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units.py
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"""Contains fundamental constants in atomic units.
Copyright (C) 2013, Joshua More and Michele Ceriotti
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http.//www.gnu.org/licenses/>.
Classes:
Constants: Class whose members are fundamental constants.
Elements: Class which contains the mass of different elements
Units: Class which contains the methods needed to transform
between different systems of units.
"""
import re
from ipi.utils.messages import verbosity, info
__all__ = ['Constants', 'Elements', 'unit_to_internal', 'unit_to_user']
class Constants:
"""Class whose members are fundamental constants.
Attributes:
kb: Boltzmann constant.
hbar: Reduced Planck's constant.
amu: Atomic mass unit.
"""
kb = 1.0
hbar = 1.0
amu = 1822.8885
class Elements(dict):
"""Class which contains the mass of different elements.
Attributes:
mass_list: A dictionary containing the masses of different elements.
Has the form {"label": Mass in a.m.u.}. Note that the generic "X"
label is assumed to be an electron.
"""
mass_list={
"X" : 1.0000/Constants.amu,
"H" : 1.00794,
"D" : 2.0141,
"Z" : 1.382943, #an interpolated H-D atom, based on y=1/sqrt(m) scaling
"H2" : 2.0160,
"He" : 4.002602,
"Li" : 6.9410,
"Be" : 9.012182,
"B" : 10.811,
"C" : 12.0107,
"N" : 14.00674,
"O" : 15.9994,
"F" : 18.998403,
"Ne" : 20.1797,
"Na" : 22.989770,
"Mg" : 24.3050,
"Al" : 26.981538,
"Si" : 28.0855,
"P" : 30.973761,
"S" : 32.066,
"Cl" : 35.4527,
"Ar" : 39.9480,
"K" : 39.0983,
"Ca" : 40.078,
"Sc" : 44.955910,
"Ti" : 47.867,
"V" : 50.9415,
"Cr" : 51.9961,
"Mn" : 54.938049,
"Fe" : 55.845,
"Co" : 58.933200,
"Ni" : 58.6934,
"Cu" : 63.546,
"Zn" : 65.39,
"Ga" : 69.723,
"Ge" : 72.61,
"As" : 74.92160,
"Se" : 78.96,
"Br" : 79.904,
"Kr" : 83.80,
"Rb" : 85.4678,
"Sr" : 87.62,
"Y" : 88.90585,
"Zr" : 91.224,
"Nb" : 92.90638,
"Mo" : 95.94,
"Tc" : 98,
"Ru" : 101.07,
"Rh" : 102.90550,
"Pd" : 106.42,
"Ag" : 107.8682,
"Cd" : 112.411,
"In" : 114.818,
"Sn" : 118.710,
"Sb" : 121.760,
"Te" : 127.60,
"I" : 126.90447,
"Xe" : 131.29,
"Cs" : 132.90545,
"Ba" : 137.327,
"La" : 138.9055,
"Ce" : 140.166,
"Pr" : 140.90765,
"Nd" : 144.24,
"Pm" : 145,
"Sm" : 150.36,
"Eu" : 151.964,
"Gd" : 157.25,
"Tb" : 158.92534,
"Dy" : 162.50,
"Ho" : 164.93032,
"Er" : 167.26,
"Tm" : 168.93241,
"Yb" : 173.04,
"Lu" : 174.967,
"Hf" : 178.49,
"Ta" : 180.9479,
"W" : 183.84,
"Re" : 186.207,
"Os" : 190.23,
"Ir" : 192.217,
"Pt" : 195.078,
"Au" : 196.96655,
"Hg" : 200.59,
"Tl" : 204.3833,
"Pb" : 207.2,
"Bi" : 208.98038,
"Po" : 209,
"At" : 210,
"Rn" : 222,
"Fr" : 223,
"Ra" : 226,
"Ac" : 227,
"Th" : 232.0381,
"Pa" : 231.03588,
"U" : 238.0289,
"Np" : 237,
"Pu" : 244,
"Am" : 243,
"Cm" : 247,
"Bk" : 247,
"Cf" : 251,
"Es" : 252,
"Fm" : 257,
"Md" : 258,
"No" : 259,
"Lr" : 262,
"Rf" : 267,
"Db" : 268,
"Sg" : 269,
"Bh" : 270,
"Hs" : 269,
"Mt" : 278,
"Ds" : 281,
"Rg" : 280,
"Cn" : 285,
"Uut" : 286,
"Fl" : 289,
"Uup" : 288,
"Lv" : 293,
"Uus" : 294,
"Uuo" : 294
}
@classmethod
def mass(cls, label):
"""Function to access the mass_list attribute.
Note that this does not require an instance of the Elements class to be
created, as this is a class method. Therefore using Elements.mass(label)
will give the mass of the element with the atomic symbol given by label.
Args:
label: The atomic symbol of the atom whose mass is required.
