1
|
Mhashal AR, Major DT. Temperature-Dependent Kinetic Isotope Effects in R67 Dihydrofolate Reductase from Path-Integral Simulations. J Phys Chem B 2021; 125:1369-1377. [PMID: 33522797 PMCID: PMC7883348 DOI: 10.1021/acs.jpcb.0c10318] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2020] [Revised: 01/05/2021] [Indexed: 11/28/2022]
Abstract
Calculation of temperature-dependent kinetic isotope effects (KIE) in enzymes presents a significant theoretical challenge. Additionally, it is not trivial to identify enzymes with available experimental accurate intrinsic KIEs in a range of temperatures. In the current work, we present a theoretical study of KIEs in the primitive R67 dihydrofolate reductase (DHFR) enzyme and compare with experimental work. The advantage of R67 DHFR is its significantly lower kinetic complexity compared to more evolved DHFR isoforms. We employ mass-perturbation-based path-integral simulations in conjunction with umbrella sampling and a hybrid quantum mechanics-molecular mechanics Hamiltonian. We obtain temperature-dependent KIEs in good agreement with experiments and ascribe the temperature-dependent KIEs primarily to zero-point energy effects. The active site in the primitive enzyme is found to be poorly preorganized, which allows excessive water access to the active site and results in loosely bound reacting ligands.
Collapse
Affiliation(s)
- Anil R. Mhashal
- Department of Chemistry and Institute
for Nanotechnology & Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Dan Thomas Major
- Department of Chemistry and Institute
for Nanotechnology & Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| |
Collapse
|
2
|
Wu Y, Car R. Quantum momentum distribution and quantum entanglement in the deep tunneling regime. J Chem Phys 2020; 152:024106. [PMID: 31941303 DOI: 10.1063/1.5133053] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we consider the momentum operator of a quantum particle directed along the displacement of two of its neighbors. A modified open-path path integral molecular dynamics is presented to sample the distribution of this directional momentum distribution, where we derive and use a new estimator for this distribution. Variationally enhanced sampling is used to obtain this distribution for an example molecule, malonaldehyde, in the very low temperature regime where deep tunneling happens. We find no secondary feature in the directional momentum distribution and that its absence is due to quantum entanglement through a further study of the reduced density matrix.
Collapse
Affiliation(s)
- Yantao Wu
- The Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Roberto Car
- The Department of Chemistry and the Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
3
|
Mhashal AR, Pshetitsky Y, Cheatum CM, Kohen A, Major DT. Evolutionary Effects on Bound Substrate pKa in Dihydrofolate Reductase. J Am Chem Soc 2018; 140:16650-16660. [DOI: 10.1021/jacs.8b09089] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Anil R. Mhashal
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Yaron Pshetitsky
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | | | - Amnon Kohen
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - Dan Thomas Major
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel
| |
Collapse
|
4
|
Mhashal AR, Pshetitsky Y, Eitan R, Cheatum CM, Kohen A, Major DT. Effect of Asp122 Mutation on the Hydride Transfer in E. coli DHFR Demonstrates the Goldilocks of Enzyme Flexibility. J Phys Chem B 2018; 122:8006-8017. [PMID: 30040418 DOI: 10.1021/acs.jpcb.8b05556] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Dihydrofolate reductase (DHFR) catalyzes the reduction of dihydrofolate (DHF) to tetrahydrofolate (THF) in the presence of NADPH. The key hydride transfer step in the reaction is facilitated by a combination of enzyme active site preorganization and correlated protein motions in the Michaelis-Menten (E:NADPH:DHF) complex. The present theoretical study employs mutagenesis to examine the relation between structural and functional properties of the enzyme. We mutate Asp122 in Escherichia coli DHFR, which is a conserved amino acid in the DHFR family. The consequent effect of the mutation on enzyme catalysis is examined from an energetic, structural and short-time dynamic perspective. Our investigations suggest that the structural and short-time dynamic perturbations caused by Asp122X mutations (X = Asn, Ser, Ala) are along the reaction coordinate and lower the rate of hydride transfer. Importantly, analysis of the correlated and principle component motions in the enzyme suggest that the mutation alters the coupled motions that are present in the wild-type enzyme. In the case of D122N and D122S, the mutations inhibit coupled motion, whereas in the case of D122A, the mutation enhances coupled motion, although all mutations result in similar rate reduction. These results emphasize a Goldilocks principle of enzyme flexibility, that is, enzymes should neither be too rigid nor too flexible.
