Calculation of the Normal Vibrations of Benzene in the First Singlet Electron-Excited State 1 B 2u

Using the CIS/6-311+G^** method, the normal vibrations of the benzene molecule in the first singlet electron-excited state ¹ B _2u have been calculated. The algorithm of calculation of the force field in dependent coordinates by the method of generalized inversion is described. A method of autoscaling in dependent natural coordinates is suggested. For six groups of natural coordinates scaling factors have been obtained, the use of which has led to agreement between the calculated and experimental frequencies of the vibrations of benzene. The frequencies of the B _1u -symmetry-type vibrations, for which there is no experimental assignment, have been calculated. The problem of selection of the force field in dependent coordinates is discussed.     

Calculation of Plane Vibration Frequencies of the Porphin Molecule

By the DFT/B3LYP method with a 6-31G^** basis set the frequencies of normal vibrations of porphin and its five derivatives have been calculated. Scaling of the force constants for plane vibrations in independent natural coordinates has been carried out. Symmetry coordinates have been introduced and a force field for plane vibrations of the porphin molecule in independent symmetry coordinates has been obtained. Based on an analysis of special matrices and the potential energy distribution, complete matching of the plane vibration frequencies of porphin and its four isotopomers has been performed.     

Calculation of Normal Vibrations of the Tetraazaporphin Molecule and Interpretation of Quasiline Spectra

Quasiline fluorescence and fluorescence-excitation spectra of tetraazaporphin and its N-deuterated derivative in n-octane at 77 K have been investigated, and the frequencies of normal vibrations in electronic states S ₀ and S ₁ have been determined. Calculation of normal vibrations of these molecules has been done and, on its basis, the experimental data are interpreted. It is shown that in the spectra, predominantly the totally symmetric vibrations of type A _g symmetry of the point D _2h symmetry group are active. Some activation of the nontotally symmetric B _1g vibrations in the fluorescence-excitation spectra is explained by the nonadiabatic interaction of the vibrational sublevels of the excited electronic state S ₁ with the purely electronic level S ₂.     

Vibronic Structures of the Ground and Excited Singlet Electronic States of Dimethylnaphthalenes Cooled in a Supersonic Jet

Abstract

Fluorescence excitation and dispersed fluorescence spectra of jet-cooled naphthalene and 2,6-, 2,7-dimethylnaphthalenes have been measured. The frequencies of optical active vibrations in the ground and first excited singlet states have been determined. The new technique for calculation of planar vibration frequencies of polycyclic benzenoid hydrocarbons in the excited electronic states has been developed. The vibration frequencies in the ground and first excited singlet states of these molecules were calculated using the developed technique and the Ohno's model. The interpretation of vibronic spectral lines based on the comparison of the calculated and experimental data was made. The calculation rms errors for the vibration frequencies in the ground electronic states of the investigated molecules do not exceed 20 cm^?1 and are approximately 1.5 times higher for excited states without additional adjustment of parameters for individual molecules.     

Calculation of Out‐of‐Plane Vibrations of a Porphin Molecule

Using the DFT/B3LYP method with the base set 631G^**, we carried out calculation of the frequencies of the normal vibrations of porphin and of its five isotopic types. Scaling of force constants for outofplane vibrations has been performed in independent natural coordinates. The symmetry coordinates are introduced and a force field for outof plane vibrations of a porphin molecule in independent coordinates of symmetry is obtained. A new correlation of the frequencies of vibrations in the type of the symmetry B _1u for the isotopic type of the d ₂ porphin molecule is suggested on the basis of discrete analysis of the distribution of a potential energy.     

Ab initio SCF CI study of the electronic spectrum of s-tetrazine

Configuration interaction (CI) studies of ground, n→ π* and π→ π* electronically excited states are reported for s-tetrazine. The first n→ π* singlet excited state (¹ B _3u ), which is responsible for the purple-red colour of the molecule, is calculated at 2·80 eV, compared to the experimental transition energy of 2·22–2·70 eV. The singlet-triplet split of the first n→ π* states (¹ B _3u and ³ B _3u states) is calculated to be 0·76 eV.

