Divalent metal ion 12-6-4 models with Panteva–Giambasu–York (PGY) pairwise corrections for balanced interactions with nucleic acids =================================================================================================================================== | Julie Puyo-Fourtine\ :sup:`1`, and Darrin M. York\ :sup:`1` | :sup:`1` Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA Learning objectives ------------------- .. start-learning-objectives - Why do we need a good description of ions–nucleic acids interactions. - Know how to apply 12-6-4 parameters and the PGY pairwise corrections in Amber. .. end-learning-objectives Relevant literature ------------------- - Panteva, M., Giambasu, G., and York, D. M. *Force Field for Mg2+, Mn2+, Zn2+, and Cd2+ Ions That Have Balanced Interactions with Nucleic Acids.* **J. Phys. Chem. B** (2015). https://doi.org/10.1021/acs.jpcb.5b10423 - Li, P., and Merz, K. M., Jr. *Taking into Account the Ion-Induced Dipole Interaction in the Nonbonded Model of Ions.* **J. Chem. Theory Comput.** (2013). https://doi.org/10.1021/ct400751u .. start-tutorial Introduction ------------ The need to model ions–nucleic acids interactions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Experimental and theoretical studies have shown that metal ions interact with nucleic acids in two main ways. First, electrostatic interactions between the negatively charged nucleic acid backbone and cations lead to a local enrichment of ions around the molecule, forming what is known as the ionic atmosphere. Its composition can be probed experimentally (for example by ion counting) and can also be described theoretically. Beyond these non-specific interactions, studies have also shown that both monovalent and divalent ions bind in a more specific manner, with well-localized binding sites. In RNA, these include coordination sites for divalent ions, especially Mg²⁺, whose presence can modify local geometry, stabilize compact tertiary folds, and interact with residues or ligands. These ions can also shift the pK\ :sub:`a` of nearby functional groups and contribute directly to catalytic activity. Such binding sites can be identified in X-ray crystallography and can also be investigated using NMR or spectroscopic techniques. However, all of these experimental approaches have limitations. In X-ray crystallography, for instance, it is often difficult to identify ions unambiguously; high, non-physiological ion concentrations are frequently required; and ion positions can be influenced by packing artifacts. As a result, many questions remain about the modes, locations, and strengths of ion binding to nucleic acids, as well as their impact on nucleic acid structure and dynamics. Molecular dynamics simulations therefore offer a valuable way to obtain a detailed, molecular-level description of these interactions, provided that they are able to represent them accurately... Limitations in modelling ions–nucleic interactions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The main challenge in simulating divalent ions comes from the absence of electronic polarization in classical, non-polarizable force fields. Atomic charges are fixed and cannot adapt to the local electrostatic environment, even though electronic density redistribution is essential for describing ion–RNA interactions. This leads to several systematic artifacts: over-stabilization of interactions with non-bridging phosphate oxygens, under-stabilization of nucleobase interactions and an incorrect balance between solvation and direct coordination. As a consequence, divalent ions such as Mg²⁺ may accumulate unrealistically at the RNA surface and remain bound too strongly and the preferred binding sites can be poorly defined, with incorrect partners being favored. Similar, although weaker, effects can also be observed for monovalent ions and for interactions between charged residues, such as salt bridges. How to overcome these limitations? