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Ideas of Quantum Chemistry P35

Ideas of Quantum Chemistry P35 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. | 306 7. Motion of Nuclei All on the right hand side of 7.15 and 7.16 is known. Therefore the new positions and the new velocities are easy to calculate.57 Now we may use the new positions and velocities as a start ones and repeat the whole procedure over and over. This makes it possible to go along the time axis in a step-like way in practice reaching even nanosecond times 10-9 sec which means millions of such steps. The procedure described above simply represents the numerical integration of 3N differential equations. If N 2000 then the task is impressive. It is so straightforward because we are dealing with a numerical not analytical solution.58 7.6.2 WHAT DOES MD OFFER US The computer simulation makes the system evolve from the initial state to the final one. The position R in 3N-dimensional space becomes a function of time and MD trajectory therefore R t represents the trajectory of the system in the configurational space. A similar statement pertains to v t . Knowing the trajectory means that we know the smallest details of the motion of all the atoms. Within the approximations used we can therefore answer any question about this motion. For example we may ask about some mean values like the mean value of the total energy potential energy kinetic energy the distance between atom 4 and atom 258 etc. All these quantities may be computed at any step of the procedure then added up and divided by the number of steps giving the mean values we require. In this way we may obtain the theoretical prediction of the mean value of the interatomic distance and then compare it to say the NMR result. In this way we may search for some correlation of motion of some atoms or correlation and groups of atoms i.e. the space correlation when this group of atoms is shifted to auto-correlation the left then another group is most often shifted to the right or the time correlation when this thing happens to the functional group G1 then after a time t that most often takes place with .