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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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2
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Shiraogawa T, Hasegawa JY. Optimization of General Molecular Properties in the Equilibrium Geometry Using Quantum Alchemy: An Inverse Molecular Design Approach. J Phys Chem A 2023; 127:4345-4353. [PMID: 37146038 DOI: 10.1021/acs.jpca.3c00205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Inverse molecular design allows the optimization of molecules in chemical space and is promising for accelerating the development of functional molecules and materials. To design realistic molecules, it is necessary to consider geometric stability during optimization. In this work, we introduce an inverse design method that optimizes molecular properties by changing the chemical composition in the equilibrium geometry. The optimization algorithm of our recently developed molecular design method has been modified to allow molecular design for general properties at a low computational cost. The proposed method is based on quantum alchemy and does not require empirical data. We demonstrate the applicability and limitations of the present method in the optimization of the electric dipole moment and atomization energy in small chemical spaces for (BF, CO), (N2, CO), BN-doped benzene derivatives, and BN-doped butane derivatives. It was found that the optimality criteria scheme adopted for updating the molecular species yields faster convergence of the optimization and requires a less computational cost. Moreover, we also investigate and discuss the applicability of quantum alchemy to the electric dipole moment.
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Affiliation(s)
- Takafumi Shiraogawa
- Institute for Catalysis, Hokkaido University, N21, W10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
| | - Jun-Ya Hasegawa
- Institute for Catalysis, Hokkaido University, N21, W10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
- Interdisciplinary Research Center for Catalytic Chemistry, National Institute of Advanced Industrial Science and Technology, Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
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3
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Abstract
We propose to relax geometries throughout chemical compound space (CCS) using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schr\"odinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both, nuclear charges and nuclear positions (named "alchemical force"), within the restricted Hartree-Fock case.We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules.We have also analysed the convergence of the alchemical force perturbation series, as well as basis set effects.Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH$_4$, NH$_3$, H$_2$O, and HF yield mean absolute errors of of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 Bohr for 4$^\text{th}$ order APDFT predictions, respectively.Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree Fock derivative for benzene we provide numerical predictions of equilibrium energies and relaxed structures of all the 17 iso-electronic charge-netural BN-doped mutants with averaged absolute deviations of $\sim$27 mHa and $\sim$0.12 Bohr, respectively.
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4
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Zamora PP, Maurelia R, Bieger K. Pyrazolon-ditiocarbonic acid and dibromoalcanes – cyclic keto-ditioacetals formation vs. open chain products: A theoretical study. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2052371] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- P. P. Zamora
- Facultad de Ciencias Naturales, Departamento de Química y Biología, Universidad de Atacama, Copiapó, Chile
| | - R. Maurelia
- Facultad de Ciencias Naturales, Departamento de Química y Biología, Universidad de Atacama, Copiapó, Chile
| | - K. Bieger
- Facultad de Ciencias Naturales, Departamento de Química y Biología, Universidad de Atacama, Copiapó, Chile
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5
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Eikey EA, Maldonado AM, Griego CD, Von Rudorff GF, Keith JA. Quantum alchemy beyond singlets: Bonding in diatomic molecules with hydrogen. J Chem Phys 2022; 156:204111. [DOI: 10.1063/5.0079487] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Emily A. Eikey
- Chemistry, University of Pittsburgh, United States of America
| | - Alex M. Maldonado
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, United States of America
| | | | | | - John A. Keith
- Dept. of Chemical & Petroleum Engineering, University of Pittsburgh, United States of America
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6
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Eikey EA, Maldonado AM, Griego CD, Von Rudorff GF, Keith JA. Evaluating quantum alchemy of atoms with thermodynamic cycles: Beyond ground electronic states. J Chem Phys 2022; 156:064106. [DOI: 10.1063/5.0079483] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emily A. Eikey
- Chemistry, University of Pittsburgh, United States of America
| | - Alex M. Maldonado
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, United States of America
| | | | | | - John A. Keith
- Dept. of Chemical & Petroleum Engineering, University of Pittsburgh, United States of America
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7
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Abstract
Doping compounds can be considered a perturbation to the nuclear charges in a molecular Hamiltonian. Expansions of this perturbation in a Taylor series, i.e., quantum alchemy, have been used in the literature to assess millions of derivative compounds at once rather than enumerating them in costly quantum chemistry calculations. So far, it was unclear whether this series even converges for small molecules, whether it can be used for geometry relaxation, and how strong this perturbation may be to still obtain convergent numbers. This work provides numerical evidence that this expansion converges and recovers the self-consistent energy of Hartree-Fock calculations. The convergence radius of this expansion is quantified for dimer examples and systematically evaluated for different basis sets, allowing for estimates of the chemical space that can be covered by perturbing one reference calculation alone. Besides electronic energy, convergence is shown for density matrix elements, molecular orbital energies, and density profiles, even for large changes in electronic structure, e.g., transforming He3 into H6. Subsequently, mixed alchemical and spatial derivatives are used to relax H2 from the electronic structure of He alone, highlighting a path to spatially relaxed quantum alchemy. Finally, the underlying code that allows for arbitrarily accurate evaluation of restricted Hartree-Fock energies and arbitrary order derivatives is made available to support future method development.
