the goodman group
university of cambridge  

   references & suggested reading


15. References & Suggested Reading

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.


Peter Kollman, University of California, San Francisco

Rob Harrison, Thomas Jefferson University, Philadelphia

Andy McCammon, University of California, San Diego

William Jorgensen, Yale University

Shoshona Wodak, Free University of Brussels

Shneior Lifson, Weizmann Institute

Martin Karplus, Harvard University

Bernard Brooks, National Institutes of Health, Bethesda

Bastian van de Graaf, Delft University of Technology

Molecular Simulations Inc., San Diego

W. Smith & T. Forester, CCP5, Daresbury Laboratory

Harold Scheraga, Cornell University

Michael Levitt, Stanford University

Werner Braun, University of Texas, Galveston

Nobuhiro Go, Kyoto University

Herman Berendsen, University of Groningen

Wilfred van Gunsteren, BIOMOS and ETH, Zurich

Ronald Levy, Rutgers University

Schodinger, Inc., Jersey City, New Jersey

N. Lou Allinger, University of Georgia

Cliff Dykstra, Indiana Univ.-Purdue Univ. at Indianapolis

Tom Halgren, Merck Research Laboratories, Rahway

Konrad Hinsen, Inst. of Structural Biology, Grenoble

Ron Elber, Cornell University

Arieh Warshal, University of Southern California

Keith Refson, Oxford University

Dietmar Paschek & Alfons Geiger, Universität Dortmund

Klaus Schulten, University of Illinois, Urbana

Andy McCammon, University of California, San Diego

Karel Zimmerman, INRA, Jouy-en-Josas, France

Anthony Stone, Cambridge University

Kevin Gilbert, Serena Software, Bloomington, Indiana

Jan Dillen, University of Pretoria, South Africa

Johan Åqvist, Uppsala University

Nohad Gresh, INSERM, CNRS, Paris

Jan Hermans, University of North Carolina

Gerard Vergoten, Université de Lille

David Spellmeyer and the Kollman Group, UCSF

Jay Ponder, Washington University, St. Louis

Axel Brünger, Stanford University

Stephen Harvey, University of Alabama, Birmingham

Florian Mueller-Plathe, ETH Zentrum, Zurich

Angelo Vedani, Biografik-Labor 3R, Basel

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, 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, Comp. Phys. Commun. , 91, 1-41 (1995)

T. P. Straatsma and J. A. McCammon, ARGOS, a Vectorized General Molecular Dynamics Program, J. Comput. Chem. , 11, 943-951 (1990)

B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan and M. Karplus, CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations, J. Comput. Chem. , 4, 187-217 (1983)

M. Levitt, M. Hirshberg, R. Sharon and V. Daggett, Potential Energy Function and Parameters for Simulations for the Molecular Dynamics of Proteins and Nucleic Acids in Solution, Comp. Phys. Commun. , 91, 215-231 (1995)

T. Schaumann, W. Braun and K. Wurtrich, The Program FANTOM for Energy Refinement of Polypeptides and Proteins Using a Newton-Raphson Minimizer in Torsion Angle Space, Biopolymers, 29, 679-694 (1990)

H. Wako, S. Endo, K. Nagayama and N. Go, FEDER/2: Program for Static and Dynamic Conformational Energy Analysis of Macro-molecules in Dihedral Angle Space, Comp. Phys. Commun. , 91, 233-251 (1995)

H. J. C. Berendsen, D. van der Spoel and R. van Drunen, GROMACS: A Message-passing Parallel Molecular Dynamics Implementation, Comp. Phys. Commun. , 91, 43-56 (1995)

GROMOS 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, The GROMOS Biomolecular Simulation Program Package, J. Phys. Chem. A, 103, 3596-3607 (1999)

D. B. Kitchen, F. Hirata, J. D. Westbrook, R. Levy, D. Kofke and M. Yarmush, Conserving Energy during Molecular Dynamics Simulations of Water, Proteins, and Proteins in Water, J. Comput. Chem. , 10, 1169-1180 (1990)

