Performance of density functionals for calculation of reductive ring-opening reaction energies of Li<Superscript>+</Superscript>-EC and Li<Superscript>+</Superscript>-VC

Reaction energies were determined for reductive ring-opening reactions of Li⁺-coordinated ethylene carbonate (EC) and vinylene carbonate (VC) by using various density functional theory (DFT) and ab-initio methods applying the basis sets up to Dunnings aug-cc-pVQZ. The methods examined include the local density functional (SVWN), the pure gradient-corrected density functionals (BLYP and BPW91), and the hybrid density functionals (B3LYP, B1LYP, B3PW91, and mPW1PW91). Comparison of the DFT results with ab-initio results indicates that the mPW1PW91 approach introduced by Adamo and Barone, is superior to all the other DFT methods (including B3LYP). The performance of more cost-effective Pople-type basis sets ranging from 6-31G(d,p) to 6-311++G(3df,3pd) was assessed at DFT levels of theory by calibrating them with the aug-cc-pVQZ results     

7-Ethyl-2,3,5,6,8-pentahydroxy-1,4-naphthoquinone (echinochrome A): a DFT study of the antioxidant mechanism

Quantum chemical calculations and the conformational analysis of dianions, radical dianions, disodium salts, and radicals of disodium salts of 7-ethyl-2,3,5,6,8-pentahydroxy-1,4-naphthoquinone (echinochrome A) were carried out at the (U)B3LYP/6-31G(d) and (U)B3LYP/6-311G(d) levels of theory. The heats of reactions of the hydroperoxyl radical (HOO^·) with the isomers of dianions and disodium salts of echinochrome A with the lowest Gibbs free energies were estimated. All reactions of these isomers of dianions and disodium salts of echinochrome A with HOO^· in the gas phase are exothermic. The isomer of the dianion of echinochrome A with the lowest Gibbs free energy, which is formed by the heterolysis of the 2β- and 6β-OH groups, is the more effective antioxidant than the isomer of the 2,6-disodium salt with the lowest Gibbs free energy.     

Redox potentials of dopamine and its supramolecular complex with aspartic acid

Dopamine (DA) can be oxidized to dopamine quinone (DAquinone) through a one-step, two-electron redox reaction. The electron transfer property of DA and its supramolecular complex with aspartic acid (Asp) has been investigated by the theoretical calculations. We calculated the standard redox potentials (E ^o) of DA/DAquinone at the MP2/6-31G(d,p)//B3LYP/6-31G(d,p), MP2/6-31+G(d,p)//B3LYP/6-31+G(d,p), MP2/6-31G(d,p)//B3LYP/6-311G(d,p), and MP2/6-311+G(d,p)//B3LYP/6-311+G(d,p) levels. Comparing the experimental value, the redox potentials of DA/DAquinone obtained at MP2//B3LYP/6-311G(d,p) and MP2//B3LYP/6-311+G(d,p) levels can be considered as the upper and lower estimates. DA can form supramolecular complex (DA-Asp) with Asp through hydrogen bond (H-bond). Therefore, the values of 0.631 and 0.628 V obtained at MP2//B3LYP/6-311G(d,p) and MP2//B3LYP/6-311+G(d,p) levels for DA-Asp/DAquinone-Asp can be proposed as the upper and lower estimates of a probable (about 0.630 V) value of the corresponding redox potential. The calculated E ^o values of DA-Asp/DAquinone-Asp at the four theoretical levels are upper than those of DA/DAquinone, which indicates that the formation of H-bonds weaken the electron-donating ability of DA.     

Quantum-Chemical Investigation of Structure and Vibration Spectrum of [C(NPCl<Subscript>3</Subscript>)<Subscript>3</Subscript>]<Superscript>+</Superscript> Cation

Structural parameters of the cation [C(NPCl₃)₃]⁺ in vacuum and in acetonitrile are calculated by the methods RHF/6-311G(3d₆), RHF/6-31(3d₅) and B3LYP/6-311(3d₅f₇). Formation energy of the free adduct (MeCN) 2[C(NPCl₃)₃]⁺ is calculated and nonspecific character of interaction of the cation with liquid acetonitrile is established. Vibration spectrum of the cation is calculated and theoretical interpretation of IR and Raman spectra of the salt [C(NPCl₃)₃]⁺[SbCl₆]^? is refined.     

