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clarify units for energy terms with angles

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This commit is contained in:
Steve Plimpton
2020-07-07 15:19:17 -06:00
parent 6bf329098e
commit 6239a579e8
12 changed files with 121 additions and 92 deletions
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7
doc/src/angle_charmm.rst
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@ -49,13 +49,14 @@ The following coefficients must be defined for each angle type via the
the data file or restart files read by the :doc:`read_data <read_data>`
or :doc:`read_restart <read_restart>` commands:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\theta_0` (degrees)
* :math:`K_{ub}` (energy/distance\^2)
* :math:`r_{ub}` (distance)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of :math:`K` are in energy/radian\^2.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
----------

42
doc/src/angle_class2.rst
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@ -41,27 +41,29 @@ The *class2* angle style uses the potential
E_{bb} & = M (r_{ij} - r_1) (r_{jk} - r_2) \\
E_{ba} & = N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2(r_{jk} - r_2)(\theta - \theta_0)
where :math:`E_a` is the angle term, :math:`E_{bb}` is a bond-bond term, and :math:`E_{ba}` is a
bond-angle term. :math:`\theta_0` is the equilibrium angle and :math:`r_1` and :math:`r_2` are
the equilibrium bond lengths.
where :math:`E_a` is the angle term, :math:`E_{bb}` is a bond-bond
term, and :math:`E_{ba}` is a bond-angle term. :math:`\theta_0` is
the equilibrium angle and :math:`r_1` and :math:`r_2` are the
equilibrium bond lengths.
See :ref:`(Sun) <angle-Sun>` for a description of the COMPASS class2 force field.
Coefficients for the :math:`E_a`, :math:`E_{bb}`, and :math:`E_{ba}` formulas must be defined for
each angle type via the :doc:`angle_coeff <angle_coeff>` command as in
the example above, or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands.
Coefficients for the :math:`E_a`, :math:`E_{bb}`, and :math:`E_{ba}`
formulas must be defined for each angle type via the :doc:`angle_coeff
<angle_coeff>` command as in the example above, or in the data file or
restart files read by the :doc:`read_data <read_data>` or
:doc:`read_restart <read_restart>` commands.
These are the 4 coefficients for the :math:`E_a` formula:
* :math:`\theta_0` (degrees)
* :math:`K_2` (energy/radian\^2)
* :math:`K_3` (energy/radian\^3)
* :math:`K_4` (energy/radian\^4)
* :math:`K_2` (energy)
* :math:`K_3` (energy)
* :math:`K_4` (energy)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of the various :math:`K` are in per-radian.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence the various :math:`K` are effectively energy
per radian\^2 or radian\^3 or radian\^4.
For the :math:`E_{bb}` formula, each line in a :doc:`angle_coeff <angle_coeff>`
command in the input script lists 4 coefficients, the first of which
@ -122,11 +124,15 @@ The *class2/p6* angle style uses the *class2* potential expanded to sixth order:
In this expanded term 6 coefficients for the :math:`E_a` formula need to be set:
* :math:`\theta_0` (degrees)
* :math:`K_2` (energy/radian\^2)
* :math:`K_3` (energy/radian\^3)
* :math:`K_4` (energy/radian\^4)
* :math:`K_5` (energy/radian\^5)
* :math:`K_6` (energy/radian\^6)
* :math:`K_2` (energy)
* :math:`K_3` (energy)
* :math:`K_4` (energy)
* :math:`K_5` (energy)
* :math:`K_6` (energy)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence the various :math:`K` are effectively energy
per radian\^2 or radian\^3 or radian\^4 or radian\^5 or radian\^6.
The bond-bond and bond-angle terms remain unchanged.

9
doc/src/angle_cross.rst
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@ -40,14 +40,15 @@ the data file or restart files read by the :doc:`read_data <read_data>`
or :doc:`read_restart <read_restart>` commands:
* :math:`K_{SS}` (energy/distance\^2)
* :math:`K_{BS0}` (energy/distance/rad)
* :math:`K_{BS1}` (energy/distance/rad)
* :math:`K_{BS0}` (energy/distance)
* :math:`K_{BS1}` (energy/distance)
* :math:`r_{12,0}` (distance)
* :math:`r_{32,0}` (distance)
* :math:`\theta_0` (degrees)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of :math:`K_{BS0}` and :math:`K_{BS1}` are in energy/distance/radian.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence the :math:`K_{BS0}` and :math:`K_{BS1}` are
effectively energy/distance per radian.
Restrictions
""""""""""""