Collapse
Affiliation(s)
- Anil R Mhashal
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry , Bar-Ilan University , Ramat-Gan 52900 , Israel
| | - Yaron Pshetitsky
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry , Bar-Ilan University , Ramat-Gan 52900 , Israel
| | - Reuven Eitan
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry , Bar-Ilan University , Ramat-Gan 52900 , Israel
| | - Christopher M Cheatum
- Department of Chemistry , University of Iowa , Iowa City , Iowa 52242 , United States
| | - Amnon Kohen
- Department of Chemistry , University of Iowa , Iowa City , Iowa 52242 , United States
| | - Dan Thomas Major
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry , Bar-Ilan University , Ramat-Gan 52900 , Israel
| |
Collapse
|
5
|
Kreis K, Tuckerman ME, Donadio D, Kremer K, Potestio R. From Classical to Quantum and Back: A Hamiltonian Scheme for Adaptive Multiresolution Classical/Path-Integral Simulations. J Chem Theory Comput 2016; 12:3030-9. [DOI: 10.1021/acs.jctc.6b00242] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Karsten Kreis
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Graduate
School Materials Science in Mainz, Johannes Gutenberg University Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Mark E. Tuckerman
- Department
of Chemistry, New York University (NYU), New York, New York 10003, United States
- Courant
Institute of Mathematical Sciences, NYU, New York, New York 10012, United States
- NYU−East
China Normal University Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Davide Donadio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Department
of Chemistry, University of California at Davis, One Shields Avenue, Davis, California 95616, United States
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| |
Collapse
|
6
|
Sinitskiy AV, Voth GA. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals. J Chem Phys 2015; 143:094104. [DOI: 10.1063/1.4929790] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anton V. Sinitskiy
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637, USA
| | - Gregory A. Voth
- Department of Chemistry, James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637, USA
| |
Collapse
|
7
|
Vardi-Kilshtain A, Nitoker N, Major DT. Nuclear quantum effects and kinetic isotope effects in enzyme reactions. Arch Biochem Biophys 2015; 582:18-27. [DOI: 10.1016/j.abb.2015.03.001] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2015] [Revised: 03/02/2015] [Accepted: 03/03/2015] [Indexed: 11/28/2022]
|
8
|
Engel H, Eitan R, Azuri A, Major DT. Nuclear quantum effects in chemical reactions via higher-order path-integral calculations. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2015.01.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
9
|
Doron D, Stojković V, Gakhar L, Vardi-Kilshtain A, Kohen A, Major DT. Free energy simulations of active-site mutants of dihydrofolate reductase. J Phys Chem B 2014; 119:906-16. [PMID: 25382260 DOI: 10.1021/jp5059963] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
This study employs hybrid quantum mechanics-molecular mechanics (QM/MM) simulations to investigate the effect of mutations of the active-site residue I14 of E. coli dihydrofolate reductase (DHFR) on the hydride transfer. Recent kinetic measurements of the I14X mutants (X = V, A, and G) indicated slower hydride transfer rates and increasingly temperature-dependent kinetic isotope effects (KIEs) with systematic reduction of the I14 side chain. The QM/MM simulations show that when the original isoleucine residue is substituted in silico by valine, alanine, or glycine (I14V, I14A, and I14G DHFR, respectively), the free energy barrier height of the hydride transfer reaction increases relative to the wild-type enzyme. These trends are in line with the single-turnover rate measurements reported for these systems. In addition, extended dynamics simulations of the reactive Michaelis complex reveal enhanced flexibility in the mutants, and in particular for the I14G mutant, including considerable fluctuations of the donor-acceptor distance (DAD) and the active-site hydrogen bonding network compared with those detected in the native enzyme. These observations suggest that the perturbations induced by the mutations partly impair the active-site environment in the reactant state. On the other hand, the average DADs at the transition state of all DHFR variants are similar. Crystal structures of I14 mutants (V, A, and G) confirmed the trend of increased flexibility of the M20 and other loops.
Collapse
Affiliation(s)
- Dvir Doron
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University , Ramat-Gan 5290002, Israel
| | | | | | | | | | | |
Collapse
|
10
|
Doron D, Kohen A, Nam K, Major DT. How Accurate Are Transition States from Simulations of Enzymatic Reactions? J Chem Theory Comput 2014; 10:1863-1871. [PMID: 24860275 PMCID: PMC4025581 DOI: 10.1021/ct5000742] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 11/30/2022]
Abstract
The rate expression of traditional transition state theory (TST) assumes no recrossing of the transition state (TS) and thermal quasi-equilibrium between the ground state and the TS. Currently, it is not well understood to what extent these assumptions influence the nature of the activated complex obtained in traditional TST-based simulations of processes in the condensed phase in general and in enzymes in particular. Here we scrutinize these assumptions by characterizing the TSs for hydride transfer catalyzed by the enzyme Escherichia coli dihydrofolate reductase obtained using various simulation approaches. Specifically, we compare the TSs obtained with common TST-based methods and a dynamics-based method. Using a recently developed accurate hybrid quantum mechanics/molecular mechanics potential, we find that the TST-based and dynamics-based methods give considerably different TS ensembles. This discrepancy, which could be due equilibrium solvation effects and the nature of the reaction coordinate employed and its motion, raises major questions about how to interpret the TSs determined by common simulation methods. We conclude that further investigation is needed to characterize the impact of various TST assumptions on the TS phase-space ensemble and on the reaction kinetics.
