1
|
Doran AE, Qiu DL, Hirata S. Monte Carlo MP2-F12 for Noncovalent Interactions: The C 60 Dimer. J Phys Chem A 2021; 125:7344-7351. [PMID: 34433271 DOI: 10.1021/acs.jpca.1c05021] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green's functions in real space and imaginary time. These integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol-1 for the C60 dimer at the center distance of 9.748 Å.
Collapse
Affiliation(s)
- Alexander E Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - David L Qiu
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| |
Collapse
|
2
|
Modrzejewski M, Yourdkhani S, Śmiga S, Klimeš J. Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage. J Chem Theory Comput 2021; 17:804-817. [PMID: 33445879 DOI: 10.1021/acs.jctc.0c00966] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH4···(H2O)20, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.
Collapse
Affiliation(s)
- Marcin Modrzejewski
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Pasteura 1, Poland.,Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Sirous Yourdkhani
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5, 87-100 Toruń, Poland
| | - Jiří Klimeš
- Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, CZ-12116 Prague 2, Czech Republic
| |
Collapse
|
3
|
Nguyen ALP, Mason TG, Freeman BD, Izgorodina EI. Prediction of lattice energy of benzene crystals: A robust theoretical approach. J Comput Chem 2021; 42:248-260. [PMID: 33231872 DOI: 10.1002/jcc.26452] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Revised: 10/29/2020] [Accepted: 10/30/2020] [Indexed: 01/09/2023]
Abstract
We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spin-ratio scaled second-order Møller-Plesset perturbation theory to predict the lattice energy of benzene crystals within 2 kJ⋅mol-1 . Inspired by the Harrison method to estimate the Madelung constant, the proposed approach calculates the lattice energy as a sum of two- and three-body interaction energies between a reference molecule and the surrounding molecules arranged in a sphere. The lattice energy converges rapidly at a radius of 13 Å. Adding the corrections to account for a higher correlated level of theory and basis set superposition for the Hartree Fock (HF) level produced a lattice energy of -57.5 kJ⋅mol-1 for the benzene crystal structure at 138 K. This estimate is within 1.6 kJ⋅mol-1 off the best theoretical prediction of -55.9 kJ⋅mol-1 . We applied this approach to calculate lattice energies of the crystal structures of phase I and phase II-polymorphs of benzene-observed at a higher temperature of 295 K. The stability of these polymorphs was correctly predicted, with phase II being energetically preferred by 3.7 kJ⋅mol-1 over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.
Collapse
Affiliation(s)
- Anh L P Nguyen
- School of Chemistry, Monash University, Clayton, Victoria, Australia
| | - Thomas G Mason
- School of Chemistry, Monash University, Clayton, Victoria, Australia
| | - Benny D Freeman
- Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas, USA
| | | |
Collapse
|
4
|
Košata J, Merkl P, Teeratchanan P, Hermann A. Stability of Hydrogen Hydrates from Second-Order Møller-Plesset Perturbation Theory. J Phys Chem Lett 2018; 9:5624-5629. [PMID: 30179509 DOI: 10.1021/acs.jpclett.8b02274] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The formation of gas hydrates and clathrates critically depends on the interaction between the host water network and the guest gas species. Density functional calculations can struggle to quantitatively capture these dispersion-type interactions. Here, we report wave function-based calculations on hydrogen hydrates that combine periodic Hartree-Fock with a localized treatment of electronic correlation. We show that local second-order Møller-Plesset perturbation theory (LMP2) reproduces the stability of the different filled-ice-like hydrates in excellent agreement with experimental data. In contrast to various dispersion-corrected density functional theory implementations, LMP2 correctly identifies the pressures needed to stabilize the C0, C1, and C2 hydrates and does not find a spurious region of stability for an ice-Ih-based dihydrate. Our results suggest that LMP2 or similar approaches can provide quantitative insights into the mechanisms of formation and eventual decomposition of molecular host-guest compounds.