15
doc/src/angle_harmonic.rst
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@ -44,11 +44,12 @@ The following coefficients must be defined for each angle type via the
the data file or restart files read by the :doc:`read_data <read_data>`
or :doc:`read_restart <read_restart>` commands:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\theta_0` (degrees)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of :math:`K` are in energy/radian\^2.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
----------
@ -61,11 +62,13 @@ produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. See the :doc:`Build package <Build_package>` doc page for more info.
LAMMPS was built with those packages. See the :doc:`Build package
<Build_package>` doc page for more info.
You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the :doc:`-suffix command-line switch <Run_options>` when you invoke LAMMPS, or you can use the
:doc:`suffix <suffix>` command in your input script.
by including their suffix, or you can use the :doc:`-suffix
command-line switch <Run_options>` when you invoke LAMMPS, or you can
use the :doc:`suffix <suffix>` command in your input script.
See the :doc:`Speed packages <Speed_packages>` doc page for more
instructions on how to use the accelerated styles effectively.

14
doc/src/angle_mm3.rst
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@ -28,20 +28,22 @@ as defined in :ref:`(Allinger) <mm3-allinger1989>`
E = K (\theta - \theta_0)^2 \left[ 1 - 0.014(\theta - \theta_0) + 5.6(10)^{-5} (\theta - \theta_0)^2 - 7.0(10)^{-7} (\theta - \theta_0)^3 + 9(10)^{-10} (\theta - \theta_0)^4 \right]
where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a
prefactor. The anharmonic prefactors have units :math:`\deg^{-n}`, for example
:math:`-0.014 \deg^{-1}`, :math:`5.6 \cdot 10^{-5} \deg^{-2}`, ...
where :math:`\theta_0` is the equilibrium value of the angle, and
:math:`K` is a prefactor. The anharmonic prefactors have units
:math:`\deg^{-n}`, for example :math:`-0.014 \deg^{-1}`, :math:`5.6
\cdot 10^{-5} \deg^{-2}`, ...
The following coefficients must be defined for each angle type via the
:doc:`angle_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read_data <read_data>`
or :doc:`read_restart <read_restart>` commands:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\theta_0` (degrees)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of :math:`K` are in energy/radian\^2.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
Restrictions
""""""""""""

11
doc/src/angle_quartic.rst
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@ -39,12 +39,13 @@ the data file or restart files read by the :doc:`read_data <read_data>`
or :doc:`read_restart <read_restart>` commands:
* :math:`\theta_0` (degrees)
* :math:`K_2` (energy/radian\^2)
* :math:`K_3` (energy/radian\^3)
* :math:`K_4` (energy/radian\^4)
* :math:`K_2` (energy)
* :math:`K_3` (energy)
* :math:`K_4` (energy)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of :math:`K` are in energy/radian\^2.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence the various :math:`K` are effectively energy
per radian\^2 or radian\^3 or radian\^4.
----------

15
doc/src/angle_sdk.rst
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@ -44,13 +44,15 @@ is included in :math:`K`.
The following coefficients must be defined for each angle type via the
:doc:`angle_coeff <angle_coeff>` command as in the example above:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\theta_0` (degrees)
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of :math:`K` are in energy/radian\^2.
The also required *lj/sdk* parameters will be extracted automatically
from the pair_style.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
The required *lj/sdk* parameters are extracted automatically from the
pair_style.
----------
@ -63,7 +65,8 @@ produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. See the :doc:`Build package <Build_package>` doc page for more info.
LAMMPS was built with those packages. See the :doc:`Build package
<Build_package>` doc page for more info.
You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the :doc:`-suffix command-line switch <Run_options>` when you invoke LAMMPS, or you can use the

38
doc/src/dihedral_class2.rst
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@ -111,34 +111,34 @@ be listed under a *AngleTorsion Coeffs* heading and you must leave out
the *at*, i.e. only list 8 coefficients after the dihedral type.
* *at*
* :math:`D_1` (energy/radian)
* :math:`D_2` (energy/radian)
* :math:`D_3` (energy/radian)
* :math:`E_1` (energy/radian)
* :math:`E_2` (energy/radian)
* :math:`E_3` (energy/radian)
* :math:`D_1` (energy)
* :math:`D_2` (energy)
* :math:`D_3` (energy)
* :math:`E_1` (energy)
* :math:`E_2` (energy)
* :math:`E_3` (energy)
* :math:`\theta_1` (degrees)
* :math:`\theta_2` (degrees)
:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but LAMMPS converts
them to radians internally; hence the units of :math:`D` and :math:`E` are in
energy/radian.
:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but
LAMMPS converts them to radians internally; hence the various
:math:`D` and :math:`E` are effectively energy per radian.
For the :math:`E_{aat}` formula, each line in a
:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists
4 coefficients, the first of which is *aat* to indicate they are
AngleAngleTorsion coefficients. In a data file, these coefficients
should be listed under a *AngleAngleTorsion Coeffs* heading and you
must leave out the *aat*, i.e. only list 3 coefficients after the
dihedral type.
For the :math:`E_{aat}` formula, each line in a :doc:`dihedral_coeff
<dihedral_coeff>` command in the input script lists 4 coefficients,
the first of which is *aat* to indicate they are AngleAngleTorsion
coefficients. In a data file, these coefficients should be listed
under a *AngleAngleTorsion Coeffs* heading and you must leave out the
*aat*, i.e. only list 3 coefficients after the dihedral type.
* *aat*
* :math:`M` (energy/radian\^2)
* :math:`M` (energy)
* :math:`\theta_1` (degrees)
* :math:`\theta_2` (degrees)
:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but LAMMPS converts
them to radians internally; hence the units of M are in energy/radian\^2.
:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but
LAMMPS converts them to radians internally; hence :math:`M` is
effectively energy per radian\^2.
For the :math:`E_{bb13}` formula, each line in a
:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists

