Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

Quantum Circuit and Mapping Algorithms for Wavepacket Dynamics: Case Study of Anharmonic Hydrogen Bonds in Protonated and Hydroxide Water Clusters

The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here, we present two algorithms that, in conjunction with other methods developed by us, may result in one set of contributions for performing quantum nuclear dynamics in arbitrary dimensions. For one of the two algorithms discussed here, we present a direct map between the Born-Oppenheimer Hamiltonian describing the nuclear wavepacket time evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer. This map is exact for three qubits, and when implemented, the dynamics of the spin states emulates those of the nuclear wavepacket in a continuous representation. However, this map becomes approximate as the number of qubits grows. In a second algorithm, we present a general quantum circuit decomposition formalism for such problems using a method called the Quantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits at the cost of increased circuit complexity. The resultant circuit is implemented on IBM's quantum simulator (QASM) for 3-7 qubits, without using a noise model so as to test the intrinsic accuracy of the method. In both cases, the wavepacket dynamics is found to be in good agreement with the classical propagation result and the corresponding vibrational frequencies obtained from the wavepacket density time evolution are in agreement to within a few tenths of a wavenumber.

Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and compared to exact diagonalization numerical results.

Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.

Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra

Calculating observable properties of chemical systems is often classically intractable and widely viewed as a promising application of quantum information processing. Here, we introduce a new framework for solving generic quantum chemical dynamics problems using quantum logic. We experimentally demonstrate a proof-of-principle instance of our method using the QSCOUT ion-trap quantum computer, where we experimentally drive the ion-trap system to emulate the quantum wavepacket dynamics corresponding to the shared-proton within an anharmonic hydrogen bonded system. Following the experimental creation and propagation of the shared-proton wavepacket on the ion-trap, we extract measurement observables such as its time-dependent spatial projection and its characteristic vibrational frequencies to spectroscopic accuracy (3.3 cm-1 wavenumbers, corresponding to >99.9% fidelity). Our approach introduces a new paradigm for studying the chemical dynamics and vibrational spectra of molecules and opens the possibility to describe the behavior of complex molecular processes with unprecedented accuracy.

Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics

Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.

Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a family of neural networks that act in parallel to represent, efficiently, the post-Hartree-Fock electronic structure energy contributions for all simplexes (fragments), and (b) a new k-means-based tessellation strategy to glean training data for high-dimensional molecular spaces and minimize the extent of training needed to construct this family of neural networks. The approach is particularly useful when coupled cluster accuracy is desired and when fragment sizes grow in order to capture nonlocal interactions accurately. The unique multidimensional k-means tessellation/clustering algorithm used to determine our training data for all fragments is shown to be extremely efficient and reduces the needed training to only 10% of data for all fragments to obtain accurate neural networks for each fragment. These fully connected dense neural networks are then used to extrapolate the potential energy surface for all molecular fragments, and these are then combined as per our graph-theoretic procedure to transfer the learning process to a full system energy for the entire AIMD trajectory at less than one-tenth the cost as compared to a regular fragmentation-based AIMD calculation.

Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance

We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H₂]_n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM's Quantum Information Science kit, known as Qiskit.

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms

We present a weighted-graph-theoretic approach to adaptively compute contributions from many-body approximations for smooth and accurate post-Hartree-Fock (pHF) ab initio molecular dynamics (AIMD) of highly fluxional chemical systems. This approach is ONIOM-like, where the full system is treated at a computationally feasible quality of treatment (density functional theory (DFT) for the size of systems considered in this publication), which is then improved through a perturbative correction that captures local many-body interactions up to a certain order within a higher level of theory (post-Hartree-Fock in this publication) described through graph-theoretic techniques. Due to the fluxional and dynamical nature of the systems studied here, these graphical representations evolve during dynamics. As a result, energetic "hops" appear as the graphical representation deforms with the evolution of the chemical and physical properties of the system. In this paper, we introduce dynamically weighted, linear combinations of graphs, where the transition between graphical representations is smoothly achieved by considering a range of neighboring graphical representations at a given instant during dynamics. We compare these trajectories with those obtained from a set of trajectories where the range of local many-body interactions considered is increased, sometimes to the maximum available limit, which yields conservative trajectories as the order of interactions is increased. The weighted-graph approach presents improved dynamics trajectories while only using lower-order many-body interaction terms. The methods are compared by computing dynamical properties through time-correlation functions and structural distribution functions. In all cases, the weighted-graph approach provides accurate results at a lower cost.

Nuclear quantum effects in enzymatic reactions: simulation of the kinetic isotope effect of phenylethylamine oxidation catalyzed by monoamine oxidase A

By using computational techniques for quantizing nuclear motion one can accurately reproduce kinetic isotope effect of enzymatic reactions, as demonstrated for phenylethylamine oxidation catalyzed by the monoamine oxidase A enzyme.

Challenges in constructing accurate methods for hydrogen transfer reactions in large biological assemblies: rare events sampling for mechanistic discovery and tensor networks for quantum nuclear effects

We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites.

Proton relays in anomalous carbocations dictate spectroscopy, stability, and mechanisms: case studies on C2H5+ and C3H3+

We present a detailed exposition of “Grothuss-like” proton shuttles in C₂H₅⁺ and C₃H₃⁺ that result in anomalous structural and spectral behavior.

