References¶
This section contains a list of the references to general theory, algorithms and implementation details which have been of use during the development of the Tinker package. Methods described in some of the references have been implemented in detail within the Tinker source code. Other references contain useful background information although the algorithms themselves are now obsolete. Still other papers contain ideas or extensions planned for future inclusion in Tinker. References for specific force field parameter sets are provided in an earlier section of this User’s Guide. This list is heavily skewed toward biomolecules in general and proteins in particular. This bias reflects our group’s major interests; however an attempt has been made to include methods which should be generally applicable.
Molecular Mechanics & Dynamics Software Packages¶
Tinker Software Tools¶
Tinker
Tinker 8: Software Tools for Molecular Design, J. A. Rackers, Z. Wang, C. Lu, M. L. Laury, L. Lagardere, M. J. Schnieders, J.-P. Piquemal, P. Ren and J. W. Ponder, J. Chem. Theory Comput., 14, 5273-5289 (2018)
Tinker-HP
Tinker-HP: A Massively Parallel Molecular Dynamics Package for Multiscale Simulations of Large Complex Systems with Advanced Point Dipole Polarizable Force Fields, L. Lagardere, L.-H. Jolly, F. Lipparini, F. Aviat, B. Stamm, Z. F. Jing, M. Harger, H. Torabifard, G. A. Cisneros, M. J. Schnieders, N. Gresh, Y. Maday, P. Y. Ren, J. W. Ponder and J.-P. Piquemal, Chem. Sci., 9, 956-972 (2018)
Tinker-OpenMM
Tinker-OpenMM: Absolute and Relative Alchemical Free Energies Using AMOEBA on GPUs, M. Harger, D. Li, Z. Wang, K. Dalby, L. Lagardere, J.-P. Piquemal, J. Ponder and P. Ren, J. Comput. Chem., 38, 2047-2055 (2017)
Alternative Molecular Modeling Software¶
AMBER Peter Kollman, University of California, San Francisco
AMMP Robert Harrison, Georgia State University, Atlanta
ARGOS J. Andrew McCammon, University of California, San Diego
BOSS William Jorgensen, Yale University
BRUGEL Shoshona Wodak, Free University of Brussels
CFF Shneior Lifson, Weizmann Institute
CHARMM Martin Karplus, Harvard University
DELPHI Bastian van de Graaf, Delft University of Technology
DISCOVER Molecular Simulations Inc., San Diego
DL_POLY Ilian Todorov & W. Smith, STFC Daresbury Laboratory
ECEPP Harold Scheraga, Cornell University
ENCAD Michael Levitt, Stanford University
FANTOM Werner Braun, University of Texas, Galveston
FEDER/2 Nobuhiro Go, Kyoto University
GROMACS Erik Lindahl, Stockholm University
GROMOS Wilfred van Gunsteren, BIOMOS and ETH, Zurich
IMPACT Ronald Levy, Temple University, Philadelphia
MACROMODEL Schodinger, Inc., New York
MM2/MM3/MM4 N. Lou Allinger, University of Georgia
MMC Cliff Dykstra, Indiana Univ.-Purdue Univ. at Indianapolis
MMFF Thomas Halgren, Merck Research Laboratories, Rahway, NJ
MMTK Konrad Hinsen, Inst. of Structural Biology, Grenoble
MOIL Ron Elber, Cornell University
MOLARIS Arieh Warshel, University of Southern California
MOLDY Keith Refson, Oxford University
MOSCITO Dietmar Paschek & Alfons Geiger, Universitat Dortmund
NAMD Klaus Schulten, University of Illinois, Urbana
OOMPAA J. Andrew McCammon, University of California, San Diego
OPENMM Peter Eastman & Vijay Pande, Stanford University
ORAL Karel Zimmerman, INRA, Jouy-en-Josas, France
ORIENT Anthony Stone, Cambridge University
PCMODEL Kevin Gilbert, Serena Software, Bloomington, Indiana
PEFF Jan Dillen, University of Pretoria, South Africa
PHENIX Paul Adams, Lawrence Berkeley Laboratory
Q Johan Aqvist, Uppsala University
SIBFA Nohad Gresh, INSERM, CNRS, Paris
SIGMA Jan Hermans, University of North Carolina
SPASIBA Gerard Vergoten, Universite de Lille
SPASMS David Spellmeyer and the Kollman Group, UCSF
UTAH5 Cornelis Altona, Leiden University, Netherlands
XPLOR/CNS Axel Brunger, Stanford University
YAMMP Stephen Harvey, University of Alabama, Birmingham
YASP Florian Mueller-Plathe, TU Darmstadt
YETI Angelo Vedani, Biografik-Labor 3R, Basel
AMBER
An Overview of the Amber Biomolecular Simulation Package, R. Salomon-Ferrer, D. A. Case, R. C. Walker, WIREs Comput. Mol. Sci. 3, 198-210 (2013)
The Amber Biomolecular Simulation Programs. D. A. Case, T. E. Cheatham, III, T. Darden, H. Gohlke, R. Luo, K. M. Merz, Jr., A. Onufriev, C. Simmerling, B. Wang and R. Woods. J. Comput. Chem., 26, 1668-1688 (2005)
AMBER, a Package of Computer Programs for Applying Molecular Mechanics, Normal Mode Analysis, Molecular Dynamics and Free Energy Calculations to Simulate the Structural and Energetic Properties of Molecules, D. A Pearlman, D. A. Case, J. W. Caldwell, W. S. Ross, T. E. Cheatham III, S. DeBolt, D. Ferguson, G. Seibel and P. Kollman, Comp. Phys. Commun., 91, 1-41 (1995)
AMMP
Stiffness and Energy Conservation in Molecular Dynamics: An Improved Integrator, R. W. Harrison, J. Comput. Chem., 14, 1112-1122 (1993)
ARGOS
ARGOS, a Vectorized General Molecular Dynamics Program, T. P. Straatsma and J. A. McCammon, J. Comput. Chem., 11, 943-951 (1990)
BOSS
Molecular Modeling of Organic and Biomolecular Systems Using BOSS and MCPRO, W. L. Jorgensen and J. Tirado-Rives, J. Comput. Chem., 26, 1689-1700 (2005)
BRUGEL
Interactive Computer Animation of Macromolecules, P. Delhaise, M. Bardiaux and S. Wodak, J. Mol. Graphics, 2, 103-106 (1984)
CHARMM
