Shrinkages of the internuclear distances in some hexafluorides of octahedral symmetry

A brief analysis of the shrinkages or shortening of the internuclear distances in many molecular systems has been made. Analytical expressions for the linear shrinkage and nonlinear shrinkage have been derived in terms of the meansquare perpendicular amplitudes. Analytical expressions for the generalized mean-square amplitudes (mean-square parallel amplitudes, mean-square perpendicular amplitudes, and mean cross products) for an octahedralXY ₆ molecule have been given in terms of the mean-square amplitude matrices. The linear and nonlinear shrinkages for the hexafluorides of sulfur, selenium, tellurium, molybdenum, technetium, ruthenium, rhodium, tungsten, rhenium, osmium, iridium, platinum, uranium, neptunium, and plutonium have been computed at 298°K and 500°K, and the results have been briefly discussed.This paper is based on a thesis to be submitted byThomas S. Adams to the Graduate School of the Valdosta State College in partial fulfillment of the requirements for the degree of Master of Science.     

Formulation of the vibrational theory in terms of redundant internal coordinates

Using the generalized inverse of matrices and the method of canonical matrices, this paper develops an unambiguous formulation of the theory of small vibrations of molecules which is valid when redundant internal coordinates are used. Such treatment includes the attainment of unambiguous relationships relating the compliance matrix (the generalized inverse of the canonical force constants matrix) with experimental data (vibrational frequencies, Coriolis coupling constants, centrifugal distortion constants and mean-square amplitudes). Moreover, expressions for the elements of the Jacobian matrices of the above magnitudes with respect to the compliance constants have been also obtained as well as some sum rule relationships.     

Theory of a new method of computing mean amplitudes of vibration and perpendicular amplitude correction coefficients

Some theoretical aspects of the calculations of mean amplitudes of vibration (l) and perpendicular amplitude correction coefficients (K) are treated. A recipe for practical computations of the l and K values is given. In contrast to the conventional methods the proposed computation of K circumvents the calculation of mean-square perpendicular amplitudes.     

Mittlere Schwingungsamplituden für einX(YZ)2-Molekülmodell mit C2v-Symmetrie: Anwendung auf die Moleküle B2O3, B2S3 und S(CN)2

Zusammenfassung Auf Grund von Symmetrieüberlegungen wird eine Methode zur Bestimmung der mittleren Amplitudenquadrate der Schwingungen einesX(YZ) ₂-Molekülmodells mit C_2v Symmetrie entwikkelt. Es werden analytische Ausdrücke für die verschiedenen mittleren Amplitudenquadrate in Termen der symmetrisierten Matrizen der mittleren Amplitudenquadrate erhalten. Die Methode wird auf die Moleküle B₂O₃, B₂S₃ und S(CN)₂ angewendet. Es werden die mittleren Amplitudenquadrate und die mittleren Schwingungsamplituden bei Zimmertemperatur für gebundene und nichtgebundene Atompaare aus den beobachteten Ramanund Infrarotgrundschwingungen sowie den Daten der Molekülstruktur berechnet. Die chemische Bedeutung der beiden verschiedenen charakteristischen Bindungen im Zusammenhang mit anderen Molekülen mit ähnlichen Bindungsverhältnissen wird kurz besprochen. Weiters werden die molaren thermodynamischen Funktionen für das Schwefeldicyanidmolekül im Temperaturbereich von 200 bis 2000° K unter Annahme eines starren Rotator-und harmonischer Oszillator-Modells berechnet.

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Mean amplitudes of vibration for an X(YZ)₂ molecule with C_2v symmetry: Application to B₂O₃, B₂S₃ and S(CN)₂

On the basis of symmetry considerations a method has been developed for the determination of the mean-square amplitudes of vibration for anX(YZ) ₂ molecular model with a C_2v symmetry. Analytical expressions for the various mean-square amplitude quantities in terms of the symmetrized mean-square amplitude matrices have been obtained. The method has been applied to the B₂O₃, B₂S₃, and S(CN)₂ molecules and mean-square amplitude quantities and mean amplitudes of vibration for both bonded and nonbonded atom pairs have been computed at room temperature from the observed Raman and infrared fundamental frequencies as well as molecular structural data. A brief discussion of the results on the chemical significance of the two different characteristic bonds has been made in relation to other molecules having similar chemical bonds. Molar thermodynamic functions for the temperature range 200–2000° K have also been computed for the sulphur dicyanide molecule on the assumption of a rigid rotator, harmonic oscillator model.