Experimental and Theoretical Investigation of the Proton-Bound Dimer of Lysine

The structure of the proton-bound lysine dimer has been investigated by infrared multiple photon dissociation (IRMPD) spectroscopy and electronic structure calculations. The structures of different possible isomers of the proton-bound lysine dimer have been optimized at the B3LYP/6-31 + G(d) level of theory and IR spectra calculated using the same computational method. Based on relative Gibbs free energies (298 K) calculated at the MP2/aug-cc-pVTZ//B3LYP/6-31 + G(d) level of theory, LL-CS01, and followed closely (1.1 kJ mol^–1) by LL-CS02 are the most stable non-zwitterionic isomers. At the MP2/aug-cc-pVTZ//6-31 + G(d) and MP2/aug-cc-pVTZ//6-31 + (d,p) levels of theory, isomer LL-CS02 is favored by 3.0 and 2.3 kJ mol^–1, respectively. The relative Gibbs free energies calculated by the aforementioned levels of theory for LL-CS01 and LL-CS02 are very close and strongly suggest that diagnostic vibrational signatures found in the IRMPD spectrum of the proton-bound dimer of lysine can be attributed to the existence of both isomers. LL-ZW01 is the most stable zwitterionic isomer, in which the zwitterionic structure of the neutral lysine is well stabilized by the protonated lysine moiety via a very strong intermolecular hydrogen bond. At the MP2/aug-cc-pVTZ//B3LYP/6-31 + G(d), MP2/aug-cc-pVTZ//6-31 + G(d) and MP2/aug-cc-pVTZ//6-31 + G(d,p) levels of theory, the most stable zwitterionic isomer (LL-ZW01) is less favored than LL-CS01 by 7.3, 4.1 and 2.3 kJ mol^–1, respectively. The experimental IRMPD spectrum also confirms that the proton-bound dimer of lysine largely exists as charge-solvated isomers. Investigation of zwitterionic and charge-solvated species of amino acids in the gas phase will aid in a further understanding of structure, property, and function of biological molecules.     

Quantum-Chemical Analysis of Coordination of Dimethylsulfoxide Molecules to Sodium and Potassium Cations

Coordination of dimethylsulfoxide molecules to the sodium and potassium cations was investigated by HF/6-31G(d)//HF/6-31G(d) and DFT(B3LYP/6-31G(d)) quantum-chemical methods. The coordination numbers of Na⁺ and K⁺ are found to be five and six, respectively. Thermal effects of complexation were calculated for each stage of the process; these were found to be 197.8, 160.1, 106.9, 88.0, 53.9 [HF/6-31G(d)] and 195.0, 158.5, 108.9, 95.7, 60.0 kJ/mole [B3LYP/6-31G(d)] for Na⁺ (one to five DMSO molecules, respectively); 146.6, 118.7, 90.2, 68.9, 70.0, 49.0 [HF/6-31G(d)] and 144.0, 117.4, 91.7, 78.9, 78.6, 56.4 kJ/mole [B3LYP/6-31G(d)] for K⁺ (one to six DMSO molecules, respectively). Structural parameters and charge distributions are given for the complexes. It is shown that solvation of sodium and potassium cations by DMSO molecules is preferable to solvation by water molecules.     

Quantum chemical analysis of possible fragmentation of [M + H]<Superscript>+</Superscript> and [M + Na]<Superscript>+</Superscript> complexes of monosubstituted methane,cyclohexane, and benzene derivatives in mass spectrometric studies

The formation and fragmentation energies of the proton and sodium cation complexes with monosubstituted methane, cyclohexane, and benzene derivatives in which carbon atoms are bonded to substituents (NH₂, OH, F, Cl, Br, ONO₂, NO₂, COOH, CN, and Ph) were calculated by the B3LYP/6-31G(d) method. For [M + Na]⁺ complexes, the formation energies are much lower (and differ from one another to a much lesser extent), while the dissociation energies are much higher, than the corresponding energies of the [M + H]⁺ complexes. Na⁺ cation shows a lower selectivity toward localization at functional groups in molecules compared to H⁺. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 246–249, February, 2008.     

