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Simbody
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Simbody
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These constants are from the CODATA 2002 set from the NIST Physics Laboratory web site http://physics.nist.gov/constants (NIST SP 961 Dec 2005). More...
Macros | |
| #define | SimTK_AVOGADROS_NUMBER 6.0221415e23L |
| Avogadro's number (NA) is defined as the number of atoms in 12g of pure Carbon-12 in its unbound, rest state. More... | |
| #define | SimTK_MASS_OF_PROTON_IN_MD 1.00727646688L |
| Mass of a proton in MD units. More... | |
| #define | SimTK_MASS_OF_NEUTRON_IN_MD 1.00866491560L |
| Mass of a neutron in MD units. More... | |
| #define | SimTK_MASS_OF_ELECTRON_IN_MD 5.4857990945e-4L |
| Mass of an electron in MD units. More... | |
| #define | SimTK_CHARGE_OF_PROTON_IN_SI 1.60217653e-19L |
| Atomic charge unit e expressed in MKS unit of Coulombs. More... | |
| #define | SimTK_CHARGE_OF_PROTON_IN_MD 1.L |
| Atomic charge unit e expressed in MD units, which uses e as its charge unit! The charge on an electron is just the negative of this value. More... | |
| #define | SimTK_MOLAR_CHARGE_IN_SI 9.6485338e+4L |
| The charge of 1 mole of protons, expressed in Coulombs. More... | |
| #define | SimTK_MOLAR_CHARGE_IN_MD SimTK_AVOGADROS_NUMBER |
| The charge of 1 mole of protons, expressed in MD units where the unit of charge is just the charge on one proton. More... | |
| #define | SimTK_LIGHTSPEED_IN_SI 2.99792458e+8L |
| Speed of light c is exact in MKS units of m/s. More... | |
| #define | SimTK_LIGHTSPEED_IN_MD 2.99792458e+5L |
| Speed of light c is exact in MD units of nm/ps. More... | |
| #define | SimTK_GRAVITATIONAL_CONSTANT_IN_SI 6.6742e-11L |
| Newton's gravitational constant G in N-m^2/kg^2 = m^3 kg^-1 s^-2. More... | |
| #define | SimTK_GRAVITATIONAL_CONSTANT_IN_MD 1.10827e-34L |
| Newton's gravitational constant G in (kJ/mol)-nm^2/u^2 = nm^3 u^-1 ps^-2. More... | |
| #define | SimTK_MAGNETIC_PERMEABILITY_IN_SI 1.256637061435917295385057353311801153678867759750042328389977837e-6L |
| Free space magnetic permeability constant mu0 in SI units (exact). More... | |
| #define | SimTK_MAGNETIC_PERMEABILITY_IN_MD 1.94259179e-8L |
| Free space magnetic permeability constant mu0 in MD units (not exact). More... | |
| #define | SimTK_ELECTRIC_PERMITTIVITY_IN_SI 8.854187817620389850536563031710750260608370166599449808102417149e-12L /* approx of exact */ |
| Free space permittivity constant e0 = 1/(mu0*c^2) Farad/m = Coulomb^2/(N-m^2) (exact in SI units). More... | |
| #define | SimTK_ELECTRIC_PERMITTIVITY_IN_MD 5.7276575e-4L |
| Free space permittivity constant e0=1/(mu0*c^2) e^2/(kN-nm^2) using MD permeability and MD lightspeed. More... | |
| #define | SimTK_COULOMB_CONSTANT_IN_SI 8.9875517873681764e+9L |
| Coulomb's constant kappa = 1/(4pi*e0)=1e-7*c^2 N-m^2/Coulomb^2 (exact in SI units). More... | |
| #define | SimTK_COULOMB_CONSTANT_IN_MD 1.38935456e+2L |
| Coulomb's constant kappa = 1/(4*pi*e0) in MD units. More... | |
| #define | SimTK_COULOMB_CONSTANT_IN_KCAL_ANGSTROM 3.32063711e+2L |
| Coulomb's constant kappa = 1/(4*pi*e0) in kcal-Angstroms/e^2. More... | |
| #define | SimTK_MOLAR_GAS_CONSTANT_SI 8.314472L |
| This is the gas constant R in (J/mol)/K. More... | |
| #define | SimTK_MOLAR_GAS_CONSTANT_MD 8.314472e-3L |
| This is the gas constant R in (kJ/mol)/K. More... | |
| #define | SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM 1.9872065e-3L |
| This is the gas constant R in (kcal/mol)/K. More... | |
| #define | SimTK_BOLTZMANN_CONSTANT_SI 1.3806505e-23L |
| Boltzmann's constant in SI units of joules/kelvin; just divide R by NA. More... | |
| #define | SimTK_BOLTZMANN_CONSTANT_MD SimTK_MOLAR_GAS_CONSTANT_MD |
| Boltzmann's constant in MD units of (kJ/mol)/kelvin; same as R. More... | |
| #define | SimTK_BOLTZMANN_CONSTANT_KCAL_ANGSTROM SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM |
| Boltzmann's constant in Kcal-Angstrom units of (kcal/mol)/kelvin; same as R. More... | |
These constants are from the CODATA 2002 set from the NIST Physics Laboratory web site http://physics.nist.gov/constants (NIST SP 961 Dec 2005).
