Using a monomer potential energy surface to perform approximate path integral molecular dynamics simulation of ab initio water at near-zero added cost

Abstract

It is now established that nuclear quantum motion plays an important role in determining water's hydrogen bonding, structure, and dynamics. Such effects are important to include in density functional theory (DFT) based molecular dynamics simulation of water. The standard way of treating nuclear quantum effects, path integral molecular dynamics (PIMD), multiplies the number of energy/force calculations by the number of beads required. In this work we introduce a method whereby PIMD can be incorporated into a DFT simulation with little extra cost and little loss in accuracy. The method is based on the many body expansion of the energy and has the benefit of including a monomer level correction to the DFT energy. Our method calculates intramolecular forces using the highly accurate monomer potential energy surface developed by Partridge-Schwenke, which is cheap to evaluate. Intermolecular forces and energies are calculated with DFT only once per timestep using the centroid positions. We show how our method may be used in conjunction with a multiple time step algorithm for an additional speedup and how it relates to ring polymer contraction and other schemes that have been introduced recently to speed up PIMD simulations. We show that our method, which we call "monomer PIMD", correctly captures changes in the structure of water found in a full PIMD simulation but at much lower computational cost.There is great interest in being able to accurately simulate liquid water at the quantum mechanical level. [1][2][3][4] The most widely used methodology for this is density functional theory. However, many density functionals fail to accurately reproduce all of the key properties of water such as its density, compressibility, and diffusion constant. Moreover, different density functionals fail in different ways. For instance, PBE creates a overstructured liquid, while many van der Waals (vdW) functionals create an understructured liquid. 5,6 There are nonetheless new meta-GGA functionals such as SCAN 7 or empirically optimized hybrid functionals such as B97M-rV 8 which are producing promising results for liquid water.Most ab initio techniques are based on the Born-Oppenheimer approximation and the assumption that nuclear dynamics can be treated classically. However, over the past two decades a wide range of studies have demonstrated that this is not a good assumption for water because the OH stretching mode of water is very quantum mechanical (zero point temperature T z = ω/2k b = 2600 K), and hydrogen nuclei are delocalized, leading to a large number of nonnegligible nuclear quantum effects (NQEs) -for a recent review, see Ceriotti, et al. 9 In the primary isotope effect, the OH distance is observed to be longer than the OD distance. In the secondary isotope effect, also called the Ubbelöhde effect, the H-bond donoracceptor (oxygen-oxygen) distance R changes upon isotopic substitution. The magnitude and direction of the change depends on the strength of the hydrogen bond, due to competing a) Electronic quantum effects. [10...

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water

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“…29 Another solution to avoid double counting is the application of PIMD with ab initio methods 9 or force fields trained on ab initio data. 25,27,30 Numerous methodological developments have also been made to calculate quantum free energy values from PIMD simulations. 31−35 In routine DFT calculations, with the optimized geometry in hand, the free energies are summed for all the different motions such as translation, rotation, and vibration, using the partition functions of the particle in the box, rigid rotor, and harmonic oscillator (RRHO) models.…”

“…When empirical water models were used in PIMD simulations, several properties deviated more from the experiments than in the classical simulations. − In these quantum simulations, the liquid water becomes less structured and less viscous. This has been explained by double counting of quantum effects: once in the parameter optimization using experimental data, second in the quantum simulations.…”

“…This is why several water models were reparametrized for accurate PIMD simulations resulting in q-SPC/Fw, q-TIP4P/f, and TIP4PQ/2005 models . Another solution to avoid double counting is the application of PIMD with ab initio methods or force fields trained on ab initio data. ,, Numerous methodological developments have also been made to calculate quantum free energy values from PIMD simulations. − …”