Editing Computational chemistry (section)

===== Split operator technique =====
How a computational method solves quantum equations impacts the accuracy and efficiency of the method. The split operator technique is one of these methods for solving differential equations. In computational chemistry, split operator technique reduces computational costs of simulating chemical systems. Computational costs are about how much time it takes for computers to calculate these chemical systems, as it can take days for more complex systems. Quantum systems are difficult and time-consuming to solve for humans. Split operator methods help computers calculate these systems quickly by solving the sub problems in a quantum [[differential equation]]. The method does this by separating the differential equation into two different equations, like when there are more than two operators. Once solved, the split equations are combined into one equation again to give an easily calculable solution.<ref name="Lukassen-2018" />

This method is used in many fields that require solving differential equations, such as [[Mathematical biology|biology]]. However, the technique comes with a splitting error. For example, with the following solution for a differential equation.<ref name="Lukassen-2018" />

<math display="inline">e^{h(A+B)} </math>

The equation can be split, but the solutions will not be exact, only similar. This is an example of first order splitting.<ref name="Lukassen-2018" />

<math display="inline">e^{h(A+B)} \approx e^{hA}e^{hB} </math>

There are ways to reduce this error, which include taking an average of two split equations.<ref name="Lukassen-2018" />

Another way to increase accuracy is to use higher order splitting. Usually, second order splitting is the most that is done because higher order splitting requires much more time to calculate and is not worth the cost. Higher order methods become too difficult to implement, and are not useful for solving differential equations despite the higher accuracy.<ref name="Lukassen-2018" />

Computational chemists spend much time making systems calculated with split operator technique more accurate while minimizing the computational cost. Calculating methods  is a massive challenge for many chemists trying to simulate molecules or chemical environments.<ref name="Lukassen-2018" />