Modeling and Calculation of the Dynamics of Spectra with Allowance for Isomerization of Complex Molecules

A semiempirical parametric method for modeling of dynamic (time-resolved) electron-vibrational spectra of complex molecules with allowance for isomer-isomer transformations is proposed. It is based on the method developed earlier for construction of three-dimensional spectra of complex molecules without regard for isomer-isomer transformations. All the matrix elements necessary for calculation of spectra can be determined by the methods developed earlier. The time dependence of the population of a large number of vibronic levels has been determined using the iteration numerical method of integrating kinetic equations. Handy computational algorithms and a specialized software for a personal computer have been developed. The computer experiments conducted have shown that the method proposed can be used for modeling of dynamic spectra of complex molecules with allowance for their isomer-isomer transformations in the real-time scale.     

Improvement of the parametric method of the theory of vibronic spectra of polyatomic molecules: Absorption spectra and the structure of butadiene, hexatriene, and octatetraene in the excited state

The structure of the excited states and absorption spectra of butadiene, hexatriene, and octatetraene are calculated by the parametric method of the theory of vibronic spectra using models of the first-and second-order approximations. It is shown that these molecular models adequately reflect the molecular structure and allow one to predict quantitatively the shape and fine vibrational structure of the absorption spectra. When passing to the second-order approximation, only two additional (angular) parameters are used. These parameters are transferable in the series of polyenes. Compared to the first-order approximation model, the second-order approximation model more accurately takes into account the angular deformations of polyenes upon their excitation and describes the intensity distribution in the vibrational spectrum, including weak lines. In addition, the calculations also quantitatively predict spectral variations in the molecular series. The parametric method is more efficient for modeling polyatomic molecules in the excited states and their vibrational spectra compared to other semiempirical and ab initio methods.     

On the stability of parameters of molecular models in the parametric method of the theory of vibronic spectra

We have studied the stability of the system of parameters used in the parametric method of the theory of vibronic spectra of polyatomic molecules with respect to whether the initial structural-dynamic model of the ground state of a molecule is formed either by the fragmentary method or by direct quantum-chemical calculation. Modeling of excited states and spectra of the stilbene-h ₁₂ and stilbene-d ₁₂ molecules showed that, although the initial models of the ground states are significantly different, calculated changes in the geometry that occur upon excitation and electronic-vibrational spectra of the models are close and quantitatively agree with experiment. This indicates that the parameters of the method are stable and are applicable for performing predictive calculations of vibronic spectra based on models of the ground states created by different methods. We show that the fragmentary method has a considerable advantage, since models created by this method take into account the continuity of the structure in series of related compounds and calculations can be easily performed for molecules of arbitrarily high complexity. We show that direct quantum-chemical calculations are important in the case of molecules with unknown structural-dynamic models of fragments in the ground states.     

Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids

We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schrödinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.     

Interpretation of the vibrational spectra of polycrystalline adenine

The infrared and Raman spectra of the tetramer of the adenine N₉H are calculated and analyzed. The vibrational spectra of polycrystalline adenine are interpreted. It is demonstrated that the method for calculating the vibrational spectra of molecular complexes formed by hydrogen bonds can be used for interpreting the vibrational spectra of polyatomic molecules in the solid state.     

Sequential spectral lines and intensity distribution in electronic-vibrational bands of free polyatomic molecules

The intensity distribution, the spectral band profile, and the temperature dependences of spectral characteristics of bands in the electronic-vibrational (vibronic) spectra of free polyatomic molecules are studied based on the concept of sequential lines (SLs) as constituent elements of these bands. It is shown that the intensity distribution in a separate electronic-vibrational band is defined by the convolution of an SL profile with the frequency distribution function of sequential transitions. Expressions for the intensity distribution in homogeneously and inhomogeneously broadened electronic-vibrational bands are derived, and specific features of their spectral behavior are determined. Using the latter results, distinguishing features or criteria of the character of broadening of the vibronic spectra of free polyatomic molecules are formulated.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

Elementary sequential spectral line and statistical properties of the thermal reservoir of free polyatomic molecules

The formation of vibronic spectra of free polyatomic molecules is studied by taking the concept of sequences as constituent elements of vibronic bands. Statistical properties of the thermal reservoir of oscillators, which randomly perturbs optically active transitions in a polyatomic molecule, are considered. The spectral shape, position, and width of the elementary sequential lines (ESL) are determined. It is shown that the ESLs have a Lorentzian shape if the perturbations are short-term and the pulse shape is symmetric about its origin. The position of the ESLs depends on the total vibrational energy of the thermal reservoir of oscillators in the initial electronic state of a molecule. The analysis of the statistical properties of the thermal reservoir of polyatomic molecules shows that one should distinguish between the ESL linewidth of individual molecules and the ESL linewidth averaged over the entire thermal ensemble. It is shown that individual molecules of the thermal ensemble that have different total vibrational energies are characterized by different widths of the ESLs. Consequently, the exchange and redistribution dynamics of the vibrational energy stored in the initial electronic state should manifest itself in the difference between the single-molecule ESL widths measured at different instants in time.     

