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.

Redundant coordinates in harmonic force-field calculations

Redundancy relations between vibrational coordinates may be linear (as for rectilinear coordinates used in deriving a G matrix), or non-linear (as for curvilinear coordinates used in formulating model force fields). It is shown that geometrically defined internal coordinates are necessarily curvilinear. Hence it is shown that linear force constants can occur in model force field calculations involving redundant coordinates, in disagreement with the recent proposal of Gussoni and Zerbi.

ASYM20: a program for force constant and normal coordinate calculations, with a critical review of the theory involved

The theory of harmonic force constant refinement calculations is reviewed, and a general-purpose program for force constant and normal coordinate calculations is described. The program, called ASYM20. is available through Quantum Chemistry Program Exchange. It will work on molecules of any symmetry containing up to 20 atoms and will produce results on a series of isotopomers as desired. The vibrational secular equations are solved in either nonredundant valence internal coordinates or symmetry coordinates. As well as calculating the (harmonic) vibrational wavenumbers and normal coordinates, the program will calculate centrifugal distortion constants, Coriolis zeta constants, harmonic contributions to the α′s. root-mean-square amplitudes of vibration, and other quantities related to gas electron-diffraction studies and thermodynamic properties. The program will work in either a predict mode, in which it calculates results from an input force field, or in a refine mode, in which it refines an input force field by least squares to fit observed data on the quantities mentioned above. Predicate values of the force constants may be included in the data set for a least-squares refinement. The program is written in FORTRAN for use on a PC or a mainframe computer. Operation is mainly controlled by steering indices in the input data file, but some interactive control is also implemented.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

Radiative forcing due to changes in ozone and methane caused by the transport sector

The year 2000 radiative forcing (RF) due to changes in O3 and CH4 (and the CH4-induced stratospheric water vapour) as a result of emissions of short-lived gases (oxides of nitrogen (NOx), carbon monoxide and non-methane hydrocarbons) from three transport sectors (ROAD, maritime SHIPping and AIRcraft) are calculated using results from five global atmospheric chemistry models. Using results from these models plus other published data, we quantify the uncertainties. The RF due to short-term O3 changes (i.e. as an immediate response to the emissions without allowing for the long-term CH4 changes) is positive and highest for ROAD transport (31mWm-2) compared to SHIP (24 mWm-2) and AIR (17 mWm-2) sectors in four of the models. All five models calculate negative RF from the CH4 perturbations, with a larger impact from the SHIP sector than for ROAD and AIR. The net RF of O3 and CH4 combined (i.e. including the impact of CH4 on ozone and stratospheric water vapour) is positive for ROAD (+16(±13)(one standard deviation) mWm-2) and AIR (+6(±5) mWm-2) traffic sectors and is negative for SHIP (-18(±10) mWm-2) sector in all five models. Global Warming Potentials (GWP) and Global Temperature change Potentials (GTP) are presented for AIR NOx emissions; there is a wide spread in the results from the 5 chemistry models, and it is shown that differences in the methane response relative to the O3 response drive much of the spread.

Variation of the mixing state of Saharan dust particles with atmospheric transport

Mineral dust is an important aerosol species in the Earth’s atmosphere and has a major source within North Africa, of which the Sahara forms the major part. Aerosol Time of Flight Mass Spectrometry (ATOFMS) is first used to determine the mixing state of dust particles collected from the land surface in the Saharan region, showing low abundance of species such as nitrate and sulphate internally mixed with the dust mineral matrix. These data are then compared with the ATOFMS single particle mass spectra of Saharan dust particles detected in the marine atmosphere in the vicinity of the Cape Verde islands, which are further compared with those from particles with longer atmospheric residence sampled at a coastal station at Mace Head, Ireland. Saharan dust particles collected near the Cape Verde Islands showed increased internally mixed nitrate but no sulphate, whilst Saharan dust particles collected on the coast of Ireland showed a very high degree of internally mixed secondary species including nitrate, sulphate and methanesulphonate. This uptake of secondary species will change the pH and hygroscopic properties of the aerosol dust and thus can influence the budgets of other reactive gases, as well as influencing the radiative properties of the particles and the availability of metals for dissolution.

A tractable means of correcting sector level TFP calculations in the face of biased technological change.

The measurement of the impact of technical change has received significant attention within the economics literature. One popular method of quantifying the impact of technical change is the use of growth accounting index numbers. However, in a recent article Nelson and Pack (1999) criticise the use of such index numbers in situations where technical change is likely to be biased in favour of one or other inputs. In particular they criticise the common approach of applying observed cost shares, as proxies for partial output elasticities, to weight the change in quantities which they claim is only valid under Hicks neutrality. Recent advances in the measurement of product and factor biases of technical change developed by Balcombe et al (2000) provide a relatively straight-forward means of correcting product and factor shares in the face of biased technical progress. This paper demonstrates the correction of both revenue and cost shares used in the construction of a TFP index for UK agriculture over the period 1953 to 2000 using both revenue and cost function share equations appended with stochastic latent variables to capture the bias effect. Technical progress is shown to be biased between both individual input and output groups. Output and input quantity aggregates are then constructed using both observed and corrected share weights and the resulting TFPs are compared. There does appear to be some significant bias in TFP if the effect of biased technical progress is not taken into account when constructing the weights

