Quantum Chemical Applications Research Articles

Effects of defects in g-C3N4 on excited-state charge distribution and transfer: Potential for improved photocatalysis.

Graphite phase carbon nitride (g-C3N4) with triazine ring structures is a polymeric metal-free semiconductor with a medium bandgap and two-dimensional layered structure. g-C3N4 has attracted attention because of its photocatalytic applications, such as the photodegradation of pollution and hydrogen production via water splitting. Defective elements and sites are two essential factors in rationally designing highly-efficient photocatalysts based on g-C3N4 at the nanoscale. When the molecule absorbs energy and enters an excited state, electrons migrate and the charge distribution changes accordingly. The properties of the excited states of g-C3N4 are related to its defect elements and sites. Therefore, it is necessary to understand the effects of defects on excited states in the design of g-C3N4 catalysts. In this paper, the excited-state characteristics of intrinsic g-C3N4 and g-C3N4 with C- and N-atom defects are analyzed by density functional theory. We apply quantum chemistry and wave function analysis to determine the hole-electron distributions and charge transfer directions. To measure and discuss the characteristics of electron excitation using quantitative numerical methods, the D, Sr, H, and t indices are calculated. Our results promote a deeper understanding of the roles of defective elements and sites in photocatalysis by g-C3N4.

Molecular Vibrational Frequencies with Multiple Quantum Protons within the Nuclear-Electronic Orbital Framework.

The nuclear-electronic orbital (NEO) approach treats all electrons and specified nuclei, typically protons, on the same quantum mechanical level. Proton vibrational excitations can be calculated using multicomponent time-dependent density functional theory (NEO-TDDFT) for fixed classical nuclei. Recently the NEO-DFT(V) approach was developed to enable the calculation of molecular vibrational frequencies for modes composed of both classical and quantum nuclei. This approach uses input from NEO-TDDFT to construct an extended NEO Hessian that depends on the expectation values of the quantum protons as well as the classical nuclear coordinates. Herein strategies are devised for extending these approaches to molecules with multiple quantum protons in a self-contained, effective, and computationally practical manner. The NEO-TDDFT method is shown to describe vibrational excitations corresponding to collective nuclear motions, such as linear combinations of proton vibrational excitations. The NEO-DFT(V) approach is shown to incorporate the most significant anharmonic effects in the molecular vibrations, particularly for the hydrogen stretching modes. These theoretical strategies pave the way for a wide range of multicomponent quantum chemistry applications.

(Invited) Atomic Scale Models of PGM-Free ORR Electrocatalysts: Activity, Stability, and Experimental Signatures of Active Site Structures within the Electrocatalysis Consortium

