MADNESS  0.10.1
constants.h
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1 /*
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31 
32 /**
33  \file constants.h
34  \brief Defines common mathematical and physical constants.
35  \ingroup libraries
36 
37  \todo We should consider a more uniform naming scheme for all of the conversion ratios.
38 */
39 
40 #ifndef MADNESS_CONSTANTS_H
41 #define MADNESS_CONSTANTS_H
42 
43 namespace madness {
44 
45  namespace constants {
46 
47  // Mathematical constants
48  const double pi = 3.14159265358979323846264338328; ///< Mathematical constant \f$\pi\f$.
49 
50 
51  // Misc physical constants and units
52 
53  const double calorie_joule_relationship = 4.184000000 ; ///< 1 kcal/mol = 4.184 kJ/mol.
54 
55  const double Debye = 3.335640035e-30 ; ///< Cm (coulomb metre).
56 
57 
58  // The following physical constants and units were obtained from NIST http://physics.nist.gov/constants
59  // on 2/2/2008. The comments contain the uncertainty and units.
60 
61  /// Mass constant in atomic units.
62  const double atomic_mass_constant = 1.660538782e-27 ; // 0.000000083e-27 kg
63 
64  /// First hyperpolarizability in atomic units.
65  const double atomic_unit_of_1st_hyperpolarizablity = 3.206361533e-53 ; // 0.000000081e-53 C^3 m^3 J^-2
66 
67  /// Second hyperpolarizability in atomic units.
68  const double atomic_unit_of_2nd_hyperpolarizablity = 6.23538095e-65 ; // 0.00000031e-65 C^4 m^4 J^-3
69 
70  /// Action in atomic units.
71  const double atomic_unit_of_action = 1.054571628e-34 ; // 0.000000053e-34 J s
72 
73  /// Charge in atomic units.
74  const double atomic_unit_of_charge = 1.602176487e-19 ; // 0.000000040e-19 C
75 
76  /// Charge density in atomic units.
77  const double atomic_unit_of_charge_density = 1.081202300e12 ; // 0.000000027 e12 C m^-3
78 
79  /// Current in atomic units.
80  const double atomic_unit_of_current = 6.62361763e-3 ; // 0.00000017e-3 A
81 
82  /// Electric dipole moment in atomic units.
83  const double atomic_unit_of_electric_dipole_moment = 8.47835281e-30 ; // 0.00000021e-30 C m
84 
85  /// Electric quadrupole moment in atomic units.
86  const double atomic_unit_of_electric_quadrupole_moment = 4.48655107e-40 ; // 0.00000011e-40 C m^2
87 
88  /// Electric field in atomic units.
89  const double atomic_unit_of_electric_field = 5.14220632e11 ; // 0.00000013 e11 V m^-1
90 
91  /// Electric field gradient in atomic units.
92  const double atomic_unit_of_electric_field_gradient = 9.71736166e21 ; // 0.00000024 e21 V m^-2
93 
94  /// Electric polarizability in atomic units.
95  const double atomic_unit_of_electric_polarizablity = 1.6487772536e-41 ; // 0.0000000034e-41 C^2 m^2 J^-1
96 
97  /// Electric potential in atomic units.
98  const double atomic_unit_of_electric_potential = 27.21138386 ; // 0.00000068 V
99 
100  /// Energy in atomic units.
101  const double atomic_unit_of_energy = 4.35974394e-18 ; // 0.00000022e-18 J
102 
103  /// Force in atomic units.
104  const double atomic_unit_of_force = 8.23872206e-8 ; // 0.00000041e-8 N
105 
106  /// Length in atomic units.
107  const double atomic_unit_of_length = 0.52917720859e-10 ; // 0.00000000036e-10 m
108 
109  /// Magnetic dipole moment in atomic units.
110  const double atomic_unit_of_magnetic_dipole_moment = 1.854801830e-23 ; // 0.000000046e-23 J T^-1
111 
112  /// Magnetic flux density in atomic units.
113  const double atomic_unit_of_magnetic_flux_density = 2.350517382e5 ; // 0.000000059 e5 T
114 
115  /// Magnetizability in atomic units.
116  const double atomic_unit_of_magnetizability = 7.891036433e-29 ; // 0.000000027e-29 J T^-2
117 
118  /// Mass in atomic units.
119  const double atomic_unit_of_mass = 9.10938215e-31 ; // 0.00000045e-31 kg
120 
121  /// Momentum in atomic units.
122  const double atomic_unit_of_momentum = 1.992851565e-24 ; // 0.000000099e-24 kg m s^-1
123 
124  /// Permittivity in atomic units.
125  const double atomic_unit_of_permittivity = 1.112650056e-10 ; // (exact) F m^-1
126 
127  /// Time in atomic units.
128  const double atomic_unit_of_time = 2.418884326505e-17 ; // 0.000000000016e-17 s
129 
130  /// Velocity in atomic units.
131  const double atomic_unit_of_velocity = 2.1876912541e6 ; // 0.0000000015 e6 m s^-1
132 
133  /// Avogadro's number.
134  const double Avogadro_constant = 6.02214179e23 ; // 0.00000030 e23 mol^-1
135 
136  /// Bohr magneton.
137  const double Bohr_magneton = 927.400915e-26 ; // 0.000023e-26 J T^-1
138 
139  /// Bohr radius.
140  const double Bohr_radius = 0.52917720859e-10 ; // 0.00000000036e-10 m
141 
142  /// Boltzmann constant.
143  const double Boltzmann_constant = 1.3806504e-23 ; // 0.0000024e-23 J K^-1
144 
145  /// Compton wavelength.
146  const double Compton_wavelength = 2.4263102175e-12 ; // 0.0000000033e-12 m
147 
148  /// Quantum of conductance, \f$ 2e^2/h \f$.
149  const double conductance_quantum = 7.7480917004e-5 ; // 0.0000000053e-5 S
150 
151  /// Electron \f$g\f$ factor.
152  const double electron_g_factor = -2.0023193043622 ; // 0.0000000000015
153 
154  /// Electron gyromagnetic ratio.
155  const double electron_gyromagnetic_ratio = 1.760859770e11 ; // 0.000000044 e11 s^-1 T^-1
156 
157  /// Electron magnetic moment.
158  const double electron_magnetic_moment = -928.476377e-26 ; // 0.000023e-26 J T^-1
159 
160  /// Electron magnetic moment anomaly.
161  const double electron_magnetic_moment_anomaly = 1.15965218111e-3 ; // 0.00000000074e-3
162 
163  /// Ratio between the electron magnetic moment and Bohr magneton.
164  const double electron_magnetic_moment_to_Bohr_magneton_ratio = -1.00115965218111 ; // 0.000000000000 74
165 
166  /// Ratio between the electron magnetic moment and nuclear magneton.
167  const double electron_magnetic_moment_to_nuclear_magneton_ratio = -1838.28197092 ; // 0.00000080
168 
169  /// Electron mass.
170  const double electron_mass = 9.10938215e-31 ; // 0.00000045e-31 kg
171 
172  /// Ratio of the electron to proton mass.
173  const double electron_proton_mass_ratio = 5.4461702177e-4 ; // 0.0000000024e-4
174 
175  /// Electron volt.
176  const double electron_volt = 1.602176487e-19 ; // 0.000000040e-19 J
177 
178  /// Electron volt to Hartree conversion.
179  const double electron_volt_hartree_relationship = 3.674932540e-2 ; // 0.000000092e-2 E_h
180 
181  /// Electron volt to Hertz relationship.
182  const double electron_volt_hertz_relationship = 2.417989454e14 ; // 0.000000060 e14 Hz
183 
184  /// Electron volt to Joule relationship.
185  const double electron_volt_joule_relationship = 1.602176487e-19 ; // 0.000000040e-19 J
186 
187  /// Elementary charge.
188  const double elementary_charge = 1.602176487e-19 ; // 0.000000040e-19 C
189 
190  /// Faraday constant.
