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.     

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]     

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.     

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.     

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.     

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.     

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.     

Fourier transform infrared spectroscopic and theoretical study of water interactions with glycine and its N-methylated derivatives

In this study we attempt to explain the molecular aspects of amino acids' hydration. Glycine and its N-methylated derivatives: N-methylglycine, N,N-dimethylglycine, and N,N,N-trimethylglycine were used as model solutes in aqueous solution, applying FT-IR spectroscopy as the experimental method. The quantitative version of the difference spectra method enabled us to obtain the solute-affected HDO spectra as probes of influenced water. The spectral results were confronted with density functional theory calculated structures of small hydration complexes of the solutes using the polarizable continuum model. It appears that the hydration of amino acids in the zwitterionic form can be understood allowing a synchronized fluctuation of hydrogen bonding between the solute and the water molecules. This effect is caused by a noncooperative interaction of water molecules with electrophilic groups of amino acid and by intramolecular hydrogen bond, allowing proton transfer from the carboxylic to the amine group, accomplishing by the chain of two to four water molecules. As a result, an instantaneous water-induced asymmetry of the carboxylate and the amino group of amino acid molecule is observed and recorded as HDO band splitting. Water molecules interacting with the carboxylate group give component bands at 2543 ± 11 and 2467 ± 15 cm(-1), whereas water molecules interacting with protons of the amine group give rise to the bands at 2611 ± 15 and 2413 ± 12 cm(-1). These hydration effects have not been recognized before and there are reasons to expect their validity for other amino acids.     

Fourier transform Raman approach to structural correlation in hemoglobin derivatives.

In order to obtain information on the structural aspects of hemoglobin (Hb), Fourier transform Raman (FT-R) measurements on various ferrous, ferric derivatives and nickel reconstituted Hb (NiHb) has been made. FT-R spectra for these derivatives were obtained by laser excitation in the near infrared region (NIR) (1064 nm) whereby the wave-number region (600-1700 cm-1) related to both porphyrin ring modes and some globin modes were monitored. Comparison of various modes was made based on previous resonance Raman (RR) results. The wave-number shifts with respect to changes in oxidation state and spin state are very similar to those observed by RR. Additional bands at 1654, 1459, and 1003 cm-1 for deoxyHb and at 1656, 1454, and 1004 cm-1 for oxy Hb can be correlated to globin modes. The shift in the position of these bands for the binding of oxygen can be related to changes in conformation during the transformation. The presence of two distinct sites in NiHb could be monitored by the use of FT-R technique.     

Fourier transform raman and density functional theory studies on the adsorption behavior of p-hydroxybenzoic acid on silver nanoparticles

Two models of p-hydroxybenzoic acid (PHBA) adsorbed on the surfaces of silver nanoparticles were established, each of them corresponding to an experimental configuration. The first model is PHBA adsorbed on one Ag atom through the carboxyl group, and the second one is PHBA adsorbed on two Ag atoms through the carboxyl and hydroxyl groups. The Raman spectra of these two models using DFT-B3PW91 with lanl2dz were calculated; it was found that the calculated Raman frequencies were in good agreement with experimental values. So one can conclude that the simplified models are probably reasonable to describe some surface-enhanced Raman experiments.     

Density functional theory study of the Fourier transform infrared and Raman spectra of Cu(II) bis-acetylacetone

Fourier transform infrared and Fourier transform Raman spectra of Cu(II) bis-acetylacetone have been obtained. The geometry, frequency and intensity of the vibrational bands of this compound and its 1,5-(13)C(2), 3-(13)C, 1,3,5-(13)C(3), 2,4-(13)C(2), (18)O(2) and 2,4-(13)C(2)-(18)O(2) derivatives were obtained by the density functional theory (DFT) with the B3LYP functional and using the 6-31G(*) and 3-21G(*) basis sets. The calculated frequencies are compared with the solid infrared and Raman spectra. All the measured infrared and Raman bands were interpreted in terms of the calculated vibrational modes. The percentage of deviation of the bond lengths and bond angles gives a good picture of the normal modes, and serves as a basis for the assignment of the wavenumbers. Most computed bands are predicted to be at higher wavenumbers than the experimental bands. The calculated geometrical parameters show slight differences compared with the experimental results. These differences can be explained by the different physical state of Cu(II) bis-acetylacetone. The DFT-B3LYP calculations assumed a free molecule in the gas phase. Analysis of the vibrational spectra indicates a strong coupling between the chelated ring modes.     

Fourier transform infrared emission spectra of MgH and MgD

High resolution Fourier transform infrared emission spectra of MgH and MgD have been recorded. The molecules were generated in an emission source that combines an electrical discharge with a high temperature furnace. Several vibration-rotation bands were observed for all six isotopomers in the X (2)Sigma(+) ground electronic state: v=1-->0 to 4-->3 for (24)MgH, v=1-->0 to 3-->2 for (25)MgH and (26)MgH, v=1-->0 to 5-->4 for (24)MgD, v=1-->0 to 4-->3 for (25)MgD and (26)MgD. The new data were combined with the previous ground state data, obtained from diode laser vibration-rotation measurements and pure rotation spectra, and spectroscopic constants were determined for the v=0 to 4 levels of (24)MgH and the v=0 to 5 levels of (24)MgD. In addition, Dunham constants and Born-Oppenheimer breakdown correction parameters were obtained in a combined fit of the six isotopomers. The equilibrium vibrational constants (omega(e)) for (24)MgH and (24)MgD were found to be 1492.776(7) cm(-1) and 1077.298(5) cm(-1), respectively, while the equilibrium rotational constants (B(e)) are 5.825 523(8) cm(-1) and 3.034 344(4) cm(-1). The associated equilibrium bond distances (r(e)) were determined to be 1.729 721(1) A for (24)MgH and 1.729 157(1) A for (24)MgD.     

Fourier transform vibrational circular dichroism and the artifact problem

FTIR vibrational circular dichroism spectra of-pinene are presented as an example of the artifact reduction capability of our new instrument design. The key to this advance is the incorporation of a lens after the sample to focus onto a relatively large detector. Baseline correction with just solvent becomes possible in some cases.     

Feature analysis of protein structure by using discrete Fourier transform and continuous wavelet transform

In this paper, discrete Fourier transform (DFT) and continuous wavelet transform (CWT) are used to predict the protein structure. Hydrophobicity plays a key role in the form of protein structure. The amino acid sequence is first mapped into hydrophobicity sequence, and then process it by DFT and CWT so that power spectral density is gained. The results show that continuous wavelet transform can extract the features of protein structure effectively and availably and has a tremendous development foreground.