1
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Dwivedi A, Lopez-Ruiz MA, Iyengar SS. Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms. J Phys Chem A 2024; 128:6774-6797. [PMID: 39101545 DOI: 10.1021/acs.jpca.4c03407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/06/2024]
Abstract
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.
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Affiliation(s)
- Anurag Dwivedi
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
- Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Miguel Angel Lopez-Ruiz
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
- Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
- Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
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2
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Iyengar SS, Schlegel HB, Sumner I, Li J. Rare Events Sampling Methods for Quantum and Classical Ab Initio Molecular Dynamics. J Phys Chem A 2024; 128:5386-5397. [PMID: 38951489 DOI: 10.1021/acs.jpca.3c07385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
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.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington 47405, Indiana, United States
| | - H Bernhard Schlegel
- Department of Chemistry, Wayne State University, Detroit 48202, Michigan, United States
| | - Isaiah Sumner
- Department of Chemistry and Biochemistry, James Madison University, Harrisonburg 22807, Virginia, United States
| | - Junjie Li
- Texas Advanced Computing Center, The University of Texas at Austin, Austin 78758, Texas, United States
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3
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Iyengar SS, Ricard TC, Zhu X. 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. J Phys Chem A 2024; 128:466-478. [PMID: 38180503 DOI: 10.1021/acs.jpca.3c05630] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
Abstract
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.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Timothy C Ricard
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Xiao Zhu
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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4
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Ricard TC, Zhu X, Iyengar SS. Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning. J Chem Theory Comput 2023. [PMID: 38019639 DOI: 10.1021/acs.jctc.3c00955] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2023]
Abstract
The accurate and efficient study of the interactions of organic matter with the surface of water is critical to a wide range of applications. For example, environmental studies have found that acidic polyfluorinated alkyl substances, especially perfluorooctanoic acid (PFOA), have spread throughout the environment and bioaccumulate into human populations residing near contaminated watersheds, leading to many systemic maladies. Thus, the study of the interactions of PFOA with water surfaces became important for the mitigation of their activity as pollutants and threats to public health. However, theoretical study of the interactions of such organic adsorbates on the surface of water, and their bulk concerted properties, often necessitates the use of ab initio methods to properly incorporate the long-range electronic properties that govern these extended systems. Notable theoretical treatments of "on-water" reactions thus far have employed hybrid DFT and semilocal DFT, but the interactions involved are weak interactions that may be best described using post-Hartree-Fock theory. Here, we aim to demonstrate the utility of a graph-theoretic approach to molecular fragmentation that accurately captures the critical "weak" interactions while maintaining an efficient ab initio treatment of the long-range periodic interactions that underpin the physics of extended systems. We apply this graph-theoretical treatment to study PFOA on the surface of water as a model system for the study of weak interactions seen in the wide range of surface interactions and reactions. The approach divides a system into a set of vertices, that are then connected through edges, faces, and higher order graph theoretic objects known as simplexes, to represent a collection of locally interacting subsystems. These subsystems are then used to construct ab initio molecular dynamics simulations and for computing multidimensional potential energy surfaces. To further improve the computational efficiency of our graph theoretic fragmentation method, we use a recently developed transfer learning protocol to construct the full system potential energy from a family of neural networks each designed to accurately model the behavior of individual simplexes. We use a unique multidimensional clustering algorithm, based on the k-means clustering methodology, to define our training space for each separate simplex. These models are used to extrapolate the energies for molecular dynamics trajectories at PFOA water interfaces, at less than one-tenth the cost as compared to a regular molecular fragmentation-based dynamics calculation with excellent agreement with couple cluster level of full system potential energies.
