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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 82, 1994 - Issue 2
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Original Articles

Formulae for the first and second derivatives of anisotropie potentials with respect to geometrical parameters

P.L.A. Popelier University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, UK
&
A.J. Stone University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, UK
Pages 411-425 | Received 12 Nov 1993, Accepted 23 Dec 1993, Published online: 23 Aug 2006

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Joseph C. R. Thacker, Alex L. Wilson, Zak E. Hughes, Matthew J. Burn, Peter I. Maxwell & Paul L. A. Popelier. (2018) Towards the simulation of biomolecules: optimisation of peptide-capped glycine using FFLUX. Molecular Simulation 44:11, pages 881-890.
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M. Leslie. (2008) DL_MULTI—A molecular dynamics program to use distributed multipole electrostatic models to simulate the dynamics of organic crystals. Molecular Physics 106:12-13, pages 1567-1578.
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Majeed S. Shaik, Michael Devereux & Paul L.A. Popelier. (2008) The importance of multipole moments when describing water and hydrated amino acid cluster geometry. Molecular Physics 106:12-13, pages 1495-1510.
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S. L. Price, S. Hamad, A. Torrisi, P. G. Karamertzanis, M. Leslie & C. R. A. Catlow. (2006) Applications Of Dl_poly And Dl_multi To Organic Molecular Crystals. Molecular Simulation 32:12-13, pages 985-997.
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L. JOUBERT & P. L. A. POPELIER. (2002) Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction. Molecular Physics 100:21, pages 3357-3365.
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ENRIQUEM. CABALEIRO-LAGO & MIGUELA. RÍOS. (1999) Intermolecular potential for acetonitrile based on ab initio calculations. Molecular Physics 96:3, pages 309-321.
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P.L.A. Popelier. (1996) Integration of atoms in molecules: a critical examination. Molecular Physics 87:5, pages 1169-1187.
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SarahL. Price. (1996) Anisotropic atom-atom potentials. Philosophical Magazine B 73:1, pages 95-106.
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Articles from other publishers (43)

Steven Y. Liem & Paul L. A. Popelier. (2019) The influence of water potential in simulation: a catabolite activator protein case study. Journal of Molecular Modeling 25:8.
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Oliver J. Backhouse, Joseph C. R. Thacker & Paul L. A. Popelier. (2019) A Re‐evaluation of Factors Controlling the Nature of Complementary Hydrogen‐Bonded Networks. ChemPhysChem 20:4, pages 555-564.
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Joseph C. R. Thacker, Mark A. Vincent & Paul L. A. Popelier. (2018) Using the Relative Energy Gradient Method with Interacting Quantum Atoms to Determine the Reaction Mechanism and Catalytic Effects in the Peptide Hydrolysis in HIV‐1 Protease. Chemistry – A European Journal 24:43, pages 11200-11210.
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James L. McDonagh, Arnaldo F. Silva, Mark A. Vincent & Paul L. A. Popelier. (2017) Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms. Journal of Chemical Theory and Computation 14:1, pages 216-224.
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Timothy J. Hughes, Shaun M. Kandathil & Paul L.A. Popelier. (2015) Accurate prediction of polarised high order electrostatic interactions for hydrogen bonded complexes using the machine learning method kriging. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 136, pages 32-41.
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H. A. Boateng & I. T. Todorov. (2015) Arbitrary order permanent Cartesian multipolar electrostatic interactions. The Journal of Chemical Physics 142:3.
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Matthew J. L. Mills & Paul L. A. Popelier. (2014) Electrostatic Forces: Formulas for the First Derivatives of a Polarizable, Anisotropic Electrostatic Potential Energy Function Based on Machine Learning. Journal of Chemical Theory and Computation 10:9, pages 3840-3856.
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Andrew C. Simmonett, Frank C. PickardIVIV, Henry F. SchaeferIIIIII & Bernard R. Brooks. (2014) An efficient algorithm for multipole energies and derivatives based on spherical harmonics and extensions to particle mesh Ewald. The Journal of Chemical Physics 140:18.