Collapse
Affiliation(s)
- Dvir Doron
- Department
of Chemistry and the Lise Meitner-Minerva Center of Computational
Quantum Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Amnon Kohen
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - Kwangho Nam
- Department
of Chemistry and Computational Life Science Cluster (CLiC), Umeå University, 901 87 Umeå, Sweden
| | - Dan Thomas Major
- Department
of Chemistry and the Lise Meitner-Minerva Center of Computational
Quantum Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel
| |
Collapse
|
11
|
Roston D, Kohen A, Doron D, Major DT. Simulations of remote mutants of dihydrofolate reductase reveal the nature of a network of residues coupled to hydride transfer. J Comput Chem 2014; 35:1411-7. [PMID: 24798860 DOI: 10.1002/jcc.23629] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2014] [Revised: 03/11/2014] [Accepted: 04/06/2014] [Indexed: 11/07/2022]
Abstract
Recent experimental and theoretical studies have proposed that enzymes involve networks of coupled residues throughout the protein that participate in motions accompanying chemical barrier crossing. Here, we have examined portions of a proposed network in dihydrofolate reductase (DHFR) using quantum mechanics/molecular mechanics simulations. The simulations use a hybrid quantum mechanics-molecular mechanics approach with a recently developed semiempirical AM1-SRP Hamiltonian that provides accurate results for this reaction. The simulations reproduce experimentally determined catalytic rates for the wild type and distant mutants of E. coli DHFR, underscoring the accuracy of the simulation protocol. Additionally, the simulations provide detailed insight into how residues remote from the active site affect the catalyzed chemistry, through changes in the thermally averaged properties along the reaction coordinate. The mutations do not greatly affect the structure of the transition state near the bond activation, but we observe differences somewhat removed from the point of C-H cleavage that affect the rate. The mutations have global effects on the thermally averaged structure that propagate throughout the enzyme and the current simulations highlight several interactions that appear to be particularly important.
Collapse
Affiliation(s)
- Daniel Roston
- Department of Chemistry, University of Iowa, Iowa City, Iowa, 52242
| | | | | | | |
Collapse
|
12
|
Doron D, Weitman M, Vardi-Kilshtain A, Azuri A, Engel H, Major DT. Multiscale Quantum-Classical Simulations of Enzymes. Isr J Chem 2014. [DOI: 10.1002/ijch.201400026] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
|
13
|
Friedman R, Boye K, Flatmark K. Molecular modelling and simulations in cancer research. Biochim Biophys Acta Rev Cancer 2013; 1836:1-14. [PMID: 23416097 DOI: 10.1016/j.bbcan.2013.02.001] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2012] [Revised: 02/04/2013] [Accepted: 02/05/2013] [Indexed: 01/12/2023]
Abstract
The complexity of cancer and the vast amount of experimental data available have made computer-aided approaches necessary. Biomolecular modelling techniques are becoming increasingly easier to use, whereas hardware and software are becoming better and cheaper. Cross-talk between theoretical and experimental scientists dealing with cancer-research from a molecular approach, however, is still uncommon. This is in contrast to other fields, such as amyloid-related diseases, where molecular modelling studies are widely acknowledged. The aim of this review paper is therefore to expose some of the more common approaches in molecular modelling to cancer scientists in simple terms, illustrating success stories while also revealing the limitations of computational studies at the molecular level.
Collapse
Affiliation(s)
- Ran Friedman
- Computational Chemistry and Biochemistry Group, School of Natural Sciences, Linnæus University, 391 82 Kalmar, Sweden.
| | | | | |
Collapse
|
14
|
Fan Y, Cembran A, Ma S, Gao J. Connecting protein conformational dynamics with catalytic function as illustrated in dihydrofolate reductase. Biochemistry 2013; 52:2036-49. [PMID: 23297871 DOI: 10.1021/bi301559q] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Combined quantum mechanics/molecular mechanics molecular dynamics simulations reveal that the M20 loop conformational dynamics of dihydrofolate reductase (DHFR) is severely restricted at the transition state of the hydride transfer as a result of the M42W/G121V double mutation. Consequently, the double-mutant enzyme has a reduced entropy of activation, i.e., increased entropic barrier, and altered temperature dependence of kinetic isotope effects in comparison with those of wild-type DHFR. Interestingly, in both wild-type DHFR and the double mutant, the average donor-acceptor distances are essentially the same in the Michaelis complex state (~3.5 Å) and the transition state (2.7 Å). It was found that an additional hydrogen bond is formed to stabilize the M20 loop in the closed conformation in the M42W/G121V double mutant. The computational results reflect a similar aim designed to knock out precisely the dynamic flexibility of the M20 loop in a different double mutant, N23PP/S148A.
