# Optics and Spectroscopy (v.108, #4)

Construction of minimizing sequence of multiparticle functions for calculating the spectrum of an atom by S. M. Orel

*(495-501)*. A method for calculating the states of a many-electron atom is proposed based on the representation of the wave function of the atom as a linear combination of multideterminant functions. Determinants are constructed from single-particle hydrogen-like functions in which the positive nuclear charge is replaced by a certain effective charge. For each single-particle function, the effective charge is calculated such that to take into account the interaction of a given electron with the spherically symmetric part of the screening charge distribution of remaining electrons. Examples of constructing approximating sequence of functions are given and results of calculations of energies of stationary states of the He and Li atoms are presented.

Application of quantum mechanical method to analysis of the intensity distribution in spectra of resonant hyper-Raman scattering of low-symmetry molecules by T. G. Burova; A. A. Anashkin

*(502-505)*. The quantum-mechanical method of calculating the relative intensities of lines in the spectra of resonant hyper-Raman scattering of polyatomic molecules in the Herzberg-Teller approximation is tested with respect to low-symmetry molecules. The method makes it possible to describe resonant Raman and hyper-Raman scattering spectra, as well as vibronic absorption spectra, from the same viewpoint based on a common set of parameters. The particular features of the implementation of the method are discussed based on the calculation of the spectra of resonant hyper-Raman scattering of chlorobenzene and adenine, and the expedience of the application of the method is illustrated. Satisfactory agreement is obtained between calculation results and available experimental data.

Description of the torsional motion in the isotopically asymmetric ionic complexes ArH

_{2}D^{+}and ArD_{2}H^{+}by A. V. Burenin*(506-511)*. The internal dynamics of the isotopically asymmetric ionic complexes ArH

_{2}D^{+}and ArD_{2}H^{+}is considered to be a distorted dynamics of the isotopically symmetric ArH_{3}^{+}complex. By using the group chain methods, a rigorous algebraic model is constructed to describe the spectrum of the asymmetric complexes with an allowance for the torsional motion of the structure of hydrogen nuclei. The model is based on the geometrical group of symmetry of internal dynamics of the isotopically symmetric ionic complex, which is used here as a noninvariant group. Calculation of coefficients of collisional broadening of ozone spectral lines induced by pressure of atmospheric gases by J. V. Buldyreva; T. P. Mishina; N. N. Lavrent’eva; A. S. Osipova

*(512-522)*. Coefficients of the broadening of ozone lines by nitrogen and oxygen pressure in the ν

_{1}+ ν_{3}band at room temperature have been calculated. Calculations were performed by two methods. The first method is a modification of the semiclassical Robert-Bonamy formalism, in which parabolic trajectories are replaced by exact trajectories. This method enables one to describe the available experimental data with an accuracy of a few percents. The second, semiempirical, method is based on a two-parameter modification of the semiclassical impact model; it gives a high-accuracy global description of line profile parameters and, keeping the main physical regularities of pressure line broadening and shifting, enables a detailed study of these regularities and their dependence on environmental parameters. In contrast to the water vapor molecule, the broadening of spectral lines of the ozone molecule depends strongly on the rotational quantum numbers, so that the fitting parameters of the semiempirical method were determined separately for low, middle, and high values of the rotational quantum number*J*. Collisional broadening and shifting of saturated absorption resonances in silicon tetrafluoride by I. R. Krylov

*(523-527)*. The broadening and shifting of 12 saturated absorption resonances of the SiF

_{4}gas induced by molecular collisions have been measured in the lasing region of a low-frequency CO_{2}laser at the*P*(30) line of the 9.4-μm band. Values of the collisional broadening are identical accurate to the measurement uncertainty. The collisional shift does not exceed 10% of the collisional broadening. This means that collisions with changes in the internal energy of molecules prevail over dephasing collisions. Influence of transit effects on optical resonances in time-separated fields by E. A. Titov

*(528-532)*. Contributions to the shift of resonance in time-separated fields from wavefront curvature of the field pulses and gravity are determined. The influence of inhomogeneity of atomic distribution in a magnetooptical trap is taken into account. The scheme for observation of the resonances that eliminates shift due to the recoil effect is considered.