Synthesis of new cyano-substituted analogues of Tröger's bases from bromo-derivatives. A stereochemical dependence of long-range (nJHH,n = 4, 5, and 6) proton–proton and proton–carbon (nJCH,n = 1, 2, 3, 4, and 5) coupling constants of these compounds

A free-catalyst microwave-assisted cyanation of brominated Tröger's base derivatives ( 2a - f ) is reported. The procedure is simple, efficient, and clean affording the nitrile compounds ( 3a - e, I ) in very good yields. Complete assignment of ¹H and ¹³C chemical shifts of 2a - f, I and 3a - d, I was achieved using gradient selected 1D nuclear magnetic resonance (NMR) techniques (1D zTOCSY, PSYCHE, DPFGSE NOE, and DEPT), homonuclear 2D NMR techniques (gCOSY and zTOCSY), and heteronuclear 2D NMR techniques (gHSQCAD/or pure-shift gHSQCAD, gHMBCAD, bsHSQCNOESY, and gHSQCAD-TOCSY) with adiabatic pulses. Determination of the long-range proton–proton coupling constants ⁿJ_HH (n = 4, 5, 6) was accomplished by simultaneous irradiation of two protons at appropriate power levels. In turn, determined coupling constants were tested by an iterative simulation program by calculating the ¹H NMR spectrum and comparing it to the experimental spectrum. The excitation-sculptured indirect-detection experiment (EXSIDE) and ¹H-¹⁵N CIGARAD-HMBC (constant time inverse-detection gradient accordion rescaled heteronuclear multiple bond correlation) were applied for determination of long-range carbon–proton coupling constants ⁿJ_CH (n = 2, 3, and 4) and for assignment of ¹⁵N chemical shift at natural abundance, respectively. DFT/B3LYP optimization studies were performed in order to determine the geometry of 2c using 6-31G(d,p), 6-311G(d,p), and 6–311 + G(d,p) basis sets. For calculation of ¹H and ¹³C chemical shifts, ⁿJ_HH (n = 2, 3, 4, 5, and 6), and ⁿJ_CH (n = 1, 2, 3, and 4) coupling constants, the GIAO method was employed at the B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), B3LYP/6-311+G(d,p), B3LYP/6-311++G(2d,2p), B3LYP/cc-pVTZ), and B3LYP/aug-cc-pVTZ) levels of theory. For the first time, a stereochemical dependence magnitude of the long-range ⁿJ_HH (n = 4, 5, and 6) and ⁿJ_CH (n = 1, 2, 3, 4, and 5) have been found in bromo-substituted analogues of Tröger's bases.     

Quantum Chemical Study of the Lithium Cation Coordination by Dimethylsulfoxide Molecules

A quantum chemical study of the lithium ion coordination by dimethylsulfoxide molecules has been performed by HF/6-31G (d), HF/6-311+(d,p), and B3LYP/6-311+(d,p) methods with full geometry optimization. The coordination number of Li⁺ in the dimethylsulfoxide was found to be equal to 4. Heats of the complex formation at each stage of the process were calculated (in kJ/mol); these are 267.2, 203.0, 122.8, and 90.5 in HF/6-31G(d); 270.6, 200.5, 108.8, and 82.9 in HF/6-311+(d,p); 256.3, 186.8, 100.8, and 80.1 in B3LYP/6-311+(d,p) for 1-4 DMSO molecules, respectively. The paper reports on the structure parameters of the complexes formed, and the corresponding charge distributions. The solvation of the lithium cation with dimethylsulfoxide molecules was shown to be more preferable than that with water molecules in the gas phase. A possibility for an Li⁺·(4DMSO)·OH^- associate to form in the DMSO medium was examined using the HF/6-311+(d,p) method.     