191  const double Faraday_constant = 96485.3399 ; // 0.0024 C mol^-1
192 
193  /// Fermi coupling constant.
194  const double Fermi_coupling_constant = 1.16637e-5 ; // 0.00001e-5 GeV^-2
195 
196  /// Fine structure constant.
197  const double fine_structure_constant = 7.2973525376e-3 ; // 0.0000000050e-3
198 
199  /// Hartree to electron volt relationship.
200  const double hartree_electron_volt_relationship = 27.21138386 ; // 0.00000068 eV
201 
202  /// Hartree energy in Joules.
203  const double Hartree_energy = 4.35974394e-18 ; // 0.00000022e-18 J
204 
205  /// Hartree energy in Hertz.
206  const double hartree_hertz_relationship = 6.579683920722e15 ; // 0.000000000044 e15 Hz
207 
208  /// Hartree energy in inverse meters.
209  const double hartree_inverse_meter_relationship = 2.194746313705e7 ; // 0.000000000015 e7 m^-1
210 
211  /// Hartree energy in Joules.
212  const double hartree_joule_relationship = 4.35974394e-18 ; // 0.00000022e-18 J
213 
214  /// Hartree energy in Kelvin.
215  const double hartree_kelvin_relationship = 3.1577465e5 ; // 0.0000055 e5 K
216 
217  /// Hertz energy in electron volts.
218  const double hertz_electron_volt_relationship = 4.13566733e-15 ; // 0.00000010e-15 eV
219 
220  /// Hertz energy in Hartrees.
221  const double hertz_hartree_relationship = 1.519829846006e-16 ; // 0.000000000010e-16 E_h
222 
223  /// Hertz energy in Joules.
224  const double hertz_joule_relationship = 6.62606896e-34 ; // 0.00000033e-34 J
225 
226  /// Hertz energy in Kelvin.
227  const double hertz_kelvin_relationship = 4.7992374e-11 ; // 0.0000084e-11 K
228 
229  /// Nuclear magneton.
230  const double nuclear_magneton = 5.05078324e-27 ; // 0.00000013e-27 J T^-1
231 
232  /// Nuclear magneton in electron volts per Tesla.
233  const double nuclear_magneton_in_eV_per_T = 3.1524512326e-8 ; // 0.0000000045e-8 eV T^-1
234 
235  /// Planck's constant.
236  const double Planck_constant = 6.62606896e-34 ; // 0.00000033e-34 J s
237 
238  /// Reduced Planck's constant.
239  const double Planck_constant_over_2_pi = 1.054571628e-34 ; // 0.000000053e-34 J s
240 
241  /// Ratio of proton to electron mass.
242  const double proton_electron_mass_ratio = 1836.15267247 ; // 0.00000080
243 
244  /// Proton \f$ g \f$ factor.
245  const double proton_g_factor = 5.585694713 ; // 0.000000046
246 
247  /// Proton gyromagnetic ratio.
248  const double proton_gyromagnetic_ratio = 2.675222099e8 ; // 0.000000070 e8 s^-1 T^-1
249 
250  /// Proton magnetic moment.
251  const double proton_magnetic_moment = 1.410606662e-26 ; // 0.000000037e-26 J T^-1
252 
253  /// Proton mass.
254  const double proton_mass = 1.672621637e-27 ; // 0.000000083e-27 kg
255 
256  /// Rydberg constant.
257  const double Rydberg_constant = 10973731.568527 ; // 0.000073 m^-1
258 
259  /// Speed of light in a vacuum.
260  const double speed_of_light_in_vacuum = 299792458 ; // (exact) m s^-1
261 
262  /// Stefan-Boltzmann constant.
263  const double Stefan_Boltzmann_constant = 5.670400e-8 ; // 0.000040e-8 W m^-2 K^-4
264 
265  /// Unified atomic mass unit.