The electrification of transportation will rely predominantly on electrochemical technologies including fuel cells and batteries. In 2016 the U.S. Department of Energy started the Electrocatalysis Consortium (ElectroCat) in order to increase U.S. competitiveness in fuel cell manufacturing. The main focus of the consortium has been how to replace rare, expensive, and non-domestically mined platinum group metals (PGMs) used as electrocatalysts in fuel cell cathodes to improve efficiency of the oxygen reduction reaction (ORR). At predicted production scale, these PGM components will be one of the dominant cost drivers for fuel cell vehicle membrane electrode assemblies and, unlike other components, will not benefit from economies of scale during mass production. Currently the most promising PGM-free ORR electrocatalysts are based on heat treated M-N-C structures (M = Mn, Fe, Co). Great strides have been made over the previous decade in improving ORR activity, 4 electron pathway selectivity, and durability of these PGM-free materials but further improvements are required to meet the application needs of these materials. Thermal treatments in the range of 800-1100 °C have been shown to produce the most ORR active PGM-free materials but these temperatures lead to highly heterogeneous structures. This heterogeneity makes it difficult to identify the atomic scale structures responsible for facilitating ORR activity (the so-called active site conundrum) and also complicates the study of their associated ORR reaction pathways and degradation mechanisms. One approach within ElectroCat to address these knowledge gaps and to improve synthesis through a targeted, rational approach is the application of computational quantum chemistry. In this approach, an inverse problem to the active site conundrum is addressed. Instead of trying to identify “what is the active site”, the approach is to build a library of plausible atomic scale structures based on theoretical and experimental input and to understand the activity, durability, and experimental signatures of each site, enabling a comparison between the structures within the library. These comparisons can address fundamental questions about active sites and guide in the interpretation of experimental data aiding in the identification and behavior of particular atomic scale structures under specific environmental conditions. The developed approaches rely heavily on high performance computing (HPC) and density functional theory (DFT) to provide input about atomic scale interactions. By studying the binding of ORR intermediates to given library member structures and application of thermochemical models, activity descriptors can be obtained as well as relative energies of proposed reaction pathways. Additionally, kinetics of bond breaking associated with proposed degradation pathways can be identified, giving proposed durability descriptors for given active site structures. Both of these approaches have provided valuable insight into the roles of transition metal species and local carbon environment for material activity and durability. Theoretical approaches can also aid in interpretation of experimental data. Quantification of the number of active sites is more complicated in PGM-free materials vs. their PGM counterparts and experimental approaches are still being developed in order to better decouple active site density and active site turn over frequency. Study of active site interaction with probe molecules, those that can be controllably added and removed from (ideally) only ORR active sites enabling site counting, can also be determined via theoretical approaches, shedding light on binding specificity and thus the veracity of proposed approaches. For Fe-bearing materials, a host of Fe-specific spectroscopies have been developed which enable direct study of this subset of proposed active site structures. These include Mössbauer spectroscopy, nuclear resonance vibrational spectroscopy (NRVS), and x-ray adsorption spectroscopy (XAS). One major drawback to these approaches is a lack of well characterized standard structures that enable assigning given peaks to particular components of the material. By producing libraries of atomic scale structures and their experimental signatures, trends in experiments can be identified. This is valuable to determine the impact of synthesis conditions on produced materials and predominance of structures produced. Also, it has been predicted that certain ligands may evolve spontaneously on these structures under certain conditions. By studying structures with various ligands and probe molecules, trends can be identified which help in determining not just predominant Fe-structures from spectroscopy but also what ligands evolve under what conditions in-situ. Combined, theoretical input for ORR activity, active site durability, and experimental interpretation will be discussed.

Quantum Chemistry in the Age of Quantum Computing.

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

A Runge–Kutta type crowded in phase algorithm for quantum chemistry problems

We focus the study presented in this paper on the solution of systems of differential equations with applications in Quantum Chemistry using finite difference methods. The research of the newly introduced algorithm proves its efficiency.

Multicomponent equation-of-motion coupled cluster singles and doubles: Theory and calculation of excitation energies for positronium hydride.

The calculation of excited states in multicomponent systems, in which more than one type of particle is described quantum mechanically, is important for a wide range of applications in chemistry and physics. The nuclear-electronic orbital (NEO) approach has been used to treat all electrons and key protons, or the positron for positronic systems, quantum mechanically on the same level with density functional theory or wavefunction-based methods. The NEO coupled cluster singles and doubles (NEO-CCSD) method has been shown to provide accurate densities, energies, and optimized geometries for multicomponent systems. Herein, the multicomponent equation-of-motion CCSD (NEO-EOM-CCSD) method is developed for the calculation of excitation energies in multicomponent systems. The working equations are derived and implemented, and the programmable equations are provided to enable others to implement this method. This approach is validated by the comparison of the ground state and first three excited state energies of positronium hydride computed with the NEO-EOM-CCSD method to the values calculated with the NEO full configuration interaction and full coupled cluster methods. The development of the NEO-EOM-CCSD method paves the way for a wide range of applications in excited state multicomponent quantum chemistry.

