Analysis of Different Fragmentation Strategies on a Variety of Large Peptides: Implementation of a Low Level of Theory in Fragment-Based Methods Can Be a Crucial Factor

Abstract

We have investigated the performance of two classes of fragmentation methods developed in our group (Molecules-in-Molecules (MIM) and Many-Overlapping-Body (MOB) expansion), to reproduce the unfragmented MP2 energies on a test set composed of 10 small to large biomolecules. They have also been assessed to recover the relative energies of different motifs of the acetyl(ala)18NH2 system. Performance of different bond-cutting environments and the use of Hartree-Fock and different density functionals (as a low level of theory) in conjunction with the fragmentation strategies have been analyzed. Our investigation shows that while a low level of theory (for recovering long-range interactions) may not be necessary for small peptides, it provides a very effective strategy to accurately reproduce the total and relative energies of larger peptides such as the different motifs of the acetyl(ala)18NH2 system. Employing M06-2X as the low level of theory, the calculated mean total energy deviation (maximum deviation) in the total MP2 energies for the 10 molecules in the test set at MIM(d=3.5Å), MIM(η=9), and MOB(d=5Å) are 1.16 (2.31), 0.72 (1.87), and 0.43 (2.02) kcal/mol, respectively. The excellent performance suggests that such fragment-based methods should be of general use for the computation of accurate energies of large biomolecular systems.

Understanding the many-body expansion for large systems. III. Critical role of four-body terms, counterpoise corrections, and cutoffs

“…In each of the remaining configurations, there is at least one inter-fragment distance greater than R cut1 , so each is excluded by the cutoff procedure of Eqs. (12) and (13).…”

“…For subsystems that exist in the switching region, meaning that R cut1 ≤ R max ≤ R cut1 + w, it is necessary to perform both the HF and the DFT calculations. The second approach is an ONIOM-type formalism, 48 inspired by the fragment-based methods introduced by Raghavachari and co-workers, 13,16,17,49,50 who use a supersystem calculation performed at an inexpensive level of theory in order to capture long-range induction effects that would otherwise be omitted in a low-order n-body calculation. This is an alternative way to account for the cooperative, long-range arrangements of fragment dipole moments.…”

“…For systems in this size range, the combination of high-level fragment calculation with a low-level supersystem calculation can afford useful results. 13,16,17,50 To put this in perspective, Table IV shows timing data for calculations on one isomer of (H 2 O) 20 using a variety of thresholds and also lists the time required for a HF/aTZ supersystem calculation. As above, all calculations are multithreaded across all 28 cores of one node.…”

“…5 An increasingly popular alternative, and one that is perhaps more easily amenable to large-scale parallelization, 6 is to adopt a fragment-based approach. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Fragmentbased methods attempt to bypass the steep non-linear scaling of traditional quantum chemistry by decomposing a large system into (a potentially very large number of) small fragments. Insofar as calculations can be performed independently on subsystems composed of these fragments, the overall method is trivially parallelizable.…”

The MOD-QM/MM Method

“…In that respect, a number of methods were previously proposed (Mayhall & Raghavachari, 2012; Saha & Raghavachari, 2015). One of them includes a standard atomic dipole description where dipole moments are induced in each atom of the MM layer, defined as the product of the atomic polarizability and the electric field at the position of the atom (Houjou, Inoue, & Sakurai, 2001; Illingworth et al, 2006; Thompson, 1996; Thompson & Schenter, 1995; Warshel, 1976).…”