F. Mahamadi, N. G. J. Richards, W. C. Guida, R. Liskamp, M. Lipton, C. Caufield, G. Chang, T. Hendrickson and W. C. Still, MacroModel-An Integrated Software System for Modeling Organic and Bioorganic Molecules Using Molecular Mechanics, J. Comput. Chem. , 11, 440-467 (1990)

N. L. Allinger, Conformational Analysis. 130. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms, J. Am. Chem. Soc. , 99, 8127-8134 (1977)

N. L. Allinger, Y. H. Yuh and J.-H. Lii, Molecular Mechanics. The MM3 Force Field for Hydrocarbons, J. Am. Chem. Soc. , 111, 8551-8566 (1989)

N. L. Allinger, K. Chen and J.-H. Lii, An Improved Force Field (MM4)

for Saturated Hydrocarbons, J. Comput. Chem. , 17, 642-668 (1996)

C. E. Dykstra, Molecular Mechanics for Weakly Interacting Assemblies of Rare Gas Atoms and Small Molecules, J. Am. Chem. Soc. , 111, 6168-6174 (1989)

T. A. Halgren, Merck Molecular Force Field. I. Basis, Form, Scope, Parameterization, and Performance of MMFF94, J. Comput. Chem. , 17, 490-516 (1996)

R. Elber, A. Roitberg, C. Simmerling, R. Goldstein, H. Li, G. Verkhiver, C. Keasar, J. Zhang and A. Ulitsky, MOIL: A Program for Simulations of Macromolecules, Comp. Phys. Commun., 91, 159-189 (1995)

See the web site at http:/

L. Kalé, R. Skeel, M. Bhandarkar, R. Brunner, A. Gursoy, N. Krawetz, J. Phillips, A. Shinozaki, K. Varadarajan and K. Schulten, NAMD2: Greater Scalability for Parallel Molecular Dynamics, J. Comput. Phys. , 151, 283-312 (1999)

G. A. Huber and J. A. McCammon, OOMPAA-Object-oriented Model for Probing Assemblages of Atoms, J. Comput. Phys. , 151, 264-282 (1999)

K. Zimmermann, ORAL: All Purpose Molecular Mechanics Simulator and Energy Minimizer, J. Comput. Chem. , 12, 310-319 (1991)

See the web site at http:/

J. L. M. Dillen, PEFF: A Program for the Development of Empirical Force Fields, J. Comput. Chem. , 13, 257-267 (1992)

See the web site at

N. Gresh, 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, J. Chim. Phys. PCB , 94, 1365-1416 (1997)

See the web site at

P. Derreumaux and G. Vergoten, A New Spectroscopic Molecular Mechanics Force-Field - Parameters For Proteins, J. Chem. Phys. , 102, 8586-8605 (1995)

See the web site at

R. K.-Z. Tan and S. C. Harvey, Yammp: Development of a Molecular Mechanics Program Using the Modular Programming Method, J. Comput. Chem. , 14, 455-470 (1993)

A. Vedani, YETI: An Interactive Molecular Mechanics Program for Small-Molecule Protein Complexes, J. Comput. Chem. , 9, 269-280 (1988)


U. Burkert and N. L. Allinger, Molecular Mechanics , American Chemical Society, Washington, D.C., 1982

K. Rasmussen, Potential Energy Functions in Conformational Analysis (Lecture Notes in Chemistry, Vol. 27)

, Springer-Verlag, Berlin, 1985

A. K. Rappé and C. J. Casewit, Molecular Mechanics across Chemistry , University Science Books, Sausalito, CA, 1997

K. Machida, Principles of Molecular Mechanics , Kodansha/John Wiley & Sons, Tokyo/New York, 1999

P. Comba and T. W. Hambley, Molecular Modeling of Inorganic Compounds , VCH, New York, 1995


M. J. Field, A Practical Introduction to the Simulation of Molecular Systems, Cambridge Univ. Press, Cambridge, 1999

A. R. Leach, Molecular Modelling: Principles and Applications , Addison Wesley Longman, Essex, England, 1996

D. Frankel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, San Diego, CA, 1996

D. C. Rapaport, The Art of Molecular Dynamics Simulation , Cambridge University Press, Cambridge, 1995

J. M. Haile, Molecular Dynamics Simulation , John Wiley and Sons, New York, 1992

M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids , Oxford University Press, Oxford, 1987

