Most of the physical phenomena are multiscale in nature and therefore, to depict it properly one requires multiscale modelling techniques, i.e. physical models that are accurate over multiple length and time scales. The seminal work by Warshel and Levitt marks the beginning of hybrid quantum mechanics/molecular mechanics (QM/MM) method as a successful strategy towards the understanding of chemistry and physics in condensed phases and especially in biological systems. Recently, these methods have been extended to problems such as light-matter interaction, where the QM sub-system is excited from the ground to the excited states. The MM environment provides a field that changes the potential energy landscape of both the ground and excited states in a distinctly different way. In this review, we discuss the general strategy of multiscale modelling with emphasis on hybrid QM/MM and the recent developments in excited state QM/MM methods.Keywords: Biological systems, hybrid quantum mechanics/molecular mechanics, multiscale.
Multiscale modellingMANY real-world phenomena are multiscale in nature, i.e. they show complex behaviour that spans over a large range of length and time scales. Length scales can span from few Å in case of bond lengths to a few microns in case of living cell. On the other hand, time scales can range from femtosecond (10 -15 s) for bond vibrations to milliseconds (10 -3 s) for protein folding. In most cases, the different scales (microscopic and macroscopic when it is the length scales) might be a continuum of varying scales. The microscopic behaviour in most cases is specific and complex, while the macroscopic behaviour can be defined by more general rules. For example, the flow of traffic or pedestrians in a crowded street. If one tracks the trajectory of individual pedestrians, they have a specific destination and, therefore, they move towards that destination while avoiding the nearest neighbour interactions or collisions. However, when one zooms out and looks at the average pattern of flow it is very similar to fluid dynamics through a constrained space.Traditionally models have been developed that describe the physics associated with a single time and length scale. However, since the real-world phenomena requires one to span over more than one scale, simulation or modelling techniques have evolved such that they can handle multiple scales in a seamless fashion 1 .
Analytical multiscale methodsAnalytical multiscale approaches have been developed for quite a few decades now. In this approach, one derives the rules (or phenomenological models) of a macroscale system from that of a microscale model. Renormalization group (RG) is a classic example of such analytical multiscale method 2 . RG has been used to study phase transitions and critical phenomena. The need for renormalization arises when there are two or more different scales (time or length) and there is no clear demarcation between them. RG is a technique to reduce the degrees of freedom by integrating out less important degrees of freedom...