What you're describing is very common, and is not limited to GAMESS and Q-Chem.
First, here's how to do it in MOLPRO, MRCC, GAMESS, Q-Chem (in fact the only electronic structure software that I regularly use which doesn't allow this type of projection into a bigger basis set, is CFOUR):
The HF calculation with the QZ basis set will be done wtih an initial guess taken from the DZ basis set. The manual might not say what is exactly happening, but it's likely to be very similar to what is done in MRCC and Q-Chem, which is to use the density obtained from the previous SCF calculation (see below).
Do your calculation with the smaller basis set, such as cc-pVDZ, then save the
VARS files and make sure they're in the folder when you're running the calculation with the bigger basis set, such as cc-pVQZ, and used the keyword
scfiguess=restart which means "SCF initial guess" is restarted from the
Also it seems in the 2020 manual that there is now a new way to do it:
"To restart an SCF calculation with the cc-pVQZ basis set from the
densities obtained with the cc-pVDZ basis give:
You already mentioned to add:
GUESS=RDMINI to the
As with the first method I suggested with MRCC, do the calculation in the smaller basis set, then run a new calculation with the bigger basis set and the keyword
SCF_GUESS = READ.
Another way is to use (as mentioned in the link you provided) the keyword
BASIS2 to give the name of the smaller basis set that you want to use, then you have the option of either using
BASISPROJTYPE=FOPPROJECTION (if you want to expand the MOs from the BASIS2 calculation into the larger basis)
BASISPROJTYPE=OVPROJECTION (if you want to construct the Fock matrix in the larger basis set using the density matrix of the initial, smaller basis set, which is what the MRCC manual says that MRCC does, then diagonalize the density matrix in the larger basis to obtain the natural orbitals as an initial guess for the SCF calculation in the larger basis).
Here's some references related to your question, that you may find helpful and/or interesting: