Fragment calculation

Gaspar, R., Jr., and R. Gaspar. 1983. Ab Initio Molecular Fragment Calculations with Pseudopotentials Model Peptide Studies. Int. J. Quantum Chem. 24, 767-771. 

Theoretical studies of such big molecules are at the present time far beyond the computational possibilities, and experimental determination of electron density is the only tool to get accurate electrostatic parameters. However, it may be possible to recover the experimental electron density by performing ab initio fragment calculations [28]. 

Coagulation Phenomena. Agglomeration and fragmentation calculations which bear direct kinship to the Fokker-Planck treatments but also include discussion of expectation of W-body systems for which the initial distribution function and dynamics cannot be or are not treated in the continuum limit. 

They have additional two publications, which have the following titles FSGO study of the Gauss-type pseudopotential for the Lithium and Lithium(l-) and its isoelectronic series, ab initio molecular fragment calculations with pseudopotentials, calculation on Li2, LiH and BeH2, and Ab initio molecular fragment calculations with pseudopotentials model peptide studies . ... 

Delaney [13] describes the solubilization mechanism as controlled by a double phenomenon the affinity of the compound for itself and the affinity of the compound for the solvent. The latter effect is simply described either by the log P property or by very sophisticated methods such as statistical thermodynamic or quantum mechanical techniques. These very intensive calculation methods have not yet proved their superiority over the simpler and faster methods that tend to mimic the successful log P fragment calculator. 

Three antimony-containing fragments Calculated percentage 19 42 31 8 ... 

Four antimony-containing fragments Calculated percentage 11 32 36 18 3... 

The two different isomers were modelled through rigid [Rh(PH3)4] fragments. Calculations at the RHF-SCF level were made through use of pseudopotentials for the rhodium and phosphorus atoms. A double- basis set was used for Rh and active hydrogen atoms, whereas a minimal basis set was employed for phosphines. The relative positions of the hydrogen atoms was completely optimized. 

For convenience, we will use the index I for the largest oligomer size in fragment calculations, namely... 

Bismuth chloride forms a simple bis(adduct) 48 with [Fe(CO)4] (Equation (95)). The Lewis-acidic bismuth atoms expand their coordination environments by sharing chloride ions. The bismuth atoms are distorted square pyramids attached to a distorted octahedral iron carbonyl fragment. Calculations on these structures indicated that a substantial charge separation remains in the products. 

The various aspects of the fragment calculations presented here for the leu -zervamicin molecule will be discussed in some detail. 

The fragment calculations are based on structural data, i.e., atomic positions, for leu -zervamicin, Ac-Leu-Ile-Gln-Iva-Ile-Thr-Aib-Leu-Aib-Hyp-Gln-Aib-Hyp-Aib-Pro-Phol obtained from a crystal structure determination.The formation of molecular orbitals follows the procedure presented in Ref. 1, with the necessary adjustments for the different peptide residues and solvents present. 

The purpose of the fragment calculations presented here is to obtain an ab initio projector matrix, P, when ab initio calculations of an entire molecule are either not feasible or considered to be too time-consuming. In our calculations, a fragment consists of an inner core or kernel and a number... 

The matrix S, defined in equation (6), is a matrix representing the overlap integrals of pairs of orbitals. For pairs of orbitals belonging to atoms that are separated by large distances, the values of the overlap integrals will be close to zero. The behavior of S is the reason why the fragment calculations can give accurate values for the elements of P for the molecule as a whole. 

The fragment calculations for the hydrated hexadecapep-tide, leu -zervamicin, were performed by defining 19 kernels as the 16 peptide residues, two clusters of water molecules and a cluster of a water and an ethanol molecule. In this application, the neighborhoods were formed with atoms within 5 A of the kernels plus a few additions to assure that all electrons were paired. The kernels and their neighborhoods are listed in Table 1. The numbers refer to the peptide residues in the sequence that were given above in the description of the chemical content of the leu -zervamicin molecule. The symbols in Table 1 correspond to those found in the crystal... 

Figure 1 A schematic diagram of the R matrix that was obtained from the fragment calculations for hydrated leu -zervamicin. The numbers in the figure label the kernels as in Table 1. The elements in the dark squares are composed of functions of the coefficients of pairs of orbitals associated with the atoms of the particular kernel. The elements in the gray squares and hatched squares ate composed of functions of the coefficients of pairs of orbitals, one of which is associated with a kernel atom of the dark square in the same row and the other is associated with an atom of the labeled neighborhood. The contents of the dark square labeled by kernel 7 are shown in Figure 2 at higher resolution...

As mentioned above, as soon as a contribution to the R matrix was obtained from a fragment calculation, it was converted to the corresponding contribution to the P matrix... 

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