Collapse
Affiliation(s)
- Jan Košata
- Centre for Science at Extreme Conditions and SUPA, School of Physics and Astronomy , The University of Edinburgh , Edinburgh EH9 3FD , United Kingdom
| | - Padryk Merkl
- Centre for Science at Extreme Conditions and SUPA, School of Physics and Astronomy , The University of Edinburgh , Edinburgh EH9 3FD , United Kingdom
| | - Pattanasak Teeratchanan
- Centre for Science at Extreme Conditions and SUPA, School of Physics and Astronomy , The University of Edinburgh , Edinburgh EH9 3FD , United Kingdom
| | - Andreas Hermann
- Centre for Science at Extreme Conditions and SUPA, School of Physics and Astronomy , The University of Edinburgh , Edinburgh EH9 3FD , United Kingdom
| |
Collapse
|
5
|
Al-Hamdani YS, Rossi M, Alfè D, Tsatsoulis T, Ramberger B, Brandenburg JG, Zen A, Kresse G, Grüneis A, Tkatchenko A, Michaelides A. Properties of the water to boron nitride interaction: From zero to two dimensions with benchmark accuracy. J Chem Phys 2017; 147:044710. [DOI: 10.1063/1.4985878] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yasmine S. Al-Hamdani
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Mariana Rossi
- Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - Dario Alfè
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Theodoros Tsatsoulis
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - Benjamin Ramberger
- University of Vienna, Faculty of Physics and Center for Computational Materials Sciences, Sensengasse 8/12, 1090 Wien, Austria
| | - Jan Gerit Brandenburg
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AH, United Kingdom
| | - Andrea Zen
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Georg Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Sciences, Sensengasse 8/12, 1090 Wien, Austria
| | - Andreas Grüneis
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Angelos Michaelides
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| |
Collapse
|
6
|
Tsatsoulis T, Hummel F, Usvyat D, Schütz M, Booth GH, Binnie SS, Gillan MJ, Alfè D, Michaelides A, Grüneis A. A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface. J Chem Phys 2017; 146:204108. [PMID: 28571392 PMCID: PMC5446292 DOI: 10.1063/1.4984048] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Accepted: 05/11/2017] [Indexed: 12/03/2022] Open
Abstract
We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals.
Collapse
Affiliation(s)
- Theodoros Tsatsoulis
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - Felix Hummel
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - Denis Usvyat
- Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-St. 2, D-12489 Berlin, Germany
| | - Martin Schütz
- Institut für Chemie, Humboldt-Universität zu Berlin, Brook-Taylor-St. 2, D-12489 Berlin, Germany
| | - George H Booth
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Simon S Binnie
- London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH, United Kingdom
| | - Michael J Gillan
- London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH, United Kingdom
| | - Dario Alfè
- London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH, United Kingdom
| | - Angelos Michaelides
- London Centre for Nanotechnology, University College London, Gordon St., London WC1H 0AH, United Kingdom
| | - Andreas Grüneis
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| |
Collapse
|
7
|
Yang X, Rees RJ, Conway W, Puxty G, Yang Q, Winkler DA. Computational Modeling and Simulation of CO2 Capture by Aqueous Amines. Chem Rev 2017; 117:9524-9593. [PMID: 28517929 DOI: 10.1021/acs.chemrev.6b00662] [Citation(s) in RCA: 67] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Xin Yang
- CSIRO Manufacturing, Bayview Avenue, Clayton 3169, Australia
- College
of Chemistry, Key Lab of Green Chemistry and Technology in Ministry
of Education, Sichuan University, Chengdu 610064, People’s Republic of China
| | - Robert J. Rees
- Data61
- CSIRO, Door 34 Goods
Shed, Village Street, Docklands VIC 3008, Australia
| | | | | | - Qi Yang
- CSIRO Manufacturing, Bayview Avenue, Clayton 3169, Australia
