METHODS OF SCALING QUANTUM MECHANICAL MOLECULAR FORCE FIELDS

$^{a}$A.G. Yagola, I.V. Kochikov, G.M. Kuramshina and Yu. A. Pentin. ``Inverse Problems of Vibrational Spectroscopy"". VSP, Utrecht. The Netherlands, 1999, Chapter 11, p. 259. $^{b}$Yu, N. Panchenko, J. Mol. Street. 410-411. 327 (1997).Author Institution: Laboratory of Molecular Spectroscopy, Division of Physical Chemistry, Department of Chemistry, M.V. Lomonosov Moscow State UniversityA comparative analysis of various methods of empirical scaling of the quantum mechanical harmonic molecular force fields has been performed. The Pulay method of scaling is stressed to be applicable most successfully in the case where the quantum mechanical force field is determined close to the Hartree-Fock limit. This makes it possible to carry out correction of this force field with maximal retention of the peculiarities inherent in the the molecule under investigation. The solution of the inverse vibrational problem using quantum mechanical force field as a starting one may be considered to be the limiting case of scaling with maximum number of scale factors. Such approach corresponds to the traditional philosophy that searching force field should be closest to the starting $one^{a}$. On the contrary, the main physical criterion used in the Pulay scaling procedure is closeness of the vibrational modes determined from the scaled force field to the vibrational modes obtained from the starting quantum mechanical force $field^{b}$

MUTUAL CO-ASSIGNMENT OF THE CALCULATED VIBRATIONAL FREQUENCIES IN THE GROUND AND LOWEST EXCITED ELECTRONIC STATES

Author Institution: Laboratory of Molecular Spectroscopy, Division of Physical; Chemistry, Department of Chemistry, Lomonosov Moscow State University; Moscow 119991, Russian Federation.The shifts of the molecular vibrational frequencies when going from the ground electronic state to the lowest excited electronic states pose some problems for the mutual co-assignment of the calculated vibrational frequencies in the different excited states. The \textit{trans}-\chem{C_2 O_2 F_2} shift of the frequency of the symmetrical $\nu$(C=O) stretching vibration between the S$_0$ and T$_1$ is 373~\wn. The feasibility of mutual co-assignments of the vibrational frequencies in these electronic states has been demonstrated for \textit{trans}-\chem{C_2 O_2 F_2}. Matrices analogous to the Duschinsky matrix, \textbf{7}\,(4), 551--566 (1937).} were used to juxtapose the $a_g$ vibrational frequencies of this molecule calculated at the CASPT2/cc-pVTZ level in the ground S$_0$ and excited triplet T$_1$ and singlet S$_1$ electronic states. The analog of the Duschinsky matrix $D$ was obtained for this molecule using the equation $D = (L_{I})^{-1} L_{II}$ where $L_{I}$ and $L_{II}$ are the matrices of the vibrational modes (normalized atomic displacements) obtained by solving the vibrational problems for the S$_0$ and T$_1$ electronic states, respectively. Choosing the dominant elements in columns of the $D$ matrix and permuting these columns to arrange these elements along the diagonal of the transformed matrix $D^\ast$ makes it possible to establish the correct mutual co-assignments of the calculated $a_g$ vibrational frequencies of the \textit{trans}-\chem{C_2 O_2 F_2} molecule in the S$_0$ and T$_1$ electronic states. The analogous procedure was performed for the \textit{trans}-\chem{C_2 O_2 F_2} molecule in the T$_1$ and S$_1$ excited electronic states. The recent reassignments of the \nub{2} and \nub{3} calculated vibrational frequencies in the \textit{trans}-\chem{C_2 O_2 F_2} molecule in the ground state were also obtained for the triplet T$_1$ and singlet S$_1$ excited electronic states. The approach set forth in this text makes it possible to juxtapose the calculated vibrational frequencies of the same molecule in the different electronic states and to refine the assignments of these frequencies. This is essential in correctly analyzing the vibronic spectra of a molecule under investigation

