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.     

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 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 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.     

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.     

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.     

Application of the Keating Bendings to the In-Plane Vibrations of Naphthalene and Benzene

An approximate force field was deduced for the in-plane vibrations of naphthalene in terms of five parameters corresponding to the coordinates: C-C and C-H stretchings, CCC (two types) and CCH Keating's bendings. Calculated frequencies were compared to observed data. On the other hand, these results were compared to those where Decius' bendings were applied. The set with Keating's bendings proved to be the superior one.

The corresponding force fields were applied to benzene, and the same general conclusion was reached.     

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.     

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.     

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.     

简正模型势函数法计算C2v三原子分子力场

采用简亚模型势函数方法,在ａｂ ｉｎｉｔｉｏ水平上计算了Ｈ２Ｏ和Ｈ２Ｓ的分子内价值标和简正内坐标的谐性力学数矩阵对角工根据这两个坐丝毫宰的关系导出了谐性力常数矩阵的其它对角和非对角元。由于避免了三格点的ａｂ ｉｎｉｔｉｏｎ计算拟合,因此计算量较少。由此计算出的分子谐振动频率与实验 令人满意的。还在简正内坐标的简单价力场近似下,计算了力常数和谐振频率。     

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 ethylbacteriochlorophyllide (A) by the density functional method

The structure, the frequencies of the normal vibrations, and the absolute IR intensities of ethylbacteriochlorophyllide (A) are calculated in the approximation of the hybrid density functional B3LYP with the 6–31 G(d) basis set. The scaling of the quantum-mechanical force constants is performed by the Pulay method. The effective force field of ethylbacteriochlorophyllide (A) in the redundant and nonredundant coordinates is obtained. The vibrational IR spectrum is modeled. On the basis of the calculations performed, the experimentally determined IR spectrum of bacteriochlorophyll (A) is interpreted.     

Condensed Aromatics. Part IX. Mean Amplitudes and Perpendicular Amplitude Coefficeints for Benzene and Naphthalene

An approximate force field for the in-plane and out-of-plane vibrations of aromatic molecules is applied to benzene and naphthalene. Refined force fields for the same molecules were produced to make them consistent with experimental frequencies. Calculated mean amplitudes of vibration and perpendicular amplitude correction coefficients are discussed. The latter quantities are given here for the first time.     

Reduction of the excess of natural coordinates in the calculation of crystal lattice vibrations

The simplification of the procedure of setting up the equations of crystal lattice vibrations in terms of dependent natural vibration coordinates by choosing a rational coordinate system and introducing symmetrical linear combinations of coordinates, thus reducing the excess of coordinates, is considered. Vibrations in a plane square lattice are used to illustrate the method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 63–67, September, 1984.     

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.     

Vibrational Spectra of the Closed Form of a Molecule of Indoline Spiroanthraceneoxazine

In an approximation of the generalized valence force field, the frequencies and forms of the normal vibrations of the free molecule of spiroanthraceneoxazine (SAO) are calculated. The vibrational spectra of SAO are measured: the IR absorption spectra in an NaCl disk and the Raman spectra in a KBr disk. The calculated and experimental data were correlated with the aid of a method of refined initial data. The results obtained agree with the calculated and experimental spectra of model and related compounds. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 5, pp. 576–571, September–October, 2005.     

Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules

The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.     

Matrix method for the determination of scaling factors for quantum-mechanical force fields

A computer-assisted method for the calculation of scaling factors for refining the quantum-mechanical force fields of polyatomic molecules by the Pulay technique is suggested. The method is an iteration procedure and does not involve the calculation of derivatives of the frequencies of vibrations with respect to the scaling factors. The correlation between the experimental and calculated frequencies upon scaling of the force field is discussed.     

The vibrational force field of halogenated aromatic molecules: In-plane vibrations of benzene and fluorobenzenes

The force fields for the in-plane vibrations of benzene and its fluoro derivatives are determined using the overlay technique. Between 36 and 39 parameters were allowed to vary in different fields and in all cases convergence on the experimental frequencies was smooth and rapid. Only one solution could be found. This solution agrees extremely well with the benzene field of Duinker and Mills. The variation of diagonal force constants in an internal valence coordinate basis set with fluorine substitution in the coordinate environment is determined. The variation in certain force constants is considerable. Thus for the CF stretching constant it is 12% for replacement of two hydrogens by two fluorines. Attempts are made to interpret these variations. Various aspects of the force constant problem for benzene are discussed.