Electrostatics interactions in classical simulations

Methods in Molecular Biology

Volumn 924, Issue , 2013, Pages 243-270

  Cisneros, G Andrés ^a   Babin, Volodymyr ^a   Sagui, Celeste ^a  

^a NONE

Author keywords

Electrostatics; Ewald summation9; Fast multipole method; Molecular dynamics; Multigrid; P3M; Particle mesh Ewald; Particle particle particle mesh; PME

Indexed keywords

SOLVENT;

ACCURACY; ALGORITHM; ARTICLE; EWALD SUMMATION METHOD; GEOMETRY; MATHEMATICAL MODEL; PRIORITY JOURNAL; SIMULATION; STATIC ELECTRICITY;

EID: 84934440491     PISSN: 10643745     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-62703-17-5_10     Document Type: Article

References (185)

1. Alper HE, Levy RM (1989) Computersimulations of the dielectric-properties of water -studies of the simple point-charge and transferable intermolecular potential models. J Chem Phys 91:1242-1251
2. Alper HE, Bassolino D, Stouch TR (1993) Computer-simulation of a phospholipid monolayer-water system -the influence of long-range forces on water-structure and dynamics. J Chem Phys 98:9798-9807
3. Alper HE, Bassolino-Klimas D, Stouch TR (1993) The limiting behavior of water hydrating a phospholipid monolayer -A computer simulation study. J Chem Phys 99:5547-5559
4. Feller SE, Pastor RW, Rojnuckarin A, Bogusz A, Brooks BR (1996) Effect of electrostatic force truncation on interfacial and transport properties of water. J Phys Chem 100:17011-17020
5. Mark P, Nilsson L (2002) Structure and dynamics of liquid water with different longrange interaction truncation and temperature control methods in molecular dynamics simulations. J Comp Chem 23:1211-1219
6. Yonetani Y (2006) Liquid water simulation: a critical examination of cutoff length. J Chem Phys 124:204501
7. Smith PE, Pettitt BM (1991) Peptides in ionic solutions: a comparison of the Ewald and switching function techniques. J Chem Phys 95:8430-8441
8. Schreiber H, Steinhauser O (1992) Cutoff size does strongly influence moleculardynamics results on solvated polypeptides. Biochemistry 31:5856-5860
9. York DM, Darden TA, Pedersen LG (1993) The effect of long-range electrostatic interactions in simulations of macromolecular crystals -A comparison of the Ewald and truncated list methods. J Chem Phys 99:8345-8348
10. York DM, Yang WT, Lee H, Darden T, Pedersen LG (1995) Toward the accurate modeling of DNA -the importance of long-range electrostatics. J Am Chem Soc 117:5001-5002
11. Cheatham III TE, Kollman PA (1997) Molecular dynamics simulations highlight structural differences among DNA:DNA, RNA:RNA, and DNA:RNA hybrid duplexes. J Am Chem Soc 119:4805-4825
12. Auffinger P, Westhof E (1998) Molecular dynamics simulations of nucleic acids. In: Encyclopedia of computational chemistry. Wiley, New York
13. Norberg J, Nilsson L (2000) On the truncation of long-range electrostatic interactions in DNA. Biophys J 79:1537-1553
14. Feller SE, Pastor RW, Rojnuckarin A, Bogusz S, Brooks BR (1996) Effect of electrostatic force truncation on interfacial and transport properties of water. J Phys Chem 100:17011-17020
15. Patra M, Karttunen M, Hyvonen MT, Falck E, Vattulainen I (2004) Lipid bilayers driven to a wrong lane in molecular dynamics simulations by subtle changes in long-range electrostatic interactions. J Phys Chem B 108:4485-4494
16. Anézo C, de Vries AH, Holtje HD, Tieleman DP (2003) Methodological issues in lipid bilayer simulations. J Phys Chem B 107:9424-9433
17. Khelashvili GA, Scott HL (2004) Combined Monte Carlo and molecular dynamics simulation of hydrated 18:0 sphingomyelincholesterol lipid bilayers. J Chem Phys 120:9841-9847
