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On the Importance of Accounting for Nuclear Quantum Effects in Ab Initio Correction CHEMISTRY, BIOPHYSICS AND COMPUTATIONAL BIOLOGY Correction for “On the importance of accounting for nuclear quantum effects in ab initio calibrated force fields in biological simulations,” by Leonid Pereyaslavets, Igor Kurnikov, Ganesh Kamath, Oleg Butin, Alexey Illarionov, Igor Leontyev, Michael Olevanov, Michael Levitt, Roger D. Kornberg, and Boris Fain, which was first published August 20, 2018; 10.1073/ pnas.1806064115 (Proc Natl Acad Sci USA 115:8878–8882). The authors note that, in line 12 of the Significance Statement, “inaccurate” should instead appear as “accurate.” Published under the PNAS license. Published online September 17, 2018. www.pnas.org/cgi/doi/10.1073/pnas.1814845115 E9258 | PNAS | September 25, 2018 | vol. 115 | no. 39 www.pnas.org Downloaded by guest on October 1, 2021 On the importance of accounting for nuclear quantum effects in ab initio calibrated force fields in biological simulations Leonid Pereyaslavetsa,1, Igor Kurnikova, Ganesh Kamatha, Oleg Butina, Alexey Illarionova, Igor Leontyeva, Michael Olevanova, Michael Levittb,1, Roger D. Kornbergb, and Boris Faina aInterX Inc., Berkeley, CA 94710; and bDepartment of Structural Biology, Stanford University School of Medicine, Stanford, CA 94305 Contributed by Michael Levitt, July 10, 2018 (sent for review April 11, 2018; reviewed by Michele Ceriotti and Glenn J. Martyna) In many important processes in chemistry, physics, and biology the Atoms and nuclei, however, do not behave classically (3, 15–18) nuclear degrees of freedom cannot be described using the laws of and quantum uncertainty in atomic position may significantly classical mechanics. At the same time, the vast majority of molecular impact the structure and properties of the ensemble. The impor- simulations that employ wide-coverage force fields treat atomic tance of these NQEs is widely known and accepted by researchers motion classically. In light of the increasing desire for and accelerated working on, for example, path integral MD (PIMD) and ab initio development of quantum mechanics (QM)-parameterized inter- MD (15), as well as by the community working on water models. action models, we reexamine whether the classical treatment is The focus on water is natural since water, due to its importance, sufficient for a simple but crucial chemical species: alkanes. We ubiquity, and anomalies is the traditional starting point for FF show that when using an interaction model or force field in development. However, water simulations can actually obscure the excellent agreement with the “gold standard” QM data, even very importance of NQEs because the various effects oppose and thus basic simulated properties of liquid alkanes, such as densities and partially cancel each other (19). At this time the widely used FFs heats of vaporization, deviate significantly from experimental val- and simulation packages rarely, if ever, consider NQEs. There are ues. Inclusion of nuclear quantum effects via techniques that treat two reasons for this. First, these FFs are empirical and thus fitted CHEMISTRY nuclear degrees of freedom using the laws of classical mechanics to reproduce experimental results; they therefore contain the brings the simulated properties much closer to reality. NQE corrections implicitly. Second, as the vast majority of in- vestigations of NQE have concentrated primarily on water (15, 20) nuclear quantum effect | path integral molecular dynamics | force field | or systems with extreme physical conditions that enhance NQE ab initio | alkanes (21, 22), the errors caused by leaving them out are thought to be minor compared with the accuracy of the FFs themselves, and istorically, simulation of biomedically important systems has hence with the expected accuracy of predictions made for bi- Hbeen done with the empirical force fields (FFs) pioneered 50 ological systems at room temperature and pressure. BIOPHYSICS AND years ago (1, 2). As computer power has increased and quantum mechanical energy calculations have become more accurate than Significance COMPUTATIONAL BIOLOGY experiment, FFs derived from this quantum mechanical data have become feasible. In future quantum mechanics (QM) parameter- In molecular modeling the motion of nuclei, especially hydro- ized FFs are likely to be much more important than empirical FFs gen, cannot be described using the laws of classical mechanics. as they can be applied to new systems without needing experi- The importance of nuclear quantum effects has long been ap- mental data for calibration. Being able to accurately reproduce preciated by the ab initio molecular dynamics and by the water experimental data with QM-based FFs is essential. The aim of this simulation communities. However, the vast majority of simu- paper is to assess the need to include nuclear quantum effects lations of biological systems performed at ambient conditions (NQEs) in simulations. Here we show that they must be included if treat atomic motion classically. Even in the