LEVEL
Given a well-behaved electronic potential energy curve for a diatomic molecule, LEVEL will "automatically locate and calculate expectation values
for all vibration–rotation levels". This means that for any operator $\hat{M}$, you can calculate the expectation values for each vibrational level $v$ and each associated rotational level $J$:
$$
\langle \psi_{v,J}| \hat{M}|\psi_{v,J}\rangle, \tag{1}
$$
which means that you can certainly calculate properties for $v=1-4$ with $J=0$ (as well as also with higher $J$ values). This program was a project that Bob Le Roy worked on since the 1960s, and had contributions from several others over the decades, including myself. The latest version available online was from 2016, so I pushed the most recent version I could find today into Github Here (let me know if you have any trouble compiling it, while I work on adding a Makefile and sample input file for you).
Advantages:
- Free and open-source
- Extremely accurate, and extremely fast (orders of magnitude faster and more black-box than other radial Schroedinger solvers I know some others have used)
- Widely used and with a rich history spanning several decades
- There's not a lot of other programs available with this type of functionality
Disadvantages:
- Only works for diatomics
- As you are a CFOUR user, you might be used to getting ground state vibrational properties in a much more black-box way. Here you'd have to build the electronic potential energy curve with a program like CFOUR, then enter it into LEVEL and climb a slight learning curve as you need to check convergence and such more manually in LEVEL than you would for single-point energy calculations (within a basis set and level of theory) in CFOUR.
- You may have to define $\hat{M}$ yourself in the FORTRAN code if the particular $\hat{M}$ that interests you is not available by default (since I've been using this software since about 15 years ago, I can probably help you with this if you want to collaborate).
