Band-shape Function Research Articles

Quantification of Overlapping VIS-Absorption Bands by Fourier-Domain Fitting of a Generalized Band Shape Function

Parameter estimation of overlapping (near-)symmetrical absorption bands with reference to quantitative determination may advantageously be performed by a new procedure that involves fitting a generalized four-parameter band shape function to the Fourier-domain representation of the second-derivative spectrum. Important features of the method are: insensitivity to linear and weakly curved baselines, inherent noise reduction, fast calculation of objective function, and band simulation capability much better than that with the Gauss or Lorentz shapes.

An extended theoretical formulation of the circular dichroism band shape of chromophore aggregates by use of the ensemble-averaged resolvent matrix method

A new theoretical formulation is given to the circular dichroism band shape of chromophore aggregates by means of the ensemble-averaged resolvent matrix method. This formulation can be used to calculate the circular dichroism band shape of chromophore aggregates having arbitrary strengths of the excited-state interactions between chromophores. Using the resolvent expansion rule, thermal and static effects upon the circular dichroism band shape are incorporated as the mean-frequency shifts of the normalized band shape functions used for ensemble averaging the resolvent matrix of chromophore aggregates. This formulation is applied to derive a generalized band shape expansion formula which gives a theoretical justification to the practical first-order Taylor expansion equation used to calculate the circular dichroism band shape of chromophore aggregates. Basic properties of the generalized band shape expansion formula are investigated by comparing it with the usual perturbation expansion equation for the circular dichroism band shape of chromophore aggregates.

Second derivative parameterization of log-normal distribution function for resolution of overlapping bands

The log-normal distribution function has been extensively applied as the band-shape function to resolve complex absorption profiles. In such profiles the second derivative is a great aid to fix the number and parameter values of the components. Second derivative parameterization of band-shape functions allows the obtention of the band parameters in a simple way. For the log-normal function, the second and third derivative expressions, necessary for this purpose, are very complex. For this reason, a set of aproximation has been introduced in order to simplify the band parameters determination. Applications of these expressions are discussed.

Isotropic Raman band shape and vibrational relaxation for molecules in the liquid state: A Critical study of some band shape functions

AbstractA band shape function for the isotropic Raman scattering described in terms of the band width in the weak coupling limit and the relaxation time of the bath mode has been proposed by summing the results of Berne et al. [J. Chem. Phys. 45, 1086 (1966)], Wang [Mol. Phys. 33, 207 (1977)] and Knauss [Mol. Phys. 36, 413 (1978)]. The results of band analyses with this function have been compared with those obtained from other conventionally used band shape and correlation functions. The present function is preferable for precise interpretation of vibrational relaxation mechanisms, particularly for those cases where temperature and concentration dependence of the band parameters are involved.

On the vibronic structure of all-trans-retinal in different environments

The great sensitivity of the electronic structure of a polyene in different environments is visualized through the all-trans-retinal molecule in solvents with different polarity. A vibronic structure in the 1 B u + ← 1 A g − transition of all-trans-retinal is detected in the second-derivative spectrum of the ordinary band-shape function. It consists mainly of a 1480 cm −1 progression. Attempts to simulate this are presented. A correlation between the resolution in the vibronic structure and the polarity of the environment of retinal is found. A second excited state of all-trans-retinal may be responsible for the changes in the vibronic structure in the different solvents.

THEORY OF INFRA-RED ABSORPTION OF MOLECULES

In this paper, we apply the adiabatic approximation model to the IR absorption of molecules. Expressions of the band shape functions for isothermal and isolated systems are obtained and using Einstein model we discuss the dependence of the band shape functions on temperature, normal coodinate shifts and energy.We also obtain a very simple expression of the correlation function when νν′<1 and discuss its effect on the band shape function

Experimental and theoretical studies of resonance Raman scattering: Temperature effects in β-carotene

The Raman excitation profile of β-carotene in isopentane solution has been measured at 118 and 298 K using stilbene dye laser excitation as well as argon laser lines. This data as well as absorption data have been analyzed by using a model which includes the conventional multimode and band shape function. With this model, the parameters of normal coordinate displacement and damping constant, and the effect of temperature and band shape function on the width and peak position can be explored. Using the same set of parameters, we have successfully fit the absorption spectra and the resonance Raman excitation profile of three fundamental bands at both low temperature and room temperature. With our approach the damping factor is found to be on the order of 50 cm−1 for β-carotene.