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ One option is to use polarizable force fields, which introduce additional terms into the standard functional form to account for electronic polarization explicitly. Approaches based on induced point dipoles and explicit multipoles provide a more realistic physical description of ion–RNA interactions. However, their higher computational cost and the difficulty of parameterization make them challenging to apply routinely, and they are not yet the preferred choice in large-scale biomolecular simulations. An alternative is to modify the standard potential to incorporate key polarization effects implicitly. Several models follow this strategy by adjusting Lennard–Jones parameters or adding correction terms. The **12-6-4 model** extends the classical Lennard–Jones potential by adding a charge-induced dipole interaction term in :math:`r^{-4}`: .. math:: U_{ij}(r_{ij}) = \frac{A_{ij}}{r_{ij}^{12}} - \frac{B_{ij}}{r_{ij}^{6}} - \frac{C_{ij}}{r_{ij}^{4}} The coefficients :math:`A_{ij}` and :math:`B_{ij}` correspond to the usual Lennard–Jones parameters, related to :math:`R_{ij}` which is the distance at which two particles have a minimum in the LJ potential, while :math:`\varepsilon_{ij}` is the well depth : .. math:: A_{ij} = \varepsilon_{ij} R_{ij}^{12}, \qquad B_{ij} = 2\,\varepsilon_{ij} R_{ij}^{6}. The additional coefficient :math:`C_{ij}` introduces the charge-induced dipole interaction, which is defined as: .. math:: C_{ij} = B_{ij}\,\kappa, where :math:`\kappa` is a scaling parameter (in units of Å⁻²) that determines the strength of the :math:`r^{-4}` contribution. However, although the original 12–6–4 model was developed to accurately reproduce bulk hydration properties, it fails to capture experimentally measured affinities for key RNA-binding sites. This limitation motivated the development of the m12–6–4 model, in which only the :math:`C_{ij}` coefficients are re-optimized based on experimental data for three representative sites: - non-bridging oxygens of phosphate - N7 of adenine - N7 of guanine The pairwise coefficient :math:`C_{ij}` for an ion interacting with a given atom type is irectly proportional to the polarizability of the atom interacting with the ion :math:`\alpha` (in :math:`\mathrm{Å^3}`): .. math:: C_{ij}(\text{ion–site}) = \frac{C_{ij}(\text{ion–water})}{\alpha(\text{water})} \times {\alpha(\text{site})} This yields several improvements: - more accurate binding free energies between X²⁺-phosphate groups - correct stabilization of nucleobase interactions - an improved balance between solvation and direct coordination - more realistic X²⁺–RNA dissociation kinetics .. figure:: /_static/files/ModularTutorials/ForceField/Panteva_corrections/12-6-4_Panteva.png :alt: Comparison of 12-6-4 and m12-6-4 ion parameters :width: 950px :align: center **Figure 1.** **A)** Comparison of the errors in the absolute binding free energies for the 12–6–4 (left) and m12–6–4 (right) Mg²⁺, Mn²⁺, Zn²⁺, and Cd²⁺ ion parameters for selected nucleic acid sites. Computed values are averages from three independent simulations, and the error bars correspond to the standard deviations. DMP = dimethyl phosphate, A = adenosine, G = guanosine. **B)** Model systems and binding sites for which pairwise parameters were tuned to reproduce the reference experimental binding free energies. The magenta sphere represents either Mg²⁺, Mn²⁺, Zn²⁺, or Cd²⁺. Tutoriel -------- .. contents:: :local: :depth: 3 Downloadable files ~~~~~~~~~~~~~~~~~~ The following files are required to build the 12-6-4 topology and apply the PGY (m12-6-4) pairwise corrections in Amber. They can be downloaded directly: - :download:`tleap-prep-PDB-2-Amber.in ` tleap input file used to generate the initial Amber topology with the 12-6-4 ion model. - :download:`1264.sh ` Shell script that prepares the ParmEd instruction file and applies the PGY corrections. - :download:`parmed_1264_na.in ` ParmEd instruction file assigning NAMG/NGMG/OPMG atom types and enabling the PGY corrections. - :download:`lj_1264_pol.dat ` Polarizability table used by `add12_6_4` to compute the :math:`C_{ij}` coefficients. Building the topology with 12-6-4 parameters ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In