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Diese Arbeit wurde durch das Stipendium NGR-41-002-003 der National Aeronautics and Space Administration unterstützt.     

The temperature dependence of the d-electron dipole strengths of cobalt(II) tetrahalides

The dipole strengths of the ⁴A₂ → ⁴T₁(F), ⁴T₁(P), d-electron transitions of the cobalt(II) tetrahalides are found to decrease with an increase in temperature, in agreement with a dynamic ligand-polarisation model for the absorption mechanism. The reduction in dipole strength is accounted for by a decrease in the coulombic coupling between the quadrupole moment of the d-electron transition of the metal ion and the transient electric dipole moment induced in the ligands, due to the anharmonic increase in the mean bond length and the progressively larger mean-square amplitudes of the bending modes of the complex ion in its ground electronic state as the temperature is raised.     

Nuclear resonance vibrational spectra of five-coordinate imidazole-ligated iron(II) porphyrinates

Nuclear resonance vibrational spectra have been obtained for six five-coordinate imidazole-ligated iron(II) porphyrinates, [Fe(Por)(L)] (Por = tetraphenylporphyrinate, octaethylporphyrinate, tetratolylporphyrinate, or protoporphyrinate IX and L = 2-methylimidazole or 1,2-dimethylimidazole). Measurements have been made on both powder and oriented crystal samples. The spectra are dominated by strong signals around 200-300 cm(-1). Although the in-plane and out-of-plane vibrations are seriously overlapped, oriented crystal spectra allow their deconvolution. Thus, oriented crystal experimental data, along with density functional theory (DFT) calculations, enable the assignment of key vibrations in the spectra. Molecular dynamics are also discussed. The nature of the Fe-N(Im) vibrations has been elaborated further than was possible from resonance Raman studies. Our study suggests that the Fe motions are coupled with the porphyrin core and peripheral groups motions. Both peripheral groups and their conformations have significant influence on the vibrational spectra (position and shape).     

Ab initio and density functional calculations of mean-square amplitudes of vibration for benzene and cubane

Mean-square amplitudes of vibration were calculated using ab initio and density functional methods for benzene and cubane. Both 6-31G^* and 6-311G^** basis sets were employed. It was found that significant improvements were achieved when electron correlation was introduced, even if only at the local density functional level. The mean-square amplitudes calculated were not effected by the basis set used for benzene and slightly improved for the highly strained cubane molecule when the larger basis set was used. An attempt was also made to improve the calculated mean-square amplitudes by making use of scale factors found in the literature, which were developed to improve the calculated frequencies. It was found that only the SCF mean-square amplitudes were significantly improved.     

Konstanten der potentiellen Energie,mittlere Schwingungs-amplituden,Bastiansen—Morino-Schrumpfeffekt,molekulare Polarisierbarkeit und absolute Ramanintensitäten der Σ g − -Sehwingungsrassen des Quecksilber(I)chlorids

Zusammenfassung Nach der gruppentheoretischen Methode wurden mit einem Feld von fünf Bindungskraftkonstanten für das Quecksilber(I)chlorid, das eine lineare symmetrische Struktur der Symmetriepunktgruppe D _h besitzt, die Konstanten der potentiellen Energie berechnet. Mit Hilfe der Symmetriekoordinaten, der mittleren Amplitudenquadrate und der verallgemeinerten mittleren Amplitudenquadrate (mittlere Parallelamplitudenquadrate, mittlere Senkrechtamplitudenquadrate und mittlere gemischte Produkte) wurden die mittleren Schwingungsamplituden der gebundenen und der nichtgebundenen Atompaare und die Schrumpfung der chemischen Bindungen für die Temperature 298° K und 500° K berechnet. Die Bindungspolarisierbarkeiten, die molekulare Polarisierbarkeit und die Ableitungen der Polarisierbarkeit, die direkt den absoluten Ramanintensitäten der völlig symmetrischen Hg–Cl- und Hg–Hg-Streckschwingungen im Elektronengrundzustand entsprechen, wurden berechnet. Dazu wurde ein halbempirisches Deltafunktionspotentialmodell angenommen und eine Variationsmethode und Deltaelektronenwellenfunktionen verwendet. Die chemische Bedeutung der Ergebnisse wird kurz behandelt.