Some remarks on first-order perturbational treatment of the connection between correlation functions and shapes of far-infrared absorption bands in liquids

The physical conditions regarding the far-IR absorption process in molecular liquids are discussed. It is shown that the well known first-order perturbational treatment of the connection between band shape and auto-correlation function of the molecular dipole moment cannot be justified within quantum statistics.

Analysis of the molecular electronic absorption spectra of shock-heated aromatic compounds

Advantage has been taken of the rapid and homogeneous heating of a sample in a shock wave to record the electronic absorption spectra of the 1A1g→1B2u transition in benzene and the corresponding 1A1→1B1 transition in toluene as a function of temperature over the range 700–1300 K, prior to thermal decomposition.A model for the band-shape function of electronic absorption spectra of symmetry-allowed and symmetry-forbidden transitions in the context of the Herzberg–Teller theory is proposed based upon the assumption of harmonic oscillators. For symmetry-forbidden transitions, frequency changes in the promoting modes are ignored and only the linear Herzberg–Teller terms are considered to account for the dependence of the electronic transition moment upon nuclear coordinates. Explicit attention is paid to the temperature dependence of the band-shape function and it is shown, in conjunction with a moment analysis of the band-shape function, how important molecular parameters may be deduced in favourable instances, which are determined chiefly by the inherent molecular complexity and symmetry point group of the molecule. It is shown by a moment analysis of the shock data that the induced and allowed transition moments in toluene are of comparable magnitude.

Theory of magnetic linear dichroism. Application to matrix-isolated atomic transitions

A general theory for magnetic linear dichroism (MLD) is presented. The derivation uses a perturbation approach together with the rigid shift approximation and includes terms in the Boltzmann population of the ground state and in the band shape function which are proportional to the square of the magnetic field strength. A six term expression for the MLD is obtained. The different terms result from the Zeeman splitting of the ground and/or excited states, the population redistribution of the ground state, or the intermixing of electronic states. Expressions for each of the six terms are given. They are functions of the electric dipole transition moments polarized parallel and perpendicular to the magnetic field and of the magnetic moments of the ground and/or excited states. Estimates are made of their relative importance for conditions of possible experimental importance. Computer simulations of the MLD band shapes for diamagnetic and paramagnetic species as a function of bandwidth and temperature are given. The effects of the varying contribution of the zeroth, first, and second derivatives of the assumed Gaussian band shape function are illustrated. The application of the method of moments to the quantitative analysis of an MLD spectrum is also discussed. Finally, the present theory is applied to atomic spectroscopy, e.g., atoms isolated in matrices. It is shown that the results of an MLD experiment combined with the results of a magnetic circular dichroism (MCD) experiment should provide an unambiguous assignment of the total angular momentum of excited electronic states in atoms.

Vibrational relaxation of hydrogen-bonded species in solution. Il. Analysis of vs(XH) absorption bands

The v s(XH) absorption bands of the following complexes have been recorded in digitised form: phenol (OH)- and phenol (OD)- dioxan in CCl 4; phenol (OH)- and phenol (OD)-acetonitrile in CCl 4; and phenol (OH)-acetonitrile in CDCl 3. All these bands are broad and nearly featureless, and have widths at half height ranging from 75 to 148 cm −1. With one possible exception they appear to be free from Fermi resonances. By least-squares fitting of the theoretical bandshape function derived in part I to the experimental spectra we have been able to estimate the parameters Δ, ω 2, and τ C which characterise the theoretical autocorrelation function, and also to determine the v s(XH) stretching frequency very accurately. In the case of phenol (OD)-dioxan in CCl 4 the discrepancies between the observed and fitted spectra can be entirely attributed to errors of observation. It is found that the Kubo parametér τ C Δ is close to unity in all cases, showing that the v s(XH) bands are subject to partial (but not extreme) motional narrowing. The v σ(XH⋯Y) vibration is always heavily damped and has a broad spectral density. The changes in the spectral profiles produced by deuteration and change of solvent are easily understood in terms of the theory. Deuteration affects the amplitude of modulation, while changing the solvent affects the value of τ C. In either case τ CΔ changes, and the speed of modulation is altered. Since the system is far from the gaussian (slow modulation) limit, the bandshape changes markedly in consequence.

