1
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Friede M, Hölzer C, Ehlert S, Grimme S. dxtb-An efficient and fully differentiable framework for extended tight-binding. J Chem Phys 2024; 161:062501. [PMID: 39120026 DOI: 10.1063/5.0216715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Accepted: 07/18/2024] [Indexed: 08/10/2024] Open
Abstract
Automatic differentiation (AD) emerged as an integral part of machine learning, accelerating model development by enabling gradient-based optimization without explicit analytical derivatives. Recently, the benefits of AD and computing arbitrary-order derivatives with respect to any variable were also recognized in the field of quantum chemistry. In this work, we present dxtb-an open-source, fully differentiable framework for semiempirical extended tight-binding (xTB) methods. Developed entirely in Python and leveraging PyTorch for array operations, dxtb facilitates extensibility and rapid prototyping while maintaining computational efficiency. Through comprehensive code vectorization and optimization, we essentially reach the speed of compiled xTB programs for high-throughput calculations of small molecules. The excellent performance also scales to large systems, and batch operability yields additional benefits for execution on parallel hardware. In particular, energy evaluations are on par with existing programs, whereas the speed of automatically differentiated nuclear derivatives is only 2 to 5 times slower compared to their analytical counterparts. We showcase the utility of AD in dxtb by calculating various molecular and spectroscopic properties, highlighting its capacity to enhance and simplify such evaluations. Furthermore, the framework streamlines optimization tasks and offers seamless integration of semiempirical quantum chemistry in machine learning, paving the way for physics-inspired end-to-end differentiable models. Ultimately, dxtb aims to further advance the capabilities of semiempirical methods, providing an extensible foundation for future developments and hybrid machine learning applications. The framework is accessible at https://github.com/grimme-lab/dxtb.
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Affiliation(s)
- Marvin Friede
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn 53115, Germany
| | - Christian Hölzer
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn 53115, Germany
| | - Sebastian Ehlert
- AI4Science, Microsoft Research, Evert van de Beekstraat 354, 1118CZ Schiphol, Netherlands
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn 53115, Germany
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2
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Voss J. Machine learning for accuracy in density functional approximations. J Comput Chem 2024; 45:1829-1845. [PMID: 38668453 DOI: 10.1002/jcc.27366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 02/16/2024] [Accepted: 03/25/2024] [Indexed: 07/21/2024]
Abstract
Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.
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Affiliation(s)
- Johannes Voss
- SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, California, USA
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3
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Zhang X, Li C, Ye HZ, Berkelbach TC, Chan GKL. Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics. J Chem Phys 2024; 161:014109. [PMID: 38949583 DOI: 10.1063/5.0212274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.
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Affiliation(s)
- Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Chenghan Li
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | | | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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4
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von Rudorff GF, Artemyev AN, Lagutin BM, Demekhin PV. Optimal photoelectron circular dichroism of a model chiral system. J Chem Phys 2024; 160:214301. [PMID: 38828821 DOI: 10.1063/5.0209161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/14/2024] [Indexed: 06/05/2024] Open
Abstract
We optimize the internuclear geometry and electronic structure of a model chiral system to achieve a maximal photoelectron circular dichroism (PECD) in its one-photon ionization by circularly polarized light. The electronic structure calculations are performed by the single center method, while the optimization is done using quantum alchemy employing a Taylor series expansion. Thereby, the effect of bond lengths and uncompensated charge distributions on the chiral response of the model is investigated theoretically in some detail. It is demonstrated that manipulating a chiral asymmetry of the ionic potential may enhance the dichroic parameter (i.e., the PECD) of the randomly oriented model system well beyond β1 = 25%. Furthermore, we demonstrate that quantum alchemy is applicable to PECD despite the unusually strong coupling of spatial and electronic degrees of freedom and discuss the relative impact of the individual degrees of freedom in this model system. We define the necessary conditions for the computational design of PECD for real (non-model) chiral molecules using our approach.
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Affiliation(s)
- Guido F von Rudorff
- Institut für Chemie, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany
- Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), Heinrich-Plett-Straße 40, 34132 Kassel, Germany
| | - Anton N Artemyev
- Institut für Physik, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany
| | - Boris M Lagutin
- Rostov State Transport University, Narodnogo Opolcheniya Square 2, 344038 Rostov-on-Don, Russia
| | - Philipp V Demekhin
- Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), Heinrich-Plett-Straße 40, 34132 Kassel, Germany
- Institut für Physik, Universität Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany
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5
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Alaa El-Din KK, Forte A, Kasim MF, Miniati F, Vinko SM. STEP: extraction of underlying physics with robust machine learning. ROYAL SOCIETY OPEN SCIENCE 2024; 11:231374. [PMID: 39100625 PMCID: PMC11296055 DOI: 10.1098/rsos.231374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Revised: 01/25/2024] [Accepted: 03/20/2024] [Indexed: 08/06/2024]
Abstract
A prevalent class of challenges in modern physics are inverse problems, where physical quantities must be extracted from experimental measurements. End-to-end machine learning approaches to inverse problems typically require constructing sophisticated estimators to achieve the desired accuracy, largely because they need to learn the complex underlying physical model. Here, we discuss an alternative paradigm: by making the physical model auto-differentiable we can construct a neural surrogate to represent the unknown physical quantity sought, while avoiding having to relearn the known physics entirely. We dub this process surrogate training embedded in physics (STEP) and illustrate that it generalizes well and is robust against overfitting and significant noise in the data. We demonstrate how STEP can be applied to perform dynamic kernel deconvolution to analyse resonant inelastic X-ray scattering spectra and show that surprisingly simple estimator architectures suffice to extract the relevant physical information.