Collapse
Affiliation(s)
- Yao Fan
- Department of Chemistry, Digital Technology Center, and Supercomputing Institute, University of Minnesota , 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455, United States
| | | | | | | |
Collapse
|
15
|
Abstract
The relationship between protein dynamics and function is a subject of considerable contemporary interest. Although protein motions are frequently observed during ligand binding and release steps, the contribution of protein motions to the catalysis of bond making/breaking processes is more difficult to probe and verify. Here, we show how the quantum mechanical hydrogen tunneling associated with enzymatic C-H bond cleavage provides a unique window into the necessity of protein dynamics for achieving optimal catalysis. Experimental findings support a hierarchy of thermodynamically equilibrated motions that control the H-donor and -acceptor distance and active-site electrostatics, creating an ensemble of conformations suitable for H-tunneling. A possible extension of this view to methyl transfer and other catalyzed reactions is also presented. The impact of understanding these dynamics on the conceptual framework for enzyme activity, inhibitor/drug design, and biomimetic catalyst design is likely to be substantial.
Collapse
Affiliation(s)
- Judith P. Klinman
- Department of Chemistry, Department of Molecular and Cell Biology, and the California Institute for Quantitative Sciences, University of California, Berkeley, California 94720;
| | - Amnon Kohen
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294;
| |
Collapse
|
16
|
Vardi-Kilshtain A, Major DT, Kohen A, Engel H, Doron D. Hybrid Quantum and Classical Simulations of the Formate Dehydrogenase Catalyzed Hydride Transfer Reaction on an Accurate Semiempirical Potential Energy Surface. J Chem Theory Comput 2012; 8:4786-96. [DOI: 10.1021/ct300628e] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alexandra Vardi-Kilshtain
- Department
of Chemistry and the Lise Meitner-Minerva Center of Computational
Quantum Chemistry, Bar-Ilan University,
Ramat-Gan 52900, Israel
| | - Dan Thomas Major
- Department
of Chemistry and the Lise Meitner-Minerva Center of Computational
Quantum Chemistry, Bar-Ilan University,
Ramat-Gan 52900, Israel
| | - Amnon Kohen
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - Hamutal Engel
- Department
of Chemistry and the Lise Meitner-Minerva Center of Computational
Quantum Chemistry, Bar-Ilan University,
Ramat-Gan 52900, Israel
| | - Dvir Doron
- Department
of Chemistry and the Lise Meitner-Minerva Center of Computational
Quantum Chemistry, Bar-Ilan University,
Ramat-Gan 52900, Israel
| |
Collapse
|
17
|
Doron D, Kohen A, Major DT. Collective Reaction Coordinate for Hybrid Quantum and Molecular Mechanics Simulations: A Case Study of the Hydride Transfer in Dihydrofolate Reductase. J Chem Theory Comput 2012; 8:2484-96. [PMID: 26588977 DOI: 10.1021/ct300235k] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The optimal description of the reaction coordinate in chemical systems is of great importance in simulating condensed phase reactions. In the current work, we present a collective reaction coordinate which is composed of several geometric coordinates which represent structural progress during the course of a hydride transfer reaction: the antisymmetric reactive stretch coordinate, the donor-acceptor distance (DAD) coordinate, and an orbital rehybridization coordinate. In this approach, the former coordinate serves as a distinguished reaction coordinate, while the latter two serve as environmental, Marcus-type inner-sphere reorganization coordinates. The classical free energy surface is obtained from multidimensional quantum mechanics-molecular mechanics (QM/MM) potential of mean force (PMF) simulations in conjunction with a general and efficient multidimensional weighted histogram method implementation. The minimum free energy path, or the collective reaction coordinate, connecting the dividing hypersurface to reactants and products, is obtained using an iterative scheme. In this approach, the string method is used to find the minimum free energy path. This path guides the multidimensional sampling, while the path is adaptively refined until convergence is achieved. As a model system, we choose the hydride transfer reaction in Escherichia coli dihydrofolate reductase (ecDHFR) using a recently developed accurate semiempirical potential energy surface. To estimate the advantages of the collective reaction coordinate, we perform activated dynamics simulations to obtain the reaction transmission coefficient. The results show that the combination of a distinguished reaction coordinate and an inner-sphere reorganization coordinate considerably reduces the dividing surface recrossing.
Collapse
Affiliation(s)
- Dvir Doron
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Amnon Kohen
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - Dan Thomas Major
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| |
Collapse
|