acids and peptides is essential for the understanding of metal binding in large peptides and proteins. Up to now, only a limited number of gas phase Ag⁺ binding affinities of model ligands (e.g., water,¹⁴ benzene,^15,16 acetone,^16,17 alcohols,^17,18 pyridine,^19,20 furan,²¹ acetonitrile,^22,23 ammonia,²³ methylamine,²³etc.) have been experimentally measured. They were determined by high-pressure mass spectrometry (HPMS),¹⁴ radiative dissociation kinetics in a Fourier transform-ion cyclotron resonance mass spectrometer (RA/FT-ICR),¹⁶ supersonic molecular beam/charge transfer photodissociation,^19–21 and threshold-CID methods.^15,17,22,23 These experimental studies were often accompanied^16–23 or augmented^24–27 by molecular orbital calculations, which provide complimentary information on the binding geometries/modes and rationalization of experimental observations. An example is the determination of the relative Ag⁺ affinities of the twenty naturally-occurring amino acids by the mass spectrometric kinetic method,⁶ and rationalization of their relative order and possible binding modes/sites by density functional theory (DFT) calculations has been reported recently.²⁸

The interaction of metal cations with amides has been studied with prototypical systems mimicking the binding of metals to the peptide bond.^29–32 The Ag⁺ affinity of formamide was reported in a DFT study of small model ligands.²⁶ Despite their biological and mass spectral relevance, the experimental Ag⁺ affinities of amides have not been studied. Here, we report the Ag⁺ binding affinities of a series of six amides, i.e., formamide (F), N-methylformamide (MF), N,N-dimethylformamide (DMF), acetamide (A), N-methylacetamide (MA) and N,N-dimethylacetamide (DMA), determined by the mass spectrometric kinetic method. In addition, we also report ab initio results on the relative stabilities of different possible Ag⁺ binding modes. The systematic study on a series of amides allows the effect of methyl substitution at the amide carbon and at the amide nitrogen (e.g., H–CONH₂versus CH₃–CONH₂, and HCONH–H versus HCONH–CH₃) on Ag⁺ binding affinity to be elucidated.

2. Experimental

2.1. Methodology

In this work, the order of relative Ag⁺ affinities among the six amides, expressed in the form of a relative affinity ladder, was first established by standard kinetic method measurements.^33,34 The absolute affinities of MF, DMF, A, MA and DMA were determined separately by extended kinetic method measurements^34–36 using methyl-substituted benzenes as the reference compounds. But this method failed in the case of formamide (F) due to the low intensity of the Ag⁺ bound heterodimers comprised of formamide and methyl-substituted benzenes. Consequently, the absolute affinity of F was determined with reference to the measured absolute affinities of MF, DMF, A, MA and DMA by the standard kinetic method.

The theoretical basis, assumptions and the methodology of the mass spectrometric kinetic method have been reviewed recently,^33,34 and only a brief outline is given here. For the competitive unimolecular dissociations of the Ag⁺ bound heterodimer complex between two ligands L₁ and L₂, [L₁ + Ag + L₂]⁺, to the Ag⁺ bound monomer complexes, [L₁ + Ag]⁺ and [L₂ + Ag]⁺ (reactions (2) and (3)), the natural logarithm of the relative rates of the competitive unimolecular dissociations, ln(k₁/k₂), can be equated to the natural logarithm of the ion intensity ratio, ln(I_[L1+Ag]/I_[L2+Ag]) by eqn. (4).

where Q^*₁ and Q^*₂ are the partition functions of the two transition states of the competing reactions, (ε₂ − ε₁) is the difference in critical energies for the two reactions, and T_eff is the ‘effective temperature’ of the dimer complex undergoing dissociation. When L₁ and L₂ are structurally similar (e.g., when L₁ and L₂ are amides in this study), the ln(Q^*₁/Q^*₂) term may be taken to be zero (i.e., Q^*₁ = Q^*₂). Also, by assuming that the heterodimer dissociates with no reverse critical energy, eqn. (4) can be simplified to eqn. (5). With this simplification, the relative Ag⁺ affinity between L₁ and L₂, i.e., Δ(ΔH) = ΔH_[L1+Ag]⁺ − ΔH_[L2+Ag]⁺, is now proportional to the ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) intensity ratio at a given T_eff. This standard kinetic method, usually expressed in the form of a relative affinity ladder, is applied in the present study to determine the relative order of Ag⁺ affinities among the six amides.

To measure the absolute Ag⁺ affinity of an unknown ligand (L₁), the dissociation of its Ag⁺ bound heterodimer with a series of reference compounds (L_n) of known Ag⁺ affinities (e.g. L₁ = acetamide and L_n = methyl-substituted benzenes in this study) have to be measured. If the unknown and reference compounds are structurally dissimilar, the ln(Q^*₁/Q_n*) term is generally non-zero, but is usually expressed as an ‘apparent’ entropic term, Δ(ΔS)^app/R, according to eqn. (6), where Δ(ΔS)^app is the difference in entropies of activation for reactions (2) and (3). By drawing analogy with the thermodynamic relation, ΔG = ΔH − TΔS, eqn. (4) now becomes eqn. (7):

where the (ΔG)^app term is given by eqn. (8):

(ΔG)^app = ΔH_{[L1 + Ag]+} − T_effΔ(ΔS)^app (8)

It should be noted that the T_eff, Δ(ΔS)^app and (ΔG)^app terms are experimentally measured values obtained according to the protocol of the extended mass spectrometric kinetic method, and are related to the non-Boltzmann distribution of internal energy of the dissociating heterodimer.^33,34 If Δ(ΔS)^app is constant for a series of structurally similar ‘reference’ ligands, then the natural logarithm of ion intensity ratio (ln(I_[L1+Ag]⁺/I_[Ln+Ag]⁺)) has to be measured at three or more effective temperatures, or internal excitation energies of the dissociating heterodimer. This is often achieved by varying the collisional kinetic energy between the Ag⁺ bound heterodimer and a collision gas, e.g. argon, in the collision cell of a triple quadrupole tandem mass spectrometer. According to eqn. (7), a plot of ln(I_[L1+Ag]⁺/I_[Ln+Ag]⁺) versus ΔH_[Ln+Ag]⁺ will yield a straight line with (ΔG)^app/RT_eff as the y-intercept and −1/RT_eff as the slope. A second plot of (ΔG)^app/RT_effversus 1/RT_eff at different effective temperatures would yield another straight line with ΔH_[L1+Ag]⁺ as the slope and −Δ(ΔS)^app/R as the y-intercept. This approach is known as the extended kinetic method,^34–36 and was used in the present study to determine the absolute Ag⁺ affinities of amides.