T. Schlick, R. D. Skeel, A. T. Brünger, L. V. Kale, J. A. Board, J. Hermans and K. Schulten, Algorithmic Challenges in Computational Molecular Biophysics, J. Comput. Phys. , 151, 9- 48 (1999)


J. A. McCammon and S. Harvey, Dynamics of Proteins and Nucleic Acids , Cambridge University Press, Cambridge, 1987

C. L. Brooks III, M. Karplus and B. M. Pettitt, Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics , John Wiley and Sons, New York, 1988

W. F. van Gunsteren, P. K. Weiner and A. J. Wilkinson, Computer Simulation of Biomolecular Systems, Vol. 1-3 , Kluwer Academic Publishers, Dordrecht, 1989-1997

T. E. Cheatham and B. R. Brooks, Recent Advances in Molecular Dynamics Simulation towards the Realistic Representation of Biomolecules in Solution, Theor. Chem. Acc. , 99, 279-288 (1998)


J. Nocedal and S. J. Wright, Numerical Optimization , Springer-Verlag, New York, 1999

S. G. Nash and A. Sofer, Linear and Nonlinear Programming , McGraw-Hill, New York, 1996

R. Fletcher, Practical Methods of Optimization , John Wiley & Sons Ltd., Chichester, 1987

D. G. Luenberger, Linear and Nonlinear Programming , 2nd Ed., Addison-Wesley, Reading, MA, 1984

P. E. Gill, W. Murray and M. H. Wright, Practical Optimization , Academic Press, New York, 1981

J. Nocedal, Updating Quasi-Newton Matrices with Limited Storage, Math. Comp. , 773-782 (1980)

S. J. Watowich, E. S. Meyer, R. Hagstrom and R. Josephs, A Stable, Rapidly Converging Conjugate Gradient Method for Energy Minimization, J. Comput. Chem. , 9, 650-661 (1988)

W. C. Davidon, Optimally Conditioned Optimization Algorithms without Line Searches, Math. Prog. , 9, 1-30 (1975)


J. W. Ponder and F. M. Richards, An Efficient Newton-like Method for Molecular Mechanics Energy Minimization of Large Molecules, J. Comput. Chem. , 8, 1016-1024 (1987)

R. S. Dembo and T. Steihaug, Truncated-Newton Algorithms for Large-Scale Unconstrained Optimization, Math. Prog. , 26, 190-212 (1983)

S. C. Eisenstat and H. F. Walker, Choosing the Forcing Terms in an Inexact Newton Method, SIAM J. Sci. Comput. , 17, 16-32 (1996)

T. Schlick and M. Overton, A Powerful Truncated Newton Method for Potential Energy Minimization, J. Comput. Chem. , 8, 1025-1039 (1987)

D. S. Kershaw, The Incomplete Cholesky-Conjugate Gradient Method for the Iterative Solution of Systems of Linear Equations, J. Comput. Phys. , 26, 43-65 (1978)

T. A. Manteuffel, An Incomplete Factorization Technique for Positive Definite Linear Systems, Math. Comp. , 34, 473-497 (1980)

P. Derreumaux, G. Zhang and T. Schlick and B. R. Brooks, A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications, J. Comput. Chem. , 15, 532-552 (1994)

I. S. Duff, A. M. Erisman and J. K. Reid, Direct Methods for Sparse Matrices , Oxford University Press, Oxford, 1986


R. V. Pappu, R. K. Hart and J. W. Ponder, Analysis and Application of Potential Energy Smoothing Methods for Global Optimization, J. Phys. Chem. B , 102, 9725-9742 (1998)

L. Piela, J. Kostrowicki and H. A. Scheraga, The Multiple-Minima Problem in the Conformational Analysis of Molecules. Deformation of the Potential Energy Hypersurface by the Diffusion Equation Method, J. Phys. Chem. , 93, 3339-3346 (1989)

J. Ma and J. E. Straub, Simulated Annealing Using the Classical Density Distribution, J. Chem. Phys. , 101, 533-541 (1994)