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Affiliation(s)
- Timothy C Ricard
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Xiao Zhu
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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5
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Iyengar SS, Zhang JH, Saha D, Ricard TC. Graph-| Q⟩⟨ C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure. J Phys Chem A 2023; 127:9334-9345. [PMID: 37906738 DOI: 10.1021/acs.jpca.3c04261] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
The accurate determination of chemical properties is known to have a critical impact on multiple fundamental chemical problems but is deeply hindered by the steep algebraic scaling of electron correlation calculations and the exponential scaling of quantum nuclear dynamics. With the advent of new quantum computing hardware and associated developments in creating new paradigms for quantum software, this avenue has been recognized as perhaps one way to address exponentially complex challenges in quantum chemistry and molecular dynamics. In this paper, we discuss a new approach to drastically reduce the quantum circuit depth (by several orders of magnitude) and help improve the accuracy in the quantum computation of electron correlation energies for large molecular systems. The method is derived from a graph-theoretic approach to molecular fragmentation and enables us to create a family of projection operators that decompose quantum circuits into separate unitary processes. Some of these processes can be treated on quantum hardware and others on classical hardware in a completely asynchronous and parallel fashion. Numerical benchmarks are provided through the computation of unitary coupled-cluster singles and doubles (UCCSD) energies for medium-sized protonated and neutral water clusters using the new quantum algorithms presented here.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Juncheng Harry Zhang
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Debadrita Saha
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Timothy C Ricard
- Department of Chemistry, Department of Physics, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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6
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Broderick DR, Herbert JM. Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration. J Chem Phys 2023; 159:174801. [PMID: 37921253 DOI: 10.1063/5.0174293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Accepted: 10/16/2023] [Indexed: 11/04/2023] Open
Abstract
The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application ("Fragme∩t"), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.
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Affiliation(s)
- Dustin R Broderick
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - John M Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
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7
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Carpenter BK. Prediction of Kinetic Product Ratios: Investigation of a Dynamically Controlled Case. J Phys Chem A 2023; 127:224-239. [PMID: 36594780 PMCID: PMC9841574 DOI: 10.1021/acs.jpca.2c08301] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Of the various factors influencing kinetically controlled product ratios, the role of nonstatistical dynamics is arguably the least well understood. In this paper, reactions were chosen in which dynamics played a dominant role in product selection, by design. Specifically, the reactions studied were the ring openings of cyclopropylidene to allene and tetramethylcyclopropylidene to tetramethylallene (2,4-dimethylpenta-2,3-diene). Both reactions have intrinsic reaction coordinates that bifurcate symmetrically, leading to products that are enantiomeric once the atoms are uniquely labeled. The question addressed in the study was whether the outcomes─that is, which product well on the potential energy surface was selected─could be predicted from their initial conditions for individual trajectories in quasiclassical dynamics simulations. Hybrid potentials were developed based on cooperative interaction between molecular mechanics and artificial neural networks, trained against data from electronic structure calculations. These potentials allowed simulations of both gas-phase and condensed-phase reactions. The outcome was that, for both reactions, prediction of initial selection of product wells could be made with >95% success from initial conditions of the trajectories in the gas phase. However, when trajectories were run for longer, looking for "final" products for each trajectory, the predictability dropped off dramatically. In the gas-phase simulations, this drop off was caused by trajectories hopping between product wells on the potential energy surface. That behavior could be suppressed in condensed phases, but then new uncertainty was introduced because the intermolecular interactions between solute and bath, necessary to permit intermolecular energy transfer and cooling of the hot initial products, often led to perturbations of the initial directions of trajectories on the potential energy surface. It would consequently appear that a general ability to predict outcomes for reactions in which nonstatistical dynamics dominate remains a challenge even in the age of sophisticated machine-learning capabilities.
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8
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Kumar A, DeGregorio N, Ricard T, Iyengar SS. Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics. J Chem Theory Comput 2022; 18:7243-7259. [PMID: 36332133 DOI: 10.1021/acs.jctc.2c00484] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
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.
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Affiliation(s)
- Anup Kumar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Nicole DeGregorio
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Timothy Ricard
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
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9
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Liu J, He X. Recent advances in quantum fragmentation approaches to complex molecular and condensed‐phase systems. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Jinfeng Liu
- Department of Basic Medicine and Clinical Pharmacy China Pharmaceutical University Nanjing China
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering East China Normal University Shanghai China
| | - Xiao He
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering East China Normal University Shanghai China
- New York University‐East China Normal University Center for Computational Chemistry New York University Shanghai Shanghai China
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10
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Zhu X, Iyengar SS. Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol. J Chem Theory Comput 2022; 18:5125-5144. [PMID: 35994592 DOI: 10.1021/acs.jctc.1c01241] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
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.
