1
|
Hu W, Li P, Wang JN, Xue Y, Mo Y, Zheng J, Pan X, Shao Y, Mei Y. Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 3. Gaussian Smoothing on Density-of-States. J Chem Theory Comput 2020; 16:6814-6822. [PMID: 32975951 PMCID: PMC7658029 DOI: 10.1021/acs.jctc.0c00794] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Calculations of the free energy profile, also known as potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied in the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio quantum mechanical/molecular mechanics (QM/MM) level of accuracy is required for the PMF, it can be formidably demanding even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of the free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events, and some low-energy conformations may get oversampled in simulations of a finite length. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method.
Collapse
Affiliation(s)
- Wenxin Hu
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Pengfei Li
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jia-Ning Wang
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yuanfei Xue
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yan Mo
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Jun Zheng
- The Computer Center, School of Data Science & Engineering, East China Normal University, Shanghai 200062, China
| | - Xiaoliang Pan
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Yihan Shao
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| |
Collapse
|
2
|
Desgranges C, Delhommelle J. Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon. J Chem Phys 2016; 144:124510. [PMID: 27036464 DOI: 10.1063/1.4944619] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.
Collapse
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| |
Collapse
|
3
|
Oyarzún B, van Westen T, Vlugt TJH. Isotropic-nematic phase equilibria of hard-sphere chain fluids—Pure components and binary mixtures. J Chem Phys 2015; 142:064903. [DOI: 10.1063/1.4907639] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
|
4
|
Hansen N, van Gunsteren WF. Practical Aspects of Free-Energy Calculations: A Review. J Chem Theory Comput 2014; 10:2632-47. [PMID: 26586503 DOI: 10.1021/ct500161f] [Citation(s) in RCA: 289] [Impact Index Per Article: 28.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.
Collapse
Affiliation(s)
- Niels Hansen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart , D-70569 Stuttgart, Germany.,Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH , CH-8093 Zürich, Switzerland
| | - Wilfred F van Gunsteren
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH , CH-8093 Zürich, Switzerland
| |
Collapse
|
5
|
Desgranges C, Delhommelle J. Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. III. Impact of combining rules on mixtures properties. J Chem Phys 2014; 140:104109. [DOI: 10.1063/1.4867498] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
|
6
|
Hicks E, Desgranges C, Delhommelle J. Adsorption and diffusion of the antiparkinsonian drug amantadine in carbon nanotubes. MOLECULAR SIMULATION 2014. [DOI: 10.1080/08927022.2013.841908] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
7
|
Koenig A, Desgranges C, Delhommelle J. Adsorption of hydrogen in covalent organic frameworks using expanded Wang–Landau simulations. MOLECULAR SIMULATION 2013. [DOI: 10.1080/08927022.2013.841907] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- A.R.V. Koenig
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, ND58202, USA
| | - C. Desgranges
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, ND58202, USA
| | - J. Delhommelle
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, ND58202, USA
| |
Collapse
|
8
|
Desgranges C, Delhommelle J. Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. I. Thermodynamic properties in the bulk and at the liquid-vapor phase boundary. J Chem Phys 2012; 136:184107. [DOI: 10.1063/1.4712023] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
|
9
|
Desgranges C, Delhommelle J. Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. II. Adsorption of atomic and molecular fluids in a porous material. J Chem Phys 2012; 136:184108. [DOI: 10.1063/1.4712025] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
|
10
|
Angioletti-Uberti S, Mognetti BM, Frenkel D. Re-entrant melting as a design principle for DNA-coated colloids. NATURE MATERIALS 2012; 11:518-522. [PMID: 22543302 DOI: 10.1038/nmat3314] [Citation(s) in RCA: 85] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2012] [Accepted: 03/23/2012] [Indexed: 05/31/2023]
Abstract
Colloids functionalized with DNA hold great promise as building blocks for complex self-assembling structures. However, the practical use of DNA-coated colloids (DNACCs) has been limited by the narrowness of the temperature window where the target structures are both thermodynamically stable and kinetically accessible. Here we propose a strategy to design DNACCs, whereby the colloidal suspensions crystallize on cooling and then melt on further cooling. In a phase diagram with such a re-entrant melting, kinetic trapping of the system in non-target structures should be strongly suppressed. We present model calculations and simulations that show that real DNA sequences exist that should bestow this unusual phase behaviour on suitably functionalized colloidal suspensions. We present our results for binary systems, but the concepts that we develop apply to multicomponent systems and should therefore open the way towards the design of truly complex self-assembling colloidal structures.