However, the (ΔG)^app and 1/RT_eff terms are in fact covariant so that the highly linear (ΔG)^app/RT_effversus 1/RT_eff (second) plot in the original extended kinetic method could be an artifact of the data analysis. To remove this possible artifact, Armentrout suggested a statistical data treatment procedure:³⁷ the ln(I_[L1+Ag]⁺/I_[Ln+Ag]⁺) term is first plotted against [ΔH_[Ln+Ag]⁺ − ΔH_avg], where ΔH_avg is the average of ΔH values of the reference compounds (L_n). The slope of this plot, m, is −1/RT_eff and the y-intercept, y₀, is [(ΔG)^app − ΔH_avg]/RT_eff. This is followed by a second plot of y₀versus−m which yields a straight line with slope of [ΔH_[L1+Ag]⁺ − ΔH_avg] and y-intercept of −Δ(ΔS)^app/R, from which the unknown ΔH_[L1+Ag]⁺ and Δ(ΔS)^app can be determined. This statistical data treatment protocol recommended by Armentrout was adopted in the present study.

2.2. Experimental procedures

The mass spectrometric system used in this work was described in a recent publication.³⁸ Briefly, standard kinetic method measurements were carried out with a Finnigan-MAT-95S magnetic(B)-electric(E) sector (MS1)-ion trap (MS2) tandem mass spectrometer (Bremen, Germany) equipped with an electrospray ionization (ESI) source.^39,40 The Ag⁺ bound heterodimers of two amides were generated from a mixture solution of amides (final concentration: 2 × 10⁻⁴ − 1 × 10⁻² M, except for formamide at 0.2 M) and silver nitrate (final concentration: 1 × 10⁻⁴ M) in methanol. The concentration of individual amides in the solution was optimized within the stated concentration range to maximize the intensity of the heterodimer ions. The solution was introduced into the ESI source at 12 μl min⁻¹, and the heterodimer ions were generated at an electrospray voltage of 2.3 kV. The ion beam was accelerated by a potential difference of 4.7 keV towards a collision cell located in the first field free region (1st FFR) between the ionization source and the magnetic sector of the B-E mass analyser (MS1). Nitrogen gas was introduced into the collision cell (8 × 10⁻⁵ mbar, as measured by an ionization gauge at the ion source region) until the intensity of the main ion beam was attenuated by ∼20%. High-energy CID (4.7 keV, laboratory scale) of the [L₁ + ¹⁰⁷Ag + L₂]⁺ heterodimer occurring in the 1st FFR was monitored by B/E-linked scanning at a scan rate of 20 s decade⁻¹.

Alternatively, the [L₁ + ¹⁰⁷Ag + L₂]⁺ heterodimer was mass-selected by MS1 (the B-E sector mass analyser) and transferred to MS2 (the ion trap mass analyser) for low-energy CID (eV, laboratory scale) measurements. Typical operating conditions of the ion-trap CID experiments were: ion injection time 200 ms, activation RF voltage 0.55 V, activation q_z at 0.25, activation time 15 ms, and helium buffer (collision gas) at 2.8 × 10⁻⁵ mbar (as measured by an ion gauge under the ion-trap chamber). Since the ion trap mass analyser was not heated, a small fraction of the dissociated Ag⁺ bound monomer complex [L₁ + Ag]⁺ and [L₂ + Ag]⁺ further reacted with trace moisture found inside the ion trap to yield the [L₁ + Ag + H₂O]⁺ and [L₂ + Ag + H₂O]⁺ cluster ions. The intensity of the cluster ion was combined (summed) with the intensity of the [L₁ + Ag]⁺ or [L₂ + Ag]⁺ ion to yield the I_[L1+Ag]⁺/I_[L2+Ag]⁺ intensity ratio.

The extended kinetic method measurements were carried out with a Quattro Ultima triple quadrupole tandem mass spectrometer (Micromass, Manchester, UK). The Ag⁺ bound heterodimers of an amide and reference methyl-substituted benzenes were generated from a mixture solution of the amide (final concentration: 2 × 10⁻⁴ − 5 × 10⁻⁴ M), methyl-substituted benzenes (final concentration: 1 × 10⁻³ − 2 × 10⁻² M) and silver nitrate (final concentration: 1 × 10⁻⁴ M) in methanol. Similar to the case of standard kinetic method measurements, the concentrations of the amide and methyl-substituted benzene in the solution were optimized within the stated concentration range to yield maximum heterodimer ion intensity. The solution was introduced into the ESI source at 12 μl min⁻¹. Typical operating conditions were: ESI capillary voltage at 3.5 kV, source temperature at 75 °C, nebulizing and desolvation N₂ gas flow rate at 500 L h⁻¹, and declustering cone gas (N₂) at 50 L h⁻¹. The [amide + ¹⁰⁷Ag + (methyl-substituted benzene)]⁺ heterodimer formed was mass-selected by the first quadrupole mass analyser (MS1), and underwent low-energy CID (10 to 30 eV, laboratory scale) in the RF-only hexapole collision cell filled with argon gas (1.88 − 1.90 × 10⁻⁵ mbar, as measured by a Penning gauge in the analyzer region, corresponding to ∼30% attenuation of the selected parent ion intensity). Daughter ion (MS/MS) scanning was carried out with the second quadrupole mass analyser (MS2) at 250–300 Th per second.

For both high-energy and low-energy CID measurements, typically 50–100 scans were accumulated (summed) to yield a measurement of the ion intensity (peak height) ratio, and the average of 4–6 measurements were taken as the final result. The reproducibility of the ion intensity ratios were <±6%, <±10% and <±10% (relative standard deviation, n = 4–6), and the logarithm of ratios were <±0.05, <±0.10 and <±0.10 for the high-energy N₂-CID, ion trap-CID and triple quadrupole low-energy CID measurements, respectively.

2.3. Reagents

All chemicals were analytical grade reagents supplied by Sigma-Aldrich Chemicals (St. Louis, MO, USA). Stock solutions of formamide (2 M), other amides (0.1 M), hexamethylbenzene (0.02 M), other methyl-substituted benzenes (0.1 M) and silver nitrate (2 × 10⁻³ M) in methanol were prepared separately before use.