18. Patra M, Hyvonen MT, Falck E, Sabouri-Ghomi M, Vattulainen I, Karttunen M (2007) Long-range interactions and parallel scalability in molecular simulations. Comp Phys Comm 176:14-22
19. Karttunen M, Rottler J, Vattulainen I, Sagui C (2008) Computational modeling of membrane bilayers. Elsevier, New York
20. Heyes DM, Barber M, Clarke JHR (1977) Molecular dynamics computer simulation of surface properties of crystalline potassium chloride. J Chem Soc Faraday Trans 2:1485-1496
21. Hautman J, Klein ML (1992) An Ewald summation method for planar surfaces and interfaces. Mol Phys 75:379-395
22. de Leeuw SW, Perram JW (1979) Electrostatic lattice sums for semi-infinite lattices. Mol Sim 37:1313-1322
23. Nijboer BRA, de Wette FW (1957) On the calculation of lattice sums. Physica 23:309-321
24. Yeh IC, Berkowitz ML (1999) Ewald summation for systems with slab geometry. J Chem Phys 111:3155-3162
25. Lekner J (1989) Summation of dipolar fields in simulated liquid-vapor interfaces. Physica A 157:826-838
26. Lekner J (1991) Summation of Coulomb fields in computer-simulated disordered systems. Physica A 176:485-498
27. Lekner J (1998) Coulomb forces and potentials in systems with an orthorhombic unit cell. Mol Sim 20:357
28. Sperb R (1994) Extension and simple proof of Lekner's summation formula for coulomb forces. Mol Sim 13:189-193
29. Sperb R (1998) An alternative to Ewald sums part I: identities for sums. Mol Sim 20:179-200
30. Sperb R (1999) An alternative to Ewald sums, part 2: the Coulomb potential in a periodic system. Mol Sim 22:199-212
31. Strebel R, Sperb R (2001) An alternative to Ewald sums. part 3: implementation and results. Mol Sim 27:61-74
32. Arnold A, Holm C (2002) A novel method for calculating electrostatic interactions in 2D periodic slab geometries. Chem Phys Lett 354:324-330
33. Arnold A, Holm C (2002) MMM2D: a fast and accurate summation method for electrostatic interactions in 2D slab geometries. Comput Phys Comm 148:327-348
34. Baker NA (2005) Improving implicit solvent simulations: a Poisson-centric view. Curr Opin Struct Bio 15:137-143
35. Stone AJ (1996) The theory of intermolecular forces. Clarendon Press, Oxford
36. Ewald P (1921) Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys 64:253-287
37. DeLeeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions I: lattice sums and dielectric constants. Proc R Soc Lond A373:27-56
38. Boresch S, Steinhauser O (1997) Presumed versus real artifacts of the Ewald summation technique: the importance of dielectric boundary conditions. Ber Bunseges Phys Chem 101:1019-1029
39. Hockney RW, Eastwood JW (1981) Computer simulation using particles. McGraw-Hill, New York
40. Pollock E, Glosli J (1996) Comments on PPPM, FMM, and the Ewald method for large periodic Coulombic systems. Comp Phys Comm 95:93-110
41. Darden TA, York DM, Pedersen LG (1993) Particle mesh Ewald: an N log(N) method for Ewald sums in large systems. J Chem Phys 98:10089-10092
42. Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen LG (1995) A smooth particle mesh Ewald method. J Chem Phys 103:8577-8593
43. York D, Yang W (1994) The fast Fourier Poisson (FFP) method for calculationg Ewald sums. J Chem Phys 101:3298-3300
44. Smith ER (1994) Calculating the pressure in simulations using periodic boundary conditions. J Stat Phys 77:449-472
45. Caillol JP (1994) Comments on the numerical simulations of electrolytes in periodic boundary conditions. J Chem Phys 101:6080-6090
46. Smith W (1982) Point multipoles in the Ewald summation. CCP5 Inform Q 4:13-25
47. Toukmaji A, Sagui C, Board JA, Darden T (2000) Efficient PME-based approach to fixed and induced dipolar interactions. J Chem Phys 113:10913-10927
