Gordon algorithm

It is interesting to compare the memory function procedure with the well known Gordon algorithm. In order to facilitate comparison with our method, we report it with an inessential change of rows and columns. The Gordon algorithm can be summarized as follows. 

The Gordon algorithm becomes inapplicable if some c, vanishes. 

Reddy, M. R. GLOGP a new algorithm for tlie estimation of log P for organic and biological molecules. Poster at Gordon Research Conf, Department of Chemistry, Gensia Inc., San Diego, CA, 1995. 

For a discussion of the algorithm, see Shampine, L. F. Gordon, M. K. "Computer Solution of Ordinary Differential Equations" Freeman San Francisco, 1975. 

G. K.-L. Chan and M. Head-Gordon, Highly correlated calculations with a polynomial cost algorithm a study of the density matrix renormahzation group. J. Chem. Phys. 116, 4462 (2002). 

The development of improved ab initio MD algorithms using DFT remains an active area. For one example of work in this area, see T. D. Kiihne, M. Krack, F. R. Mohamed, and M. Parrinello, Phys. Rev. Lett. 98 (2007), 066401. Similar work exists for performing MD using high-level quantum chemistry techniques, as described, for example, in J. M. Herbert and M. Head-Gordon, Phys. Chem. Chem. Phys. 7 (2005), 3629. 

M. Gordon and W. H. T. Davison [2] (1952) were the first to develop a simple algorithm which allows K to be determined for any CBS. Another basic paper is that of M. J. S. Dewar and H. C. Longuet-Higgins [3] (1952) who found the formula... 

The present paper is a review of the P-V path method. The concept of the P-V path was proposed by Gordon and Davison in 1952. In the last few years this method has been greatly developed and has become one of the important approaches for investigating Kekule structures of benzenoid hydrocarbons. The superiority of this method is its simplicity and visualization. According to the properties of the P-V path, some algorithmic approaches have been developed for deciding whether a benzenoid or a coronoid hydrocarbon is Kekulean. In 1985, John and Sachs introduced the concept of the P-V matrix and deduced the John-Sachs theorem which states that the absolute value of the determinant of the P-V matrix of a benzenoid or a coronoid hydrocarbon G is equal to the number of Kekule structures of G. 

Zeleznik and Gordon (2) and VanZeggeren and Storey (3) concentrate on thermodynamic fundamentals and numerical methods. Their conclusions should be reassessed in view of recent developments in numerical algorithms. 

Gordon and McBride (27), working at the NASA Lewis Research Center, developed an algorithm similar to the RAND Method. They minimized ... 

Gordon and Herman have also proposed a variety of formulae which allow one to compute the distance between the original picture and the reconstructed matrix, and therefore to evaluate the efficiency of a reconstruction algorithm. The ART method, in conclusion, is simple, fast and versatile, which explains why it has become an ideal starting-point for research on a new class of reconstruction algorithms. 

Gordon, R., and Herman, G.T. 1974. Three-dimensional reconstruction from projections a review of algorithms. International Review of Cytology, 38,111-151. 

In Table II we report the same illustrative example following the Gordon procedure. The convenience of the memory function method is apparent. Furthermore, the Gordon method fails unless 0, a restriction which is overcome in the memory function method. Another quite interesting P-algorithm has been provided by H ggi et al., and we refer to the original papers for illustration and discussion of stability aspects. 

M. J. Frisch, M. Head-Gordon, and J. A. Pople, Chem. Phys. Lett., 166, 281 (1990). Semi-Direct Algorithms for the MP2 Energy and Gradient. 

Ivanciuc, O. and Devillers, J. (2000). Algorithms and Software for the Computation of Topological Indices and Structure-property Models. In Topological Indices and Related Descriptors in QSAR and QSPR (Devillers, J. and Balaban, A.T, eds.), Gordon Breach, Amsterdam (The Netherlands), pp. 779-804. 

The product-difference (PD) algorithm was developed by Gordon (1968) and is based on the theory of continued fractions of Stieltjes. The first step is to construct a matrix P with... 

The most recent integral algorithms evolved with, and were influenced by, the advent of supercomputer technologies - if a new method cannot be "vectorized" and/or "parallelized", it faces a cool reception these days - and, of these, the Obara-Saika-Schlegel (OS) [53, 54], Head-Gordon-Pople (HGP) [55] and PRISM [61] algorithms are the most significant. 

In addition to stimulating a number of variations on the HGP theme, the seminal paper by Head-Gordon and Pople [55] also served to catalyse the development of a completely different approach to the Contraction Problem called the PRISM algorithm. 

By comparing Figures 1 and 2 with the descriptions in Sections 3.7 and 3.9, it becomes immediately apparent that the classical McMurchie-Davidson and Head-Gordon-Pople algorithms correspond to the MD-TTCTC and HGP-TCCTT paths, respectively. 

In a similar vein, it was a number of conversations with Martin Head-Gordon, shortly after his discovery of the algorithm which now bears his name, that sparked my early interest in the theory of Molecular Integrals. 

D. B. Gordon, S. L. Mayo. Branch-and-terminate a combinatorial optimization algorithm for protein design. Structure Fold Des. 1999, 7, 1089-1098. 

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