Molecular internal space applications

The development and application of molecular shape descriptors is an active area in computational chemistry and biology. The main goal of our work is to develop mathematical descriptors that can determine whether two molecules have comparable shapes. In this chapter we present a series of molecular shape descriptors developed oti the basis of molecular vdW space. The molecules are treated in the hard sphere approximation, as a body composed from a collection of atomic fused spheres. Each sphere is centered in the corresponding nucleus and it is characterized by its Cartesian coordinates and by its vdW radius, r. These molecular vdW shape descriptors depend only on the internal structure of the molecule, being invariants to any translation and rotation movement. Consequently, they may inform us that two molecules have comparable shapes, but since they carry no information about the absolute orientation or position of the molecule, they are not useful for computing molecular superposition. 

Xpert Rule is widely used in industrial and scientific applications, one of them performed in cooperation with NASA and Rockwell Aerospace. It is called NASA s Contamination Control Engineering Design Guidelines Expert System and was developed by Rockwell International s Space Systems Division. It was developed for education in contamination control processes and is designed as an interactive guide to assist with quantifying contamination for sensitive surfaces. The tool enables the user to quantify molecular and particulate contamination requirements for solar arrays, thermal control surfaces, or optical sensors [24],... 

Debashis Mukherjee is a Professor of Physical Chemistry and the Director of the Indian Association for the Cultivation of Science, Calcutta, India. He has been one of the earliest developers of a class of multi-reference coupled cluster theories and also of the coupled cluster based linear response theory. Other contributions by him are in the resolution of the size-extensivity problem for multi-reference theories using an incomplete model space and in the size-extensive intermediate Hamiltonian formalism. His research interests focus on the development and applications of non-relativistic and relativistic theories of many-body molecular electronic structure and theoretical spectroscopy, quantum many-body dynamics and statistical held theory of many-body systems. He is a member of the International Academy of the Quantum Molecular Science, a Fellow of the Third World Academy of Science, the Indian National Science Academy and the Indian Academy of Sciences. He is the recipient of the Shantiswarup Bhatnagar Prize of the Council of Scientihc and Industrial Research of the Government of India. 

Instead of the usual Cartesians, we can also apply a complete and non-redundant set of the so-called internal coordinates. In order to understand their application in vibrational calculations, let us consider a molecular system consisting of N nuclei let the Cartesian displacement vectors of the nuclei bedi,d2.---./ A around their equilibrium geometry in the usual three-dimensional Euclidean space E3. (The expression for the n-th Cartesian displacement vector is dn = Pn — P% where p is the instantaneous position vector of the n-th nucleus, and /0° is the position vector of the same nucleus at equilibrium. Hereafter, these position vectors correspond to an arbitrary origin. Note that for simplicity, we omit the explicit use of the atomic masses, i.e., do not use mass-weighted Cartesians.) A single-point 5 of a hypothetical 3iV-dimensional space (5 Iftsw), defined as... 

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