48. Aguado A, Madden P (2003) Ewald summation of electrostatic multipole interactions up to the quadrupolar level. J Chem Phys 119:7471-7483
49. Sagui C, Pedersen LG, Darden TA (2004) Towards an accurate representation of electrostatics in classical force fields: efficient implementation of multipolar interactions in biomolecular simulations. J Chem Phys 120:73-87
50. Smith W (1987) Coping with the pressure: how to calculate the virial. CCP5 Information Quarterly 26:43-50
51. Alejandre J, Tildesley DJ, Chapela GA (1995) Molecular dynamics simulation of the orthobaric densities and surface tension of water. J Chem Phys 102:4574-4583
52. Nose S, Klein M (1983) Constant pressure molecular dynamics for molecular systems. Mol Phys 50:1055-76
53. Brown D, Clarke JHR (1991) A loose coupling, constant-pressure, molecular dynamics algorithm for use in the modelling of polymer materials. Comp Phys Comm 62:360-369
54. Reif MM, Kraeutler V, Kastenholz MA, Daura X, Huenenberger PH (2009) Molecular dynamics simulations of a reversibly folding beta-Heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions. J Phys Chem B 113:3112-3128
55. Villarreal MA, Montich GG (2005) On the Ewald artifacts in computer simulations. The test-case of the octaalanine peptide with charged termini. J Biomol Struct Dyn 23:135-142
56. Monticelli L, Colombo G (2004) The influence of simulation conditions in molecular dynamics investigations of model beta-sheet peptides. Theo Chem Acc 112:145-157
57. Monticelli L, Simoes C, Belvisi L, Colombo G (2006) Assessing the influence of electrostatic schemes on molecular dynamics simulations of secondary structure forming peptides. Journal of Physics: condensed Matter 18: S329-S345
58. Babin V, Roland C, Darden TA, Sagui C (2006) The free energy landscape of small peptides as obtained from metadynamics with umbrella sampling corrections. J Chem Phys 125:204909
59. Levy RM, Gallicchio E (1998) Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies, and in modeling electrostatic effects. Ann Rev Phys Chem 49:531-567
60. Hummer G, Pratt LR, Garcia AE (1996) On the free energy of ionic hydration. J Phys Chem 100:1206-1215
61. Figuereido F, Buono GSD, Levy RM (1997) On finite-size corrections to the free energy of ionic hydration. J Phys Chem B 101:5622-5623
62. Hummer G, Pratt LR, Garcia AE (1997) Ion sizes and finite-size corrections for ionicsolvation free energies. J Chem Phys 107:9275-9277
63. Sakane S, Ashbaugh HS, Wood RH (1998) Continuum corrections to the polarization and thermodynamic properties of Ewald sum simulations for ions and ion pairs at infinite dimulation. J Phys Chem B 102:5673-5682
64. Darden T, Pearlman D, Pedersen L (1998) Ionic charging free energies: spherical versus periodic boundary conditions. J Chem Phys 109:10921-10935
65. Herce D, Darden T, Sagui C (2003) Calculation of ionic charging free energies in simulation systems with atomic charges, dipoles and quadrupoles. J Chem Phys 119:7621-7632
66. Ferrell R, Bertschinger E (1994) Particlemesh methods on the connection machine. J Mod Phys 5:933-956
67. Toukmaji A, Board JA (1996) Ewald sum techniques in perspective: a survey. Comp Phys Comm 95:78-92
68. Darden T, Toukmaji A, Pedersen L (1997) Long-range electrostatic effects in biomolecular simulations. J Chim Phys 94:1346-1364
69. Deserno M, Holm C (1998) How to mesh up Ewald sums i: a theoretical and numerical comparison of various particle mesh routines. J Chem Phys 109:7678-7693
70. Sagui C, Darden TA (1999) Molecular dynamics simulations of biomolecules: longrange electrostatic Effects. Annu Rev Biophys Biomol Struct 28:155-179