266  const double unified_atomic_mass_unit = 1.660538782e-27 ; // 0.000000083e-27 kg
267 
268  /// Atomic mass in atomic units
269  const double atomic_mass_in_au = 1822.88848;
270 
271  /// conversion from atomic units in reciprocal centimeter
272  const double au2invcm = 219474.6313705;
273 
274  /// the dielectric constant \f$\epsilon_0\f$, or the permittivity of vacuum
275  const double dielectric_constant = 8.854187817e-12; // F m^{-1}
276 
277  /// speed of light in vacuum in au
278  const double speed_of_light_in_vacuum_in_au = 1.0/fine_structure_constant; // \approx 137
279 
280  }
281 
282 }
283 
284 #endif
const double hartree_hertz_relationship
Hartree energy in Hertz.
Definition: constants.h:206
const double electron_volt_hertz_relationship
Electron volt to Hertz relationship.
Definition: constants.h:182
const double atomic_unit_of_electric_quadrupole_moment
Electric quadrupole moment in atomic units.
Definition: constants.h:86
const double atomic_unit_of_2nd_hyperpolarizablity
Second hyperpolarizability in atomic units.
Definition: constants.h:68
const double atomic_unit_of_charge_density
Charge density in atomic units.
Definition: constants.h:77
const double proton_mass
Proton mass.
Definition: constants.h:254
const double hartree_inverse_meter_relationship
Hartree energy in inverse meters.
Definition: constants.h:209
const double atomic_unit_of_energy
Energy in atomic units.
Definition: constants.h:101
const double atomic_unit_of_action
Action in atomic units.
Definition: constants.h:71
const double electron_volt_joule_relationship
Electron volt to Joule relationship.
Definition: constants.h:185
const double fine_structure_constant
Fine structure constant.
Definition: constants.h:197
const double atomic_unit_of_time
Time in atomic units.
Definition: constants.h:128
const double nuclear_magneton_in_eV_per_T
Nuclear magneton in electron volts per Tesla.
Definition: constants.h:233
const double atomic_unit_of_electric_dipole_moment
Electric dipole moment in atomic units.
Definition: constants.h:83
const double atomic_unit_of_force
Force in atomic units.
Definition: constants.h:104
const double Avogadro_constant
Avogadro's number.
Definition: constants.h:134
const double atomic_unit_of_1st_hyperpolarizablity
First hyperpolarizability in atomic units.
Definition: constants.h:65
const double electron_magnetic_moment_to_nuclear_magneton_ratio
Ratio between the electron magnetic moment and nuclear magneton.
Definition: constants.h:167
const double atomic_unit_of_charge
Charge in atomic units.
Definition: constants.h:74
const double atomic_unit_of_magnetic_dipole_moment
Magnetic dipole moment in atomic units.
Definition: constants.h:110
const double atomic_unit_of_electric_field_gradient
Electric field gradient in atomic units.
Definition: constants.h:92
const double electron_magnetic_moment_to_Bohr_magneton_ratio
Ratio between the electron magnetic moment and Bohr magneton.
Definition: constants.h:164
const double Hartree_energy
Hartree energy in Joules.
Definition: constants.h:203
const double proton_gyromagnetic_ratio
Proton gyromagnetic ratio.
Definition: constants.h:248
const double hertz_hartree_relationship
Hertz energy in Hartrees.
Definition: constants.h:221
const double electron_gyromagnetic_ratio
Electron gyromagnetic ratio.
Definition: constants.h:155
const double proton_electron_mass_ratio
Ratio of proton to electron mass.
Definition: constants.h:242
const double Fermi_coupling_constant
Fermi coupling constant.
Definition: constants.h:194
const double electron_volt_hartree_relationship
Electron volt to Hartree conversion.
Definition: constants.h:179
const double hertz_electron_volt_relationship
Hertz energy in electron volts.
Definition: constants.h:218
const double atomic_unit_of_current
Current in atomic units.
Definition: constants.h:80
const double elementary_charge
Elementary charge.
Definition: constants.h:188
const double Bohr_magneton
Bohr magneton.
