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Zope RR, Yamamoto Y, Baruah T. How well do one-electron self-interaction-correction methods perform for systems with fractional electrons? J Chem Phys 2024; 160:084102. [PMID: 38385511 DOI: 10.1063/5.0182773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/28/2024] [Indexed: 02/23/2024] Open
Abstract
Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (zσ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew-Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of H2+ and He2+ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li+ to F- at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.
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Affiliation(s)
- Rajendra R Zope
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
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Folkestad SD, Matveeva R, Høyvik IM, Koch H. Implementation of Occupied and Virtual Edmiston-Ruedenberg Orbitals Using Cholesky Decomposed Integrals. J Chem Theory Comput 2022; 18:4733-4744. [PMID: 35856495 PMCID: PMC9367017 DOI: 10.1021/acs.jctc.2c00261] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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We present a trust-region optimization of the Edmiston–Ruedenberg
orbital localization function. The approach is used to localize both
the occupied and the virtual orbitals and is the first demonstration
of general virtual orbital localization using the Edmiston–Ruedenberg
localization function. In the Edmiston–Ruedenberg approach,
the sum of the orbital self-repulsion energies is maximized to obtain
the localized orbitals. The Cholesky decomposition reduces the cost
of transforming the electron repulsion integrals, and the overall
scaling of our implementation is . The optimization is performed with all
quantities in the molecular orbital basis, and the localization of
the occupied orbitals is often less expensive than the corresponding
self-consistent field (SCF) optimization. Furthermore, the occupied
orbital localization scales linearly with the basis set. For the virtual
space, the cost is significantly higher than the SCF optimization.
The orbital spreads of the resulting virtual Edmiston–Ruedenberg
orbitals are larger than for other, less expensive, orbital localization
functions. This indicates that other localization procedures are more
suitable for applications such as local post-Hartree–Fock calculations.
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Affiliation(s)
- Sarai Dery Folkestad
- Department of Chemistry, The Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Regina Matveeva
- Department of Chemistry, The Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Ida-Marie Høyvik
- Department of Chemistry, The Norwegian University of Science and Technology, Trondheim 7491, Norway
| | - Henrik Koch
- Department of Chemistry, The Norwegian University of Science and Technology, Trondheim 7491, Norway
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Clement MC, Wang X, Valeev EF. Robust Pipek-Mezey Orbital Localization in Periodic Solids. J Chem Theory Comput 2021; 17:7406-7415. [PMID: 34739235 DOI: 10.1021/acs.jctc.1c00238] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We describe a robust method for determining Pipek-Mezey (PM) Wannier functions (WF), recently introduced by Jónsson et al. (J. Chem. Theor. Chem. 2017, 13, 460), which provide some formal advantages over the more common Boys (also known as maximally-localized) Wannier functions. The Broyden-Fletcher-Goldfarb-Shanno-based PMWF solver is demonstrated to yield dramatically faster convergence compared to the alternatives (steepest ascent and conjugate gradient) in a variety of one-, two-, and three-dimensional solids (including some with vanishing gaps) and can be used to obtain Wannier functions robustly in supercells with thousands of atoms. Evaluation of the PM functional and its gradient in periodic linear combination of atomic orbital representation used a particularly simple definition of atomic charges obtained by Moore-Penrose pseudoinverse projection onto the minimal atomic orbital basis. An automated "canonicalize phase then randomize" method for generating the initial guess for WFs contributes significantly to the robustness of the solver.
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Affiliation(s)
- Marjory C Clement
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Xiao Wang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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Luo Z, Khaliullin RZ. Variable-Metric Localization of Occupied and Virtual Orbitals. J Chem Theory Comput 2021; 17:5568-5581. [PMID: 34370474 DOI: 10.1021/acs.jctc.1c00379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The key idea of the variable-metric approach to orbital localization is to allow nonorthogonality between orbitals while, at the same time, preventing them from becoming linearly dependent. The variable-metric localization has been shown to improve the locality of occupied nonorthogonal orbitals relative to their orthogonal counterparts. In this work, numerous localization algorithms are designed and tested to exploit the conceptual simplicity of the variable-metric approach with the goal of creating a straightforward and reliable localization procedure for virtual orbitals. The implemented algorithms include the steepest descent, conjugate gradient (CG), limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), and hybrid procedures as well as trust-region (TR) methods based on the CG and Cauchy-point subproblem solvers. Comparative analysis shows that the CG-based TR algorithm is the best overall method to obtain nonorthogonal localized molecular orbitals (NLMOs), occupied or virtual. The L-BFGS and CG algorithms can also be used to obtain NLMOs reliably but often at higher computational cost. Extensive tests demonstrate that the implemented methods allow us to obtain well-localized Boys-Foster (i.e., maximally localized Wannier functions) and Pipek-Mezey, orthogonal and nonorthogonal, and occupied and virtual orbitals for a variety of gas-phase molecules and periodic materials. The tests also show that virtual NLMOs, which have not been described before, are, on average, 13% (Boys-Foster) and 18% (Pipek-Mezey) more localized than their orthogonal counterparts.
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Affiliation(s)
- Ziling Luo
- Department of Chemistry, McGill University, 801 Sherbrooke St. West, Montreal QC H3A 0B8, Canada
| | - Rustam Z Khaliullin
- Department of Chemistry, McGill University, 801 Sherbrooke St. West, Montreal QC H3A 0B8, Canada
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Akter S, Vargas JA, Sharkas K, Peralta JE, Jackson KA, Baruah T, Zope RR. How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations? Phys Chem Chem Phys 2021; 23:18678-18685. [PMID: 34612405 DOI: 10.1039/d0cp06512a] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys., 2018, 20, 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew-Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi-Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys., 2019, 151, 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.
