1
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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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Shiraogawa T, Hasegawa JY. Exploration of Chemical Space for Designing Functional Molecules Accounting for Geometric Stability. J Phys Chem Lett 2022; 13:8620-8627. [PMID: 36073988 DOI: 10.1021/acs.jpclett.2c02355] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The design of functional molecules is regarded as searching for molecules with desired functionalities in chemical space populated by candidate molecules. Considering the geometric stability of molecules during the search process is crucial for designing realistic molecules. Here, we propose a method for designing functional molecules by exploring chemical space while explicitly accounting for geometric stability based on computational quantum alchemy. The proposed design method allows the simultaneous prediction of functional molecule in the equilibrium structure and its target desired property in an inverse design fashion without preparing the molecular geometries and performing brute-force screening. The applicability of the design method is proven by obtaining molecules with the desired atomization and electronic energies in various chemical spaces: (BF, CO), (CH4, NH3), 18 BN-doped benzene derivatives, and 3.1 × 105 BN-doped phenanthrene derivatives.
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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
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4
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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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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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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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7
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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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8
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Mezey PG. From quantum similarity measures to quantum analogy functors: tools for QShAR, quantitative shape-activity relations. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02745-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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9
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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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10
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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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11
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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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12
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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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13
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Geerlings P, Chamorro E, Chattaraj PK, De Proft F, Gázquez JL, Liu S, Morell C, Toro-Labbé A, Vela A, Ayers P. Conceptual density functional theory: status, prospects, issues. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-2546-7] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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14
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Affiliation(s)
- Marco Foscato
- Department of Chemistry, University of Bergen, Allégaten 41, N-5007 Bergen, Norway
| | - Vidar R. Jensen
- Department of Chemistry, University of Bergen, Allégaten 41, N-5007 Bergen, Norway
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15
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von Rudorff GF, von Lilienfeld OA. Rapid and accurate molecular deprotonation energies from quantum alchemy. Phys Chem Chem Phys 2020; 22:10519-10525. [PMID: 31960870 DOI: 10.1039/c9cp06471k] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
We assess the applicability of alchemical perturbation density functional theory (APDFT) for quickly and accurately estimating deprotonation energies. We have considered all possible single and double deprotonations in one hundred small organic molecules drawn at random from QM9 [Ramakrishnan et al., JCTC, 2015]. Numerical evidence is presented for 5160 deprotonated species at both HF/def2-TZVP and CCSD/6-31G* levels of theory. We show that the perturbation expansion formalism of APDFT quickly converges to reliable results: using CCSD electron densities and derivatives, regular Hartree-Fock calculations are outperformed at the second or third order for ranking all possible doubly or singly deprotonated molecules, respectively. CCSD single deprotonation energies are reproduced within 1.4 kcal mol-1 on average within third order APDFT. We introduce a hybrid approach where the computational cost of APDFT is reduced even further by mixing first order terms at a higher level of theory (CCSD) with higher order terms at a lower level of theory only (HF). We find that this approach reaches 2 kcal mol-1 accuracy in absolute deprotonation energies compared to CCSD at 2% of the computational cost of third order APDFT.
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Affiliation(s)
- 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, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.
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16
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von Rudorff GF, von Lilienfeld OA. Atoms in Molecules from Alchemical Perturbation Density Functional Theory. J Phys Chem B 2019; 123:10073-10082. [PMID: 31647233 DOI: 10.1021/acs.jpcb.9b07799] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Based on thermodynamic integration, we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas (jellium) as a reference and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this universal choice affords unambiguous and exact definitions of energies and electron densities of AIMs. Numerical results are presented for neutral small molecules (CO, N2, BF, CO2), various small molecules with different electronic hybridization states of carbon (CH4, C2H6, C2H4, C2H2, HCN), and all of the possible BN-doped mutants connecting benzene to borazine (C2nB3-nN3-nH6, 0 ≤ n ≤ 3). Our results, as well as comparison to atomic energy estimates resulting from either DFT trained neural network models or atomic basis set overlap within CCSD, suggest that APDFT based AIMs enable meaningful, interesting, and counterintuitive interpretations of chemical bonding and molecular electron densities.
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Affiliation(s)
- 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 , Klingelbergstrasse 80 , CH-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 , Klingelbergstrasse 80 , CH-4056 Basel , Switzerland
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17
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Chakraborty S, Kayastha P, Ramakrishnan R. The chemical space of B, N-substituted polycyclic aromatic hydrocarbons: Combinatorial enumeration and high-throughput first-principles modeling. J Chem Phys 2019; 150:114106. [PMID: 30902009 DOI: 10.1063/1.5088083] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Combinatorial introduction of heteroatoms in the two-dimensional framework of aromatic hydrocarbons opens up possibilities to design compound libraries exhibiting desirable photovoltaic and photochemical properties. Exhaustive enumeration and first-principles characterization of this chemical space provide indispensable insights for rational compound design strategies. Here, for the smallest seventy-seven Kekulean-benzenoid polycyclic systems, we reveal combinatorial substitution of C atom pairs with the isosteric and isoelectronic B, N pairs to result in 7 453 041 547 842 (7.4 tera) unique molecules. We present comprehensive frequency distributions of this chemical space, analyze trends, and discuss a symmetry-controlled selectivity manifestable in synthesis product yield. Furthermore, by performing high-throughput ab initio density functional theory calculations of over thirty-three thousand (33k) representative molecules, we discuss quantitative trends in the structural stability and inter-property relationships across heteroarenes. Our results indicate a significant fraction of the 33k molecules to be electronically active in the 1.5-2.5 eV region, encompassing the most intense region of the solar spectrum, indicating their suitability as potential light-harvesting molecular components in photo-catalyzed solar cells.
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Affiliation(s)
- Sabyasachi Chakraborty
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Prakriti Kayastha
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Raghunathan Ramakrishnan
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500107, India
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18
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Balawender R, Lesiuk M, De Proft F, Van Alsenoy C, Geerlings P. Exploring chemical space with alchemical derivatives: alchemical transformations of H through Ar and their ions as a proof of concept. Phys Chem Chem Phys 2019; 21:23865-23879. [DOI: 10.1039/c9cp03935j] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Alchemical derivatives have been used previously to obtain information about transformations in which the number of electrons is unchanged. Here an approach for combining changes in both the number of electrons and the nuclear charge is presented.
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Affiliation(s)
- Robert Balawender
- Institute of Physical Chemistry
- Polish Academy of Sciences
- Warsaw
- Poland
| | | | - Frank De Proft
- Research Group of General Chemistry (ALGC)
- Vrije Universiteit Brussel
- Faculteit Wetenschappen en Bio-ingenieurswetenschappen
- Brussels
- Belgium
| | | | - Paul Geerlings
- Research Group of General Chemistry (ALGC)
- Vrije Universiteit Brussel
- Faculteit Wetenschappen en Bio-ingenieurswetenschappen
- Brussels
- Belgium
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