[CHM 331] Re: partition functions issue

[Andrew J. Pounds]

On 12/07/2011 07:16 PM, Hunter.L.Taylor wrote:
>
> Dr. Pounds,
>
>   In the textbook it says that the translational partition function 
> includes a V term (volume). However, the partition functions that you 
> gave us in the sheet of code in class today said that the 
> translational partition function was evaluated at q/v, which negates 
> the use of a volume term.
>

When I wrote the code I didn't want to have a variable called 
g_over_v_H2 and
q_over_v_H.     I could have written the lines


q_H2 = qoverv_diatomic( m_H2, theta_v_H2, theta_r_H2,
                         g0_H2, D0_H2, sigma_H2, k, h, T );

and

q_H = qoverv_atomic( m_H, g0_H, k, h, T);

with

q_over_v_H = qoverv_diatomic( m_H2, theta_v_H2, theta_r_H2,
                           g0_H2, D0_H2, sigma_H2, k, h, T );

and

q_over_H = qoverv_atomic( m_H, g0_H, k, h, T);

If you are doing the equilibrium constant calculations you will be 
evaluating q/V as described on pages 594-596 of your text.


> If you could tell me which version is correct it would be greatly 
> appreciated. Also, in the sheet of code for 16G, the partition 
> functions all start using the term q, does this always refer to the 
> translational partition function, or does it indicate the partition 
> function calculated just before the current one? (since each of the 
> equations begins either q=q*.... or q=q/....) Any insight you could 
> give would be appreciated.
>
> --Hunter Taylor
>

Okay -- so it's now clear to me that some of you have never done any 
type of programming before...  Here's the deal -- the set of expressions

        q = pow(2.0*pi*m*k*T/(h*h),1.5);     // Translational
        q = q * T / (theta_r * sigma );      // Rotational
        q = q / (1.0 - exp(-theta_v/T) );    // Vibrational
        q = q * g0 * exp(D0/(k*T));          // Electronic

are obviously calculating q/V for a diatomic (see equation 16.90 in your 
text).   I could have written it like this...

q_over_v = pow(2.0*pi*m*k*T/(h*h),1.5) * T / (theta_r * sigma ) / (1.0 - 
exp(-theta_v/T) ) * g0 * exp(D0/(k*T));

However, to make it MUCH easier to read and check for errors I broke it 
into pieces.  The variable q in the four lines above (which I could have 
named q_over_v -- but I just chose q here to save space)  carries its 
value from the previous line -- so it is exactly the same as the long 
nasty equation.  I did this to encourage you to write you equations 
using a similar methodology (much easier to check for errors.)

As an example look at the following piece of code

    q = 1          (q equals one after this)
    q = q * 2    (after the assignment q would equal 2)
    q = q * 3    (after the assignment q would equal 6)

  Hope that helps.




-- 
Andrew J. Pounds, Ph.D.  (pounds at theochem.mercer.edu)
Associate Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627

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