71. Sagui C, Darden TA (1999) P3M and PME: a comparison of the two methods. In: Pratt LR, Hummer G (eds) Simulation and theory of electrostatic interactions in solution. AIP, Melville, NY
72. Case DA, Cheatham TE III, Darden T, Gohlke H, Luo R, Merz KM Jr., Onufriev A, Simmerling C, Wang B, Woods R (2005) The Amber biomolecular simulation programs. J Comput Chem 26:1668-1688
73. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM: a program for macromolecular energy, minimization and dynamics calculations. J Comp Chem 4:187-217
74. Phillips J, Braun R, Wang W, Gumbart J, Tajkhorshid E, Villa E, Chipot C, Skeel R, Kale L, Schulten K (2005) Scalable molecular dynamics with NAMD. J Comp Chem 26:1781-1802
75. Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theo Comp 4:435-447
76. Bowers KJ, Chow E, Xu H, Dror RO, Eastwood MP, Gregersen BA, Klepeis JL, Kolossvary I, Moraes MA, Sacerdoti FD, Salmon JK, Shan Y, Shaw DE (2006) Scalable algorithms for molecular dynamics simulations on commodity clusters. In: SC '06: proceedings of the 2006 ACM/IEEE conference on supercomputing. ACM Press
77. Cerutti DS, Duke RE, Darden TA, Lybrand TP (2009) Staggered mesh Ewald: an extension of the smooth particle-mesh Ewald method adding great versatility. J Chem Theory Comput 5:2322-2338
78. Chen L, Langdon AB, Birdsall CK (1974) Reduction of grid effects in simulation plasmas. J Comp Phys 14:200-222
79. Hockney RW, Eastwood JW (1988) Computer simulation using particles. Adam Hilger, Bristol 80. Cerutti DS, Case DA (2010) Multi-level ewald: a hybrid multigrid/fast Fourier transform approach to the electrostatic particlemesh problem. J Chem Theory Comput 6:443-458
80. Duke RE (2006) Amber 9 manual: amber. scripps.edu/doc9/amber9.pdf. AMBER 9
81. D. A. Case et al., University of California, San Francisco
82. Schulten K, Phillips JC, Kale LV, Bhatele A (2008) In: Bader D (ed) Petascale computing: algorithms and applications. Chapman & Hall/CRC Press, New York
83. Brandt A (1977) Multi-level adaptive solutions to boundary value problems. Math Comput 31:333-390
84. Brandt A (1994) SIAM J Num Anal 31:1695
85. Brandt A (2001) Multiscale scientific computation: review 2001. In: Barth TJ, Chan TF, Haimes R (eds) Multiscale and multiresolution methods: theory and applications. Springer Verlag, Heidelberg
86. Beck TL (2000) Real-space mesh techniques in density-functional theory. Rev Mod Phys 72:1041-1080
87. Honig B,NichollsA (1995) Classical electrostatics in biology and chemistry. Science 268:1144-1149
88. Holst M, Saied F (1993) Multigrid solution of the Poisson-Boltzmann equation. J Comp Chem 14:105-113
89. Holst M, Kozack RE, Saied F, Subramaniam S (1994) Treatment of electrostatic effects in proteins: multigrid-based Newton iterative method for solution of the full Poisson-Boltzmann equation. Proteins Struct Fun Gen 18:231-241
90. Holst M, Saied F (1995) Numerical solution of the nonlinear Poisson-Boltzmann equation: developing more robust and efficient methods. J Comp Chem 16:337-364
91. Ripoll DR, Vorobjev YN, Liwo A, Vila JA, Scheraga HA (1996) Coupling between folding and ionization equilibria: effects of pH on the conformational preferences of polypeptides. J Mol Biol 264:770-783
92. Vorobjev YN, Scheraga HA (1997) A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent. J Comp Chem 18:569-583
93. Qian X, Schlick T (2002) Efficient multipletime-step integrators with distance-based force splitting for particle-mesh-Ewald molecular dynamics simulations. J Chem Phys 116:5971-5983