6
doc/src/dihedral_quadratic.rst
View File

@ -39,9 +39,13 @@ above, or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\phi_0` (degrees)
:math:`\phi_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
----------
Styles with a *gpu*\ , *intel*\ , *kk*\ , *omp*\ , or *opt* suffix are

8
doc/src/fix_restrain.rst
View File

@ -183,11 +183,13 @@ the restraint is
with the following coefficients:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\theta_0` (degrees)
:math:`K` and :math:`\theta_0` are specified with the fix. Note that the usual 1/2
factor is included in :math:`K`.
:math:`K` and :math:`\theta_0` are specified with the fix.
:math:`\theta_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2. Note that the usual 1/2 factor is included in :math:`K`.
----------

33
doc/src/improper_class2.rst
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@ -74,29 +74,31 @@ commands.
These are the 2 coefficients for the :math:`E_i` formula:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\chi_0` (degrees)
:math:`\chi_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2.
:math:`\chi_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
For the :math:`E_{aa}` formula, each line in a
:doc:`improper_coeff <improper_coeff>` command in the input script lists
7 coefficients, the first of which is *aa* to indicate they are
AngleAngle coefficients. In a data file, these coefficients should be
listed under a *AngleAngle Coeffs* heading and you must leave out the
*aa*, i.e. only list 6 coefficients after the improper type.
For the :math:`E_{aa}` formula, each line in a :doc:`improper_coeff
<improper_coeff>` command in the input script lists 7 coefficients,
the first of which is *aa* to indicate they are AngleAngle
coefficients. In a data file, these coefficients should be listed
under a *AngleAngle Coeffs* heading and you must leave out the *aa*,
i.e. only list 6 coefficients after the improper type.
* *aa*
* :math:`M_1` (energy/distance)
* :math:`M_2` (energy/distance)
* :math:`M_3` (energy/distance)
* :math:`M_1` (energy)
* :math:`M_2` (energy)
* :math:`M_3` (energy)
* :math:`\theta_1` (degrees)
* :math:`\theta_2` (degrees)
* :math:`\theta_3` (degrees)
The theta values are specified in degrees, but LAMMPS converts them to
radians internally; hence the units of M are in energy/radian\^2.
The :math:`\theta` values are specified in degrees, but LAMMPS
converts them to radians internally; hence the hence the various
:math:`M` are effectively energy per radian\^2.
----------
@ -109,7 +111,8 @@ produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. See the :doc:`Build package <Build_package>` doc page for more info.
LAMMPS was built with those packages. See the :doc:`Build package
<Build_package>` doc page for more info.
You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the :doc:`-suffix command-line switch <Run_options>` when you invoke LAMMPS, or you can use the

15
doc/src/improper_harmonic.rst
View File

@ -59,11 +59,12 @@ above, or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands:
* :math:`K` (energy/radian\^2)
* :math:`K` (energy)
* :math:`\chi_0` (degrees)
:math:`\chi_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2.
:math:`\chi_0` is specified in degrees, but LAMMPS converts it to
radians internally; hence :math:`K` is effectively energy per
radian\^2.
----------
@ -76,11 +77,13 @@ produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
USER-OMP and OPT packages, respectively. They are only enabled if
LAMMPS was built with those packages. See the :doc:`Build package <Build_package>` doc page for more info.
LAMMPS was built with those packages. See the :doc:`Build package
<Build_package>` doc page for more info.
You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the :doc:`-suffix command-line switch <Run_options>` when you invoke LAMMPS, or you can use the
:doc:`suffix <suffix>` command in your input script.
by including their suffix, or you can use the :doc:`-suffix
command-line switch <Run_options>` when you invoke LAMMPS, or you can
use the :doc:`suffix <suffix>` command in your input script.
See the :doc:`Speed packages <Speed_packages>` doc page for more
instructions on how to use the accelerated styles effectively.