3. Theoretical methods

Calculations were carried out on various platforms using the Gaussian98 package⁴¹ of programs. In this work, we made use of a protocol which has been found to be reliable for estimating the binding energies of Ag⁺ for organic ligands.^24,25 In this protocol, the geometries of the amides and the Ag⁺-amide complexes are optimized at the MP2(FC) level with 3-21G(d) and [HW,3-21G(d)] basis sets, respectively. The harmonic vibrational frequencies of the optimized species are calculated at the same levels of theory, in order to characterize the nature of the stationary points and to estimate the zero-point vibrational energies (ZPVEs). To correct for the general overestimation of theoretical frequencies, the ZPVEs are scaled by 0.94. Based on these optimized structures, single-point energy calculations at the CCSD(T)/STO-3G(d), MP2/STO-3G(d) and MP2/[HW(f),6-31+G(d)] levels are performed. The total energy E of a given species at 0 K and at the theoretical level of CCSD(T)/[HW(f),6-31+G(d)] is approximated by the following additivity relation:

E ≈ CCSD(T)/STO-3G(d) − MP2/STO-3G(d) + MP2/[HW(f),6-31+G(d)] + (ZPVE * 0.94) (9)

Thus, the Ag⁺ binding affinities of the various amides at 0 K (ΔH₀) is given by:

ΔH₀ = E_Ag⁺ + E_amide − E_{Ag⁺–amide} (10)

where E_Ag+, E_amide, E_{Ag⁺–amide} are the total energies of the silver cation, the amide ligand and the Ag⁺–amide complex at 0 K, respectively, calculated using eqn. (9).

4. Results and discussion

4.1. Experimental determination of relative and absolute Ag⁺ binding affinities of amides

Previous studies on K⁺/Na⁺ affinities of amides showed that some of the amides have very similar metal cation affinities.⁴² As will be shown later (Table 2), such small difference (less than 2 kJ mol⁻¹) in Ag⁺ affinities is also found in the case of Ag⁺ binding to N-methylformamide (MF) and acetamide (A). The standard kinetic method is well known for its ability to detect small differences in binding affinities as small as 0.8 kJ mol⁻¹ (∼0.2 kcal mol⁻¹).⁴³ Hence, we first attempted to establish the order of Ag⁺ affinities by monitoring the dissociation of Ag⁺ bound heterodimers formed among the six amides.

Table 1 Theoretical Ag⁺ affinities (kJ mol⁻¹) at 0 K, ΔH₀, of reference compounds used in this study

Reference compound	ΔH0^a
a From refs. 25 and 44. The reference Ag^+ affinities are theoretical values obtained at the CCSD(T)/[HW(f),6-31+G(d)] level of theory based on additivity scheme, eqn. (9).
Toluene (Tol)	168
m-Xylene (m-Xy)	181
1,3,5-Trimethylbenzene (1,3,5-Me3Bz)	193
1,2,4,5-Tetramethylbenzene (1,2,4,5-Me4Bz)	200
Pentamethylbenzene (Me5Bz)	209
Hexamethylbenzene (Me6Bz)	217

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Table 2 Experimental Ag⁺ affinities (in kJ mol⁻¹), ΔH, and Δ(ΔS_Ag+)^app (in J mol⁻¹ K⁻¹) of amides determined by the extended kinetic method ^a

Amides	ΔH	Δ(ΔSAg+)^app	Reference compound
a Weighted results with experimental uncertainties given as ±SD (90% confidence level) in the format of ref. 37.
N-Methylformamide (MF)	179.1 ± 0.4 (0.8)	3.8 ± 1.0 (1.9)	Tol, m-Xy, 1,3,5-Me3Bz, 1,2,4,5-Me4Bz
Acetamide (A)	180.7 ± 0.2 (0.4)	2.8 ± 0.6 (1.0)	Tol, 1,3,5-Me3Bz, 1,2,4,5-Me4Bz
N,N-Dimethylformamide (DMF)	193.1 ± 0.5 (0.9)	−0.8 ± 1.3 (2.4)	1,3,5-Me3Bz, 1,2,4,5-Me4Bz, Me5Bz, Me6Bz
N-Methylacetamide (MA)	198.2 ± 0.6 (1.1)	0.4 ± 1.6 (3.0)	1,3,5-Me3Bz, 1,2,4,5-Me4Bz, Me5Bz, Me6Bz
N,N-Dimethylacetamide (DMA)	207.6 ± 0.2 (0.5)	−5.8 ± 0.7 (1.3)	1,3,5-Me3Bz, 1,2,4,5-Me4Bz, Me5Bz, Me6Bz

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A typical ESI mass spectrum generated from a methanolic mixture solution of acetamide (A) and N-methylacetamide (MA) is shown in Fig. 1(a). The major peaks in the mass spectrum are due to the heterodimer ion, [MA + Ag + A]⁺ (m/z 239 and 241), and the homodimer ions [2A + Ag]⁺ (m/z 225 and 227) and [2MA + Ag]⁺ (m/z 253 and 255). Due to the presence of ¹⁰⁷Ag and ¹⁰⁹Ag isotopes, each heterodimer or homodimer ion shows two peaks in the mass spectrum, but only the [MA + ¹⁰⁷Ag + A]⁺ heterodimer ion was chosen and mass-selected for the kinetic method measurements.

Fig. 1 (a) Positive ESI mass spectrum of Ag⁺ cationized acetamide/N-methylacetamide complexes, and (b) High-energy (4.7 keV, laboratory scale) N₂-CID mass spectrum of the [MA + ¹⁰⁷Ag + A]⁺ heterodimer (MA = N-methylacetamide and A = acetamide).

The high-energy collision-induced dissociation (CID) mass spectrum (B/E-linked scan) of the Ag⁺ bound heterodimer complex, [MA + ¹⁰⁷Ag + A]⁺, is shown in Fig. 1(b). The complex dissociates by competitive elimination of MA and A yielding two major fragment ions at m/z 166 ([A + ¹⁰⁷Ag]⁺) and m/z 180 ([MA + ¹⁰⁷Ag]⁺), respectively. The higher abundance of [MA + ¹⁰⁷Ag]⁺ suggests that MA has a higher Ag⁺ binding affinity than A. The natural logarithm of the ion intensity ratio [MA + ¹⁰⁷Ag]⁺/[A + ¹⁰⁷Ag]⁺ is equal to 0.58, which is directly proportional to the relative Ag⁺ affinity, Δ(ΔH) = ΔH_[MA+Ag]⁺ − ΔH_[A+Ag]⁺. However, the relative Ag⁺ affinities of isobaric amides, such as MF/A and DMF/MA, cannot be compared directly by pairing them in a heterodimer complex. Hence, the relative Ag⁺ affinities of isobaric amides were determined from heterodimers in which these amides are paired up with other amides.

The experimentally measured ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values (where L₁, L₂ = amides, and the ¹⁰⁷Ag isotope is simply denoted by Ag hereafter) are summarized in a relative Ag⁺ affinity ladder shown in Fig. 2. The values under the heading ln(I_[L1+Ag]⁺/I_[DMF+Ag]⁺) are the cumulative average values of successive stair-steps, and are expressed relative to N,N-dimethylformamide (DMF). As shown in Fig. 2, the ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values are internally consistent for all the Ag⁺ bound heterodimers of amides. For example, the sum of ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values for the MF/F and MA/MF pairs is 0.60 + 0.71 = 1.31, while the sum of ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values of the A/F and MA/A pairs is 0.76 + 0.58 = 1.34, with an absolute deviation of only 0.03. The internal consistency of intensity ratios obtained for the relative affinity ladder shown in Fig. 2 suggests that entropic effects are minimal (i.e., T_effΔ(ΔS)^app ≈ 0 in eqn. (8)) for the dissociation of Ag⁺ bound heterodimers among amides, and the ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) ratio can be equated to the relative affinity term, Δ(ΔH)/RT_eff, as shown in eqn. (5).

