Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, trimethylgermyl, and trimethylstannyl derivatives of 3,3-dimethylcyclopropene VIII. 3,3-Dimethyl-1,2-bis-(trimethylstannyl)cyclopropene

The quantum mechanical force fields of 3,3-dimethyl-1,2-bis-(tert-butyl)cyclopropene (I), 3,3-dimethyl-1,2-bis-(trimethylsilyl)cyclopropene (II), 3,3-dimethyl-1,2-bis-(trimethylgermyl)cyclopropene (III), and 3,3-dimethyl-1,2-bis-(trimethylstannyl)cyclopropene (IV) were calculated at the HF/3-21G*//HF/3-21G* level. The scale factors which were optimized previously for the HF/3-21G*//HF/3-21G* quantum mechanical force field of 3,3-dimethyl-1-(trimethylsilyl)cyclopropene were used for correction of the force fields of these molecules. Good agreement between the frequencies calculated from these scaled force fields and the well-analyzed and assigned experimental frequencies of II and III suggests the transferability of these scale factors and the possibility of the spectroscopically accurate prediction of the vibrational spectrum of IV. Some regularities in the changes of the vibrational frequencies were found for this molecular series.     

Vibrational spectra and ab initio analysis of tert-butyl,trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethylcyclopropene. I. 3,3-Dimethyl-1,2-bis(tert-butyl)cyclopropene

The geometrical parameters of 3,3-dimethyl-1,2-bis(tert-butyl)cyclopropene were optimised completely at the HF/6-31G* level. The HF/6-31G*//HF/6-31G* force field was calculated and scaled using Pulay's scaling procedure. The set of 17 scale factors (for a 105-dimensional problem) was compiled from the sets obtained previously for 3,3-dimethyl-1-butene and 1-methyl-, 1,2-dimethyl-, and 3,3-dimethylcyclopropene. The vibrational problem was solved using the scaled quantum mechanical force field (QMFF) and assignments of the vibrational frequencies of 3,3-dimethyl-1,2-bis(tert-butyl)cyclopropene were considered in comparison with the known assignments of 3,3-dimethyl-1-butene and 3,3-dimethylcyclopropene. Assignments of four experimental IR bands of 3,3-dimethyl-1,2-bis(tert-butyl)cyclopropene given in the literature are suggested.     

Vibrational spectra and ab initio analysis of tert-butyl,trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethylcyclopropene IV. 3,3-dimethyl-1,2-bis(trimethylgermyl)cyclopropene

The infrared (IR) and Raman spectra of 3,3-dimethyl-1,2-bis(trimethylgermyl)cyclopropene (I) were measured in the liquid phase. Total geometry optimisation was performed at the HF/6-31G* level. The HF/6-31G*//HF6-31G* quantum mechanical force field (QMFF) was calculated and used to determine the theoretical fundamental vibrational frequencies, their predicted IR intensities, Raman activities, and Raman depolarisation ratios. Using Pulay's scaling method and the theoretical molecular geometry, the QMFF of I was scaled by a set of scaling factors comprised of elements transferred from the sets used to correct the QMFF's of 3,3-dimethylbutene-1, and 1-methyl-, 1,2-dimethyl-, and 3,3-dimethylcyclopropene (17 scale factors for a 105-dimensional problem). This set of scale factors was used previously to correct the QMFF of 3,3-dimethyl-1,2-bis(tert-butyl)cyclopropene and 3,3-dimethyl-1,2-bis(trimethylsilyl)cyclopropene. The scaled QMFF obtained was used to solve the vibrational problem. Differential Raman cross-sections were calculated using the quantum mechanical values of the Raman activities. The appropriate theoretical spectrograms for the Raman and IR spectra of I were constructed. Assignments of the experimental vibrational spectra of I are given. They take into account the calculated potential energy distributions and the correlation between the estimations of the experimental IR and Raman intensities and Raman depolarisation ratios and the corresponding theoretical values calculated using the unscaled QMFF.     

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, trimethylgermyl, trimethylstannyl, and trimethylplumbyl derivatives of 3,3-dimethylcyclopropene IX. 3,3-Dimethyl-1-(trimethylplumbyl)cyclopropene

The geometrical parameters and quantum mechanical force fields (QMFF's) of 3,3-dimethyl-1-(trimethylplumbyl)cyclopropene (I), 3,3-dimethyl-1-(t-butyl)cyclopropene (II), 3,3-dimethyl-1-(trimethylsilyl)cyclopropene (III), 3,3-dimethyl-1-(trimethylgermyl)cyclopropene (IV), and 3,3-dimethyl-1-(trimethylstannyl)cyclopropene (V) were calculated at the pseudopotential (HF/SDDAll) level. Analysis of the optimised geometrical parameters was performed. The set of scale factors for correction of the pseudopotential QMFF of III was determined using its earlier well-characterised vibrational spectrum. Transferral of the set of scale factors obtained for III to the QMFF's of I, II, IV and V was followed by calculation of the fundamental vibrational frequencies. Analysis of the results for these molecules revealed some peculiarities in the vibrational frequencies obtained at the pseudopotential level.     