7-Ethyl-2,3,5,6,8-pentahydroxy-1,4-naphthoquinone (echinochrome A): A DFT study of the antioxidant mechanism. 1. Interaction of echinochrome A with hydroperoxyl radical

The molecular geometry and electronic structure of hydroxy-substituted naphthazarin (NZ)-7-ethyl-2,3,5,6,8-pentahydroxy-1,4-naphthoquinone (echinochrome A, (Et)NZ(β-OH)₃, 1) were calculated by the B3LYP/6-311G(d) method. The influence of the (i) character of the β-OH groups dissociation and (ii) conformational mobility of molecule 1 and the anions, radicals, and radical anions derived from 1 on the energy of their reactions with hydroperoxyl radical was studied by the (U)B3LYP/6-31G and (U)B3LYP/6-311G(d) methods. The enol-enolic tautomerism due to the transfer of hydrogen atoms of α-OH groups and rotational isomerism of the β-OH groups at the C(2) and C(3) atoms and of the α-OH groups at the C(5) and C(8) atoms were studied. The equilibrium in the gas-phase reaction 1 + ^•OOH ⇄ (Et)(HO-β)₂NZ(β-O^•) + HOOH (1) (quenching of hydroperoxyl radical) is shifted to the separated reagents. Heterolysis of the O—H bond in one of the three β-hydroxy groups considerably reduces the energy of subsequent O—H bond homolysis in either of the two remaining β-hydroxy groups. As a consequence, the reaction (Et)(HO-β)₂NZ(β-O⁻) + ^•OOH ⇄ (Et)(HO-β,⁻O-β)NZ(β-O^•) + HOOH (2) (quenching of hydroperoxyl radical) becomes exothermic and the equilibrium is shifted to the formation of hydrogen peroxide. The Gibbs energy gain in reaction (2) varies from −6.4 to −10.9 kcal mol⁻¹ depending on which β-hydroxy group is involved in the O—H bond homolysis. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 400–415, March, 2007.     

7-Ethyl-2,3,5,6,8-pentahydroxy-1,4-naphthoquinone (echinochrome A): a DFT study of the antioxidant mechanism 2.* The structure of monosodium salts of echinochrome A and their reactions with the hydroperoxyl radical

The relative gas-phase acidities of all OH groups of 7-ethyl-2,3,5,6,8-pentahydroxy-1,4-naphthoquinone (echinochrome A, 1) were evaluated by the B3LYP/6-311G(d) and B3LYP/6-311G(d,p) methods. Calculations predict that gB-OH groups at the C(2) and C(6) atoms are the most acidic in molecule 1and their acidity is higher than that of o-nitrophenol. Conformational analysis of undissociated monosodium salts of 1and their radicals was performed. It was shown that gas-phase quenching reactions of the hydroperoxyl radical by mono-sodium salts of 1are exothermic.     

Influence of Transition Metal Cationization versus Sodium Cationization and Protonation on the Gas-Phase Tautomeric Conformations and Stability of Uracil: Application to [Ura+Cu]<Superscript>+</Superscript> and [Ura+Ag]<Superscript>+</Superscript>

The gas-phase conformations of transition metal cation-uracil complexes, [Ura+Cu]⁺ and [Ura+Ag]⁺, were examined via infrared multiple photon dissociation (IRMPD) action spectroscopy and theoretical calculations. IRMPD action spectra were measured over the IR fingerprint and hydrogen-stretching regions. Structures and linear IR spectra of the stable tautomeric conformations of these complexes were initially determined at the B3LYP/6-31G(d) level. The four most stable structures computed were also examined at the B3LYP/def2-TZVPPD level to improve the accuracy of the predicted IR spectra. Two very favorable modes of binding are found for [Ura+Cu]⁺ and [Ura+Ag]⁺ that involve O2N3 bidentate binding to the 2-keto-4-hydroxy minor tautomer and O4 monodentate binding to the canonical 2,4-diketo tautomer of Ura. Comparisons between the measured IRMPD and calculated IR spectra enable elucidation of the conformers present in the experiments. These comparisons indicate that both favorable binding modes are represented in the experimental tautomeric conformations of [Ura+Cu]⁺ and [Ura+Ag]⁺. B3LYP suggests that Cu⁺ exhibits a slight preference for O4 binding, whereas Ag⁺ exhibits a slight preference for O2N3 binding. In contrast, MP2 suggests that both Cu⁺ and Ag⁺ exhibit a more significant preference for O2N3 binding. The relative band intensities suggest that O4 binding conformers comprise a larger portion of the population for [Ura+Ag]⁺ than [Ura+Cu]⁺. The dissociation behavior and relative stabilities of the [Ura+M]⁺ complexes, M⁺ = Cu⁺, Ag⁺, H⁺, and Na⁺) are examined via energy-resolved collision-induced dissociation experiments. The IRMPD spectra, dissociation behaviors, and binding preferences of Cu⁺ and Ag⁺ are compared with previous and present results for those of H⁺ and Na⁺.

