Simbody  3.7

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...
 

Detailed Description

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).

Uncertainty
Uncertainties are given in the CODATA set as the one-std-deviation uncertainty in the last 2 digits of the given value. That means that there is about a 68% chance that the last two digits are as shown +/- the uncertainty.

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|

Macro Definition Documentation

◆ SimTK_AVOGADROS_NUMBER

#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).

uncertainty
10e16

◆ SimTK_MASS_OF_PROTON_IN_MD

#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.

uncertainty
13e-11
See also
SimTK_AVOGADROS_NUMBER

◆ SimTK_MASS_OF_NEUTRON_IN_MD

#define SimTK_MASS_OF_NEUTRON_IN_MD   1.00866491560L

Mass of a neutron in MD units.

uncertainty
55e-11
See also
SimTK_MASS_OF_PROTON_IN_MD

◆ SimTK_MASS_OF_ELECTRON_IN_MD

#define SimTK_MASS_OF_ELECTRON_IN_MD   5.4857990945e-4L

Mass of an electron in MD units.

uncertainty
24e-14
See also
SimTK_MASS_OF_PROTON_IN_MD

◆ SimTK_CHARGE_OF_PROTON_IN_SI

#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.

uncertainty
14e-27

◆ SimTK_CHARGE_OF_PROTON_IN_MD

#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.

uncertainty
exact (duh!)

◆ SimTK_MOLAR_CHARGE_IN_SI

#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
uncertainty
18e-3

◆ SimTK_MOLAR_CHARGE_IN_MD

#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.

See also
SimTK_AVOGADROS_NUMBER

◆ SimTK_LIGHTSPEED_IN_SI

#define SimTK_LIGHTSPEED_IN_SI   2.99792458e+8L

Speed of light c is exact in MKS units of m/s.

uncertainty
exact
See also
SimTK_LIGHTSPEED_IN_MD

◆ SimTK_LIGHTSPEED_IN_MD

#define SimTK_LIGHTSPEED_IN_MD   2.99792458e+5L

Speed of light c is exact in MD units of nm/ps.

uncertainty
exact
See also
SimTK_LIGHTSPEED_IN_SI

◆ SimTK_GRAVITATIONAL_CONSTANT_IN_SI

#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).

uncertainty
10e-15
See also
SimTK_GRAVITATIONAL_CONSTANT_IN_MD

◆ SimTK_GRAVITATIONAL_CONSTANT_IN_MD

#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!

uncertainty
17e-39
See also
SimTK_GRAVITATIONAL_CONSTANT_IN_SI

◆ SimTK_MAGNETIC_PERMEABILITY_IN_SI

#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
uncertainty
approximation of an exact quantity
See also
SimTK_ELECTRIC_PERMITTIVITY_IN_SI

◆ SimTK_MAGNETIC_PERMEABILITY_IN_MD

#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)
uncertainty
47e-16
See also
SimTK_ELECTRIC_PERMITTIVITY_IN_MD

◆ SimTK_ELECTRIC_PERMITTIVITY_IN_SI

#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).

uncertainty
approximation of an exact quantity
See also
SimTK_MAGNETIC_PERMEABILITY_IN_SI

◆ SimTK_ELECTRIC_PERMITTIVITY_IN_MD

#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.

uncertainty
14e-11
See also
SimTK_MAGNETIC_PERMEABILITY_IN_MD

◆ SimTK_COULOMB_CONSTANT_IN_SI

#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.

uncertainty
exact

◆ SimTK_COULOMB_CONSTANT_IN_MD

#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)
uncertainty
33e-6

◆ SimTK_COULOMB_CONSTANT_IN_KCAL_ANGSTROM

#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).

uncertainty
80e-6

◆ SimTK_MOLAR_GAS_CONSTANT_SI

#define SimTK_MOLAR_GAS_CONSTANT_SI   8.314472L

This is the gas constant R in (J/mol)/K.

uncertainty
15e-6

◆ SimTK_MOLAR_GAS_CONSTANT_MD

#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.

uncertainty
15e-9

◆ SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM

#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.

uncertainty
36e-10

◆ SimTK_BOLTZMANN_CONSTANT_SI

#define SimTK_BOLTZMANN_CONSTANT_SI   1.3806505e-23L

Boltzmann's constant in SI units of joules/kelvin; just divide R by NA.

uncertainty
24e-30

◆ SimTK_BOLTZMANN_CONSTANT_MD

#define SimTK_BOLTZMANN_CONSTANT_MD   SimTK_MOLAR_GAS_CONSTANT_MD

Boltzmann's constant in MD units of (kJ/mol)/kelvin; same as R.

See also
SimTK_MOLAR_GAS_CONSTANT_MD

◆ SimTK_BOLTZMANN_CONSTANT_KCAL_ANGSTROM

#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.

See also
SimTK_MOLAR_GAS_CONSTANT_KCAL_ANGSTROM