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Affiliation(s)
- Xiao Zhu
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington 47405, Indiana, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington 47405, Indiana, United States
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11
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Zhang JH, Iyengar SS. Graph-| Q⟩⟨ C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance. J Chem Theory Comput 2022; 18:2885-2899. [PMID: 35412836 DOI: 10.1021/acs.jctc.1c01303] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Juncheng Harry Zhang
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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12
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Kumar A, DeGregorio N, Iyengar SS. Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions. J Chem Theory Comput 2021; 17:6671-6690. [PMID: 34623129 DOI: 10.1021/acs.jctc.1c00065] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
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.
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Affiliation(s)
- Anup Kumar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Nicole DeGregorio
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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13
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Zhang JH, Ricard TC, Haycraft C, Iyengar SS. Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms. J Chem Theory Comput 2021; 17:2672-2690. [PMID: 33891416 DOI: 10.1021/acs.jctc.0c01287] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
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.
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Affiliation(s)
- Juncheng Harry Zhang
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Timothy C Ricard
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Cody Haycraft
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
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14
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Paz ASP, Glover WJ. Diabatic Many-Body Expansion: Development and Application to Charge-Transfer Reactions. J Chem Theory Comput 2021; 17:1497-1511. [DOI: 10.1021/acs.jctc.0c01231] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Amiel S. P. Paz
- NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshang Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, United States
| | - William J. Glover
- NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshang Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, United States
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15
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Ricard TC, Iyengar SS. Efficient and Accurate Approach To Estimate Hybrid Functional and Large Basis-Set Contributions to Condensed-Phase Systems and Molecule–Surface Interactions. J Chem Theory Comput 2020; 16:4790-4812. [DOI: 10.1021/acs.jctc.9b01089] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Timothy C. Ricard
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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16
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Liu J, He X. Fragment-based quantum mechanical approach to biomolecules, molecular clusters, molecular crystals and liquids. Phys Chem Chem Phys 2020; 22:12341-12367. [PMID: 32459230 DOI: 10.1039/d0cp01095b] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
To study large molecular systems beyond the system size that the current state-of-the-art ab initio electronic structure methods could handle, fragment-based quantum mechanical (QM) approaches have been developed over the past years, and proved to be efficient in dealing with large molecular systems at various ab initio levels. According to the fragmentation approach, a large molecular system can be divided into subsystems (fragments), and subsequently the property of the whole system can be approximately obtained by taking a proper combination of the corresponding terms of individual fragments. Therefore, the standard QM calculation of a large system could be circumvented by carrying out a series of calculations on small fragments, which significantly promotes computational efficiency. The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is one of the fragment-based QM approaches which has been developed by our research group in recent years. This Perspective presents the theoretical framework of this fragmentation method and its applications in biomolecules, molecular clusters, molecular crystals and liquids, including total energy calculation, protein-ligand/protein binding affinity prediction, geometry optimization, vibrational spectrum simulation, ab initio molecular dynamics simulation, and prediction of excited-state properties.
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Affiliation(s)
- Jinfeng Liu
- Department of Basic Medicine and Clinical Pharmacy, China Pharmaceutical University, Nanjing, 210009, China
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17
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Noffke BW, Beckett D, Li LS, Raghavachari K. Aromatic Fragmentation Based on a Ring Overlap Scheme: An Algorithm for Large Polycyclic Aromatic Hydrocarbons Using the Molecules-in-Molecules Fragmentation-Based Method. J Chem Theory Comput 2020; 16:2160-2171. [DOI: 10.1021/acs.jctc.9b00566] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Benjamin W. Noffke
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Daniel Beckett
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Liang-shi Li
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
| | - Krishnan Raghavachari
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
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18
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DeGregorio N, Iyengar SS. 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. Faraday Discuss 2020; 221:379-405. [DOI: 10.1039/c9fd00071b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites.
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Affiliation(s)
- Nicole DeGregorio
- Department of Chemistry
- Department of Physics
- Indiana University
- Bloomington
- USA
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19
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Kumar A, Iyengar SS. Fragment-Based Electronic Structure for Potential Energy Surfaces Using a Superposition of Fragmentation Topologies. J Chem Theory Comput 2019; 15:5769-5786. [DOI: 10.1021/acs.jctc.9b00608] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Anup Kumar
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana-47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana-47405, United States
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20
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Liu J, Sun H, Glover WJ, He X. Prediction of Excited-State Properties of Oligoacene Crystals Using Fragment-Based Quantum Mechanical Method. J Phys Chem A 2019; 123:5407-5417. [PMID: 31187994 DOI: 10.1021/acs.jpca.8b12552] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S1) and triplet excitation energies (T1), in excellent agreement with the full-system quantum mechanical calculations. Using this method, we also investigated the performance of different density functionals in predicting the excited-state properties of the oligoacene crystals. Among the 13 tested functionals, B3LYP and MN15 give the two lowest overall mean unsigned errors with reference to the experimental S1 and T1 excitation energies. The EE-GMF approach can be readily utilized for studying the excited-state properties of large-scale organic solids at diverse ab initio levels.
