Symmetry coordinates of nonrigid molecules

Motivated by Altmann’s definition of symmetry groups of nonrigid molecules, Wigner’s method of obtaining the symmetry coordinates of a molecule is extended to nonrigid molecules with free internal rotations. The molecule BF₂ CH₃ is exemplified.     

Barriers to internal rotation and tunnelling splittings of the torsional states in the HO(CH2)OH,DO(CH2)OH and DO(CH2)OD molecules

Torsional states caused by vibrations of hydroxyl groups in the methanediol molecule and its two deuterated analogues – DO(CH₂)OH and DO(CH₂)OD were analysed at MP2/cc-pVTZ and CCSD(T)/cc-pVQZ levels of theory. In the first case, 2D PES and 2D surfaces of kinematic coefficients were calculated with geometry optimisation for all other geometric parameters, and in the second case, only the energy of optimised configurations at the MP2/cc-pVTZ level of theory was determined. Then 2D PES was recounted to the complete basis set (CBS) limit by extrapolating the results of calculations at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory The calculated values were then averaged over four equivalent points on the coordinate plane. Hamiltonian matrices were constructed using DVR and Fourier methods. After their subsequent diagonalization, the energies of the stationary torsional states were computed. Their classification by C_2V(M) and C_S(M) molecular symmetry groups has been performed. The splitting values due to the tunnelling of the thirty most deeply located torsional states in the three studied molecules were also determined. The torsional states, internal rotation barriers, and tunnelling frequencies in the molecules of methanediol and hydrogen trioxide were compared.     

Analysis of torsional vibrations of an ethane molecule

Based on the solution for the Mathieu equation, we obtained wave functions for the internal rotation of an ethane molecule that satisfy the symmetry properties of the group G₃₆. We calculated the frequency of the principal torsional transition (273 cm⁻¹). The types of symmetry of the energy levels and transition probabilities in IR and Raman spectra are determined. We note drawbacks of divisible permutable-inverse nuclear groups and the groups of molecular symmetry associated with their construction, as well as difficulties that appear when equivalent rotations are used. The possibility of avoiding the application of an extended group is indicated. Belarusian State University, 4, F. Skorina Ave., Minsk, 220050, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 26–31, January–February, 1997.     

Calculation and analysis of the frequencies of normal vibrations of 2,3-Di-O-nitro-methyl-β-D-glucopyranoside

A calculation of the frequencies and forms of the normal vibrations of the 31-atom molecule 2,3-di-O-nitromethyl-β-D-glucopyranoside has been performed. Particular emphasis has been placed on the interpretation of the strongest bands in the spectrum of 2,3-di-O-nitro-methyl-β-D-glucopyranoside, which are due to vibrations of the nitrate groups. The present work has been reported at the IV International Congress of theoretically competent chemists, Jerusalem (Israel), July 7–12, 1996. B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 724–728, November–December, 1997.     

Analysis of electronic vibration spectra of tetrabenzoporphin molecules on the basis of calculations of their normal vibrations

Quasi-line fluorescence and fluorescence-excitation spectra of tetrabenzoporphin (H₂TBP) and its deuterated derivative (D₂TBP) in n-octane at 77 K were measured and analyzed. A calculation of normal vibrations of the H₂TBP and D₂TBP molecules has been performed. The normal vibrations of these molecules were calculated with the use of the valence force fields of porphin and phenanthrene (the direct spectral problem was solved). Good agreement between the calculated and measured frequencies of the investigated normal vibrations has been obtained without correction of the transfered force constants. A detailed interpretation of the fluorescence spectra obtained is presented. It is shown that on deuteration of H₂TBP, the behavior of the quasi-lines in the fluorescence-excitation spectra in the region of resonance with the S₂←S₀ transition becomes more complex. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 3, pp. 375–382, May–June, 1999.     

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.     

Calculation of the normal modes of CH3OP(s)Cl2 and (CH3O)2P(S)Cl

Frequency and form are deduced for the normal modes. The calculated and observed deformation frequencies of the CH₃O group agree only if the force field of that group has C_S symmetry. The C-O, P-O, P=S, and P-Cl modes are examined for characteristic behavior. The integral intensities of the corresponding bands are reported for trichlorothiophosphate, methyldichlorothiophosphate, dimethylchlorothiophosphate, and trimethylthiophospate.The behavior of the integral intensity of the P=S band is discussed.     

Vibrational properties of polysiloxanes: from dimer to oligomers and polymers. 1. Structural and vibrational properties of hexamethyldisiloxane (CH3)3SiOSi(CH3)3

The hexamethyldisiloxane (HMDS)(CH₃)₃SiOSi(CH₃)₃ molecule is one of the basic building blocks of silicones and polysiloxanes, as it is used for many chain terminations. Far‐infrared, mid‐infrared, and polarized Raman spectroscopic studies, combined with quantum chemical calculations and vibrational normal mode analyses, were performed for the HMDS molecule. The internal rotation of the trimethylsilyl group was calculated to be nearly free. The large‐amplitude bending motion was found very anharmonic with a barrier to linearity below 4 kJ/mol. Exhaustive assignments of observed wavenumbers have been performed on the basis of calculated potential energy distributions (PED) and atomic displacements. By isotopic ¹⁶O ¹⁸O substitution, the Si O Si symmetric and antisymmetric stretching modes shift from 521 and 1074 cm⁻¹ to 514 and 1028 cm⁻¹, respectively. This spectroscopic observation provides convincing evidence that the molecule is bent with an angle estimated at around 150°. The comparison of HMDS vibrational spectra with the vibrational spectra of some siloxane derivatives reveals strong effects of silicon substituents on the Si O Si symmetric and antisymmetric stretchings. The Si O Si siloxane bridge group plays a key role in the properties of the HMDS molecule and may also account for some important silicone polymer properties such as their very low glass transition, their high compressibility, and their low surface tension. Copyright © 2009 John Wiley & Sons, Ltd.     

