Atomic frame heavy

Thii MNDO niijthod has 22 iiniqiiLi iwo-ctMUer two-eliicLron irUti-gials Ibr each pair ol heavy (non-hydrogen ) atoms in iheir local atomic frame. They are ... 

The terms of this type must be summed over all bonds between the heavy atoms. The formulae eqs. (3.100), (3.101) represent the potential energy of the molecular system as a quadratic function on small variations of the variables wf. This may be used either in a frame of a linear response analysis of reaction of the system of hybridization tetrahedra to various perturbations or (if the hybridization tetrahedra are supplied by fictitious inertia momenta) as potential energy of the system of the tetrahedra in a frame of a Car-Parinello-like [46] procedure. 

Figure 11 (see color section). Longitudinal H-bond relay comprised of CHQs and water, (a) Tubular polymer structure of a single nanotube obtained with X-ray analysis for the heavy atoms and with ab initio calculations for the H-orientations (top and side views), (b) One of the four pillar frames of short H-bonds represents a 1-D H-bond relay composed of a series of consecutive OH groups [hydroxyl groups (—OH) in CHQs and the OHs in water molecules]. Reproduced by permission of American Chemical Society Ref. [54]. 

In the frame of ab initio methods, much attention was paid in the last decades to the fields of relativity and correlation. Relativistic approximations have been defined in all-electron schemes [1] able to handle correlation, even using sophisticated Cl methods. Unfortunately such methods are very computer resource demanding, and are therefore severely limited to systems containing at most two heavy atoms. Three ingredients can be employed, separately or altogether to improve the efficiency in the calculations ... 

Most discrete MTP implementations are similar in many respects, e.g., limited expansion up to order 2-4, spherical harmonic description, interaction calculation in the atoms local frames. Hence, what distinguishes these force fields and implementations from each other is primarily in how they treat the other interaction terms. Most importantly, static multipoles only consist of a first-order perturbation of the electrostatic operator. Describing second-order effects leads to polarizability—the charge density s ability to respond to an external electric field—a critical aspect of certain systems (e.g., dielectric changes) [62-64]. Here, possible implementations are ordered in terms of increased overall accuracy (and thus computational investment and larger parametrization effort). Given the heavy requirements of such refined force fields, it is important to point out that "more is not always better," and each system of interest will call for a fine balance of accuracy and statistical sampling. 

For molecular skeletons with only first-row heavy atoms (C, N, O) the CNDO/S procedure gives reasonable electron density distributions. Then, if one relates the total CNDO/S electron densities of the terminal carbon atoms in the parent cumulenic systems H2C=X=Y (11,42,43,49 X, Y = C, N, O) to the C chemical shifts of the methyl carbon atoms in corresponding methyl-phenyl compounds MePhC=X=Y (Fig. 18), a total electron density of about 4.15 e is estimated for the terminal carbon atom in thioketene (50) (Schs (MePhC=C=S) = 10.5 ppm (97a)). This is near the PNO-CEPA value for 50, Therefore, it seems that the calculated CNDO/S electron density distribution does not reflect the actual situation in the cumulenic skeleton, if a second-row atom is a constituent atom of the cumulenic frame. 

The validity of the preceding relations is guarenteed by the fact that the infrared excitation v s is concerned with a motion retaining the overall linear heavy atom arrangement of the cumulenic frame. 

The experimental heavy atom X-ray frame was kept rigid, but all 0-H and C-H bond lengths and bond angles were optimized using AMI." Heavy atom X-ray frame from [163]. Heavy atom X-ray frame from [162]. AMI energies of MM2 optimized stmctures. Heavy-atom X-ray frame from [164]. 

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