Philosophy of scaling the quantum mechanical molecular force field versus philosophy of solving the inverse vibrational problem

Vibrational analysis and valence force field for nitrotoluenes, dimethylanilines and some substituted methylbenzenes

The Fourier transform infrared (FTIR) and Raman spectra of 2-amino-4-nitrotoluene; 2-amino-5-nitrotoluene; 2,4-dimethylaniline; 2,5-dimethylaniline; 2,6-dimethylaniline; 1,2,4-trimethylbenzene; 1,3,5-trimethylbenzene and pentamethylbenzene have been recorded in the range 4000-400 cm(-1) and 4000-30 cm(-1), respectively. A normal coordinate analysis was carried out for both in-plane and out-of-plane vibrations of these molecules using an 81-parameter modified valence force field. The force constants were refined using 369 frequencies of eight molecules in the overlay least-squares technique. The reliability of the force constants was tested by making a zero-order calculation for both in-plane and out-of-plane vibrations for five related molecules. The potential energy distributions and eigen vectors calculated in the process were used to make unambiguous vibrational assignments of all the fundamentals.

A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies

A general formulation to compute anharmonic vibrational averages and transition properties at the second-order of perturbation theory is derived from the Rayleigh-Schrödinger development. This approach is intended to be applicable to any property expanded as a Taylor series up to the third order with respect to normal coordinates or their associated momenta. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments. From those, infrared and vibrational circular dichroism spectra can be readily obtained. This fully automatic procedure has been applied to several chiral molecules of small-to-medium sizes and compared to the standard double harmonic approximation and to experimental data.

Simulation of IR and Raman spectral based on scaled DFT force fields: a case study of 2-amino 4-hydroxy 6-trifluoromethylpyrimidine, with emphasis on band assignment

This work deals with the vibrational spectroscopy of 2-amino 4-hydroxy 6-triflouromethylpyrimidine (AHFMP) by means of quantum chemical calculations. The mid and far FTIR and FT-Raman spectra were measured in the condensed state. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT) with the standard B3LYP/6-31G* and B3LYP/6-311+G** method and basic set combinations. Normal co-ordinate calculations were performed with the DFT force field corrected by a recommended set of scaling factors yielding fairly good agreement between observed and calculated frequencies. Simulation of infrared and Raman spectra utilizing the results of these calculations led to excellent overall agreement with the observed spectral patterns. The SQM approach applying selective scaling of the DFT force field was shown to be superior to the uniform scaling method in its ability to allow for making modifications in the band assignment, resulting in more accurate simulation of IR and Raman Spectra.

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, trimethylgermyl, trimethylstannyl, and trimethylplumbyl derivatives of 3,3-dimethylcyclopropene X. Some regularities

The changes in the vibrational frequencies of 1-tert-butyl and 1,2-di-tert-butyl derivatives of 3,3-dimethylcyclopropene brought about by substitution of the central carbon atom (X) of the tert-butyl moieties by Si, Ge, Sn, or Pb atoms are examined. The most important decrease in the vibrational frequencies implicating the X(CH(3))(3) moieties is noted for substitution of X=C by Si. The substitutions of Si by Ge or Ge by Sn or Sn by Pb are not accompanied by the pronounced frequency shifts observed for the C-->Si transition. An explanation is given for trends in these vibrational frequencies for the transitions X=C-->Si-->Ge-->Sn-->Pb. It is concluded that there are lower limiting values of the vibrational frequencies of a molecular moiety which are approached when the mass of its isovalent atom is increased. This leads to the formation of cluster regions in the vibrational spectra for the frequencies of the SnC(3) and PbC(3) moieties.

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

The quantum mechanical force fields (QMFF's) of 3,3-dimethyl-1-(tert-butyl)cyclopropene (I), 3,3-dimethyl-1-(trimethylsilyl)cyclopropene (II), 3,3-dimethyl-1-(trimethylgermyl)cyclopropene (III), and 3,3-dimethyl-1-(trimethylstannyl)cyclopropene (IV) were calculated at the HF/3-21G*//HF/3-21G* level. The set of scale factors for the correction of HF/3-21G*//HF/3-21G* QMFF of II was determined using its well-characterised vibrational spectrum. Transferral of the set of scale factors obtained for II to the QMFF's of I, III and IV and calculation of the fundamental frequencies resulted in good agreement between the calculated and previously assigned experimental frequencies of III. This again demonstrates the feasibility of transferral of a set of scale factors obtained for the correction of the QMFF of a molecule to others containing heteroatoms from the same column of the Mendeleyev Periodic Table. Thus the calculations performed permitted the accurate assignment of the fundamental vibrational frequencies in the experimental IR spectrum of IV. The vibrational frequencies of 3,3-dimethyl-1-(tert-butyl)cyclopropene (I) were also calculated from the HF/6-31G*//HF/6-31G* QMFF, scaled by the set of scale factors used previously for the HF/6-31G*//HF/6-31G* QMFF's of II and III. Regularities in the trends of some vibrational frequencies with increasing atomic number of the heteroatom are observed.

s-trans-1,3-Butadiene and Isotopomers: Vibrational Spectra, Scaled Quantum-Chemical Force Fields, Fermi Resonances, and C−H Bond Properties

Quadratic quantum-chemical force fields have been determined for s-trans-1,3-butadiene using B3LYP and MP2 methods. Basis sets included 6-311++G, cc-pVTZ, and aug-cc-pVTZ. Scaling of the force fields was based on frequency data for up to 11 isotopomers, some of these data being original. A total of 18 scale factors were employed, with, in addition, an alteration to one off-diagonal force constant in the A(u) species. MP2 calculations without f functions in the basis perform badly in respect of out-of-plane bending mode frequencies. Centrifugal distortion constants and harmonic contributions to vibration-rotation constants (alphas) have been calculated. Existing experimental frequency data for all isotopomers are scrutinized, and a number of reassignments and diagnoses of Fermi resonance made, particularly in the nu(CH) region. The three types of CH bond in butadiene were characterized in terms of bond length and isolated CH stretching frequency, the latter reflecting data in the nu(CD) region. Broad agreement was achieved with earlier results from local mode studies. Differences in CH bond properties resemble similar differences in propene. A simplified sample setup for recording FT-Raman spectra of gases was applied to four isotopomers of butadiene.

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.

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 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-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.

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.