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Density functional calculations at B3LYP/6-31+G(d) and B3LYP/DZVP are reported for Mg(NH 3 ) n +· , where n = 1–6 and for some solvated ions Mg(NH 3 ) n +· … NH 3 ( n = 1–3, 6). After correction for basis set superposition errors, the enthalpies for sequential addition of NH 3 to Mg +· resulting from direct coordination to the metal are 38.1, 26.6, 21.2, 13.7, 12.1, and 11.3 kcal mol −1 . The free energies for these same addition reactions are all negative, although for complexes with n ≥ 4 the values are very small. Attempts at optimising structures with higher coordination numbers all resulted in the formation of solvated octahedral complexes. Enthalpies for solvation through hydrogen bonding to one of the ligated NH 3 molecules are all less than 16 kcal mol −1 and decrease rapidly as the number of ligated NH 3 molecules increases. Molecular orbital calculations at B3LYP/DZVP have been used to optimise structures for ions Ag(NH 3 ) n + , where n = 1–6. The five-coordinate and six-coordinate structures have very small binding enthalpies (4.3 and 2.6 kcal mol −1 ) and the free energies for formation of these ions are positive. The binding energies for the addition of the first and second NH 3 molecules added to Ag + are 40.1 and 36.1 kcal mol −1 , while those for the third and fourth additions are much smaller (15.1 and 11.0 kcal mol −1 ). Adducts up to n = 3 have been detected in electrospray experiments. The first three adducts of Ag + with NH 3 have been formed in the selected ion flow tube apparatus and multicollision induced dissociation experiments show Ag(NH 3 ) 3 + to have a lower binding enthalpy than both Ag(NH 3 ) 2 + and Ag(NH 3 ) + .

The coordination of the electronic ground states of Mg+, (c-C5H5)Mg+, and (c-C5H5)2Mg+ with the straight-chain saturated hydrocarbons methane, ethane, n-propane, n-butane, n-pentane, n-hexane, and n-heptane has been investigated in the gas phase in helium at room temperature and moderate pressures. Reaction rate coefficients and product distributions were measured with the selected-ion flow tube (SIFT) technique operating at 294 ± 3 K and a helium buffer-gas pressure of 0.35 ± 0.01 Torr. Rate coefficients were measured for all observed ligation steps (or upper limits in the case of nonreactions), and bond connectivities in the coordinated ions were probed with multicollision-induced dissociation. Only single ligation was observed. The rate of ligation was found to depend on the size of the saturated hydrocarbon, increasing with increasing size until the collision rate is reached, and on the degree of ligation with c-C5H5. Mg+ was found to be unreactive with methane and ethane, k < 10-13 cm3 molecule-1 s-1...

Calculations at B3LYP/6-31+G(d) show c-C4H3+ to have a singlet ground state, with the triplet being 19.5 kcal mol−1 higher in energy. Singlet c-C4H3+ has a puckered ring structure (Cs symmetry) with an out-of-plane angle of 51.4°. The barrier to inversion via the planar ring structure (C2v symmetry) is 29.1 kcal mol−1. In the puckered ring the cross–ring distance between CH groups is 1.793 A and the Wiberg bond order is 0.436, indicating considerable interaction. The stability of the singlet state then is attributed to homoaromaticity. Ion c-C4H3+ in its triplet state is planar, but with alternate bonds being long and short, reminiscent of the geometries of c-C4H4 and c-C4H4+. Substitution of H atoms by CN groups stabilises the triplet state relative to the singlet, and for C4(CN)3+ the triplet is only 8.4 kcal mol−1 higher. Substitution also reduces the out-of-plane angle of the ions in the singlet state, going from 51.4° in the unsubstituted ion c-C4H3+ to 43.4 kcal mol−1 in C4(CN)3+. A CN group adjacent (α) to the carbene centre reduces the barrier by ∼7 kcal mol−1 whereas substitution at the opposite carbon (β position) reduces it by ∼2 kcal mol−1. These effects are roughly additive, with C4(CN)3+ having a barrier to inversion of only 12.9 kcal mol−1.

A combined experimental and theoretical approach has been employed to establish the basicity and proton affinity of SiF4 and the structure of SiF4H 1 . The kinetics and energetics for the transfer of a proton between SiF4 ,N 2, and Xe have been explored experimentally in helium at 0.35 6 0.02 torr and 297 6 3 K with a selected-ion flow tube apparatus. The results of equilibrium constant measurements are reported that provide a basicity and proton affinity for SiF4 at 297 6 3 K of 111.4 6 1.0 and 117.7 6 1.2 kcal mol 21 , respectively. These values are more than 2.5 kcal mol 21 lower than currently recommended values. The basicity order was determined to be GB(Xe) . GB(SiF4) . GB(N2), while the proton-affinity order was shown to be PA(Xe) . PA(N2) . PA (SiF4). Ab initio molecular orbital computations at MP4SDTQ(fc)/ 6-31111G(3df,3pd) using geometries from B3LYP/6-311G(d,p) indicate a value for PA(SiF4) 5 118.7 kcal mol 21 that is in good agreement with experiment. Also, the most stable structure of SiF4H 1 is shown to correspond to a core SiF3 cation solvated by HF with a binding energy of 43.9 kcal mol 21 . Support for this structure is found in separate SIFT collision induced dissociation (CID) measurements that indicate exclusive loss of HF. (J Am Soc Mass

