1
|
Isamura BK, Lobb KA. A multiscale ONIOM study of the buckminsterfullerene (C 60) Diels-Alder reaction: from model design to reaction path analysis. J Mol Model 2022; 28:327. [PMID: 36138156 DOI: 10.1007/s00894-022-05319-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 09/06/2022] [Indexed: 11/29/2022]
Abstract
The hybrid ONIOM (Our own N-layered Integrated molecular Orbital and molecular Mechanics) formalism is employed to investigate the Diels-Alder reaction of the buckminsterfullerene C60. Our computations suggest that the ONIOM2(M06-2X/6-31G(d): SVWN/STO-3G) model, enclosing both the diene and the pyracyclene fragment of C60 in the higher-layer, provides a reasonable trade-off between accuracy and computational cost as it comes to predicting reaction energetics. Moreover, the frontier molecular orbital (FMO) theory and activation strain model (ASM) are jointly relied on to rationalize the effect of -OH and -CN substituents on the activation barrier of this reaction. Finally, reaction paths are scrutinized to get insight into the various forces underpinning the process of cycloadduct formation.
Collapse
Affiliation(s)
| | - Kevin Alan Lobb
- Department of Chemistry, Rhodes University, Eastern Cape, Makhanda, 6140, South Africa.,Research Unit in Bioinformatics (RUBi), Rhodes University, Eastern Cape, Makhanda, 6140, South Africa
| |
Collapse
|
2
|
Bryenton KR, Adeleke AA, Dale SG, Johnson ER. Delocalization error: The greatest outstanding challenge in density‐functional theory. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1631] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Kyle R. Bryenton
- Department of Physics and Atmospheric Science Dalhousie University Halifax Nova Scotia Canada
| | | | - Stephen G. Dale
- Queensland Micro‐ and Nanotechnology Centre Griffith University Nathan Queensland Australia
| | - Erin R. Johnson
- Department of Physics and Atmospheric Science Dalhousie University Halifax Nova Scotia Canada
- Department of Chemistry Dalhousie University Halifax Nova Scotia Canada
| |
Collapse
|
3
|
The structure of 1,3-butadiene clusters. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02742-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
4
|
Nam S, Cho E, Sim E, Burke K. Explaining and Fixing DFT Failures for Torsional Barriers. J Phys Chem Lett 2021; 12:2796-2804. [PMID: 33710903 DOI: 10.1021/acs.jpclett.1c00426] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Most torsional barriers are predicted with high accuracies (about 1 kJ/mol) by standard semilocal functionals, but a small subset was found to have much larger errors. We created a database of almost 300 carbon-carbon torsional barriers, including 12 poorly behaved barriers, that stem from the Y═C-X group, where Y is O or S and X is a halide. Functionals with enhanced exchange mixing (about 50%) worked well for all barriers. We found that poor actors have delocalization errors caused by hyperconjugation. These problematic calculations are density-sensitive (i.e., DFT predictions change noticeably with the density), and using HF densities (HF-DFT) fixes these issues. For example, conventional B3LYP performs as accurately as exchange-enhanced functionals if the HF density is used. For long-chain conjugated molecules, HF-DFT can be much better than exchange-enhanced functionals. We suggest that HF-PBE0 has the best overall performance.
Collapse
Affiliation(s)
- Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Eunbyol Cho
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, South Korea
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
| |
Collapse
|
5
|
Tahchieva DN, Bakowies D, Ramakrishnan R, von Lilienfeld OA. Torsional Potentials of Glyoxal, Oxalyl Halides, and Their Thiocarbonyl Derivatives: Challenges for Popular Density Functional Approximations. J Chem Theory Comput 2018; 14:4806-4817. [PMID: 30011363 DOI: 10.1021/acs.jctc.8b00174] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The reliability of popular density functionals was studied for the description of torsional profiles of 36 molecules: glyoxal, oxalyl halides, and their thiocarbonyl derivatives. HF and 18 functionals of varying complexity, from local density to range-separated hybrid approximations and double-hybrid, have been considered and benchmarked against CCSD(T)-level rotational profiles. For molecules containing heavy halogens, most functionals fail to reproduce barrier heights accurately and a number of functionals introduce spurious minima. Dispersion corrections show no improvement. Calibrated torsion-corrected atom-centered potentials rectify the shortcomings of PBE and also improve on σ-hole based intermolecular binding in dimers and crystals.
