Intracule functional models. II. Analytically integrable kernels

We present, within the framework of intracule functional theory (IFT), a class of kernels whose correlation integrals can be found in closed form. This approach affords three major advantages over other kernels that we have considered previously; ease of implementation, computational efficiency, and numerical stability. We show that even the simplest member of the class yields reasonable estimates of the correlation energies of 18 atomic and 56 molecular systems and we conclude that this kernel class will prove useful in the development of future IFT models.     

Intracule functional models: I. Angle-corrected correlation kernels

We explore the merits of applying a simple angle-dependent correction to the correlation kernel within the framework of Hartree-Fock-Wigner theory. Based on numerical results for the first eighteen atoms, we conclude that such a correction offers a significant improvement over the action kernel that we and others have explored previously.     

Intracule functional models. V. Recurrence relations for two-electron integrals in position and momentum space

The approach used by Ahlrichs [Phys. Chem. Chem. Phys., 2006, 8, 3072] to derive the Obara-Saika recurrence relation (RR) for two-electron integrals over Gaussian basis functions, is used to derive an 18-term RR for six-dimensional integrals in phase space and 8-term RRs for three-dimensional integrals in position or momentum space. The 18-term RR reduces to a 5-term RR in the special cases of Dot and Posmom intracule integrals in Fourier space. We use these RRs to show explicitly how to construct Position, Momentum, Omega, Dot and Posmom intracule integrals recursively.     

Vibrational spectroscopy of the electrode-electrolyte interface: Part IV. Fourier transform infrared spectroscopy: Experimental considerations

The experimental considerations necessary to effect successful recording of in situ vibrational spectroscopy at the electrode-solution interface are described. In this work, the Fourier transform infrared spectrometer is used.     

The History of Ozone. Part III

The introduction of ozone into organic chemistry is due to the work of C. D. Harries, first in Berlin but mainly in Kiel, during the period 1903–1916. He established experimental procedures for ozonolysis, demonstrated the generality of the reaction of unsaturated compounds with ozone, and showed that ozone could be used for the synthesis of a variety of sensitive compounds. Most important for the future development of organic chemistry, he established that ozonolysis could be an important tool for determining the structures of organic compounds. He also initiated investigations into the mechanism of ozone reactions with alkenes, which culminated about forty years later in the Criegee mechanism for ozonolysis.     

Application of Wigner and Husimi intracule based electron correlation models to excited states

A new approach to the electron correlation problem based on phase space intracules derived from the Wigner distribution is applied to excited states. The computed electron correlation energy reduces the mean absolute error in the prediction of the excitation energies of 55 atomic excited states from 0.65 eV for unrestricted Hartree-Fock to 0.32 eV. This compares favorably to a mean absolute deviation of 0.52 eV for second order Moller-Plesset perturbation theory and 0.35 eV for the Lee-Yang-Parr functional. An analogous correlation model based on the Husimi distribution is developed. Predicted correlation energies and excitation energies from this model are significantly worse than for the Wigner intracule based model. Alternative correlation kernels may be more suitable for the Husimi intracule based approach.     

The re-discovery of the fast Fourier transform algorithm

The discovery of the fast Fourier transform (FFT) algorithm and the subsequent development of algorithmic and numerical methods based on it have had an enormous impact on the ability of computers to process digital representations of signals, or functions. At first, the FFT was regarded as entirely new. However, attention and wide publicity led to an unfolding of its pre-electronic computer history going back to Gauss. The present paper describes the author's own involvement and experience with the FFT algorithm.The author is grateful for permission from the Association for Computing Machinery to allow the present paper to bear some similarity with the paper,How the FFT Gained Acceptance, ref. [28]     

Fourier transform microwave spectroscopy and Fourier transform microwave-millimeter wave double resonance spectroscopy of the ClOO radical

Pure rotational spectra of the ClOO radical for the (35)Cl and (37)Cl isotopomers have been observed using Fourier transform microwave and Fourier transform microwave-millimeter wave double resonance spectroscopy. The rotational, centrifugal, spin-rotation coupling, and hyperfine coupling constants have been determined by least-squares fits of the observed transition frequencies. The molecular constants indicate that the electronic ground state is 2A". The r(0) structure is determined to be r(0)(ClO)=2.075 A, r(0)(OO)=1.227 A, and theta;(0)(ClOO)=116.4 degrees . Several highly accurate ab initio calculations have also been performed. Some of them turned out to be inaccurate because it is necessary to take into account both static and dynamic electronic correlations. Only multireference (single and double) configuration interaction calculations with large basis sets reproduce the present experimental results. The anharmonic force constants obtained by the ab initio calculations are used to determine the r(e) structure, r(e)(ClO)=2.084(1) A, r(e)(OO)=1.206(2) A, and theta;(e)(ClOO)=115.4(1) degrees . Unique features of the ClOO radical have become clear by the present experiment and the ab initio calculations.     

