Molecular modeling spectra calculations

At the other end of the spectrum are the ab initio quantum molecular models, which are rigorous within the Hartree-Fock/ Roothaan—Hall (HF/RH) formalisms. Electronic structure is calculated, and dependent properties are derivable. In theory, full reaction profiles can be modeled. In practice, however, their speed makes it impractical to apply the more accurate... 

In order to clarify the relationship between cross peaks and carbon proton inter-atomic distances, molecular model for the anti-parallel p-sheet conformation of PG and PLV have been calculated using reference data (Wiithrich, et al.)117 by the X-PLOR 3.1 program, and we measured the carbon-proton distances from the modeled structure (Table 14). The distances between the carbons and their directly bonded protons are ca. 1.1 A and their signals can be observed in the FSLG C H HETCOR spectrum with contact time of 0.2 ms. Further, in the FSLG C H HETCOR spectrum with a contact time of 0.5 ms the signals corresponding... 

Quantitative Calculations. These attempts to connect physical and chemical properties with models are helpful to chemists and, in the hands of organic chemists, molecular models have led to marvelous advances, but physicists are inclined to object to them because they are inadequate in more quantitative fields. We were rather pleased with the assignment of definite bands in the spectrum of ethyl bromide to corresponding bonds in the molecule and... 

In order to correlate the solid state and solution phase structures, molecular modelling using the exciton matrix method was used to predict the CD spectrum of 1 from its crystal structure and was compared to the CD spectrum obtained in CHC13 solutions [23]. The matrix parameters for NDI were created using the Franck-Condon data derived from complete-active space self-consistent fields (CASSCF) calculations, combined with multi-configurational second-order perturbation theory (CASPT2). 

Astrand, P.-O., Karlstrom, G., Engdahl, A., and Nelander, B., Novel model for calculating the intermolecular part of the infrared spectrum for molecular complexes, J. Chem. Phys. 102, 3534-3554 (1995). 

Theoretical photoelectron spectrum has been calculated by the use of DV-Xa molecular orbital method combined with the calculation of atomic photoionization cross section in Hartree-Fock-Slater model. A calculation of the photoionization cross section has been performed for flexible numerical atomic orbitals including the excited atomic orbitals which are employed for basis functions in the molecular orbital calculation. Some variation of the photoionization cross section is seen when a reconstruction of the atomic orbital due to change in the effective charge takes place. This affects the molecular photoelectron spectrum to a certain extent. 

The popularity of the SOS methods in calculations of non-linear optical properties of molecules is due to the so-called few-states approximations. The sum-over-states formalism defines the response of a system in terms of the spectroscopic parameters, like excitations energies and transition moments between various excited states. Depending on the level of approximation, those states may be electronic or vibronic or electronic-vibrational-rotational ones. Under the assumption that there are few states which contribute more than others, the summation over the whole spectrum of the Hamiltonian can be reduced to those states. In a very special case, one may include only one excited state which is assumed to dominate the molecular response through the given order in perturbation expansion. The first applications of two-level model to calculations of j3 date from late 1970s [93, 94]. The two-states model for first-order hyperpolarizability with only one excited state included can be written as ... 

The spectroscopic and photochemical properties of the synthetic carotenoid, locked-15,15 -cA-spheroidene, were studied by absorption, fluorescence, CD, fast transient absorption and EPR spectroscopies in solution and after incorporation into the RC of Rb. sphaeroides R-26.1. High performance liquid chromatography (HPLC) purification of the synthetic molecule reveal the presence of several Ai-cis geometric isomers in addition to the mono-c/x isomer of locked-15,15 -c/x-spheroidene. In solution, the absorption spectrum of the purified mono-cA sample was red-shifted and showed a large c/x-peak at 351 nm compared to unlocked all-spheroidene. Spectroscopic studies of the purified locked-15,15 -mono-c/x molecule in solution revealed a more stable manifold of excited states compared to the unlocked spheroidene. Molecular modeling and semi-empirical calculations revealed that geometric isomerization and structural factors affect the room temperature spectra. RCs of Rb. sphaeroides R-26.1 in which the locked-15,15 -c/x-spheroidene was incorporated showed no difference in either the spectroscopic properties or photochemistry compared to RCs in which unlocked spheroidene was incorporated or to Rb. sphaeroides wild type strain 2.4.1 RCs which naturally contain spheroidene. The data indicate that the natural selection of a c/x-isomer of spheroidene for incorporation into native RCs of Rb. sphaeroides wild type strain 2.4.1 was probably more determined by the structure or assembly of the RC protein than by any special quality of the c/x-isomer of the carotenoid that would affect its ability to accept triplet energy from the primary donor or to carry out photoprotection. 

We assume that the above-indicated drawback of the present model can be avoided (or at least reduced) if a new paradigm [mentioned below in Section X.B.4(ii)] of the molecular model will be constructed. In our opinion, this drawback of the present model is stipulated by the following. In view of Eq. (11) the libration lifetime T0r is determined by the experimental Debye relaxation time td, so variation of Tor cannot be used for other corrections of the calculated spectra. In the proposed new paradigm it is desirable to use Tor for the latter purpose, while a correct describing of the low-frequency Debye spectrum is assumed to be reached by variation of additional parameter(s). 

We see from Fig. lib that the Raman spectrum changes rather weakly in the employed temperature range (see, e.g., the experimental RS in Fig. 4 and the calculated RS in the right column of Fig. 1 lb). In view of Table VII, such behavior of the RS is obtained if the fitted model parameters g ,p , and y , pertaining to the transverse-vibration mechanism (d), exhibit a substantial change in the temperature interval of our interest. Due to the demonstrated steepness of the RS with respect to temperature, the agreement with experiment of the employed molecular model is attained for rather definite values of these parameters. We conclude that simultaneous application of the dielectric and Raman spectroscopy allows us to increase reliability of the employed molecular model. 

We see from Fig. 26a (solid line 1) that the loss spectrum, calculated for our model with the same parameters, as chosen above (Table IX), exhibits resonance lines at the frequencies v < 50 cm-1. At v < 20 cm-1 the calculated solid loss curve 1, becoming nonresonant, coincides with the nonresonant dashed curve 2 calculated from Eqs. (72)-(74) with cfit = 2.35. Both loss s" curves 1 and 2 decrease linearly with v (in the log-log plot) in the interval from 50 to 0.1 cm-1 For further decrease of frequency the empirical dependence (72) exhibits a minimum at v about 0.1 cm-1 (viz, in the millimeter wavelength region). Near this minimum and at lower frequencies, our molecular model should not be applied. 

The obtained relationship for such /(co) turned out to be a rational function of the SF L(z). The obtained formula allows calculation of /(co) (for any specific molecular model) in all the frequency region, including the low-frequency part of the spectrum. In its high-frequency part such /(co) coincides with the Boitzmann susceptibility /B(co). 

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