Observation of simultaneous ν

_{1}(SF_{6}) + ν_{3}(NF_{3}) and ν_{2}(SF_{6}) + ν_{3}(NF_{3}) transitions enhanced by the resonance dipole-dipole interaction with the ν_{1}+ ν_{3}and ν_{2}+ ν_{3}states of the SF_{6}molecule by V. N. Bocharov; A. P. Burtsev; E. V. Dubrovskaya; T. D. Kolomiitsova; D. N. Shchepkin*(533-543)*. IR spectra of the solution of SF

_{6}molecules in liquid NF_{3}at 84 K have been recorded. In a solvent transmission window of 1500–1750 cm^{−1}, two wide absorption bands with pronounced peaks in the high-frequency part are observed. The profile of these bands is explained by the influence of the resonance dipole-dipole (RDD) interaction of the states of the simultaneous transition ν_{1}(SF_{6}) + ν_{3}(NF_{3}) and ν_{2}(SF_{6}) + ν_{3}(NF_{3}) with the states (ν_{1}+ ν_{3}) and (ν_{2}+ ν_{3}) of the SF_{6}molecules, respectively. The use of three isotopic modifications^{32}SF_{6},^{33}SF_{6}, and^{34}SF_{6}has allowed us to vary the resonance detuning and thus to change the strength of the RDD interaction. With the liquid near the melting point being represented as a close-packed cubic crystal, the profile was calculated and its spectral characteristics were determined. The frequencies of the main peaks coincide with the experimental values accurate to the error. Investigation of excited-state proton transfer in 3-hydroxyflavone molecules by V. I. Tomin

*(544-552)*. The dual fluorescence spectra of 3-hydroxyflavone molecules excited by electromagnetic radiation in the region of the

*S*_{1}and*S*_{2}absorption bands in the temperature region of 20–80°C are studied using the dynamic quenching of the excited state. An analysis of the fluorescence parameters shows that heating the solution from room temperature to 60°C increases the proton transfer rate by a factor of 1.24 in the case of standard excitation into the main absorption band and even stronger (by a factor of 6.9) in the case of excitation into the second absorption band. The presence of a quencher reduces the yield of the two emission bands and noticeably increases the proton transfer rate, by a factor of 1.16 at room temperature and by a factor of 1.25 at 80°C. Upon excitation into the second singlet band, the transfer rate increases even more (especially at higher temperatures), by a factors of 1.24 and 3.5 for the same temperatures. The temperature dependences of the transfer rate constant allowed us to estimate the activation energies of the proton transfer reaction under different physical conditions and reach conclusions about the mechanism by which this reaction proceeds. It is found that the proton transfer activation energy decreases from 500 to 360 cm^{−1}when measured in temperature ranges of 20–40 and 20–60°C. The introduction of a quencher with a concentration of 5 × 10^{−3}M increases the activation barrier to 534 and 471 cm^{−1}in the same temperature ranges. Self-assembling effects and mechanisms of interchromophore interactions in porphyrin pentads by E. I. Sagun; É. I. Zenkevich; V. N. Knyukshto; A. M. Shulga; N. V. Ivashin

*(553-570)*. The directional self-assembly of nanosized, structurally organized pentads that include five tetrapyrrole macrocycles and are based on the two-point coordination interaction of two covalently bound dimers of Zn porphyrins (homo-and heterodimers) with molecules of either the free base or the Cu complex of tetrametapyridyl-substituted porphyrin extra ligand is implemented in methylcyclohexane at 295 K. Using the method of the density functional theory (DFT) in the B3LYP/6-31

*g*(*d*) approximation, the geometry of the pentad is fully optimized and the main factors that determine its redox properties are determined. The energies of the lowest excited states of the pentad are calculated by the ZINDO/S method, and it is shown that the occurrence of identical molecules in the system facilitates the formation of excitonic states with different contributions from the charge-transfer component. The directional energy transfer and the photoinduced electron transfer, which leads to the formation of a low-lying charge-transfer state (CT state), are studied and the rate constants of these two processes are determined (*k*_{ET}∼ 10^{11}s^{−1}and*k*_{PET}≈ (1.8−6.0) × 10^{9}s^{−1}, respectively). The strong effect of the temperature of the solvent on the efficiency of relaxation processes in pentad complexes under study is revealed and studied. Roles played by the low-lying CT state and*d-π*exchange effects (the Cu-contained pentad) in fluorescence quenching of pentad complexes are determined. Effect of water vapors on the luminescence of cation-exchange membranes modified by Pt(II) and Ru(II) complexes and Nile blue by M. S. Khakhalina; D. N. Musaeva; I. Yu. Tikhomirova; M. V. Puzyk