Fig. 2 Experimentally measured ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values for N₂-CID decomposition of Ag⁺ bound heterodimers of amides. The ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values are the natural logarithm of ion intensity ratios. The data presented under the heading ln(I_[L+Ag]⁺/I_[DMF+Ag]⁺) are the average ± standard deviation of cumulative values expressed relative to N,N-dimethylformamide (DMF). The value in parenthesis is the arithmetic difference of ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) values. The ln(I_[L1+Ag]⁺/I_[L2+Ag]⁺) lines are not drawn to scale for clarity.

Here we found that, the order of the Ag⁺ affinities of the six amides were: F < MF < A < DMF < MA < DMA. To confirm this order of Ag⁺ affinities obtained under high-energy (keV, laboratory scale) N₂-CID conditions, another relative affinity ladder similar to Fig. 2 was obtained at a lower collisional energy (eV, laboratory scale) or effective temperature (T_eff) in the ion trap mass analyzer (MS2) of the tandem mass spectrometer system. The same order of Ag⁺ affinities: F < MF < A < DMF < MA < DMA was found, confirming that the entropic term, T_effΔ(ΔS)^app, is indeed negligibly small under different collisional excitation (T_eff) conditions.

Having established the order of Ag⁺ affinities among the six amides, we conducted separate extended kinetic method measurements to determine the absolute Ag⁺ affinities of the amides. For this purpose, a series of structurally similar reference compounds of known Ag⁺ affinities is required. However, reference Ag⁺ affinities comparable to those of the amides have not been reported in the literature. In another study, we have established the theoretical Ag⁺ affinities at 0 K of a series of methyl-substituted benzenes (Table 1), which include toluene (Tol), m-xylene (m-Xy), 1,3,5-trimethylbenzene (1,3,5-Me₃Bz), 1,2,4,5-tetramethylbenzene (1,2,4,5-Me₄Bz), pentamethylbenzene (Me₅Bz) and hexamethylbenzene (Me₆Bz).⁴⁴ By applying kinetic method measurements and using the Ag⁺ affinities shown in Table 1 as reference values, we were able to obtain Ag⁺ affinities in agreement with the literature values of benzene (to within ±5 kJ mol⁻¹),^15,16 acetone (±8 kJ mol⁻¹)^16,17 and acetonitrile (±8 kJ mol⁻¹)^22,23 determined by either the RA/FT-ICR (quoted uncertainty ±19 kJ mol⁻¹),¹⁶ or the threshold-CID method (±6–8 kJ mol⁻¹).^15,17,22,23 This series of methyl-substituted benzenes were found to form Ag⁺ bound heterodimers with amides (except formamide) under electrospray ionization conditions. Furthermore, kinetic method measurements indicated that they have comparable Ag⁺ affinities as the amides. Consequently, the methyl-substituted benzenes and their theoretical Ag⁺ affinity values (with an estimated error bar of ±10 kJ mol⁻¹) were adopted as reference compounds/values in the present study.

A typical low-energy CID triple quadrupole MS/MS spectrum (15 eV, laboratory scale) of the [L₁ + Ag + L_n]⁺ heterodimer (L₁ = N-methylformamide (MF) and L_n = toluene (Tol)) is shown in Fig. 3. For the extended kinetic method determinations, a series of I_[MF+Ag]⁺/I_[Ln+Ag]⁺ ion intensity ratios (where L_n = Tol, m-Xy, 1,3,5-Me₃Bz, 1,2,4,5-Me₄Bz) were measured over a range of 13–23 eV collision energies. As illustrated in Fig. 4(a), a plot of ln(I_[MF+Ag]⁺/I_[Ln+Ag]⁺) versus [ΔH_[Ln+Ag]⁺ − ΔH_avg] yields a regression line whose slope and y-intercept render the effective temperature (T_eff) of the dissociation heterodimers [MF + Ag + L_n]⁺ and term, respectively. By plotting the term against 1/RT_eff (Fig. 4(b)), the Ag⁺ affinity of N-methylformamide (MF), ΔH_[MF+Ag]⁺, and the Δ(ΔS)^app term in the protocol of the extended kinetic method were obtained. Similar treatments were applied to determine the Ag⁺ affinities of DMF, A, MA and DMA, and the results are listed in Table 2. Strictly speaking, due to the non-Boltzmann distribution of internal energy of the dissociating heterodimers, the Ag⁺ affinities measured by the kinetic method were obtained at an unspecified temperature.^33,34 For this reason, we shall denote the experimental Ag⁺ affinities reported in this study as enthalpy of binding, ΔH, without a specified temperature. Additionally, we note that the temperature correction (estimated from standard statistical formula⁴⁵) is generally small for system of this size such that ΔH₀ and ΔH₂₉₈ differ only by 1–2 kJ mol⁻¹. Thus, for simplicity, as we have chosen theoretical ΔH₀ as reference values in the kinetic method determinations, we shall compare the experimental kinetic method values with the theoretical binding affinities at 0 K (ΔH₀) in the following discussion.

Fig. 3 Triple quadrupole MS/MS (15 eV, laboratory scale) mass spectrum of the [MF + Ag + Tol]⁺ heterodimer using argon as collision gas (MF = N-methylformamide and Tol = toluene).

Fig. 4 (a) Plot of ln(I_[MF+Ag]⁺/I_[Ln+Ag]⁺) versus [ΔH_[Ln+Ag]⁺ − ΔH_avg] at different collision energies and (b) plot of versus 1/RT_eff for the heterodimers [MF + Ag + L_n]⁺ (MF = N-methylformamide, L_n = Tol, m-Xy, 1,3,5-Me₃Bz and 1,2,4,5-Me₄Bz). The line is an unweighted regression line. The Ag⁺ affinity of MF, ΔH_[MF+Ag]⁺, and the apparent entropy changes, Δ(ΔS_Ag+)^app, are expressed as unweighted values.

On the other hand, the Ag⁺ affinities determined by the extended kinetic method were found in the order: DMA > MA > DMF > A > MF, in agreement with that established by standard kinetic method measurements mentioned earlier. The agreement between independent kinetic method measurements provides confidence to the order of absolute Ag⁺ affinities established in this study.

