Mollified impulse method

This article is organized as follows Sect. 2 explains why it seems important to use symplectic integrators. Sect. 3 describes the Verlet-I/r-RESPA impulse MTS method, Sect. 4 presents the 5 femtosecond time step barrier. Sect. 5 introduce a possible solution termed the mollified impulse method (MOLLY), and Sect. 6 gives the results of preliminary numerical tests with MOLLY. 

The derivation of the mollified impulse method in [7] suggests that the same integrator be used for the auxiliary problem as that used for integrating the reduced primary problem M d fdt )X = F X) between impulses. Of eourse, Ax(x) is also needed. For the partitionings + j/aiow typically used in MD, this would lead unfortunately to a matrix Ax(x) with a great many nonzeros. However, it is probably important to take into account only the fastest components of [7]. Hence, it would seem sufficient to use only the fastest forces jjj averaging calculation. 

A different long-time-step method was previously proposed by Garci a-Archilla, Sanz-Serna, and Skeel [8]. Their mollified impulse method, which is based on the concept of operator splitting and also reduces to the Verlet scheme for A = 0 and admits second-order error estimates independently of the frequencies of A, reads as follows when applied to (1) ... 

Lecture Notes in Computational Science and Engineering (LNCSE), 24, 146 (2002). Overcoming Instabihties in Verlet-I/R-Respa with the Mollified Impulse Method. 

A number of methods have been proposed to overcome the MTS barrier, including averaging methods that mollify the impulse, allowing time steps of up to 6fs while maintaining the favorably small energy drift attained by impulse MTS methods with 4fs time steps. We will omit here the details of these time-stepping algorithms but point to a reference that explicitly provides implementation details. 

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