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Sitha S. Ortho-para interconversion of nuclear states of H 2O through replica transition state: prospect of quantum entanglement at homodromic Bjerrum defect site. J Mol Model 2023; 29:242. [PMID: 37436555 PMCID: PMC10338397 DOI: 10.1007/s00894-023-05646-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 07/01/2023] [Indexed: 07/13/2023]
Abstract
CONTEXT From a nuclear spin prospective, water exists as para and ortho nuclear spin isomers (isotopomers). Spin interconversions in isolated molecules of water are forbidden, but many recent reports have shown them to happen in bulk, through dynamic proton exchanges happening between interconnected networks of a large array of water molecules. In this contribution, a possible explanation for an unexpected slow or delayed interconversion of ortho-para water in ice observed in an earlier reported experiment is provided. Using the results of quantum mechanical investigations, we have discussed the roles played by Bjerrum defects in the dynamic proton exchanges and ortho-para spin state interconversions. We guess that at the sites of the Bjerrum defects, there are possibilities of quantum entanglements of states, through pairwise interactions. Based on the perfectly correlated exchange happening via a replica transition state, we speculate that it can have significant influences on ortho-para interconversions of water. We also conjecture that the overall ortho-para interconversion is not a continuous process, rather can be imagined to be happening serendipitously, but within the boundary of the rules of quantum mechanics. METHODS All computations were performed with Gaussian 09 program. B3LYP/6-31++G(d,p) methodology was used to compute all the stationary points. Further energy corrections were computed using CCSD(T)/aug-cc-pVTZ methodology. Intrinsic reaction coordinate (IRC) path computations were carried out for the transition states.
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Affiliation(s)
- Sanyasi Sitha
- Department of Chemical Sciences, APK Campus, University of Johannesburg, PO Box 524, Auckland Park, Johannesburg, 2006, South Africa.
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2
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Hudson PS, Woodcock HL, Boresch S. Use of Interaction Energies in QM/MM Free Energy Simulations. J Chem Theory Comput 2019; 15:4632-4645. [PMID: 31142113 DOI: 10.1021/acs.jctc.9b00084] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.
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Affiliation(s)
- Phillip S Hudson
- Department of Chemistry , University of South Florida , 4202 East Fowler Avenue, CHE205 , Tampa , Florida 33620-5250 , United States.,Laboratory of Computational Biology , National Institutes of Health, National Heart, Lung and Blood Institute , 12 South Drive, Rm 3053 , Bethesda , Maryland 20892-5690 , United States
| | - H Lee Woodcock
- Department of Chemistry , University of South Florida , 4202 East Fowler Avenue, CHE205 , Tampa , Florida 33620-5250 , United States
| | - Stefan Boresch
- Faculty of Chemistry, Department of Computational Biological Chemistry , University of Vienna , Währingerstraße 17 , Vienna A-1090 , Austria
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Bistafa C, Kitamura Y, Martins-Costa MTC, Nagaoka M, Ruiz-López MF. Cost-Effective Method for Free-Energy Minimization in Complex Systems with Elaborated Ab Initio Potentials. J Chem Theory Comput 2018; 14:3262-3271. [DOI: 10.1021/acs.jctc.8b00271] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Carlos Bistafa
- Department of Complex Systems Science, Graduate School of Informatics, Nagoya University, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648601, Japan
| | - Yukichi Kitamura
- Department of Complex Systems Science, Graduate School of Informatics, Nagoya University, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648601, Japan
| | - Marilia T. C. Martins-Costa
- Laboratoire de Physique et Chimie Théoriques, UMR CNRS 7019, Faculté des Sciences et Technologies, Université de Lorraine, CNRS, BP 70239, 54506 Vandoeuvre-lès-Nancy Cedex,France
| | - Masataka Nagaoka
- Department of Complex Systems Science, Graduate School of Informatics, Nagoya University, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648601, Japan
- ESICB, Kyoto University, Kyodai Katsura, Nishikyo-ku, Kyoto 6158520, Japan
- Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Honmachi, Kawaguchi 3320012, Japan
| | - Manuel F. Ruiz-López
- Laboratoire de Physique et Chimie Théoriques, UMR CNRS 7019, Faculté des Sciences et Technologies, Université de Lorraine, CNRS, BP 70239, 54506 Vandoeuvre-lès-Nancy Cedex,France
- Future Value Creation Research Center, Graduate School of Informatics, Nagoya University, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648601, Japan
