Objects Mixture Species Molecule Manifold | <Prev Next> |

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. PGOPHER uses an
equation close to this, providing Tvib and Tspin are set to
their default values (-1).(T is automatically
created as a parameter here.) |

exp(-(E-EB)/(kB*T)) | Population equation actually used by PGOPHER
if Tvib and Tspin are set to
their default values (-1). |

exp(-(E-Orign)/(kB*T)) *exp(-(Origin-EB)/(kB*Simulation.Tvib)) |
Population equation actually used by PGOPHER
if Tvib is not
the default, but Tspin
is. |

exp(-b*(J-Jcentre)^2) |
A Gaussian distribution in 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. |

exp(-(E-EB)/(kB*Temperature))+A2*Temperature/T2*exp(-(E-EB)/(kB*T2)) |
Bi-exponential rotational population distribution, with an additional temperature, T2, created as a parameter. A2 is the relative amount with temperature T2. The scaling factor Temperature/T2 takes account of the fact that rotational partition functions are approximately proportional to T, making ratio of components with the two temperatures approximately 1:A2. |

Notes:

- To have any effect,
`Active`must be set to true.

- The calculated values are multiplied by the degeneracy,
*g*, so*g*should not be included in the function. - See expressions for more
details on format.

- The function is held in the comment field for the object; in
the constants window an
enlarged text window replaces the normal comments window. (If
you want to add comments to the function use # or // to start
the comment, or enclose it in {...} or /* ... */.)

- 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.

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. (Note k will be taken as a
quantum number) |

J |
J for the state |

Symmetry |
The symmetry number of the
state |

Index |
The eigenvalue number of the
state |

MJ |
M for the state - only set
if external fields are present_{J} |

Origin |
The origin of the vibronic state. This is
normally the value of the Origin parameter for the
state, but for linear molecules a correction is applied so
that the value is approximately the energy of the
lowest rotational level. (A similar offset is applied in the
vibrational structure mode.) |

EB |
The AssumedOrigin
for the molecule (if not set to the default) or else the
lowest vibronic state origin (defined as above), considering
only states for which Initial = True. |

Width |
The calculated width for 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.

For asymmetric tops the standard quantum numbersFor linear molecules:

Omega |
The Omega quantum number |

Fn | The spin component, 1 for F_{1},
2 for F_{2}, etc.Note that for versions before 8.0.171 the values were divided by 2. |

For symmetric tops:

K |
The absolute value of K |

Kl |
The sign of Kl but separably
degenerate point groups have additional in this variable. |

For vibrating molecules:

v1, v2, ... |
Vibrational quantum numbers |

l1, l2, ... |
Vibrational angular momentum quantum number,
for degenerate modes only. |

Lambda |
Electronic orbital angular momentum, Λ. |

Omega |
Electronic angular momentum, Ω. |

In addition any parameter can be referred to by giving the name in dotted notation. For example the current global temperature can be referred to using

Active | Set true to use the function provided to calculate the
population |

nDebug |
If non zero, write the values of all the
variables and the value of the function on each evaluation
to the log window. See debugging
for options on the output. To see any output the expression
must not be blank - simply set to "Value" to see
the defaults in action. |