C. Tsoo and C. L. Brooks, Cluster Structure Determination Using Gaussian Density Distribution Global Minimization Methods, J. Chem. Phys. , 101, 6405-6411 (1994)

S. Nakamura, H. Hirose, M. Ikeguchi and J. Doi, Conformational Energy Minimization Using a Two-Stage Method, J. Phys. Chem. , 99, 8374-8378 (1995)

T. Huber, A. E. Torda and W. F. van Gunsteren, Structure Optimization Combining Soft- Core Interaction Functions, the Diffusion Equation Method, and Molecular Dynamics, J. Phys. Chem. A , 101, 5926-5930 (1997)

S. Schelstraete and H. Verschelde, Finding Minimum-Energy Configurations of Lennard- Jones Clusters Using an Effective Potential, J. Phys. Chem. A , 101, 310-315 (1998)

I. Andricioaei and J. E. Straub, Global Optimization Using Bad Derivatives: Derivative-Free Method for Molecular Energy Minimization, J. Comput. Chem. , 19, 1445-1455 (1998)

L. Piela, Search for the Most Stable Structures on Potential Energy Surfaces, Coll. Czech. Chem. Commun. , 63, 1368-1380 (1998)


A. O. Griewank, Generalized Descent for Global Optimization, J. Opt. Theor. Appl. , 34, 11- 39 (1981)

R. A. R. Butler and E. E. Slaminka, An Evaluation of the Sniffer Global Optimization Algorithm Using Standard Test Functions, J. Comput. Phys. , 99, 28-32 (1993)

J. W. Rogers and R. A. Donnelly, Potential Transformation Methods for Large-Scale Global Optimization, SIAM J. Optim. , 5, 871-891 (1995)


D. Beeman, Some Multistep Methods for Use in Molecular Dynamics Calculations, J. Comput. Phys. , 20, 130-139 (1976)

M. Levitt and H. Meirovitch, Integrating the Equations of Motion, J. Mol. Biol. , 168, 617- 620 (1983)

J. Aqvist, W. F. van Gunsteren, M. Leijonmarck and O. Tapia, A Molecular Dynamics Study of the C-Terminal Fragment of the L7/L12 Ribosomal Protein, J. Mol. Biol. , 183, 461-477 (1985)

W. C. Swope, H. C. Andersen, P. H. Berens and K. R. Wilson, A Computer Simulation Method for the Calculation of Equilibrium Constants for the Formation of Physical Clusters of Molecules: Application to Small Water Clusters, J. Chem. Phys. , 76, 637-649 (1982)


W. F. van Gunsteren and H. J. C. Berendsen, Algorithms for Macromolecular Dynamics and Constraint Dynamics, Mol. Phys. , 34, 1311-1327 (1977)

G. Ciccotti, M. Ferrario and J.-P. Ryckaert, Molecular Dynamics of Rigid Systems in Cartesian Coordinates: A General Formulation, Mol. Phys. , 47, 1253-1264 (1982)

H. C. Andersen, Rattle: A "Velocity" Version of the Shake Algorithm for Molecular Dynamics Calculations, J. Comput. Phys. , 52, 24-34 (1983)

R. Kutteh, RATTLE Recipe for General Holonomic Constraints: Angle and Torsion Constraints, CCP5 Newsletter , 46, 9-17 (1998)

[available from the web site at] B. J. Palmer, Direct Application of SHAKE to the Velocity Verlet Algorithm, J. Comput. Phys., 104, 470-472 (1993)

S. Miyamoto and P. A. Kollman, SETTLE: An Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Models, J. Comput. Chem. , 13, 952-962 (1992)

B. Hess, H. Bekker, H. J. C. Berendsen and J. G. E. M. Fraaije, LINCS: A Linear Constraint Solver for Molecular Simulations, J. Comput. Chem. , 18, 1463-1472 (1997)

J. T. Slusher and P. T. Cummings, Non-Iterative Constraint Dynamics using Velocity- Explicit Verlet Methods, Mol. Simul. , 18, 213-224 (1996)


