Ab initio Calculation of Normal Vibrations of Chlorobenzene in the First Singlet Electron-Excitebd State 1 B 2

An analysis of experimental assignments of the frequencies of normal vibrations of chlorobenzene in the first singlet electron-excited state ¹ B ₂ has been performed with the use of two quantum-mechanical prediction methods — the method of frequency shifts and the method of transfer of scaling factors. Based on the data of this analysis, a new assignment of a number of vibration frequencies has been made. Normal vibrations of the chlorobenzene molecule in the excited state have been calculated by the CIS method with a 6-311 + G ^** basic set. An algorithm of autoscaling in dependent natural coordinates has been proposed. The force field of chlorobenzene has been scaled in dependent natural coordinates. It is shown that the scaling factors of benzene in the electron state ¹ B _2u can be used for calculating the frequencies of normal vibrations of chlorobenzene in the first singlet excited state ¹ B ₂.     

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.     

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 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.     

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.     

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.     

Comparison of Theoretical Methods and Basis Sets for ab initio and DFT Calculations of the Structure and Frequencies of Normal Vibrations of Polyatomic Molecules

The dependence of the quality of calculation of the geometric parameters and frequencies of normal vibrations on the choice of the theoretical method and the basis set of Gaussian functions has been investigated within the framework of four approximations (DFT/B3LYP, HF, MP2, MP3), using benzene and s-triazine molecules as an example. It has been shown that the molecular parameters calculated using the basis set without polarization functions within the framework of any of the above theoretical methods agree poorly with the experimental data. It has been concluded that the use of the basis set 6-31G(d) within the framework of these methods with allowance for the electron correlation for calculating the geometric parameters and frequencies of normal vibrations of polyatomic cyclic compounds is most optimum in terms of the relation between the expenditure of time and the quality of the calculation. The coefficients of linear scaling of frequencies have been obtained by the DFT/B3LYP method for 22 basis sets that were tested on porphin, pyrrole, indene, and pyridine molecules. Atypically large errors in determining the frequencies of some benzene and s-triazine vibrations have been obtained in a number of quantum-mechanical calculations with large basis sets. The changes in the force field for these cases have been investigated with the example of the benzene molecule.     

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.     

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.     

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 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.     

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.     

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).     

The magnetic circular dichroism spectrum of the 1 B 2u ←1 A 1g transition of benzene in the vapour phase

The magnetic circular dichroism (MCD) spectrum of the ¹ B _2u ←¹ A _1g transition of benzene has been measured in the vapour phase. Many of the bands due to transitions between single vibronic levels display A terms. It has been shown that the angular momentum arises by vibronic mixing both of the ¹ E _1u state with the ¹ B _1u state and of the ¹ E _2g states with the ¹ A _1g ground state by e _2g vibrations. The magnitudes and signs of the experimental and calculated ratios, A/D, for the A ₀ ⁰ vibronic origin are in excellent agreement. Two strong MCD progressions of opposite sign with B-term dispersion have been observed in regions of low absorption. These are identified with vibronic origins due to the v ₈ and v ₉ e _2g modes. By contrast the MCD spectrum of hexadeuterobenzene vapour has a much lower magneto-rotational strength and displays none of the striking features of the benzene MCD spectrum.     

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.     

Atypical intensity distribution in the Raman spectrum of 9,10-anthraquinone

The structure, the frequencies of the normal vibrations, and the absolute intensities of the bands in the IR and Raman spectra of 9,10-anthraquinone and its four symmetrical isotopomers are calculated in terms of the DFT/B3LYP method with the 6-31G(d) basis set. The effective harmonic force field of 9,10-anthraquinone is found by the Pulay method. A technique for directly obtaining the effective force fields without using experimental data on the frequencies of fundamental vibrations is proposed. An atypical intensity distribution in the Raman spectrum of 9,10-anthraquinone between two totally symmetric A _g and two nontotally symmetric B _3g vibrations is found. A new interpretation of these four experimentally observed vibrational Raman bands is proposed.     

Transverse scattering of radiation upon focusing of pump laser beam to line in experiments on X-ray laser

The force matrix of the SO₂ molecule is calculated without using a priori assumptions on the nature of the force field. The calculations are performed using a comparatively new 3N-matrix method based on the experimental frequencies of characteristic normal vibrations of ³²S¹⁶O₂, ³²S¹⁸O₂, and ³⁴S¹⁶O₂ molecules. It is shown that the direction of the chemical bond between chemically bound S and O atoms does not coincide with the direction of the straight line that connects the nuclei of these atoms. The angle between these directions (deviation angle) is determined. In the approximation of harmonic vibrations, the deviation angle is Δ = 1.092°. The effect of the anharmonicity of vibrations on the deviation angle is evaluated.     

Theoretical prediction of vibrational spectra: The out-of-plane force field and vibrational spectra of pyridine

The harmonic force field for the out-of-plane vibrations of pyridine has been calculated from ab initio Hartree-Fock wavefunctions obtained with a 4–21 basis set of contracted Gaussians. To account for systematic errors, the calculated force constants were scaled, using only two independent sclae factors which were transferred unchanged from benzene. The resulting scaled quantum mechanical force field, which is strictly a priori in that it is not based on any experimental data on pyridine, predicts the 64 out-of-plane fundamental frequencies of pyridine and its deuterated isotopomers of C_2v symmetry with a mean deviation from experiment of only 8.5 cm^?1. Addition of polarization functions to the basis set for the nitrogen atom and refinement of the two scale factors by fitting them to the observed pyridine spectra produce no significant improvement in the fit. Assignments of the vibrational spectra are discussed.     

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.     

Quantum-mechanical calculation of the frequencies of the normal vibrations and intensities of the IR and Raman bands of pyridine N-oxide

The frequencies of the normal vibrations and the intensities of the bands in the IR and Raman spectra of pyridine N-oxide and three of its isotopomers are calculated with the density functional theory by using the Becke exchange and Lee-Yang-Parr correlation functionals with the 6?311+G(d, p) basis set. The scaling of the force constants in independent natural coordinates is performed. The force field of pyridine N-oxide in independent symmetry coordinates is obtained. A new assignment of the frequencies of some vibrations in the isotopomers is proposed. On the basis of the calculated frequencies and intensities, the vibrational IR and Raman spectra of pyridine N-oxide are modeled.