The interaction of nitrogen lone pair orbitals (n-orbitals) is studied in terms of the ordering of the n π* excited states and found that the SCF orbital ordering is qualitatively in accord with the ordering of the n π* excited states in the CI level.

The first π→ π* excited state (¹ B _2u ) is calculated at 5·99 eV, slightly above the observed range of absorption. Numerous other high-lying singlet states as well as the triplet states have been calculated and they are used to verify several proposals relating to the excited state dynamics in the photo-physical studies of s-tetrazine.     

Density-Functional Theory Calculations of Normal Modes and Raman Intensities for Tetraazaporphin

The structure, harmonic frequencies, and nonresonance Raman intensities for porphin, tetraazaporphin (TAP), and three of its isotopomers are calculated by the density-functional theory of B3LYP/6-31G(d). Scaling of force constants for porphin in nonredundant natural coordinates is performed. The scaling factors obtained were used to predict the force field and normal modes of TAP and three of its isotopomers. Two alternative methods are used to carry out reliable assignment of the TAP frequencies: wavenumber-linear scaling method and frequency-shift method. There is good agreement between the frequencies predicted within the framework of the three methods used. The conservativeness of the out-of-plane B _2g - and B _3g -modes for porphin and TAP is examined. The Raman spectrum for TAP is simulated. A refinement of the assignment of the experimental frequencies for TAP of even symmetry types on the basis of the calculations performed is made.     

Calculation of Normal Vibrations and Interpretation of the Quasiline Spectra of Tetraazachlorin

Quasiline fluorescence and fluorescence-excitation spectra of tetraazachlorin and its N-deuterated derivative in n-octane at 77 K have been investigated and the frequencies of the normal vibrations for the electronic states S ₀ and S ₁ have been determined. Calculation of the normal vibrations of these molecules has been done and used to interpret the experimental data. Based on the results of analysis of the intensities in the spectra, the change in the structure of the molecule in the electronic state S ₁ is discussed.     

The out-of-plane vibrational modes of chlorobenzene in its ground and first singlet excited states

The study of 2699 Å electronic band system of chlorobenzene has been extended to extract out all the six b₁ and three a₂ modes in both the ground state (^eA₁) and the electronically excited first singlet state (^eB₂). The procedure of the extraction of these modes on the basis of observed sequences, cross-sequences, and overtones has especially been elaborated. Strong Fermi interaction has been observed between the vibrational level ν′_6b and combination level ν′_16a + ν′_16b in ^eB₂ state. The uniqueness of the assignments of the modes has been critically discussed.     

Density Functional Theory Calculations of Normal Modes and Infrared Intensities for Tetraazaporphin

By the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and band intensities in the IR spectra of porphin, tetraazaporphin (TAP), and three of its isotopomers have been calculated. Scaling of the force constants for porphin vibrations in nonredundant natural coordinates has been performed. The obtained scaling factors are used to predict the force field and normal modes of TAP and three of its isotopomers. To carry out a reliable assignment of the TAP frequencies, two alternative methods have been used: a wavenumber-linear scaling method and the frequency-shift method. There is good agreement between the frequencies predicted by the three methods used. The IR absorption spectrum of TAP has been simulated. Assignments of the observed experimental frequencies of TAP of odd symmetry types are suggested.     

Calculation of the IR Spectrum of Ethyl Chlorophyllide a by the Method of Density Functional

The structure, frequencies of normal vibrations, and the absolute IR intensities of ethyl chlorophyllide a have been calculated by the DFT/B3LYP/6-31G(d) density functional method. The force constants have been scaled by the Pulay method. The force field of ethyl chlorophyllide a has been obtained in independent and dependent natural coordinates. The vibrational IR spectrum of ethyl chlorophyllide a has been modeled. The experimental IR spectrum of chlorophyll a has been interpreted on the basis of the calculation performed.     