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Robin Chaudret, Julia Contreras-Garcia, Mickaël Delcey, Olivier Parisel, Weitao Yang & Jean-Philip Piquemal. (2014) Revisiting H 2 O Nucleation around Au + and Hg 2+ : The Peculiar “Pseudo-Soft” Character of the Gold Cation . Journal of Chemical Theory and Computation 10:5, pages 1900-1909.
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Yongna Yuan, Matthew J L Mills & Paul LA Popelier. (2014) Multipolar electrostatics based on the Kriging machine learning method: an application to serine. Journal of Molecular Modeling 20:4.
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Salvatore Cardamone, Timothy J. Hughes & Paul L. A. Popelier. (2014) Multipolar electrostatics. Physical Chemistry Chemical Physics 16:22, pages 10367.
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Steven Y. Liem & Paul L. A. Popelier. (2014) The hydration of serine: multipole moments versus point charges. Physical Chemistry Chemical Physics 16:9, pages 4122.
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Dwaipayan Chakrabarti, Halim Kusumaatmaja, Victor Rühle & David J. Wales. (2014) Exploring energy landscapes: from molecular to mesoscopic systems. Phys. Chem. Chem. Phys. 16:11, pages 5014-5025.
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Shaun M. Kandathil, Timothy L. Fletcher, Yongna Yuan, Joshua Knowles & Paul L. A. Popelier. (2013) Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine. Journal of Computational Chemistry 34:21, pages 1850-1861.
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Matthew J. L. Mills, Glenn I. Hawe, Christopher M. Handley & Paul L. A. Popelier. (2013) Unified approach to multipolar polarisation and charge transfer for ions: microhydrated Na+. Physical Chemistry Chemical Physics 15:41, pages 18249.
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Matthew J. L. Mills & Paul L. A. Popelier. (2012) Polarisable multipolar electrostatics from the machine learning method Kriging: an application to alanine. Theoretical Chemistry Accounts 131:3.
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Matthew J.L. Mills & Paul L.A. Popelier. (2011) Intramolecular polarisable multipolar electrostatics from the machine learning method Kriging. Computational and Theoretical Chemistry 975:1-3, pages 42-51.
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Steven Y. Liem, Majeed S. Shaik & Paul L. A. Popelier. (2011) Aqueous Imidazole Solutions: A Structural Perspective from Simulations with High-Rank Electrostatic Multipole Moments. The Journal of Physical Chemistry B 115:39, pages 11389-11398.
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William Challacombe, Jim Chelikowsky, Jeffrey Grossman, Arkady V. Krasheninnikov, Fedor Y. Naumkin, George C. Schatz, Gotthard Seifert, Jayant K Singh, David Wales, Mark Wilson, Alessandro Fortunelli, Stefano Sanvito, Malcolm Heggie & Eva ZurekDwaipayan Chakrabarti, Szilard N. Fejer & David J. Wales. 2011. Computational Nanoscience. Computational Nanoscience 58 81 .
Paul L. A. Popelier. 2012. Modern Charge-Density Analysis. Modern Charge-Density Analysis 505 526 .
Dennis M. Elking, Lalith Perera, Robert Duke, Thomas Darden & Lee G. Pedersen. (2010) Atomic forces for geometry‐dependent point multipole and Gaussian multipole models. Journal of Computational Chemistry 31:15, pages 2702-2713.
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Glenn I. HawePaul L.A. Popelier. (2010) A water potential based on multipole moments trained by machine learning — Reducing maximum energy errors. Canadian Journal of Chemistry 88:11, pages 1104-1111.
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Majeed S. Shaik, Steven Y. Liem & Paul L. A. Popelier. (2010) Properties of liquid water from a systematic refinement of a high-rank multipolar electrostatic potential. The Journal of Chemical Physics 132:17.