Collapse
Affiliation(s)
- Diana N Tahchieva
- 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
| | - Dirk Bakowies
- 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
| | - Raghunathan Ramakrishnan
- 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
| |
Collapse
|
6
|
|
7
|
Amat A, Angelis FD, Sgamellotti A, Fantacci S. Theoretical investigation of the structural and electronic properties of luteolin, apigenin and their deprotonated species. ACTA ACUST UNITED AC 2008. [DOI: 10.1016/j.theochem.2008.07.036] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
|
8
|
Santiso EE, Buongiorno Nardelli M, Gubbins KE. A remarkable shape-catalytic effect of confinement on the rotational isomerization of small hydrocarbons. J Chem Phys 2008; 128:034704. [DOI: 10.1063/1.2819238] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
|
9
|
Sancho-García JC, Pérez-Jiménez AJ. Performance of multi-configurational calculations for a 1,4-bis(phenylethynyl)benzene derivative conjugated molecule. Phys Chem Chem Phys 2008; 10:2308-15. [DOI: 10.1039/b719080h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
|
10
|
Wong BM, Raman S. Thermodynamic calculations for molecules with asymmetric internal rotors—application to 1,3-butadiene. J Comput Chem 2007; 28:759-66. [PMID: 17226834 DOI: 10.1002/jcc.20536] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We present quantum mechanical partition functions, free energies, entropies, and heat capacities of 1,3-butadiene derived from ab initio calculations. Our technique makes use of a reaction path-like Hamiltonian to couple all 23 vibrational modes to the large-amplitude torsion, which involves heavy asymmetric functional groups. Ab initio calculations were performed at the B3LYP, MP2, and CCSD(T) levels of theory and compared with experimental values as a reference case. By using the ab initio potentials and projected frequencies, simple perturbative expressions are presented for computing the couplings of all the vibrational modes to the large-amplitude torsion. The expressions are particularly suited for programming in the new STAR-P software platform which automatically parallelizes our codes with distributed memory via a familiar MATLAB interface. Using the efficient parallelization scheme of STAR-P, we obtain thermodynamic properties of 1,3-butadiene for temperatures ranging from 50 to 500 K. The free energies, entropies, and heat capacities obtained from our perturbative formulas are compared with conventional approximations and experimental values found in thermodynamic tables.
Collapse
Affiliation(s)
- Bryan M Wong
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
| | | |
Collapse
|
11
|
Sancho-García J. Assessment of density-functional models for organic molecular semiconductors: The role of Hartree–Fock exchange in charge-transfer processes. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2006.11.002] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
12
|
Deleuze MS, Knippenberg S. Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories. J Chem Phys 2006; 125:104309. [PMID: 16999528 DOI: 10.1063/1.2209690] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within approximately 0.2 eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense pi(-2) pi(*+1) satellite at approximately 13.1 eV in the ionization spectrum of the s-trans conformer.
