Subject: G92 calculation of corrections for enthalpies

From: [email-masked] (Michael Frisch)
Date: Wed, 19 Apr 95 17:47:06 EDT

>     Has anyone else noticed that G92 doesn't correct calculate the H-H(0)
    >     corrections (the thermal energies)?  They can be off by as much as a factor
    >     of 10!  The problem appears to be in the calculation of the vibrational
    >     contribution.  Since we can duplicate the JANAF data, I assume we are doing
    >     the calculation correctly.  
    >     
    > We've certainly checked these by hand.  There are different conventions for
    > different purposes, so perhaps you could be more specific about what you're
    > doing and what you expect the program is doing.
    > 
    > Mike Frisch
    
Someone asked me to be more specific.  Gaussian 92 produces thermal
corrections which include vibrational energy in the harmonic approximation,
(i.e., assuming a Boltzman distribution of vibrational states using the
expressions from standard stat mech texts, such as McQuarrie's book),
rotational energies assuming a rigid rotor (i.e., 3/2 kT) and translational
energies (also 3/2 kT).

Since most of the vibrational energy is zero-point energy, which is
trivially verified, I don't see how this term or the overall thermal energy
could be off by an order of magnitude.

Partition functions are computed relative to both the bottom of the
vibrational well and with respect to the lowest vibrational state.  Which of
these to use depends on whether your convention is to include the zero point
terms in the activation barrier for a reaction or in the pre-factor when
computing a reaction rate.  Heat capacities also reported and are computed
using expressions from McQuarrie's book.  Neither of these quantities is
relevent to computing reaction energies, enthalpies, or free energies.

The original question referred to energies but also uses the expression
H-H(0), so I don't know if the question refers to energies or enthalpies.
Just in case, I'll comment on computing enthalpies.

Gaussian 92 doesn't compute enthalpies at all.  To convert the energy at
a finite temperature to an enthalpy, one needs to know the Delta(PV) between
the system and it's standard state.  In practice, the easy thing to do is
to compute a Delta-E for a reaction and then convert to a Delta-H of reaction
by assuming an ideal gas and correcting by RT * Delta(N) (change in number of
molecules in the reaction).

Gaussian 94 does report an enthalpy, which is the energy at the requested
temperature plus RT.  This is not a Delta-H with respect to a standard state,
but can be used to compute a Delta-H for a reaction by simply taking the
algebraic sum of the enthalpies printed by the program for reactants and
products, in which case the extra RT terms just automatically sum up to the
RT * Delta(N) correction above.

That's as much as I can say without knowing more specifically what the
discrepancy in the orginal posting referrs to.

Mike Frisch
[email-masked]
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