CHARMM: The Biomolecular Simulation Program, B. R. Brooks, C. L. Brooks III, A. D. Mackerell, L. Nilsson, R. J. Petrella, B. Roux, Y. Won, G. Archontis, C. Bartels, S. Boresch A. Caflisch, L. Caves, Q. Cui, A. R. Dinner, M. Feig, S. Fischer, J. Gao, M. Hodoscek, W. Im, K. Kuczera, T. Lazaridis, J. Ma, V. Ovchinnikov, E. Paci, R. W. Pastor, C. B. Post, J. Z. Pu, M. Schaefer, B. Tidor, R. M. Venable, H. L. Woodcock, X. Wu, W. Yang, D. M. York, and M. Karplus, J. Comput. Chem., 30, 1545-1615 (2009)
CHARMM: The Energy Function and Its Parameterization with an Overview of the Program, A. D. MacKerell, Jr., B. Brooks, C. L. Brooks, III, L. Nilsson, B. Roux, Y. Won, and M. Karplus, in The Encyclopedia of Computational Chemistry, Vol. 1, pg. 271-277, John Wiley & Sons, Chichester, 1998
CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations, B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan and M. Karplus, J. Comput. Chem., 4, 187-217 (1983)
DELPHI
Delft Molecular Mechanics: A New Approach to Hydrocarbon Force Fields. Inclusion of a Geometry-Dependent Charge Calculation, A. C. T. van Duin, J. M. A. Baas and B. van de Graaf, J. Chem. Soc. Faraday Trans., 90, 2881-2895 (1994)
DL_POLY
DL_POLY_3: New Dimensions in Molecular Simulations via Massive Parallelism, I. T. Todorov, W. Smith, K. Trachenko and M. T. Dove, J. Mater. Chem., 16, 1911-1918 (2006)
ENCAD
Potential Energy Function and Parameters for Simulations for the Molecular Dynamics of Proteins and Nucleic Acids in Solution, M. Levitt, M. Hirshberg, R. Sharon and V. Daggett, Comp. Phys. Commun., 91, 215-231 (1995)
FANTOM
The Program FANTOM for Energy Refinement of Polypeptides and Proteins Using a Newton-Raphson Minimizer in Torsion Angle Space, T. Schaumann, W. Braun and K. Wurtrich, Biopolymers, 29, 679-694 (1990)
FEDER/2
FEDER/2: Program for Static and Dynamic Conformational Energy Analysis of Macro-molecules in Dihedral Angle Space, H. Wako, S. Endo, K. Nagayama and N. Go, Comp. Phys. Commun., 91, 233-251 (1995)
GROMACS
GROMACS: High Performance Molecular Simulations Through Multi-Level Parallelism from Laptops to Supercomputers, M. J. Abraham, T. Murtola, R. Schultz, S. Pall, J. C. Smith, B. Hess and E. Lindahl, SoftwareX, 1-2, 19-25 (2015)
GROMACS 4.5: A High-Throughput and Highly Parallel Open Source Molecular Simulation Toolkit, S. Pronk, S. Pall, R. Schulz, P. Larsson, P. Bjelkmar, R. Apostolov, M. R. Shirts, J. C. Smith, P. M. Kasson, D. van der Spoel, B. Hess and E. Lindahl, Bioinformatics, 29, 845-854 (2013)
GROMACS 3.0: A Package for Molecular Simulation and Trajectory Analysis, E. Lindahl, B. Hess and D. van der Spoel, J. Mol. Model., 7, 306-317 (2001)
GROMOS
The GROMOS Biomolecular Simulation Program Package, W. R. P. Scott, P. H. Hunenberger , I. G. Tironi, A. E. Mark, S. R. Billeter, J. Fennen, A. E. Torda, T. Huber, P. Kruger, W. F. van Gunsteren, J. Phys. Chem. A, 103, 3596-3607 (1999)
IMPACT
Integrated Modeling Program, Applide Chemical Theory (IMPACT), J. L. Banks, H. S. Beard, Y. Cao, A. E. Cho, W. Damm, R. Farid, A. K. Felts, T. A. Halgren, D. T. Mainz, J. R. Maple, R. Murphy, D. M. Philipp, M. P. Repasky, L. Y. Zhang, B. J. Berne, R. A. Friesner, E. Gallicchio and R. M. Levy, J. Comput. Chem., 26, 1752-1780 (2005)
MACROMODEL
MacroModel: An Integrated Software System for Modeling Organic and Bioorganic Molecules Using Molecular Mechanics, F. Mahamadi, N. G. J. Richards, W. C. Guida, R. Liskamp, M. Lipton, C. Caufield, G. Chang, T. Hendrickson and W. C. Still, J. Comput. Chem., 11, 440-467 (1990)
MM2
Conformational Analysis. 130. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms, N. L. Allinger, J. Am. Chem. Soc., 99, 8127-8134 (1977)
MM3
Molecular Mechanics. The MM3 Force Field for Hydrocarbons, N. L. Allinger, Y. H. Yuh and J.-H. Lii, J. Am. Chem. Soc., 111, 8551-8566 (1989)
MM4
An Improved Force Field (MM4) for Saturated Hydrocarbons, N. L. Allinger, K. Chen and J.-H. Lii, J. Comput. Chem., 17, 642-668 (1996)
MMC
Molecular Mechanics for Weakly Interacting Assemblies of Rare Gas Atoms and Small Molecules, C. E. Dykstra, J. Am. Chem. Soc., 111, 6168-6174 (1989)
MMFF
Merck Molecular Force Field. I. Basis, Form, Scope, Parameterization, and Performance of MMFF94, T. A. Halgren, J. Comput. Chem., 17, 490-516 (1996)
MOIL
MOIL: A Program for Simulations of Macromolecules, R. Elber, A. Roitberg, C. Simmerling, R. Goldstein, H. Li, G. Verkhiver, C. Keasar, J. Zhang and A. Ulitsky, Comp. Phys. Commun., 91, 159-189 (1995)
MOSCITO
Information available at the site http://139.30.122.11/MOSCITO/
NAMD
Scalable Molecular Dynamics with NAMD, J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R. D. Skeel, L. Kale and K. Schulten, J. Comput. Chem., 26, 1781-1802 (2005)
OOMPAA
OOMPAA: Object-oriented Model for Probing Assemblages of Atoms, G. A. Huber and J. A. McCammon, J. Comput. Phys., 151, 264-282 (1999)
ORAL
ORAL: All Purpose Molecular Mechanics Simulator and Energy Minimizer, K. Zimmermann, J. Comput. Chem., 12, 310-319 (1991)
ORIENT
Orient: A Program for Studying Interactions Between Molecules, Version 5.0, A. J. Stone, A. Dullweber, O. Engkvist, E. Fraschini, M. P. Hodges, A. W. Meredith, D. R. Nutt, P. L. A. Popelier and D. J. Wales, University of Cambridge, 2018
Information available at the site http://www-stone.ch.cam.ac.uk/programs.html#Orient/
