Editorial pubs.acs.org/JPCL
Accurate and Efficient Quantum Chemistry by Locality of Chemical Interactions
T
describe the scaling under two prominent strategies for energy estimation used for quantum computation in chemistry, namely, quantum phase estimation and Hamiltonian averaging. They discuss the bounds on the cost of both strategies. They further investigate examples where an oracle is not available to provide input states, demonstrating the need for developing advanced techniques for state preparation. The Perspective by McClean et al. demonstrates a bright future for quantum chemistry with quantum computers. Noncovalent interactions, including π−π stacking, hydrogen bonding, and van der Waals interactions, determine the spacing and orientation between nonbonded molecular segments present in many chemical and biological systems, such as molecular crystals, polymers, liquids, proteins, DNA, and so forth. The Perspective by Jan Gerit Brandenburg, Manuel Hochheim, Thomas Bredow, and Stefan Grimme9 discusses calculation of weak interaction with minimal basis sets and semiempirical methods. The authors overview various levels of complexity of such calculations and classify the available quantum chemical methods according to computational cost and generality. Different approximations based on either canonical HF theory or semilocal density functionals are presented. The authors benchmark the performance of the methods using small, medium, and large molecular complexes and molecular crystals with different chemical groups and interaction types. Particular attention is given to computation of absolute interaction energies. The accuracy of the proposed low-cost methods is evaluated by comparing with high-level reference data. The mean errors of the binding energies obtained with the simplified schemes are 10−30% and are only twice larger than those of DFT with London dispersion (DFTD).10 Many of the tested methods perform very well for neutral and moderately polar systems and, at the same time, achieve computational savings of up to 2 orders of magnitude. As systems investigated by quantum chemical approaches grow, one can take full advantage of the local nature of chemical interaction to improve computational efficiency and achieve linear scaling with system size.
he Schrö dinger equation provides the information required to calculate static and dynamic properties of arbitrary systems. It allows one to investigate the structure of molecular crystal polymorphs,1 protein folding,2 charge and exciton dynamics in electronic,3 spintronic,4 photocatalytic,5 and photovoltaic6 devices, and many other systems and processes. However, the many-body nature of the electronic problem makes the first-principles solution extremely challenging. Accurate results can be obtained through a basis set expansion of the wave function and evaluation of many-electron integrals. A direct approach of this type is not practical with classical computers due to the huge computational cost and storage requirements even for small systems. Fortunately, many phenomena can be captured at the mean-field level, eliminating an explicit many-body description and resulting in an effective independent-particle model. The Hartree−Fock (HF) method, developed in the 1930s, is a mean-field model that includes the Pauli exclusion principle. Density functional theory (DFT), invented in the 1960s and made practical in the 1990s, takes a significant further step to incorporate electron correlations arising from both the Pauli principle and Coulomb interactions. Chemical intuition suggests that many interactions are local, as exemplified by the valence bond theory proposed parallel to HF in the early days of quantum chemistry. The current issue of J. Phys. Chem. Lett. includes two Perspectives that summarize recent developments in implementing localized and minimal basis sets within the scope of HF and DFT. They offer a systematic route toward accurate quantum chemistry with acceptable cost. Representing a quantum chemical problem with another quantum system, which forms the core of a quantum computer, is a very attractive idea.7 Replacing a classical computer with a quantum mechanical counterpart can lead to enormous advantages for certain types of problems. The linear superposition of the on and off states of a qubit is governed by the same Schrödinger equation that underlies quantum chemistry. The Perspective by Jarrod R. McClean, Ryan Babbush, Peter J. Love, and Alán Aspuru-Guzik8 focuses on the spatial locality of physical interactions and highlights the impact of a local basis set on scaling for quantum chemistry on a quantum computer. The authors start by introducing the electronic structure problem in traditional quantum chemistry and point out that utilization of a local basis for the second-quantized Hamiltonian may lead to impressive linear scaling. They explore in detail the scaling of quantum computation with widely used Gaussian atomic orbitals. Having considered the cutoffs for the overlaps between Gaussian basis functions and a bound on the largest integral, they suggest a simple strategy to truncate the exact Hamiltonian and achieve the desired accuracy in state energies. The idea is illustrated with hydrogen and alkane chains of increasing length, quantifying the indicated scaling advantage. The most common quantum algorithms for quantum chemistry are discussed. Assuming that an oracle is capable of producing good approximations to the desired eigenstates, the authors © 2014 American Chemical Society
Linjun Wang Oleg V. Prezhdo*
■
Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
AUTHOR INFORMATION
Notes
Views expressed in this Editorial are those of the authors and not necessarily the views of the ACS.
■
RELATED READINGS
(1) Woodley, S. M.; Catlow, R. Crystal Structure Prediction from First Principles. Nat. Mater. 2008, 7, 937−946.
Published: December 18, 2014 4317
dx.doi.org/10.1021/jz5024256 | J. Phys. Chem. Lett. 2014, 5, 4317−4318
The Journal of Physical Chemistry Letters
Editorial
(2) Schueler-Furman, O.; Wang, C.; Bradley, P.; Misura, K.; Baker, D. Progress in Modeling of Protein Structures and Interactions. Science 2005, 310, 638−642. (3) Wang, L.; Nan, G.; Yang, X.; Peng, Q.; Li, Q.; Shuai, Z. Computational Methods for Design of Organic Materials with High Charge Mobility. Chem. Soc. Rev. 2010, 39, 423−434. (4) Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molnár, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Spintronics: A Spin-Based Electronics Vision for the Future. Science 2001, 294, 1488−1495. (5) Akimov, A. V.; Neukirch, A. J.; Prezhdo, O. V. Theoretical Insights into Photoinduced Charge Transfer and Catalysis at Oxide Interfaces. Chem. Rev. 2013, 113, 4496−4565. (6) Zhang, Y.; Meng, L.; Yam, C.; Chen, G. Quantum-Mechanical Prediction of Nanoscale Photovoltaics. J. Phys. Chem. Lett. 2014, 5, 1272−1277. (7) Aspuru-Guzik, A.; Dutoi, A. D.; Love, P. J.; Head-Gordon, M. Simulated Quantum Computation of Molecular Energies. Science 2005, 309, 1704−1707. (8) McClean, J. R.; Babbush, R.; Love, P. J.; Aspuru-Guzik, A. Exploiting Locality in Quantum Computation for Quantum Chemistry. J. Phys. Chem. Lett. 2014, 5, 4275−4284. (9) Brandenburg, J. G.; Hochheim, M.; Bredow, T.; Grimme, S. LowCost Quantum Chemical Methods for Noncovalent Interactions. J. Phys. Chem. Lett. 2014, 5, 4275−4284. (10) Brandenburg, J. G.; Grimme, S. Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB). J. Phys. Chem. Lett. 2014, 5, 1785−1789.
4318
dx.doi.org/10.1021/jz5024256 | J. Phys. Chem. Lett. 2014, 5, 4317−4318