Returns:
A float giving the mass of the atom with atomic symbol label.
"""
try:
return cls.mass_list[label]*Constants.amu
except KeyError:
info("Unknown element given, you must specify the mass", verbosity.low)
return -1.0
# these are the conversion FROM the unit stated to internal (atomic) units
UnitMap = {
"undefined": {
"" : 1.00
},
"energy": {
"" : 1.00,
"atomic_unit" : 1.00,
"electronvolt" : 0.036749326,
"j/mol" : 0.00000038087989,
"cal/mol" : 0.0000015946679,
"kelvin" : 3.1668152e-06
},
"temperature": {
"" : 1.00,
"atomic_unit" : 1.00,
"kelvin" : 3.1668152e-06
},
"time": {
"" : 1.00,
"atomic_unit" : 1.00,
"second" : 4.1341373e+16
},
"frequency" : { # NB Internally, ANGULAR frequencies are used.
"" : 1.00,
"atomic_unit" : 1.00,
"inversecm" : 4.5563353e-06,
"hertz*rad" : 2.4188843e-17,
"hertz" : 1.5198298e-16
},
"ms-momentum" : { # TODO fill up units here (mass-scaled momentum)
"" : 1.00,
"atomic_unit" : 1.00
},
"length" : {
"" : 1.00,
"atomic_unit" : 1.00,
"angstrom" : 1.8897261,
"meter" : 1.8897261e+10
},
"volume" : {
"" : 1.00,
"atomic_unit" : 1.00,
"angstrom3" : 6.748334231,
},
"velocity": {
"" : 1.00,
"atomic_unit" : 1.00,
"m/s" : 4.5710289e-7
},
"momentum": {
"" : 1.00,
"atomic_unit" : 1.00
},
"mass": {
"" : 1.00,
"atomic_unit" : 1.00,
"dalton" : 1.00*Constants.amu,
"electronmass" : 1.00
},
"pressure" : {
"" : 1.00,
"atomic_unit" : 1.00,
"bar" : 3.398827377e-9,
"atmosphere" : 3.44386184e-9,
"pascal" : 3.398827377e-14
},
"density" : {
"" : 1.00,
"atomic_unit" : 1.00,
"g/cm3" : 162.67263
},
"force" : {
"" : 1.00,
"atomic_unit" : 1.00,
"newton" : 12137805
}
}
# a list of magnitude prefixes
UnitPrefix = {
"" : 1.0,
"yotta" : 1e24, "zetta" : 1e21, "exa" : 1e18, "peta" : 1e15,
"tera" : 1e12, "giga" : 1e9, "mega" : 1e6, "kilo" : 1e3,
"milli" : 1e-3, "micro" : 1e-6, "nano" : 1e-9, "pico" : 1e-12,
"femto" : 1e-15, "atto" : 1e-18, "zepto" : 1e-21, "yocto" : 1e-24
}
# builds a RE to match prefix and split out the base unit
UnitPrefixRE = ""
for key in UnitPrefix:
UnitPrefixRE = UnitPrefixRE + key + "|"
UnitPrefixRE = " *(" + UnitPrefixRE[1:] + ")(.*) *"
UnitPrefixRE = re.compile(UnitPrefixRE)
########################################################################
# Atomic units are used EVERYWHERE internally. In order to quickly #
# interface with any "outside" unit, we set up a simple conversion #
# library. #
########################################################################
def unit_to_internal(family, unit, number):
"""Converts a number of given dimensions and units into internal units.
Args:
family: The dimensionality of the number.
unit: The units 'number' is originally in.
number: The value of the parameter in the units 'unit'.
Returns:
The number in internal units.
Raises:
ValueError: Raised if the user specified units aren't given in the
UnitMap dictionary.
IndexError: Raised if the programmer specified dimensionality for the
parameter isn't in UnitMap. Shouldn't happen, for obvious reasons.
TypeError: Raised if the prefix is correct, but the base unit is not, in
the user specified unit string.
"""
if not (family == "number" or family in UnitMap):
raise IndexError(family + " is an undefined units kind.")
if family == "number":
return number
if unit == "":
prefix = ""
base = ""
else:
m = UnitPrefixRE.match(unit);
if m is None:
raise ValueError("Unit " + unit + " is not structured with a prefix+base syntax.")
prefix = m.group(1)
base = m.group(2)
if not prefix in UnitPrefix:
raise TypeError(prefix + " is not a valid unit prefix.")
if not base in UnitMap[family]:
raise TypeError(base + " is an undefined unit for kind " + family + ".")
return number*UnitMap[family][base]*UnitPrefix[prefix]
def unit_to_user(family, unit, number):
"""Converts a number of given dimensions from internal to user units.
Args:
family: The dimensionality of the number.
unit: The units 'number' should be changed to.
number: The value of the parameter in internal units.
Returns:
The number in the user specified units
"""
return number/unit_to_internal(family, unit, 1.0)

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