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Potential energy constants, mean amplitudes of vibration, bastiansen—Morino shrinkage effect, molecular polarizability and absolute raman intensities of the _g ^– -Modes of mercury(I) chloride

Potential energy constants have been evaluated by the group theoretical method employing a five constant valence force field for mercurous chloride possessing a linear symmetrical structure with the symmetry point group D _h. On the basis of the symmetry coordinates, mean-square amplitude quantities, generalized mean-square amplitude quantities (mean-square parallel amplitudes, mean-square perpendicular amplitudes, and mean cross products), mean amplitudes of vibration for the bonded and nonbonded atom pairs, and shrinkages of chemical bonds have been computed at the temperatures 298° K and 500° K. Bond polarizabilities, molecular polarizability, and polarizability derivatives corresponding to the absoluteRaman intensities of totally symmetrical Hg–Cl and Hg–Hg stretching vibrations in the ground electronic state have been calculated from a semi-empirical delta-function potential model by using a variational method and also deltafunction electronic wave functions. A brief discussion of the chemical significance of the results is given.

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Diese Arbeit wurde von dem U.S., Army Research Office-Durham unter dem Zeichen Grant AROD-31-124-6864 unterstützt.     

An investigation of the adiabatic potential energy surface of a Pseudo-Jahn-Teller complex using X-ray diffraction

X-ray diffraction combined with theoretical results obtained for isolated molecules can reveal many topologic features of the adiabatic potential energy surface (APS) of pseudo-Jahn-Teller Cu(II) complexes. Single-crystal x-ray results of acetatobis (1,10-phenanthroline)copper(II) perchlorate from 10 to 351 K are presented. The observed Cu-O bond length changes of 0.26 and 0.38 Å are rationalized in terms of a one-dimensional APS with two nonequivalent minima. The Silver and Getz model of vibronic coupling applied to the temperature variation of the Cu-O bond lengths is not obeyed. The actual structures of the conformers associated with the energy minima were determined from the x-ray data. A means of estimating the pseudo-Jahn-Teller radius using mean-square vibrational amplitudes along the Cu-O bonds is also discussed.     

Conformational and vibrational study of platinum(II) anticancer drugs: cis-diamminedichloro-platinum(II) as a case study

A conformational and vibrational analysis of cisplatin [cis-diamminedichloro-platinum(II)] (cDDP) is reported. Several theory methods (from Hartree-Fock to Moller-Plesset and density functional theory) combined with different all-electron basis sets are evaluated, in view of determining the best suited strategy for accurately representing this molecule. This choice is based on the best compromise between accuracy and computational requirements. Different scaling models of the cDDP vibrational modes were tested for obtaining the best scaling factors to be used in this type of inorganic systems. The structural parameters and vibrational results predicted by the calculations are compared with the corresponding experimental data, namely, x-ray structure, and Raman and inelastic neutron scattering spectra. Finally, a complete assignment of the cDDP vibrational spectra is presented.     

