Calculation of intensity in the resonance Raman and two-photon absorption spectra of polyatomic molecules

A direct method for calculating the resonance Raman and two-photon absorption spectra of polyatomic molecules is described in detail The method is based on the adiabatic model and uses Herzberg-Teller’s approximation. Relations ruling out direct summation over vibrational quantum numbers of excited electronic states and representing the matrix elements of the Green function of a multidimensional oscillator as functions of vibration frequencies and Dushinsky transformation parameters are derived. The relations are convenient for constructing algorithms. Translated from Zhumal Struktumoi Khimii, Vol. 38, No. 2, pp. 248–255, March–April, 1997.     

Comparison between IR absorption and raman scattering spectra of liquid and supercritical 1-butanol

Raman spectra of 1-butanol have been obtained at a constant pressure of 500 bar up to 350 degrees C and along isotherms 250, 300, and 350 degrees C up to 600 bar. The purpose of the experiment was to compare responses of Raman and IR absorption spectroscopy to the forming of O-H...O bonds in alcohols. As a result, some important inferences were drawn from the experiment. In particular, it has been estimated quantitatively how the intensity of Raman scattering in the region of the OH band depends on the extent of hydrogen bonding. As might be expected, the dependence is much weaker than in the case of the IR absorption. As was shown, the ratio of integrated intensities of bonded molecules in the absorption and scattering spectra is a constant and does not depend on temperature and density. The effect of cooperativity of hydrogen bonds is confirmed. It was also found that even at high pressures, a noticeable amount of nonbonded molecules exists at room temperature.     

The effect of collisions on vibrational energy distribution in polyatomic molecules

We approach the problem of the effect of collisions on infrared absorption by an experimental and modeling study of a well-understood system, absorption of CO₂ laser radiation by cold CF₄. The spectroscopy, collisional energy transfer rates, and laser characteristics are all known. We conclude that the dominant collisional processes that influence the vibrational energy distribution during infrared laser absorption are rotational energy transfer-rotational relaxation and pressure broadening.     

Non-Aqueous surface-enhanced raman scattering spectra of benzene

Raman spectra of benzene at Ag electrode of electrochemical systems using alcohols as solvents were studied. Complicated potential dependence of benzene SERS band is attributed to competition between various adsorption states, the stability of which seems to depend on electrode potential and co-adsorption electrochemistry.     

To the theory of electron scattering by polyatomic molecules

Within the Born-Oppenheimer adiabatic perturbation theory, an equation was obtained for the intensity of fast electron scattering by polyatomic molecules. All of its parameters are explicitly defined by vibronic interaction in a molecule; due to this, quantum chemical calculations are fully applicable to electron diffraction studies of molecular geometries. Engels Anti-Aircraft Missile Higher Military School. Translated fromZhurmal Strukturnoi Khimii, Vol. 35, No. 2, pp. 40–45, March–April, 1994. Translated by L. Smolina     

Anion effect on surface-enhanced raman scattering of water molecules on silver electrodes

The anion effect on the surface-enhanced Raman scattering (SERS) of interfacial water molecules on Ag electrodes has been studied by adding concentrated KCl, KBr, KI or KF solution to dilute solutions. SERS of the interfacial water was detected after adding concentrated KCl, KBr or KI solution, but not in the case of concentrated KF solution.     

Angular distribution of intensity of rayleigh scattering from comblike branched molecules

The angular distribution function P(θ) for intensity of light scattered by a dilute solution of comblike branched molecules has been determined for three situations of some interest for evaluation of experimental data: (1) the molecules are identical with branches of equal length attached equidistantly along linear backbone chains; (2) the molecules are homogeneous in mass, with the same number of branches on each molecule, but the branches are distributed at random along the chain; (3) branches and main chains are still uniform, but the molecules are heterogeneous in mass with the number of branches per molecule distributed according to the binomial distribution and the branches in any molecule spaced randomly along the backbone. Examination of numerical results shows that the scattering functions for models (1) and (2) are not very different. The function for case (3) is somewhat different from the others when the mean number of branches per molecule is small but they contain a large fraction of the mass of the molecule. Over a limited range of the pertinent variables (corresponding roughly to observations on typical vinyl polymers of molecular weights up to 10⁶) all three functions agree quite well with P(θ) for homogeneous linear chains with the same mean-square radius of gyration.     

Multiple-scattering method in the theory of photoelectron and absorption spectra polyatomic systems

Conclusion Within the framework of the –'muffin-tin–' approximation the LS equations reduce to a system of linear algebraic equations of type (8), the order of which increases with increasing number of atoms in the system. In this paper the solution of this system of equations for the whole system is replaced by the solution of systems of equations of lower order (9) and (10) for isolated clusters. This advantage is in general fictitious owing to the weak convergence of the solution of Eqs. (20) and (21) with respect to L. However, for highly-symmetrical clusters the series in L converges and the proposed method greatly reduces the computing work. The advantages of the method are most clearly seen in the high-energy limit (23) and (27), in which the dependence on L vanishes.Institute of Inorganic Chemistry, Academy of Sciences of the USSR, Siberian Branch. Translated from Zhurnal Strukturnoi Khimii, Vol. 17, No. 1, pp. 22–28, January–February, 1976.     

Excitation profiles of resonance raman spectra in condensed media

A simple model, obtained by reducing a multimode system to a simple coordinate, is proposed to explain the broadening of RRS in liquid or solid media. It is shown that the coherent excitation of the near continuous background of low-frequency modes can cause homogeneous broadening of RRS profiles. The model is applied to the excitation profile of β-carotene.     

