Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

Temperature- and Pressure-induced Proton Transfer in the 1:1 Adduct Formed between Squaric Acid and 4,4 '-Bipyridine

We have applied a combination of spectroscopic and diffraction methods to study the adduct formed between squaric acid and bypridine, which has been postulated to exhibit proton transfer associated with a single-crystal to single-crystal phase transition at ca. 450 K. A combination of X-ray single-crystal and very-high flux powder neutron diffraction data confirmed that a proton does transfer from the acid to the base in the high-temperature form. Powder X-ray diffraction measurements demonstrated that the transition was reversible but that a significant kinetic energy barrier must be overcome to revert to the original structure. Computational modeling is consistent with these results. Modeling also revealed that, while the proton transfer event would be strongly discouraged in the gas phase, it occurs in the solid state due to the increase in charge state of the molecular ions and their arrangement inside the lattice. The color change is attributed to a narrowing of the squaric acid to bipyridine charge-transfer energy gap. Finally, evidence for the possible existence of two further phases at high pressure is also presented.

Calcium carbonate solubilization through H-proton release from some legumes grown in calcareous saline-sodic soils

Increasing levels of CO2 and H+ proton in the rhizosphere from some legumes may play an important role in calcite dissolution of calcareous salt affected soils. Soils planted with white and brown varieties of cowpea (Vigna unguiculata L.) and hyacinth bean (Dolichos lablab L.) relying on either fertilizer N (KNO3) or N-fixation were compared against soils to which gypsum was applied and a control without plants and gypsum application to study the possibility of Ca2+ release from calcite and Na+ leaching. As compared to plants relying on inorganic N, leachates from all pore volumes (0·5, 1·0, 1·5, 2·0 pore volume) in lysimeters planted with N-fixing hyacinth bean contained significantly higher concentrations of HCO with lower concentrations from lysimeters planted with white cowpea relying on N-fixation. However, the lowest concentrations of HCO were recorded in the gypsum and control treatments. In initial leaching, lysimeters planted with N-fixing plants maintained similar leachate Ca2+ and Na+ concentrations compared to gypsum amended soils. However, gypsum amended soils were found to have a prolonged positive effect on Na+ removal. It might be concluded that some legumes that are known to fix N in calcareous salt affected soils may be an alternative ameliorant to the extremely expensive gypsum through calcite solubilization and a consequent release of Ca2+.

Force constants and dipole‐moment derivatives of molecules from perturbed Hartree–Fock calculations

General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂ϕi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.

Determination of the vibrational transition moment ratio for the Coriolis interacting v9 and v10 fundamentals of allene

Comparison between observed and calculated infrared band contours has been made to determine the vibrational transition moment ratio |M10/M9| for the Coriolis interacting ν9 and ν10 perpendicular fundamentals of allene-h4. The ratio obtained is appreciably lower than that of a previous estimate and the result obtained by integrated band intensity measurements of Overend and Crawford. From the best estimate of the ratio, the dipole moment derivatives of the two bands are determined; the value for the weaker band ν9 is subject to a large uncertainty.

Argon predissociation spectroscopy of the OH-center dot H2O and Cl-center dot H2O complexes in the 1000-1900 cm(-1) region: Intramolecular bending transitions and the search for the shared-proton fundamental in the hydroxide monohydrate

We present argon predissociation vibrational spectra of the OH-.H2O and Cl-.H2O complexes in the 1000-1900 cm(-1) energy range, far below the OH stretching region reported in previous studies. This extension allows us to explore the fundamental transitions of the intramolecular bending vibrations associated with the water molecule, as well as that of the shared proton inferred from previous assignments of overtones in the higher energy region. Although the water bending fundamental in the Cl-.H2O spectrum is in very good agreement with expectations, the OH-.H2O spectrum is quite different than anticipated, being dominated by a strong feature at 1090 cm(-1). New full-diniensionality calculations of the OH-.H2O vibrational level structure using diffusion Monte Carlo and the VSCF/CI methods indicate this band arises from excitation of the shared proton.

Intramolecular proton transfer in [Ph2B-OH2](+). Participation of a phenyl group

Ab initio calculations at the HF/6-31+G* level on [Ph2B-OH2](+) show that in the gas phase the structure with the proton attached to an ipso C is lower in energy than the one with the proton on the oxygen atom by 8.40 kcal mol(-1). The transition states and reaction paths for intramolecular proton transfer in [Ph2B-OH2](+) have also been studied.

Characterising the variability and extremes of the stratospheric polar vortices using 2D moment analysis

The mean state, variability and extreme variability of the stratospheric polar vortices, with an emphasis on the Northern Hemisphere vortex, are examined using 2-dimensional moment analysis and Extreme Value Theory (EVT). The use of moments as an analysis to ol gives rise to information about the vortex area, centroid latitude, aspect ratio and kurtosis. The application of EVT to these moment derived quantaties allows the extreme variability of the vortex to be assessed. The data used for this study is ECMWF ERA-40 potential vorticity fields on interpolated isentropic surfaces that range from 450K-1450K. Analyses show that the most extreme vortex variability occurs most commonly in late January and early February, consistent with when most planetary wave driving from the troposphere is observed. Composites around sudden stratospheric warming (SSW) events reveal that the moment diagnostics evolve in statistically different ways between vortex splitting events and vortex displacement events, in contrast to the traditional diagnostics. Histograms of the vortex diagnostics on the 850K (∼10hPa) surface over the 1958-2001 period are fitted with parametric distributions, and show that SSW events comprise the majority of data in the tails of the distributions. The distribution of each diagnostic is computed on various surfaces throughout the depth of the stratosphere, and shows that in general the vortex becomes more circular with higher filamentation at the upper levels. The Northern Hemisphere (NH) and Southern Hemisphere (SH) vortices are also compared through the analysis of their respective vortex diagnostics, and confirm that the SH vortex is less variable and lacks extreme events compared to the NH vortex. Finally extreme value theory is used to statistically mo del the vortex diagnostics and make inferences about the underlying dynamics of the polar vortices.

Highly proton-ordered water structures on oxygen precovered Ru{0001}

We present helium scattering measurements of a water ad-layer grown on a O(2 1)/Ru(0001) surface. The adsorbed water layer results in a well ordered helium diffraction pattern with systematic extinctions of diffraction spots due to glide line symmetries. The data reflects a well-defined surface structure that maintains proton order even at surprisingly high temperatures of 140 K. The diffraction data we measure is consistent with a structure recently derived from STM measurements performed at 6 K. Comparison with recent DFT calculation is in partial agreement, suggesting that these calculations might be underestimating the contribution of relative water molecule orientations to the binding energy.

Harringtonian virtue: Harrington, Machiavelli, and the method of the 'Moment'

This article presents a reinterpretation of James Harrington's writings. It takes issue with J. G. A. Pocock's reading, which treats him as importing into England a Machiavellian ‘language of political thought’. This reading is the basis of Pocock's stress on the republicanism of eighteenth-century opposition values. Harrington's writings were in fact a most implausible channel for such ideas. His outlook owed much to Stoicism. Unlike the Florentine, he admired the contemplative life; was sympathetic to commerce; and was relaxed about the threat of ‘corruption’ (a concept that he did not understand). These views can be associated with his apparent aims: the preservation of a national church with a salaried but politically impotent clergy; and the restoration of the royalist gentry to a leading role in English politics. Pocock's hypothesis is shown to be conditioned by his method; its weaknesses reflect some difficulties inherent in the notion of ‘languages of thought’.