| | - David A. Winkler
- CSIRO Manufacturing, Bayview Avenue, Clayton 3169, Australia
- Monash Institute of Pharmaceutical Sciences, 392 Royal Parade, Parkville 3052, Australia
- Latrobe Institute for Molecular Science, Bundoora 3046, Australia
- School
of
Chemical and Physical Science, Flinders University, Bedford Park 5042, Australia
| |
Collapse
|
8
|
Zen A, Roch LM, Cox SJ, Hu XL, Sorella S, Alfè D, Michaelides A. Toward Accurate Adsorption Energetics on Clay Surfaces. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2016; 120:26402-26413. [PMID: 27917256 PMCID: PMC5126707 DOI: 10.1021/acs.jpcc.6b09559] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2016] [Revised: 10/31/2016] [Indexed: 05/31/2023]
Abstract
Clay minerals are ubiquitous in nature, and the manner in which they interact with their surroundings has important industrial and environmental implications. Consequently, a molecular-level understanding of the adsorption of molecules on clay surfaces is crucial. In this regard computer simulations play an important role, yet the accuracy of widely used empirical force fields (FF) and density functional theory (DFT) exchange-correlation functionals is often unclear in adsorption systems dominated by weak interactions. Herein we present results from quantum Monte Carlo (QMC) for water and methanol adsorption on the prototypical clay kaolinite. To the best of our knowledge, this is the first time QMC has been used to investigate adsorption at a complex, natural surface such as a clay. As well as being valuable in their own right, the QMC benchmarks obtained provide reference data against which the performance of cheaper DFT methods can be tested. Indeed using various DFT exchange-correlation functionals yields a very broad range of adsorption energies, and it is unclear a priori which evaluation is better. QMC reveals that in the systems considered here it is essential to account for van der Waals (vdW) dispersion forces since this alters both the absolute and relative adsorption energies of water and methanol. We show, via FF simulations, that incorrect relative energies can lead to significant changes in the interfacial densities of water and methanol solutions at the kaolinite interface. Despite the clear improvements offered by the vdW-corrected and the vdW-inclusive functionals, absolute adsorption energies are often overestimated, suggesting that the treatment of vdW forces in DFT is not yet a solved problem.
Collapse
Affiliation(s)
- Andrea Zen
- Thomas
Young Centre and London Centre for Nanotechnology, 17−19 Gordon Street, London WC1H 0AH, United
Kingdom
- Department
of Physics and Astronomy, University College
London, Gower Street, London WC1E 6BT, United Kingdom
| | - Loïc M. Roch
- Thomas
Young Centre and London Centre for Nanotechnology, 17−19 Gordon Street, London WC1H 0AH, United
Kingdom
- Department
of Physics and Astronomy, University College
London, Gower Street, London WC1E 6BT, United Kingdom
| | - Stephen J. Cox
- Thomas
Young Centre and London Centre for Nanotechnology, 17−19 Gordon Street, London WC1H 0AH, United
Kingdom
- Department
of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
| | - Xiao Liang Hu
- Thomas
Young Centre and London Centre for Nanotechnology, 17−19 Gordon Street, London WC1H 0AH, United
Kingdom
- Department
of Physics and Astronomy, University College
London, Gower Street, London WC1E 6BT, United Kingdom
| | - Sandro Sorella
- SISSA−International
School for Advanced Studies, Via Bonomea 26, 34136 Trieste, Italy
- INFM
Democritos National Simulation Center, 34151 Trieste, Italy
| | - Dario Alfè
- Thomas
Young Centre and London Centre for Nanotechnology, 17−19 Gordon Street, London WC1H 0AH, United
Kingdom
- Department
of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United
Kingdom
| | - Angelos Michaelides
- Thomas
Young Centre and London Centre for Nanotechnology, 17−19 Gordon Street, London WC1H 0AH, United
Kingdom
- Department
of Physics and Astronomy, University College
London, Gower Street, London WC1E 6BT, United Kingdom
| |
