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doi: 10.1007/BF02578057pmid: N/A
A new approach to the analysis of the force fields of polyatomic molecules is discussed. The results of quantum chemical calculations in combination with experimental data are used in a regularizing procedure, where the nonempirical matrix of the force constants determines the stabilizer of Tikhonov's functional. The use of stable numerical methods allows the specific modeling of the force fields of polyatomic molecules with due account of rotational isomerism.
doi: 10.1007/BF02578058pmid: N/A
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.
doi: 10.1007/BF02578059pmid: N/A
A method of variational solution of anharmonic vibration problems using a mixed Morse—anharmonic basis is proposed. The basis functions are the products of the Morse oscillator eigenfunctions for vibrations of peripheral bonds, the harmonic oscillator eigenfunctions for almost harmonic skeletal and deformation vibrations, and the anharmonic basis functions for essentially anharmonic skeletal and deformation vibrations. The anharmonic basis wave functions are taken as a linear combination of the Morse and harmonic oscillator eigenfunctions. The introduction of the combined Morse—anharmonic functions allows one to factorize the solution of a problem into a series of individual blocks according to the fragmentary structure of molecules.
doi: 10.1007/BF02578060pmid: N/A
A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H2O, H2S, NO2, SO2, and ClO2 molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions.
doi: 10.1007/BF02578061pmid: N/A
A semiempirical one-parameter model is proposed to describe the dynamic and electrooptic properties of hydrogen bonds. The model allows one to determine all parameters that are necessary for calculating the vibrational spectra of complexes using the strength of intermolecular binding. The experimental IR spectra of some hydrogen-bonded systems are compared to the corresponding spectra calculated by this model. It is shown that the model is applicable to calculating the first-to-third order vibrations of any hydrogen-bonded complex.
doi: 10.1007/BF02578062pmid: N/A
Experimental data (obtained by the authors and taken from the literature) on the structure and conformations of carbonyl molecules in the ground and lower excited electronic states are presented. The structure of carbonyl fragments, the orientation of substituent groups, the energy of the molecules in excited states, and the potential functions of the internal rotation and inversion are considered. The structural similarities of the molecules are discussed.
Gastilovich, E.; Mikhailova, K.; Ni, B.
doi: 10.1007/BF02578063pmid: N/A
This paper deals with the mechanisms of localization of Franck-Condon vibronic coupling of πσ*- or πlπ*-orbital type in a few vibrational modes, (LVM) in excited electronic states of polyatomic molecules. The analysis of vibronic coupling uses highly symmetric basis sets (for representing MO structures and normal coordinates ξR) as well as simplified models that relate the shift ΔR of the electron potential minima along the normal coordinates to the MO structure and to ξR in the form of analytical expressions. The modes that are active in LVM are determined from the experimental luminescence spectra. These ideas about approximately high local symmetry of vibronic coupling in benzene fragments as well as the estimates of ΔR depending on variations in the MO structure explain the experimental results.
doi: 10.1007/BF02578064pmid: N/A
This paper studies changes in the matrix elements (Ump) of spin-orbit coupling between the nπ*- and ππ*-states, which are induced by the (“chair,” “bath”) distortions of the nuclear configurations of molecules. The analysis is performed for acridine molecules in which the n-pz atomic orbital (AO) of the heteroatom is directed along the C2 symmetry axis. Earlier, for molecules with a planar nuclear configuration of C2v symmetry and with the heteroatom lying on the C2 axis, we established the dependence of Ump on the symmetry of ππ*-states [Γ(ππ*)=A1 or B2]. The values of Ump differ by more than one order of magnitude; this is in line with the difference between the interconversion rate constants (Kisc; two or three orders). In this work we have found that this contrast in Ump (and, accordingly, in Kisc) is retained when the nuclear configuration of the acridine molecule is distorted to the “chair” (AC-A) configuration, although the individuality of both molecular orbital types (nσ-MO and π-MO) and states nπ* and ππ* is annihilated to a certain extent. For the “bath” (AC-B) conformation the difference in Ump considerably diminishes. Reasons for the changes in the matrix elements of spin-orbit coupling and rate constants of the S-T conversion are analyzed. The available energy level diagram is critically analyzed, and a slightly different diagam as well as a scheme of nonradiating deactivation of acridine are suggested.
doi: 10.1007/BF02578065pmid: N/A
Correct assignment of calculated and experimental frequencies, as well as corservation of the initial assignment in case of a random coincidence of two frequencies during the solution of an inverse spectral problem, are important problems in spectroscopy of polyatomic molecules. Vibrations are classified according to their form, which is thought to be a more reliable basis for assignment than frequency. We offer a PC program to determine the type of vibrations according to their form (obtained by solving a direct vibrational problem) in a given system of vibrational basis set functions. Optimization of systems of basis set functions for molecules with six-membered rings is discussed.
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