Molecular integral algorithms

D. Janezid and F. Merzel. An efficient symplectic integration algorithm for molecular dynamics simulations. J. Chem. Info. Comp. Set, 35 321-326, 1995. 

Janezic, D., Merzel, F. An Efficient Symplectic Integration Algorithm for Molecular Dynamics Simulations. J. Chem. Inf. Comput. Sci. 35 (1995) 321-326... 

Fincham D and Heyes D M 1982. Integration Algorithms in Molecular Dynamics. CCP5 Quarterly 6A 10. 

Prepare a molecule for a molecular dynamics simulation. If the forces on atoms are too large, the integration algorithm may fail during a molecular dynamics calculation. 

Mechanism. The thermal cracking of hydrocarbons proceeds via a free-radical mechanism (20). Since that discovery, many reaction schemes have been proposed for various hydrocarbon feeds (21—24). Since radicals are neutral species with a short life, their concentrations under reaction conditions are extremely small. Therefore, the integration of continuity equations involving radical and molecular species requires special integration algorithms (25). An approximate method known as pseudo steady-state approximation has been used in chemical kinetics for many years (26,27). The errors associated with various approximations in predicting the product distribution have been given (28). 

Despite the interest to obtain AO integral algorithms over cartesian exponential orbitals or STO fimctions [43] in a computational universe dominated by GTO basis sets [2], this research was started as a piece of a latter project related to Quantum Molecular Similarity [44], with the concurrent aim to have the chance to study big sized molecules in a SCF framework, say, without the need to manipulate a huge number of AO functions. 

Implementation of the whole set of integral algorithms within the ARIADNE molecular program [66a] as well as MOLSIMIL molecular Quantum Similarity code [66b], developed in our Laboratory is under way. A discussion on the sequential, vector and parallel programming features of the CETO integral calculation will be ptablished elsewhere. Perhaps other available ETO functions, left unexplored on this paper, will be studied in the near future and the... 

Similiar problems are known in classical MD simulations, where intramolecular and intermolecular dynamics evolve on different time scales. One possible solution to this problem is the method of multiple time scale propagators which is describede in section 5. Berne and co-workers [21] first used different time steps to integrate the intra- and intermolecular degrees of freedom in order to reduce the computational effort drastically. The method is based on a Trotter-factorization of the classical Liouville-operator for the time evolution of the classical system, resulting in a time reversible propagation scheme. The multiple time scale approach has also been used to speed up Car-Parrinello simulations [20] and ab initio molecular dynamics algorithms [21]. 

G. J. Martyna, A. Hughes, and M. E. Tuckerman (1999) Molecular dynamics algorithms for path integrals at constant pressure. J. Chem,. Phys. 110, p. 3275... 

The direct Cl method was proposed in 1972 by Roos. The idea of this method is to avoid the explicit construction and storage of the large Hamilton matrix. Instead, the eigenvectors are found iteratively. The basic operation in each iteration is to form the vector g = H c directly from the molecular integrals and the trial vector c. The optimum algorithm to form this product... 

Another way to view MD simulation is as a technique to probe the atomic positions and momenta that are available to a molecular system under certain conditions. In other words, MD is a statistical mechanics method that can be used to obtain a set of configurations distributed according to a certain statistical ensemble. The natural ensemble for MD simulation is the microcanonical ensemble, where the total energy E, volume V, and amount of particles N (NVE) are constant. Modifications of the integration algorithm also allow for the sampling of other ensembles, such as the canonical ensemble (NVT) with constant temperature... 

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. 

We have recently developed an efficient computational scheme for the four-component method that employs four-component contraction for molecular basis spinors and the new atomic spinor (AS) integral algorithm [130-132]. In the following sections we will briefly introduce our new relativistic scheme. 

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