Ultrafast vibrational dynamics of SCN(-) and N3(-) in polar solvents studied by nonlinear infrared spectroscopy

In this paper, we report on our investigation into the vibrational dynamics of the antisymmetric stretching modes of SCN(-) and N(3)(-) in several polar solvents. We used an infrared (IR) pump-probe method to study orientational relaxation processes. In two aprotic solvents (N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO)), the anisotropy decay shows a bimodal feature, whereas in other solvents the anisotropy decay can be fitted well by a single exponential function. We consider that the relative contribution of fast-decaying components is smaller in the other solvents than in DMF and DMSO. We discuss the possible origins of the different anisotropy decay behavior in different solvents. From the three-pulse IR photon echo measurements for SCN(-) and N(3)(-), we found that the time-correlation functions (TCFs) of vibrational frequency fluctuations decay on two different time scales, one of which is less than 100 fs and the other is approximately 3-6 ps. In aprotic solvents, the fast-decaying components of the TCFs on a <100 fs time scale play an important role in the vibrational frequency fluctuation, although the contribution of collective solvent reorganization in aprotic solvents was clearly observed to have small amplitudes. On the other hand, we found that the amplitude of components that decay in a few picoseconds and/or the constant offset of the TCF in protic solvents is relatively large compared with that in aprotic solvents. With the formation and dissociation of hydrogen bonds between ion solute and solvent molecules, the spectra of different solvated species are exchanged with each other and merged into one band. We considered that this exchange may be an origin of slow-decaying components of the TCFs and that the decay of the TCFs corresponds to the time scales of the exchange for protic solvents such as formamide. The mechanism of vibrational frequency fluctuations for the antisymmetric stretching modes of SCN(-) and N(3)(-) is discussed in terms of the difference between protic and aprotic solvents.     

Influence of the "innocent" ligands on the MLCT excited-state behavior of mono(bipyridine)ruthenium(II) complexes: a comparison of X-ray structures and 77 K luminescence properties

The variations in the nonchromophoric ligands of [Ru(L)4bpy]2+ complexes are shown to result in large changes in emission band shapes, even when the emission energies are similar. These changes in band shape are systematically examined by means of the generation of empirical reorganizational energy profiles (emreps) from the observed emission spectra (Xie, P.; et al. J. Phys. Chem. A 2005, 109, 4671), where these profiles provide convenient probes of the differences in distortions from the ground-state structures of the 2,2-bipyridine (bpy) ligands (for distortion modes near 1500 cm(-1)) in the metal-to-ligand charge-transfer (MLCT) excited states for a series of complexes with the same ruthenium(II) bipyridine chromophore. The bpy ligand is nearly planar in the X-ray structures of the complexes with (L)4 = (NH3)4, triethylenetetraamine (trien), and 1,4,7,10-tetraazacyclododecane ([12]aneN4). However, for (L)4 = 5,12-rac-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, the X-ray crystal structure shows that the bpy ligand is twisted in the ground state (a result of methyl/bpy stereochemical repulsion) and the emrep amplitude at about 1500 cm(-1) is significantly larger for this structure than for the complex with (L)4 = 1,4,8,11-tetraazacyclotetradecane, consistent with larger reorganizational energies of the bpy distortion modes in order to form a planar (bpy(-)) moiety in the excited state of the former. The trien and [12]aneN4 complexes have very nearly the same emission energies, yet the 40% smaller vibronic sideband intensity of the latter indicates that the MLCT excited state is significantly less distorted; this smaller distortion and the related shift in the distribution of distortion mode reorganizational energy amplitudes is apparently related to the 36-fold longer lifetime for (L)4 = [12]aneN4 than for (L)4 = trien. For the majority (77%) of the [Ru(L)4bpy]2+ complexes examined, there is a systematic decrease in emrep amplitudes near 1500 cm(-1), consistent with decreasing excited-state distortion, with the excited-state energy as is expected for ground state-excited state configurational mixing in a simple two-state model. However, the complexes with L = [12]aneN4, 1,4,7,10-tetraazacyclododeca-1-ene, and (py)4 all have smaller emrep amplitudes and thus less distorted excited states than related complexes with the same emission energy. The observations are not consistent with simple two-state models and seem to require an additional distortion induced by excited state-excited state configurational mixing in most complexes. Because the stereochemical constraints of the coordinated [12]aneN4 ligand restrict tetragonal distortions around the metal, configurational mixing of the 3MLCT excited state with a triplet ligand-field excited state of Ru(II) could account for some of the variations in excited-state distortion. The large number of vibrational distortion modes and their small vibrational reorganizational energies in these complexes indicate that a very large number of relaxation channels contribute to the variations in 3MLCT lifetimes and that the metal-ligand skeletal modes are likely to contribute to some of these channels.     