Fourier transform of spherical Laguerre Gaussian functions and its application in molecular integrals

The Fourier transform of the spherical Laguerre Gaussian‐type function (LGTF), L ${}_{\text{n}}^{\text{l}\text{+½}}$ (αr²)r^lY_lm( r̂ )e, was derived. Applying the Fourier transform convolution theorem, the basic two‐center integrals over the general two‐electron irregular solid harmonic operator, Y_LM( r̂ ₁₂)/r (which becomes Coulomb repulsion, spin–other‐orbit interaction or spin–spin interaction when L=0, 1, or 2, respectively) as well as the overlap were evaluated analytically. These basic integral results generate the two‐electron integrals of the Coulomb type, hybrid type, and exchange type as well as that of three‐ and four‐center. The formulas obtained, which are general for electronic wave functions of unrestricted quantum numbers n, l, and m, are expressed explicitly in terms of nuclear spherical LGTFs of internuclear geometrical variables. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 265–273, 1999     

Fourier transform infrared and Raman spectra, vibrational assignment and density functional theory calculations of naphthazarin

FT Raman and FTIR spectra of Naphthazarin (5,8-dihydroxy-1,4-naphthoquinone) and its deuterated analogue are recorded. Comparison between the spectra obtained by two techniques, a series of density functional theory (DFT) calculations and the spectral behavior upon deuteration were used for the assignment of the vibrational spectra of this compound. The calculated vibrational frequencies by the B3LYP, B3PW91, G96LYP, G96P86, and MPWLYP density functionals are generally consistent with the observed spectra. Infrared and Raman vibrational transitions predicted by B3LYP/6-311++G** are reported for the titled compound and its deuterated analogous and the assignments are discussed. All experimental and theoretical results support a relatively weak hydrogen bond in naphthazarin (NZ), compared with that in the enol form of normal beta-diketones. The observed nuOH/nuOD and gammaOH/gammaOD appear at about 3060/2220 and 790/560 cm(-1), respectively, which are consistent with the calculated hydrogen bond geometry and proton chemical shift results. Two bands at about 350 and 290 cm(-1) are assigned to the O...O stretching modes belong to A1 and B2 species, respectively.     

Fourier transform Raman and infrared spectra and normal coordinate analysis of organo-arsenic(III), -antimony(III) and -bismuth(III) thiolates

The FT-Raman and infrared spectra of (PhS)BiPh2, (PhS)2BiPh, (PhS)3Sb, (PhS)3Sb, (PhS)3As and (PhSe)BiPh2 were measured in the range 3600-100 cm(-1). A normal coordinate analysis was performed for all substances in terms of the calculation and discussion of the force constants which are dependent on the element-sulphur and element-selenium group using a modified valence force field. Furthermore, for all compounds 1H-NMR, 13C-NMR and MS data were also given. The investigation of the microbiological activity of some substances against Escherichia coli was an additional aspect because of their strong bactericidal and fungicidal effects.     

Quantitative aqueous attenuated total reflectance Fourier transform infrared spectroscopy : Part II. Integrated molar absorptivities of alkyl carboxylates

A quantitative attenuated total reflectance Fourier transform infrared (ATR-FT-IR) spectroscopic method is developed for the analysis of total carboxylate concentration, [COO⁻], in aqueous solution. The short (12–13 μm) and highly reproducible pathlength of the ATR cell permits quantitative subtraction of the water peak at 1640 cm⁻¹. Carboxylate quantitation is based on the area of the asymmetric stretching peak, which is nearly independent of compound structure. The molar absorptivity of alkyl carboxylates in water is 438 ± 58 l mol⁻¹ cm⁻¹, and the integrated molar absorptivity is 2.95 ± 0.08 × 10⁴ l mol⁻¹ cm⁻² (n = 15 compounds, 0.1 M ≤ [COO⁻] ≤ 1.5 M). The [COO⁻] in solutions of mixed carboxylates is measured with a root mean square error of 2.4% and a small (+1.5) positive bias. The accuracy of the method is limited by the assumption that integrated absorbance is constant for all COO⁻ groups.     

The gas-phase decomposition of methylsilane. Part III. Kinetics

The homogeneous gas-phase decomposition kinetics of methylsilane and methylsilane-d₃ have been investigated by the comparative-rate-single-pulse shock-tube technique at total pressures of 4700 torr in the 1125–1250 K temperature range. Three primary processes occur: CH₃SiH₃ → CH₃SiH + H₂ (1), CH₃SiH₃ → CH₄ + SiH₂ (2), and CH₃SiH₃ → CH₂ = SiH₂ + H₂ (3). The high-pressure rate constants for the primary processes in CH₃SiH₃ obtained by RRKM calculations are log (k₁ + k₃) (s^?1) = 15.2 - 64,780 Cal/θ and log k₂ (s^?) = 14.50 - 67,600 → 2800 Cal/θ. For CH₃SiD₃ these same rate constants are log k₁ (s^?) = 14.99 - 64,700 cal/θ log k₂ (s^?) = 14.68 – 66,700 → 2000 cal/θ, and log k₃ (s^?) = 14.3 ? 64,700 cal/θ.     