Born-Oppenheimer Molecular Dynamics Study on Proton Dynamics of Strong Hydrogen Bonds in Aspirin Crystals, with Emphasis on Differences between Two Crystal Forms

In this study, the proton dynamics of hydrogen bonds for two forms of crystalline aspirin was investigated by the Born-Oppenheimer molecular dynamics (BOMD) method. Analysis of the geometrical parameters of hydrogen bonds using BOMD reveals significant differences in hydrogen bonding between the two crystalline forms of aspirin, Form I and Form II. Analysis of the trajectory for Form I shows spontaneous proton transfer in cyclic dimers, which is absent in Form II. Quantization of the O-H stretching modes allows a detailed discussion on the strength of hydrogen-bonding interactions. The focal point of our study is examination of the hydrogen bond characteristics in the crystal structure and clarification of the influence of hydrogen bonding on the presence of the two crystalline forms of aspirin. In the BOMD method, thermal motions were taken into account. Solving the Schrödinger equation for the snapshots of 2D proton potentials, extracted from MD, gives the best agreement with IR spectra. The character of medium-strong hydrogen bonds in Form I of aspirin was compared with that of weaker hydrogen bonds in aspirin Form II. Two proton minima are present in the potential function for the hydrogen bonds in Form I. The band contours, calculated by using one- and two-dimensional O-H quantization, reflect the differences in the hydrogen bond strengths between the two crystalline forms of aspirin, as well as the strong hydrogen bonding in the cyclic dimers of Form I and the medium-strong hydrogen bonding in Form II.

A Grotthuss-like proton shuttle in the anomalous C2H3+ carbocation: energetic and vibrational properties for isotopologues

The proton shuttle in C₂H₃⁺ is reminiscent of the Grotthuss proton transfer mechanism.

Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates

This article presents a general computational approach for efficient simulations of anharmonic vibrational spectra in chemical systems. An automated local-mode vibrational approach is presented, which borrows techniques from localized molecular orbitals in electronic structure theory. This approach generates spatially localized vibrational modes, in contrast to the delocalization exhibited by canonical normal modes. The method is rigorously tested across a series of chemical systems, ranging from small molecules to large water clusters and a protonated dipeptide. It is interfaced with exact, grid-based approaches, as well as vibrational self-consistent field methods. Most significantly, this new set of reference coordinates exhibits a well-behaved spatial decay of mode couplings, which allows for a systematic, a priori truncation of mode couplings and increased computational efficiency. Convergence can typically be reached by including modes within only about 4 Å. The local nature of this truncation suggests particular promise for the ab initio simulation of anharmonic vibrational motion in large systems, where connection to experimental spectra is currently most challenging.

Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

"Pump-probe" atom-centered density matrix propagation studies to gauge anharmonicity and energy repartitioning in atmospheric reactive adducts: case study of the OH + isoprene and OH + butadiene reaction intermediates

Time-resolved "pump-probe" ab initio molecular dynamics studies are constructed to probe the stability of reaction intermediates, the mechanism of energy transfer, and energy repartitioning, for moieties involved during the interaction of volatile organic compunds with hydroxyl radical. These systems are of prime importance in the atmosphere. Specifically, the stability of reaction intermediates of hydroxyl radical adducts to isoprene and butadiene molecules is used as a case study to develop novel computational techniques involving "pump-probe" ab initio molecular dynamics. Starting with the various possible hydroxyl radical adducts to isoprene and butadiene, select vibrational modes of each of the adducts are populated with excess energy to mimic the initial conditions of an experiment. The flow of energy into the remaining modes is then probed by subjecting the excited adducts to ab initio molecular dynamics simulations. It is found that the stability of the adducts arises directly due to the anhormonically driven coupling of the modes to facilitate repartitioning of the excess vibrational energy. This kind of vibrational repartitioning has a critical influence on the energy density.

Car-Parrinello simulation of the vibrational spectrum of a medium strong hydrogen bond by two-dimensional quantization of the nuclear motion: application to 2-hydroxy-5-nitrobenzamide

The nature of medium strong intra- and intermolecular hydrogen bonding in 2-hydroxy-5-nitrobenzamide in the crystal phase was examined by infrared spectroscopy and Car-Parrinello molecular dynamics simulation. The focal point of our study was the part of the infrared spectra associated with the O-H and N-H stretching modes that are very sensitive to the strength of hydrogen bonding. For spectra calculations we used an isolated dimer and the fully periodic crystal environment. We calculated the spectra by using harmonic approximation, the time course of the dipole moment function as obtained from the Car-Parrinello simulation, and the quantization of the nuclear motion of the proton for an instantaneous snapshot of the structures in one and two dimensions. Although quantitative assessment of the agreement between the computed and experimental band contour is difficult due to the fact that the experimental band is very broad, we feel that the most reasonable qualitative agreement with the experiment is obtained from snapshot structures and two-dimensional quantization of the proton motion. We have also critically examined the methods of constructing the one-dimensional proton potential. Perspectives are given for the treatment of nuclear quantum effects in biocatalysis.

Quantum wavepacket ab initio molecular dynamics: generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.

Analysis of Hydrogen Tunneling in an Enzyme Active Site using von Neumann Measurements

We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme, soybean lipoxygenase-1, by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the "transition state" towards the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further "tailor" the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.