this tutorial, the goal is to learn how to apply these corrections for divalent cations interacting with nucleic acids. Magnesium will be used as an example here. The first step is to prepare a standard Amber topology using the 12-6-4 Mg²⁺ model. We assume you have an AmberTools environment activated, for example: .. code-block:: bash mamba activate AmberTools25 We start from an input PDB file named ``SYSTEM.pdb`` that contains an RNA molecule and one or several Mg²⁺ ions. Run ``tleap`` with the following input file. The tleap input file ^^^^^^^^^^^^^^^^^^^^ .. code-block:: bash set default nocenter on # Do not recenter the molecule ### Sourcing amber force fields ############################################### source leaprc.RNA.OL3 # RNA force field OL3 source leaprc.water.tip4pew # TIP4P-Ew water model source leaprc.gaff2 # GAFF2 for small molecules loadamberparams frcmod.ions234lm_1264_tip4pew # 12-6-4 metal-ion parameters ### Loading structure from file ############################################## mol = loadpdb "SYSTEM.pdb" ### Adding counter ions ###################################################### addions mol NA 0 # Neutralize system ### Defining box & solvation ################################################# solvateoct mol TIP4PEWBOX 9 # 9 Å truncated octahedron box ### Adding bulk salt (example: 0.14 M NaCl) ################################# addionsrand mol NA 29 CL 29 6.0 # Random replacement, 6 Å min distance ### Saving ################################################################### saveamberparm mol SYSTEM.parm7 SYSTEM.rst7 quit After running: .. code-block:: bash tleap -f tleap-prep-PDB-2-Amber.in you will obtain: - ``SYSTEM.parm7`` (topology) - ``SYSTEM.rst7`` (coordinates) These files include the **12-6-4 Mg²⁺ model**. Applying the PGY pairwise corrections ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The m12-6-4 (PGY) corrections are applied in a **second pass** using ParmEd. The script ``1264.sh`` ^^^^^^^^^^^^^^^^^^^^^^ This helper script inserts the proper output file names and runs ParmEd: .. code-block:: bash #!/bin/bash # Usage: ./1264.sh SYSTEM name=$1 cat parmed_1264_na.in > parmed.${name}.in sed -i '/^outparm/d' parmed.${name}.in cat <> parmed.${name}.in outparm ${name}_1264.parm7 ${name}_1264.rst7 EOF parmed -i parmed.${name}.in -p ${name}.parm7 -c ${name}.rst7 Make executable: .. code-block:: bash chmod +x 1264.sh The file ``parmed_1264_na.in`` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This file applies the PGY-specific N7(A), N7(G), and OP corrections: .. code-block:: bash setOverwrite True change AMBER_ATOM_TYPE :A*,DA*@N7 NAMG change AMBER_ATOM_TYPE :G*,DG*@N7 NGMG change AMBER_ATOM_TYPE :*@OP* OPMG addLJType @%NAMG addLJType @%NGMG addLJType @%OPMG add12_6_4 @%Mg2+ watermodel TIP4PEW polfile lj_1264_pol.dat printLJMatrix @%Mg2+ outparm NAME.parm7 NAME.rst7 Polarizabilities (``lj_1264_pol.dat``) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Below is the full content of the ``lj_1264_pol.dat`` file: .. code-block:: none H 0.387 Referenced or adopted from Miller JACS,112,8533(1990) HC 0.387 Referenced or adopted from Miller JACS,112,8533(1990) H0 0.387 Referenced or adopted from Miller JACS,112,8533(1990) H1 0.387 Referenced or adopted from Miller JACS,112,8533(1990) H2 0.387 Referenced or adopted from Miller JACS,112,8533(1990) H3 0.387 Referenced or adopted from Miller JACS,112,8533(1990) HA 0.387 Referenced or adopted from Miller JACS,112,8533(1990) H4 0.387 Referenced or adopted from Miller JACS,112,8533(1990) H5 0.387 Referenced or adopted from Miller JACS,112,8533(1990) HO 0.000 Keep its C4 terms consistent with its 12-6 LJ parameters HS 0.387 Referenced or adopted from Miller JACS,112,8533(1990) HP 0.387 Referenced or adopted from Miller JACS,112,8533(1990) HZ 0.387 Referenced or adopted from Miller JACS,112,8533(1990) h1 0.387 Referenced or adopted from Miller JACS,112,8533(1990) h2 0.387 Referenced or adopted from Miller JACS,112,8533(1990) h3 0.387 Referenced or adopted from Miller JACS,112,8533(1990) h4 0.387 Referenced or adopted from Miller JACS,112,8533(1990) h5 