The coordination of the electronic ground states of Mg+, (c-C5H5)Mg+, and (c-C5H5)2Mg+ with the inorganic molecules H2, NH3, H2O, N2, CO, NO, O2, CO2, N2O, and NO2 has been investigated in the gas phase at room temperature and moderate pressures. Reaction rate coefficients and product distributions were measured with the selected-ion flow tube (SIFT) technique operating at 294 ± 3 K and a helium buffer-gas pressure of 0.35 ± 0.01 Torr. Rate coefficients were measured for all observed ligation steps (or upper limits in the case of nonreactions), and bond connectivities in the coordinated ions were probed with multicollision-induced dissociation. The rates and extent of ligation were found to depend on the degree of ligation with c-C5H5 and the nature and size of the inorganic ligand. Mg+ was found to be unreactive except with ammonia, which was found to add slowly (k = 4 × 10-12 cm3 molecule-1 s-1). Single ligation of Mg+ with c-C5H5 substantially enhances the efficiency of ligation; the initial ligation i...

Molecular orbital calculations were carried out for the neutral and ionic species that occur in the gas-phase chemistry of magnesium in the presence of oxygen and hydrogen including Mg 1 , MgO, MgOH, MgOH 1 , MgOH2 , Mg(OH)2, HOMgOH2 , and the hydrate structure MgOH 1 ...( OH 2). Standard enthalpies of formation for these species were obtained from single-point calculations at the QCISD(T)(full)/6-31111G(2df,p) and CCSD(T)(full)/6-31111G(2df,p) levels of theory using geometrical parameters obtained from MP2(full)/6-31111G(d,p) optimizations. These DHf values provide a recommended and self-consistent set with uncertainties as small as 612.6 kJ mol 21 (63 kcal mol 21 ) for deriving thermodynamic properties. The properties of interest include the proton affinities PA298 of MgO, MgOH, and Mg(OH)2, ionization energy IE0 of MgOH, bond dissociation energies D0 of Mg‐O, Mg‐OH, MgO‐H, HOMg‐OH, Mg‐OH 1 , H2O‐Mg 1 , and H2O‐MgOH 1 ; the latter two are hydration energies. Values in the literature, both experimental and theoretical, for many of these quantities show considerable scatter and a detailed comparison is made. Magnesium ions in fuel-rich, H2‐O2‐N2 flames at atmospheric pressure in the temperature range 1820 ‐2400 K were investigated experimentally by sampling the flames doped with magnesium through a nozzle into a mass spectrometer. It was shown that the interconversion of Mg 1 and MgOH 1 proceeds by way of the three-body reaction of Mg 1 with OH, in support of Sugden’s criterion that this occurs in flames if the weak HO‐Mg 1 bond has a dissociation energy less than 335 kJ mol 21 . The proton affinity PA 298 (MgO) was measured to be 1056 6 29 kJ mol 21 (252 6 7 kcal mol 21 ) along with approximate values for PA298 (MgOH) 5 919 kJ mol 21 (220 kcal mol 21 ) and PA298 [Mg(OH)2] 5 878 kJ mol 21 (210 kcal mol 21 ). Values were estimated for the electron‐ion recombination coefficient for MgH mOn molecular ions of 2 3 10 27 cm 3 molecule 21 s 21 , and for Mg 1 of 4 3 10 224 T 21 cm 6 molecule 22 s 21 similar to those for alkali metal ions. Finally, small rate coefficients for the chemi-ionization of magnesium via the reactions of Mg 1 OH and MgO 1 H to give MgOH 1 were estimated to be 4.832 3 10 29 exp(255 700/T) and 3.341 3 10 29 exp(232 970/T )c m 3 molecule 21 s 21 , respectively. (Int J Mass Spectrom 184 (1999) 153‐173) © 1999 Elsevier Science B.V.

Experimental results are reported that track the kinetics of the sequential ligation of Mg+, Fe+, (c-C5H5)Mg+, and (c-C5H5)Fe+ with ammonia in the gas phase as a function of the number of ligands added. The energetics of the sequential ligation of Mg+ with ammonia has also been followed theoretically. Molecular orbital calculations with density functional theory (DFT) performed at the B3LYP/6-31+G(d) level have been used to compute the binding energies for direct coordination of the ammonia molecules with Mg+ and for solvation that involves N−H···N interactions. Single-point calculations were also done using the optimized geometries from B3LYP/6-31+G(d) at B3LYP/6-311++G(2df,p) and MP4SDTQ(fc)/6-311++G(2df,p). Relative binding energies and standard enthalpies of formation (ΔH°f,298) have been calculated at all three levels of theory investigated. The experiments were performed with a selected-ion flow tube (SIFT) apparatus in helium buffer gas at 0.35 ± 0.01 Torr and 294 ± 3 K. The measured rate coefficie...

Ab initio molecular orbital calculations are reported for all neutrals, anions, and cations of the formula NHm (m = 1−3) and for their chlorinated analogues NHmCln (m + n = 1, 2, or 3). Structures ...

Given the increasing number of English Language Learners (ELLs) in post-secondary environments (Roessingh & Douglas, 2012), educational practices such as availability of language support for mathematics should be assessed to ensure that all students’ needs are met. To explore the effects of language on mathematics in ELLs, mathematical test items were presented in four language contexts: vocabulary knowledge, negation, preposition use, and atypical sentence structure. Sixty students enrolled in mathematics courses volunteered to complete the mathematics task. Results suggest that math items falling into each of the four language contexts disadvantage ELLs, highlighting that the needs of ELLs should be considered at all levels, from classroom practices to educational policy.