*(571-573)*. The surface of a cation-exchange membrane was modified by the [PtEnPpy]

^{+}, [PtEnBt]^{+}, [PtEnTpy]^{+}, [RuBpy_{3}]^{+2}, and NB^{+}, (En is ethylenediamine; Ppy, Bt, Tpy are α-deprotonated forms of 2-phenylpyridine, 2-phenylbenzothiazole, and 2-(2′-thienyl)pyridine, respectively; Bpy is 2,2′-bipyridyl, and NB^{+}is Nile blue) ions, which exhibit intense luminescence. It is found that the quenching of the luminescence of the modified cation-exchange membrane by water vapors depends on the nature of the excited electronic state of the immobilized cation. Optical and electrochemical properties of cyclometalated Rh(III) complexes based on 4,6-diphenylpyrimidine with ethylenediamine, 2,2′-bipyridyl, and 1,10-phenanthroline by E. V. Ivanova; K. P. Balashev

*(574-580)*. The [Rh(Hdp)

_{2}(N∧N)]ClO_{4}complexes (Hdp^{−}is the monodeprotonated form of 4,6-diphenylpyrimidine and (N∧N) is ethylenediamine, 2,2′-bipyridyl, and 1,10-phenanthroline) are synthesized and characterized by^{1}H and^{13}C NMR, IR, electronic absorption, and emission spectroscopy, as well as by cyclic voltammetry. The magnetic equivalence of two cyclometalated 4,6-diphenylpyrimidine ligands in the composition of complexes points to the*cis*position of metalated phenyl rings in the inner sphere. Quasi-reversible one-electron reduction waves are attributed to the ligand-centered electron transfer to the π* antibonding orbital of heterocyclic ligands, while irreversible oxidation waves are associated with electron detachment from the Rh-C σ bonding orbital of the {Rh(Hdp)_{2}} metal-complex fragment. The characteristic long-wave-length absorption bands and the vibrationally structured phosphorescence bands of complexes are assigned to the spin-allowed and spin-forbidden charge-transfer optical transitions between the σ_{Rh-C}and π_{Hdp}* orbitals localized on the {Rh(Hdp)_{2}} fragment of the complex. Scattering of surface plasmon-polaritons and volume waves by thin gold films by S. I. Lysenko; B. A. Snopok; V. A. Sterligov

*(581-590)*. The specific features of elastic scattering of volume waves and surface plasmon polaritons by polycrystalline gold films have been investigated. An analysis of the relative scattered energy, power spectral density of surface roughness, and integral and angular dependences of scattering of waves of different nature indicates a strong nonradiative multiple scattering of surface plasmon polaritons in gold films. When roughness increases, this scattering leads to an increase in scattering isotropy and to a partial loss of structural information about gold films. The analysis of the scattered energy of surface plasmon polaritons with application of the data on multifractal dimension of gold surface indicates also that the radiative scattering of surface plasmon polaritons depends on both the rms surface roughness and the surface wave propagation length.

Optical constants of nanosized films of metal titanium by T. I. Grigor’eva; T. Kh. Khasanov

*(591-597)*. A new ellipsometric technique for optical measurements of the refraction and extinction indices and thickness of nanosized metal-titanium films in air is proposed and implemented. It is shown that the determination of optical constants of titanium films by measuring the ellipsometric parameters Ψ and Δ for a light beam incident upon the metal/substrate interface through the substrate of fused silica allows one to obtain optical constants of the metal, which correlate well with the results of the most reliable measurements performed in vacuum chambers. In this case, one can additionally determine the thickness and refractive index of the natural oxide film on the titanium surface. The obtained values of the optical constants of titanium,

*n*_{2}= 3.42 ± 0.05 and*k*_{2}= 3.75 ± 0.05 (λ = 632.8 nm), agree well with the results of the measurements made in vacuum. The proposed technique makes it possible to measure the thicknesses of titanium films within the range 7–30 nm with an accuracy of 0.7 nm. The technique is tested on titanium films deposited onto fused silica substrates obtained by vacuum thermal evaporation. The possible error of determining the thickness due to various additional factors is estimated. The results of ellipsometric measurements of the thickness are compared with the data obtained from parallel measurements of electric resistance of the films. IR spectrum and localization of excitation of reaction center of photosystem II in triplet state by N. V. Ivashin