0.387 Referenced or adopted from Miller JACS,112,8533(1990) ha 0.387 Referenced or adopted from Miller JACS,112,8533(1990) hc 0.387 Referenced or adopted from Miller JACS,112,8533(1990) hn 0.387 Referenced or adopted from Miller JACS,112,8533(1990) ho 0.000 Keep its C4 terms consistent with its 12-6 LJ parameters hp 0.387 Referenced or adopted from Miller JACS,112,8533(1990) hs 0.387 Referenced or adopted from Miller JACS,112,8533(1990) hx 0.387 Referenced or adopted from Miller JACS,112,8533(1990) Hc 0.387 Referenced or adopted from Miller JACS,112,8533(1990) Ha 0.387 Referenced or adopted from Miller JACS,112,8533(1990) Ho 0.000 Keep its C4 terms consistent with its 12-6 LJ parameters Hp 0.387 Referenced or adopted from Miller JACS,112,8533(1990) C 1.352 Referenced or adopted from Miller JACS,112,8533(1990) C* 1.352 Referenced or adopted from Miller JACS,112,8533(1990) C4 1.352 Referenced or adopted from Miller JACS,112,8533(1990) C5 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CA 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CB 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CC 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CD 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CK 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CM 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CN 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CO 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CP 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CQ 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CR 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CS 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CV 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CW 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CY 1.352 Referenced or adopted from Miller JACS,112,8533(1990) CZ 1.352 Referenced or adopted from Miller JACS,112,8533(1990) C2 1.352 Referenced or adopted from Miller JACS,112,8533(1990) C1 1.352 Referenced or adopted from Miller JACS,112,8533(1990) c 1.352 Referenced or adopted from Miller JACS,112,8533(1990) c2 1.352 Referenced or adopted from Miller JACS,112,8533(1990) ca 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cc 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cd 1.352 Referenced or adopted from Miller JACS,112,8533(1990) ce 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cf 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cp 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cq 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cu 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cv 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cx 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cy 1.352 Referenced or adopted from Miller JACS,112,8533(1990) cz 1.352 Referenced or adopted from Miller JACS,112,8533(1990) 2C 1.061 Referenced or adopted from Miller JACS,112,8533(1990) 3C 1.061 Referenced or adopted from Miller JACS,112,8533(1990) C8 1.061 Referenced or adopted from Miller JACS,112,8533(1990) CI 1.061 Referenced or adopted from Miller JACS,112,8533(1990) CT 1.061 Referenced or adopted from Miller JACS,112,8533(1990) CX 1.061 Referenced or adopted from Miller JACS,112,8533(1990) XC 1.061 Referenced or adopted from Miller JACS,112,8533(1990) TG 1.061 Referenced or adopted from Miller JACS,112,8533(1990) c3 1.061 Referenced or adopted from Miller JACS,112,8533(1990) C7 1.061 Referenced or adopted from Miller JACS,112,8533(1990) CJ 1.061 Referenced or adopted from Miller JACS,112,8533(1990) c1 1.283 Referenced or adopted from Miller JACS,112,8533(1990) cg 1.283 Referenced or adopted from Miller JACS,112,8533(1990) ch 1.283 Referenced or adopted from Miller JACS,112,8533(1990) Cg 1.061 Referenced or adoptedfrom Miller JACS,112,8533(1990) Cy 1.061 Referenced or adopted from Miller JACS,112,8533(1990) Cp 1.061 Referenced or adopted from Miller JACS,112,8533(1990) Ck 1.352 Referenced or adopted from Miller JACS,112,8533(1990) Cj 1.352 Referenced or adopted from Miller JACS,112,8533(1990) N 1.090 Referenced or adopted from Miller JACS,112,8533(1990) N* 