Isotopic invariants of pyramidal symmetrical XY3 molecules and evaluation of molecular constants

The isotopic invariants of pyramidal symmetrical XY₃ molecules are calculated in terms of frequencies, Coriolis coupling constants, molecular geometry parameters and masses of the constituent atoms. These invariants are used to evaluate force constants, compliance constants and mean amplitudes of vibration of four sets of 12 isotopic molecules.     

The morse-like model for the potential function of linear XY2 molecules

A Morse-like model with four adjustable constants is suggested for the potential function of linear XY₂ molecules. By transferring the parameters from diatomic molecules the number of constants can be further reduced. It is shown that this model quantitatively reproduces the general valence force field of CO₂ and CS₂ established from spectroscopic data.     

Ab initio Description of Nuclear Motion in Nonrigid M k XY n (k≥1) Molecules with Quasirigid XY n Fragments

For nonrigid M _k XY _n (k1) molecules, a model is constructed that describes the motion of k M nuclei relative to the quasirigid XY _n fragment taking into account 3^* k degrees of freedom. The parameters of the potential and kinetic terms of the model Hamiltonian are determined from results of ab initio calculations of the properties of a molecule and its fragments. Solutions of the corresponding Schrödinger equations are obtained by a variational method using bases constructed from products of spherical harmonics and harmonic–oscillator eigenfunctions. The form of model Hamiltonians for nonrigid MXY₄ and M₂XY₄ molecules with quasitetrahedral XY₄ fragments are discussed in detail. Group–theoretical analysis of the symmetry of the Hamiltonians is performed. It is shown that the molecular symmetry groups of nonrigid MXY₄ and M₂XY₄ molecules are the G ₂₄ and G ₄₈ groups, which are isomorphic to the T _d and O _h point groups, respectively.     

Normal Coordinate Analysis in Cartesian Space I. Planar Symmetric Xn Molecules

Normal coordinate analysis of X_n type molecules can be carried out in the Cartesian space as well as in the internal space. Force constants in Cartesian coordinates for aromatic compounds belonging to D_nh group are calculated. The force constants of benzene are evaluated from vibrational frequencies both in the ground state and the ¹B_1u excited state. The calculated frequencies of planar carbon vibration of annulene of any N are tabulated. The normal coordinates derived from the calculation of 10-annulene are roughly the same of naphthalene derived more elaborated by Scherer. The normal modes in 10-annulene are indeed good approximations to the ones in naphthalene. This conclusion is valid for the other aromatic compounds.     

Korrelationen von „out-of-plane“-Kraftkonstanten planarerXYCZ-Moleküle mit Elektronegativitätswerten

Several linear relations of mean electronegativities with force constants for carbonyl and thiocarbonyl out-of-plane deformations of planarXYCZ molecules have been found. The influence of the correspondingG matrix element on these relations has been shown.

     

Nonempirical Study of Nuclear Dynamics in Nonrigid LiReO4 and K2SO4 Molecules

The previously developed nonempirical model for M _k XY _n (k 1) nonrigid molecules describing the motion of k M nuclei relative to a quasirigid XY _n fragment is used to study the dynamics of nuclei in LiReO₄ and K₂SO₄ molecules. The parameters of the kinetic and potential parts of the model Hamiltonian and dipole moment functions are determined from results of ab initio calculations of the molecules and their fragments by the Hartree—Fock and CISD + Q configurational interaction methods. The dynamic problem is solved by the variational method. Energy levels, transition frequencies, transition dipole moments, and mean geometrical parameters of the molecules are calculated. It is shown that the lowest energy levels of LiReO₄ and K₂SO₄ molecules can be described with high accuracy in a harmonic approximation using a quasirigid, single–minimum model, whereas for the energy levels located near and above the barriers of intramolecular rearrangements, these approximations are completely unsuitable.     

