Dyads, structural calculations

A preferable system is poly(p-fluorostyrene) doped into poly(styrene). Since rotations about the 1,4 phenyl axis do not alter the position of the fluorine, the F spin may be regarded as being at the end of a long "bond" to the backbone carbon. In standard RIS theory, this polymer would be treated with dyad statistical weights to automatically take into account conformations of the vinyl monomer unit which are excluded on steric grounds. We have found it more convenient to retain the monad statistical weight structure employed for the poly(methylene) calculations. The calculations reproduce the experimental unperturbed dimensions quite well when a reasonable set of hard sphere exclusion distances is employed. 

Statistical characteristics of the chemical structure of a heteropolymer, which pertain to the second type, describe the pattern of arrangement of units along macromolecules. The best known among such characteristics are fractions P Uk of directed sequences Uk incorporating k monomeric units. The simplest of them are the dyads U2, the complete set of which for a binary copolymer is composed of four pairs MiMi,MiM2,M2Mi,M2M2. Their calculation turns out to be rather useful for two reasons. 

Protonation State. At optimal pH for enzymatic activity ( 5-6) [101, 102, 105], the Asp dyad can in principle exist in three protonation states, a deprotonated, a mono-protonated or a doubly protonated form. Because hydrogen atoms cffe invisible in the X-ray structure, evidence for a specific protonation state must be inferred indirectly by spectroscopic or titration measurements. Up to now, the existence of the doubly protonated, neutral form hfree enzyme. The existence of the deprotonated, doubly negative form is supported by a recent NMR study [102] at pH 6. However, this study has been subjected to criticism [106] and it is not conclusive. Our ab initio simulations of this form show that the Asp dyad is unstable even in the ps timesccde because of the strong Asp-Asp repulsion, which turns out to be -t-30 kcal/mol as estimated with a simple electrostatic model [100]). Thus, our calculations do not support the existence of this form. 

Conditional probabilities can then be used to calculate structural features of the copolymers or to evaluate statistical features of the copolymerization mechanism. If terms such as P(A), P(AA), and P(ABA) are used to represent unconditional probabilities of finding monomer xmits, dyads, triads, etc. in the polymer chain, and if terms such as P(A/A), P(A/AB) and P(b/BBB) are used to represent conditional probabilities that A or B xmits follow other monomer xmits or monomer sequences in the copolymer chain, a copolymer can be considered to obey Bernoullian statistics if P(a) = P(A/a) =... 

If both mono-ads and dyads are measured, a statistical parameter can be calculated that yields information about whether the distribution of the structures is random, and whether it tends towards an alternating or block distribution. This order parameter, x,... 

As it was reported earlier in the subject literature, the NLO values of [60]fullerene-dyads calculated with the aid of the PM3 method show satisfactory agreement with the DFT results and experimental third harmonic generation values [1]. Here, we also use the PM6 method [15], The studied systems are presented in Fig.5.3. The top structure is [60]fullerene-dyad composed of fullerene and free base porphyrin linked by conjugated linear carbon spacer. In the middle structure, the free base por-... 

The structure(Zn,Ph)-property(a,/ ,7,) relationship has been investigated in this work by semiempirical PM3 and PM6 methods. The ZnTPP-(C)4-[60] dyad was found to exhibit large values of second hyperpolarizability. We found almost linear correlation between the size of the conjugated polyalkynyl linkage and the optical properties of the whole fullerene-porphyrin dyad. As a part of the present study, we have found that the nonlinear optical properties of model donor-substimted [60]fullerene derivatives are poorly described by the BLYP functional. The long-range corrected LC-BLYP functional, on the other hand, successfully cures the overshoot problem both for / and 7. The calculations for A-methylfulleropyrrolidine shows that the linear absorption spectra is reproduced quite well by conventional PBEO and B3LYP functionals. 

When a new monomer unit is formed at the end of a growing polymer chain, the probability of generating m and r sequences are denoted by and P, respectively. We can consider polymer chain propagation following Bernoullian statistics, where the probability of producing a new m or r structure at the end of the chain is not affected by the stereochemistry of the previous monomer. In this case, when a monomer is added to the chain, the relative fractions and NMR signal intensities from m and r dyads are determined by the addition probabilities Pm and P. The relative triad fractions, and, therefore, relative intensities of mm, rr and mr/rm triad s signals, can be calculated by eqs [58]-[63]. 

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