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Fu H, Shao X, Chipot C, Cai W. Extended Adaptive Biasing Force Algorithm. An On-the-Fly Implementation for Accurate Free-Energy Calculations. J Chem Theory Comput 2016; 12:3506-13. [PMID: 27398726 DOI: 10.1021/acs.jctc.6b00447] [Citation(s) in RCA: 88] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Proper use of the adaptive biasing force (ABF) algorithm in free-energy calculations needs certain prerequisites to be met, namely, that the Jacobian for the metric transformation and its first derivative be available and the coarse variables be independent and fully decoupled from any holonomic constraint or geometric restraint, thereby limiting singularly the field of application of the approach. The extended ABF (eABF) algorithm circumvents these intrinsic limitations by applying the time-dependent bias onto a fictitious particle coupled to the coarse variable of interest by means of a stiff spring. However, with the current implementation of eABF in the popular molecular dynamics engine NAMD, a trajectory-based post-treatment is necessary to derive the underlying free-energy change. Usually, such a posthoc analysis leads to a decrease in the reliability of the free-energy estimates due to the inevitable loss of information, as well as to a drop in efficiency, which stems from substantial read-write accesses to file systems. We have developed a user-friendly, on-the-fly code for performing eABF simulations within NAMD. In the present contribution, this code is probed in eight illustrative examples. The performance of the algorithm is compared with traditional ABF, on the one hand, and the original eABF implementation combined with a posthoc analysis, on the other hand. Our results indicate that the on-the-fly eABF algorithm (i) supplies the correct free-energy landscape in those critical cases where the coarse variables at play are coupled to either each other or to geometric restraints or holonomic constraints, (ii) greatly improves the reliability of the free-energy change, compared to the outcome of a posthoc analysis, and (iii) represents a negligible additional computational effort compared to regular ABF. Moreover, in the proposed implementation, guidelines for choosing two parameters of the eABF algorithm, namely the stiffness of the spring and the mass of the fictitious particles, are proposed. The present on-the-fly eABF implementation can be viewed as the second generation of the ABF algorithm, expected to be widely utilized in the theoretical investigation of recognition and association phenomena relevant to physics, chemistry, and biology.
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Affiliation(s)
| | - Xueguang Shao
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche No. 7565, Université de Lorraine , B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France.,Theoretical and Computational Biophysics Group, Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.,Department of Physics, University of Illinois at Urbana-Champaign , 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Wensheng Cai
- Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, China
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Tritzant-Martinez Y, Zeng T, Broom A, Meiering E, Le Roy RJ, Roy PN. On the analytical representation of free energy profiles with a Morse/long-range model: Application to the water dimer. J Chem Phys 2013; 138:234103. [DOI: 10.1063/1.4810006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zhang P, Tian L, Zhang ZP, Shao G, Li JC. Investigation of the hydrogen bonding in ice Ih by first-principles density function methods. J Chem Phys 2012; 137:044504. [PMID: 22852628 DOI: 10.1063/1.4736853] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
It is a well recognized difficult task to simulate the vibrational dynamics of ices using the density functional theory (DFT), and there has thus been rather limited success in modelling the inelastic neutron scattering (INS) spectra for even the simplest structure of ice, ice Ih, particularly in the translational region below 400 cm(-1). The reason is partly due to the complex nature of hydrogen bonding (H-bond) among water-water molecules which require considerable improvement of the quantum mechanical simulation methods, and partly owing to the randomness of protons in ice structures which often requires simulation of large super-lattices. In this report, we present the first series of successful simulation results for ice Ih using DFT methods. On the basis of the recent advancement in the DFT programs, we have achieved for the first time theoretical outcomes that not only reproduce the rotational frequencies between 500 to 1200 cm(-1) for ice Ih, but also the two optic peaks at ∼240 and 320 cm(-1) in the translational region of the INS spectra [J. C. Li, J. Chem. Phys 105, 6733 (1996)]. Besides, we have also investigated the impact of pairwise configurations of H(2)O molecules on the H-bond and found that different proton arrangements of pairwise H(2)O in the ice Ih crystal lattice could not alter the nature of H-bond as significantly as suggested in an early paper [J. C. Li and D. K. Ross, Nature (London) 365, 327 (1993)], i.e., reproducing the two experimental optic peaks do not need to invoke the two H-bonds as proposed in the previous model which led to considerable debates. The results of this work suggest that the observed optic peaks may be attributed to the coupling between the two bands of H-O stretching modes in H(2)O. The current computational work is expected to shed new light on the nature of the H-bonds in water, and in addition to offer a new approach towards probing the interaction between water and biomaterials for which H-bond is essential.