1.090 Referenced or adopted from Miller JACS,112,8533(1990) N2 1.090 Referenced or adopted from Miller JACS,112,8533(1990) N3 1.090 Referenced or adopted from Miller JACS,112,8533(1990) NA 1.090 Referenced or adopted from Miller JACS,112,8533(1990) NB 1.090 Referenced or adopted from Miller JACS,112,8533(1990) NAMG 1.910 From Panteva et al. JPCB, 2015,119,15460 NGMG 1.925 From Panteva et al. JPCB, 2015,119,15460 NAMN 1.770 From Panteva et al. JPCB, 2015,119,15460 NGMN 1.860 From Panteva et al. JPCB, 2015,119,15460 NAZN 1.480 From Panteva et al. JPCB, 2015,119,15460 NGZN 1.640 From Panteva et al. JPCB, 2015,119,15460 NACD 1.580 From Panteva et al. JPCB, 2015,119,15460 NGCD 1.920 From Panteva et al. JPCB, 2015,119,15460 NC 1.090 Referenced or adopted from Miller JACS,112,8533(1990) ND 1.090 Referenced or adopted from Miller JACS,112,8533(1990) NL 1.090 Referenced or adopted from Miller JACS,112,8533(1990) NT 1.090 Referenced or adopted from Miller JACS,112,8533(1990) NY 1.090 Referenced or adopted from Miller JACS,112,8533(1990) TN 1.090 Referenced or adopted from Miller JACS,112,8533(1990) n 1.090 Referenced or adopted from Miller JACS,112,8533(1990) n1 1.090 Referenced or adopted from Miller JACS,112,8533(1990) n2 1.090 Referenced or adopted from Miller JACS,112,8533(1990) n3 1.090 Referenced or adopted from Miller JACS,112,8533(1990) n4 1.090 Referenced or adopted from Miller JACS,112,8533(1990) na 1.090 Referenced or adopted from Miller JACS,112,8533(1990) nb 1.090 Referenced or adopted from Miller JACS,112,8533(1990) nc 1.090 Referenced or adopted from Miller JACS,112,8533(1990) nd 1.090 Referenced or adopted from Miller JACS,112,8533(1990) ne 1.090 Referenced or adopted from Miller JACS,112,8533(1990) nf 1.090 Referenced or adopted from Miller JACS,112,8533(1990) nh 1.090 Referenced or adopted from Miller JACS,112,8533(1990) no 1.090 Referenced or adopted from Miller JACS,112,8533(1990) Ng 1.090 Referenced or adopted from Miller JACS,112,8533(1990) O 0.569 Referenced or adopted from Miller JACS,112,8533(1990) O2 0.569 Referenced or adopted from Miller JACS,112,8533(1990) O3 0.569 Referenced or adopted from Miller JACS,112,8533(1990) OD 0.569 Referenced or adoptedfrom Miller JACS,112,8533(1990) OP 0.569 Referenced or adopted from Miller JACS,112,8533(1990) OPMG 0.170 From Panteva et al. JPCB, 2015,119,15460 OPMN 0.370 From Panteva et al. JPCB, 2015,119,15460 OPZN 0.510 From Panteva et al. JPCB, 2015,119,15460 OPCD 0.680 From Panteva et al. JPCB, 2015,119,15460 OA 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) OH 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) OS 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) OY 0.637 Added by AG OZ 0.637 Added by AG OX 0.637 Added by AG OW 1.444 From "The Structure and Properties of Water" by Eisenberg & Kauzmann o 0.569 Referenced or adoptedfrom Miller JACS,112,8533(1990) oh 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) os 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) ow 1.444 From "The Structure and Properties of Water" by Eisenberg & Kauzmann Oh 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) Os 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) Oy 0.637 Referenced or adoptedfrom Miller JACS,112,8533(1990) S 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) SH 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) s 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) s2 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) s4 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) s6 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) sh 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) ss 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) sx 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) sy 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) Sm 3.000 Referenced or adoptedfrom Miller JACS,112,8533(1990) P 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) p2 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) p3 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) p4 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) p5 