Collapse
Affiliation(s)
- M S Deleuze
- Theoretical Physical Chemistry, Department SBG, Hasselt University, Agoralaan, Gebouw D, B-3590 Diepenbeek, Belgium.
| | | |
Collapse
|
13
|
Celebre G, Concistré M, De Luca G, Longeri M, Pileio G. Intrinsic Information Content of NMR Dipolar Couplings: A Conformational Investigation of 1,3-Butadiene in a Nematic Phase. Chemphyschem 2006; 7:1930-43. [PMID: 16871617 DOI: 10.1002/cphc.200600220] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
The conformational equilibrium of 1,3-butadiene in a condensed fluid phase is investigated by liquid-crystal NMR spectroscopy. The full set of D(HH) and D(CH) dipolar couplings is determined from the analysis of the (1)H spectra of the three 1,3-butadiene most-abundant isotopomers (i.e. the all (12)C and the two single-labeled (13)C isotopomers) for a total of 21 independent dipolar couplings. A very good starting set of spectral parameters for the analysis of the (1)H spectrum is determined in a semiautomated way by the analysis of the (N-1) (specifically, N=6, the number of 1/2 spin nuclei in the spin system) quantum refocused (5QR), and not (5Q), spectra. As an alternative approach, a Monte Carlo (MC) numerical simulation, capable of predicting the solute ordering, is tested to simulate the 5QR spectrum. The set of D(ij) couplings is very good, proving that the MC method can represent a novel, valid alternative to the existing spectral simplification procedures. The experimentally determined dipolar-coupling data set is fully compatible with the 1,3-butadiene conformational distribution reported in the literature for isolated molecules, indicating the presence of about 99 % of s-trans conformer. With regards to the remaining 1 %, in spite of the direct and very strong dependence of the observables on the molecular structure, it was not possible to discriminate between the planar s-cis and s-gauche forms, both of which produce a very good fit of the dipolar couplings. Vibrational corrections, up to the anharmonic term, were applied; the calculated geometrical parameters are in good- although not exact-agreement with those reported in the literature from experimental and theoretical investigations. This result can be considered as supporting the methodology used for obtaining the structure and conformational distribution of a flexible molecule in a liquid phase.
Collapse
Affiliation(s)
- Giorgio Celebre
- Universitá della Calabria, Dipartimento di Chimica Via P. Bucci, 87030 Arcavacata di Rende (Cs), Italy
| | | | | | | | | |
Collapse
|
14
|
Karpfen * A, Parasuk V. Accurate torsional potentials in conjugated systems: ab initio and density functional calculations on 1,3-butadiene and monohalogenated butadienes. Mol Phys 2006. [DOI: 10.1080/00268970410001726863] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Alfred Karpfen *
- a Institute for Theoretical Chemistry and Structural Biology , University of Vienna , Währinger Strae 17 , A-1090 Vienna , Austria
| | - Vudhichai Parasuk
- b Department of Chemistry , Faculty of Science, Chulalongkorn University , Patumwan , Bangkok , 10330 Thailand
| |
Collapse
|
15
|
Sancho-García JC. Assessing a new nonempirical density functional: Difficulties in treating π-conjugation effects. J Chem Phys 2006; 124:124112. [PMID: 16599667 DOI: 10.1063/1.2180774] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The reliability of the Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation functional for the description of conjugation effects in model pi-conjugated systems has been thoroughly assessed through the calculation of torsion energy profiles. The functional reproduces qualitatively the shape of torsional potentials but, interestingly, the mixing of TPSS and exact exchange governs the quantitative results: thus, well-defined hybrid extensions of the functional are consistently employed to improve the results. The hybrid approaches led to more accurate descriptions of conjugation effects but, however, the finest performance along the whole range of dihedral angles was obtained by a customized mixing of pure or hybrid TPSS functionals and wave function methods in a multicoefficient fashion. Despite the successful construction of this nonempirical functional, higher rungs of the ladder of methods in which TPSS is based are hoped to reduce the errors with respect to reference data for pi-conjugated systems.