Pseudo-exact force constants from coriolis coupling constants

A method has been developed to calculate Pseudo-Exact Force Constants from ζ-constants after truncating a higher dimensional secular equation with the High Low Frequency Separation Method (PE-HFS and PE-LFS method). A procedure to reduce the C-matrix is presented and the conditions for the applicability will be discussed. The present method is applicable to many cases where only one ζ-constant can be measured (e.g., if some band contours are disturbed and prevent the determination of all ζ-values). It is also possible to get excellent starting force constants for a least square programme in cases where sufficient data are known. The effectiveness of the different first order ζ-constants in fixing the force constants has been pointed out. The pseudo ζ sum rule for the truncated secular equation is also discussed. A proof for the sign rule for ζ-constants for xzy₃ (C_3v) type molecules [ζ(δ_as(XY₃)) < 0 and ζ(?_r(XY₃)) > 0] is given.     

Potentialfeld- und Kraftkonstanten voncis- undtrans-Difluordiazin

Zusammenfassung Ancis-Difluordiazin planarer Konfiguration mit C_2v-Symmetrie und antrans-Difluordiazin planarer Konfiguration mit zentrosymmetrischer Struktur mit C_2h-Symmetrie wurde eine Schwingungs- und Strukturanalyse unter Verwendung eines modifizierten Valenzkraftfeldes mit sechs Kraftkonstanten ausgeführt. Die Berechnung der Kraftkonstanten erfolgte nach gruppentheoretischen Methoden auf der Grundlage der Ergebnisse neuerer Struktur- und verfeinerter Schwingungsanalysen. Die Ergebnisse werden mit den an Molekülen mit ähnlichen chemischen Bindungen und angenähert identischen Kernabständen erhobenen verglichen.

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Potential field and force constants of cis- and trans-difluorodiazines

Vibrational and structural analysis ofcis-difluorodiazine possessing a planar configuration with C_2v symmetry and oftrans-difluorodiazine possessing a planar configuration of centrosymmetrical structure with C_2h symmetry has briefly been made. A modified six-force constant valence force field has been employed and the force constants have been evaluated from the recent structural and refined vibrational data for bothcis- andtrans-difluorodiazines by the group theoretical method. A brief discussion of the results has been made in relation to other molecules having similar chemical bonds with nearly identical internuclear distances.

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Mit 2 Abbildungen     

An ab initio study of the relationship between the O?H bond length and the harmonic and anharmonic stretching force constants for planar molecules containing C?OH,N?OH,and O?OH groups

The O? H bond length and the quadratic, cubic, and quartic stretching force constants, calculated ab initio using the unscaled 4-31G basis set with full geometry optimization, are reported for 30 planar conformers of ten molecules contaning either the C? OH, N? OH, or O? OH group. The data are analyzed in terms of the general form of Clark's equation, and the power functions and exponential functions proposed by Herschbach and Laurie. In the case of the quadratic constants, significant trends are found in the values of the parameters depending on whether the O? H group is bonded to carbon, nitrogen, or oxygen, and whether it is non-hydrogen-bonded or involved in intramolecular hydrogen bond formation in four-, five-, or six-membered rings. Using data for diatomic molecules, O? H, and C? H bonds, and the C?O and C? C bonds in planar monosubstituted carbonyl compounds, the parameter d_ij in the power function equation for quadratic constants, which can be regarded as the distance of closest approach of the two nuclei, is shown to increase progressively along the series (i) diatomic molecule; (ii) similar bond in a polyatomic environment with one of the two atoms covalently bonded to a neighboring atom; (iii) as in (ii) but with the second atom hydrogen bonded; and (iv) with both atoms covalently bonded to neighboring atoms.     

Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

Zur formelmäßigen Berechnung der Zuordnung von schwingungsspektroskopischen Frequenzen

For Analytical Calculation of Assignments of Vibrational Spectroscopic Frequencies Using the normal coordinate treatment we calculate assignments of vibrational spectroscopic frequencies of the systems X₃ ( D _3h) and X₄ ( T d) and partially of the systems XY₄ ( D _4h) and XY₆ ( O _h).     

Rate constants for the addition of the 2-hydroxy-2-propyl radical to alkenes in solution

Absolute rate constants for the addition of the 2-hydroxy-2-propyl radical to 18 substituted alkenes (CH₂ = CXY) were determined at (296 ± 1) K in 2-propanol by time-resolved electronspin-resonance spectroscopy. With alkene substitution the rate constants vary by more than 6 orders of magnitude. For 3,3-dimethyl-but-1-ene the temperature dependence is given by log k/M^?1 · s^?1 = 6.4 minus;; 19.1/Θ where Θ = 2.303 RT in kJ/mol^?1. As shown by a good correlation with the alkene electron affinities, log k₂₉₆/M^?1 · s^?1 = 6.46 + 1.71 · EA/eV (r = 0.930), 2-hydroxy-2-propyl is a very nucleophilic radical, and its addition rates are highly governed by polar effects. © 1993 John Wiley & Sons, Inc.     

