Efficiently Capturing Weak Interactions in ab Initio Molecular Dynamics with on-the-Fly Basis Set Extrapolation

Abstract

Weak interactions have a critical role in accurately portraying conformational change. However, the computational study of these often requires large basis electronic structure calculations that are generally cost-prohibitive within ab initio molecular dynamics. Here, we present a new approach to efficiently obtain AIMD trajectories in agreement with large, triple-ζ, polarized valence basis functions, at much reduced computational cost. For example, it follows from our studies that AIMD trajectories can indeed be constructed in agreement with basis sets such as 6-311++G(2df,2pd) with computational effort commensurate with those from much smaller basis sets such as 6-31+G(d), for polypeptide systems with 100+ atoms. The method is based on molecular fragmentation and allows a range-specified repartitioning of intramolecular (and potentially intermolecular) interactions where noncovalent interactions are selectively assembled using a piece-wise reconstruction based on a set-theoretic inclusion−exclusion principle generalization of ONIOM. Through a simplex decomposition of molecular systems the approach efficiently provides the necessary many-body interactions to faithfully represent noncovalent interactions at the large basis limit. Conformational stabilization energies are provided at close to the complete-basis limit at much reduced cost, and similarly AIMD trajectories (both Born−Oppenheimer and Car−Parrinello-type) are obtained in agreement with very large basis set sizes, in an extremely efficient and accurate manner. The method is demonstrated through simulations on polypeptide fragments of a variety of sizes.

Embedded, graph‐theoretically defined many‐body approximations for wavefunction‐in‐DFT and DFT‐in‐DFT: Applications to gas‐ and condensed‐phase ab initio molecular dynamics, and potential surfaces for quantum nuclear effects

“…The basis set extrapolations demonstrated in ref. [43] maintain the same electronic structure methods for both the high and low levels of theory with only the basis set choice changing, as seen from Figure 2B. As we will see later, and as shown in refs.…”

“…[42‐44] from a graph‐theoretic decomposition of the molecular structure. We have shown [ 42,44,45 ] that this procedure captures the accuracy at higher levels of theory and basis (level, 1 above) at computational costs commensurate with that from level, 0. The low computational cost associated with this procedure may be inferred from Figure 2.…”

“…Following the graphical decomposition of molecular system as per the above prescriptions, in refs. [44,45], we replace the appearance of each rank‐ r simplex in Equation ), numbered using the index α r , by an energy correction corresponding to the molecular interactions captured by the specific simplex: where the summation over α r is over all rank‐ r simplexes, that is, rank‐ r many‐body expansions. Furthermore, by comparison with Equation ), it is clear that Equation ) represents one part of the summation in the many‐body expansion, and hence here the graphical decomposition is essentially used to adaptively determine the many‐body expansion that is embedded within a calculation that represents the full system, consistent with Equation ).…”

“…[44], we demonstrated MP2‐quality potential energy surfaces at DFT costs using multiple graphical descriptions of the system. In ref. [45] we adapted this approach to compute condensed‐phase electronic‐structure‐based lattice energies for adsorbates on the surface of water, using higher rung DFT functionals [ 50,90,91 ] at much reduced costs. The approach also allows large basis set studies in condensed‐matter systems. Our studies are performed using an MPI parallelized C++ module with embedded python function calls that computes the energy and forces by spawning out the rank‐ r simplex calculations.…”

“…Furthermore, we have also shown in ref. [45] how condensed‐phase simulations on interfaces and liquids may be constructed with hybrid DFT accuracy at gradient‐corrected DFT accuracy. The approach utilizes graph‐theoretic methods to perform an ONIOM‐type decomposition of the system where the individual extrapolatory components in the ONIOM expression are obtained from many‐body theory.…”