Harmonic force field: An approximate relationship between the exact nonrelativistic and the Hartree–Fock limit values of the force constants

Molecular structure and vibrational study of diprotonated guanazolium using DFT calculations and FT-IR and FT-Raman spectroscopies

The purpose of this manuscript is to discuss our investigations of diprotonated guanazolium chloride using vibrational spectroscopy and quantum chemical methods. The solid phase FT-IR and FT-Raman spectra were recorded in the regions 4000-400cm(-1) and 3600-50cm(-1) respectively, and the band assignments were supported by deuteration effects. Different sites of diprotonation have been theoretically examined at the B3LYP/6-31G level. The results of energy calculations show that the diprotonation process occurs with the two pyridine-like nitrogen N2 and N4 of the triazole ring. The molecular structure, harmonic vibrational wave numbers, infrared intensities and Raman activities were calculated for this form by DFT/B3LYP methods, using a 6-31G basis set. Both the optimized geometries and the theoretical and experimental spectra for diprotonated guanazolium under a stable form are compared with theoretical and experimental data of the neutral molecule reported in our previous work. This comparison reveals that the diprotonation occurs on the triazolic nucleus, and provide information about the hydrogen bonding in the crystal. The scaled vibrational wave number values of the diprotonated form are in close agreement with the experimental data. The normal vibrations were characterized in terms of potential energy distribution (PED) using the VEDA 4 program.

Tautomeric purine forms of 2-amino-6-chloropurine (N9H10 and N7H10): structures, vibrational assignments, NBO analysis, hyperpolarizability, HOMO-LUMO study using B3 based density functional calculations

Two purine tautomers of 2-amino-6-chloropurine (ACP), in labeled as N(9)H(10) and N(7)H(10), were investigated by vibrational spectroscopy and quantum chemical method. The FT-IR and FT-Raman spectra of ACP have been recorded in the regions 4000-400 cm(-1) and 3500-100 cm(-1), respectively. The measured spectra were interpreted by aid of a normal coordinate analysis following DFT full geometry optimization and vibrational frequency calculations at B3LYP/6-311++G(d,p) level. First-order hyperpolarizability, HOMO and LUMO energies were calculated at same level of theory. The calculated molecular geometry has been compared with the X-ray data. The observed and calculated frequencies were found in good agreement. The obtained NBO data and second-order perturbation energy values to elucidate the Lewis and non-Lewis types of bonding structures in the purine tautomer N(9)H(10), have indicated the presence of an intramolecular hyperconjucative interaction between lone pair N and N-C bond orbital.

Application of the multi-parameter SQM harmonic force field, and ESFF harmonic frequencies scaling procedures to the determination of the vibrational spectra of silicon- and sulfur(II)-containing compounds

Multi-parameter scaling techniques, such as Scaled Quantum Mechanical (SQM) force field [J. Am. Chem. Soc. 105 (1983) 7037-7047; J. Phys. Chem. A 102 (1998) 1412-1424] or Effective Scaling Frequency Factor (ESFF) [Chem. Phys. Lett. 446 (2007) 191-198; J. Mol. Spectrosc. 264 (2010) 66-74] techniques, are very powerful in the theoretical prediction of the vibrational spectra of complex molecules. In the present work sets of transferable SQM and ESFF scaling factors (within the valence coordinates based schemes) that can be applied to silicon- and sulfur(II)-containing compounds have been determined. A number of VDZ- and VTZ-quality basis sets were used in conjunction with the B3LYP density functional. Eight molecules typically used in the synthesis of silica-based materials were chosen, and theoretical modes were assigned to bands detected on their IR or Raman spectra. This set was augmented with a set of 10 auxiliary, sulfur(II)-containing molecules, for which only "pure" vibrations involving S-containing motifs were assigned. This led to the set of more than 600 individual vibrations. Five factors attributed to these motifs were optimized. Scaling factors attributed to the characteristic types of internal coordinates including the second-row atoms and chlorine, which are applicable to the present molecules were preset. Their values, optimized for Baker's training set of molecules [J. Phys. Chem. A 102 (1998) 1412-1424] for all basis sets considered in this work, were also found, extending thus the applicability of the multi-parameter scaling methods. New scaling factors exhibit low statistical uncertainties. Reasonable agreement between experimental and SQM- or ESFF-scaled frequencies was obtained even for the 6-31G* basis set (RMS<12cm(-1)); extension of the basis set by adding polarization function on hydrogen atoms and/or diffuse functions provides significant improvement of the results, for which the RMS values are often (well) below 10 cm(-1). In addition, SQM scaling factors were found to occasionally exhibit large deviations from unity, which is to be contrasted with ESFF scaling factors.