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Affiliation(s)
- Sharmin Akter
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA.
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Akter S, Yamamoto Y, Zope RR, Baruah T. Static dipole polarizabilities of polyacenes using self-interaction-corrected density functional approximations. J Chem Phys 2021; 154:114305. [DOI: 10.1063/5.0041265] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sharmin Akter
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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7
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Diaz CM, Suryanarayana P, Xu Q, Baruah T, Pask JE, Zope RR. Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals. J Chem Phys 2021; 154:084112. [DOI: 10.1063/5.0031341] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Carlos M. Diaz
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Qimen Xu
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - John E. Pask
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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8
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Yamamoto Y, Romero S, Baruah T, Zope RR. Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions. J Chem Phys 2020; 152:174112. [DOI: 10.1063/5.0004738] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Selim Romero
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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9
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Høyvik IM, Jørgensen P. Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals. Chem Rev 2016; 116:3306-27. [DOI: 10.1021/acs.chemrev.5b00492] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ida-Marie Høyvik
- Department
of Chemistry, The Norwegian University of Science and Technology, Høgskoleringen 5, 7491 Trondheim, Norway
| | - Poul Jørgensen
- qLEAP
Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
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10
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Zhang C, Li S. An efficient localization procedure for large systems using a sequential transformation strategy. J Chem Phys 2014; 141:244106. [DOI: 10.1063/1.4904292] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chenyang Zhang
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, People’s Republic of China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, People’s Republic of China
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Lehtola S, Jónsson H. Pipek–Mezey Orbital Localization Using Various Partial Charge Estimates. J Chem Theory Comput 2014; 10:642-9. [DOI: 10.1021/ct401016x] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Susi Lehtola
- COMP
Centre of Excellence, Department of Applied Physics, Aalto University School of Science,
P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
| | - Hannes Jónsson
- COMP
Centre of Excellence, Department of Applied Physics, Aalto University School of Science,
P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
- Faculty
of Physical Sciences, University of Iceland, Reykjavı́k, Iceland
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12
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Lehtola S, Jónsson H. Unitary Optimization of Localized Molecular Orbitals. J Chem Theory Comput 2013; 9:5365-72. [DOI: 10.1021/ct400793q] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Susi Lehtola
- COMP Centre of Excellence, Department of
Applied Physics, School of Science, Aalto University, P.O.
Box 11000, FI-00076 Aalto, Espoo, Finland
| | - Hannes Jónsson
- COMP Centre of Excellence, Department of
Applied Physics, School of Science, Aalto University, P.O.
Box 11000, FI-00076 Aalto, Espoo, Finland
- Faculty of Physical Sciences, University of Iceland, 101 Reykjavík, Iceland
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Oña OB, Alcoba DR, Torre A, Lain L, Torres-Vega JJ, Tiznado W. Orbital Localization Criterion as a Complementary Tool in the Bonding Analysis by Means of Electron Localization Function: Study of the Sin(BH)5-n2- (n = 0–5) Clusters. J Phys Chem A 2013; 117:12953-8. [DOI: 10.1021/jp4081228] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Ofelia B. Oña
- Instituto de Investigaciones
Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo
Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (s/n), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Diego R. Alcoba
- Departamento de Física, Facultad
de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Alicia Torre
- Departamento de Química Física, Facultad
de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Luis Lain
- Departamento de Química Física, Facultad
de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Juan J. Torres-Vega
- Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Av. República 275, Santiago de Chile, Chile
| | - William Tiznado
- Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Av. República 275, Santiago de Chile, Chile
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Alcoba DR, Lain L, Torre A, Bochicchio RC. An orbital localization criterion based on the theory of “fuzzy” atoms. J Comput Chem 2006; 27:596-608. [PMID: 16470667 DOI: 10.1002/jcc.20373] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
This work proposes a new procedure for localizing molecular and natural orbitals. The localization criterion presented here is based on the partitioning of the overlap matrix into atomic contributions within the theory of "fuzzy" atoms. Our approach has several advantages over other schemes: it is computationally inexpensive, preserves the sigma/pi-separability in planar systems and provides a straightforward interpretation of the resulting orbitals in terms of their localization indices and atomic occupancies. The corresponding algorithm has been implemented and its efficiency tested on selected molecular systems.
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Affiliation(s)
- Diego R Alcoba
- Departamento de Química Física, Facultad de Ciencias, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain.
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Sano T. Elementary Jacobi rotation method for generalized valence bond perfect-pairing calculations combined with simple procedure for generating reliable initial orbitals. ACTA ACUST UNITED AC 2000. [DOI: 10.1016/s0166-1280(99)00484-4] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Sano T, Matsuoka O. Towards a Calculation of the Electronic Structures of Macromolecules. I. Quadratically Convergent Method for a Direct Calculation of Localized Molecular Orbitals. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1996. [DOI: 10.1246/bcsj.69.2195] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Sano T, I'Haya YJ. Acceleration of convergence in iterative methods when solving Newton-Raphson equations in second-order SCF calculations for energy-localized orbitals. Chem Phys Lett 1990. [DOI: 10.1016/0009-2614(90)87160-s] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Cioslowski J. Bulk properties from finite‐cluster calculations. V. Pseudo‐Wannier orbitals from molecular orbital calculations on finite clusters. J Chem Phys 1990. [DOI: 10.1063/1.458132] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pipek J, Mezey PG. A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J Chem Phys 1989. [DOI: 10.1063/1.456588] [Citation(s) in RCA: 1358] [Impact Index Per Article: 38.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Taylor CA, Zerner MC, Ramsey B. Ab initio electronic structure calculations of the C2H5B potential energy surface: The stability of borirane. J Organomet Chem 1986. [DOI: 10.1016/s0022-328x(00)99339-2] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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