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.

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).

Molecular structure of 2,5-dihydropyrrole (C4NH7), obtained by gas-phase electron diffraction and theoretical calculations

The structure of 2,5-dihydropyrrole (C4NH7) has been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing third-order Moller-Plesset (MP3) level of theory and the 6-311+G(d,p) basis set. Several theoretical calculations were performed. From theoretical calculations using MP3/6-311+G(d,p) evidence was obtained for the presence of an axial (63%) (N-H bond axial to the CNC plane) and an equatorial conformer (37%) (N-H bond equatorial to the CNC plane). The five-membered ring was found to be puckered with the CNC plane inclined at 21.8 (38)° to the plane of the four carbon atoms.

Molecular structures of trimethylchlorogermane, (CH3)(3)GeCl, and trimethylbromogermane, (CH3)(3)GeBr, obtained by gas-phase electron diffraction and theoretical calculations

The structures of trimethylchlorogermane ((CH3)(3)GeCl) and trimethylbromogermane ((CH3)(3)GeBr) have been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing second-order Moller-Plesset (MP2) level of theory and the 6-311+G(d) basis set. All the electrons were included in the correlation calculation. The results from the ab initio calculations indicated that these molecules have C-3v symmetry, and models with this symmetry were used in the electron diffraction analysis. The results for the principal distances (r(g)) and angles (angle(alpha)) from the combined GED/ab initio study of trimethylchlorogermane (with estimated 2sigma uncertainties) are: r(Ge-C) = 1.950(4) Angstrom, r(Ge-Cl) = 2.173(4) Angstrom, r(C-H) = 1.090(9) Angstrom, angleCGeC = 112.7(7)degrees, angleCGeCl = 106.0(8)degrees, angleGeCH = 107.8(12)degrees. The results for the principal distances (r(g)) and angles (angle(alpha)) from the combined GED/ab initio study of trimethylbromogermane (with estimated 2sigma uncertainties) are: r(Ge-C) = 1.952(7) Angstrom, r(Ge-Br) = 2.325(4) Angstrom, r(C-H) = 1. 140(28) Angstrom, angleCGeC = 114.2(11)degrees, angleCGeBr = 104.2(13)degrees, angleGeCH 106.9(43)degrees. Local C-3v symmetry and staggered conformation were assumed for the methyl groups.

Molecular structures of benzoic acid and 2-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of benzoic acid (C6H5COOH) and 2-hydroxybenzoic acid (C6H4OHCOOH) have been determined in the gas phase by electron diffraction using results from quantum chemical calculations to inform restraints used on the structural parameters. Theoretical methods (HF and MP2/6-311+G(d, p)) predict two conformers for benzoic acid, one which is 25.0 kJ mol(-1) (MP2) lower in energy than the other. In the low-energy form, the carboxyl group is coplanar with the phenyl ring and the O-H group eclipses the C=O bond. Theoretical calculations (HF and MP2/6-311+ G(d, p)) carried out for 2-hydroxybenzoic acid gave evidence for seven stable conformers but one low-energy form (11.7 kJ mol-1 lower in energy (MP2)) which again has the carboxyl group coplanar with the phenyl ring, the O-H of the carboxyl group eclipsing the C=O bond and the C=O of the carboxyl group oriented toward the O-H group of the phenyl ring. The effects of internal hydrogen bonding in 2-hydroxybenzoic acid can be clearly observed by comparison of pertinent structural parameters between the two compounds. These differences for 2-hydroxybenzoic acid include a shorter exocyclic C-C bond, a lengthening of the ring C-C bond between the substituents, and a shortening of the carboxylic single C-O bond.

Molecular structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid have been determined by gas-phase electron diffraction using results from quantum chemical calculations to inform the choice of restraints applied to some of the structural parameters. The results from the study presented here demonstrate that resonance hybrids are not as helpful in rationalizing the structures of 2-, 3-, and 4-hydroxybenzoic acids as are models based upon electrostatic effects.

Surprisingly slow reaction of dimethylsilylene with dimethylgermane: time-resolved kinetic studies and related quantum chemical calculations

Time-resolved studies of silylene, SiH2, and dimethylsilylene, SiMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to obtain rate constants for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas phase. SiMe2 + Me2GeH2 was studied at five temperatures in the range 299-555 K. Problems of substrate UV absorption at 193 nm at temperatures above 400 K meant that only three temperatures could be used reliably for rate constant measurement. These rate constants gave the Arrhenius parameters log(A/cm(3) molecule(-1) s(-1)) = -13.25 +/- 0.16 and E-a = -(5.01 +/- 1.01) kJ mol(-1). Only room temperature studies of SiH2 were carried out. These gave values of (4.05 +/- 0.06) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + Me2GeH2 at 295 K) and also (4.41 +/- 0.07) x 10(-10) cm(3) molecule(-1) s(-1) (SiH2 + MeGeH3 at 296 K). Rate constant comparisons show the surprising result that SiMe2 reacts 12.5 times slower with Me2GeH2 than with Me2SiH2. Quantum chemical calculations (G2(MP2,SVP)//B3LYP level) of the model Si-H and Ge-H insertion processes of SiMe2 with SiH4/MeSiH3 and GeH4/MeGeH3 support these findings and show that the lower reactivity of SiMe2 with Ge-H bonds is caused by a higher secondary barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper. Other, related, comparisons of silylene reactivity are also presented.