Collapse
Affiliation(s)
- J C Sancho-García
- Departamento de Química Física, Universidad de Alicante, E-03080 Alicante, Spain.
| |
Collapse
|
16
|
Fabiano E, Della Sala F. Torsional potential of π-conjugated molecules using the localized Hartree–Fock Kohn–Sham exchange potential. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2005.11.008] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
17
|
|
18
|
Sancho-García JC, Cornil J. Anchoring the Torsional Potential of Biphenyl at the ab Initio Level: The Role of Basis Set versus Correlation Effects. J Chem Theory Comput 2005; 1:581-9. [DOI: 10.1021/ct0500242] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- J. C. Sancho-García
- Laboratory for Chemistry of Novel Materials, Center for Research in Molecular Electronics and Photonics, University of Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium, and Departamento de Química-Física, Universidad de Alicante, E-03080 Alicante, Spain
| | - J. Cornil
- Laboratory for Chemistry of Novel Materials, Center for Research in Molecular Electronics and Photonics, University of Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium, and Departamento de Química-Física, Universidad de Alicante, E-03080 Alicante, Spain
| |
Collapse
|
19
|
Sancho-García JC. Assessment of Recently Developed Multicoefficient Strategies for the Treatment of π-Conjugated Molecules. J Phys Chem A 2005; 109:3470-5. [PMID: 16833684 DOI: 10.1021/jp0445371] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Newly developed hybrid functionals (MPW1k and BB1k) have been systematically applied for the description of conjugation effects in organic molecules. These functionals are also used as part of the recently developed general-purpose multicoefficient methods MC3MPW and MC3BB. The performance of the various approaches is compared not only for relative energies but also through the calculation of torsion energy profiles for critical comparison with available reference data; thus, a numerical criterion depending on local behavior could be correspondingly defined. The results show that MC3-based methods are very accurate when faced to other approaches having comparable computational cost; thus, paving the way toward new applications and achievements in the field of conjugated materials.
Collapse
Affiliation(s)
- J C Sancho-García
- Departamento de Química-Física, Universidad de Alicante, E-03080 Alicante, Spain.
| |
Collapse
|
20
|
Jacquemin D, Andre JM, Perpete EA. Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: An assessment of electron correlation contributions. J Chem Phys 2004; 121:4389-96. [PMID: 15332990 DOI: 10.1063/1.1775181] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order Møller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.
Collapse
Affiliation(s)
- Denis Jacquemin
- Laboratoire de Chimie Theorique Appliquee, Facultes Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium
| | | | | |
Collapse
|
21
|
Sancho-García JC, Cornil J. Assessment of recently developed exchange-correlation functionals for the description of torsion potentials in π-conjugated molecules. J Chem Phys 2004; 121:3096-101. [PMID: 15291619 DOI: 10.1063/1.1774976] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Newly developed exchange-correlation functionals in density functional theory (DFT) have been applied to describe conjugation effects in organic molecules. The performance of the various approaches is assessed through the calculation of torsion energy profiles and their critical comparison with available experimental data. Our results indicate that the OPTX-B95 exchange-correlation functional as well as its corresponding hybrid versions perform better than the well-established BLYP or B3LYP schemes when dealing with pi-conjugated molecules. In contrast, the recently introduced VSXC functional is not as reliable as other DFT methods for the systems examined here.
Collapse
Affiliation(s)
- Juan Carlos Sancho-García
- Laboratory for Chemistry of Novel Materials, Center for Research in Molecular Electronics and Photonics, University of Mons-Hainaut, Place du Parc 20, B-7000, Belgium.
| | | |
Collapse
|
22
|
Sancho-Garcı́a JC, Pérez-Jiménez AJ. Nitrobenzene rotational energy barrier: A survey of several ab initio methods. J Chem Phys 2003. [DOI: 10.1063/1.1597632] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
23
|
Assessment of the reliability of the Perdew–Burke–Ernzerhof functionals in the determination of torsional potentials in π-conjugated molecules. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(03)01086-8] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
24
|
Lynch BJ, Zhao Y, Truhlar DG. Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory. J Phys Chem A 2003. [DOI: 10.1021/jp021590l] [Citation(s) in RCA: 628] [Impact Index Per Article: 29.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Benjamin J. Lynch
- Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Yan Zhao
- Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| | - Donald G. Truhlar
- Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431
| |
Collapse
|