94. Press W, Teukolsky SA, Vettering WT, Flannery BP (1992) Numerical recipes in FORTRAN: the art of scientific computing. Cambridge University Press, Cambridge
95. Zaslavsky L, Schlick T (1998) An adaptive multigrid technique for evaluating longrange forces in biomolecular simulations. Appl Math Comput 97:237-250
96. Sagui C, Darden TA (2001) Multigrid methods for classical molecular dynamics simulations of biomolecules. J Chem Phys 114:6578-6591
97. Hackbush W (1985) Multigrid methods and applications. Springer, Berlin
98. Briggs EL, Sullivan DJ, Bernholc J (1996) A real-space multigrid-based approach to largescale electronic structure calculations. Phys Rev B 54:14362-14375
99. Skeel RD, Tezcan I, Hardy DJ (2002) Multiple grid methods for classical molecular dynamics. J Comp Chem 23:673-684
100. Goedecker S, Chauvin C (2003) Combining multigrid and wavelet ideas to construct more efficient multiscale algorithms. J Theo Comp Chem 2:483-495
101. Izaguirre JA, Hampton SS, Matthey T (2005) Parallel multigrid summation for the N-body problem. J Parall Distrib Comp 65:949-962
102. Banerjee S, J A Board J (2005) Efficient charge assignment and back interpolation in multigrid methods for molecular dynamics. J Comp Chem 26:957-967
103. Shan Y, Klepeis JL, Eastwood MP, Dror RO, Shaw DE (2005) Gaussian split Ewald: A fast Ewald mesh method for molecular simulation. J Chem Phys 122:054101
104. Groot RD (2003) Electrostatic interactions in dissipative particle dynamics -simulation of polyelectrolytes and anionic surfactants. J Chem Phys 118:11265-11277
105. Bishop T, Skeel R, Schulten K (1997) Difficulties with multiple stepping and fast multipole algorithm in molecular dynamics. J Comp Chem 18:1785-91
106. Greengard L, Rokhlin V (1987) A fast algorithm for particle simultations. J Comp Phys 73:325-348
107. Board JA, Causey JW, Leathrum JF, Windemuth A, Schulten K (1992) Accelerated molecular dynamics simulation with the parallel fast multipole algorithm. Chem Phys Lett 198:89-94
108. Schmidt KE, Lee MA (1991) Implementing the fast multipole method in three dimensions. J Stat Phys 63:1223-1235
109. Lambert CG, Darden TA, Board JA (1996) A multipole-based method for efficient calculation of forces and potentials in macroscopic periodic assemblies of particles. J Comp Phys 126:274-285
110. Figueirido F, Levy R, Zhou R, Berne B (1997) Large scale simulation of macromolecules in solution: combining the periodic fast multipole method with multiple time step integrators. J Chem Phys 106:9835-9849
111. Greengard LF (1988) The rapid evaluation of potential fields in particle systems. The MIT Press, Cambridge
112. Greengard LF (1994) Fast algorithms for classical physics. Science 265:909-914
113. Greengard L, Rokhlin V (1997) A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 6:229-270
114. Greengard L, Rokhlin V (1997) A fast algorithm for particle simulation. J Comput Phys 135:280-292
115. Cheng H, Greengard L, Rokhlin V (1999) A fast adaptive multipole algorithm in three dimensions. J Chem Phys 155:468-498
116. Fenley M, Olson W, Chua K, Boschitsch A (1994) Fast adaptive multipole method for computation of electrostatic energy in simulations of polyelectrolyte DNA. J Comp Chem 17:976
117. Zhou R, Berne B (1995) A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems. J Chem Phys 103:9444-9459
118. Ogata S, Campbell T, Kalia R, Nakano A, Vashishta P, Vemparala S (2003) Scalable and portable implementation of the fast multipole method on parallel computers. Comp Phys Comm 153:445-461
119. Kurzak J, Pettitt BM (2005) Massively parallel implementation of a fast multipole method for distributed memory machines. J Parall Distrib Comp 65:870-881