Structures and thermochemistry of methyl ethyl sulfide and its hydroperoxides: HOOCH2SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH,and radicals

Hydroperoxides and the corresponding peroxy radicals are important intermediates during the partial oxidation of methyl ethyl sulfide (CH₃SCH₂CH₃) in both atmospheric chemistry and in combustion. Structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔH_f^o, S^o and C_p(T)) of 3 corresponding hydroperoxides CH₂(OOH)SCH₂CH₃, CH₃SCH(OOH)CH₃, CH₃SCH₂CH₂OOH of methyl ethyl sulfides, and the radicals formed via loss of a hydrogen atom are important to understanding the oxidation reactions of MES. The lowest energy molecular structures were identified using the density functional B3LYP/6‐311G(2d,d,p) level of theory. Standard enthalpies of formation (ΔH_f^o₂₉₈) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods. Isodesmic reactions were used to determine ?H_f^o values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31G(d,p) level theory. Contributions for S^o₂₉₈ and C_p(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions. The recommended values for enthalpies of formation of the most stable conformers of CH₃SCH₂CH_2, CH₂(OOH)SCH₂CH₃, CH₃SCH(OOH)CH₃, and CH₃SCH₂CH₂OOH are ?14.0, ?33.0, ?37.2, and ?32.7 kcal/mol, respectively. Group additivity values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxides. Groups for use in group additivity estimation of sulfur peroxide thermochemical properties were developed.     

Existence and transition properties of the three-deuteron muonic molecule (3d,2e -,μ-)

We calculated the energy and the size of the three-deuteron muonic molecule (3d,2e ^-,μ^-) = D₃μ. It turns out that this system possesses two equilibrium positions, one at distances typical for muonic molecules, the second one at the usual molecular size. We show, moreover, that the fusion probability of the three deuterons is considerably enhanced due to the existence of a ⁶Li^* threshold resonance. Our estimates indicate that this probability is considerably higher than the decay rate of the competing Auger transition. This revised version was published online in August 2006 with corrections to the Cover Date.     

丙酮分子团簇(CH3COCH3)n(n=6,7)的稳定构型

用密度泛函(DFT)理论方法研究了丙酮分子团簇(CH3COCH3)n(n=6,7)的稳定构型及与各构型相应的能量。根据稳定构型的稳定性顺序推测了丙酮分子团簇结构的增长趋势。     

CH(CH3)3 的耦合CH伸缩和弯曲振动的纠缠

以不同的多极量子数和初态,我们用约化的线性熵研究CH(CH3)3 的耦合CH伸缩和弯曲振动的动力学纠缠,结果表明：在多极量子数大于等于３时,态|0,2N>的最大纠缠能在较短的时间内得到;态|N,0>的纠缠振荡频率比态|0,2N>的要小,而振荡的幅度要大．     

Structural and thermochemical properties of methyl ethyl sulfide alcohols: HOCH2SCH2CH3, CH3SCH(OH)CH3, CH3SCH2CH2OH,and radicals corresponding to loss of H atom

Sulfide alkoxy radicals are important intermediates during the partial oxidation of alkyl sulfides in atmospheric chemistry and in combustion. The atmospheric reaction sequence to formation of the alkoxy radicals includes (1) initial reaction with OH to create a radical on a carbon site, (2) the carbon radical then associates with ³O₂ to form a peroxy radical, and (3) an NO radical reacts with the peroxy radical to form an alkoxy radical (RO?) plus NO₂. This study determines structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (Δ_fH°, S°, and C_p(T)) of 3 corresponding alcohols HOCH₂SCH₂CH₃, CH₃SCH(OH)CH₃, and CH₃SCH₂CH₂OH of methyl ethyl sulfides studied in order to characterize the thermochemistry of the respective alkoxy radicals. The lowest energy molecular structures were calculated using the B3LYP density functional level of theory with the 6‐311G(2d,d,p) basis set. Standard enthalpies of formation (Δ_fH°₂₉₈) for the radicals and their parent molecules were calculated using B3LYP/6‐31 + G(2d,p), CBS‐QB3, M062x/6‐311 + g(2d,p), and G3MP2B3 methods. Isodesmic reactions were used to determine ?_fH° values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31 + G(d,p) level theory. The contributions for S°₂₉₈ and C_p(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by CBS‐QB3 calculations, with contributions from torsion frequencies replaced by internal rotor contributions. Group additivity and hydrogen bond increment values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxide molecules and their radicals.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

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.