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Graphical Abstract ?

     

Theoretical investigation on cyclohexane dehydrogenation catalyzed by V<Subscript>2</Subscript><Superscript>+</Superscript> in gas-phase

The dehydrogenation reaction mechanism of cyclohexane catalyzed by dimer transition metal cluster V₂⁺ has been investigated at the B3LYP/6-31G (d, p) level of density functional theory. Density of states (DOS) graph is used to understand more deeply the roles of the front molecular orbital of the initial complexes. After the first molecular dehydrogenation, the reaction mainly consists of two competition mechanisms. First, the C-H bonds of cyclohexane can be effectively activated by the V₂⁺ cation, yielding the same-face dehydrogenation products. Second, the C-C bonds are activated, forming the different-face dehydrogenation products. Our calculations indicate that the reaction takes place more easily along the low-spin potential energy surface on the same-face and is a low-barrier or even barrier-free transformation. Carbon-carbon single bonds are nonpolar and generally far less reactive. A comparison of the reaction mechanism of V₂⁺ and congener Ti₂⁺ with cyclohexane has been presented. The bond dissociation energies (BDEs) of V₂⁺ are greater than that of Ti₂⁺, leading to difficulties in forming sandwich complexes in the different-face dehydrogenation of cyclohexane, and the same-face dehydrogenation is an important reaction channel.     

The associations of macrocyclic ethers with cations in 1,4-dioxane/water mixtures; potentiometric Na+ and K+ binding measurements and computational study

This paper deals with the study of different degrees of association constants of Na⁺ and K⁺ ions with macrocycles of [12]crown-4, [15]crown-5, [18]crown-6, and Diaza[18]crown-6 in (1:1)dioxane/water mixture using the sodium and potassium ion selective electrodes (ISE). The gas phase molecular mechanical and quantum chemical calculations of [18]crown-6 and diaza[18]crown-6 were performed at MM+, AM1, MINDO/3, HF/6-31G(d), and B3LYP/6-31G(d) levels with the help of Gaussian03 program. Conformational abilities were compared with the ion binding results of ISE measurements. The results were also discussed in terms of oxygen charges and enthalpy stabilized association mechanism.     

Theoretical study of the addition and abstraction reactions of hydroxyl radical with uracil

The addition as well as abstraction reactions of hydroxyl radical (OH) with the nucleic acid base, uracil (U), in the gas phase has been explored at the B3LYP/6-31+G(d,p) level of density functional theory (DFT). The energy barrier of the OH addition to both the C5 and C6 positions of the uracil is less than 1 kcal/mol while the hydrogen abstractions (H-abstractions) from either the N1 or the N3 positions are ∼9.5 kcal/mol. Further the energetics of these reactions are assessed by applying the effect of aqueous medium through the polarizable continuum model (PCM). Both the gas and the solution phase data established that the thermodynamic and kinetic factors are more favorable for the OH addition to either C5 or C6 positions of the uracil than the H-abstraction reactions. Moreover, calculations at the MPW1K/6-31+G(d,p), CCSD(T)/6-31+G(d,p)//B3LYP/6-31+G(d,p) and CCSD(T)/6-31+G(d,p)//MPW1K/6-31+G(d,p) levels of theoretical methods qualitatively supported the B3LYP/6-31+G(d,p) results.     

Metal ion shuttling mechanism through thiacalix[4]crown: a computational study

The first computational study on the alkali metal ion shuttling mechanism through thiacalix[4]biscrown-5 has been performed using density functional theory (MPWB1K/6-31G(d)//B3LYP/6-31G(d)). The activation free energy for K⁺ ion shuttling through the calix tube of thiacalix[4]biscrown-5 is computed to be 12.7 kcal/mol which is in good agreement with the experimental value. Throughout the shuttling process, K⁺ ion maintains the maximum electrostatic interactions with ether oxygens of crown rings, which contributes to lower the activation barrier of the shuttling process.     

