Yuezhi Mao

Advanced Potential Energy Surfaces for Molecular Simulation

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

TINKTEP: A fully self-consistent, mutually polarizable QM/MM approach based on the AMOEBA force field

We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the onetep linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in tinker. Distributed multipole analysis is used to obtain, on the fly, a classical representation of the QM subsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA. We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations.

Assessing many-body contributions to intermolecular interactions of the AMOEBA force field using energy decomposition analysis of electronic structure calculations

In this work, we evaluate the accuracy of the classical AMOEBA model for representing many-body interactions, such as polarization, charge transfer, and Pauli repulsion and dispersion, through comparison against an energy decomposition method based on absolutely localized molecular orbitals (ALMO-EDA) for the water trimer and a variety of ion-water systems. When the 2- and 3-body contributions according to the many-body expansion are analyzed for the ion-water trimer systems examined here, the 3-body contributions to Pauli repulsion and dispersion are found to be negligible under ALMO-EDA, thereby supporting the validity of the pairwise-additive approximation in AMOEBAs 14-7 van der Waals term. However AMOEBA shows imperfect cancellation of errors for the missing effects of charge transfer and incorrectness in the distance dependence for polarization when compared with the corresponding ALMO-EDA terms. We trace the larger 2-body followed by 3-body polarization errors to the Thole damping scheme used in AMOEBA, and although the width parameter in Thole damping can be changed to improve agreement with the ALMO-EDA polarization for points about equilibrium, the correct profile of polarization as a function of intermolecular distance cannot be reproduced. The results suggest that there is a need for re-examining the damping and polarization model used in the AMOEBA force field and provide further insights into the formulations of polarizable force fields in general.

Superposition of Fragment Excitations for Excited States of Large Clusters with Application to Helium Clusters.

We develop a local excited-state method, based on the configuration interaction singles (CIS) wave function, for large atomic and molecular clusters. This method exploits the properties of absolutely localized molecular orbitals (ALMOs), which strictly limits the total number of excitations, and results in formal scaling with the third power of the system size for computing the full spectrum of ALMO-CIS excited states. The derivation of the equations and design of the algorithm are discussed in detail, with particular emphasis on the computational scaling. Clusters containing ∼500 atoms were used in evaluating the scaling, which agrees with the theoretical predictions, and the accuracy of the method is evaluated with respect to standard CIS. A pioneering application to the size dependence of the helium cluster spectrum is also presented for clusters of 25-231 atoms, the largest of which results in the computation of 2310 excited states per sampled cluster geometry.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH3, NH4+, CN-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

Simulating the absorption spectra of helium clusters (N = 70, 150, 231, 300) using a charge transfer correction to superposition of fragment single excitations

Simulations of the n = 2 absorption spectra of HeN (N = 70, 150, 231, 300) clusters are reported, with nuclear configurations sampled by path integral molecular dynamics. The electronic structure is treated by a new approach, ALMO-CIS+CT, which is a formulation of configuration interaction singles (CIS) based on absolutely localized molecular orbitals (ALMOs). The method generalizes the previously reported ALMO-CIS model [K. D. Closser et al. J. Chem. Theory Comput. 11, 5791 (2015)] to include spatially localized charge transfer (CT) effects. It is designed to recover large numbers of excited states in atomic and molecular clusters, such as the entire n = 2 Rydberg band in helium clusters. ALMO-CIS+CT is shown to recover most of the error caused by neglecting charge transfer in ALMO-CIS and has comparable accuracy to standard CIS for helium clusters. For the n = 2 band, CT stabilizes states towards the blue edge by up to 0.5 eV. ALMO-CIS+CT retains the formal cubic scaling of ALMO-CIS with respect to system size. With improvements to the implementation over that originally reported for ALMO-CIS, ALMO-CIS+CT is able to treat helium clusters with hundreds of atoms using modest computing resources. A detailed simulation of the absorption spectra associated with the 2s and 2p bands of helium clusters up to 300 atoms is reported, using path integral molecular dynamics with a spherical boundary condition to generate atomic configurations at 3 K. The main features of experimentally reported fluorescence excitation spectra for helium clusters are reproduced.

Energy decomposition analysis for exciplexes using absolutely localized molecular orbitals

An energy decomposition analysis (EDA) scheme is developed for understanding the intermolecular interaction involving molecules in their excited states. The EDA utilizes absolutely localized molecular orbitals to define intermediate states and is compatible with excited state methods based on linear response theory such as configuration interaction singles and time-dependent density functional theory. The shift in excitation energy when an excited molecule interacts with the environment is decomposed into frozen, polarization, and charge transfer contributions, and the frozen term can be further separated into Pauli repulsion and electrostatics. These terms can be added to their counterparts obtained from the ground state EDA to form a decomposition of the total interaction energy. The EDA scheme is applied to study a variety of systems, including some model systems to demonstrate the correct behavior of all the proposed energy components as well as more realistic systems such as hydrogen-bonding complexes (e.g., formamide-water, pyridine/pyrimidine-water) and halide (F-, Cl-)-water clusters that involve charge-transfer-to-solvent excitations.