Ideas of Quantum Chemistry P36 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 316 7. Motion of Nuclei Fig. . A scheme showing why the acceleration ifji of the spinorbital has to be of the same sign as that of -F i. Time arbitrary units goes from up t 0 downwards t 3 where the time step is At 1. On the left hand side the changes localized in 1D space x axis of are shown in a schematic way in single small square units . It is seen that the velocity of the change is not constant and the corresponding acceleration is equal to 1. Now let us imagine for simplicity that function F i has its non-zero values precisely where 0 and let us consider two cases a F i 0 and b F i 0. In such a situation we may easily foresee the sign of the mean value of the energy F i of an electron occupying spinorbital . In situation a the conclusion for changes of is keep that way or in other words even increase the acceleration i i making it proportional to -F i. In b the corresponding conclusion is suppress these changes or in other words decrease the acceleration . making it negative as -F i. Thus in both cases we have pa i -F i which agrees with eq. . In both cases there is a trend to lower orbital energy Si i F i . a Fipi o b FVi 0 1 1 0 r L_ V zlAftf 0 1 1 V ilAft o o 1 1 V il i o r L_ Pi F 0 1 1 Cellular automata 317 From Fig. it is seen that it would be desirable to have the acceleration ijij with the same sign as -F . This is equivalent to increase the changes that lower the corresponding orbital energy and to suppress the changes that make it higher. The spinorbitals obtained in the numerical integration have to be corrected for orthonormality as is assured by the second term in . The prize for the elegance of the Car-Parrinello method is the computation time which allows one to treat systems currently up to a few hundreds of atoms while MD may even deal with a million of atoms . The integration interval has to be decreased by a factor of 10 . fs instead of 1 fs which allows us to reach simulation times of the order of 10-100 .