The molecular structure of hexamethyldigermane determined by gas-phase electron diffraction with theoretical calculations for (CH3)3M-M(CH3)3 Where M = C, Si, and Ge

Gas-phase electron diffraction (GED) data together with results from ab initio molecular orbital calculations (HF and MP2/6-311+G(d,p)) have been used to determine the structure of hexamethyldigermane ((CH3)3Ge-Ge(CH3)3). The equilibrium symmetry is D3d, but the molecule has a very low-frequency, largeamplitude, torsional mode (φCGeGeC) that lowers the thermal average symmetry. The effect of this largeamplitude mode on the interatomic distances was described by a dynamic model which consisted of a set of pseudoconformers spaced at even intervals. The amount of each pseudoconformer was obtained from the ab initio calculations (HF/6-311+G(d,p)). The results for the principal distances (ra) and angles (∠h1) obtained from the combined GED/ab initio (with estimated 1σ uncertainties) are r(Ge-Ge) ) 2.417(2) Å, r(Ge-C) ) 1.956(1) Å, r(C-H) ) 1.097(5) Å, ∠GeGeC ) 110.5(2)°, and ∠GeCH ) 108.8(6)°. Theoretical calculations were performed for the related molecules ((CH3)3Si-Si(CH3)3 and (CH3)3C-C(CH3)3).

EfeO-cupredoxins: major new members of the cupredoxin superfamily with roles in bacterial iron transport

The EfeUOB system of Escherichia coli is a tripartite, low pH, ferrous iron transporter. It resembles the high-affinity iron transporter (Ftr1p-Fet3p) of yeast in that EfeU is homologous to Ftr1p, an integral-membrane iron-permease. However, EfeUOB lacks an equivalent of the Fet3p component—the multicopper oxidase with three cupredoxin-like domains. EfeO and EfeB are periplasmic but their precise roles are unclear. EfeO consists primarily of a C-terminal peptidase-M75 domain with a conserved ‘HxxE’ motif potentially involved in metal binding. The smaller N-terminal domain (EfeO-N) is predicted to be cupredoxin (Cup) like, suggesting a previously unrecognised similarity between EfeO and Fet3p. Our structural modelling of the E. coli EfeO Cup domain identifies two potential metal-binding sites. Site I is predicted to bind Cu2+ using three conserved residues (C41 and 103, and E66) and M101. Of these, only one (C103) is conserved in classical cupredoxins where it also acts as a Cu ligand. Site II most probably binds Fe3+ and consists of four well conserved surface Glu residues. Phylogenetic analysis indicates that the EfeO-Cup domains form a novel Cup family, designated the ‘EfeO-Cup’ family. Structural modelling of two other representative EfeO-Cup domains indicates that different subfamilies employ distinct ligand sets at their proposed metal-binding sites. The ~100 efeO homologues in the bacterial sequence databases are all associated with various iron-transport related genes indicating a common role for EfeO-Cup proteins in iron transport, supporting a new copper-iron connection in biology.

Characterization of a gamma-aminobutyric acid transport system of rhizobium leguminosarum bv. viciae 3841

Spontaneous mutants of Rhizobium leguminosarum bv. viciae 3841 were isolated that grow faster than the wild type on gamma-aminobutyric acid (GABA) as the sole carbon and nitrogen source. These strains (RU1736 and RU1816) have frameshift mutations (gtsR101 and gtsR102, respectively) in a GntR-type regulator (GtsR) that result in a high rate of constitutive GABA transport. Tn5 mutagenesis and quantitative reverse transcription-PCR showed that GstR regulates expression of a large operon (pRL100242 to pRL100252) on the Sym plasmid that is required for GABA uptake. An ABC transport system, GtsABCD (for GABA transport system) (pRL100248-51), of the spermidine/putrescine family is part of this operon. GtsA is a periplasmic binding protein, GtsB and GtsC are integral membrane proteins, and GtsD is an ATP-binding subunit. Expression of gtsABCD from a lacZ promoter confirmed that it alone is responsible for high rates of GABA transport, enabling rapid growth of strain 3841 on GABA. Gts transports open-chain compounds with four or five carbon atoms with carboxyl and amino groups at, or close to, opposite termini. However, aromatic compounds with similar spacing between carboxyl and amino groups are excellent inhibitors of GABA uptake so they may also be transported. In addition to the ABC transporter, the operon contains two putative mono-oxygenases, a putative hydrolase, a putative aldehyde dehydrogenase, and a succinate semialdehyde dehydrogenase. This suggests the operon may be involved in the transport and breakdown of a more complex precursor to GABA. Gts is not expressed in pea bacteroids, and gtsB mutants are unaltered in their symbiotic phenotype, suggesting that Bra is the only GABA transport system available for amino acid cycling.