Linear Response Polarizability Theory of the UV, ORD, and CD Bandshapes of Helical Biopolymers. Single- and Double-Stranded Polyadenylic Acids

Abstract The UV, ORD, and CD spectral bandshapes of polyadenylic acid (poly A) have been investigated theoretically in order to challenge the problems of whether discrimination of the single- and double-stranded poly A’s is computationally possible and of what structure poly A holds in a neutral solution. A linear response polarizability theory is applied to the derivation of UV, ORD, and CD bandshape functions of a polymer composed of N identical monomers. Using the observed and/or assumed values for the spectral bandshape of the adenine monomer, the UV, ORD, and CD spectra of both single- and double-stranded poly A’s are calculated by changing geometrical parameters. The single-stranded poly A at neutral pH is assumed to have a regular helical structure which is regarded as a counterpart of the double helix form of the double-stranded poly A. This model leads to the chainlength (N) effect which in turn suggests that the structure of poly A in a neutral solution is very flexible and is such that it can be approximated as a random assembly of adenine dirners and/or trimers, when the theoretical spectra of both the single- and double-stranded poly A’s are compared.

Circular dichroism theory for unordered polypeptides: A Green operator technique

A Green operator technique used within a suspectibility framework is employed to express the circular dichroism of a diamide which is taken as a model for an unordered polypeptide system. The formulation contains all common mechanisms that give rise to circular dichroism and has the advantage that band shape functions can be included for each absorption band of each isolated nonoverlapping chromophore. The rotational strengths, transition frequencies, and polymer band shapes are determined by solving a complex eigenvalue problem.

Theory of vibrational relaxation and infrared absorption in condensed media

In this paper, we develop a theoretical model for vibrational relaxation of vibrons in condensed media based on the breakdown of the adiabatic separation of vibron (high frequency) and phonon (low frequency) motion. The conditions under which the adiabatic approximation of the vibron–phonon system is valid are examined. The present model is also applied to the ir absorption in condensed media; the band shape function and the dipole correlation function are obtained. The relation between the vibrational relaxation and the ir absorption is discussed.

Studies on Ag- Centers in Alkali Halides. IV. Characteristic Features of Ag- Centers

The absorption, emission and its excitation spectra of Ag - centers in NaCl, NaBr and RbCl crystals were investigated at various temperatures. Most of the properties of these centers were found to be qualitatively similar to those of potassium halides, except that NaBr does not show C emission. The third moment of the C band shape function was obtained as a function of temperature for KCl and RbCl, and was compared favorably with the Nasu-kojima theory. It is concluded that the linear electron-lattice coupling approximation is quite satisfactory for Ag - centers in various substances so far studied.

π-SCF studies of the circular dichroism and electronic spectra of alkaloids containing the aniline chromophore. The stereochemical configuration of calycanthine and caracurine-II

The absorption and c.d. spectra of calycanthine and caracurine-II have been extended to 53 kK, and the π→π* transition energies and dipole and rotational strengths of the two alkaloids have been calculated in the π-SCF approximation using the dipole-velocity procedure. Theoretical absorption and c.d. spectra have been obtained for the alkaloids from the calculated quantities with a curve-plotter using a Gaussian band-shape function. The spectra computed for the previously assigned configurations of the two alkaloids reproduce the qualitative form of the experimental curves with magnitudes of the correct order. The π-SCF calculations are found to support the general features of the point–dipole exciton treatment of the electronic states and stereochemical configuration of chiral dimeric π-systems in cases where the latter method is applicable, e.g. calycanthine, but the former method is of wider scope and covers cases, e.g. caracurine-II where the latter fails.

A COMPARISON OF OPTIMIZATION METHODS FOR FITTING CURVES TO INFRARED BAND ENVELOPES

A comparison has been made of seven numerical methods of fitting infrared absorption band envelopes with analytical functions using nonlinear least squares approximations. Gauss and Cauchy (Lorentz) band shape functions are used, and also sum and product combinations of the two. The methods have been compared with respect to both the degree of convergence and to the computation time needed to achieve an acceptable fit.The most effective method has matched the overlap envelope of a steroid spectrum containing 16 bands; this necessitated the optimization of 65 variables. More complex spectra can be dealt with by a "moving subspace" modification in which only the parameters of a group of adjacent bands are adjusted at one time. Automatic computer programs have been written for five of the methods, and for the moving subspace modification. These will be published elsewhere.If the computed curve is convoluted with the spectral slit function before making the least squares calculations, the distortion of the observed spectrum caused by the finite spectral slit width can be corrected. In some cases this method of diminishing the slit distortion is better than direct methods, particularly when dealing with strongly overlapped bands.