However, we found the Ag⁺ bound heterodimer between formamide (F) and methyl-substituted benzenes could not be easily generated by electrospray ionization; the heterodimer ion intensity was too weak so that the intensity ratios of its dissociation product ions could not be quantitatively measured. Hence, the absolute Ag⁺ affinity of F cannot be determined by the extended kinetic method. To obtain the absolute Ag⁺ affinity of F, the Ag⁺ affinities of MF, DMF, A, MA and DMA determined by the extended kinetic method were used to construct a ‘calibration plot’ of high-energy (keV) N₂-CID ln(I_[L+Ag]⁺/I_[DMF+Ag]⁺) intensity ratio values (as shown in Fig. 2) versus ΔH_[L+Ag]⁺ (L = MF, DMF, A, MA and DMA) according to eqn. (5), and the Ag⁺ affinity of F was determined by extrapolation of the plot (Fig. 5(a)). Another plot based on the ln(I_[L+Ag]⁺/I_[DMF+Ag]⁺) values obtained under low-energy (eV) ion trap-CID conditions is shown in Fig. 5(b). From the slopes of the plots, the effective temperatures (T_eff) are found to be 2,759 K and 625 K for high-energy N₂-CID and ion trap-CID, respectively. The Ag⁺ affinity of F so determined is summarized in Table 3, and the average of the N₂-CID and ion trap-CID affinity values is taken as the final absolute Ag⁺ affinity for formamide (F).

Table 3 Experimental Ag⁺ affinities (kJ mol⁻¹) of amides determined by the standard kinetic method

Amides	Ion trap-CID ^a (Teff = 625 K)	N2-CID ^a (Teff = 2,759 K)	Average ^b
a The Ag^+ affinity of F was determined from the low-energy ion trap-CID and high-energy N2-CID calibration plots (Fig. 5) using the Ag^+ affinities of MF, A, DMF, MA and DMA shown in Table 2 as calibration points. The uncertainties are expressed as ±SD of the linear regression analysis (ref. 46) of the calibration plots as shown in Fig. 5. b Average ±SD of ion trap-CID and N2-CID values, with standard deviation obtained from the equation s^2 = s^21 + s^22, where s1 and s2 are the SD of ion trap-CID and N2-CID values, respectively.
Formamide (F)	159.4 ± 0.7	165.2 ± 0.3	162.3 ± 0.8

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Fig. 5 Plot of (a) high energy N₂-CID (4.7 keV, laboratory scale) and (b) low-energy ion trap-CID (eV, laboratory scale) ln(I_[L+Ag]⁺/I_[DMF+Ag]⁺) values versus Ag⁺ affinities (ΔH_[L+Ag]⁺) of MF, A, DMF, MA and DMA (solid circles ●) determined by the extended kinetic method. The Ag⁺ affinity of F (open circles ○) was determined by extrapolation of the plot.

As shown in Tables 2 and 3, the experimental uncertainty of both the extended and standard kinetic measurements is ±1 kJ mol⁻¹. Combining the error bar (±10 kJ mol⁻¹) of our chosen reference Ag⁺ affinity values, the overall uncertainty in our experimental absolute Ag⁺ affinities of the six amides is estimated to be ±11 kJ mol⁻¹. Hence, the experimental affinity values are rounded off to integer values here and in the discussion hereafter to reflect the actual uncertainty of our experimental and theoretical values. As illustrated in Tables 2 and 3, the Ag⁺ affinities of the six amides (F < MF < A < DMF < MA < DMA) span over a relatively wide range of 162–208 kJ mol⁻¹. Hence, our experimental results indicate that methyl substitution either at the amide amino nitrogen or the amide carbon has a significant enhancing effect on the Ag⁺ binding strength to the amide ligand.

4.2. Theoretical binding geometries and affinities of Ag⁺-amide complexes

In order to obtain a better understanding on the Ag⁺ binding interactions that give rise to the measured Ag⁺ binding affinities, we conducted ab initio molecular orbital calculations to obtain the geometries and the absolute affinities of different Ag⁺-amide binding modes. Amides have two basic sites which can compete for Ag⁺ binding in the monodentate or bidentate mode. Previously, the carbonyl oxygen has been found to be the most preferred site for protonation and cation binding by a number of metal ions, such as Li⁺, Na⁺, K⁺, Mg⁺, Al⁺ and Cu⁺.^29,32,47 For Ag⁺, we have investigated the possibility of five modes of binding as shown in Fig. 6, where the cation is coordinated to: (I) the carbonyl oxygen, (II) both the carbonyl oxygen and amino nitrogen, (III) the amino nitrogen, (IV) the π bond of carbonyl group and (V) perpendicularly to the C–N bond. We found that, for all six amides (F, MF, DMF, A, MA and DMA), mode (I) is the global minima while mode (II) is the local minima. Mode (III) is only stable for MF and DMF. Upon optimization, modes (IV) and (V) yield one of the aforementioned minima. The optimized geometries of these Ag⁺–amide complexes are shown in Fig. 7. The energetics of various species are summarized in Table 4. In this table, the mode of binding is labeled after the abbreviation for the ligand. For example, MF_I, MF_II, MF_III are the three modes of Ag⁺ binding to N-methylformamide ligand, MF. Given the partial double bond character of the C–N bond, MF and MA (and hence their Ag⁺ bound complexes in mode (I) as well) are found in two conformations. For simplicity, we use “cis” and “trans” to distinguish these two forms, in which the C_methyl–N–C=O dihedral angle is 0° and 180°, respectively.

Fig. 6 The possible binding modes of Ag⁺-amide complexes (R₀, R₁ and R₂ = H and/or CH₃).

Fig. 7 The optimized geometries of the amide ligands (F, MF, DMF, A, MA and DMA, at the MP2/3-21G(d) level) and the Ag⁺-amide complexes (at the MP2/HW,3-21G(d) level), where R₁, R₂ = H and/or CH₃. The selected bond lengths (in Å) are presented as follows: for R₁ = R₂ = H: normal fonts; R₁ = H, R₂ = CH₃: normal fonts in brackets for the cis-conformer of mode (I); R₁ = CH₃, R₂ = H: italic fonts in brackets for trans-conformer of mode (I); and R₁ = R₂ = CH₃: square brackets. The dipole moment vector of amides in mode (I) geometry is shown by arrow (not to scale).