120. Kurzak J, Pettitt BM (2006) Fast multipole methods for particle dynamics. Molecular Simulation 32:775-790
121. Maggs AC, Rossetto V (2002) Paper1. Phys Rev Lett 88:196402
122. Alastuey A, Appel W (2000) Physica A 276:508
123. Rottler J, Maggs AC (2004) Local molecular dynamics with coulombic interactions. Phys Rev Lett 93:170201
124. Pasichnyk I, Duenweg B (2004) bla. J Phys Cond Mat 16:S3999
125. Rottler J (2007) Local electrostatics algorithm for classical molecular dynamics simulations. J Chem Phys 127
126. Dixon R, Kollman P (1997) Advancing beyond the atom-centered model in additive and non-Additive molecular mechanics. J Comp Chem 18:1632-1646
127. Wheatley R, Mitchell J (1994) Gaussian multipoles in practice: electrostatic energies for Intermolecular potentials. J Comp Chem 15:1187-1198
128. Bayly C, Cieplak P, Cornell W, Kollman P (1993) A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges -the RESP model. J Phys Chem 97:10269-10280
129. Francl MM, Chirlian LA (1999) The pluses and minuses of mapping atomic charges to Electrostatic potentials. In: Lipkowitz K, Boyd DB (eds) Reviews in computational chemistry. VCH Publishers, New York
130. Price S (1999) In: Lipkowitz K, Boyd DB (eds) Reviews in computational chemistry, VCH Publishers, New York
131. Popelier P (2000) Atoms in molecules: an introduction. Prentice Hall, Harlow
132. Kosov DS, Popelier PLA (2000) Atomic partitioning of molecular electrostatic potentials. J Phys Chem A 104:7339-7345
133. Popelier PLA, Joubert L, Kosov DS (2001) Convergence of the electrostatic interaction based on topological atoms. J Phys Chem A 105:8254-8261
134. Popelier PLA, Kosov DS (2001) J Chem Phys 114:6539-6547
135. Proft FD, Alsenov CV, Peeters A, Langenaeker W, Geerlings P (2002) Atomic charges, dipole moments and Fukai functions using the Hirshfeld partitioning of the electron density. J Comp Chem 23:1198-1209
136. Bader R (1990) Atoms in molecules: a quantum theory. Clarendon Press, Oxford
137. Sagui C, Pomorski P, Darden TA, Roland C (2004) Ab initio calculation of electrostatic multipoles with Wannier functions for largescale biomolecular simulations. J Chem Phys 120:4530-4544
138. Yu H, Hansson T, van Gunsteren WF (2003) Development of a simple, self-consistent polarizable model for liquid water. J Chem Phys 118:221-234
139. Lamoureux G, Alexander D MacKerell J, Roux B (2003) A simple polarizable model of water based on classical Drude oscillators. J Chem Phys 119:5185-5197
140. Rick SW, Stuart SJ, Berne BJ (1994) Dynamical fluctuating charge force fields: Application to liquid water. J Chem Phys 101:6141-6156
141. Ribeiro MCC, Almeida LCJ (1999) Fluctuating charge model for polyatomic ionic systems: a test case with diatomic anions. J Chem Phys 110:11445-11448
142. Caldwell J, Dang LX, Kollman PA (1990) Implementation of nonadditive intermolecular potentials by use of molecular dynamics: development of a water-water potential and water-ion cluster interactions. J Am Chem Soc 112:9144-9147
143. Ren P, Ponder JW (2003) Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B 107:5933-5947
144. Eling D, Darden TA, Woods RJ (2007) Gaussian induced dipole polarization model. J Comp Chem 28:1261-1274
145. Ponder JW,Wu C, Ren P, Pande VS, Chodera JD, Schnieders MJ, Haque I, Mobley DL, Lambrecht DS, Robert A DiStasio Jr., Head-Gordon M, Clark GNI, Johnson ME, Head-Gordon T (2010) Current status of the AMOEBA polarizable force field. J Phys Chem B 114:2549-2564
146. Case DA, Cheatham III TE, Darden TA, Gohlke H, Luo R, Merz KM Jr., Onufirev A, Simmerling C, Wang B, Woods RJ (2005) The Amber biomolecular simulation programs. J Comp Chem 26:1668-1688