Definition: constants.h:137
const double hertz_kelvin_relationship
Hertz energy in Kelvin.
Definition: constants.h:227
const double hartree_joule_relationship
Hartree energy in Joules.
Definition: constants.h:212
const double electron_g_factor
Electron factor.
Definition: constants.h:152
const double speed_of_light_in_vacuum
Speed of light in a vacuum.
Definition: constants.h:260
const double electron_volt
Electron volt.
Definition: constants.h:176
const double hartree_kelvin_relationship
Hartree energy in Kelvin.
Definition: constants.h:215
const double au2invcm
conversion from atomic units in reciprocal centimeter
Definition: constants.h:272
const double pi
Mathematical constant .
Definition: constants.h:48
const double atomic_mass_constant
Mass constant in atomic units.
Definition: constants.h:62
const double atomic_unit_of_mass
Mass in atomic units.
Definition: constants.h:119
const double Planck_constant_over_2_pi
Reduced Planck's constant.
Definition: constants.h:239
const double atomic_unit_of_velocity
Velocity in atomic units.
Definition: constants.h:131
const double calorie_joule_relationship
1 kcal/mol = 4.184 kJ/mol.
Definition: constants.h:53
const double atomic_mass_in_au
Atomic mass in atomic units.
Definition: constants.h:269
const double nuclear_magneton
Nuclear magneton.
Definition: constants.h:230
const double atomic_unit_of_magnetic_flux_density
Magnetic flux density in atomic units.
Definition: constants.h:113
const double dielectric_constant
the dielectric constant , or the permittivity of vacuum
Definition: constants.h:275
const double electron_magnetic_moment_anomaly
Electron magnetic moment anomaly.
Definition: constants.h:161
const double electron_mass
Electron mass.
Definition: constants.h:170
const double Planck_constant
Planck's constant.
Definition: constants.h:236
const double atomic_unit_of_electric_field
Electric field in atomic units.
Definition: constants.h:89
const double Boltzmann_constant
Boltzmann constant.
Definition: constants.h:143
const double Debye
Cm (coulomb metre).
Definition: constants.h:55
const double electron_magnetic_moment
Electron magnetic moment.
Definition: constants.h:158
const double Compton_wavelength
Compton wavelength.
Definition: constants.h:146
const double atomic_unit_of_magnetizability
Magnetizability in atomic units.
Definition: constants.h:116
const double atomic_unit_of_electric_polarizablity
Electric polarizability in atomic units.
Definition: constants.h:95
const double Bohr_radius
Bohr radius.
Definition: constants.h:140
const double hartree_electron_volt_relationship
Hartree to electron volt relationship.
Definition: constants.h:200
const double proton_magnetic_moment
Proton magnetic moment.
Definition: constants.h:251
const double atomic_unit_of_permittivity
Permittivity in atomic units.
Definition: constants.h:125
const double Faraday_constant
Faraday constant.
Definition: constants.h:191
const double conductance_quantum
Quantum of conductance, .
Definition: constants.h:149
const double electron_proton_mass_ratio
Ratio of the electron to proton mass.
Definition: constants.h:173
const double proton_g_factor
Proton factor.
Definition: constants.h:245
const double speed_of_light_in_vacuum_in_au
speed of light in vacuum in au
Definition: constants.h:278
const double unified_atomic_mass_unit
Unified atomic mass unit.
Definition: constants.h:266
const double atomic_unit_of_momentum
Momentum in atomic units.
Definition: constants.h:122
const double hertz_joule_relationship
Hertz energy in Joules.
Definition: constants.h:224
const double atomic_unit_of_electric_potential
Electric potential in atomic units.
Definition: constants.h:98
const double Rydberg_constant
Rydberg constant.
Definition: constants.h:257
const double Stefan_Boltzmann_constant
Stefan-Boltzmann constant.
Definition: constants.h:263
const double atomic_unit_of_length
Length in atomic units.
Definition: constants.h:107
File holds all helper structures necessary for the CC_Operator and CC2 class.
Definition: DFParameters.h:10