PCMODEL
PCMODEL V9.0: Molecular Modeling Software, User’s Manual, Serena Software, Bloomington, IN, 2004
PEFF
PEFF: A Program for the Development of Empirical Force Fields, J. L. M. Dillen, J. Comput. Chem., 13, 257-267 (1992)
PHENIX
Macromolecular Structure Determination Using X-rays, Neutrons and Electrons: Recent Developments in Phenix, D. Liebschner, P. V. Afonine, M. L. Baker, G. Bunkóczi, V. B. Chen, T. I. Croll, B. Hintze, L.-W. Hung, S. Jain, A. J. McCoy, N. W. Moriarty, R. D. Oeffner, B. K. Poon, M. G. Prisant, R. J. Read, J. S. Richardson, D. C. Richardson, M. D. Sammito, O. V. Sobolev, D. H. Stockwell, T. C. Terwilliger, A. G. Urzhumtsev, L. L. Videau, C. J. Williams and P. D. Adams, Acta Cryst., D75, 861-877 (2019)
Q
Q: A Molecular Dynamics Program for Free Energy Calculations and Empirical Valene Bond Simulations in Biomolecular Systems, J. Marelius, K. Kolmodin, I. Feierberg and J. Aqvist, J. Mol. Graphics Modell., 16, 213-225 (1998)
SIBFA
Inter- and Intramolecular Interactions. Inception and Refinements of the SIBFA, Molecular Mechanics (SMM) Procedure, a Separable, Polarizable Methodology Grounded on ab Initio SCF/MP2 Computations. Examples of Applications to Molecular Recognition Problems, N. Gresh, J. Chim. Phys. PCB, 94, 1365-1416 (1997)
SIGMA
The Sigma MD Program and a Generic Interface Applicable to Multi-Functional Programs with Complex, Hierarchical Command Structure, G. Mann, R. Yun, L. Nyland, J. Prins, J. Board and J. Hermans, in Computational Methods for Macromolecules: Challenges and Applications, T. Schlick and H.-H. Gan, Eds., Springer, 2002
UTAH5
UTAH5: A Versatile Programme Package for the Calculation of Molecular Properties by Force Field Methods, D. H. Faber and C. Altona, Computers & Chemistry, 1, 203-213 (1977)
YAMMP
Yammp: Development of a Molecular Mechanics Program Using the Modular Programming Method, R. K.-Z. Tan and S. C. Harvey, J. Comput. Chem., 14, 455-470 (1993)
YASP
YASP: A Molecular Simulation Package, F. Mueller-Plathe, Comput. Phys. Commun., 78, 77-94 (1993)
YETI
YETI: An Interactive Molecular Mechanics Program for Small-Molecule Protein Complexes, A. Vedani, J. Comput. Chem., 9, 269-280 (1988)
Literature References by Topic¶
Molecular Mechanics Methodology¶
Molecular Mechanics, U. Burkert and N. L. Allinger, American Chemical Society, Washington, D.C., 1982
Molecular Structure: Understanding Steric and Electronic Effects from Molecular Mechanics, N. L. Allinger and D. W. Rogers, John Wiley & Sons, Hoboken, New Jersey, 2010
Molecular Modeling of Inorganic Compounds, 2nd Ed., P. Comba and T. W. Hambley, Wiley-VCH, New York, 2001
Principles of Molecular Mechanics, K. Machida, Kodansha/John Wiley & Sons, Tokyo/New York, 1999
Molecular Mechanics Across Chemistry, A. K. Rappe and C. J. Casewit, University Science Books, Sausalito, CA, 1997
Potential Energy Functions in Conformational Analysis (Lecture Notes in Chemistry, Vol. 27), K. Rasmussen, Springer-Verlag, Berlin, 1985
Intermolecular Interactions¶
The Theory of Intermolecular Forces, 2nd Ed., A. J. Stone, Oxford University Press, 2013
Intermolecular and Surface Forces, 3rd Ed., J. N. Israelachvili, Academic Press, Amsterdam, 2013
Intermolecular Forces: Their Origin and Determination, G. C. Maitland, M. Rigby, E. B. Smith and W. A. Wakeham, Oxford University Press, 1981
Computer Simulation Methodology¶
Computer Simulation of Liquids, M. P. Allen and D. J. Tildesley, Oxford University Press, Oxford, 1987
Essentials of Computational Chemistry: Theories and Models, C. J. Cramer, John Wiley and Sons, New York, 2002
A Practical Introduction to the Simulation of Molecular Systems, M. J. Field, Cambridge Univ. Press, Cambridge, 1999
Understanding Molecular Simulation: From Algorithms to Applications, 2nd Ed., D. Frankel and B. Smit, Academic Press, San Diego, CA, 2001
Molecular Dynamics Simulation: Elementary Methods, J. M. Haile, John Wiley and Sons, New York, 1992
Introduction to Computational Chemistry, F. Jensen, John Wiley and Sons, New York, 1998
Molecular Modelling: Principles and Applications, 2nd Ed., A. R. Leach, Addison Wesley Longman, Essex, England, 2001
The Art of Molecular Dynamics Simulation, 2nd Ed., D. C. Rapaport, Cambridge University Press, Cambridge, 2004
Molecular Modeling and Simulation: An Interdisciplinary Guide, 2nd Ed., T. Schlick, Springer-Verlag, New York, 2010
Modeling of Biological Macromolecules¶
Computational Biochemistry and Biophysics, O. M. Becker, A. D. MacKerell, Jr., B. Roux and M. Watanabe, Eds., Marcel Dekker, New York, 2001
Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, C. L. Brooks III, M. Karplus and B. M. Pettitt, John Wiley and Sons, New York, 1988
Protein Simulations (Advances in Protein Chemistry, Vol. 66), V. Daggett, Ed., Academic Press/Elsevier, New York, 2003
Dynamics of Proteins and Nucleic Acids, J. A. McCammon and S. Harvey, Cambridge University Press, Cambridge, 1987
Computer Simulation of Biomolecular Systems, Vol. 1-3, W. F. van Gunsteren, P. K. Weiner and A. J. Wilkinson, Kluwer Academic Publishers, Dordrecht, 1989-1997
Nonlinear Optimization Algorithms¶
Numerical Optimization, 2nd Ed., J. Nocedal and S. J. Wright, Springer-Verlag, New York, 2006
Linear and Nonlinear Programming, 2nd Ed., I. Griva, S. G. Nash and A. Sofer, SIAM, Philadelphia, 2009