M. P. Allen, Brownian Dynamics Simulation of a Chemical Reaction in Solution, Mol. Phys. , 40, 1073-1087 (1980)

W. F. van Gunsteren and H. J. C. Berendsen, Algorithms for Brownian Dynamics, Mol. Phys., 45, 637-647 (1982)

F. Guarnieri and W. C. Still, A Rapidly Convergent Simulation Method: Mixed Monte Carlo/Stochastic Dynamics, J. Comput. Chem. , 15, 1302-1310 (1994)

M. G. Paterlini and D. M. Ferguson, Constant Temperature Simulations using the Langevin Equation with Velocity Verlet Integration, Chem. Phys. , 236, 243-252 (1998)


H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola and J. R. Haak, Molecular Dynamics with Coupling to an External Bath, J. Chem. Phys. , 81, 3684-3690 (1984)

W. G. Hoover, Canonical Dynamics: Equilibrium Phase-space Distributions, Phys. Rev. A , 31, 1695-1697 (1985)

J. J. Morales, S. Toxvaerd and L. F. Rull, Computer Simulation of a Phase Transition at Constant Temperature and Pressure, Phys. Rev. A , 34, 1495-1498 (1986)

B. R. Brooks, Algorithms for Molecular Dynamics at Constant Temperature and Pressure, Internal Report of Division of Computer Research and Technology, National Institutes of Health, 1988. M. Levitt, Molecular Dynamics of Native Protein: Computer Simulation of Trajectories, J. Mol. Biol. , 168, 595-620 (1983)


J. R. Maple, U. Dinar and A. T. Hagler, Derivation of Force Fields for Molecular Mechanics and Dynamics from ab initio Energy Surfaces, Proc. Natl. Acad. Sci. USA , 85, 5350-5354 (1988)

S.-H. Lee, K. Palmo and S. Krimm, New Out-of-Plane Angle and Bond Angle Internal Coordinates and Related Potential Energy Functions for Molecular Mechanics and Dynamics Simulations, J. Comput. Chem. , 20, 1067-1084 (1999)


K. J. Miller, R. J. Hinde and J. Anderson, First and Second Derivative Matrix Elements for the Stretching, Bending, and Torsional Energy, J. Comput. Chem. , 10, 63-76 (1989)

D. H. Faber and C. Altona, UTAH5: A Versatile Programme Package for the Calculation of Molecular Properties by Force Field Methods, Computers & Chemistry , 1, 203-213 (1977)

W. C. Swope and D. M. Ferguson, Alternative Expressions for Energies and Forces Due to Angle Bending and Torsional Energy, Report G320-3561, J. Comput. Chem. , 13, 585-594 (1992)

A. Blondel and M. Karplus, New Formulation for Derivatives of Torsion Angles and Improper Torsion Angles in Molecular Mechanics: Elimination of Singularities, J. Comput. Chem., 17, 1132-1141 (1996)

R. E. Tuzun, D. W. Noid and B. G. Sumpter, Efficient Treatment of Out-of-Plane Bend and Improper Torsion Interactions in MM2, MM3, and MM4 Molecular Mechanics Calculations, J. Comput. Chem. , 18, 1804-1811 (1997)


M. Levitt, C. Sander and P. S. Stern, Protein Normal-mode Dynamics: Trypsin Inhibitor, Crambin, Ribonuclease and Lysozyme, J. Mol. Biol. , 181, 423-447 (1985)

M. Levitt, Protein Folding by Restrained Energy Minimization and Molecular Dynamics, J. Mol. Biol. , 170, 723-764 (1983)

H. Wako and N. Go, Algorithm for Rapid Calculation of Hessian of Conformational Energy Function of Proteins by Supercomputer, J. Comput. Chem. , 8, 625-635 (1987)

H. Abe, W. Braun, T. Noguti and N. Go, Rapid Calculation of First and Second Derivatives of Conformational Energy with Respect to Dihedral Angles for Proteins: General Recurrent Equations, Computers & Chemistry , 8, 239-247 (1984)

T. Noguti and N. Go, A Method of Rapid Calculation of a Second Derivative Matrix of Conformational Energy for Large Molecules, J. Phys. Soc. Japan , 52, 3685-3690 (1983)


