Structure and vibrational frequency for

Table I. Correlation of Structure and Vibrational Frequency for CO Chemisorbed on Transition Metal Surfaces...

The molecular structure and vibrational frequencies for all the considered hydrof-ullerenes were calculated in terms of the density functional theory at the B3LYP/6-31G theory level using the PC GAMESS/Firefly software (Schmidt et al. 1993 Granovsky 2009). The atomic masses were taken from Loss (2003). 

It is not clear that the experimental results are for pure all-trans-poly-methineimine, as other cis-transoid and trans-cisoid structures are possible. In fact, Hirao and Iwata recently stated that the experiment results are for cis-transoid-polymethineimine, and reported DFT results with the L3YP functional [87]. To clarify this issue, we are calculating the MBPT(2) structures and vibrational frequencies for other isomers of polymethineimine. Further experiments are also needed to compare with theory. 

Practical Considerations in Calculations. In order to calculate kinetic energy release distributions, structures and vibrational frequencies for the various species are required. These are taken from the literature where possible, or estimated from literature values of similar species. The details of the kinetic energy release distributions are found to va only weakly with structure or vibrational frequencies over the entire physically reasonable range for these quantities. The distributions are strongly dependent on the total energy available to the dissociating complex, and hence in our model to the AH of reaction. Often all heats of formation of product and reactants are well known except one, the organometallic product ion. This quantity can then be used as a parameter and varied until the best fit with experiment is obtained. 

Brothers SM, Darensbourg MY, Hall MB (2011) Modeling structures and vibrational frequencies for dinitrosyl iron complexes (DNICs) with density functional theory. Inorg Chem 50 8532-8540... 

At least two semiempirical methods, MINDO/3 and MNDO, have been applied successfully to the study of linear polymers using conventional solid-state theoretical techniques. The MINDO/3 calculation, showed how the band-structure of polyethylene could be calculated, while in the MNDO calculation, the optimized geometry, electronic band structure, and vibrational frequencies for polyethylene were calculated. These calculation used conventional methods, which rely on the factorization of the infinite Hamiltonian into complex symmetry adapted functions, followed by the use of those functions in the construction of a real density matrix. A more general solid-state method has been developed, but like the other conventional methods, it is very slow, and these methods have not been used to any great extent. 

Hartree-Fock theory is very useful for providing initial, first-level predictions for many systems. It is also reasonably good at computing the structures and vibrational frequencies of stable molecules and some transition states. As such, it is a good base-level theory. However, its neglect of electron correlation makes it unsuitable for some purposes. For example, it is insufficient for accurate modeling of the energetics of reactions and bond dissociation. 

Another important question deals with the intramolecular and unimolecular dynamics of the X-—RY and XR -Y- complexes. The interaction between the ion and molecule in these complexes is weak, similar to the intermolecular interactions for van der Waals molecules with hydrogen-bonding interactions like the hydrogen fluoride and water dimers.16 There are only small changes in the structure and vibrational frequencies of the RY and RX molecules when they form the ion-dipole complexes. In the complex, the vibrational frequencies of the intramolecular modes of the molecule are much higher than are the vibrational frequencies of the intermolecular modes, which are formed when the ion and molecule associate. This is illustrated in Table 1, where the vibrational frequencies for CH3C1 and the Cr-CHjCl complex are compared. Because of the disparity between the frequencies for the intermolecular and intramolecular modes, intramolecular vibrational energy redistribution (IVR) between these two types of modes may be slow in the ion-dipole complex.16... 

The structure of the ground state of linear polyenes has been the subject of several theoretical studies12-37. Molecular geometries and vibrational frequencies for polyenes up to C18H20 have been reported. Much emphasis has been placed on the calculation of force constants that can be used in the construction of force fields. 