Practical Methods of Optimization, R. Fletcher, John Wiley & Sons Ltd., Chichester, 1987
Linear and Nonlinear Programming, 4th Ed., D. G. Luenberger and Y. Ye, Springer, New York, 2016
Practical Optimization, P. E. Gill, W. Murray and M. H. Wright, Academic Press, New York, 1981
Updating Quasi-Newton Matrices with Limited Storage, J. Nocedal, Math. Comp., 773-782 (1980)
A Stable, Rapidly Converging Conjugate Gradient Method for Energy Minimization, S. J. Watowich, E. S. Meyer, R. Hagstrom and R. Josephs, J. Comput. Chem., 9, 650-661 (1988)
Optimally Conditioned Optimization Algorithms without Line Searches, W. C. Davidon, Math. Prog., 9, 1-30 (1975)
Truncated Newton Optimization¶
An Efficient Newton-like Method for Molecular Mechanics Energy Minimization of Large Molecules, J. W. Ponder and F. M. Richards, J. Comput. Chem., 8, 1016-1024 (1987)
Truncated-Newton Algorithms for Large-Scale Unconstrained Optimization, R. S. Dembo and T. Steihaug, Math. Prog., 26, 190-212 (1983)
Choosing the Forcing Terms in an Inexact Newton Method, S. C. Eisenstat and H. F. Walker, SIAM J. Sci. Comput., 17, 16-32 (1996)
A Powerful Truncated Newton Method for Potential Energy Minimization, T. Schlick and M. Overton, J. Comput. Chem., 8, 1025-1039 (1987)
The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations, D. S. Kershaw, J. Comput. Phys., 26, 43-65 (1978)
An Incomplete Factorization Technique for Positive Definite Linear Systems, T. A. Manteuffel, Math. Comp., 34, 473-497 (1980)
A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications, P. Derreumaux, G. Zhang and T. Schlick and B. R. Brooks, J. Comput. Chem., 15, 532-552 (1994)
Direct Methods for Sparse Matrices, I. S. Duff, A. M. Erisman and J. K. Reid, Oxford University Press, Oxford, 1986
Potential Energy Smoothing¶
Analysis and Application of Potential Energy Smoothing Methods for Global Optimization, R. V. Pappu, R. K. Hart and J. W. Ponder, J. Phys. Chem. B, 102, 9725-9742 (1998)
The Multiple-Minima Problem in the Conformational Analysis of Molecules. Deformation of the Potential Energy Hypersurface by the Diffusion Equation Method, L. Piela, J. Kostrowicki and H. A. Scheraga, J. Phys. Chem., 93, 3339-3346 (1989)
Simulated Annealing Using the Classical Density Distribution, J. Ma and J. E. Straub, J. Chem. Phys., 101, 533-541 (1994)
Cluster Structure Determination Using Gaussian Density Distribution Global Minimization Methods, C. Tsoo and C. L. Brooks, J. Chem. Phys., 101, 6405-6411 (1994)
Conformational Energy Minimization Using a Two-Stage Method, S. Nakamura, H. Hirose, M. Ikeguchi and J. Doi, J. Phys. Chem., 99, 8374-8378 (1995)
Structure Optimization Combining Soft-Core Interaction Functions, the Diffusion Equation Method, and Molecular Dynamics, T. Huber, A. E. Torda and W. F. van Gunsteren, J. Phys. Chem. A, 101, 5926-5930 (1997)
Finding Minimum-Energy Configurations of Lennard-Jones Clusters Using an Effective Potential, S. Schelstraete and H. Verschelde, J. Phys. Chem. A, 101, 310-315 (1998)
Global Optimization Using Bad Derivatives: Derivative-Free Method for Molecular Energy Minimization, I. Andricioaei and J. E. Straub, J. Comput. Chem., 19, 1445-1455 (1998)
Search for the Most Stable Structures on Potential Energy Surfaces, L. Piela, Coll. Czech. Chem. Commun., 63, 1368-1380 (1998)
“Sniffer” Global Optimization¶
Generalized Descent for Global Optimization, A. O. Griewank, J. Opt. Theor. Appl., 34, 11-39 (1981)
An Evaluation of the Sniffer Global Optimization Algorithm Using Standard Test Functions, R. A. R. Butler and E. E. Slaminka, J. Comput. Phys., 99, 28-32 (1993)
Potential Transformation Methods for Large-Scale Global Optimization, J. W. Rogers and R. A. Donnelly, SIAM J. Optim., 5, 871-891 (1995)
Integration Methods for Molecular Dynamics¶
Molecular Dynamics With Deterministic and Stochastic Numerical Methods, B. Leimkuhler and C. Matthews, Springer, New York, 2015
Pushing the Limits of Multiple-Time-Step Strategies for Polarizable Point Dipole Molecular Dynamics, L. Lagardere, F. Aviat and J.-P. Piquemal, J. Phys. Chem. Lett., 10, 2593-2599 (2019)
Some Multistep Methods for Use in Molecular Dynamics Calculations, D. Beeman, J. Comput. Phys., 20, 130-139 (1976)
Integrating the Equations of Motion, M. Levitt and H. Meirovitch, J. Mol. Biol., 168, 617-620 (1983)
A Molecular Dynamics Study of the C-Terminal Fragment of the L7/L12 Ribosomal Protein, J. Aqvist, W. F. van Gunsteren, M. Leijonmarck and O. Tapia, J. Mol. Biol., 183, 461-477 (1985)
A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules: Application to Small Water Clusters, W. C. Swope, H. C. Andersen, P. H. Berens and K. R. Wilson, J. Chem. Phys., 76, 637-649 (1982)
A Multiple-Time-Step Molecular Dynamics Algorithm for Macromolecules, D. D. Humphreys, R. A. Friesner and B. J. Berne, J. Phys. Chem., 98, 6885-6892 (1994)
Efficient Multiple-Time-Step Integrators with Distance-Based Force Splitting for Particle-Mesh-Ewald Molecular Dynamics Simulations, X. Qian and T. Schlick, J. Chem. Phys., 115, 4019-4029 (2001)
Constraint Dynamics¶
Algorithms for Macromolecular Dynamics and Constraint Dynamics, W. F. van Gunsteren and H. J. C. Berendsen, Mol. Phys., 34, 1311-1327 (1977)