Table 4 Total energies (E, in E_h) of Ag⁺, amides and Ag⁺-amide complexes, binding affinities (ΔH₀) and deformation energies (E_def)

Species	E ^a	ΔH0^b	Edef^c
a Total energies at 0 K, calculated by eqn. (9), in Eh. b Binding affinities at 0 K, calculated by eqn. (10), in kJ mol^−1. c Deformation energies^48 at 0 K, calculated at approximate CCSD(T)/6-31+G(d) based on the additivity scheme: CCSD(T)/STO-3G(d) − MP2/STO-3G(d) + MP2/6-31+G(d) + ( 0.94 * ZPVE), in kJ mol^−1.
Ag^+	−145.01049	—	—
Formamide (F)	−169.40063	—	—
cis-N-Methylformamide (cis-MF)	−208.54986	—	—
trans-N-Methylformamide (trans-MF)	−208.54866	—	—
N,N-Dimethylformamide (DMF)	−247.70199	—	—
Acetamide (A)	−208.56555	—	—
cis-N-Methylacetamide (cis-MA)	−247.71483	—	—
trans-N-Methylacetamide (trans-MA)	−247.71257	—	—
N,N-Dimethylacetamide (DMA)	−286.86307	—	—
F_I	−314.47780	175	8
F_II	−314.45840	124	72
cis-MF_I	−353.63265	190	9
trans-MF_I	−353.63181	191	10
MF_II	−353.60995	130	78
MF_III	−353.60924	128	22
DMF_I	−392.78899	201	12
DMF_II	−392.76538	139	80
DMF_III	−392.76393	135	28
A_I	−353.64899	192	8
A_II	−353.63361	151	70
cis-MA_I	−392.80350	205	9
trans-MA_I	−392.80073	204	10
MA_II	−392.78398	154	80
DMA_I	−431.95454	213	12
DMA_II	−431.93908	172	70

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The effect of Ag⁺ complexation on the geometry of the formamide ligands (F, MF and DMF) can be summarized as follows. When the Ag⁺ coordinates to the amide oxygen in a monodentate fashion in mode (I), it induces minor changes to the geometry on the ligands: the C=O bonds are lengthened (by ∼0.04 Å) while the C–N bonds are shortened (∼0.05 Å), and the O=C–N angles are reduced by ∼2°. Similar observations have also been reported for the Cu⁺–formamide complex.³² On the other hand, when the cation is coordinated to the amino nitrogen in mode (II) or (III), the geometry around the amino nitrogen is changed from planar to pyramidal. The C–N bond is lengthened substantially (by ∼ 0.11Å), while the C=O bond remains virtually unchanged. A very similar trend is found in the acetamides (A, MA and DMA) except that no stable monodentate amino binding mode (III) complexes can be found. The results show that the binding of Ag⁺ on the amide nitrogen can disrupt the planar structures of the amides possibly by interacting with the lone pair electrons of the nitrogen atom.^29,30

In terms of binding affinities, Ag⁺-amide complexes in modes (II) and (III) are less stable than the corresponding mode (I) by at least 40 kJ mol⁻¹, depending on the ligands (Table 4). The relative instability of mode (II) could be related to their large deformation energies (E_def, Table 4),⁴⁸ arising mainly from the compression of O=C–N bond angle (by ∼7°) when Ag⁺ bridges between the carbonyl oxygen and the amino nitrogen. For mode (III), the E_def is comparable to that of mode (I). Hence, the very low stability of mode (III) suggests that some favorable interactions between the cation and the ligand have been reduced. We attribute the instability of mode (III) to the very large angle deviation between Ag⁺ and the dipole moment vector. For binding modes (I) and (II), the alignment between Ag⁺ and the dipole moment vector, on average, is ∼5° and ∼16°, respectively, but it becomes at least 38° for mode (III). It is this “misalignment” of Ag⁺ with the dipole moment that is likely to be responsible for the decrease in ion–dipole interaction, thus reducing the stability of the Ag⁺–amide complex in mode (III).

The theoretical Ag⁺ binding energies at 0 K of amides in the most stable configuration, i.e., binding mode (I), are compared with the experimental values in Table 5. For the six amides studied, the absolute theoretical Ag⁺ affinities are systematically 5–13 kJ mol⁻¹ greater than the experimental values. The discrepancies probably could arise from the basis-set-superposition-error (BSSE).²⁶ Nevertheless, even without this correction, the overall agreement in absolute affinities is reasonable (with an average deviation of 10 kJ mol⁻¹, n = 6). More importantly, the protocol adopted here has reproduced the order of relative binding affinities determined by the kinetic method, with an average deviation of ±3 kJ mol⁻¹ (n = 6). Given the saving on computer time, we have chosen not to carry out the BSSE correction.

Table 5 Comparison of experimental and theoretical Ag⁺ affinities (kJ mol⁻¹) of amides

	ΔH
Amides	Theoretical ^a	Experimental ^b	ΔH(Expt) − ΔH0 (Theory)	Δ(ΔH)(Expt) − Δ(ΔH0)(Theory)^c
a Theoretical Ag^+ affinities (ΔH0) at 0 K were determined at the approximate CCSD(T)/[HW(f),6-31+G(d)] level of theory. The values listed refer to the most stable geometries stated in the text. b This work. Experimental Ag^+ affinities, ΔH, as listed in Tables 2 and 3. c Relative Ag^+ affinity, Δ(ΔH)(Expt) or Δ(ΔH0)(Theory), expressed with reference to N,N-dimethylformamide (DMF).
Formamide (F)	175	162	−13	−5
N-Methylformamide (MF)	191	179	−12	−4
Acetamide (A)	192	181	−11	−3
N,N-Dimethylformamide (DMF)	201	193	−8	0
N-Methylacetamide (MA)	205	198	−7	1
N,N-Dimethylacetamide (DMA)	213	208	−5	3

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Previously, Boutreau et al. have obtained an Ag⁺ affinity of 194 kJ mol⁻¹ for formamide at the B3LYP/BASIS2//B3LYP/BASIS1 level.²⁶ As their method of correlation and basis set are different from ours, a direct comparison with our ab initio value of 175 kJ mol⁻¹ is not possible. If BSSE correction is included, the theoretical B3LYP affinity decreased to 182 kJ mol⁻¹, but is still 20 kJ mol⁻¹ too high compared to our experimental value of 162 kJ mol⁻¹. This could be due to the combined errors of the experimental determination and theoretical estimation. In this regard, we note that a diffuse function is not employed in the B3LYP calculations,²⁶ which has been shown previously to be important in our work.²⁵

4.3. Binding nature in Ag⁺-amide complexes

Ag⁺ binding to ligands have been shown to be mainly electrostatic in nature, with some contribution from covalent binding.^25,26 As shown in Table 4, the binding energies of Ag⁺ towards the carbonyl oxygen of amides (i.e., mode (I)) range from 175 to 213 kJ mol⁻¹, which are ∼40–60 kJ mol⁻¹ stronger than the binding to the amino nitrogen (mode (III)) and the bidentate binding form (mode (II)). This is in contrast to the known preference of Ag⁺ binding to a nitrogen rather than an oxygen site, as shown by the greater Ag⁺ affinity of NH₃ (by ∼40 kJ mol⁻¹) when compared to that of H₂O.²⁵ Amides are known to possess relatively large dipole moments (3.73–4.39 Debye) when compared to ammonia (1.47 Debye).⁴⁹ As Ag⁺ is found in close alignment with the molecular dipole moment vector in the Ag⁺-amide complexes (Fig. 7), we attribute the preferred Ag⁺⋯O=C binding to the exceptionally strong Ag⁺-dipole interaction. The importance of ion-dipole interaction has also been noted in previous studies of Li⁺/Na⁺ binding to formamide (F),³¹ and Na⁺ binding to acetamide (A) and N-methylacetamide (MA).³⁰

