1.. index:: dihedral_style class2 2.. index:: dihedral_style class2/omp 3.. index:: dihedral_style class2/kk 4 5dihedral_style class2 command 6============================= 7 8Accelerator Variants: *class2/omp*, *class2/kk* 9 10Syntax 11"""""" 12 13.. code-block:: LAMMPS 14 15 dihedral_style class2 16 17Examples 18"""""""" 19 20.. code-block:: LAMMPS 21 22 dihedral_style class2 23 dihedral_coeff 1 100 75 100 70 80 60 24 dihedral_coeff * mbt 3.5945 0.1704 -0.5490 1.5228 25 dihedral_coeff * ebt 0.3417 0.3264 -0.9036 0.1368 0.0 -0.8080 1.0119 1.1010 26 dihedral_coeff 2 at 0.0 -0.1850 -0.7963 -2.0220 0.0 -0.3991 110.2453 105.1270 27 dihedral_coeff * aat -13.5271 110.2453 105.1270 28 dihedral_coeff * bb13 0.0 1.0119 1.1010 29 30Description 31""""""""""" 32 33The *class2* dihedral style uses the potential 34 35.. math:: 36 37 E = & E_d + E_{mbt} + E_{ebt} + E_{at} + E_{aat} + E_{bb13} \\ 38 E_d = & \sum_{n=1}^{3} K_n [ 1 - \cos (n \phi - \phi_n) ] \\ 39 E_{mbt} = & (r_{jk} - r_2) [ A_1 \cos (\phi) + A_2 \cos (2\phi) + A_3 \cos (3\phi) ] \\ 40 E_{ebt} = & (r_{ij} - r_1) [ B_1 \cos (\phi) + B_2 \cos (2\phi) + B_3 \cos (3\phi) ] + \\ 41 & (r_{kl} - r_3) [ C_1 \cos (\phi) + C_2 \cos (2\phi) + C_3 \cos (3\phi) ] \\ 42 E_{at} = & (\theta_{ijk} - \theta_1) [ D_1 \cos (\phi) + D_2 \cos (2\phi) + D_3 \cos (3\phi) ] + \\ 43 & (\theta_{jkl} - \theta_2) [ E_1 \cos (\phi) + E_2 \cos (2\phi) + E_3 \cos (3\phi) ] \\ 44 E_{aat} = & M (\theta_{ijk} - \theta_1) (\theta_{jkl} - \theta_2) \cos (\phi) \\ 45 E_{bb13} = & N (r_{ij} - r_1) (r_{kl} - r_3) 46 47where :math:`E_d` is the dihedral term, :math:`E_{mbt}` is a middle-bond-torsion term, 48:math:`E_{ebt}` is an end-bond-torsion term, :math:`E_{at}` is an angle-torsion term, :math:`E_{aat}` 49is an angle-angle-torsion term, and :math:`E_{bb13}` is a bond-bond-13 term. 50 51:math:`\theta_1` and :math:`\theta_2` are equilibrium angles and :math:`r_1`, :math:`r_2`, and 52:math:`r_3` are equilibrium bond lengths. 53 54See :ref:`(Sun) <dihedral-Sun>` for a description of the COMPASS class2 force field. 55 56Coefficients for the :math:`E_d`, :math:`E_{mbt}`, :math:`E_{ebt}`, 57:math:`E_{at}`, :math:`E_{aat}`, and :math:`E_{bb13}` formulas must be 58defined for each dihedral type via the :doc:`dihedral_coeff <dihedral_coeff>` 59command as in the example above, or in the data file 60or restart files read by the :doc:`read_data <read_data>` or 61:doc:`read_restart <read_restart>` commands. 62 63These are the 6 coefficients for the :math:`E_d` formula: 64 65* :math:`K_1` (energy) 66* :math:`\phi_1` (degrees) 67* :math:`K_2` (energy) 68* :math:`\phi_2` (degrees) 69* :math:`K_3` (energy) 70* :math:`phi_3` (degrees) 71 72For the :math:`E_{mbt}` formula, each line in a 73:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists 745 coefficients, the first of which is *mbt* to indicate they are 75MiddleBondTorsion coefficients. In a data file, these coefficients 76should be listed under a *MiddleBondTorsion Coeffs* heading and you 77must leave out the *mbt*, i.e. only list 4 coefficients after the 78dihedral type. 79 80* *mbt* 81* :math:`A_1` (energy/distance) 82* :math:`A_2` (energy/distance) 83* :math:`A_3` (energy/distance) 84* :math:`r_2` (distance) 