Molecular Dynamics of Rigid Systems in Cartesian Coordinates: A General Formulation, G. Ciccotti, M. Ferrario and J.-P. Ryckaert, Mol. Phys., 47, 1253-1264 (1982)
Rattle: A “Velocity” Version of the Shake Algorithm for Molecular Dynamics Calculations, H. C. Andersen, J. Comput. Phys., 52, 24-34 (1983)
RATTLE Recipe for General Holonomic Constraints: Angle and Torsion Constraints, R. Kutteh, CCP5 Newsletter, 46, 9-17 (1998), available from the site https://www.ccp5.ac.uk/infoweb/newsletters/
Direct Application of SHAKE to the Velocity Verlet Algorithm, B. J. Palmer, J. Comput. Phys., 104, 470-472 (1993)
SETTLE: An Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Models, S. Miyamoto and P. A. Kollman, J. Comput. Chem., 13, 952-962 (1992)
LINCS: A Linear Constraint Solver for Molecular Simulations, B. Hess, H. Bekker, H. J. C. Berendsen and J. G. E. M. Fraaije, J. Comput. Chem., 18, 1463-1472 (1997)
Non-Iterative Constraint Dynamics using Velocity-Explicit Verlet Methods, J. T. Slusher and P. T. Cummings, Mol. Simul., 18, 213-224 (1996)
Langevin, Brownian and Stochastic Dynamics¶
Brownian Dynamics Simulation of a Chemical Reaction in Solution, M. P. Allen, Mol. Phys., 40, 1073-1087 (1980)
Algorithms for Brownian Dynamics, W. F. van Gunsteren and H. J. C. Berendsen, Mol. Phys., 45, 637-647 (1982)
A Rapidly Convergent Simulation Method: Mixed Monte Carlo/Stochastic Dynamics, F. Guarnieri and W. C. Still, J. Comput. Chem., 15, 1302-1310 (1994)
Constant Temperature Simulations using the Langevin Equation with Velocity Verlet Integration, M. G. Paterlini and D. M. Ferguson, Chem. Phys., 236, 243-252 (1998)
Constant Temperature and Pressure Dynamics¶
Molecular Dynamics with Coupling to an External Bath, H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola and J. R. Haak, J. Chem. Phys., 81, 3684-3690 (1984)
Canonical Dynamics: Equilibrium Phase-space Distributions, W. G. Hoover, Phys. Rev. A, 31, 1695-1697 (1985)
Computer Simulation of a Phase Transition at Constant Temperature and Pressure, J. J. Morales, S. Toxvaerd and L. F. Rull, Phys. Rev. A, 34, 1495-1498 (1986)
Algorithms for Molecular Dynamics at Constant Temperature and Pressure, B. R. Brooks, Internal Report of Division of Computer Research and Technology, National Institutes of Health, 1988.
Molecular Dynamics of Native Protein: Computer Simulation of Trajectories, M. Levitt, J. Mol. Biol., 168, 595-620 (1983)
Out-of-Plane Deformation Terms¶
Derivation of Force Fields for Molecular Mechanics and Dynamics from ab initio Energy Surfaces, J. R. Maple, U. Dinar and A. T. Hagler, Proc. Natl. Acad. Sci. USA, 85, 5350-5354 (1988)
New Out-of-Plane Angle and Bond Angle Internal Coordinates and Related Potential Energy Functions for Molecular Mechanics and Dynamics Simulations, S.-H. Lee, K. Palmo and S. Krimm, J. Comput. Chem., 20, 1067-1084 (1999)
Geometry-Dependent Charge Flux Terms¶
Geometry-Dependent Atomic Charges: Methodology and Application to Alkanes, Aldehydes, Ketones, and Amides, U. Dinar and A. T. Hagler, J. Comput. Chem., 16, 154-170 (1995)
Inclusion of Charge and Polarizability Fluxes Provides Needed Physical Accuracy in Molecular Mechanics Force Fields, K. Palmo, B. Mannifors, N. G. Mirkin and S. Krimm, Chem. Phys. Lett., 429, 628-632 (2006)
Implementation of Geometry-Dependent Charge Flux into the Polarizable AMOEBA+ Potential, C. Liu, J.-P. Piquemal and P. Ren, J. Phys. Chem. Lett., 11, 419-426 (2020)
Analytical Derivatives of Potential Functions¶
First and Second Derivative Matrix Elements for the Stretching, Bending, and Torsional Energy, K. J. Miller, R. J. Hinde and J. Anderson, J. Comput. Chem., 10, 63-76 (1989)
Alternative Expressions for Energies and Forces Due to Angle Bending and Torsional Energy, Report G320-3561, W. C. Swope and D. M. Ferguson, J. Comput. Chem., 13, 585-594 (1992)
New Formulation for Derivatives of Torsion Angles and Improper Torsion Angles in Molecular Mechanics: Elimination of Singularities, A. Blondel and M. Karplus, J. Comput. Chem., 17, 1132-1141 (1996)
Efficient Treatment of Out-of-Plane Bend and Improper Torsion Interactions in MM2, MM3, and MM4 Molecular Mechanics Calculations, R. E. Tuzun, D. W. Noid and B. G. Sumpter, J. Comput. Chem., 18, 1804-1811 (1997)
Torsional Space Derivatives and Normal Modes¶
Protein Normal-mode Dynamics: Trypsin Inhibitor, Crambin, Ribonuclease and Lysozyme, M. Levitt, C. Sander and P. S. Stern, J. Mol. Biol., 181, 423-447 (1985)
Protein Folding by Restrained Energy Minimization and Molecular Dynamics, M. Levitt, J. Mol. Biol., 170, 723-764 (1983)
Algorithm for Rapid Calculation of Hessian of Conformational Energy Function of Proteins by Supercomputer, H. Wako and N. Go, J. Comput. Chem., 8, 625-635 (1987)
Rapid Calculation of First and Second Derivatives of Conformational Energy with Respect to Dihedral Angles for Proteins: General Recurrent Equations, H. Abe, W. Braun, T. Noguti and N. Go, Computers & Chemistry, 8, 239-247 (1984)
A Method of Rapid Calculation of a Second Derivative Matrix of Conformational Energy for Large Molecules, T. Noguti and N. Go, J. Phys. Soc. Japan, 52, 3685-3690 (1983)
Analytical Surface Area and Volume¶
Analytical Molecular Surface Calculation, M. L. Connolly, J. Appl. Cryst., 16, 548-558 (1983)
Computation of Molecular Volume, M. L. Connolly, J. Am. Chem. Soc., 107, 1118-1124 (1985)