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Affiliation(s)
- Jinfeng Liu
- Department of Basic Medicine and Clinical Pharmacy , China Pharmaceutical University , Nanjing 210009 , China
| | | | - William J Glover
- NYU Shanghai , Shanghai 200122 , China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai , Shanghai 200062 , China.,Department of Chemistry , New York University , New York , New York 10003 , United States
| | - Xiao He
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai , Shanghai 200062 , China
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Ricard TC, Iyengar SS. Efficiently Capturing Weak Interactions in ab Initio Molecular Dynamics with on-the-Fly Basis Set Extrapolation. J Chem Theory Comput 2018; 14:5535-5552. [DOI: 10.1021/acs.jctc.8b00803] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Timothy C. Ricard
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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22
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Ricard TC, Haycraft C, Iyengar SS. Adaptive, Geometric Networks for Efficient Coarse-Grained Ab Initio Molecular Dynamics with Post-Hartree–Fock Accuracy. J Chem Theory Comput 2018; 14:2852-2866. [DOI: 10.1021/acs.jctc.8b00186] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Timothy C. Ricard
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Cody Haycraft
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
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23
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DeGregorio N, Iyengar SS. Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions. J Chem Theory Comput 2017; 14:30-47. [DOI: 10.1021/acs.jctc.7b00927] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Nicole DeGregorio
- Department of Chemistry and
Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and
Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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Haycraft C, Li J, Iyengar SS. Efficient, “On-the-Fly”, Born–Oppenheimer and Car–Parrinello-type Dynamics with Coupled Cluster Accuracy through Fragment Based Electronic Structure. J Chem Theory Comput 2017; 13:1887-1901. [DOI: 10.1021/acs.jctc.6b01107] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Cody Haycraft
- Department of Chemistry and
Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Junjie Li
- Department of Chemistry and
Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and
Department of Physics, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
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Sager LM, Iyengar SS. Proton relays in anomalous carbocations dictate spectroscopy, stability, and mechanisms: case studies on C2H5+ and C3H3+. Phys Chem Chem Phys 2017; 19:27801-27816. [DOI: 10.1039/c7cp05577c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a detailed exposition of “Grothuss-like” proton shuttles in C2H5+ and C3H3+ that result in anomalous structural and spectral behavior.
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Affiliation(s)
- LeeAnn M. Sager
- Department of Chemistry and Department of Physics
- Indiana University
- Bloomington
- USA
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Li J, Haycraft C, Iyengar SS. Hybrid Extended Lagrangian, Post-Hartree–Fock Born–Oppenheimer ab Initio Molecular Dynamics Using Fragment-Based Electronic Structure. J Chem Theory Comput 2016; 12:2493-508. [DOI: 10.1021/acs.jctc.6b00001] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Junjie Li
- Department of Chemistry and
Department of Physics, Indiana University, 800 E. Kirkwood Ave., Bloomington, Indiana 47405, United States
| | - Cody Haycraft
- Department of Chemistry and
Department of Physics, Indiana University, 800 E. Kirkwood Ave., Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and
Department of Physics, Indiana University, 800 E. Kirkwood Ave., Bloomington, Indiana 47405, United States
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Li J, Pacheco AB, Raghavachari K, Iyengar SS. A Grotthuss-like proton shuttle in the anomalous C2H3+ carbocation: energetic and vibrational properties for isotopologues. Phys Chem Chem Phys 2016; 18:29395-29411. [DOI: 10.1039/c6cp04450f] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The proton shuttle in C2H3+ is reminiscent of the Grotthuss proton transfer mechanism.
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Affiliation(s)
- Junjie Li
- Department of Chemistry and Department of Physics
- Indiana University
- Bloomington
- USA
| | - Alexander B. Pacheco
- Department of Chemistry and Department of Physics
- Indiana University
- Bloomington
- USA
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