Theoretical calculations of R2Ge give bond parameters and vibrational frequencies. For example, Me2Ge has calculated GeC = 202 pm and CGeC = 98° with the Ge-C stretches at 560 cm-1 (Ai) and 497 cm-1 (Bi). As the latter agree reasonably with experimental values from matrix-isolated species (527 and 541 cm-1), the structural values are probably good indications. 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

The DFT calculated temperature profiles are somewhat different for Cu-(tj1-02 i) and Co(i71-02 I). The maximum is predicted to occur at a lower temperature for the copper complex, which also exhibits the larger 180 EIE. An explanation for this behavior again can be found within the DFT calculations and the analysis of vibrational frequencies. Comparing the gas-phase structures and vibrational frequencies below 100 cm-1 indicates an isotope shift that is more than two times greater for Co(p1-02)Sal (7.7 cm ) than for Cu(rj1-02)TMG3Tren (3.0-3.4 cm-1). Therefore, the more temperature-dependent 180 EIE is associated with the greater isotope sensitivity of the low-frequency vibrational modes. This observation underscores the... 

The most basic information that is needed for constructing a global potential energy surface for gas phase MD simulations is the structures and vibrational frequencies. The earliest information about gas-phase RDX molecular structures was obtained from theoretical calculations [54-58]. In 1984 Karpowicz and Brill [59] reported Fourier transform infrared spectra for vapor-phase (and for the a - and p -phase) RDX in 1984, however, their data precluded a complete description of the molecular conformations and vibrational spectroscopy. More recently, Shishkov et al. [60] presented a more complete description based on electron-scattering data and molecular modeling. They concluded that the data were best reproduced by RDX in the chair conformation with all the nitro groups in axial positions. 

Figure 4-10 Electronic structures and vibrational frequencies of porphyrins containing M=0 and M=N groups. For the sources of vibrational frequencies, see Ref. 23.

Cao ZX, Hall MB. Modeling the active sites in metalloenzymes. 3. Density functional calculations on models for [Fe]-hydrogenase structures and vibrational frequencies of the observed redox forms and the reaction mechanism at the diiron active center. J Am Chem Soc. 2001 123(16) 3734-42. 

In earlier work,i 3 Allinger et al. determined MM2 parameters for organoselenium and -tellurium compounds. The selenium parameters were fit to structures and vibrational frequencies of methyl selenol, dimethyl selenide, ethyl selenol, and tetrahydroselenophene. The structures of the tellurium analogs were also calculated, but since only a bond length for Te—C and a bond angle for C-Te-C from dimethyltelluride were known, the authors were unable to compare the results to experimental data. 

AlOAlO according to ab initio calculations (7) but 27 kcal mol" less stable according to MNDO calculations (8-9). Also possible is rhombic Dgj AlOgAl with an 0-0 bond similar to that predicted by ab initio methods for LlOgLl (14). This geometry was not considered in the ab initio study (7) and showed no minimum in the MNDO study (8). Better calculations are needed to resolve the question. Thermochemical and spectral evidence is inconclusive (15). Uncertainties in the structure and vibrational frequencies cause an uncertainty of 3 cal K mol" in S and -(G -H )/T at 2000 K. Estimated values for the rhombic peroxide (6) are -1 cal K" mol" lower at 2000 K but this difference could be plausibly reversed by use of lower frequencies. 

Wilkins (1 ) has previously reported thermal functions for SF which cover an extended temperature range (0-6000 K). These functions are based on a pyramidal structure and vibrational frequencies obtained from estimated force constants. Since this structure now appears to be incorrect, our functions are believed to be more reliable. 

The molecular structure and vibrational frequencies are those measured by Gibler et al. (7) for the SFg ion in the solid... 

The thermal functions which would result from the use of the available structural and vibrational Inbformation for the remaining polyatomic species, are biased In the same way as for Sg(g). Some of the necessary Information is derived from condensed phase spectra (rather than gas phase spectra), as with the octamer, the low-valued vibrational frequencies (and possibly the structure) may need to be adjusted. In any event, the use of the existing spectroscopic data (unaltered) leads to calculated entropies which are unreasonable when used in a 3rd law analysis to mesh in the vapor pressure with these thermal functions. 

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