Semiempirical parametric method in the theory of vibronic spectra of polyatomic molecules

A semiempirical parametric method for calculating the vibrational structure of the electronic spectra of polyatomic molecules is developed; the method is based on the adiabatic molecular model and uses a single parametric system for all excited states. Within the model approach, simplified analytical expressions for potential surface variation during molecular excitation are derived; the expressions include the principal terms according to the order of magnitude. The first and second derivatives of Coulomb and resonance one-electron integrals with respect to natural coordinates in a basis set of hybrid atomic orbitals are used as parameters. It is shown that the parameters possess distinct locality, are transferable in molecular series, and may be easily ranked according to absolute values; describing a molecular model requires few most significant parameters. Excitation-induced variations of potential surfaces and absorption spectra of some molecules (butadiene, hexatriene, octatetraene) are calculated using only two parameters, which are the same for all molecules. The results of calculations are in good agreement with the experimental data. Supported by RFFR grant No. 95-03-08808. V.I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhumal Struckturnoi Khimii, Vol. 37, No. 3, pp. 419–431, May–June, 1996.     

Group theory approach for raman scattering of triatomic molecules

The symmetry of the rotation-vibration spectra for triatomic molecules is described by means of the group U(5). Group theory approach is adopted to give the transition matrix elements for calculation of the cross sections of vibrational and rotational Raman scattering. The results are in good agreement with the experimental values.     

New algorithm and software for analyzing the vibronic spectra of polyatomic molecules

A new algorithm for automatic assignment of the resolved vibrational structure of the electronic absorption spectra of diatomic and polyatomic molecules is suggested. Translated fromZhurnal Struktumoi Khimii, Vol. 38, No. 2, pp. 363–368, March–April, 1997.     

A study on the sizes and concentrations of gold nanoparticles by spectra of absorption, resonance Rayleigh scattering and resonance non-linear scattering

Liquid phase gold nanoparticles with different diameters and colors can be prepared using sodium citrate reduction method by controlling the amounts of sodium citrate. The mean diameters of gold nanoparticles are measured by transmission electron microscope (TEM). Gold nanoparticles with different sizes have specific absorption spectra. When the diameters of nanoparticles is between 12 and 41 nm, the maximum absorption peaks locate at 520-530 nm and there are red shifts gradually with the increase of diameters of gold nanoparticles. And when the size of gold nanoparticle is constant, the absorbance is proportional to the concentration of gold. Obvious resonance Rayleigh scattering (RRS) and the resonance non-linear scattering such as second-order scattering (SOS) and frequency-doubling scattering (FDS) appear at the same time as well, and the maximum scattering peaks are located at 286 nm (RRS), 480 nm (SOS) and 310 nm (FDS), respectively. When the concentration of gold is constant, absorbance and the intensities of RRS, SOS and FDS (I(RRS), I(SOS) and I(FDS)) have linear relationships with the diameters of gold nanoparticles. When the diameter of gold nanoparticle is constant, the absorbance and I(RRS), I(SOS), I(FDS) are directly proportional to the concentrations of gold nanoparticles. Therefore, it is very useful for studying the liquid phase gold nanoparticles by investigating the absorption, RRS, SOS and FDS spectra.     

Novel methods for calculating the fine vibronic spectra of polyatomic molecules

Novel approximate methods for calculating the vibrational structure of the electronic spectra of polyatomic molecules—a method for the direct calculation of the overlap integrals of vibrational wave functions for the electronic states involved in a transition and a variational method for the solution of the vibrational problem for the excited states—are discussed. The methods are based on the consideration of the displacement and entanglement of normal coordinates, the quasiorthogonality of the Dushinsky transformation, and the classification of the states by total vibrational quantum numbers. Matrix perturbation theory is employed. It is shown that the accuracy of these methods compares well with the accuracy of the available “exact” techniques (the errors are ∼1 cm⁻¹ for frequency and 10% for relative intensity). At the same time, calculations by the new methods are performed more than two orders of magnitude faster than by the previously known methods. K. A. Timiryazev Agricultural Academy, Moscow. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 217–230, March–April, 1995. Translated by I. Izvekova     

Jahn-Teller effect and resonance raman spectra of highly spin-degenerate molecules with application to FeBr4−

We give a model calculation of the resonance Raman amplitude of spin-degenerate molecules that are subject to Jahn-Teller distortion. The method is applied to the resonance Raman excitation profiles of the ν₃(t₂) and ν₁(3_1g) modes of FeBr₄^?.     

Calculation of vibronic spectra of polyatomic molecules in the franck—condon and herzberg—teller approximations: Part II. Spectral distribution curves of absorption coefficients

A method for calculating the vibrational structure of electron spectra of polyatomic molecules was suggested in Part I. This is based on the general methods developed for matrix element calculation and the semi-empirical approach to the determination of the parameters of excited state potential surfaces, which involves correlations between the lengths, force constants and indices of bonds. Correlations for the C—C and C—H bonds are presented here. Results on the vibronic spectra for butadiene, hexatriene, diphenylhexatriene, toluene, p-xylene, and benzonitrile are discussed. Manifestations of various effects (Dushinsky effect, effect of temperature distribution of molecules, vibronic interaction) in the vibronic spectra are analyzed quantitatively and the uncertainties resulting from the neglect of these effects are determined. The convergence of the Herzberg—Teller expansion is estimated.