Structural and Energetic Effects in the Molecular Recognition of Acetylated Amino Acids by 18-Crown-6

Absolute 18-crown-6 (18C6) binding affinities of four protonated acetylated amino acids (AcAAs) are determined using guided ion beam tandem mass spectrometry techniques. The AcAAs examined in this work include: N-terminal acetylated lysine (N_???CAcLys), histidine (N_???CAcHis), and arginine (N_???CAcArg) as well as side chain acetylated lysine (N_???CAcLys). The kinetic-energy-dependent cross sections for collision-induced dissociation (CID) of the (AcAA)H⁺(18C6) complexes are analyzed using an empirical threshold law to extract absolute 0 and 298?K (AcAA)H⁺?18C6 bond dissociation energies (BDEs) after accounting for the effects of multiple collisions, kinetic and internal energy distributions of the reactants, and unimolecular dissociation lifetimes. Theoretical electronic structure calculations are performed to determine stable geometries and energetics for neutral and protonated 18C6 and the AcAAs as well as the proton bound complexes of these species, (AcAA)H⁺(18C6), at the B3LYP/6-311+G(2d,2p)//B3LYP/6-31?G* and M06/6-311+G(2d,2p)//B3LYP/6-31G* levels of theory. For all four (AcAA)H⁺(18C6) complexes, loss of neutral 18C6 corresponds to the most favorable dissociation pathway. At elevated energies, products arising from sequential dissociation of the primary CID product, H⁺(AcAA), are also observed. Protonated N_???CAcLys exhibits a greater 18C6 binding affinity than other protonated N_???CAcAAs, suggesting that the side chains of Lys residues are the preferred binding sites for 18C6 complexation to peptides and proteins. N_???CAcLys exhibits a greater 18C6 binding affinity than N_???CAcLys, suggesting that binding of 18C6 to the side chain of Lys residues is more favorable than to the N-terminal amino group of Lys.     

Theoretical study of the conformational energy hypersurface of cyclotrisarcosyl

The multidimensional Conformational Potential Energy Hypersurface (PEHS) of cyclotrisarcosyl was comprehensively investigated at the DFT (B3LYP/6-31G(d), B3LYP/6-31G(d,p) and B3LYP/6-311++G(d,p)), levels of theory. The equilibrium structures, their relative stability, and the Transition State (TS) structures involved in the conformational interconversion pathways were analyzed. Aug-cc-pVTZ//B3LYP/6-311++G(d,p) and MP2/6-31G(d)//B3LYP/6-311++G(d,p) single point calculations predict a symmetric cis-cis-cis crown conformation as the energetically preferred form for this compound, which is in agreement with the experimental data. The conformational interconversion between the global minimum and the twist form requires 20.88 kcal mol-1 at the MP2/6-31G(d)//B3LYP/6-311++G(d,p) level of theory. Our results allow us to form a concise idea about the internal intricacies of the PEHSs of this cyclic tripeptide, describing the conformations as well as the conformational interconversion processes in this hypersurface. In addition, a comparative analysis between the conformational behaviors of cyclotrisarcosyl with that previously reported for cyclotriglycine was carried out     

Sodium Cation Affinities of Commonly Used MALDI Matrices Determined by Guided Ion Beam Tandem Mass Spectrometry

The sodium cation affinities of six commonly used MALDI matrices are determined here using guided ion beam tandem mass spectrometry techniques. The collision-induced dissociation behavior of six sodium cationized MALDI matrices, Na⁺(MALDI), with Xe is studied as a function of kinetic energy. The MALDI matrices examined here include: nicotinic acid, quinoline, 3-aminoquinoline, 4-nitroaniline, picolinic acid, and 3-hydroxypicolinic acid. In all cases, the primary dissociation pathway corresponds to endothermic loss of the intact MALDI matrix. The cross section thresholds are interpreted to yield zero and 298 K Na⁺−MALDI bond dissociation energies (BDEs), or sodium cation affinities, after accounting for the effects of multiple ion-neutral collisions, the kinetic and internal energy distributions of the reactants, and dissociation lifetimes. Density functional theory calculations at the B3LYP/6-311+G(2d,2p)//B3LYP/6-31G* and MP2(full)/6-311+G(2d,2p)//B3LYP/6-31G* levels of theory are used to characterized the structures and energetics for these systems. The calculated BDEs exhibit very good agreement with the measured values for most systems. The experimental and theoretical Na⁺−MALDI BDEs determined here are compared with those previously measured by cation transfer equilibrium methods.