Molecular Surfaces: A Review, M. L. Connolly, available from the site https://web.archive.org/web/20120311082019/http://www.netsci.org/Science/Compchem/feature14.html/
Algorithms for Calculating Excluded Volume and Its Derivatives as a Function of Molecular Conformation and Their Use in Energy Minimization, C. E. Kundrot, J. W. Ponder and F. M. Richards, J. Comput. Chem., 12, 402-409 (1991)
Solvent Accessible Surface Area and Excluded Volume in Proteins, T. J. Richmond, J. Mol. Biol., 178, 63-89 (1984)
Atomic Solvation Parameters Applied to Molecular Dynamics of Proteins in Solution, L. Wesson and D. Eisenberg, Protein Science, 1, 227-235 (1992)
Implementation of Solvent Effect in Molecular Mechanics, Part 3. The First- and Second-order Analytical Derivatives of Excluded Volume, V. Gononea and E. Osawa, J. Mol. Struct. (Theochem), 311 305-324 (1994)
Exact Calculation of the Volume and Surface Area of Fused Hard-sphere Molecules with Unequal Atomic Radii, K. D. Gibson and H. A. Scheraga, Mol. Phys., 62, 1247-1265 (1987)
Surface Area of the Intersection of Three Spheres with Unequal Radii: A Simplified Analytical Formula, K. D. Gibson and H. A. Scheraga, Mol. Phys., 64, 641-644 (1988)
A Rapid Method for Calculating Derivatives of Solvent Accessible Surface Areas of Molecules, S. Sridharan, A. Nichols and K. A. Sharp, J. Comput, Chem., 16, 1038-1044 (1995)
Approximate Surface Area and Volume¶
Analytical Approximation to the Accessible Surface Area of Proteins, S. J. Wodak and J. Janin, Proc. Natl. Acad. Sci. USA, 77, 1736-1740 (1980)
A Rapid Approximation to the Solvent Accessible Surface Areas of Atoms, W. Hasel, T. F. Hendrickson and W. C. Still, Tetrahedron Comput. Method., 1, 103-116 (1988)
Approximate Solvent-Accessible Surface Areas from Tetrahedrally Directed Neighber Densities, J. Weiser, P. S. Shenkin and W. C. Still, Biopolymers, 50, 373-380 (1999)
Boundary Conditions and Neighbor Methods¶
On Searching Neighbors in Computer Simulations of Macromolecular Systems, W. F. van Gunsteren, H. J. C. Berendsen, F. Colonna, D. Perahia, J. P. Hollenberg and D. Lellouch, J. Comput. Chem., 5, 272-279 (1984)
Molecular Dynamics on Vector Computers, F. Sullivan, R. D. Mountain and J. O’Connell, J. Comput. Phys., 61, 138-153 (1985)
A Vectorized “Near Neighbors” Algorithm of Order N Using a Monotonic Logical Grid, J. Boris, J. Comput. Phys., 66, 1-20 (1986)
Geometric Properties of the Monotonic Lagrangian Grid Algorithm for Near Neighbors Calculations, S. G. Lambrakos and J. P. Boris, J. Comput. Phys., 73, 183-202 (1987)
The Role of Long Ranged Forces in Determining the Structure and Properties of Liquid Water, T. A. Andrea, W. C. Swope and H. C. Andersen, J. Chem. Phys., 79, 4576-4584 (1983)
Geometrical Considerations in Model Systems with Periodic Boundary Conditions, D. N. Theodorou and U. W. Suter, J. Chem. Phys., 82, 955-966 (1985)
A Hierarchical O(NlogN) Force-calculation Algorithm, J. Barnes and P. Hut, Nature, 234, 446-449 (1986)
Cutoff and Truncation Methods¶
New Spherical-Cutoff Methods for Long-Range Forces in Macromolecular Simulation, P. J. Steinbach and B. R. Brooks, J. Comput. Chem., 15, 667-683 (1993)
The Effects of Truncating Long-Range Forces on Protein Dynamics, R. J. Loncharich and B. R. Brooks, Proteins, 6, 32-45 (1989)
Structural and Energetic Effects of Truncating Long Ranged Interactions in Ionic and Polar Fluids, C. L. Brooks III, B. M. Pettitt and M. Karplus, J. Chem. Phys., 83, 5897-5908 (1985)
Ewald Summation Techniques¶
Ewald Summation Techniques in Perspective: A Survey, A. Y. Toukmaji and J. A. Board, Jr., Comp. Phys. Commun., 95, 73-92 (1996)
New Tricks for Modelers from the Crystallography Toolkit: The Particle Mesh Ewald Algorithm and its Use in Nucleic Acid Simulations, T. Darden, L. Perera, L. Li and L. Pedersen, Structure, 7, R550-R60 (1999)
Particle Mesh Ewald: An Nlog(N) Method for Ewald Sums in Large Systems, T. Darden, D. York and L. G. Pedersen, J. Chem. Phys., 98, 10089-10092 (1993)
A Smooth Particle Mesh Ewald Method, U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee and L. G. Pedersen, J. Chem. Phys., 103, 8577-8593 (1995)
Point Multipoles in the Ewald Summation (Revisited), W. Smith, CCP5 Newsletter, 46, 18-30 (1998), available at the site https://www.ccp5.ac.uk/infoweb/newsletters/
Effect of Electrostatic Force Truncation on Interfacial and Transport Properties of Water, S. E. Feller, R. W. Pastor, A. Rojnuckarin, S. Bogusz and B. R. Brooks, J. Phys. Chem., 100, 17011-17020 (1996)
Molecular Dynamics Simulations of a Polyalanine Octapeptide under Ewald Boundary Conditions: Influence of Artificial Periodicity on Peptide Conformation, W. Weber, P. H. Hunenberger and J. A. McCammon, J. Phys. Chem. B, 104, 3668-3675 (2000)
Conjugated and Aromatic Systems¶
Molecular Mechanics (MM3) Calculations on Conjugated Hydrocarbons, N. L. Allinger, F. Li, L. Yan and J. C. Tai, J. Comput. Chem., 11, 868-895 (1990)
The MMP2 Calculational Method, J. T. Sprague, J. C. Tai, Y. Yuh and N. L. Allinger, J. Comput. Chem., 8, 581-603 (1987)
A Molecular Orbital Based Molecular Mechanics Approach to Study Conjugated Hydrocarbons, J. Kao, J. Am. Chem. Soc., 109, 3818-3829 (1987)