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Affiliation(s)
| | | | | | | | - Sam M. Vinko
- Department of Physics, University of Oxford, Oxford, UK
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot, OX11 0QX, UK
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6
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Domenichini G. Extending the definition of atomic basis sets to atoms with fractional nuclear charge. J Chem Phys 2024; 160:124107. [PMID: 38526100 DOI: 10.1063/5.0196383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2024] [Accepted: 03/10/2024] [Indexed: 03/26/2024] Open
Abstract
Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a non-physical system in which an atom possess a non-integer nuclear charge. A correct quantum mechanical treatment of these systems is limited by the fact that finite size atomic basis sets do not define exponents and contraction coefficients for fractional charge atoms. This paper proposes a solution to this problem and shows that a smooth interpolation of the atomic orbital coefficients and exponents across the periodic table is a convenient way to produce accurate alchemical predictions, even using small size basis sets.
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Affiliation(s)
- Giorgio Domenichini
- Faculty of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
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7
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Wang W, Whitfield JD. Basis Set Generation and Optimization in the NISQ Era with Quiqbox.jl. J Chem Theory Comput 2023; 19:8032-8052. [PMID: 37924295 DOI: 10.1021/acs.jctc.3c00011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2023]
Abstract
In the noisy intermediate-scale quantum era, ab initio computation of electronic structure problems has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. Basis sets play a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of single-particle basis sets, we propose a framework for more customizable basis set generation and optimization. This framework allows composite basis sets to go beyond typical basis set frameworks, such as atomic basis sets, by introducing the concept of mixed-contracted Gaussian-type orbitals. These basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source software package named "Quiqbox" in the Julia programming language. We demonstrate various examples of using Quiqbox for basis set optimization and generation, ranging from optimizing atomic basis sets on the Hartree-Fock level, preparing the initial state for variational quantum eigensolver computation, and constructing basis sets with completely delocalized orbitals. We also include various benchmarks of Quiqbox for basis set optimization and ab initial electronic structure computation.
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Affiliation(s)
- Weishi Wang
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - James D Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, United States
- AWS Center for Quantum Computing, Pasadena, California 91106, United States
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8
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Mahajan A, Kurian JS, Lee J, Reichman DR, Sharma S. Response properties in phaseless auxiliary field quantum Monte Carlo. J Chem Phys 2023; 159:184101. [PMID: 37937933 DOI: 10.1063/5.0171996] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/11/2023] [Indexed: 11/09/2023] Open
Abstract
We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.
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Affiliation(s)
- Ankit Mahajan
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Jo S Kurian
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
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9
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Di Felice R, Mayes ML, Richard RM, Williams-Young DB, Chan GKL, de Jong WA, Govind N, Head-Gordon M, Hermes MR, Kowalski K, Li X, Lischka H, Mueller KT, Mutlu E, Niklasson AMN, Pederson MR, Peng B, Shepard R, Valeev EF, van Schilfgaarde M, Vlaisavljevich B, Windus TL, Xantheas SS, Zhang X, Zimmerman PM. A Perspective on Sustainable Computational Chemistry Software Development and Integration. J Chem Theory Comput 2023; 19:7056-7076. [PMID: 37769271 PMCID: PMC10601486 DOI: 10.1021/acs.jctc.3c00419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Indexed: 09/30/2023]
Abstract
The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.
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Affiliation(s)
- Rosa Di Felice
- Departments
of Physics and Astronomy and Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, United States
- CNR-NANO
Modena, Modena 41125, Italy
| | - Maricris L. Mayes
- Department
of Chemistry and Biochemistry, University
of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, United States
| | | | | | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Wibe A. de Jong
- Lawrence
Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Niranjan Govind
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Martin Head-Gordon
- Pitzer Center
for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Karol Kowalski
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Karl T. Mueller
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Erdal Mutlu
- Advanced
Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Bo Peng
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | | | - Bess Vlaisavljevich
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University and
Ames Laboratory, Ames, Iowa 50011, United States
| | - Sotiris S. Xantheas
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
- Advanced
Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Xing Zhang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Paul M. Zimmerman
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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10
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Liang J, Feng X, Liu X, Head-Gordon M. Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments. J Chem Phys 2023; 158:204109. [PMID: 37218699 PMCID: PMC10208678 DOI: 10.1063/5.0152838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2023] [Accepted: 04/27/2023] [Indexed: 05/24/2023] Open
Abstract
VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).