*(598-607)*. Using the density functional theory, vibrations of different model forms of the chlorophyll

*a*molecule in the ground and triplet states have been calculated. The assignment of the experimental difference IR spectrum corresponding to the formation of the triplet state of the photosynthetic reaction center of photosystem II has been proposed on this basis. It has been shown that molecules of accessory chlorophyll B*A*_{ }and B*B*_{ }located between the special pair and H*A*_{ }and H*B*_{ }pheophytin molecules can be involved in the intermolecular hydrogen bond with the water molecule. The energy of this interaction in the triplet state of molecules for B*A*_{ }is larger on 6 kcal/mol. This allows us to relate this pigment to the location of the triplet excitation at the reaction center of photosystem II. Specific features of provitamin

*D*_{3}photoisomerization in a cholesteric liquid crystal by T. N. Orlova; I. P. Terenetskaya*(608-612)*. The method of UV absorption spectroscopy is used to study the influence of the cholesteric pitch on the efficiency of previtamin

*D*(photoisomer of provitamin*D*_{3})*cis-trans*isomerization in a cholesteric liquid crystal (nematic + optically active dopant + provitamin*D*_{3}). It is found that a change in pitch from 14 to 0.364 μm due to an increase in the concentration of an optically active dopant in a wide range (1.6–61 wt %) only slightly reduces the efficiency of the*cis-trans*isomerization. However, small changes in pitch (0.364–0.368 μm) due to an increase in the provitamin*D*_{3}concentration within the range of 0.07–2.2 wt % significantly increase the efficiency. Reducing in the influence of provitamin*D*_{3}concentration on the*cis-trans*isomerization efficiency with an increase in mesophase temperature was found in both nematic and cholesteric liquid crystals up to the disappearing of the concentration dependence in the isotropic phase. Altogether, the obtained results indicate the collective character of*cis-trans*isomerization in liquid crystals due to the ordering of the medium. Absorption spectra of thin layers of solid solutions Cs

_{2}(Cd1 −*x*_{ }Zn*x*_{ })I_{4}by V. K. Miloslavsky; O. N. Yunakova; E. N. Kovalenko*(613-617)*. The excitonic absorption spectra of thin films of ferroelectric Cs

_{2}CdI_{4}and Cs_{2}ZnI_{4}solid solutions are studied for the first time. It is found that, within the whole range of molar concentrations*x*, the spectra of Cs_{2}(Cd1 −*x*_{ }Zn*x*_{ })I_{4}comprise two bands that originate from the bands of the two compounds. It is shown that the exciton transfer occurs most efficiently between the tetrahedrons CdI_{4}and ZnI_{4}along the*b*axis of the crystal. Unusual behavior of the concentration with regards to the maxima of long-wavelength excitonic bands*E**m*_{ }(*x*) agrees well with the developed theory that takes into account dependence on*x*of the matrix element of the intertetrahedron exciton transfer and that is similar to the theory of Davydov’s splitting in molecular crystals. Amplification of ultimately-short pulses in graphene in the presence of a high-frequency field by N. N. Yanushkina; M. B. Belonenko; N. G. Lebedev

*(618-623)*. The Maxwell equations for an electromagnetic field propagating in graphene are considered taking into account strong Coulomb repulsion between electrons of the same site possessing opposite spin projections. The derived effective equation has the form of a classical 2D sine-Gordon equation. Electrons are treated in terms of quantum formalism with allowance for the dispersion law in the presence of Coulomb interaction. The effective equation is analyzed numerically and the effect of Coulomb repulsion is revealed. It is shown that the system in an external homogeneous electromagnetic field, with its period much shorter than the characteristic pulse length, may show the amplification of an ultimately short pulse.

Phase effects during parametric conversion in layer structures by R. J. Kasumova; A. Karimi

*(624-627)*. Coupled-wave equations that describe the parametric amplification and generation of a sum frequency in a three-layer structure are studied theoretically in the constant-intensity approximation taking into account the inverse effect of the excited wave on the phase of the pumping wave. For this purpose, the approximation of constant intensity of the fundamental radiation is applied not to the layer structure as a whole but to each separately taken layer. In this case, the complex amplitudes of the interacting waves at the output of each layer are the input values of the corresponding complex amplitudes for the next layer. Analytical expressions obtained in the constant-intensity approximation for the efficiency of conversion to the sum frequency were analyzed numerically for different parameters of the problem. The efficiency of parametric amplification at a high frequency was found to depend on the intensity of the signal wave at a low frequency.