Conformational Analysis: Heats of Formation of Conjugated Hydrocarbons by the Force Field Method, J. Kao and N. L. Allinger, J. Am. Chem. Soc., 99, 975-986 (1977)
Accurate Heats of Atomization and Accurate Bond Lengths: Benzenoid Hydrocarbons, D. H. Lo and M. A. Whitehead, Can. J. Chem., 46, 2027-2040 (1968)
Hetero-atomic Molecules: Semi-empirical Molecular Orbital Calculations and Prediction of Physical Properties, G. D. Zeiss and M. A. Whitehead, J. Chem. Soc. A, 1727-1738 (1971)
Free Energy Simulation Methods¶
Free Energy Calculations: Applications to Chemical and Biochemical Phenomena, P. Kollman, Chem. Rev., 93, 2395-2417 (1993)
Ligand-Receptor Interactions, B. L. Tembe and J. A. McCammon, Computers & Chemistry, 8, 281-283 (1984)
Monte Carlo Simulation of Differences in Free Energy of Hydration, W. L. Jorgensen and C. Ravimohan, J. Chem. Phys., 83, 3050-3054 (1985)
Efficient Computation of Absolute Free Energies of Binding by Computer Simulations: Application to the Methane Dimer in Water, W. L. Jorgensen, J. K. Buckner, S. Boudon and J. Tirado-Rives, J. Chem. Phys., 89, 3742-3746 (1988)
Thermodynamics of Aqueous Solvation: Solution Properties of Alcohols and Alkanes, S. H. Fleischman and C. L. Brooks III, J. Chem. Phys., 87, 3029-3037 (1987)
An Approach to the Application of Free Energy Perturbation Methods Using Molecular Dynamics, U. C. Singh, F. K. Brown, P. A. Bash and P. A. Kollman, J. Am. Chem. Soc., 109, 1607-1614 (1987)
A New Method for Carrying out Free Energy Perturbation Calculations: Dynamically Modified Windows, D. A. Pearlman and P. A. Kollman, J. Chem. Phys., 90, 2460-2470 (1989)
Free Energy of Hydrophobic Hydration: A Molecular Dynamics Study of Noble Gases in Water, T. P. Straatsma, H. J. C. Berendsen and J. P. M. Postma, J. Chem. Phys., 85, 6720-6727 (1986)
Free Energy of Ionic Hydration: Analysis of a Thermodynamic Integration Technique to Evaluate Free Energy Differences by Molecular Dynamics Simulations, T. P. Straatsma and H. J. C. Berendsen, J. Chem. Phys., 89, 5876-5886 (1988)
The Finite Difference Thermodynamic Integration, Tested on Calculating the Hydration Free Energy Difference between Acetone and Dimethylamine in Water, M. Mezei, J. Chem. Phys., 86, 7084-7088 (1987)
Decomposition of the Free Energy of a System in Terms of Specific Interactions, A. E. Mark and W. F. van Gunsteren, J. Mol. Biol., 240, 167-176 (1994)
The Meaning of Copmponent Analysis: Decomposition of the Free Energy in Terms of Specific Interactions, S. Boresch and M. Karplus, J. Mol. Biol., 254, 801-807 (1995)
Methods for Parameter Determination¶
Molecular Mechanics Parameters, N. L. Allinger, X. Zhou and J. Bergsma, J. Mol. Struct. (THEOCHEM), 312, 69-83 (1994)
The Atom-Atom Potential Method: Application to Organic Molecular Solids, A. J. Pertsin and A. I. Kitaigorodsky, Springer-Verlag, Berlin, 1987
Transferable Empirical Nonbonded Potential Functions, D. E. Williams, in Crystal Cohesion and Conformational Energies, Ed. by R. M. Metzger, Springer-Verlag, Berlin, 1981
A Procedure for Obtaining Energy Parameters from Crystal Packing, A. T. Hagler and S. Lifson, Acta Cryst., B30, 1336-1341 (1974)
Consistent Force Field Studies of Intermolecular Forces in Hydrogen-Bonded Crystals: A Benchmark for the Objective Comparison of Alternative Force Fields, A. T. Hagler, S. Lifson and P. Dauber, J. Am. Chem. Soc., 101, 5122-5130 (1979)
Optimized Intermolecular Potential Functions for Liquid Hydrocarbons, W. L. Jorgensen, J. D. Madura and C. J. Swenson, J. Am. Chem. Soc., 106, 6638-6646 (1984)
Optimized Intermolecular Potential Functions for Amides and Peptides: Structure and Properties of Liquid Amides, W. L. Jorgensen and C. J. Swenson, J. Am. Chem. Soc., 107, 569-578 (1985)
Derivation of Force Fields for Molecular Mechanics and Dynamics from ab Initio Surfaces, J. R. Maple, U. Dinur and A. T. Hagler, Proc. Nat. Acad. Sci. USA, 85, 5350-5354 (1988)
Direct Evaluation of Nonbonding Interactions from ab Initio Calculations, U. Dinur and A. T. Hagler, J. Am. Chem. Soc., 111, 5149-5151 (1989)
Electrostatic Interactions¶
Towards More Accurate Model Intermolecular Potentials for Organic Molecules, S. L. Price, Rev. Comput. Chem., 14, 225-289 (2000)
A Transferable Distributed Multipole Model for the Electrostatic Interactions of Peptides and Amides, C. H. Faerman and S. L. Price, J. Am. Chem. Soc., 112, 4915-4926 (1990)
Electrostatic Interaction Potentials in Molecular Force Fields, C. E. Dykstra, Chem. Rev., 93, 2339-2353 (1993)
Accurate Modeling of the Intramolecular Electrostatic Energy of Proteins, M. J. Dudek and J. W. Ponder, J. Comput. Chem., 16, 791-816 (1995)
An Improved Description of the Molecular Charge Density in Force Fields with Atomic Multipole Moments, U. Koch and E. Egert, J. Comput. Chem., 16, 937-944 (1995)
Representation of the Molecular Electrostatic Potential by Atomic Multipole and Bond Dipole Models, D. E. Williams, J. Comput. Chem., 9, 745-763 (1988)
Critical Analysis of Electric Field Modeling: Formamide, F. Colonna, E. Evleth and J. G. Angyan, J. Comput. Chem., 13, 1234-1245 (1992)
Polarization Effects¶
Incorporating Electric Polarizabilities in Water-Water Interaction Potentials, S. Kuwajima and A. Warshel, J. Phys. Chem., 94, 460-466 (1990)
Structure and Properties of Neat Liquids Using Nonadditive Molecular Dynamics: Water, Methanol, and N-Methylacetamide, J. W. Caldwell and P. A. Kollman, J. Phys. Chem., 99, 6208-6219 (1995)