Universal quantum control through deep reinforcement learning

Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To leverage these powerful capabilities for quantum control optimization, we propose a new control framework to simultaneously optimize the speed and fidelity of quantum computation against both leakage and stochastic control errors. For a broad family of two-qubit unitary gates that are important for quantum simulation of many-electron systems, we improve the control robustness by adding control noise into training environments for reinforcement learning agents trained with trusted-region-policy-optimization. The agent control solutions demonstrate a two-order-of-magnitude reduction in average-gate-error over baseline stochastic-gradient-descent solutions and up to a one-order-of-magnitude reduction in gate time from optimal gate synthesis counterparts. These significant improvements in both fidelity and runtime are achieved by combining new physical understandings and state-of-the-art machine learning techniques. Our results open a venue for wider applications in quantum simulation, quantum chemistry and quantum supremacy tests using near-term quantum devices.

Domain‐specific virtual processors as a portable programming and execution model for parallel computational workloads on modern heterogeneous high‐performance computing architectures

AbstractWe advocate domain‐specific virtual processors (DSVP) as a portability layer for expressing and executing domain‐specific computational workloads on modern heterogeneous HPC architectures, with applications in quantum chemistry. Specifically, in this article we extend, generalize and better formalize the concept of a domain‐specific virtual processor as applied to scientific high‐performance computing. In particular, we introduce a system‐wide recursive (hierarchical) hardware encapsulation mechanism into the DSVP architecture and specify a concrete microarchitectural design of an abstract DSVP from which specialized DSVP implementations can be derived for specific scientific domains. Subsequently, we demonstrate, an example of a domain‐specific virtual processor specialized to numerical tensor algebra workloads, which is implemented in the ExaTENSOR library developed by the author with a primary focus on the quantum many‐body computational workloads on large‐scale GPU‐accelerated HPC platforms.

Multireference Approaches to Spin‐State Energetics of Transition Metal Complexes Utilizing the Density Matrix Renormalization Group

AbstractThe accurate and reliable calculation of different electronic states in transition metal systems is a persistent challenge for theoretical chemistry. The widespread use of density functional theory for computing the relative energies of states with different spin in transition metal complexes not only has not discouraged, but often, owing to its limitations, has motivated the development and refinement of first‐principles wavefunction–based methods, including both single‐reference and multireference approaches. A significant boost for the latter has been the emergence of the density matrix renormalization group (DMRG) as a reliable tool in applied quantum chemistry. By enabling the use of larger active spaces than conventionally possible, DMRG has opened up areas of transition metal chemistry that were previously inaccessible to multireference approaches. The present perspective provides an overview of representative studies that make use of DMRG methods and discusses recent applications to spin‐state energetics of transition metal systems. These range from mononuclear to exchange‐coupled systems that define an important emerging field of DMRG applications. Major achievements are highlighted and potential pitfalls are identified with a view toward future methodological developments as well as extensions in the applicability of DMRG‐based approaches to problems of spin‐state energetics and exchange‐coupling in transition metal chemistry.

Dieter Cremer's contribution to the field of theoretical chemistry

AbstractThis legacy article reviews the contributions of Dieter Cremer (1944‐2017) to the field of theoretical chemistry, highlighting his major accomplishments in method development and applied quantum chemistry, which has led to many advances in the field. His work reflects an extraordinary breadth and deep understanding of theory, which is needed to solve complex chemical problems. His passion for science has inspired many colleagues in the past and will do so in the future.

The inverse and derivative connecting problems for some hypergeometric polynomials