Normal coordinate analysis and mean amplitudes of bis(2,2,6,6-tetramethylheptane-3,5-dionato)uranyl

A normal coordinate analysis has been performed for bis(2,2,6,6-tetramethylheptane-3,5-dionato)uranyl according to two simplified models: (i) a 35-atom model consisting of one tetramethylheptanedionate ligand attached to uranyl; symmetry C_2V and (ii) a 31-particle model of the whole complex, where the methyl groups are taken as point masses; symmetry D_2h. The construction of independent symmetry coordinates by the “method of fragments” is described. Calculated vibrational frequencies are reported along with mean amplitudes (l- values) and perpendicular amplitude coefficients (K- values) for selected interatomic distances.     

Spectroscopic and theoretical study of Cu(II), Zn(II), Ni(II), Co(II) and Cd(II) complexes of glyoxilic acid oxime

The paper presents a detailed experimental and theoretical study of five metal complexes of glyoxilic acid oxime (gaoH2), Cu(gaoH)2(H2O)2 (1), Zn(gaoH)2(H2O)2 (2), Co(gaoH)2(H2O)2 (3), Ni(gaoH)2(H2O)2 (4) and [Cd(gaoH)2(H2O)2].H2O (5). The electronic and vibrational spectra were measured and discussed as to the most sensitive to the M-L binding bands. Two different types of coordination were considered for gaoH- ligand: bidentate through the carboxylic oxygen and oxime nitrogen in 1-4 and mixed bidentate and bridging through the COO group in 5. It is shown that the spectral behavior of the nu(COO) modes can be used to predict bridging ligand coordination. DFT(B3LYP/6-31++G(d,p)) calculations on model compounds: neutral, anionic and radical forms of gao and Cu(gaoH)2, have been carried out to correlate geometries, electronic and vibrational structures. The results obtained were used to assist the electronic and vibrational analysis of the complexes studied. The effect of the metal-ligand interactions (electrostatic and covalent) on the geometry structure of the ligand was investigated.     

Molecular Dynamics Simulations for Ice Modifications II and IX

Molecular vibrations of water (H₂O and D₂O) in crystals of ice II and ice IX are studied by molecular dynamics in a rigid bond approximation with a fixed bond angle. Using an atom-atomic potential PM for describing the interactions between water molecules in ice II (N = 576 molecules) and ice IX (N = 768) in an NVE ensemble leads to reproduction of the structure of both types of ice. For all water molecules and separately for each system of crystallographically equivalent water molecules in ice crystals, we defined the time dependence of the mean-square displacement of the center of mass of the molecule, the autocorrelation function of velocity for the center of mass, and the autocorrelation function of velocity for hydrogen (deuterium) atoms. The densities of vibrational states are calculated as Fourier integrals of the corresponding autocorrelation functions. In the case of ice II, the densities of states agree well with the experimental incoherent inelastic neutron scattering spectra. In the case of ice IX, agreement is worse. For both polymorphs, the mean-square displacement and the densities of vibrational states of the center of mass of the molecule and the hydrogen (deuterium) atom differ slightly between molecules belonging to different systems of crystallographic positions. This is explained by the difference in their environments.     

Structure-parameter and force-field refinement for lead dihalide molecules

Conclusions It has been shown for PbF₂ that one can process electron-diffraction data for molecules containing heavy atoms on the basis of atomic scattering amplitudes calculated with a relativistic approximation for the atomic electron density. The errors in calculating the atomicscattering amplitudes explain the previous discrepancies in the observed values for the Pb-Cl amplitudes in PbCl₂ derived in two independent researches. The differences between those values are now not so considerable, and they may be explained as due to experimental error or to the processing of the measurements in Hungary for most of the scattering angles having been performed without the relativistic corrections to the electron density.Our mean-square vibration amplitudes and the measured frequencies can be used with our semiempirical relationships for the force constants to determine the potential-energy parameters for those molecules and to estimate the vibrational frequencies for PbI₂, which have not been measured.I am indebted to Professor V. P. Spiridonov and staff at the vapor electron-diffraction laboratory at Moscow University for providing the observed values for the reduced molecular component of the scattering intensities for lead dihalides and for valuable comments in discussion on the draft.High-Temperature Institute, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 1, pp. 54–59, January–February, 1991.     