Ref: P.J. Mohr and B.N. Taylor, Rev. Mod. Phys. 77(1) (2005).
How to combine uncertainties (extracted from http://physics.nist.gov/cuu/Uncertainty/combination.html): Assume measured quantities are x1, y1 with u1=uncertainty(x1), u2=uncertainty(x2). We want to combine them into a new quantity y and calculate u=uncertainty(y).
Addition rule: y = a1*x1 + a2*x2 for factors a1,a2.
then u^2 = a1*u1^2 + a2*u2^2
Multiplication rule y = a*x1^e1*x2^e2 for factor a and exponents e1,e2.
Let ur1=u1/|x1|, ur2=u2/|x2| be the relative uncertainties, ur is u/|y|.
then ur^2 = e1^2*ur1^2 + e2^2*ur2^2, u = ur*|y|
| #define SimTK_AVOGADROS_NUMBER 6.0221415e23L |
Avogadro's number (NA) is defined as the number of atoms in 12g of pure Carbon-12 in its unbound, rest state.
The number is 1 mole (mol).
| #define SimTK_MASS_OF_PROTON_IN_MD 1.00727646688L |
Mass of a proton in MD units.
The atomic mass unit u (or amu) is defined as 1/12 of the mass of a Carbon-12 atom, unbound and in its rest state. This definition matched to Avogadro's number's definition ensures that 1 mole of particles of mass 1u each has total mass exactly 1g. This is synonymous with the dalton (Da), with units of g/mole, so 1u = 1Dalton = 1g/mole. We will use Da for this mass unit, with kDa being a common mass measure for large biomolecules.
| #define SimTK_MASS_OF_NEUTRON_IN_MD 1.00866491560L |
| #define SimTK_MASS_OF_ELECTRON_IN_MD 5.4857990945e-4L |
| #define SimTK_CHARGE_OF_PROTON_IN_SI 1.60217653e-19L |
Atomic charge unit e expressed in MKS unit of Coulombs.
The charge on an electron is just the negative of this value.
| #define SimTK_CHARGE_OF_PROTON_IN_MD 1.L |
Atomic charge unit e expressed in MD units, which uses e as its charge unit! The charge on an electron is just the negative of this value.
| #define SimTK_MOLAR_CHARGE_IN_SI 9.6485338e+4L |
The charge of 1 mole of protons, expressed in Coulombs.
1.60217653(14)e-19 C/e * 6.0221415(10)e23 = 9.6485338(18)e+4
| #define SimTK_MOLAR_CHARGE_IN_MD SimTK_AVOGADROS_NUMBER |
The charge of 1 mole of protons, expressed in MD units where the unit of charge is just the charge on one proton.
So in MD units this is just Avogadro's number.
| #define SimTK_LIGHTSPEED_IN_SI 2.99792458e+8L |
| #define SimTK_LIGHTSPEED_IN_MD 2.99792458e+5L |
| #define SimTK_GRAVITATIONAL_CONSTANT_IN_SI 6.6742e-11L |
Newton's gravitational constant G in N-m^2/kg^2 = m^3 kg^-1 s^-2.