Schwingungsspektroskopische hochdruckschemata einfacher verbindungen

Infrared spectroscopic investigations show that the following schemes are valid for the triatomic ions N₃^? and NO₂^? at high pressure. (1) High pressure strongly increases the stretching force constants of a linear system like N₃^? compared with the data at normal pressure. For statistical reasons the bond angle α is unchanged, in agreement with the fact that the bending force constant f_α is unaffected within experimental accuracy. (2) Statistical considerations predict a decrease in α for bent molecules XY₂(C_2v at high pressure. For NO₂^?, this decrease is about 3° at 35 kbar, combined with a significant increase in the bending force constant f_°. Both the stretching force constant f_NO and the interaction force constant f_NO/NO decrease considerably.     

Symmetry properties of chemical graphs. V. Internal rotation in XY⋅3XY⋅2XY3

Structures XY?₃XY?₂XY₃ of symmetry C_2v (of which propane is an example) are examined and the rearrangement due to the internal rotation of the end groups XY₃ studied. The isomerization graph is constructed, various forms of which are displayed and the symmetry of which has been determined. The order of the group is 72. There are nine prime (irreducible) representations (4A + E + 4G) with the following partitioning of the elements into classes: 1, 4², 6², 9, 12², 18. When the mechanism for rearrangement is generalized to include enantiomers, a duplex graph is produced with the order of the group 144 which is isomorphic to the group S₂(S₃,S₂) (generalized wreath product of the symmetric group S₂ and S₃). The corresponding graph has been constructed and displayed in one of more symmetrical forms. Isomorphism of groups of order 144 is discussed and a procedure is outlined in which correspondence between distinctive combinatorial objects is established by inducing permutations of m elements from available permutations of n elements. The scheme is based on selection of suitable graph invariants in one system and their labeling as m objects which form the basis for representation of the symmetry for the other system.     

The angle deformation force field for the hydrogen-bonded heterodimer CH3CN⋯HF determined with the aid of the centrifugal distortion constant DJK

The relationships between the valence force field and the centrifugal distortion constants are established for a molecule of the general type XY₃WZ?AB and are used in the case of CH₃CN?HF to determine the angle deformation force field by employing D_JK in combination with the wavenumbers of the appropriate vibrational modes.     

2,4,6‐Trifluorobenzonitrile

The title compound, C₇H₂F₃N, contains three crystallographically independent molecules in the crystal structure; two of these molecules have symmetry m and the third has symmetry mm. Each independent molecule forms a planar or approximately planar layer with its own kind. There are three different types of interlayer contacts, two of which are similar to each other, while the third is distinctly different. The packing within the layers is similar to that found in 2,5‐ and 3,6‐difluorobenzonitrile, with weak C—H...N interactions holding the molecules in the layers. The remarkable feature of this structure is the presence of more than one type of interlayer interaction.     

Conformational investigations on cyclic dipeptides containing a proline residue by means of 13C n.m.r. spectroscopy

The amounts of boat (A) and planar (B) forms for the equilibrium state in D₂O and CD₃OD/d₆-DMSO (1:1) were calculated for seven proline-containing cyclic dipeptides from their ¹³C n.m.r. spectra. For c-Pro-Val the thermodynamic functions for the conversion between the boat and planar forms have been obtained from measurements of equilibrium constants at different temperatures.     

Triplet-state ESR spectra of aromatic molecules oriented in stretched polyethylene films

Triplet-state ESR spectra show that when the aromatic molecules anthracene, anthracene-d₁₀, terphenyl, and acridine are dissolved in stretched, low-density polyethylene films, a fraction of these solute molecules become oriented with their X axis along the stretch direction but with their XY planes oriented randomly to the stretch direction. The fraction of molecules involved in the orientation process is largest for terphenyl.