In general, an increase in the number of methyl substituents increases Ag⁺ binding affinity. In our results, the binding energies of Ag⁺ in mode (I) of F, trans-MF and DMF are 175, 191 and 201 kJ mol⁻¹, respectively. This increasing trend coincides with the increasing polarizabilities (in 10⁻²⁴ cm³ units) of F (4.08), MF (5.91) and DMF (7.81),⁵⁰ while the molecular dipole moments (in Debyes) of F (3.73), MF (3.83) and DMF (3.82),⁴⁹ remain more or less unchanged. Thus, the increasing trend of the binding energies with the methyl substituents can be attributed to the increasing polarizabilities of the neutral amides, which enhance the binding through ion-induced dipole interaction. In addition, the electron-donating property of the methyl substituent also increases the availability of lone pairs of carbonyl oxygen and amino nitrogen, which in turn strengthens the binding with Ag⁺ through charge-transfer interaction. A recent study on the effect of alkylation of N- and O-donor ligands on the binding strength to Ag⁺ has also shown that the electron donating property of alkyl substituent can strengthen the binding through σ-donating interaction.⁵¹

Here, the effect of methyl group on Ag⁺ affinities of amides is further discussed in terms of N-methyl (by comparison within the formamide and acetamide series) and C-methyl (by comparison between the formamide and acetamide series) substituent effect. The N-methyl substituent enhancement is more significant in the monodentate binding mode (I) (average ∼12 kJ mol⁻¹) than that in the bidentate binding mode (II) (average ∼9 kJ mol⁻¹), except for DMA. On the contrary, the C-methyl substituent effect is more pronounced in mode (II) (average ∼28 kJ mol⁻¹) than in mode (I) (average ∼14 kJ mol⁻¹). The results imply that preferential binding (mode (I) versus (II)) of Ag⁺ at the amide linkage can possibly be controlled by different substituents at the carbonyl carbon and/or amino nitrogen. In fact, a systematic study of the substituent effect on the binding geometries and binding affinities of Ag⁺ towards the amide linkage is underway in our laboratory.

Lastly, we have plotted the experimental Ag⁺ affinities against the proton affinities (PA)⁵² and lithium cation affinities (LCA)³⁸ of these six amides (Fig. 8). Excellent linear correlation is found (r² ∼ 0.99) for both series. While the good correlation with LCA can be attributed to the similarity in the electrostatic nature of binding, the correlation with PA cannot, as proton-amide interaction is covalent in nature. The good correlation with PA simply reflects the fact that substituent effects on chemically related ligands are essentially additive in nature.

Fig. 8 Correlation of experimental Ag⁺ affinities with (a) proton affinities (PA) and (b) lithium cation affinities (LCA) for the six amides.

5. Conclusion

This is a first systematic study of the binding energies, binding nature and preferential binding sites of Ag⁺-amide complexes. The absolute binding energies of Ag⁺-amide complexes were measured by the mass spectrometric kinetic method and theoretically estimated effectively at the CCSD(T)/[HW(f),6-31+G(d)] level of theory. Both experimental and theoretical Ag⁺ affinities were found in the order: F < MF < A < DMF < MA < DMA. The agreement between experimental and theoretical absolute Ag⁺ affinities is good, with an average deviation ±10 kJ mol⁻¹ (n = 6, Table 5).

Various possible modes of Ag⁺ binding to the six amides are studied theoretically, and cation binding to O=C (mode (I)) is found to be preferred over the other modes by at least 40 kJ mol⁻¹. With the shortening of the C–N bond in mode (I) (compared to the free ligand), one would associate this with a strengthening of the bond, and hence an increase in the amide rotational barrier. Interestingly, variable temperature proton NMR experiments conducted on DMA have suggested otherwise, as the barrier is found to be reduced in the presence of Ag⁺.^53,54 Given the biological importance of amides as models of peptide bonds, we have carried out further theoretical studies on the effect of Ag⁺ on the rotational barrier of amides and the results of the study will be reported in due course.

Acknowledgements

K. M. Ng acknowledges the support of a post-doctoral fellowship from the Croucher Foundation. W. K. Li is grateful to the Computer Services Center at the Chinese University of Hong Kong for generous allocation of computation time on the SGI Origin 2000 High Performance Server. The work described in this paper was partially supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. CUHK3275/00P to WKL, PolyU 5157/98P and PolyU 5190/00P to CWT), and the Area of Strategic Development Fund of the Hong Kong Polytechnic University (Project No. A024 to CWT).