Collapse
|
11
|
Martinez-Veracoechea FJ, Mladek BM, Tkachenko AV, Frenkel D. Design rule for colloidal crystals of DNA-functionalized particles. PHYSICAL REVIEW LETTERS 2011; 107:045902. [PMID: 21867023 DOI: 10.1103/physrevlett.107.045902] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Indexed: 05/31/2023]
Abstract
We report a Monte Carlo simulation study of the phase behavior of colloids coated with long, flexible DNA chains. We find that an important change occurs in the phase diagram when the number of DNAs per colloid is decreased below a critical value. In this case, the triple point disappears and the condensed phase that coexists with the vapor is always liquid. Our simulations thus explain why, in the dilute solutions typically used in experiments, colloids coated with a small number of DNA strands cannot crystallize. We understand this behavior in terms of the discrete nature of DNA binding.
Collapse
|
12
|
Borrero EE, Dellago C. Overcoming barriers in trajectory space: mechanism and kinetics of rare events via Wang-Landau enhanced transition path sampling. J Chem Phys 2011; 133:134112. [PMID: 20942528 DOI: 10.1063/1.3496376] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Within the framework of transition path sampling (TPS), activation energies can be computed as path ensemble averages without a priori information about the reaction mechanism [C. Dellago and P. G. Bolhuis, Mol. Simul. 30, 795 (2004)]. Activation energies computed for different conditions can then be used to determine by numerical integration the rate constant for a system of interest from the rate constant known for a reference system. However, in systems with complex potential energy surfaces, multiple reaction pathways may exist making ergodic sampling of trajectory space difficult. Here, we present a combination of TPS with the Wang-Landau (WL) flat-histogram algorithm for an efficient sampling of the transition path ensemble. This method, denoted by WL-TPS, has the advantage that from one single simulation, activation energies at different temperatures can be determined even for systems with multiple reaction mechanisms. The proposed methodology for rate constant calculations does not require the knowledge of the reaction coordinate and is generally applicable to Arrhenius and non-Arrhenius processes. We illustrate the applicability of this technique by studying a two-dimensional toy system consisting of a triatomic molecule immersed in a fluid of repulsive soft disks. We also provide an expression for the calculation of activation volumes from path averages such that the pressure dependence of the rate constant can be obtained by numerical integration.
Collapse
Affiliation(s)
- Ernesto E Borrero
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | | |
Collapse
|
13
|
Do H, Wheatley RJ, Hirst JD. Molecular simulation of the binary mixture of 1–1–1–2–tetrafluoroethane and carbon dioxide. Phys Chem Chem Phys 2011; 13:15708-13. [DOI: 10.1039/c1cp21419e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
|
14
|
Lintuvuori JS, Wilson MR. Statistical temperature molecular dynamics simulations applied to phase transitions in liquid crystalline systems. J Chem Phys 2010; 132:224902. [DOI: 10.1063/1.3429620] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
|
15
|
Desgranges C, Hicks J, Magness A, Delhommelle J. Phase equilibria of polyaromatic hydrocarbons by hybrid Monte Carlo Wang–Landau simulations. Mol Phys 2010. [DOI: 10.1080/00268970903544238] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- C. Desgranges
- a Department of Chemistry , University of North Dakota , 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| | - J.M. Hicks
- a Department of Chemistry , University of North Dakota , 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| | - A. Magness
- b Department of Physics and Astrophysics , University of North Dakota , 101 Cornell Street Stop 7129, Grand Forks, North Dakota 58202, USA
| | - J. Delhommelle
- a Department of Chemistry , University of North Dakota , 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
- b Department of Physics and Astrophysics , University of North Dakota , 101 Cornell Street Stop 7129, Grand Forks, North Dakota 58202, USA
| |
Collapse
|
16
|
Abreu CRA. Isochronal sampling in non-Boltzmann Monte Carlo methods. J Chem Phys 2009; 131:154113. [DOI: 10.1063/1.3245304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Charlles R A Abreu
- School of Chemical Engineering, State University of Campinas, Campinas, Sao Paulo 13083-970, Brazil.