Molecular geometry and vibrational studies of 3,5-diamino-1,2,4-triazole using quantum chemical calculations and FT-IR and FT-Raman spectroscopies

The 3,5-diamino-1,2,4-triazole (guanazole) was investigated by vibrational spectroscopy and quantum methods. The solid phase FT-IR and FT-Raman spectra were recorded in the region 4000-400 cm(-1) and 3600-50 cm(-1) respectively, and the band assignments were supported by deuteration effects. The results of energy calculations have shown that the most stable form is 1H-3,5-diamino-1,2,4-triazole under C1 symmetry. For this form, the molecular structure, harmonic vibrational wave numbers, infrared intensities and Raman activities were calculated by the ab initio/HF and DFT/B3LYP methods using 6-31G* basis set. The calculated geometrical parameters of the guanazole molecule using B3LYP methodology are in good agreement with the previously reported X-ray data, and the scaled vibrational wave number values are in good agreement with the experimental data. The normal vibrations were characterized in terms of potential energy distribution (PEDs) using VEDA 4 program.

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.

Vibrational spectra and ab initio analysis of tert-butyl, trimethylsilyl, trimethylgermyl, trimethylstannyl and trimethylplumbyl derivatives of 3,3-dimethylcyclopropene. XI. Secondary periodicity

Regularities of changes in the structural parameters and vibrational wavenumbers for certain moieties of the title compounds are presented. The optimized geometrical parameters and the force fields of the di- and monosubstituted 3,3-dimethylcyclopropenes were determined at the HF/3-21G* and HF/DDAll pseudopotential levels, respectively. These theoretical levels were chosen because of peculiarities of Gaussian 03 suite of programs for the Sn and Pb atoms. The theoretical vibrational wavenumbers were calculated using the corresponding scaled force fields. The regularities obtained in the form of zigzag lines for the properties as a function of the period number of X in the Mendeleyev Periodic Table are analogous to regularities that are characteristic of properties of the atoms of the 14 (IVA) group. This is known as the secondary periodicity phenomenon.

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, 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, 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.

Transferability of parameters of strictly local geminals' wave function and possibility of sequential derivation of molecular mechanics

The problem of substantiation of molecular mechanics (MM) remains actual due to growing popularity of hybrid quantum/classical (QM/MM) schemes. Recently proposed deductive molecular mechanics (DMM) seems to be a natural tool to derive mechanistic models of molecular energy (classical force fields) from a suitable quantum mechanical (QM) description of molecular structure. It is based on an assumption that the trial wave function underlying the MM description is one of the antisymmetrized product of strictly local geminals (SLG). A proof of transferability of electronic structure parameters (ESPs) in this approximation is an essential component of a logical framework for the transition from the QM to an MM description because it allows constructing expressions for potential energy surfaces by proper consideration of the response of the ESPs to the variations of geometry parameters. In the present article the ESPs defining density matrix elements and basis one-electron states (hybrid orbitals-HOs) in the SLG approximation are formally considered. The transferability of the density matrix elements with respect to the parameters of molecular electronic structure and the linear response relations for the HOs are proven to take place under very nonrestrictive conditions. Special attention is paid to numerical estimates of the ESPs' features giving an "experimental" support to approximate expressions for the molecular energy.

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.

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.