M. L. Connolly, Analytical Molecular Surface Calculation, J. Appl. Cryst. , 16, 548-558 (1983)

M. L. Connolly, Computation of Molecular Volume, J. Am. Chem. Soc. , 107, 1118-1124 (1985)

M. L. Connolly, Molecular Surfaces: A Review, available from the web site at C. E. Kundrot, J. W. Ponder and F. M. Richards, Algorithms for Calculating Excluded Volume and Its Derivatives as a Function of Molecular Conformation and Their Use in Energy Minimization, J. Comput. Chem. , 12, 402-409 (1991)

T. J. Richmond, Solvent Accessible Surface Area and Excluded Volume in Proteins, J. Mol. Biol., 178, 63-89 (1984)

L. Wesson and D. Eisenberg, Atomic Solvation Parameters Applied to Molecular Dynamics of Proteins in Solution, Protein Science , 1, 227-235 (1992)

V. Gononea and E. Osawa, Implementation of Solvent Effect in Molecular Mechanics, Part 3. The First- and Second-order Analytical Derivatives of Excluded Volume, J. Mol. Struct. (Theochem)

, 311 305-324 (1994)

K. D. Gibson and H. A. Scheraga, Exact Calculation of the Volume and Surface Area of Fused Hard-sphere Molecules with Unequal Atomic Radii, Mol. Phys. , 62, 1247-1265 (1987)

K. D. Gibson and H. A. Scheraga, Surface Area of the Intersection of Three Spheres with Unequal Radii: A Simplified Analytical Formula, Mol. Phys. , 64, 641-644 (1988)

S. Sridharan, A. Nichols and K. A. Sharp, A Rapid Method for Calculating Derivatives of Solvent Accessible Surface Areas of Molecules, J. Comput, Chem. , 16, 1038-1044 (1995)


S. J. Wodak and J. Janin, Analytical Approximation to the Accessible Surface Area of Proteins, Proc. Natl. Acad. Sci. USA , 77, 1736-1740 (1980)

W. Hasel, T. F. Hendrickson and W. C. Still, A Rapid Approximation to the Solvent Accessible Surface Areas of Atoms, Tetrahedron Comput. Method. , 1, 103-116 (1988)

J. Weiser, P. S. Shenkin and W. C. Still, Approximate Solvent-Accessible Surface Areas from Tetrahedrally Directed Neighber Densities, Biopolymers, 50, 373-380 (1999)


W. F. van Gunsteren, H. J. C. Berendsen, F. Colonna, D. Perahia, J. P. Hollenberg and D. Lellouch, On Searching Neighbors in Computer Simulations of Macromolecular Systems, J. Comput. Chem. , 5, 272-279 (1984)

F. Sullivan, R. D. Mountain and J. O'Connell, Molecular Dynamics on Vector Computers, J. Comput. Phys. , 61, 138-153 (1985)

J. Boris, A Vectorized "Near Neighbors" Algorithm of Order N Using a Monotonic Logical Grid, J. Comput. Phys. , 66, 1-20 (1986)

S. G. Lambrakos and J. P. Boris, Geometric Properties of the Monotonic Lagrangian Grid Algorithm for Near Neighbors Calculations, J. Comput. Phys. , 73, 183-202 (1987)

T. A. Andrea, W. C. Swope and H. C. Andersen, The Role of Long Ranged Forces in Determining the Structure and Properties of Liquid Water, J. Chem. Phys. , 79, 4576-4584 (1983)

D. N. Theodorou and U. W. Suter, Geometrical Considerations in Model Systems with Periodic Boundary Conditions, J. Chem. Phys. , 82, 955-966 (1985)

J. Barnes and P. Hut, A Hierarchical O(NlogN)

Force-calculation Algorithm, Nature, 234, 446-449 (1986)


P. J. Steinbach and B. R. Brooks, New Spherical-Cutoff Methods for Long-Range Forces in Macromolecular Simulation, J. Comput. Chem. , 15, 667-683 (1993)

R. J. Loncharich and B. R. Brooks, The Effects of Truncating Long-Range Forces on Protein Dynamics, Proteins, 6, 32-45 (1989)

