Molecular code structure

Over the last thirty years, international collaboration and cooperation on a scale rarely witnessed in science has led to the development of several very sophisticated software packages for ab initio molecular electronic structure calculations. In the early days, such packages were freely distributed amongst workers in the field. Today, you buy executable code, a licence and professional documentation just as with any software package. 

H.M. Quiney and S. Wilson, Literate programming in quantum chemistry A collaborative approach to code development for molecular electronic structure theory, Molec. Phys. 103, 389 (2005). 

Abstract. BERTHA is a 4-component relativistic molecular structure program based on relativistic Gaussian (G-spinor) basis sets which is intended to make affordable studies of atomic and molecular electronic structure, particularly of systems containing high-Z elements. This paper reviews some of the novel technical features embodied in the code, and assesses its current status, its potential and its prospects. 

Beside the descriptors, further attempts have been made to encode the 3D molecular structures with functions. Such are 3D-MoRSE code [54] spectrum-like representations [55] and radial distribution functions [56]. Also, experimentally determined infrared, mass, or NMR spectra can be taken to represent a molecule [57]. Another example is comparative molecular field analysis (CoMFA) where the molecular 3D structures are optimized together with the receptor [58]. This approach is often applied in drug design or in specific toxicology studies where the receptor is known. The field of molecular descriptors and molecular representations has exploded in the recent decades. Over 200 programs for calculating descriptors and different QSAR applications are listed on web page [59]. 

Goldbeck RA, Esquerra RM, Holt JM, Ackers GK, Kliger DS. The molecular code for hemoglobin allostery revealed by linking the thermodynamics and kinetics of quaternary structural change. 1. Microstate linear free energy relations. Biochemistry 2004 43 12048-12064. 

Another attempt to formalize the distribution of software for atomic and molecular physics is the journal Computer Physics Communications K. V. Roberts, Comput. Phys. Commun., 1969, 1, 1 which published both scientific papers and computer programs. In spite of the continued success of this journal, it has nevertheless has to be observed that few complete quantum chemical packages have been published via this mechanism, although there are exceptions. For example, the HONDO code, The general atomic and molecular electronic structure system HONDO version 7.0 was published in Computer Physics Communications in 1989. ... 

In principle, all four-component molecular electronic structure codes work like their nonrelativistic relatives. This is, of course, due to the formal similarity of the theories where one-electron Schrbdinger operators are replaced by four-component Dirac operators enforcing a four-component spinor basis. Obviously, the spin symmetry must be treated in a different way, i.e. it is replaced by the time-reversal symmetry being the basis of Kramers theorem. Point group symmetry is replaced by the theory of double groups, since spatial and spin coordinates cannot be treated separately. 

The strategy of this approach was to develop a set of molecular codes corresponding to the number of self-avoiding paths of each length in a molecule, for use both as a convenient representation in subsequent similarity searches [52-54], and as a quantitative measure of structural complexity. Since the basic calculation method for these codes was again based on counting bonds, it is easy to visualize how these path codes are related to the Weiner index (Fig. 13.1-3). While these initial molecular codes did not address... 

The development of DFT band structure calculations in the condensed matter physics community have followed a similar course as that described for the molecular codes in chemistry. DPT was... 

We will try to answer some of these questions in this chapter. The emphasis will be on representation and characterization of molecules rather than the questions concerning molecular similarity and structure-property relationships. We will differentiate between the representation and the characterization. The former is based on molecular codes and the latter on structural invariants. The codes allow one to represent a structure without loss of information, hence they allow one to reconstmct the object fully from a given code. Invariants represent mathematical properties of a structure and are therefore useful in structure-property analysis, as well as in comparisons of different stmctures. The list of invariants need not be unique, hence, invariants do not generally allow reconstruction. Figuratively speaking, characterization depicts various... 

In a series of articles Mezey and Arteca studied topological properties of molecular surfaces in order to quantify molecular shape. " They characterized the shape by considering curvatures of portions of the molecular surface that have distinct topological properties. We will focus attention on a characterization of the molecular shape by binary molecular codes. Instead of considering the general problem of molecular shapes, we will consider a simpler task, namely, the characterization of the shapes of planar benzenoids. It will be revealed that the approach applies to the characterization of the shape of an arbitrary closed planar curve. A satisfactory code for the periphery of a simple benzenoid should be linear, have structural origin, be simple, have similar lengths for objects of similar size, be unique, and should allow reconstruction. 

We now have all the pieces of code needed to implement all the steps in the calculation of molecular electronic structure by the expansion method ... 

The design and codes developed in the last chapter work when tested with the two representative cases. But these cases are both rather trivial compared with the tasks which might be expected of a program for the calculation of molecular electronic structure six or seven basis functions is hardly typical. 

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