new-generation a QM parameterized FF is to correctly reproduce bulk properties. force fields parameterized from quantum mechanics these ef- Molecular mechanics (3, 4) bridges the precise calculation of fects are thought to be minor compared with other inaccura- interactions of a few atoms at rest by ab initio methods (QM) (4, 5) cies at room temperature and pressure. We show that a force with the larger numbers of atoms and dynamic simulations over field in excellent agreement with quantum mechanical ener- long time scales essential to predict measured bulk properties of gies and forces will not produce acceptably inaccurate predic- matter. The starting component of molecular mechanics is an ef- tions at ambient conditions unless the nuclear motion and fective Newtonian interaction model, or FF (4, 6). In this work we interaction are accounted for in the simulation. employ a FF parameterized by agreement with QM-derived en- ergies, forces, and monomer properties (we expand on this choice Author contributions: L.P., M.L., and B.F. designed research; L.P., I.K., G.K., O.B., A.I., I.L., in Discussion). Once the interaction energies and forces have been M.O., and B.F. performed research; L.P., G.K., and B.F. analyzed data; and M.L., R.D.K., and adequately described, the quantities of interest are obtained by B.F. wrote the paper. sampling the potential surface of a large molecular ensemble via Reviewers: M.C., Ecole Polytechnique Federale de Lausanne; and G.J.M., Pimpernel Sci- ence, Software and Technology. various means, usually Monte Carlo or Newtonian molecular dy- namics (MD) (3, 4, 7). The sampling machinery encompasses many The authors declare no conflict of interest. This open access article is distributed under Creative Commons Attribution-NonCommercial- critical parts such as proper maintenance of ensemble temperature NoDerivatives License 4.0 (CC BY-NC-ND). and pressure, careful integration and truncation practices, en- Data deposition: All parameters, binaries, and data to validate the Arbalest MD software hanced sampling techniques that overcome energy barriers, limi- and reproduce the results presented in this work are available upon request. – tations of machine precision, and many others (3, 7 13). 1To whom correspondence may be addressed. Email: [email protected] In Monte Carlo and MD sampling, the Born–Oppenheimer or [email protected]. approximation (14) decouples the electron degrees of freedom This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. from nuclear motion: the former are treated as instantaneous and 1073/pnas.1806064115/-/DCSupplemental. the latter, conventionally, as classical Newtonian point masses. www.pnas.org/cgi/doi/10.1073/pnas.1806064115 PNAS Latest Articles | 1of5 Valuable exceptions are the works of Martyna and coworkers, (37) from aug-cc-pVTZ to aug-cc-pVQZ basis sets] + CCSD(T)/aug-cc-pVTZ - MP2/ who investigated NQEs for weakly interacting species: the noble aug-cc-pVTZ basis sets. This level of theory is known as the “gold standard” gases helium and xenon (17) and alkanes (16, 23). These re- (38) and is commonly used as a benchmark in the computational chemistry searchers discovered that the NQE, as modeled by PIMD (17, 23), community. The ArrowFF is fitted to these gold-standard energy values. In significantly alters the molar volume of weakly interacting liquid Fig. 1A we plot energy values for the ArrowFF with corresponding QM en- ergies for a diverse set of alkane dimers. In Fig. 1 B and C we show the alkanes (16, 23). Since alkanes are literally the backbone of all agreement between ArrowFF and QM along the dissociation curves for the organic molecules (16), this work emphatically suggests that the minima of methane–methane and ethane–ethane dimers. inclusion of NQE should not be limited to strongly interacting As seen from Fig. 1 A–C the agreement between ArrowFF and QM dimer systems. Some of the effects may, in fact, be more prominent in energies is excellent everywhere, including the high-energy regions of sig- weaker interactions such as those occurring in nonpolar environ- nificant electron overlap. ments. However, as Martyna and coworkers used a relatively A direct proof that many-body ArrowFF energies also agree with their QM simple empirical FF which did not closely agree with QM energies, counterparts is difficult because precise determination of QM energies of large the question of whether simulations with a quantum mechanically clusters is computationally costly. For alkanes, however, we can infer this in- parameterized FF must include NQE remained open. directly. Using a high level of theory [the level of theory for the trimer is HF(aug- The ArrowFF is InterX’s medium-precision polarizable FF. cc-pV5Z) + df-MP2/(aug-cc-pVQZ ->aug-cc-pV5Z) + CCSD(T)/(aug-cc-pVTZ ->aug- > Agreement with QM properties and energies is only one of many cc-pVQZ)-MP2/(aug-cc-pVTZ - aug-cc-pVQZ)] we calculate the nonadditive several guiding principles in ArrowFF design. Some of the other trimerization energy of the optimal methane trimer to be 0.014 kcal/mol.
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