85 86For the :math:`E_{ebt}` formula, each line in a 87:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists 889 coefficients, the first of which is *ebt* to indicate they are 89EndBondTorsion coefficients. In a data file, these coefficients 90should be listed under a *EndBondTorsion Coeffs* heading and you must 91leave out the *ebt*, i.e. only list 8 coefficients after the dihedral 92type. 93 94* *ebt* 95* :math:`B_1` (energy/distance) 96* :math:`B_2` (energy/distance) 97* :math:`B_3` (energy/distance) 98* :math:`C_1` (energy/distance) 99* :math:`C_2` (energy/distance) 100* :math:`C_3` (energy/distance) 101* :math:`r_1` (distance) 102* :math:`r_3` (distance) 103 104For the :math:`E_{at}` formula, each line in a 105:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists 1069 coefficients, the first of which is *at* to indicate they are 107AngleTorsion coefficients. In a data file, these coefficients should 108be listed under a *AngleTorsion Coeffs* heading and you must leave out 109the *at*, i.e. only list 8 coefficients after the dihedral type. 110 111* *at* 112* :math:`D_1` (energy) 113* :math:`D_2` (energy) 114* :math:`D_3` (energy) 115* :math:`E_1` (energy) 116* :math:`E_2` (energy) 117* :math:`E_3` (energy) 118* :math:`\theta_1` (degrees) 119* :math:`\theta_2` (degrees) 120 121:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but 122LAMMPS converts them to radians internally; hence the various 123:math:`D` and :math:`E` are effectively energy per radian. 124 125For the :math:`E_{aat}` formula, each line in a :doc:`dihedral_coeff 126<dihedral_coeff>` command in the input script lists 4 coefficients, 127the first of which is *aat* to indicate they are AngleAngleTorsion 128coefficients. In a data file, these coefficients should be listed 129under a *AngleAngleTorsion Coeffs* heading and you must leave out the 130*aat*, i.e. only list 3 coefficients after the dihedral type. 131 132* *aat* 133* :math:`M` (energy) 134* :math:`\theta_1` (degrees) 135* :math:`\theta_2` (degrees) 136 137:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but 138LAMMPS converts them to radians internally; hence :math:`M` is 139effectively energy per radian\^2. 140 141For the :math:`E_{bb13}` formula, each line in a 142:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists 1434 coefficients, the first of which is *bb13* to indicate they are 144BondBond13 coefficients. In a data file, these coefficients should be 145listed under a *BondBond13 Coeffs* heading and you must leave out the 146*bb13*, i.e. only list 3 coefficients after the dihedral type. 147 148* *bb13* 149* :math:`N` (energy/distance\^2) 150* :math:`r_1` (distance) 151* :math:`r_3` (distance) 152 153---------- 154 155.. include:: accel_styles.rst 156 157---------- 158 159Restrictions 160"""""""""""" 161 162This dihedral style can only be used if LAMMPS was built with the 163CLASS2 package. See the :doc:`Build package <Build_package>` doc 164page for more info. 165 166Related commands 167"""""""""""""""" 168 169:doc:`dihedral_coeff <dihedral_coeff>` 170 171Default 172""""""" 173 174none 175 176---------- 177 178.. _dihedral-Sun: 179 180**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998). 181