C. L. Brooks III, B. M. Pettitt and M. Karplus, Structural and Energetic Effects of Truncating Long Ranged Interactions in Ionic and Polar Fluids, J. Chem. Phys. , 83, 5897- 5908 (1985)


A. Y. Toukmaji and J. A. Board, Jr., Ewald Summation Techniques in Perspective: A Survey, Comp. Phys. Commun. , 95, 73-92 (1996)

T. Darden, L. Perera, L. Li and L. Pedersen, New Tricks for Modelers from the Crystallography Toolkit: The Particle Mesh Ewald Algorithm and its Use in Nucleic Acid Simulations, Structure, 7, R550-R60 (1999)

T. Darden, D. York and L. G. Pedersen, Particle Mesh Ewald: An N·log( N)

Method for Ewald Sums in Large Systems, J. Chem. Phys. , 98, 10089-10092 (1993)

U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee and L. G. Pedersen, A Smooth Particle Mesh Ewald Method, J. Chem. Phys. , 103, 8577-8593 (1995)

W. Smith, Point Multipoles in the Ewald Summation (Revisited), CCP5 Newsletter , 46, 18- 30 (1998)

[available from] S. E. Feller, R. W. Pastor, A. Rojnuckarin, S. Bogusz and B. R. Brooks, Effect of Electrostatic Force Truncation on Interfacial and Transport Properties of Water, J. Phys. Chem. , 100, 17011-17020 (1996)

W. Weber, P. H. Hünenberger and J. A. McCammon, Molecular Dynamics Simulations of a Polyalanine Octapeptide under Ewald Boundary Conditions: Influence of Artificial Periodicity on Peptide Conformation, J. Phys. Chem. B , 104, 3668-3675 (2000)


N. L. Allinger, F. Li, L. Yan and J. C. Tai, Molecular Mechanics (MM3)

Calculations on Conjugated Hydrocarbons, J. Comput. Chem. , 11, 868-895 (1990)

J. T. Sprague, J. C. Tai, Y. Yuh and N. L. Allinger, The MMP2 Calculational Method, J. Comput. Chem. , 8, 581-603 (1987)

J. Kao, A Molecular Orbital Based Molecular Mechanics Approach to Study Conjugated Hydrocarbons, J. Am. Chem. Soc. , 109, 3818-3829 (1987)

J. Kao and N. L. Allinger, Conformational Analysis: Heats of Formation of Conjugated Hydrocarbons by the Force Field Method, J. Am. Chem. Soc. , 99, 975-986 (1977)

D. H. Lo and M. A. Whitehead, Accurate Heats of Atomization and Accurate Bond Lengths: Benzenoid Hydrocarbons, Can. J. Chem. , 46, 2027-2040 (1968)

G. D. Zeiss and M. A. Whitehead, Hetero-atomic Molecules: Semi-empirical Molecular Orbital Calculations and Prediction of Physical Properties, J. Chem. Soc. A , 1727-1738 (1971)


P. Kollman, Free Energy Calculations: Applications to Chemical and Biochemical Phenomena, Chem. Rev. , 93, 2395-2417 (1993)

B. L. Tembe and J. A. McCammon, Ligand-Receptor Interactions, Computers & Chemistry , 8, 281-283 (1984)

W. L. Jorgensen and C. Ravimohan, Monte Carlo Simulation of Differences in Free Energy of Hydration, J. Chem. Phys. , 83, 3050-3054 (1985)

W. L. Jorgensen, J. K. Buckner, S. Boudon and J. Tirado-Rives, Efficient Computation of Absolute Free Energies of Binding by Computer Simulations: Application to the Methane Dimer in Water, J. Chem. Phys. , 89, 3742-3746 (1988)

S. H. Fleischman and C. L. Brooks III, Thermodynamics of Aqueous Solvation: Solution Properties of Alcohols and Alkanes, J. Chem. Phys. , 87, 3029-3037 (1987)

U. C. Singh, F. K. Brown, P. A. Bash and P. A. Kollman, An Approach to the Application of Free Energy Perturbation Methods Using Molecular Dynamics, J. Am. Chem. Soc. , 109, 1607-1614 (1987)

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