Vibrational spectra and ab initio analysis of tert-butyl,trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethylcyclopropene II. 3,3-Dimethyl-1,2-bis(trimethylsilyl)cyclopropene

The IR and Raman spectra of 3,3-dimethyl-1,2-bis(trimethylsilyl)cyclopropene (I) (synthesised using standard procedures) were measured in the liquid phase. Total geometry optimisation was performed at the HF/6-31G* level. The HF/6-31G*//HF/6-31G* quantum mechanical force field (QMFF) was calculated and used to determine the theoretical fundamental vibrational frequencies, their predicted IR intensities, Raman activities, and Raman depolarisation ratios. Using Pulay's scaling method and the theoretical molecular geometry, the QMFF of I was scaled by a set of scaling factors used previously for 3,3-dimethyl-1,2-bis(tert-butyl)cyclopropene (17 scale factors for a 105-dimensional problem). The scaled QMFF obtained was used to solve the vibrational problem. The quantum mechanical values of the Raman activities were converted to differential Raman cross sections. The figures for the experimental and theoretical Raman and IR spectra are presented. Assignments of the experimental vibrational spectra of I are given. They take into account the calculated potential energy distribution and the correlation between the estimations of the experimental IR and Raman intensities and Raman depolarisation ratios and the corresponding theoretical values (including Raman cross sections) calculated using the unscaled QMFF.     

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethyl cyclopropene V. 3,3-dimethyl-1-(trimethylgermyl)cyclopropene

3,3-dimethyl-1-(trimethylgermyl)cyclopropene (I) was synthesised using a standard procedure. The IR and Raman spectra of I in the liquid phase were measured. The molecular geometry of I was optimised completely at the HF/6-31G* level. The HF/6-31G*//HF/6-31G* force field was calculated and scaled using the set of scale factors transferred from those determined previously for scaling the theoretical force fields of 3,3-dimethylbutene-1 and 1-methyl-, 1,2-dimethyl-, and 3,3-dimethylcyclopropene. The assignments of the observed vibrational bands were performed using the theoretical frequencies calculated from the scaled HF/6-31G*//HF/6-31G* force field and the ab initio values of the IR intensities, Raman cross-sections and depolarisation ratios. The theoretical spectra are given. The completely optimised structural parameters of I and its vibrational frequencies are compared with corresponding data of related molecules.     

Vibrational spectra and ab initio analysis of tert-butyl,trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethylcyclopropene III. 3,3-Dimethyl-1-(trimethylsilyl)cyclopropene

The experimental Raman and IR vibrational spectra of 3,3-dimethyl-1-(trimethylsilyl)cyclopropene in the liquid phase were recorded. Total geometry optimisation was carried out at the HF/6-31G* level and the HF/6-31G*//HF/6-31G* force field was computed. This force field was corrected by scale factors determined previously (using Pulay's method) for correction of the HF/6-31G*//HF/6-31G* force fields of 3,3-dimethylbutene-1, 1-methyl-, 1,2-dimethyl-, and 3,3-dimethylcyclopropene. The theoretical vibrational frequencies calculated from the scaled quantum mechanical force field and the theoretical intensities obtained from the quantum mechanical calculation were used to construct predicted spectra and to perform the vibrational analysis of the experimental spectra.     

Predictive Abilities of Scaled Quantum Mechanical Molecular Force Fields: Application to 1,3-Butadiene

The positions of some IR bands of the s-trans-1,3-butadiene-h ₆ and -1,1,2-d ₃ isotopomers in the gas phase have been measured using a Brucker IFS 120 HR spectrometer with a resolution of 2 cm^–1. The structural parameters of the s-trans- and s-gauche-1,3-butadiene conformers were optimized completely at the MP2/6-31G* theoretical level and their MP2/6-31G*//MP2/6-31G* quantum mechanical force fields (QMFFs) were calculated. Using only the experimental vibrational frequencies of s-trans-1,3-butadiene-h ₆ the QMFF of the s-trans conformer was corrected by Pulay's scaling method (eight scale factors were involved). The scaled QMFF was used to calculate the mean vibrational amplitudes and the Coriolis coupling constants of s-trans-1,3-butadiene-h ₆ and the vibrational frequencies of 12 of its deuterated isotopomers. The set of scale factors obtained for correction of the s-trans QMFF was transferred to the QMFF of the s-gauche conformer. Its theoretical vibrational spectrum and those of some deuterated and C¹³ isotopomers were calculated. The ability of this scaling approach (transferring of scale factors) to predict the vibrational frequencies of rotational conformers and their isotopomers, as well as other molecular characteristics, and to permit detection of perturbations of the experimental bands are discussed.     