Photoinduced Intramolecular Electron Transfer and Electronic Coupling Interactions in π- Expanded Imidazole Derivatives

An intramolecular excited charge transfer (CT) analysis of imidazole derivatives has been made. The determined electronic transition dipole moments has been used to estimate the electronic coupling interactions between the excited charge transfer singlet state (¹CT) and the ground state (S₀) or the locally excited state (¹LE). The properties of excited ¹CT state imidazole derivatives have been exploited by the significant contribution of the electronic coupling interactions. The excited state intramolecular proton transfer (ESIPT) analysis has also been discussed.     

The probabilities of triplet-singlet transitions in aromatic hydrocarbons and ketones

Calculations have been performed on the probabilities of triplet-singlet transitions in benzene and acetone in connection with the decay times of the phosphorescence. The transition probability was determined from the extent to which excited singlet states are mixed with the triplet state. The assumption that in benzene the phosphorescent state has ³ B_2u properties—so that the ¹ B_1u singlet state is mixed with it-—yields the best agreement with the experimental data. In the case of acetone the phosphorescence was considered as a triplet-singlet transition in which only the electrons of the CO group are involved. In both cases the agreement with experiment is as satisfactory as in other calculations on transition probabilities, the figures for the decay times being 190 and 7 seconds for benzene and 7·8 and 0·6 milliseconds for acetone. The ratio of the calculated decay times is in good agreement with the experimental result (2·4×10⁴ and 1·2×1O⁴).     

Green's function analysis of the optically allowed vibrations of crystals: Application to diboron tetrafluoride

The Green's function method developed for the study of the molecular vibrations has been extended to the optically allowed vibrations of crystals taking B₂F₄ as an example. Isotopic rules for the i.r. active fundamentals have been derived. The force constants and the frequencies of ¹⁰B₂F₄ have also been estimated.     

Effect of the Central Atom of a Metal on the Structure and Frequencies of the Normal Vibrations of the Porphin Ligand

The structure and frequencies of the normal vibrations of the molecules of porphin, Mg-, Zh-, and Ni-porphin were calculated by the density-functional method in the B3LYP/6-31G(d) approximation, and correlation of their frequencies was made. The force fields have been obtained in dependent natural coordinates. It is shown that the majority of changes in the vibrational frequencies in transition from porphin to its metal complexes correlate with changes in the structure of the pyrrole and pyrrolenine rings of the porphin ligand.     

A deuteron magnetic resonance study of deuterated hydrazine sulphate

The Urey-Bradley force constants of the fluorosulphate radical in the ground ² A ₂ and the excited ² E electronic states and the fluorosulphate anion in the ground ¹ A ₁ electronic state were calculated using published fundamental frequencies. The analysis was carried out within Wilson's FG formalism and the constants were evaluated by a computer program based on the least-squares-fit method. The normal coordinates and the potential energy distributions were also determined. Results support the assignments of the fundamental frequencies—the ground state values for the radical have so far been obtained only from the analysis of its electronic spectrum.     

Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

Analysis of the Resonance Raman Scattering Spectra and Line Spectra of Tetrabenzoporphin Metal Complexes

On the basis of the calculations of normal vibrations of Zn– and Cu–tetrabenzoporphin, the literature spectra of resonance Raman scattering of the above compounds and the fluorescence spectra of Zn–tetrabenzoporphin are interpreted. The nonmirror character of the fluorescence and fluorescence excitation spectra is noted for some B _1g symmetry type vibrations of the point group of symmetry D _4h caused by the symmetry breakdown of a molecule in its electronic state S ₁ due to the Jahn–Teller effect.     

Calculation of the Force Field for the Benzene Molecule by the Density Functional Method in the Dependent Natural Coordinates

The B3LYP method with the 6-311 + G** basic set is used to calculate normal vibrations of the benzene molecule and its two isotopes. An algorithm for calculating the force field in the dependent coordinates is described. An autoscaling method in the dependent natural coordinates is suggested. Scaling factors are calculated for four groups of natural coordinates. Their use provided good agreement between the calculated and experimental frequencies of plane and non-plane vibrations of the benzene molecule. The force field in the benzene molecule is calculated in the dependent natural coordinates. The problem of choosing the force field in the dependent coordinates is discussed.