Molecular dynamics,root-mean-square amplitudes,statistical thermodynamics,and molecular polarizability for the isotopic species of dioxygen monofluoride

A brief survey of vibrational spectral studies for the four isotopic species of dioxygen monofluoride has been made. On the basis of group theoretical considerations, symmetry coordinates have been constructed and kinetic energy matrices (orG matrix elements), potential energy matrices, and secular equations have been derived to calculate the valence force constants. The mean-square amplitudes and root-mean-square amplitudes for both the bonded and nonbonded atom pairs have been calculated at the room temperature. On the basis of a rigid rotator and harmonic oscillator model, enthalpy function, free enthalpy function, entropy, and heat capacity have been calculated from 200 to 2000 °K for all the four isotopic species. On the basis of a delta-function potential model based on the variational method and delta-function electronic wave functions, the bond parallel components, the bond perpendicular components, the contribution by the nonbonding electrons, and the average molecular polarizability have been calculated. The results obtained from these studies clearly confirm a double bond character for the oxygen—oxygen distance and a bond order of less than one-half for the oxygen—fluorine distance. The results have been discussed in relation to the nature of the two characteristic bonds involved in this molecular system.     

The semiclassical self-consistent-field (SC-SCF) approach to energy levels of coupled vibrational modes. II. The semiclassical state-interaction procedure

A method for obtaining energy levels of coupled vibrational modes is described, that utilizes a state-interaction approach combined with semiclassical approximations. The method starts with a semiclassical self-consistent-field calculation of the coupled problem, and uses the eigenstates of the resulting Hartree-like separable SCF vibrational hamiltonian to define a basis set of Hartree products in which the full vibrational hamiltonian is represented and diagonalized. Matrix elements of any interaction potential between single-mode states are approximated semiclassically as the Fourier component of the interaction at the frequency corresponding to the SCF eigenvalue difference. A Fourier-component expression can also be given for the overlap between non-orthogonal single mode states. Thus no wavefunctions ever need to be defined. Application to a sample two-mode problem shows that the method is highly accurate. Further possible applications, in particular to intramolecular rate calculations are noted.     

Intensities of infrared bands in molecular mechanics (MM3)

The MM3 molecular mechanics program calculates a fair representation of vibrational frequencies for molecules. To make this information more useful, a qualitative intensity calculation has been added, as is described herein. Because each bond in the molecule is assigned a dipole moment, and the vibrational amplitudes are known from the frequency calculation, the change in dipole moment corresponding to each normal mode is readily calculated. In some cases a charge flux has to be added empirically for bond stretchings. This relatively simple calculation has been applied to a number of different functional groups, and gives band intensities adequate for dividing the bands into very strong, strong, medium, weak, or very weak (forbidden) categories. © 1992 by John Wiley & Sons, Inc.     

Ab initio studies on vibrational spectra of Ni(II), Pd(II), and Pt(II) complexes of M'X4(2-) and M'OS3(2-) (M' = Mo, W; X = O, S)

The vibrational spectra of MM'2X8(2-) and trans-MM'2S6O2(2-) (M = Ni(II), Pd(II), Pt(II); M' = Mo, W; X = O, S) are calculated using ab initio method at RHF/LanL2DZ level. The calculated vibrational frequencies of MM'2S8(2-) and trans-MM'2O2S6(2-) are evaluated via comparison with experimental data. The results obtained by this method have the deviation <5% for M'S and MS stretching vibrational frequencies, however, relatively higher deviation is obtained for M'O stretching vibrational frequencies. Some vibrational frequencies of these complexes that have not been experimentally reported are also predicted and some of the experimental values are assigned.