147. Day PN, Jensen JH, Gordon MS, Webb SP, Stevens WJ, Krauss M, Garmer D, Basch H, Cohen D (1996) An effective fragment method for modeling solvent effects in quantum mechanical calculations. J Chem Phys 105:1968-1986
148. Gagliardi L, Lindh R, Karlstrom G (2004) Local properties of quantum chemical systems: the LoProp approach. J Chem Phys 121:4494-4500
149. Gresh N, Claverie P, Pullman A (1982) Computation of intermolecular interactions: expansion of a charge energy contribution in the framework of an additive procedure -Application to hydrogen bonded systems. Int J Quantum Chem 22:199
150. Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD (2005) Determination of electrostatic parameters for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput 1:153-168
151. Jungwirth P, Tobias D (2002) Ions at the air/water interface. J Phys Chem B 106:6361-6373
152. Baucom J, Transue T, Fuentes-Cabrera M, Krahn J, Darden T, Sagui C (2004) Molecular dynamics simulations of the d (CCAACGTTGG)2 decamer in crystal environment: comparison of atomic point-charge, extra-point and polarizable force fields. J Chem Phys 121:6998-7008
153. Vrbka L, Mucha M, Minofar B, Jungwirth P, Brown E, Tobias D (2004) Propensity of soft ions for the air/water interface. Curr Opin Coll Interface Sci 9:67-73
154. Herce D, Perera L, Darden T, Sagui C (2005) Surface solvation for an ion in a water cluster. J Chem Phys 122:024513
155. Babin V, Baucom J, Darden TA, Sagui C (2006) Molecular dynamics simulations of DNA with polarizable force fields: convergence of an ideal B-DNA structure to the crystallographic structure. J Phys Chem B 110:11571-11581
156. Harder E, Anisimov VM, Whitfield TW, MacKerell AD, Roux B (2008) Understanding the dielectric properties of liquid amides from a polarizable force field. J Phys Chem B 112:3509-3521
157. Vladimirov E, Ivanova A, Roesch N (2008) Effect of solvent polarization on the reorganization energy of electron transfer from molecular dynamics simulations. J Chem Phys 129
158. Harder E, MacKerell AD, Roux B (2009) Many-body polarization effects and the membrane dipole potential. J Am Chem Soc 131:2760
159. Vladimirov E, Ivanova A, Roesch N (2009) Solvent reorganization energies in A-DNA, B-DNA, and rhodamine 6G-DNA complexes from molecular dynamics simulations with a polarizable force field. J Phys Chem B 113:4425-4434
160. Cieplak P, Dupradeau FY, Duan Y, Wang J (2009) Polarization effects in molecular mechanical force fields. J Phys Condens Matter 21: 333102
161. Yan T, Wang Y, Knox C (2010) On the structure of ionic liquids: comparisons between electronically polarizable and nonpolarizable models I. J Phys Chem B 114:6905-6921
162. Sagui C, Roland C, Pedersen LG, Darden TA (2005) New distributed multipole methods for accurate electrostatics in large-scale biomolecular simulations. In: Leimkuhler B, Chipot C, Elber R, Laaksonen A, Mark A, Schlick T, Schuette C, Skeel R (eds) New algorithms for macromolecular simulations. Springer, Berlin
163. McMurchie L, Davidson E (1978) One-And two-electron integrals over cartesian Gaussian functions. J Comput Phys 26:218-231
164. Ren P, Ponder JW (2002) A consistent treatment of inter-And intramolecular polarization in molecular mechanics calculations. J Comput Chem 23:1497-1506
165. Ponder JW, Case DA (2003) Force fields for protein simulation. Adv Protein Chem 66:27
166. Ren P, Ponder JW (2004) Temperature and pressure dependence of the AMOEBA water model. J Phys Chem B 108:13427-13437