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Affiliation(s)
- Jiashu Liang
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA
| | | | - Xiao Liu
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA
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11
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Tan CW, Pickard CJ, Witt WC. Automatic differentiation for orbital-free density functional theory. J Chem Phys 2023; 158:124801. [PMID: 37003740 DOI: 10.1063/5.0138429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023] Open
Abstract
Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance burden. Furthermore, fully differentiable simulation tools enable direct evaluation of challenging derivatives-including those directly related to properties measurable by experiment-that are conventionally computed with finite difference methods. Here, we investigate automatic differentiation in the context of orbital-free density functional theory (OFDFT) simulations of materials, introducing PROFESS-AD. Its automatic evaluation of properties derived from first derivatives, including functional potentials, forces, and stresses, facilitates the development and testing of new density functionals, while its direct evaluation of properties requiring higher-order derivatives, such as bulk moduli, elastic constants, and force constants, offers more concise implementations than conventional finite difference methods. For these reasons, PROFESS-AD serves as an excellent prototyping tool and provides new opportunities for OFDFT.
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Affiliation(s)
- Chuin Wei Tan
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - Chris J Pickard
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
| | - William C Witt
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
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12
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Vargas-Hernández RA, Jorner K, Pollice R, Aspuru-Guzik A. Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation. J Chem Phys 2023; 158:104801. [PMID: 36922116 DOI: 10.1063/5.0137103] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/19/2023] Open
Abstract
Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel's π-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations using standard gradient-based optimization algorithms.
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Affiliation(s)
- Rodrigo A Vargas-Hernández
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Kjell Jorner
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Robert Pollice
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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13
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Zhang X, Chan GKL. Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond. J Chem Phys 2022; 157:204801. [DOI: 10.1063/5.0118200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
We introduce an extension to the PySCF package, which makes it automatically differentiable. The implementation strategy is discussed, and example applications are presented to demonstrate the automatic differentiation framework for quantum chemistry methodology development. These include orbital optimization, properties, excited-state energies, and derivative couplings, at the mean-field level and beyond, in both molecules and solids. We also discuss some current limitations and directions for future work.
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Affiliation(s)
- Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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14
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Yoshikawa N, Sumita M. Automatic Differentiation for the Direct Minimization Approach to the Hartree–Fock Method. J Phys Chem A 2022; 126:8487-8493. [DOI: 10.1021/acs.jpca.2c05922] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Naruki Yoshikawa
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
| | - Masato Sumita
- Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihombashi, Chuo-ku, Tokyo 103-0027, Japan
- International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
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15
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Krug SL, von Rudorff GF, von Lilienfeld OA. Relative energies without electronic perturbations via alchemical integral transform. J Chem Phys 2022; 157:164109. [DOI: 10.1063/5.0111511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that the energy of a perturbed system can be fully recovered from the unperturbed system’s electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2 p + 1)-th energy derivative. Without the need for derivatives of the electron density, this allows us to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one by one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential and in the range of machine accuracy for hydrogen-like atoms. Considering isoelectronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree–Fock reference numbers.
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Affiliation(s)
- Simon León Krug
- University of Vienna, Computational Materials Physics, Kolingasse 14-16, 1090 Vienna, Austria
- Machine Learning Group, Technische Universität Berlin and Institute for the Foundations of Learning and Data, 10587 Berlin, Germany
| | - Guido Falk von Rudorff
- University of Vienna, Computational Materials Physics, Kolingasse 14-16, 1090 Vienna, Austria
- Institute for Pure and Applied Mathematics (IPAM), University of California, Los Angeles, 460 Portola Plaza, Los Angeles, California 90095, USA
| | - O. Anatole von Lilienfeld
- Machine Learning Group, Technische Universität Berlin and Institute for the Foundations of Learning and Data, 10587 Berlin, Germany
- Vector Institute for Artificial Intelligence, Toronto, Ontario, M5S 1M1, Canada
- Departments of Chemistry, Materials Science and Engineering, and Physics, University of Toronto, St. George Campus, Toronto, Ontario M5S 1A7, Canada
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16
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Bac S, Patra A, Kron KJ, Mallikarjun Sharada S. Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry. J Phys Chem A 2022; 126:7795-7805. [DOI: 10.1021/acs.jpca.2c05459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Selin Bac
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California90089, United States
| | - Abhilash Patra
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California90089, United States
| | - Kareesa J. Kron
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California90089, United States
| | - Shaama Mallikarjun Sharada
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California90089, United States
- Department of Chemistry, University of Southern California, Los Angeles, California90089, United States
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