Calculation and interpretation of the fine structure fluorescence spectra of anthracene upon resonance excitation of vibronic states

The vibrational structure of the spectra of fluorescence of anthracene obtained upon resonance excitation of vibronic states is calculated and analyzed by the parametric method of the theory of the vibronic spectra of complex molecules. The theoretical and experimental spectra agree qualitatively with each other, which indicates that this method of modeling such spectra is efficient. The parameterization of molecular models obtained upon calculation of the ordinary fluorescence and absorption spectra is completely applicable to the calculation of the fluorescence spectra considered. A total interpretation of the spectra is presented.     

Intracavity Laser Spectroscopy of NiCl System G: Identification of a [13.0] Π3/2 State

The (0,0) vibronic band of NiCl system G with a bandhead near 12 961 cm⁻¹ was recorded at high resolution in absorption using intracavity laser spectroscopy (ILS). For the ILS absorption spectra, the NiCl molecules were produced in a nickel hollow cathode, operated with a small amount of CCl₄, and line positions were referenced to iodine spectra. Fourier transform (FT) emission spectroscopy was used to record an extensive region of the spectrum used in a vibronic analysis of system G. For the FT spectra, excited NiCl molecules were produced in a high-temperature King-type carbon tube furnace. We show that this transition is the (0,0) vibronic band associated with a newly identified ²Π_3/2 excited state and the X²Π_3/2 ground state. The molecular constants for the new ²Π_3/2 electronic state are derived from the rotational analysis. Improved vibronic constants for the band are obtained from analysis of the FT spectra.     

Application of quantum mechanical method to analysis of the intensity distribution in spectra of resonant hyper-Raman scattering of low-symmetry molecules

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.     

Computer Resolution and Franck-Condon Analysis of the Electronic Absorption Spectrum of KMnO4 in Water

Abstract

The electronic absorptíon spectrum of KMnO₄ in water solution was analyzed. The spectral contour was resolved into component bands and then Franck-Condon approach was applied. In the investigated range of 13000–48000 cm^?1 a presence of three structureless and of two vibronic strong bands was stated. The change in the Mn-O equilibrium bond length was found to be 10.5pm for 2e·1t₁ transition (vibronic band about 18000cm^?1) and to be 16pm for the 2e·3t₂ transition (vibronic band about. 30000cm_?1). The appropriate wavenumber of the vibrational mode in these excited electronic states was found to be 735cm^?1 and about 780cm^?1, respectively. The ground electronic state wavenumber of the totally symmetric vibrational mode was fitted to be equal to 828cm^?1. Details of the proposed method of computer elaboration of electronic spectra with vibrational structure were discussed.

Electronic absorption spectra of some inorganic comppunds consist of a number of strongly overlapped bands due to their vibronic structure.^1–5 A detailed analysis of spectral contours of such compounds provides some useful information about their structure in both ground excited electronic states.

The electronic spectrum of permanganate ion is the typical example of vibronic spectra.¹ The main part of the past works based on the analysis of permanganate ion spectra in low temperatures and different polarizations. In such conditions the vibronic structure is rather good resolved and can be effectively studies.^1,3,6 Spectra of solutions as a rule are relatively poor resolved so their analysis has to be more sophisticated.

The main purpose of this work is a presentation of a new computer method for an effective study of vibronic spectra of solutions. This method has been applied to the electronic absorption spectrum of KMnO₄ in water. The method allowed us to fit the geometric parameters of spectral contour, to establish the origins and parameters of two progressions in the UV/VIS range as well as to calculate the changes in the Mn-0 equilibrium bond lengths and vibrational energy resulting from the electronic excitations of the soluted permanganate ion.     