Zone structure of regimes of monochromatic reflected radiation in the parametric doppler effect in plasma by N. N. Rosanov

*(628-633)*. The presence of regimes of nonmonochromatic reflected radiation for monochromatic radiation incident on an inhomogeneity moving in the direction of incident radiation is demonstrated for the parametric Doppler effect in plasma. For collisionless plasma, these regimes are related to the transparency of the plasma for incident radiation and its opacity (the total internal reflection) for the reflected radiation. On the plane of parameters of the problem, the velocity of the inhomogeneity and the frequency of the incident radiation, a zone structure (allowed and forbidden zones) of the domains of the existence of the regime of a monochromatic reflected wave is found.

Response of multipass schemes to radiation with complex frequency by N. N. Rosanov

*(634-636)*. The response of multipass schemes, such as a layer of a medium and multiple-beam interferometer to a radiation pulse with an exponential intensity variation, which is equivalent to the complex frequency of the radiation, is analyzed. Stability conditions of the stationary regime of the scheme are determined.

New method for measuring the IR surface impedance of metals by V. B. Zon; B. A. Zon; V. G. Klyuev; A. N. Latyshev; D. A. Minakov; O. V. Ovchinnikov

*(637-639)*. A method for measuring the IR optical properties of metals, which implies the analysis of the angular distribution of the photons emitted from the edge of a metal plate due to the conversion of thermal surface plasmons, has been theoretically and experimentally shown. In this work an increased accuracy of the proposed method in the IR region is demonstrated in comparison with more conventional methods based on the Fresnel formulas. This conclusion is supported experimentally with data obtained from the surface impedance measurement of copper in the range from 8 to 9 μm at 185°C.

Vavilov-Cherenkov like effect in metal nanofilms by V. S. Zuev; G. Ya. Zueva

*(640-643)*. The so-called surface plasmon polaritons, i.e., natural waves with a low phase velocity (much lower than the speed of light in a vacuum), exist in silver, gold, and copper nanofilms and nanowires. Electrons that are relatively slow in comparison with those that emit Cherenkov light in a homogeneous medium produce plasmons. The dispersion relations for the corresponding plasmons and the emission angles of plasmons with corresponding frequencies are calculated. It is shown that devices based on detecting Cherenkov light in nanofilms and nanowires can be used to detect low-energy electrons.

Thermal effect of pump radiation in two-layer microparticles with a semiconductor nanostructure shell by L. G. Astafyeva; G. P. Ledneva

*(644-650)*. It is established that the character of heat release inside a two-layer microparticle with a sapphire core and a semiconductor shell is inhomogeneous and is determined by the shell thickness and the core radius. Depending on the thickness of the semiconductor shell, peak values of the heat-source function are achieved in illuminated and/or shadow hemispheres near the particle surface and can exceed energy of the incident radiation by several orders of magnitude. As a result, heating can occur in the illuminated or shadow hemisphere of the microparticle, or simultaneously in both hemispheres depending on thickness of the strongly absorbing shell.

Complex resonance and relaxation oscillations in a laser by N. N. Rosanov

*(651-655)*. Resonance that arises upon excitation of a harmonic oscillator, which is exemplified by relaxation oscillations in a laser by a pump pulse with an exponentially varying modulation depth is analyzed. Limitations of the complex-resonance approach associated with simultaneous excitation of free and forced oscillations are discussed.

Determining the complex point-spread function of a scanning differential heterodyne microscope by I. M. Akhmedzhanov; D. V. Baranov; E. M. Zolotov

*(656-662)*. For a scanning differential heterodyne microscope, the two-dimensional point spread function and the pupil function are determined from experimental measurements of the intensity distribution of a probing beam. The phase components of these functions were restored from the measured distributions using the Gerchberg-Saxton algorithm. Based on the two-dimensional pupil function, the three-dimensional point-spread function is determined in the scalar approximation using the Debye integral. The aberration function of the microscope is analyzed from the viewpoint of the composition of aberrations and method of their balancing. The focusing adjustment criterion of the microscope for an object under study by the phase response from the test structure is considered.

Contents of the following issues of

*Opticheskiĭ Zhurnal*(*Journal of Optical Technology*) by L. V. Enushevskaya*(663-664)*.