Given two polynomial sets $\{ P_n(x) \}_{n\geq 0},$ and $\{ Q_n(x) \}_{n\geq 0}$ such that $\deg ( P_n(x) ) = \deg ( Q_n(x) )=n.$ The so-called connection problem between them asks to find coefficients $\alpha_{n,k}$ in the expression $\displaystyle Q_n(x) =\sum_{k=0}^{n} \alpha_{n,k} P_k(x).$ The connection problem for different types of polynomials has a long history, and it is still of interest. The connection coefficients play an important role in many problems in pure and applied mathematics, especially in combinatorics, mathematical physics and quantum chemical applications. For the particular case $Q_n(x)=x^n$ the connection problem is called the inversion problem associated to $\{P_n(x)\}_{n\geq 0}.$ The particular case $Q_n(x)=P'_{n+1}(x)$ is called the derivative connecting problem for polynomial family $\{ P_n(x) \}_{n\geq 0}.$ In this paper, we give a closed-form expression of the inversion and the derivative coefficients for hypergeometric polynomials of the form $${}_2 F_1 \left[ \left. \begin{array}{c} -n, a \\ b \end{array} \right | z \right], {}_2 F_1 \left[ \left. \begin{array}{c} -n, n+a \\ b \end{array} \right | z \right], {}_2 F_1 \left[ \left. \begin{array}{c} -n, a \\ \pm n +b \end{array} \right | z \right],$$ where $\displaystyle {}_2 F_1 \left[ \left. \begin{array}{c} a, b \\ c \end{array} \right | z \right] =\sum_{k=0}^{\infty} \frac{(a)_k (b)_k}{(c)_k} \frac{z^k}{k!},$ is the Gauss hypergeometric function and $(x)_n$ denotes the Pochhammer symbol defined by $$\displaystyle (x)_n=\begin{cases}1, n=0, \\x(x+1)(x+2)\cdots (x+n-1) , n>0.\end{cases}$$ All polynomials are considered over the field of real numbers.

Dynamic Adaptable Asynchronous Progress Model for MPI RMA Multiphase Applications

Casper is a process-based asynchronous progress model for MPI one-sided communication on multi- and many-core architectures. The one-sided communication is not truly one-sided in most MPI implementations: the target process still relies on software progress to complete incoming operations. Casper allows the user to specify an arbitrary number of cores dedicated to background ghost processes and transparently redirects the RMA operations to ghost processes by utilizing the PMPI redirection and MPI-3 shared-memory technologies. Although Casper benefits applications that suffer from lack of asynchronous progress, the operation redirection design might not support complex multiphase applications effectively, which often involve dynamically changing communication density and computing workloads. In this paper, we present an adaptive mechanism in Casper to address the limitation of static asynchronous progress in multiphase applications. We exploit two adaptive strategies, a user-guided strategy and a fully transparent and automatic strategy based on self-profiling and prediction, to dynamically reconfigure the asynchronous progress in Casper according to real-time performance characteristics during multiphase execution. We evaluate the adaptive approaches in both microbenchmarks and a real quantum chemistry application suite, NWChem, on the Cray XC30 supercomputer and an Intel Omni-Path cluster.

Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.

Introducing Quantum Chemistry in Chemical Engineering Curriculum

Due to the wide and the ever-increasing strategic applications of quantum chemistry in chemical industries, it is important to introduce chemical engineering students to illustrative case studies that deploy molecular modeling in the design of reactors and derivation of thermochemical functions. Herein, we demonstrate how quantum chemical calculations can be implemented within a unit on the chemical reaction engineering to obtain properties that are typically measured in the laboratory classes, namely, reaction rate constants, fractional conversion of reactants, and residence time. A rigorous coupling between quantum chemistry and chemical reaction engineering is expected to encourage students to appreciate the accuracy and the practicality of molecular calculations in process modeling and design of novel materials.

