How to obtain spectroscopic constants Omega_e, Alpha_e, B_e, D_e and D_0 from centrifugal constants?
I need to compute a spectroscopic constants of $N_2^+$ states and I would like to do it using LEVEL16 software, due to its high interpolation flexibility.
But it seems, that LEVEL16 can only compute centrifugal distortion constants directly, while I need even the others like $B_e, \omega_e, \alpha_e$ etc.
So, my current LEVEL16 output looks like this (full output is attached in the very bottom of this question):
Matrix element arguments are powers of the distance r (in Angstroms) Coefficients of expansion for radial matrix element/expectation value argument: 1.000000D+00 -2.000000D-01 3.000000D-02 -4.000000D-03 Find 4 potential minima: Vmin=************************************************ at mesh points R = 1.07800 <PHONE_NUMBER> 3.72200 4.72500 Find 4 potential maxima: Vmax=************************************************ at mesh points R = 3.54100 3.62900 3.75900 10.00000 E(v= 0, J= 0)=********** Bv= 2.<PHONE_NUMBER> -Dv= -5.7294D-06 Hv= -2.9963D-11 Lv= -5.2792D-16 Mv= 2.2663D-20 Nv= 4.3228D-25 Ov= -5.1173D-30 E(v= 0, J= 0)=*********** <M(r)>= <PHONE_NUMBER> <KE>= 613.747 <X** 1>= 1.<PHONE_NUMBER> <X** 2>= 1.18212033 <X** 3>= 1.28688369
Now, I know, that
$G(v) \approx \omega_e\left(v + \frac{1}{2} \right) + \omega_e x_e\left(v + \frac{1}{2} \right)^2 + \omega_e y_e\left(v + \frac{1}{2}\right)^3 + \omega_e z_e\left(v + \frac{1}{2} \right)^4$
$B_v \approx B_e - \alpha_e\left(v + \frac{1}{2}\right) + \gamma_e\left(v + \frac{1}{2}\right)^2$
$D_v \approx D_e + \beta_e\left(v + \frac{1}{2}\right)$
but I don't see, how can I achieve the active constants here? Let's take $D_e = D_0 + G(v)$ as an example - if I had an energy of a lowest vibrational state, I'd be able to at least determine the dissociation energy, but I don't see $G(0)$ anywhere...
So, is there any parameter in LEVEL16 I've overlooked? Or did I just forget about some principle?
Complete LEVEL16 output
``` Reduced masses below are based on atoms 1 & 2 with charges (+0/2) and (+2/2), respectively, with subtraction/addition of 0 and 2 half-electron masses.
Computation of N2+ (B2 SigmaU+) spectroscopic constants
Generate ZMU= 7.00126270151(u) & BZ= 4.153171609D-01((1/cm-1)(1/Ang2)) from atomic masses: 14.00307400443 & 14.00197684461(u) Since the molecule is an ion with charge +1 use Watson's charge-adjusted reduced mass mu = M1M2/[M1 + M2 - (+1)me] Integrate from RMIN= 0.800 to RMAX= 10.00 with mesh RH= 0.001000(Angst)
Potential-1 for N( 14)- N( 14) ================================ State has OMEGA= 0 and energy asymptote: Y(lim)=**(cm-1) Perform cubic spline interpolation over the 84 input points To make input points Y(i) consistent with Y(lim), add Y(shift)= 0.0000 Scale input points: (distance) 1.000000000D+00 & (energy) 8. 374