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Abstract
Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.
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Affiliation(s)
- Bing Huang
- Faculty
of Physics, University of Vienna, 1090 Vienna, Austria
| | - O. Anatole von Lilienfeld
- Faculty
of Physics, University of Vienna, 1090 Vienna, Austria
- Institute
of Physical Chemistry and National Center for Computational Design
and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
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9
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Lemm D, von Rudorff GF, von Lilienfeld OA. Machine learning based energy-free structure predictions of molecules, transition states, and solids. Nat Commun 2021; 12:4468. [PMID: 34294693 PMCID: PMC8298673 DOI: 10.1038/s41467-021-24525-7] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Accepted: 06/22/2021] [Indexed: 02/06/2023] Open
Abstract
The computational prediction of atomistic structure is a long-standing problem in physics, chemistry, materials, and biology. Conventionally, force-fields or ab initio methods determine structure through energy minimization, which is either approximate or computationally demanding. This accuracy/cost trade-off prohibits the generation of synthetic big data sets accounting for chemical space with atomistic detail. Exploiting implicit correlations among relaxed structures in training data sets, our machine learning model Graph-To-Structure (G2S) generalizes across compound space in order to infer interatomic distances for out-of-sample compounds, effectively enabling the direct reconstruction of coordinates, and thereby bypassing the conventional energy optimization task. The numerical evidence collected includes 3D coordinate predictions for organic molecules, transition states, and crystalline solids. G2S improves systematically with training set size, reaching mean absolute interatomic distance prediction errors of less than 0.2 Å for less than eight thousand training structures - on par or better than conventional structure generators. Applicability tests of G2S include successful predictions for systems which typically require manual intervention, improved initial guesses for subsequent conventional ab initio based relaxation, and input generation for subsequent use of structure based quantum machine learning models.
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Affiliation(s)
- Dominik Lemm
- Faculty of Physics, University of Vienna, Vienna, Austria
| | | | - O Anatole von Lilienfeld
- Faculty of Physics, University of Vienna, Vienna, Austria.
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Basel, Switzerland.
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von Rudorff GF, von Lilienfeld OA. Simplifying inverse materials design problems for fixed lattices with alchemical chirality. SCIENCE ADVANCES 2021; 7:eabf1173. [PMID: 34138735 PMCID: PMC8133750 DOI: 10.1126/sciadv.abf1173] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 03/25/2021] [Indexed: 05/03/2023]
Abstract
Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting "alchemical" enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.
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Affiliation(s)
- Guido Falk von Rudorff
- University of Vienna, Faculty of Physics, Kolingasse 14-16, 1090 Vienna, Austria
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
| | - O Anatole von Lilienfeld
- University of Vienna, Faculty of Physics, Kolingasse 14-16, 1090 Vienna, Austria.