Si~2Cl~6分子的内旋转能垒和振动基频的理论研究

用从头算方法HF/6-31G^*^*和密度函方法B3LYP/6-31G^*^*,对Si~2Cl~6分子的平衡几何构型进行优化,优化的结果与实验结果吻合得较好.并用上述两种不同的方法计算Si~2Cl~6分子的内旋转能垒,结果分别为8.786和6.694kJ/mol,其中DFT方法的计算结果与实验结果4.18kJ/mol吻合得较好.对Si~2Cl~6分子的振动基频进行计算.用HF/6-31G^*^*SQM力场所计算的频率理论值与实验值的平均误差为7.3cm^-^1,用B3LYP/6-31G^*^*未标度的力场所计算的频率理论值与实验值的平均误差为6.0cm^-^1.该密度泛函方法(B3LYP/~6-31G^*^*)的理论计算值比用HF/6-31G^*^*标度后的SQM力场计算的频率与实验值(除Si--Si键扭转振动基频之外的11条振动基频)吻合得更好.并给出了Si--Si键扭转振动基频的预测值。     

Tert-butyl N-(2-bromocyclohex-2-enyl)-N-(2-furylmethyl)carbamate的结构和振动光谱

The molecular structure, conformafional stability, and vibrational frequencies of ten-butyl N-（2- bromocyclohex-2-enyl）-N-（2-furylmethyl）carbamate （TBBFC） were investigated by utilizing the Hartree-Fock （HF） and density functional theory （DFT） ab initio calculations with 6-31G ^＊ and 6-31G^＊ ＊ basis sets. The optimized bond length and angle values obtained by HF method showed the best agreement with the experimental values. Comparison of the observed and calculated fundamental vibrational frequencies indicated that B3LYP was superior to the scaled HF approach for molecular problems. Optimal uniform scaling factors calculated for the title compound are 0.899/0.904, 0.958/0.961, and 0.988/0.989 for HF, B3LYP, and BLYP （6-31G ^＊/6-31G ^＊ ＊）, respectively.     

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, and trimethylgermyl derivatives of 3,3-dimethylcyclopropene. VI: Application of observed trends to stannyl derivatives

The effects of substitution of X = C by Si or Ge in X(CH(3))(3) moieties attached to the formal double bond of 3,3-dimethylcyclopropene are examined. Regularities in observed trends of vibrational frequencies implicating the moieties containing the X atom, as the X atomic mass is increased, are extrapolated to X = Sn. The results of this extrapolation made it possible to assign the known experimental vibrational frequencies of 3,3-dimethyl-1-(trimethylstannyl)cyclopropene and 3,3-dimethyl-1,2-bis(trimethylstannyl)cyclopropene.     

Ab initio spectrograms of the molecular vibrational spectrum

Theoretical spectrograms of the vibrational spectrum of 3,3-dimethylcyclopropene were constructed and juxtaposed with the experimental Raman and IR spectrograms. The theoretical spectrograms are represented as sets of vertical lines starting from the points corresponding to the values of the vibrational frequencies calculated from the scaled quantum-mechanical (QM) force field obtained at the HF/6-31G*//HF/6-31G* level. Two theoretical Raman spectrograms were constructed. In the first case, the heights of the vertical lines correspond to the QM values of the Raman scattering activities. In the second case they represent the relative differential Raman cross-sections calculated using the QM values of Raman scattering activities. The initial vibrational mode matrix remains virtually unchanged upon scaling of the QM force constant matrix because the dispersion of the scale factor values is low. Therefore, the heights of the theoretical lines for the IR spectrogram represent the QM intensities directly. The theoretical spectrogram based on the relative differential Raman cross-sections was shown to depict the experimental Raman spectrum more adequately. This makes it possible to use the results of the corresponding QM calculations more completely and obtain well-substantiated assignments of the vibrational frequencies.     

Vibrational spectra and ab initio analysis of tert-butyl,trimethylsilyl, trimethylgermyl,trimethylstannyl and trimethylplumbyl derivatives of 3,3-dimethylcyclopropene. XII. 1,2-Di-tert-butyl-3,3-dimethylcyclopropene

The synthesis of 1,2-di-tert-butyl-3,3-dimethylcyclopropene (I) is performed and its IR and Raman spectra are measured. Optimized geometries of I are obtained at the HF/6-31G* and CCSD/cc-pVDZ levels. The ab initio calculated spectra are used for the assignments of the experimental spectral data. The results obtained are compared with the corresponding data for 3,3-dimethylbut-1-ene and 3,3-dimethylcyclopropene. These experimental data and the total vibrational analysis of I supplement the information obtained in the series of investigations of tert-butyl, trimethylsilyl, trimethylgermyl, trimethylstannyl, and trimethylplumbyl derivatives of 3,3-dimethylcyclopropene.     

