The error in absorption measurements, caused by the use of non-monochromatic light-I Parabolic functions

The errors in absorption measurements in spectrophotometry, caused by the use of non-chromatic light, have been calculated. Parabolic functions have been assumed for the wavelength-dependence of the intensity of the incident light falling on the cell and of the absorbance of the compound measured. Results of the calculations may be used to predict non-linearity of absorbance-concentration curves or photometric titration curves.     

The error in absorption measurements caused by the use of non-monochromatic light-III Application to linear calibration curves

When in spectrophotometry the absorption is measured with non-monochromatic light, a curved calibration curve is often obtained. Some errors are introduced if a linear calibration curve is still used. The magnitude of these errors has been calculated.     

Quantitative evaluation of atomic absorption error functions

The variation in standard deviation with transmittance for a large number of elements has been expressed in terms of four component error functions, each one characteristic of one (or more) possible sources of noise associated with the measurement of transmittance (or absorbance). The magnitude of the contribution of each of the component functions has been measured quantitatively, and it is shown that the major component in nearly every case is that related to noise associated with the dynamic nature of the flame. For many elements, the smallest relative error occurs at an absorbance between 0·35 and 0·61 units; the range from 0·2 to 0·7 absorbance units (50 × to 200 × the observed analytical sensitivity) is suggested as the most precise working range for a wide variety of elements.     

Modified Cartesian Gaussian functions and their use in quantum chemistry

The general formula for the electron-electron repulsion integral in the modified Cartesian Gaussian basis set derived in Ref. [1] is simplified. A general relation between the standard and modified CG functions is given. A possible use of the modified CG functions to quantum chemical calculations which include the correlation factor r_ij² is indicated.     

The convolution of Gaussian absorption curves

Summary The convolution of Gaussian absorption curves using orthogonal polynomials has been studied. An absorption curve can usually be considered as a sum of Gaussian curves. The p₂-convoluted log A versus curve is independent of concentration and path-length and the optimum coefficient can be used as an index of purity for absorbing compounds.

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Transformation Gaußscher Absorptionskurven

Zusammenfassung Die Transformation von Gaußschen Absorptionskurven unter Verwendung von Orthogonalpolynomen wurde untersucht, denn in der Regel kann eine Absorptionskurve als Summe von Gauß-Kurven betrachtet werden. Der quadratische Polynomkoeffizient aus log A gegen ist unabhängig von Konzentration und Schichtdicke und kann als Reinheitsindex benutzt werden.

     

The far-infrared absorption of dichloromethane determined by spot frequency measurements

The absorption of dichloromethane at 298 K has been measured at 14 spot frequencies from 33 to 213 cm⁻¹ using an Apollo far-i.r. laser system with methanol as the lasing gas optically pumped by a 50 W CO₂ laser. The results agree with those obtained by Fourier transform interferometry and allow a greater accuracy in the measurement of absolute intensity and spectral moments for this intensely absorbing liquid. The band profile is rationalized using a three parameter Mori continued fraction with two of the parameters predetermined from knowledge of the Debye relaxation time and the (forth moment) mean square torque.     

Modified Gaussian functions and their use in quantum chemistry. I. Integrals

A modified Gaussian function g(u, v, w, a, R ) = const s(a, R ) is considered where l = u + v + w, s (a, R ) is a 1s-type Gaussian function centered at R , a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R . General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.     

A measure of the error in wave functions

The quantity ? = (Φ||(H ? E)Φ|) gives a measure of the error in the approximate solution, Φ (with corresponding energy expectation value E), to an eigenfunction of the Hamiltonian operator H of the system under consideration; this quantity vanishes for the exact function ψ. In a percentage scale (with 0% error for the exact function and 100% for a reference, approximate function), the error of Φ may be expressed as 100(?/?_r), where ?_r corresponds to the reference function (e.g., obtained with a minimal basis set). This approach eliminates the need of knowing beforehand the exact solution in order to have an estimate of the error of an approximate solution.     

Hydrogen-type orbitals in terms of Gaussian functions

We express the hydrogen-type orbitals as integral transforms of Gaussian functions. The topographic features of the analytical expressions for the weight functions provide ways for the design of basis sets. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 143–150, 1997     

Optimal use of the recurrence relations for the evaluation of molecular integrals over Cartesian Gaussian basis functions

We consider the tree search problem for the recurrence relation that appears in the evaluation of molecular integrals over Cartesian Gaussian basis functions. A systematic way of performing tree search is shown. By applying the result of tree searching to the LRL2 method of Lindh, Ryu, and Liu (LRL) (J. Chem. Phys., 95 , 5889 1991), which is an auxiliary function-based method, we obtain significant reductions of the floating point operations (FLOPS) counts in the K⁴ region. The resulting FLOPS counts in the K⁴ region are comparable up to [dd|dd] angular momentum cases to the LRL1 method of LRL, currently the method requiring least FLOPS for [dd|dd] and higher angular momentum basis functions. For [ff|ff], [gg|gg], [hh|hh], and [ii|ii] cases, the required FLOPS are 24, 40, 51, and 59%, respectively, less than the LRL1 method in the K⁴ region. These are the best FLOPS counts available in the literature for high angular momentum cases. Also, there will be no overhead in either the K² or K⁰ region in implementing the present scheme. This should lead to more efficient codes of integral evaluations for higher angular momentum cases than any other existing codes. © 1993 John Wiley & Sons, Inc.     

