By Tim Spiller, Hoi-Kwong Lo
This publication is predicated on a lecture sequence held at Hewlett-Packard Labs, easy study Institute within the Mathematical Sciences (BRIMS), Bristol from November 1996 to April 1997, and in addition contains different contributions.
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One component of a force field is the energy arising from compression and stretching a bond. 21 Molecular Mechanics This component is often approximated as a harmonic oscillator and can be calculated using Hooke’s law. 1 2 V spring = --- K r ( r – r 0 ) 2 (7) The bonding between two atoms is analogous to a spring connecting two masses. Using this analogy, equation 7 gives the potential energy of the system of masses, Vspring, and the force constant of the spring, Kr . The equilibrium and displaced distances of the atoms in a bond are r0 and r.
Some systems converge poorly, particularly those with multiple bonds or weak interactions between open-shell systems. HyperChem includes two convergence accelerators. One is the default convergence accelerator, effective in speeding up normally Calculation Methods 47 Quantum Mechanics convergent calculations. The other, called the Direct Inversion in the Iterative Subspace (DIIS) method, is available for all the SCF methods in HyperChem. You can turn on this accelerator in the Semi-empirical Options dialog box or in the Ab Initio Options dialog box.
For quantitative details of quantum mechanics calculations and how HyperChem implements them, see the second part of this book, Theory and Methods. Ab initio quantum mechanics methods have evolved for many decades. The speed and accuracy of ab initio calculations have been greatly improved by developing new algorithms and introducing better basis functions. Semi-empirical quantum mechanics methods have evolved over the last three decades. Using today’s microcomputers, they can produce meaningful, often quantitative, results for large molecular systems.