Source Code for Module lib.physical_constants

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2007-2015 Edward d'Auvergne                                   # 
  4  #                                                                             # 
  5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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 19  #                                                                             # 
 20  ############################################################################### 
 21   
 22  # Module docstring. 
 23  """Module containing all physical constants used in relax, as well as all associated functions.""" 
 24   
 25   
 26  # Python module imports. 
 27  from math import pi 
 28  from string import ascii_letters, digits 
 29   
 30  # relax module imports. 
 31  from lib.float import nan 
 32   
 33   
 34  # Misc. constants. 
 35  ################## 
 36   
 37  h = 6.62606876 * 1e-34 
 38  """Planck's constant.""" 
 39   
 40  h_bar = h / (2.0 * pi) 
 41  """Dirac's constant.""" 
 42   
 43  mu0 = 4.0 * pi * 1e-7 
 44  """The magnetic constant or the permeability of vacuum.""" 
 45   
 46  kB = 1.380650424 * 1e-23 
 47  """Boltzmann's constant in SI units of J.K^-1 (the last 2 digits of '24' are within the measured error limits).""" 
 48   
 49   
 50  # CSA and bond lengths. 
 51  ####################### 
 52   
 53  N15_CSA = -172 * 1e-6 
 54  """The 15N CSA in the NH bond (default value).""" 
 55   
 56  NH_BOND_LENGTH = 1.02 * 1e-10 
 57  """The length of the NH bond (default value).""" 
 58   
 59  NH_BOND_LENGTH_RDC = 1.041 * 1e-10 
 60  """The length of the NH bond for RDCs (from Ottiger, M. and Bax A., J. Am. Chem. Soc. (1998), 120, 12334-12341).""" 
 61   
 62  CA_HA_BOND_LENGTH_RDC = 1.118 * 1e-10 
 63  """The length of the C_alpha-H_alpha bond for RDCs (from Ottiger, M. and Bax A., J. Am. Chem. Soc. (1998), 120, 12334-12341).""" 
 64   
 65  CA_C_BOND_LENGTH_RDC = 1.526 * 1e-10 
 66  """The length of the C_alpha-C_prime bond for RDCs (from Ottiger, M. and Bax A., J. Am. Chem. Soc. (1998), 120, 12334-12341).""" 
 67   
 68  C_N_BOND_LENGTH_RDC = 1.329 * 1e-10 
 69  """The length of the C_prime-N bond for RDCs (from Ottiger, M. and Bax A., J. Am. Chem. Soc. (1998), 120, 12334-12341).""" 
 70   
 71  C_HN_BOND_LENGTH_RDC = 2.067 * 1e-10 
 72  """The length of the C_prime-HN bond for RDCs (from Ottiger, M. and Bax A., J. Am. Chem. Soc. (1998), 120, 12334-12341).""" 
 73   
 74   
 75   
 76  # The dipolar constant. 
 77  ####################### 
 78   
 79 -def dipolar_constant(gx, gh, r): 
 80      """Calculate the dipolar constant. 
 81   
 82      The dipolar constant is defined as:: 
 83   
 84                mu0 gI.gS.h_bar 
 85          d = - --- ----------- , 
 86                4pi    r**3 
 87   
 88      where: 
 89          - mu0 is the permeability of free space, 
 90          - gI and gS are the gyromagnetic ratios of the I and S spins, 
 91          - h_bar is Dirac's constant which is equal to Planck's constant divided by 2pi, 
 92          - r is the distance between the two spins. 
 93   
 94   
 95      @param gx:  The gyromagnetic ratio of the heteronucleus (or first spin). 
 96      @type gx:   float 
 97      @param gh:  The gyromagnetic ratio of the proton (or second spin). 
 98      @type gh:   float 
 99      @param r:   The distance between the two nuclei. 
100      @type r:    float 
101      """ 
102   
103      # Catch zero bond lengths, returning NaN. 
104      if r == 0: 
105          return nan 
106   
107      # Calculate and return the value. 
108      return - mu0 / (4.0*pi) * gx * gh * h_bar / r**3 
109   
110   
111  # The pseudocontact shift constant. 
112  ################################### 
113   
114 -def pcs_constant(T, Bo, r): 
115      """Calculate the pseudocontact shift constant. 
116   
117      The pseudocontact shift constant is defined as:: 
118   
119              mu0 15kT   1 
120          d = --- ----- ---- , 
121              4pi Bo**2 r**3 
122   
123      where: 
124          - mu0 is the permeability of free space, 
125          - k is Boltzmann's constant, 
126          - T is the absolute temperature, 
127          - Bo is the magnetic field strength, 
128          - r is the distance between the paramagnetic centre (electron spin) and the nuclear spin. 
129   
130   
131      @param T:   The temperature in kelvin. 
132      @type T:    float 
133      @param Bo:  The magnetic field strength. 
134      @type Bo:   float 
135      @param r:   The distance between the two nuclei. 
136      @type r:    float 
137      """ 
138   
139      # Catch zero bond lengths, returning NaN. 
140      if r == 0: 
141          return nan 
142   
143      # Calculate and return the value. 
144      return mu0 / (4.0*pi) * 15.0 * kB * T / Bo**2 / r**3 
145   
146   
147   
148  # Element info. 
149  ############### 
150   
151 -def element_from_isotope(isotope): 
152      """Determine and return the element name for the given isotope. 
153   
154      @param isotope: The isotope name, such as '1H', '15N'. 
155      @type isotope:  str 
156      @return:        The element name. 
157      @rtype:         str 
158      """ 
159   
160      # Remove the digit characters. 
161      return isotope.strip(digits) 
162   
163   
164 -def number_from_isotope(isotope): 
165      """Determine and return the isotope number for the given isotope. 
166   
167      @param isotope: The isotope name, such as '1H', '15N'. 
168      @type isotope:  str 
169      @return:        The isotope number. 
170      @rtype:         int 
171      """ 
172   
173      # Remove the digit characters. 
174      return int(isotope.strip(ascii_letters)) 
175