On the q-deformed exponential-type potentials

In this work, both non-deformed and q-deformed exactly solvable multiparameter exponential-type potentials $$V^{\pm }(r)$$ are obtained; $$V^{+}(r=x)$$ stands for one-dimensional potential and $$V^{-}(r)$$ for the radial part of s-states used in the treatment of vibrational properties of diatomic molecules. As a first result, we show that non-deformed potentials arise from non-q-dependent parameters involved in $$V^{\pm }(r)$$ and rather correspond to a class of q-shifted exponential-type potentials obtained from the Arai’s q-deformed hyperbolic functions. As a second result, by using q-dependent parameters in $$V^{\pm }(r)$$ it is possible to obtain true q-deformed exponential-type potentials. As a useful application of these potentials, some examples of q-deformed exponential-type potentials are considered by means of a proper selection of the involved parameters. Our proposal is general and can be viewed as a unified treatment to the study of q-deformed exponential-type potentials with the advantage that it is not necessary to use a specialized method for solving the Schrodinger equation to each specific potential because many of them are obtained as particular cases of $$V^{\pm }(r)$$ . Furthermore, new q-deformed potentials used as interesting alternatives in quantum chemical applications can be derived.

Evaluation of dataflow programming models for electronic structure theory

SummaryDataflow programming models have been growing in popularity as a means to deliver a good balance between performance and portability in the post‐petascale era. In this paper, we evaluate different dataflow programming models for electronic structure methods and compare them in terms of programmability, resource utilization, and scalability. In particular, we evaluate two programming paradigms for expressing scientific applications in a dataflow form: (1) explicit dataflow, where the dataflow is specified explicitly by the developer, and (2) implicit dataflow, where a task scheduling runtime derives the dataflow using per‐task data‐access information embedded in a serial program. We discuss our findings and present a thorough experimental analysis using methods from the NWChem quantum chemistry application as our case study, and OpenMP, StarPU, and PaRSEC as the task‐based runtimes that enable the different forms of dataflow execution. Furthermore, we derive an abstract model to explore the limits of the different dataflow programming paradigms.

Gradient-based stochastic estimation of the density matrix

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S−(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

A PARALLEL ALGORITHM OF ICSYM FOR COMPLEX SYMMETRIC LINEAR SYSTEMS IN QUANTUM CHEMISTRY

Computational effort is a common issue for solving large-scale complex symmetric linear systems, particularly in quantum chemistry applications. In order to alleviate this problem, we propose a parallel algorithm of improved conjugate gradient-type iterative (CSYM). Using three-term recurrence relation and orthogonal properties of residual vectors to replace the tridiagonalization process of classical CSYM, which allows to decrease the degree of the reduce-operator from two to one communication at each iteration and to reduce the amount of vector updates and vector multiplications. Several numerical examples are implemented to show that high performance of proposed improved version is obtained both in convergent rate and in parallel efficiency.

Chiral phosphoric acid catalysis: from numbers to insights.

Chiral phosphoric acids (CPAs) have emerged as powerful organocatalysts for asymmetric reactions, and applications of computational quantum chemistry have revealed important insights into the activity and selectivity of these catalysts. In this tutorial review, we provide an overview of computational tools at the disposal of computational organic chemists and demonstrate their application to a wide array of CPA catalysed reactions. Predictive models of the stereochemical outcome of these reactions are discussed along with specific examples of representative reactions and an outlook on remaining challenges in this area.

Core and Uncore Joint Frequency Scaling Strategy

Energy-proportional computing is one of the foremost constraints in the design of next generation exascale systems. These systems must have a very high FLOP-per-watt ratio to be sustainable, which requires tremendous improvements in power efficiency for modern computing systems. This paper focuses on the processor—as still the biggest contributor to the power usage—by considering both its core and uncore power subsystems. The uncore describes those processor functions that are not handled by the core, such as L3 cache and on-chip interconnect, and contributes significantly to the total system power. The uncore frequency scaling (UFS) capability has been available to the user since the Intel Haswell processor generation. In this paper, performance and power models are proposed to use both the UFS and dynamic voltage and frequency scaling (DVFS) to reduce the energy consumption in parallel applications. Then, these models are incorporated into a runtime strategy that performs processor frequency scaling during parallel application execution. The strategy can be implemented at the kernel/firmware level, which makes it suitable for improving the energy efficiency of exascale design. Experiments on a 20-core Haswell-EP machine using the quantum chemistry application GAMESS and NAS benchmark resulted in up to 24% energy savings with as little as 2% performance loss.