| |
Collapse
|
17
|
Desgranges C, Delhommelle J. Phase equilibria of molecular fluids via hybrid Monte Carlo Wang–Landau simulations: Applications to benzene and n-alkanes. J Chem Phys 2009; 130:244109. [DOI: 10.1063/1.3158605] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
18
|
Martínez-Veracoechea FJ, Escobedo FA. Variance Minimization of Free Energy Estimates from Optimized Expanded Ensembles. J Phys Chem B 2008; 112:8120-8. [DOI: 10.1021/jp801688p] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Fernando A. Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853
| |
Collapse
|
19
|
Ytreberg FM, Zuckerman DM. A black-box re-weighting analysis can correct flawed simulation data. Proc Natl Acad Sci U S A 2008; 105:7982-7. [PMID: 18544653 PMCID: PMC2786942 DOI: 10.1073/pnas.0706063105] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2007] [Indexed: 11/18/2022] Open
Abstract
There is a great need for improved statistical sampling in a range of physical, chemical, and biological systems. Even simulations based on correct algorithms suffer from statistical error, which can be substantial or even dominant when slow processes are involved. Further, in key biomolecular applications, such as the determination of protein structures from NMR data, non-Boltzmann-distributed ensembles are generated. We therefore have developed the "black-box" strategy for re-weighting a set of configurations generated by arbitrary means to produce an ensemble distributed according to any target distribution. In contrast to previous algorithmic efforts, the black-box approach exploits the configuration-space density observed in a simulation, rather than assuming a desired distribution has been generated. Successful implementations of the strategy, which reduce both statistical error and bias, are developed for a one-dimensional system, and a 50-atom peptide, for which the correct 250-to-1 population ratio is recovered from a heavily biased ensemble.
Collapse
Affiliation(s)
- F. Marty Ytreberg
- *Department of Physics, University of Idaho, Moscow, ID 83844-0903; and
| | - Daniel M. Zuckerman
- Department of Computational Biology, University of Pittsburgh, 3501 Fifth Avenue, Pittsburgh, PA 152601
| |
Collapse
|
20
|
John BS, Juhlin C, Escobedo FA. Phase behavior of colloidal hard perfect tetragonal parallelepipeds. J Chem Phys 2008; 128:044909. [DOI: 10.1063/1.2819091] [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
|
21
|
Wang F, Stuart SJ, Latour RA. Calculation of adsorption free energy for solute-surface interactions using biased replica-exchange molecular dynamics. Biointerphases 2008; 3:9-18. [PMID: 19768127 PMCID: PMC2746080 DOI: 10.1116/1.2840054] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The adsorption behavior of a biomolecule, such as a peptide or protein, to a functionalized surface is of fundamental importance for a broad range of applications in biotechnology. The adsorption free energy for these types of interactions can be determined from a molecular dynamics simulation using the partitioning between adsorbed and nonadsorbed states, provided that sufficient sampling of both states is obtained. However, if interactions between the solute and the surface are strong, the solute will tend to be trapped near the surface during the simulation, thus preventing the adsorption free energy from being calculated by this method. This situation occurs even when using an advanced sampling algorithm such as replica-exchange molecular dynamics (REMD). In this paper, the authors demonstrate the fundamental basis of this problem using a model system consisting of one sodium ion (Na(+)) as the solute positioned over a surface functionalized with one negatively charged group (COO(-)) in explicit water. With this simple system, the authors show that sufficient sampling in the coordinate normal to the surface cannot be obtained by conventional REMD alone. The authors then present a method to overcome this problem through the use of an adaptive windowed-umbrella sampling technique to develop a biased-energy function that is combined with REMD. This approach provides an effective method for the calculation of adsorption free energy for solute-surface interactions.