Collapse
|
9
|
Zeng Q, Li J, Huang H, Wang X, Yang M. Polarization response of clathrate hydrates capsulated with guest molecules. J Chem Phys 2016; 144:204308. [PMID: 27250307 DOI: 10.1063/1.4952417] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Clathrate hydrates are characterized by their water cages encapsulating various guest atoms or molecules. The polarization effect of these guest-cage complexes was studied with combined density functional theory and finite-field calculations. An addition rule was noted for these systems whose total polarizability is approximately equal to the polarizability sum of the guest and the cage. However, their distributional polarizability computed with Hirshfeld partitioning scheme indicates that the guest-cage interaction has considerable influence on their polarization response. The polarization of encapsulated guest is reduced while the polarization of water cage is enhanced. The counteraction of these two opposite effects leads to the almost unchanged total polarizability. Further analysis reveals that the reduced polarizability of encapsulated guest results from the shielding effect of water cage against the external field and the enhanced polarizability of water cage from the enhanced bonding of hydrogen bonds among water molecules. Although the charge transfer through the hydrogen bonds is rather small in the water cage, the polarization response of clathrate hydrates is sensitive to the changes of hydrogen bonding strength. The guest encapsulation strengthens the hydrogen bonding network and leads to enhanced polarizability.
Collapse
Affiliation(s)
- Qun Zeng
- Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), Mianyang 621900, China
| | - Jinshan Li
- Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), Mianyang 621900, China
| | - Hui Huang
- Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), Mianyang 621900, China
| | - Xinqin Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610065, People's Republic of China
| | - Mingli Yang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610065, People's Republic of China
| |
Collapse
|
10
|
Affiliation(s)
- Matúš Dubecký
- Regional
Centre of Advanced Technologies and Materials, Department of Physical
Chemistry, Faculty of Science, Palacký University Olomouc, tř.
17 listopadu 12, 771 46 Olomouc, Czech Republic
| | - Lubos Mitas
- Department
of Physics and CHiPS, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Petr Jurečka
- Regional
Centre of Advanced Technologies and Materials, Department of Physical
Chemistry, Faculty of Science, Palacký University Olomouc, tř.
17 listopadu 12, 771 46 Olomouc, Czech Republic
| |
Collapse
|
11
|
Abstract
Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.
Collapse
Affiliation(s)
- Gregory J O Beran
- Department of Chemistry, University of California , Riverside, California 92521, United States
| |
Collapse
|
12
|
Salazar-Cano JR, Guevara-García A, Vargas R, Restrepo A, Garza J. Hydrogen bonds in methane–water clusters. Phys Chem Chem Phys 2016; 18:23508-15. [DOI: 10.1039/c6cp04086a] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Water–methane clusters are stable at low temperatures as those found in Mars. Water cages enveloping methane are stable, although they present small probability to occur.
Collapse
Affiliation(s)
- Juan-Ramón Salazar-Cano
- Departamento de Química
- División de Ciencias Básicas e Ingeniería
- Universidad Autónoma Metropolitana-Iztapalapa
- San Rafael Atlixco 186
- México City
| | - Alfredo Guevara-García
- Departamento de Química
- División de Ciencias Básicas e Ingeniería
- Universidad Autónoma Metropolitana-Iztapalapa
- San Rafael Atlixco 186
- México City
| | - Rubicelia Vargas
- Departamento de Química
- División de Ciencias Básicas e Ingeniería
- Universidad Autónoma Metropolitana-Iztapalapa
- San Rafael Atlixco 186
- México City
| | | | - Jorge Garza
- Departamento de Química
- División de Ciencias Básicas e Ingeniería
- Universidad Autónoma Metropolitana-Iztapalapa
- San Rafael Atlixco 186
- México City
| |
Collapse
|