An evaluation of harmonic vibrational frequency scale factors

Scale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zero-point vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.     

Density functional theory study on the structure and vibrational spectra for cyanuric chloride

The molecular structure and vibrational spectra of cyanuric chloride have been investigated by density functional theory (DFT) using standard B3LYP/6-31G* and B3LYP/6-311+G** method and basis set combinations. The DFT force field transformed to natural internal coordinates was corrected by a well-established set of scale factors that were found to be transferable to the title compound. Both the calculated structural parameters and vibrational frequencies are in good agreement with the available experimental data.     

Computational studies of the structure and vibrational spectra of hexafluorodisilane

Ab initio calculations predict that D_3d symmetry of Si₂F₆ is more stable than D_3h symmetry. The calculated potential barrier to internal rotation was 0.77, 0.73 and 0.78 kcal/mol using HF/6-31G*, B3LYP/6-31G* and MP2/6-31G* methods respectively, which was in good agreement with the experimental value between 0.51±0.10 and 0.73±0.14 kcal/mol. The optimized geometries, harmonic force fields, infrared intensities, Raman activities, and vibrational frequencies are reported for D_3d symmetry of Si₂F₆ from HF/6-31G* and B3LYP/6-31G*. A normal coordinate analysis was carried out. The average error between the scaled DFT frequencies obtained from the B3LYP/6-31G* calculation and observed frequencies was 4.2 cm⁻¹ and the average error between the scaled HF and observed frequencies was 2.2 cm⁻¹.     

Effect of electron correlation on theoretical vibrational frequencies

Theoretical HF /6-31G * (Hartree–Fock, 6-31G * basis set) and MP 2/6-31G * (second-order Møller–Plesset, 6-31G * basis set) vibrational frequencies based on complete quadratic force fields have been obtained for a set of 36 one- and two-heavy-atom molecules comprising first-row elements for which experimental spectroscopic data are available. Frequencies calculated at the HF /6-31G * level are an average of 12.6% higher than experimental values. Partial treatment of electron correlation via the perturbation method of Møller and Plesset, terminated at second order, leads to a significant reduction in this error, although theoretical MP 2/6-31G * frequencies are still larger than the experimental quantities by 7.3%. Part of the difference may be traced to the restriction of quadratic force fields, as comparison with experimental harmonic frequencies shows deviations of only 9.5% and 4.7% for the two levels, respectively. The calculated frequencies are used in conjunction with the corresponding theoretical equilibrium structures to obtain absolute molecular entropies, which may in turn be used to yield entropies of reaction. These latter quantities are generally in good accord with entropies derived using experimental structures and frequencies.     

An ab Initio study of conformational properties of (Z,Z)-, (E,Z)- and (E,E)-cycloocta-1,5-diene

Ab initio calculations at HF/6-31G* level of theory for geometry optimization and MP2/6-31G*//HF/6-31G* for a single point total energy calculation are reported for the three geometrical isomers of cycloocta-l,5-diene 1–3.     

Calculated structures and relative stabilities of furoxan,some 1,2-dinitrosoethylenes and other isomers

The structures and relative stabilities of furoxan and some of its isomers, e.g., the 1,2-dinitrosoethylenes, have been determined by means of ab initio Hartee–Fock and Møller–Plesset calculations. Geometries were optimized at the HF/3-21G, HF/6-31G* and MP2/6-31G* levels, and subsequently used for computing MP2/6-31G*, MP3/6-31G*, and MP4/6-31G* energies. The results are markedly affected by the inclusion of electronic correlation, which renders three of the isomers unstable. It also emphasizes the importance of a zwitterionic contribution to the structure of furoxan, which promotes ring-opening through a cis 1,2-dinitrosoethylene intermediate/transition state that has an MP4/6-31G*//MP2/6-31G* energy that is 31.6 kcal/mol above furoxan.     

Theoretical Study on the Structure and Vibrational Spectra for4-methyl-3-penten-2-one

The4-methyl-3-penten-2-oneisanimportanta,0-unsaturedketonemoleculeandanimportantligandoftheorganometalliccompounds.Untilnow,somepropertiesofphoto-chemistryandexcitedstateshavebeenexperimentallystudied'-#andconformationofthemoleculewerealsostudiedinexperiments"'.Standardinfraredgratingspectrumwasalsoobtainedin1970'.However,therearenodensityfunctionaltheory(DFT)calculationsofthismoleculeintheliterature.Recently,densityfunctionaltheoryhasbeenacceptedbytheahinitioquantumchemistrycommunityasacost…