Custom Population Functions

As an alternative to the built in Boltzmann population distributions, or specifying a population for each state individually (see Non-Boltzmann Populations), a function can be given in terms of various standard state properties instead. This is done by creating a "Custom Population Function" object under the appropriate Manifold object. The standard mathematical operators are available, and possible functions might include:

 exp(-E/(kB*T)) 

The standard Boltzmann equation that PGOPHER would use, providing Tvib and Tspin are set to their default values.(T is automatically created as a parameter here.)

exp(-b*(J-Jcentre)^2)

          

A Gaussian distribution is J, centered on Jcentre. (Jcentre is automatically created as a parameter here .)

Result*(E<Emax)

Standard distribution, but discarding all states above Emax. The comparison operators evaluate to 1 if the comparison is true, and 0 for false allowing simple if...then...else logic. (Emax is automatically created as a parameter.)

sqrt(max(Emax-E,0))

          

A statistical distribution with a cut off energy of Emax. (Emax is automatically created as a parameter.)

Result*(1+2*(mod(J,3)=0))

          

Standard distribution, but scaling levels with J divisible by 3 by 3.

The calculated values are multiplied by the degeneracy, g, so g should not be included in the function.

In the current initial implementation, the function is given in the Comment field for the manifold; this will probably change in future versions.

Any unknown variables in the function are automatically created as parameters on simulating, or on right clicking on the node and selecting "Check Variables"

Unwanted variables that are no longer in the expression can be removed by right clicking on the parameter and selecting remove.

AutoQConverge will need to be set to off for many choices of function.

Built In Variables

Result

          

The population PGOPHER would use if Active is set to false

E

The state energy

kB

The Boltzmann constant in the current energy units/K

J

J for the state

Symmetry

          

The symmetry number of the state

Index

          

The eigenvalue number of the state

Additional quantum numbers are also available, depending on the molecule type. They are based on the dominant basis state, so may not be exact for strongly mixed states.

Omega

The Omega quantum number

Fn

The spin component, 1 for F₁, 2 for F₂, etc.
Note that for versions before 8.0.171 the values were divided by 2.

The absolute value of K

The sign of Kl

Simulation.Tvib

exp(-E/(kB*T))	The standard Boltzmann equation that PGOPHER would use, providing `Tvib` and `Tspin` are set to their default values.`(T` is automatically created as a parameter here.)
exp(-b*(J-Jcentre)^2)	A Gaussian distribution is J, centered on Jcentre. (Jcentre is automatically created as a parameter here .)
Result*(E<Emax)	Standard distribution, but discarding all states above Emax. The comparison operators evaluate to 1 if the comparison is true, and 0 for false allowing simple if...then...else logic. (Emax is automatically created as a parameter.)
sqrt(max(Emax-E,0))	A statistical distribution with a cut off energy of Emax. (Emax is automatically created as a parameter.)
Result(1+2(mod(J,3)=0))	Standard distribution, but scaling levels with J divisible by 3 by 3.

Result	The population PGOPHER would use if Active is set to false
E	The state energy
kB	The Boltzmann constant in the current energy units/K
J	J for the state
Symmetry	The symmetry number of the state
Index	The eigenvalue number of the state

Custom Population Functions

Built In Variables

Settings