A convergent multipole expansion for 1,3 and 1,4 Coulomb interactions.

Traditionally force fields express 1,3 and 1,4 interactions as bonded terms via potentials that involve valence and torsion angles, respectively. These interactions are not modeled by point charge terms, which are confined to electrostatic interactions between more distant atoms (1,n where n>4). Here we show that both 1,3 and 1,4 interactions can be described on the same footing as 1,n (n>4) interactions by a convergent multipole expansion of the Coulomb energy of the participating atom pairs. The atomic multipole moments are generated by the theory of quantum chemical topology. The procedure to make the multipole expansion convergent is based on a "shift procedure" described in earlier work [L. Joubert and P. L. A. Popelier, Molec. Phys. 100, 3357 (2002)].

[1]  W. Mooij,et al.  Multipoles versus charges in the 1999 crystal structure prediction test , 2001 .

[2]  Paul L. A. Popelier,et al.  Convergence of the multipole expansion for electrostatic potentials of finite topological atoms , 2000 .

[3]  Anthony J. Stone,et al.  Distributed multipole analysis, or how to describe a molecular charge distribution , 1981 .

[4]  William Jones,et al.  Beyond the isotropic atom model in crystal structure prediction of rigid molecules: atomic multipoles versus point charges , 2005 .

[5]  J. Ponder,et al.  Force fields for protein simulations. , 2003, Advances in protein chemistry.

[6]  Evelio Francisco,et al.  Two‐electron integrations in the Quantum Theory of Atoms in Molecules with correlated wave functions , 2005, J. Comput. Chem..

[7]  Celeste Sagui,et al.  Towards an accurate representation of electrostatics in classical force fields: efficient implementation of multipolar interactions in biomolecular simulations. , 2004, The Journal of chemical physics.

[8]  Frank J. J. Leusen,et al.  A study of different approaches to the electrostatic interaction in force field methods for organic crystals , 2003 .

[9]  A. Hinchliffe,et al.  Chemical Modelling: Applications and Theory , 2008 .

[10]  H. Jónsson,et al.  Electric fields in ice and near water clusters , 2000 .

[11]  Philip Coppens,et al.  Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning , 2004, J. Comput. Chem..

[12]  Constantinos C. Pantelides,et al.  Optimal Site Charge Models for Molecular Electrostatic Potentials , 2004 .

[13]  Quantum topological atoms , 2002 .

[14]  Jay W. Ponder,et al.  Accurate modeling of the intramolecular electrostatic energy of proteins , 1995, J. Comput. Chem..

[15]  Paul L. A. Popelier,et al.  Atom–atom partitioning of intramolecular and intermolecular Coulomb energy , 2001 .

[16]  R. Parr.  Density-functional theory of atoms and molecules , 1989 .

[17]  Laurent Joubert,et al.  Convergence of the electrostatic interaction based on topological atoms , 2001 .

[18]  P. Popelier,et al.  The electrostatic potential generated by topological atoms. II. Inverse multipole moments. , 2005, The Journal of chemical physics.

[19]  P. Popelier,et al.  The electrostatic potential generated by topological atoms: a continuous multipole method leading to larger convergence regions , 2003 .

[20]  Paul L. A. Popelier,et al.  Atoms in Molecules: An Introduction , 2000 .

[21]  Á. M. Pendás,et al.  Two-electron integrations in the quantum theory of atoms in molecules. , 2004, The Journal of chemical physics.

[22]  Force Field Modelling of Conformational Energies , 2004 .

[23]  R. Bader.  Atoms in molecules : a quantum theory , 1990 .

[24]  P. Salvador,et al.  One- and two-center energy components in the atoms in molecules theory , 2001 .

[25]  P. Coppens,et al.  Combination of the exact potential and multipole methods (EP/MM) for evaluation of intermolecular electrostatic interaction energies with pseudoatom representation of molecular electron densities , 2004 .

[26]  Paul L. A. Popelier,et al.  Atomic partitioning of molecular electrostatic potentials , 2000 .

[27]  Laurent Joubert,et al.  Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction , 2002 .

[28]  Christof Hättig,et al.  Recurrence relations for the direct calculation of spherical multipole interaction tensors and Coulomb-type interaction energies , 1996 .

[29]  V. Marcon,et al.  Molecular Modeling of Crystalline Oligothiophenes: Testing and Development of Improved Force Fields , 2004 .