The trans-isomer of formanilide studied by microwave Fourier transform spectroscopy

The rotational spectra of the trans-isomer of formanilide was recorded by microwave Fourier transform spectroscopy. The rotational and centrifugal distorsion constants as well as the quadrupole coupling constants have been accurately determined. It is shown that the stable conformation corresponds to a planar structure. The energy barrier between this conformation and the less stable one (the amino group lies in a plane perpendicular to the phenyl ring) has been evaluated by ab initio calculations.     

Fourier transform infrared and Raman spectral analysis of trans-1,4-polyisoprene.

Polyisoprene is the most widely used polymer in industry and commerce. Fourier transform infrared (FTIR) and Raman spectra of trans-1,4-polyisoprene have been recorded in the range of 4000-400 and 4000-100 cm(-1), respectively. In the present investigation, detailed assignments of the observed fundamental bands of trans-1,4-polyisoprene has been analysed in terms of peak positions and relative intensities. With the hope of providing more and effective information on the fundamental vibrations, a normal co-ordinate analysis has been performed on trans-1,4polyisoprene, by assuming Cs symmetry. The simple general valance force field (SGVFF) method has been employed in normal co-ordinate analysis and to calculate the potential energy distribution (PED) for each fundamental vibration. The PED contribution corresponding to each of the observed frequencies shows the reliability and accuracy of the spectral analysis. The validity of the SGVFF method as a practical tool for complete analysis of vibrational spectra, even for a polymer of this complexity, is confirmed in the present work.     

Density functional theory study of Fourier transform infrared and Raman spectra of 2-amino-5-chloro benzonitrile

The vibrational spectra of 2-amino-5-chloro benzonitrile (ACB) have been obtained by density functional theory (DFT) calculations. Normal coordinate analysis has been carried out to support the vibrational analysis. The results were compared with the experimental values. With the help of scaling procedures, the observed FTIR and FT Raman vibrational frequencies were analysed and compared with the theoretically predicted vibrational spectra. The assignments of bands to various normal modes of the molecules were also carried out.     

Principles of Fourier transform ion cyclotron resonance mass spectrometry and its application in structural biology

Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry has become increasingly significant within recent years. The inherently ultra-high resolution and mass accuracy allow unequivocal assignments of chemical formulae to be made and further structural elucidation can be conducted through the utilization of tandem mass spectrometry techniques. With the advent of electrospray ionization (ESI), FT-ICR mass spectrometry has become a powerful tool for the investigation of biological macromolecules, such as the study of non-covalent interactions of proteins. In this article, the basic principles are highlighted, some of the techniques employed are described and examples of applications are provided, with particular respect being paid to the field of characterization of biomolecules.     

A Fourier transform time-of-flight mass spectrometer. A SIMION calculation approach

A new kind of approach to time-of-flight type spectrometers is presented on the basis of SIMION calculations. The detector studied is a short cylindrical tube capacitor closed with parallel plates at both ends. The main principle of operation is to force ions of equal energy to circulate in the volume between the two tubes on a path of equal radius and measure their flight times pro revolution which corresponds to the frequency of oscillation. By performing spectral analysis on the received signal through transformation from the time domain to frequency space the different masses can be detected.To study the expected performance of the FT-TOF detector, calculations of ion trajectories have been made by varying the dimensions and electric potentials of the electrodes. The effect of the beam position, variations in the angle of entrance and ion energy to the trajectories was calculated to monitor the resolution that is achievable.     

The effect of apodization and finite resolution on Fourier transform Raman spectra

The effects that finite resolution and choice of apodization function have on Fourier transform (FT) Raman spectra are illustrated by the 839 cm⁻¹ (ν₁) and 914 cm⁻¹ bands of KMnO₄. FT-Raman spectra were recorded at 0.5, 1, 2, 4, 8, 16 and 32 cm⁻¹ resolution using boxcar, Norton—Beer (strong, medium and weak) and triangular apodization functions at each resolution. The results show the dramatic changes in bandshape that occur as the ratio (resolution/true full width at half height of band) increases. The changes were measured in terms of the full width at half height of the band, the height of the band, the area of the band and the bandshape (expressed as a sum of Lorentzian and Gaussian lines). At a given resolution the degree to which each of these characteristics is affected is strongly dependent on the choice of the apodization function.     

Synthesis of phenylpyrrolylpyrroles. Part III

Several ethyl 3-[(3-aryl-4-methyl)-2(1H)-pyrrolyl]-4-methyl-1H-pyrrole-2-carboxylates have been synthesized using two successive ethyl isocyanide addition-cyclizations to the appropriate nitropropene derivatives.