167. Qian W, Krimm S (2005) Limitations of the molecular multipole expansion treatment of electrostatic interactions for C-H...O and O-H...O hydrogen bonds and application of a general charge density approach. J Phys Chem A 109:5608-5618
168. Cisneros GA, Piquemal JP, Darden TA (2005) Intermolecular electrostatic energies using density fitting. J Chem Phys 123:044109
169. Piquemal JP, Gresh N, Giessner-Prettre C (2003) Improved formulas for the calculation of the electrostatic contribution to the intermolecular interaction energy from multipolar expansion of the electronic distribution. J Phys Chem A 107:10353-10359
170. Cisneros GA, Tholander SNI, Parisel O, Darden TA, Elking D, Perera L, Piquemal JP (2008) Simple formulas for improved point-charge electrostatics in classical force fields and hybrid quantum mechanical/molecular mechanical embedding. Int J Quantum Chem 108:1905-1912
171. Freitag MA, Gordon MS, Jensen JH, Stevens WJ (2000) Evaluation of charge penetration between distributed multipolar expansions. J Chem Phys 112:7300-7306
172. Wang B, Truhlar DG (2010) Including charge penetration effects in molecular modeling. J Chem Theo Comp 6:3330
173. Volkov A, Koritsanszky T, Coppens P (2004) Combination of the exact potential and multipole methods (EP/MM) for evaluation of intermolecular electrostatic interaction energies with pseudoatom representation of molecular electron densities. Chem Phys Lett 391:170-175
174. Volkov A, Li X, Koritsanszky T, Coppens P (2004) Ab initio quality electrostatic atomic and molecular properties including intermolecular energies from a transferable theoretical pseudoatom databank. J Phys Chem A 108:4283-4300
175. Volkov A, Coppens P (2004) Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning. J Comp Chem 25:921-934
176. Gavezzotti A (2002) Calculation of intermolecular interaction energies by direct numerical integration over electron densities I. Electrostatic and polarization energies in molecular crystals. J Phys Chem B 106:4145-4154
177. Piquemal JP, Cisneros GA, Reinhardt P, Gresh N, Darden TA (2006) Towards a force field based on density fitting. J Chem Phys 124:104101
178. Cisneros GA, Piquemal JP, Darden TA (2006) Generalization of the Gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods. J Chem Phys 125:184101
179. Bagus PS, Hermann K, Bauschlicher CW Jr. (1984) A new analysis of charge transfer and polarization for ligand-metal bonding: model studies for Al4CO and Al4NH3. J Chem Phys 80:4378-4386
180. Piquemal JP, Marquez A, Parisel O, Giessner-Prettre C (2005) A CSOV study of the difference between HF and DFT intermolecular interaction energy values: the importance of the charge transfer contribution. J Comp Chem 26:1052-1062
181. Darden TA (2007) In: Shmueli U (ed) Dual bases in crystallographic computing in international tables of chrystallography. Kluwer Academic Publishers, Dordrecht
182. Cisneros GA, Elking DM, Piquemal JP, Darden TA (2007) Numerical fitting of molecular properties to Hermite Gaussians. J Phys Chem A 111:12049-12056
183. Elking DM, Cisneros GA, Piquemal JP, Darden TA, Pedersen LG (2010) Gaussian multipole model (GMM). J Chem Theo Comp 6:190-202
184. Godbout N, Andzelm J (1998) DGauss Version 2.0, 2.1, 2.3, 4.0: the file that contains the A1 and P1 auxiliary basis sets can be obtained from the CCL WWW site at http://ccl.osc. edu/cca/data/basis-sets/DGauss/basis.v3. html. Computational Chemistry List, Ltd., Ohio
185. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO, Eastwood MP, Bank JA, Jumper JM, Salmon JK, Shan Y, Wriggers W (2010) Atomic-level characterization of the structural dynamics of proteins. Science 330:341-346