Hydration characterization of N-vinylcaprolactam polymers by absorption millimeter-wave measurements

Water molecules in the polymer hydration shell known as bound water lose their mobility in comparison with unperturbed water. This effect was quantified by absorption measurements in the millimeter-wave range of microwaves (1–10 mm, 30–300 GHz). Hydration measurements were performed for poly(N-vinylcaprolactam) (PNVCL) and copolymers of N-vinylcaprolactam (NVCL) and N-vinylimidazol (NVIA). The association of hydrophobic groups in PNVCL upon coil-to-globule transition was found to cause a decrease in the relative hydration number, which is the relative amount of bound water per solute molecule as measured by microwave method at 31 GHz. Millimeter-wave hydration measurements were confirmed by the determinations of specific heat capacity (c _p) with differential scanning calorimetry. Hydration determinations of NVCL/NVIA copolymers revealed that they associate via hydrophobic clustering with a decrease in hydration of hydrophobic groups.     

Bond functions,covalent potential curves,and the basis set superposition error

In the current practice of quantum chemistry, it is not clear whether corrections for basis set superposition errors should be applied to the calculation of potential energy curves, in order to improve agreement with experimental data. To examine this question, spectroscopic parameters derived from theoretical potential curves are reported for the homonuclear diatomics C₂, N₂, O₂, and F₂, using a configuration interaction method. Three different basis sets were used, including double zeta plus polarization, triple zeta plus double polarization, and double zeta polarization augmented by bond functions. The bond function basis sets, which were optimized in the preceding paper to obtain accurate dissociation energies, also gave the most accurate parameters. The potential curves were then corrected for basis set superposition error using the counterpoise correction, and the spectroscopic parameters were computed again. The BSSE-corrected curves showed worse agreement with experiment for all properties than the original (uncorrected) curves. The reasons for this finding are discussed. In addition to the numerical results, some problems in the application of the BSSE correction to basis sets containing bond functions are shown. In particular, there is an overcounting of the lowering due to the bond functions, regardless of which type of correction is applied. Also, genuine BSSE affects cannot be separated from energy-lowering effects due to basis set incompleteness, and we postulate that it is the latter which is strongly dominant in the calculation of covalent potential curves. Based on these arguments, two conclusions follow: (1) application of BSSE corrections to potential curves should not be routinely applied in situations where the bonding is strong, and (2) appropriate use of bond functions can lead to systematic improvement in the quality of potential curves.     

Analytical applications of laser moding caused by intracavity absorption

A continuous CO₂ laser with a reflecting mirror can operate at several wavelengths simultaneously. If an organic vapor is introduced into a separate cavity in the laser optical path, the laser will sometimes mode rapidly causing some lasing lines to diminish to zero and others to become enhanced; this has been observed even for very low amounts (10^-5 g) of organic gases. Laser intercavity absorption spectroscopy depends on overlap of a vibrational—rotational line of a sample with a laser transition line. The absorption by the sample greatly affects the laser wavetrain at that particular wavelength and interferes with the lasing action. The technique is not based on Beer's law, and the detection limits observed are orders of magnitude better than those of conventional infrared absorption spectroscopy. Two laser systems were used and various organic gases were studied. When a totally reflecting mirror which permitted free moding was used, the detection limits found were 0.14 μg, 0.95 μg and 0.60 μg for vinyl chloride, propylene, and ethylene, respectively. When a grating was used as the rear cavity optics restricting the wavelengths of the laser lines, the detection limits were 140 μg, 94 μg, 63 μg and 0.26 μg for vinyl chloride, propylene. ethylene and ethyl chloride, respectively.     

Abnormal broadening in triplet-to-triplet absorption spectra caused by aromatic solvents

The triplet-triplet absorption spectra of a number of aromatic molecules were shown to be broadened in low temperature matrices formed by aromatic solvents (toluene, 4-isopropylbiphenyl) as compared with those in aliphatic solvents (ethanol, methylcyclohexane, triethylamine). The effect is exponentially dependent on the energy of the upper triplet state of the solute molecule. The phenomenon is discussed in terms of a strong exchange-resonance interaction between the triplet states of solute and solvent.     

The evaluation of electronic extracule and intracule densities and related probability functions in terms of Gaussian basis functions

The evaluation of the basic two-electron integrals involved in the calculation of extracule and intracule densities is described. Expressions are given for the evaluation of the related spherically averaged, longitudinal, and transverse probability functions from wave functions constructed from Gaussian basis sets. All results are expressed in closed analytical forms which are suited to efficient coding. Given that certain pair densities can be related to experimental scattering cross sections, the formulae reported herein will facilitate further comparison between experiment and theory and lead to a more comprehensive understanding of the electronic structures of molecules.     

Parameter-independent error correction for potential measurements by reference electrode in lithium-ion batteries

The safety monitoring of lithium-ion batteries(LIBs) is of great significance for realizing all-climate and full-lifespan battery management. In-situ measurement of anode potential with implanted reference electrodes(REs) has proven to be effective to monitor and avoid the occurrence of severe side reactions like Li plating to ensure the safe and fast charging. However, the intrinsic measurement errors caused by local blocking effects, which also can be referred to as potential artefacts, are se...