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Majeed S. Shaik, Steven Y. Liem, Yongna Yuan & Paul L. A. Popelier. (2010) Simulation of liquid imidazole using a high-rank quantum topological electrostatic potential. Physical Chemistry Chemical Physics 12:45, pages 15040.
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Dwaipayan Chakrabarti & David J. Wales. (2009) Simulations of rigid bodies in an angle-axis framework. Physical Chemistry Chemical Physics 11:12, pages 1970.
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Julien Pilmé & Jean‐Philip Piquemal. (2008) Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments. Journal of Computational Chemistry 29:9, pages 1440-1449.
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Claude Millot. 2005. Intermolecular Forces and Clusters I. Intermolecular Forces and Clusters I 125 148 .
Graeme M. Day, Sarah L. Price & Maurice Leslie. (2003) Atomistic Calculations of Phonon Frequencies and Thermodynamic Quantities for Crystals of Rigid Organic Molecules. The Journal of Physical Chemistry B 107:39, pages 10919-10933.
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Jay W. Ponder & David A. Case. 2003. Protein Simulations. Protein Simulations 27 85 .
P. L. A. Popelier, L. Joubert & D. S. Kosov. (2001) Convergence of the Electrostatic Interaction Based on Topological Atoms. The Journal of Physical Chemistry A 105:35, pages 8254-8261.
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Graeme M. Day, Sarah L. Price & Maurice Leslie. (2000) Elastic Constant Calculations for Molecular Organic Crystals. Crystal Growth & Design 1:1, pages 13-27.
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Graeme M. Day & Sarah L. Price. 2001. Handbook of Elastic Properties of Solids, Liquids, and Gases. Handbook of Elastic Properties of Solids, Liquids, and Gases 3 50 .
Sarah L. Price. 2000. Reviews in Computational Chemistry. Reviews in Computational Chemistry 225 289 .
J. Faeder, N. Delaney, P.E. Maslen & R. Parson. (1998) Modeling structure and dynamics of solvated molecular ions: Photodissociation and recombination in I2−(CO2). Chemical Physics 239:1-3, pages 525-547.
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Jonathon K. GregoryDavid C. Clary. (1997) Theoretical Study of the Cage Water Hexamer Structure. The Journal of Physical Chemistry A 101:36, pages 6813-6819.
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Christof Hättig. (1997) On the calculation of derivatives for Coulomb-type interaction energies and general anisotropic pair potentials. Chemical Physics Letters 268:5-6, pages 521-530.
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S.L. Price. 1997. Computer Modeling in Inorganic Crystallography. Computer Modeling in Inorganic Crystallography 269 293 .
P. N. M. Hoang, S. Picaud, C. Girardet & A. W. Meredith. (1996) Structure of CO monolayer adsorbed on NaCl(100) from molecular dynamics. The Journal of Chemical Physics 105:18, pages 8453-8462.
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Jonathon K. Gregory & David C. Clary. (1996) Tunneling dynamics in water tetramer and pentamer. The Journal of Chemical Physics 105:16, pages 6626-6633.
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Uwe Koch & Ernst Egert. (2004) An improved description of the molecular charge density in force fields with atomic multipole moments. Journal of Computational Chemistry 16:8, pages 937-944.
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David J. Wales, Anthony J. Stone & Paul L.A. Popelier. (1995) Potential energy surfaces of several van der Waals complexes modelled using distributed multipoles. Chemical Physics Letters 240:1-3, pages 89-96.
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D. J. Willock, S. L. Price, M. Leslie & C. R. A. Catlow. (2004) The relaxation of molecular crystal structures using a distributed multipole electrostatic model. Journal of Computational Chemistry 16:5, pages 628-647.
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P.-O. Åstrand, P. Linse & G. Karlström. (1995) Molecular dynamics study of water adopting a potential function with explicit atomic dipole moments and anisotropic polarizabilities. Chemical Physics 191:1-3, pages 195-202.
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