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
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11
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Christensen AS, von Lilienfeld OA. On the role of gradients for machine learning of molecular energies and forces. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/abba6f] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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12
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Domenichini G, von Rudorff GF, von Lilienfeld OA. Effects of perturbation order and basis set on alchemical predictions. J Chem Phys 2020; 153:144118. [PMID: 33086815 DOI: 10.1063/5.0023590] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Alchemical perturbation density functional theory has been shown to be an efficient and computationally inexpensive way to explore chemical compound space. We investigate approximations made, in terms of atomic basis sets and the perturbation order, introduce an electron-density based estimate of errors of the alchemical prediction, and propose a correction for effects due to basis set incompleteness. Our numerical analysis of potential energy estimates, and resulting binding curves, is based on coupled-cluster single double (CCSD) reference results and is limited to all neutral diatomics with 14 electrons (AlH⋯NN). The method predicts binding energy, equilibrium distance, and vibrational frequencies of neighboring out-of-sample diatomics with near CCSD quality using perturbations up to the fifth order. We also discuss simultaneous alchemical mutations at multiple sites in benzene.
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Affiliation(s)
- Giorgio Domenichini
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
| | - Guido Falk von Rudorff
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
| | - O Anatole von Lilienfeld
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
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13
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Westermayr J, Marquetand P. Deep learning for UV absorption spectra with SchNarc: First steps toward transferability in chemical compound space. J Chem Phys 2020; 153:154112. [DOI: 10.1063/5.0021915] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- J. Westermayr
- Faculty of Chemistry, Institute of Theoretical Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - P. Marquetand
- Faculty of Chemistry, Institute of Theoretical Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Faculty of Chemistry, Data Science @ Uni Vienna, University of Vienna, Währinger Str. 29, 1090 Vienna, Austria
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14
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Griego CD, Zhao L, Saravanan K, Keith JA. Machine learning corrected alchemical perturbation density functional theory for catalysis applications. AIChE J 2020. [DOI: 10.1002/aic.17041] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Charles D. Griego
- Department of Chemical and Petroleum Engineering Swanson School of Engineering, University of Pittsburgh Pittsburgh Pennsylvania USA
| | - Lingyan Zhao
- Department of Chemical and Petroleum Engineering Swanson School of Engineering, University of Pittsburgh Pittsburgh Pennsylvania USA
| | - Karthikeyan Saravanan
- Department of Chemical and Petroleum Engineering Swanson School of Engineering, University of Pittsburgh Pittsburgh Pennsylvania USA
| | - John A. Keith
- Department of Chemical and Petroleum Engineering Swanson School of Engineering, University of Pittsburgh Pittsburgh Pennsylvania USA
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15
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Westermayr J, Marquetand P. Machine learning and excited-state molecular dynamics. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/ab9c3e] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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16
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Muñoz M, Robles-Navarro A, Fuentealba P, Cárdenas C. Predicting Deprotonation Sites Using Alchemical Derivatives. J Phys Chem A 2020; 124:3754-3760. [PMID: 32286831 DOI: 10.1021/acs.jpca.9b09472] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
An alchemical transformation is any process, physical or fictitious, that connects two points in the chemical space. A particularly important transformation is the vanishing of a proton, whose energy can be linked to the proton dissociation enthalpy of acids. In this work we assess the reliability of alchemical derivatives in predicting the proton dissociation enthalpy of a diverse series of mono- and polyprotic molecules. Alchemical derivatives perform remarkably well in ranking the proton affinity of all molecules. Additionally, alchemical derivatives could be use also as a predictive tool because their predictions correlate quite well with calculations based on energy differences and experimental values. Although second-order alchemical derivatives underestimate the dissociation enthalpy, the deviation seems to be almost constant. This makes alchemical derivatives extremely accurate to evaluate the difference in proton affinity between two acid sites of polyprotic molecule. Finally, we show that the reason for the underestimation of the dissociation enthalpy is most likely the contribution of higher-order derivatives.
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Affiliation(s)
- Macarena Muñoz
- Facultad de Ingenierı́a y Ciencias, Universidad Adolfo Ibañez, Diagonal Las Torres 2640, Santiago 7941169, Chile
| | - Andrés Robles-Navarro
- Departamento de Fı́sica, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago Casilla 653, Chile.,Centro para el Desarrollo de la Nanociencia y la Nanotecnologı́a (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
| | - Patricio Fuentealba
- Departamento de Fı́sica, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago Casilla 653, Chile.,Centro para el Desarrollo de la Nanociencia y la Nanotecnologı́a (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
| | - Carlos Cárdenas
- Departamento de Fı́sica, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago Casilla 653, Chile.,Centro para el Desarrollo de la Nanociencia y la Nanotecnologı́a (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
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