References

1. R. A. Wigley and R. R. Brooks, in Noble Metals and Biological Systems: Their Role in Medicine, Mineral Exploration, and the Environment, ed. R. R. Brooks, Boca Raton, CRC Press, 1992, 277–301.
2. N. Farrell, in Transition Metal Complexes as Drugs and Chemotherapeutic Agents, eds. R. Ugo and B. R. James, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989, 208–221.
3. H. G. Petering, Pharmacol. Ther. A., 1976, 1, 127–130.
4. C. L. Fox and S. M. Modak, Antimicrob. Agents Chemother., 1974, 5, 582–588.
5. C. Dart, M. L. Leyland, P. J. Spencer, P. R. Stanfiel and M. J. Sutcliffe, J. Physiol. (London), 1998, 511, 25–32.
6. V. W. M. Lee, H. Li, T. C. Lau, R. Guevremont and K. W. M. Siu, J. Am. Soc. Mass Spectrom., 1998, 9, 760–766.
7. E. R. Talaty, B. A. Asiri Perera, A. L. Gallardo, J. M. Barr and M. J. Van Stipdonk, J. Phys. Chem. A, 2001, 105, 8059–8068.
8. T. Shoeib, A. C. Hopkinson and K. W. M. Siu, J. Phys. Chem. B, 2001, 105, 12 399–12 409.
9. H. B. Li, K. W. M. Siu, R. Guevremont and J. C. Yves Le Blanc, J. Am. Soc. Mass Spectrom., 1997, 8, 781–792.
10. K. Chu, T. Shoeib, X. Guo, C. F. Rodriquez, T. C. Lau, A. C. Hopkinson and K. W. M. Siu, J. Am. Soc. Mass Spectrom., 2001, 12, 163–175.
11. T. Shoeib, C. F. Rodriquez, K. W. M. Siu and A. C. Hopkinson, Phys. Chem. Chem. Phys., 2001, 3, 853–861.
12. K. Chu, X. Guo, T. C. Lau and K. W. M. Siu, Anal. Chem., 1999, 71, 2364–2372.
13. K. Chu, D. M. Cox, X. Guo, I. Kireeva, T. C. Lau, J. C. McDermott and K. W. M. Siu, Anal. Chem., 2002, 74, 2072–2082.
14. P. M. Holland and A. W. Castleman, Jr., J. Chem. Phys., 1982, 76, 4195–4205.
15. Y.-M. Chen and P. B. Armentrout, Chem. Phys. Lett., 1993, 210, 123–128.
16. Y.-P. Ho, Y.-C. Yang, S. J. Klippenstein and R. C. Dunbar, J. Phys. Chem. A, 1997, 101, 3338–3347.
17. H. El Aribi, T. Shoeib, Y. Ling, C. F. Rodriquez, A. C. Hopkinson and K. W. M. Siu, J. Phys. Chem. A, 2002, 106, 2908–2914.
18. S. A. McLuckey, A. E. Schoen and R. G. Cooks, J. Am. Chem. Soc., 1982, 104, 848–850.
19. Y.-S. Yang and C.-S. Yeh, Chem. Phys. Lett., 1999, 305, 395–400.
20. P.-H. Su and C. -S. Yeh, Chem. Phys. Lett., 2000, 331, 420–424.
21. Y.-S. Yang, W.-Y. Hsu, H.-F. Lee, Y.-C. Huang, C.-S. Yeh and C.-H. Hu, J. Phys. Chem. A, 1999, 103, 11 287–11 292.
22. T. Shoeib, H. El Aribi, K. W. M. Siu and A. C. Hopkinson, J. Phys. Chem. A, 2001, 105, 710–719.
23. H. El Aribi, C. F. Rodriquez, T. Shoeib, Y. Ling, A. C. Hopkinson and K. W. M. Siu, J. Phys. Chem. A, 2002, 106, 8798–8805.
24. N. L. Ma, K. M. Ng and C. W. Tsang, Chem. Phys. Lett., 1997, 277, 306–310.
25. N. L. Ma, Chem. Phys. Lett., 1998, 297, 230–238.
26. L. Boutreau, E. Leon, A. Luna, P. Toulhoat and J. Tortajada, Chem. Phys. Lett., 2001, 338, 74–82.
27. J. M. Barr and M. J. Van Stipdonk, Rapid Commun. Mass Spectrom., 2002, 16, 566–578.
28. T. Shoeib, K. W. M. Siu and A. C. Hopkinson, J. Phys. Chem. A, 2002, 106, 6121–6128.
29. J. Tortajada, E. Leon, J. P. Morizur, A. Luna, O. Mo and M. Yanez, J. Phys. Chem., 1995, 99, 13 890–13 898.
30. B. Roux and M. Karplus, J. Comput. Chem., 1995, 16, 690–704.
31. M. Remko, Mol. Phys., 1997, 91, 929–936.
32. Luna, B. Amekraz, J. Tortajada, J. P. Morizur, M. Alcami, O. Mo and M. Yanez, J. Am. Chem. Soc., 1998, 120, 5411–5426.
33. R. G. Cooks and P. S. H. Wong, Acc. Chem. Res., 1998, 31, 379–386.
34. R. G. Cooks, J. T. Koskinen and P. D. Thomas, J. Mass Spectrom., 1999, 34, 85–92.
35. B. A. Cerda and C. Wesdemiotis, J. Am. Chem. Soc., 1996, 118, 11 884–11 892.
36. X. Cheng, Z. Wu and C. Fenselau, J. Am. Chem. Soc., 1993, 115, 4844–4848.
37. P. B. Armentrout, J. Am. Chem. Soc. Mass Spectrom., 2000, 11, 371–379.
38. Y. Tsang, F. M. Siu, N. L. Ma and C. W. Tsang, Rapid Commun. Mass Spectrom., 2002, 16, 229–237.
39. W. Huels, H. Muenster, R. Pesch, E. Schroeder, Proc. 44th ASMS Conf. Mass Spectrometry Allied Topics, Portland, Oregon, 1996, May 12–16, 1147.
40. J. C. Schwartz, R. E. Kaiser, Jr., R. G. Cooks and P. J. Savickas, Int. J. Mass Spectrom. Ion Processes, 1990, 98, 209–224.
41. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, Ö. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komáromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, M. Head-Gordon, E. S. Replogle and J. A. Pople, Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh PA, 1998.
42. J. S. Klassen, S. G. Anderson, A. T. Blades and P. Kebarle, J. Phys. Chem., 1996, 100, 14 218–14 227.
43. T. I. Williams, J. W. Denault and R. G. Cooks, Int. J. Mass Spectrom., 2001, 210/211, 133–146.
44. K. M. Ng, Y. P. Wong, H. M. Ho, N. L. Ma and C. W. Tsang, J. Phys. Chem. A, submitted.
45. J. E. Del Bene, H. D. Mettee, M. F. Frisch, B. T. Luke and J. A. Pople, J. Phys. Chem., 1983, 87, 3279–3282.
46. P. C. Meier and R. E. Zünd, in Statistical Methods in Analytical Chemistry, Wiley, New York, 2nd edn., 2000, pp. 91–136.
47. F. M. Siu, N. L. Ma and C. W. Tsang, J. Chem. Phys., 2001, 114, 7045–7051.
48. The deformation energy, defined as E(neutral amide in a conformation of complexed form) − E(neutral amide in the most stable, uncomplexed form), is calculated at the CCSD(T)/6-31+G(d) level with ZPVE correction. It represents the destabilization energy arising from structural stain that the amide experienced in the complexed form.
49. J. A. Dean, in Lange's Handbook of Chemistry, McGraw-Hill, 15th edn., 1999, 5.105–5.129.
50. J. Applequist, J. R. Carl and K.-K. Fung, J. Am. Chem. Soc., 1972, 94, 2952–2960.
51. N. Widmer-Cooper, L. F. Lindoy and J. R. Reimers, J. Phys. Chem. A, 2001, 105, 6567–6574.
52. E. P. Hunter and S. G. Lias, in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, ed. W. G. Mallard and P. J. Linstrom, National Institute of Standards and Technology, Gaithersburg MD, 1998, p.20 899, http://webbook.nist.gov/.
53. P. A. Temussi and F. J. Quadrifoglio, J. Chem. Soc., Chem. Commun., 1968, 844–845.
54. E. E. Waghorne, A. J. I. Ward, T. G. Clune and B. G. Cox, J. Chem. Soc., Faraday Trans. 1, 1980, 76, 1131–1137.

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