TRANSFERABILITY OF SCALE FACTORS VERSUS TRANSFERABILITY OF FORCE CONSTANTS

$^{a}$A.G. Yagola, I.V. Kochikov, G.M. Kuramshina and Yu. A. Pentin. ``Inverse Problems of Vibrational Spectroscopy"". VSP, Utrecht, The Netherlands, 1999. Chapter 11, p. 259. $^{b}$Yu, N. Panchenko, J. Struct. Chem. 40, 548 (1999) (Russian pagination).Author Institution: Laboratory of Molecular Spectroscopy, Division of Physical Chemistry, Department of Chemistry, M.V. Lomonosov Moscow State UniversityIn the techniques for solving the inverse vibrational problem on the basis of quantum-mechanical force fields, it is assumed that the force constants are the same for quasi-equivalent coordinates in similar structural moieties of related $molecules^{a}$. Clearly, this approach ignores characteristics of the force field of each particular molecule. Indeed, this concept implies that all responsibility for possible shifts of frequencies and other spectral features of related molecules (to which the force constants are transferred) lies with changes in the inverse kinetic energy matrix. With scaling of quantum-mechanical force fields, the relative errors indroduced during quantum-mechanical calculations of force constants at a certain theoretical level are assumed to be approximately the same for quasi-equivalent coordinates in similar structural fragments of related molecules. This assumption imposes less stringent constraints than the assumption of trasferability of force constants in series of related $molecules^{b}$

VIBRATIONAL ANHARMONICITY AND SCALING THE QUANTUM MECHANICAL MOLECULAR FORCE FIELD

$^{a}$ Yu. N. Panchenko, P. Pulay and F. T\""{o}r\""{o}k, J. Mol. Struct. 34, 283 (1976); V.I. Pupyshev, Yu.N. Panchenko, Ch. W. Bock and G. Pongor, J. Chem. Phys. 94, 1247 (1991); Yu. N. Panchenko, G.R. De Mar\'{e} and V.I. Pupyshev, J. Phys. Chem. 99, 17544 (1995); Yu. N. Panchenko, Moscow Univ. Chem. Bull. 51 (5), 23 (1996). $^{b}$ D.M. Dennison, Rev. Mod, Phys. 12, 175 (1940); G.E. Hansen and D.M. Dennison, J. Chem. Phys. 20, 313 (1952).Author Institution: Laboratory of Molecular Spectroscopy, Division of Physical Chemistry, Department of Chemistry, M.V. Lomonosov Moscow State University; Laboratory of Molecular Structure and Quantum Mechanics, Division of Physical Chemistry, Department of Chemistry, M.V. Lomonosov Moscow State University; Chemistry Department, Philadelphia College of Textiles \& ScienceThe interrelationship between the scale factors obtained using Pulay's $method^{a}$ from the anharmonic and the harmonized vibrational frequencies of a light molecule and its heavy analogue is considered in terms of a Morse potential. The determination of the scale factors from the vibrational frequencies of a light molecule is shown to result in smaller deviations of the calculated and experimental vibrational frequencies of its heavy analogue than those of the reverse procedure. In this context the extent to which Dennison's $rule^{b}$ is satisfied is also discussed

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 Au 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 ν(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 ν(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 PULAY'S SCALE FACTORS IN THE IVa GROUP OF THE MENDELEYEV PERIODIC SYSTEM