Extension of the MIRS computer package for the modeling of molecular spectra: From effective to full ab initio ro-vibrational Hamiltonians in irreducible tensor form

The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version [Nikitin AV, Champion JP, Tyuterev VlG. The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules. J Quant Spectrosc Radiat Transf 2003;82:239–49.] was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possibilities for spectra calculations and modeling by getting rid of several previous limitations particularly for the size of polyads and the number of tensors involved. It allows dealing with overlapping polyads and includes more efficient and faster algorithms for the calculation of coefficients related to molecular symmetry properties (6C, 9C and 12C symbols for C_3v, T_d, and O_h point groups) and for better convergence of least-square-fit iterations as well. The new version is not limited to polyad effective models. It also allows direct predictions using full ab initio ro-vibrational normal mode Hamiltonians converted into the irreducible tensor form. Illustrative examples on CH₃D, CH₄, CH₃Cl, CH₃F and PH₃ are reported reflecting the present status of data available. It is written in C++ for standard PC computer operating under Windows. The full package including on-line documentation and recent data are freely available at http://www.iao.ru/mirs/mirs.htm or http://xeon.univ-reims.fr/Mirs/ or http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/MIRS.html and as supplementary data from the online version of the article.     

Fourier Transform and Intracavity Laser Spectroscopy of NiCl System H: Identification of a [12.3] Σ State

The (0,0) vibronic band of NiCl system H near 12 259 cm⁻¹ was recorded at high resolution in absorption using intracavity laser spectroscopy (ILS) and in emission by Fourier transform (FT) spectroscopy. Though it was originally assigned in 1962 as the (1,1) vibronic band of ²Π_3/2-X²Δ_5/2, we have shown that this transition is the (0,0) vibronic band associated with a newly identified ²Σ⁺ excited state and the X²Π_3/2 ground state. The molecular constants for the new ²Σ⁺ electronic state were derived from the rotational analysis. For the ILS absorption spectra, the NiCl molecules were produced in a nickel hollow cathode, operated with a small amount of CCl₄. Line positions were referenced to iodine spectra observed from a heated extracavity cell using the intracavity laser as the light source. For the FT spectra, excited NiCl molecules were produced in a King-type carbon tube furnace.     

A new formulation of the quantum problem in the theory of spectra of polyatomic molecules

A new approach to calculate energy levels and wave functions of polyatomic molecules with a definite geometric structure of the system assumed from the very beginning has been suggested. The effect of nuclear vibrations has been taken into account explicitly when separating variables in the Hamiltonian of the electronic state problem. The problem of the energy matrix formation has been discussed. It has been shown that some common patterns in higher-order vibrational spectra and in vibronic spectra can be explained without using concepts of anharmonism and changing the potential well parameters for an electron-excited state as compared to those for the ground state.     

Pulsed Doppler-free two-photon spectroscopy of polyatomic molecules

Doppler-free two-photon electronic spectra of a large polyatomic molecule are recorded for the first time with pulsed laser radiation of near Fourier-transform limited bandwidth (Δv～100 MHz). The resolution obtained is sufficient to resolve individual rotational lines. Due to the high density of these rotational transitions a strong Doppler-broadened background is observed, which is, however, subtantially reduced by suitable choice of photon polarizations. Different vibronic bands of benzene (C₆H₆) are investigated and very accurate rotational constants are found.     

Methods for calculation of ir intensities in polyatomic molecules: A comparative study

Various methods for calculating intensities in ir spectra of polyatomic molecules are reviewed against the current theory of small vibrations of polyatomic molecules. The valence optical theory based on the representation of the molecular dipole moment as the sum of dipole moments of bonds has been shown to be erroneous. Of the two calculation procedures which use no assumptions on the molecular dipole moment, the Mayants-Averbukh method is shown to have certain advantages over the polar tensor method.     

Calculation of the vibronic spectra and structure of methylstyrene in the excited state by the parametric method

Calculations of the excited-state structure and of the absorption and radiation spectra of trans-β-methylstyrene are performed by the parametric method for models of the first and second approximations. Only three of the parameters, being constant in a series of related compounds, are used for molecular fragments. In the calculation, the main regularities observed in electronic spectra are reproduced, and an analysis and interpretation of their fine vibrational structure are carried out. The use of the model of the second approximation with a single additional parameter allows more accurate reproduction of angular deformations of the molecule under excitation and of the characteristic changes observed in the low-frequency spectral region in the series of diphenyl polyenes, stilbene, styrene, and methylstyrene molecules. It is shown that the parameters of the second approximation (just as of the first one) possess the transference property in the homological series of molecules. In modeling complex molecules in excited states and their vibronic spectra, the parametric method is more efficient than the ab initio one. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp. 148–153, March–April, 2000.