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Affiliation(s)
- P Zhang
- School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, United Kingdom
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Beierlein FR, Michel J, Essex JW. A Simple QM/MM Approach for Capturing Polarization Effects in Protein−Ligand Binding Free Energy Calculations. J Phys Chem B 2011; 115:4911-26. [DOI: 10.1021/jp109054j] [Citation(s) in RCA: 82] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Frank R. Beierlein
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Julien Michel
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Jonathan W. Essex
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
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Retegan M, Martins-Costa M, Ruiz-López MF. Free energy calculations using dual-level Born–Oppenheimer molecular dynamics. J Chem Phys 2010; 133:064103. [DOI: 10.1063/1.3466767] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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Calvo F, Douady J, Spiegelman F. Accurate evaporation rates of pure and doped water clusters in vacuum: A statistico-dynamical approach. J Chem Phys 2010; 132:024305. [DOI: 10.1063/1.3280168] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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10
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Crosby LD, Kathmann SM, Windus TL. Implementation of dynamical nucleation theory with quantum potentials. J Comput Chem 2009; 30:743-9. [DOI: 10.1002/jcc.21098] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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Yao L, He R, Mebel A, Lin S. On the calculation of the dissociation rate constant of the water dimer by the ab initio anharmonic RRKM theory. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.01.074] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Abstract
The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.
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Affiliation(s)
- Lonnie D Crosby
- Department of Chemistry, Iowa State University and Ames Laboratory, Ames, Iowa 50010, USA
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van der Kamp MW, Shaw KE, Woods CJ, Mulholland AJ. Biomolecular simulation and modelling: status, progress and prospects. J R Soc Interface 2008; 5 Suppl 3:S173-90. [PMID: 18611844 PMCID: PMC2706107 DOI: 10.1098/rsif.2008.0105.focus] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2008] [Revised: 06/05/2008] [Accepted: 06/06/2008] [Indexed: 11/12/2022] Open
Abstract
Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.
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Affiliation(s)
| | | | | | - Adrian J. Mulholland
- Centre for Computational Chemistry, School of Chemistry, University of BristolBristol BS8 1TS, UK
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Kathmann SM, Palmer BJ, Schenter GK, Garrett BC. Activation energies and potentials of mean force for water cluster evaporation. J Chem Phys 2008; 128:064306. [DOI: 10.1063/1.2837282] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Woods CJ, Manby FR, Mulholland AJ. An efficient method for the calculation of quantum mechanics/molecular mechanics free energies. J Chem Phys 2008; 128:014109. [DOI: 10.1063/1.2805379] [Citation(s) in RCA: 85] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lodola A, Woods CJ, Mulholland AJ. Applications and Advances of QM/MM Methods in Computational Enzymology. ANNUAL REPORTS IN COMPUTATIONAL CHEMISTRY 2008. [DOI: 10.1016/s1574-1400(08)00009-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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Jiang YQ, Xie ZX. A New Conformation of a Water Hexamer Chain and its Reversible Formation/Removal in the Host Channel by Gas–Solid Reaction. Supramol Chem 2006. [DOI: 10.1080/10610270500067616] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Ya-Qi Jiang
- a Department of Chemistry and State Key Laboratory for Physical Chemistry of Solid Surfaces , Xiamen University , Xiamen, 361005, China
| | - Zhao-Xiong Xie
- a Department of Chemistry and State Key Laboratory for Physical Chemistry of Solid Surfaces , Xiamen University , Xiamen, 361005, China
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Liu J, Yang L, Doren DJ. Comparison of TIP5P water model and TIP4P water model in cluster nucleation kinetics study through umbrella sampling and free energy perturbation. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.10.026] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Free energy perturbation and dynamical nucleation study of water dimer and trimer through TIP5P water model. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2005.09.053] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Rod TH, Ryde U. Accurate QM/MM Free Energy Calculations of Enzyme Reactions: Methylation by CatecholO-Methyltransferase. J Chem Theory Comput 2005; 1:1240-51. [DOI: 10.1021/ct0501102] [Citation(s) in RCA: 119] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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