$^{a}$ P.C. Hariharan and J.A. Pople, Chem. Phys. Lett. 16, 217 (1972). $^{b}$ Yu. N. Pancbenko, P. Pulay and F. T\""{o}r\""{o}k, J. Mol. Structure 34, 283 (1976); V.I. Pupyshev, Yu. N. Panchenko, Ch. W. Bock and G. Pongor, J. Chem. Phys. 94, 1247 (1991); Yu. N. Panchenko, G.R. De Mar\'{e} and V.I. Pupyshev, J. Phys. Chem. 99, 17544 (1995); Yu. N. Panchenko, Moscow Univ. Chem. Bull. 51 (5), 23 (1996).Author Institution: Laboratory of Molecular Spectroscopy, Division of Physical Chemistry, Department of Chemistry, M.V. Lomonosov Moscow State University; Laboratoire de Chimie Physique Mol\'{e}culaire, Facult\'{e} des Sciences, CP 160/09, Universit\'{e} Libre de Bruxelles; Laboratory of Molecular Structure and Quantum Mechanics, Division of Physical Chemistry, Department of Chemistry, M.V. Lomonosov Moscow State University, Moscow 119899, Russian Federation.Ab initio quantum mechanical calculations were performed for structures and force fields $(HF/6-31G^{\ast}//HF/6-31G^{\ast a})$ of 3,3-dimethylbutene-1, cyclopropene, 1-methylcyclopropene, and 1-trimethylsilyl-, 1,2-bis(trimethylsilyl)-, 1-trimethylgermyl-, 1,2-bis(trimethylgermyl)-, 1-trimethylstannyl-, and 1,2-bis(trimethylstannyl)-3,3-dimethylcyclopropene. Scale factors for correction of the quantum mechanical force fields of cyclopropene, 1-methylcyclopropene, and 3,3-dimethylbutene-1 were determined using Pulay's scaling $method.^{b}$ Only the experimental vibrational frequencies of the light isotopomers of these molecules were used in the scaling procedure. The set of scale factors obtained was transferred to the quantum mechanical force fields of all the other molecules mentioned above. The vibrational problems for these molecules were solved. Complete vibrational analyses were carried out for the whole set of these related compounds. Transferability of scale factors for series of related compounds of cyclopropene with heteroatoms from the IVa group of the Mendeleyev Periodic System of chemical elements was demonstrated

REGULARITIES IN VIBRATIONAL SPECTRA OF 1-TERT-BUTYL AND 1,2-DI-TERT-BUTYL DERIVATIVES OF 3,3-DIMETHYLCYCLOPROPENE AND THEIR SILICON, GERMANIUM, AND TIN ANALOGUES

{Yu. N. Panchenko, G. R. De Mare, A. V. Abramenkov, M. S. Baird, V. V. Tverezovsky, A. V. Nizovtsev, and I. G. Bolesov, \textit{Spectrochim. Acta{G. R. De Mare, Yu. N. Panchenko, A. V. Abramenkov, M. S. Baird, V. V. Tverezovsky, A. V. Nizovtsev, and I. G. Bolesov, \textit{Spectrochim. ActaAuthor Institution: Laboratory of Molecular Spectroscopy, Division of Physical Chemistry,; Department of Chemistry, M. V. Lomonosov Moscow State University,; Moscow 119899, Russian Federation; Service de Chimie Quantique et de Photophysique; (Atomes, Molecules et Atmospheres), Faculte des Sciences; CP160/09, Universite Libre de Bruxelles,; Av. F. D. Roosevelt 50, B1050, Brussels, Belgium; Laboratory of Molecular Structure and Quantum Mechanics,; Division of Physical Chemistry, Department of Chemistry,; M. V. Lomonosov Moscow State University,; Moscow 119899, Russian FederationThe changes in the vibrational frequencies of 1-\textit{tert}-butyl and 1,2-di-\textit{tert}-butyl derivatives of 3,3-dimethylcyclopropene which occur when the central carbon atoms of the \textit{tert}-butyl moieties are substituted by silicon, germanium, or tin atoms are examined. The major decrease in the vibrational frequencies concerned (first of all the frequencies of moieties implicating the hetero atoms) is noted for the substitution of the C atom by the Si atom. Indeed, the shifts of these vibrational frequencies on going from the silicon analogue to the germanium one and from the germanium analogue to the tin one are not as pronounced as those for the C${}\to{}$Si transition.% }, \underline{\textbf{59A}}, 1733 (2003) (and references therein).}$^{,}$% }, \underline{\textbf{60A}}, 519 (2003) (and references therein).} An explanation is given for such characteristic changes in these vibrational frequencies for the transitions C${}\to{}$Si${}\to{}$Ge${}\to{}$Sn. The formation of cluster regions in the vibrational spectra is shown for the frequencies of the stretching vibrations of the SnC$_3$ moieties. It is concluded that the vibrational frequencies corresponding to moieties containing the hetero-atoms tend towards lower limiting values as the mass of the isovalent atoms is increased