The force between two point masses m1,m2 separated by a distance d is
F = -G m1*m2/d^2
(with the "-" indicating an attractive force).
| #define SimTK_GRAVITATIONAL_CONSTANT_IN_MD 1.10827e-34L |
Newton's gravitational constant G in (kJ/mol)-nm^2/u^2 = nm^3 u^-1 ps^-2.
Conversion is (nm/m)^3 (u/kg)^-1 (ps/s)^-2
= 1.66053886(28)e-24L (uncertainty: 28e-32)
This is why gravity doesn't matter in molecular systems. Don't try this in single precision – you'll run out of exponent!
| #define SimTK_MAGNETIC_PERMEABILITY_IN_SI 1.256637061435917295385057353311801153678867759750042328389977837e-6L |
Free space magnetic permeability constant mu0 in SI units (exact).
= 4*pi * 1e-7 exactly in N/A^2 (Newtons/Ampere^2) = kg-m/C^2
| #define SimTK_MAGNETIC_PERMEABILITY_IN_MD 1.94259179e-8L |
Free space magnetic permeability constant mu0 in MD units (not exact).
Convert kg->g/mole, m->nm, C->e = (4*pi*1e5)*1.60217653e-19^2*6.0221415e23
(exact in SI units, but not exact here)
| #define SimTK_ELECTRIC_PERMITTIVITY_IN_SI 8.854187817620389850536563031710750260608370166599449808102417149e-12L /* approx of exact */ |
Free space permittivity constant e0 = 1/(mu0*c^2) Farad/m = Coulomb^2/(N-m^2) (exact in SI units).
| #define SimTK_ELECTRIC_PERMITTIVITY_IN_MD 5.7276575e-4L |
Free space permittivity constant e0=1/(mu0*c^2) e^2/(kN-nm^2) using MD permeability and MD lightspeed.
| #define SimTK_COULOMB_CONSTANT_IN_SI 8.9875517873681764e+9L |
Coulomb's constant kappa = 1/(4pi*e0)=1e-7*c^2 N-m^2/Coulomb^2 (exact in SI units).
This is the constant that appears in Coulomb's law f(r)= kappa*q1*q2/r^2.
| #define SimTK_COULOMB_CONSTANT_IN_MD 1.38935456e+2L |
Coulomb's constant kappa = 1/(4*pi*e0) in MD units.
This is the constant that appears in Coulomb's law f(r)= kappa*q1*q2/r^2.
Coulomb's consant in MD units uses MD e0 & c:
1/(4*pi*e0)=1e5*1.60217653e-19^2*6.0221415e23*c^2 kN-nm^2/e^2 (=kJ-nm/e^2)
(exact in SI units but not exact in MD)
| #define SimTK_COULOMB_CONSTANT_IN_KCAL_ANGSTROM 3.32063711e+2L |
Coulomb's constant kappa = 1/(4*pi*e0) in kcal-Angstroms/e^2.
This is the constant that appears in Coulomb's law f(r)= kappa*q1*q2/r^2. This is an exact conversion from MD units (which are inexact).
| #define SimTK_MOLAR_GAS_CONSTANT_SI 8.314472L |
This is the gas constant R in (J/mol)/K.
| #define SimTK_MOLAR_GAS_CONSTANT_MD 8.314472e-3L |
This is the gas constant R in (kJ/mol)/K.
This is an exact conversion from SI units, differing only in the use of kJ here vs. J in SI.
| #define SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM 1.9872065e-3L |
This is the gas constant R in (kcal/mol)/K.
This is an exact conversion from MD units, differing only in the use of kcal here vs. kJ in MD.
| #define SimTK_BOLTZMANN_CONSTANT_SI 1.3806505e-23L |
Boltzmann's constant in SI units of joules/kelvin; just divide R by NA.
| #define SimTK_BOLTZMANN_CONSTANT_MD SimTK_MOLAR_GAS_CONSTANT_MD |
Boltzmann's constant in MD units of (kJ/mol)/kelvin; same as R.
| #define SimTK_BOLTZMANN_CONSTANT_KCAL_ANGSTROM SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM |
Boltzmann's constant in Kcal-Angstrom units of (kcal/mol)/kelvin; same as R.
1.8.8