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) pb 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) pc 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) pd 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) pe 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) pf 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) px 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) py 1.538 Referenced or adoptedfrom Miller JACS,112,8533(1990) PX 1.538 Added by AG F 0.32 From Applequist et al. JACS,94,2952(1972) Cl 1.91 From Applequist et al. JACS,94,2952(1972) Br 2.88 From Applequist et al. JACS,94,2952(1972) I 4.69 From Applequist et al. JACS,94,2952(1972) f 0.32 From Applequist et al. JACS,94,2952(1972) cl 1.91 From Applequist et al. JACS,94,2952(1972) br 2.88 From Applequist et al. JACS,94,2952(1972) i 4.69 From Applequist et al. JACS,94,2952(1972) Li 0.029 From Sangster & Atwood J. Phys. C 11,1541(1978) Li+ 0.029 From Sangster & Atwood J. Phys. C 11,1541(1978) IP 0.2495 From Sangster & Atwood J. Phys. C 11,1541(1978) Na 0.2495 From Sangster & Atwood J. Phys. C 11,1541(1978) Na+ 0.2495 From Sangster & Atwood J. Phys. C 11,1541(1978) K 1.0571 From Sangster & Atwood J. Phys. C 11,1541(1978) K+ 1.0571 From Sangster & Atwood J. Phys. C 11,1541(1978) Rb 1.5600 From Sangster & Atwood J. Phys. C 11,1541(1978) Rb+ 1.5600 From Sangster & Atwood J. Phys. C 11,1541(1978) Cs 2.5880 From Sangster & Atwood J. Phys. C 11,1541(1978) Cs+ 2.5880 From Sangster & Atwood J. Phys. C 11,1541(1978) F- 0.9743 From Sangster & Atwood J. Phys. C 11,1541(1978) Cl- 3.2350 From Sangster & Atwood J. Phys. C 11,1541(1978) IM 3.2350 From Sangster & Atwood J. Phys. C 11,1541(1978) Br- 4.5330 From Sangster & Atwood J. Phys. C 11,1541(1978) I- 6.7629 From Sangster & Atwood J. Phys. C 11,1541(1978) Be2+ 0.0067 Calculated from B3LYP/6-311++G(2d,2p) Cu2+ 0.413 Calculated from B3LYP/6-311++G(2d,2p) CU 0.413 Calculated from B3LYP/6-311++G(2d,2p) Ni2+ 0.395 Calculated from B3LYP/6-311++G(2d,2p) Zn 0.344 Calculated from B3LYP/6-311++G(2d,2p) ZN 0.344 Calculated from B3LYP/6-311++G(2d,2p) Zn2+ 0.344 Calculated from B3LYP/6-311++G(2d,2p) Co2+ 0.447 Calculated from B3LYP/6-311++G(2d,2p) Cr2+ 0.623 Calculated from B3LYP/6-311++G(2d,2p) Fe 0.518 Calculated from B3LYP/6-311++G(2d,2p) FE 0.518 Calculated from B3LYP/6-311++G(2d,2p) Fe2+ 0.518 Calculated from B3LYP/6-311++G(2d,2p) Mg 0.048 Calculated from B3LYP/6-311++G(2d,2p) MG 0.048 Calculated from B3LYP/6-311++G(2d,2p) Mg2+ 0.048 Calculated from B3LYP/6-311++G(2d,2p) V2+ 0.620 Calculated from B3LYP/6-311++G(2d,2p) Mn2+ 0.534 Calculated from B3LYP/6-311++G(2d,2p) Hg2+ 0.707 Calculated from B3LYP/SDD Cd2+ 0.427 Calculated from B3LYP/SDD Ca2+ 0.477 Calculated from B3LYP/6-311++G(2d,2p) C0 0.477 Calculated from B3LYP/6-311++G(2d,2p) Sn2+ 3.083 Calculated from B3LYP/SDD Sr2+ 0.813 Calculated from B3LYP/SDD Ba2+ 1.496 Calculated from B3LYP/SDD HW 0.000 Water hydrogen / dummy atom hw 0.000 Water hydrogen / dummy atom EP 0.000 Water hydrogen / dummy atom EPW 0.000 Water hydrogen / dummy atom EP1 0.000 Water hydrogen / dummy atom EP2 0.000 Water hydrogen / dummy atom LP 0.000 Lone pair site Al3+ 0.031 Calculated from B3LYP/6-311++G(2d,2p) Fe3+ 0.297 Calculated from B3LYP/6-311++G(2d,2p) Cr3+ 0.352 Calculated from B3LYP/6-311++G(2d,2p) Y3+ 0.597 Calculated from B3LYP/SDD La3+ 1.141 Calculated from B3LYP/SDD Pr3+ 1.101 Calculated from B3LYP/SDD Nd3+ 1.047 Calculated from B3LYP/SDD Sm3+ 0.927 Calculated from B3LYP/SDD Eu3+ 0.885 Calculated from B3LYP/SDD Tm3+ 0.675 Calculated from B3LYP/SDD Lu3+ 0.629 Calculated from B3LYP/SDD Zr4+ 0.436 Calculated from B3LYP/SDD U4+ 1.044 Calculated from B3LYP/SDD Th4+ 1.141 Calculated from B3LYP/SDD M0 0.000 Treat as zero Output files ^^^^^^^^^^^^ Running: .. code-block:: bash ./1264.sh SYSTEM produces: - ``SYSTEM_1264.parm7`` - ``SYSTEM_1264.rst7`` .. figure:: /_static/files/ModularTutorials/ForceField/Panteva_corrections/output.png :alt: Output :width: 950px :align: center **Figure 2.** Screenshot of the output showing the interaction matrix involving magnesium. .. end-tutorial