Collapse
Affiliation(s)
- Feng Wang
- Department of Bioengineering, Clemson University, Clemson, South Carolina 29634
| | - Steven J. Stuart
- Department of Chemistry, Clemson University, Clemson, South Carolina 29634
| | - Robert A. Latour
- Department of Bioengineering, Clemson University, Clemson, South Carolina 29634
| |
Collapse
|
22
|
Ganzenmüller G, Camp PJ. Applications of Wang-Landau sampling to determine phase equilibria in complex fluids. J Chem Phys 2007; 127:154504. [DOI: 10.1063/1.2794042] [Citation(s) in RCA: 79] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
23
|
Meirovitch H. Recent developments in methodologies for calculating the entropy and free energy of biological systems by computer simulation. Curr Opin Struct Biol 2007; 17:181-6. [PMID: 17395451 DOI: 10.1016/j.sbi.2007.03.016] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2006] [Revised: 01/11/2007] [Accepted: 03/16/2007] [Indexed: 10/23/2022]
Abstract
The Helmholtz free energy, F, plays an important role in proteins because of their rugged potential energy surface, which is 'decorated' with a tremendous number of local wells (denoted microstates, m). F governs protein folding, whereas differences DeltaF(mn) determine the relative populations of microstates that are visited by a flexible cyclic peptide or a flexible protein segment (e.g. a surface loop). Recently developed methodologies for calculating DeltaF(mn) (and entropy differences, DeltaS(mn)) mainly use thermodynamic integration and calculation of the absolute F; interesting new approaches in these categories are the adaptive integration method and the hypothetical scanning molecular dynamics method, respectively.
Collapse
Affiliation(s)
- Hagai Meirovitch
- Department of Computational Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA 15260, USA.
| |
Collapse
|
24
|
Escobedo FA. Simulation of the density of states in isothermal and adiabatic ensembles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056701. [PMID: 16803068 DOI: 10.1103/physreve.73.056701] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2006] [Indexed: 05/10/2023]
Abstract
This paper provides a unified treatment of the fundamental methods used to obtain the density of states via molecular simulations with isothermal ensembles (IEs) and adiabatic ensembles (AEs). Our analysis and results show that provides a natural bridge to go back and forth between IE and AE simulation data. They also underline the difference between the density of states of potential energy macrostates and that of total energy macrostates Omega, even though both provide access to the thermodynamic properties of the system. Visited-states approaches and transition matrix methods are described and applied to the Lennard-Jones fluid to target omega and Omega as functions of energy and volume macrostates. It is shown that one can obtain omega via a generalized acceptance-ratio formula that is applicable regardless of the conditions at which the ensemble is simulated. In this way, one can obtain while performing conventional IE or AE simulations, and do it at no extra cost and with a higher accuracy than is achievable with histogram methods.
Collapse
Affiliation(s)
- Fernando A Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
| |
Collapse
|
25
|
Escobedo FA, Abreu CRA. On the use of transition matrix methods with extended ensembles. J Chem Phys 2006; 124:104110. [PMID: 16542071 DOI: 10.1063/1.2174010] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Different extended ensemble schemes for non-Boltzmann sampling (NBS) of a selected reaction coordinate lambda were formulated so that they employ (i) "variable" sampling window schemes (that include the "successive umbrella sampling" method) to comprehensibly explore the lambda domain and (ii) transition matrix methods to iteratively obtain the underlying free-energy eta landscape (or "importance" weights) associated with lambda. The connection between "acceptance ratio" and transition matrix methods was first established to form the basis of the approach for estimating eta(lambda). The validity and performance of the different NBS schemes were then assessed using as lambda coordinate the configurational energy of the Lennard-Jones fluid. For the cases studied, it was found that the convergence rate in the estimation of eta is little affected by the use of data from high-order transitions, while it is noticeably improved by the use of a broader window of sampling in the variable window methods. Finally, it is shown how an "elastic" window of sampling can be used to effectively enact (nonuniform) preferential sampling over the lambda domain, and how to stitch the weights from separate one-dimensional NBS runs to produce a eta surface over a two-dimensional domain.
Collapse
Affiliation(s)
- Fernando A Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA.
| | | |
Collapse
|