An Anisotropic Polarizable Water Model: Incorporation of All-Atom Polarizabilities into Molecular Mechanics Force Fields, D. N. Bernardo, Y. Ding, K. Kroegh-Jespersen and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994)
Molecular and Atomic Polarizabilities: Thole’s Model Revisited, P. T. van Duijnen and M. Swart, J. Phys. Chem. A, 102, 2399-2407 (1998)
Calculation of the Molecular Polarizability Tensor, K. J. Miller, J. Am. Chem. Soc., 112, 8543-8551 (1990)
An Atom Dipole Interaction Model for Molecular Polarizability. Application to Polyatomic Molecules and Determination of Atom Polarizabilities, J. Applequist, J. R. Carl and K.-K. Fung, J. Am. Chem. Soc., 94, 2952-2960 (1972)
Atom Charge Transfer in Molecular Polarizabilities. Application of the Olson-Sundberg Model to Aliphatic and Aromatic Hydrocarbons, J. Applequist, J. Phys. Chem., 97, 6016-6023 (1993)
Distributed Polarizabilities, A. J. Stone, Mol. Phys., 56, 1065-1082 (1985)
A Distributed Model of the Electrical Response of Organic Molecules, J. M. Stout and C. E. Dykstra, J. Phys. Chem. A, 102, 1576-1582 (1998)
Macroscopic Treatment of Solvent¶
Continuum Solvation Models: Classical and Quantum Mechanical Implementations, C. J. Cramer and D. G. Truhlar, Rev. Comput. Chem., 6, 1-72 (1995)
Implicit Solvation Models, B. Roux and T. Simonson, Biophys. Chem., 78, 1-20 (1999)
Introduction to Continuum Electrostatics with Molecular Applications, M. K. Gilson, available at the site http://gilsonlab.umbi.umd.edu/
Surface Area-Based Solvation Models¶
Solvation Energy in Protein Folding and Binding, D. Eisenberg and A. D. McLachlan, Nature, 319, 199-203 (1986)
Atomic Solvation Parameters Applied to Molecular Dynamics of Proteins in Solution, L. Wesson and D. Eisenberg, Prot. Sci., 1, 227-235 (1992)
Accessible Surface Areas as a Measure of the Thermodynamic Parameters of Hydration of Peptides, T. Ooi, M. Oobatake, G. Nemethy and H. A. Scheraga, Proc. Natl. Acad. Sci. USA, 84, 3086-3090 (1987)
An Efficient, Differentiable Hydration Potential for Peptides and Proteins, J. D. Augspurger and H. A. Scheraga, J. Comput. Chem., 17, 1549-1558 (1996)
Generalized Born Solvation Models¶
A Semiempirical Treatment of Solvation for Molecular Mechanics and Dynamics, W. C. Still, A. Tempczyk, R. C. Hawley and T. Hendrickson, J. Am. Chem. Soc., 112, 6127-6129 (1990)
The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii, D. Qiu, P. S. Shenkin, F. P. Hollinger and W. C. Still, J. Phys. Chem. A, 101, 3005-3014 (1997)
Pairwise Solute Descreening of Solute Charges from a Dielectric Medium, G. D. Hawkins, C. J. Cramer and D. G. Truhlar, Chem. Phys. Lett., 246, 122-129 (1995)
Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium, G. D. Hawkins, C. J. Cramer and D. G. Truhlar, J. Phys. Chem., 100, 19824-19839 (1996)
Modification of the Generalized Born Model Suitable for Macromolecules, A. Onufriev, D. Bashford and D. A. Case, J. Phys. Chem. B, 104, 3712-3720 (2000)
A Comprehensive Analytical Treatment of Continuum Electrostatics, M. Schaefer and M. Karplus, J. Phys. Chem., 100, 1578-1599 (1996)
Solution Conformations and Thermodynamics of Structured Peptides: Molecular Dynamics Simulation with an Implicit Solvation Model, M. Schaefer, C. Bartels and M. Karplus, J. Mol. Biol., 284, 835-848 (1998)
Superposition of Coordinate Sets¶
An Algorithm for the Simultaneous Superposition of a Structural Series, S. J. Kearsley, J. Comput. Chem., 11, 1187-1192 (1990)
A Note on the Rotational Superposition Problem, R. Diamond, Acta Cryst., A44, 211-216 (1988)
Rapid Comparison of Protein Structures, A. D. McLachlan, Acta Cryst., A38, 871-873 (1982)
Some Uses of a Best Molecular Fit Routine, S. C. Nyburg, Acta Cryst., B30, 251-253 (1974)
Location of Transition States¶
Reaction Path Study of Conformational Transitions and Helix Formation in a Tetrapeptide, R. Czerminski and R. Elber, Proc. Nat. Acad. Sci. USA, 86, 6963 (1989)
Finding Saddles on Multidimensional Potential Surfaces, R. S. Berry, H. L. Davis and T. L. Beck, Chem. Phys. Lett., 147, 13 (1988)
Reaction Paths on Multidimensional Energy Hypersurfaces, K. Muller, Ang. Chem. Int. Ed. Engl., 19, 1-13 (1980)
Locating Transition States, S. Bell and J. S. Crighton, J. Chem. Phys., 80, 2464-2475 (1984)
Conjugate Peak Refinement: An Algorithm for Finding Reaction Paths and Accurate Transition States in Systems with Many Degrees of Freedom, S. Fischer and M. Karplus, Chem. Phys. Lett., 194, 252-261 (1992)
A New Method of Saddle-Point Location for the Calculation of Defect Migration Energies, J. E. Sinclair and R. Fletcher, J. Phys. C, 7, 864-870 (1974)
A Method for Determining Reaction Paths in Large Molecules: Application to Myoglobin, R. Elber and M. Karplus, Chem. Phys. Lett., 139, 375-380 (1987)
On Finding Stationary States on Large-Molecule Potential Energy Surfaces, D. T. Nguyen and D. A. Case, J. Phys. Chem., 89, 4020-4026 (1985)
The Synchronous-Transit Method for Determining Reaction Pathways and Locating Molecular Transition States, T. A. Halgren and W. N. Lipscomb, Chem. Phys. Lett., 49, 225-232 (1977)
Event-Based Relaxation of Continuous Disordered Systems, G. T. Barkema and N. Mousseau, Phys. Rev. Lett., 77, 4358-4361 (1996)