Wednesday 6 January 2016

physical chemistry - 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 3.58200 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= 2.0436791 -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)=*********** = 0.8129565017 = 613.747

= 1.08679787 = 1.18212033 = 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/Ang**2))
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 = M1*M2/[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)* 8.065600000D+03
to get required internal units [Angstroms & cm-1 for potentials]
r(i) Y(i) r(i) Y(i) r(i) Y(i)

---------------------- ---------------------- ----------------------
0.800000************* 2.200000************* 3.650000*************
0.850000************* 2.250000************* 3.700000*************
0.900000************* 2.300000************* 3.750000*************
0.950000************* 2.400000************* 3.800000*************
1.000000************* 2.450000************* 3.850000*************
1.050000************* 2.500000************* 3.900000*************
1.100000************* 2.550000************* 3.950000*************
1.150000************* 2.600000************* 4.000000*************
1.200000************* 2.650000************* 4.050000*************

1.250000************* 2.700000************* 4.100000*************
1.300000************* 2.750000************* 4.150000*************
1.350000************* 2.800000************* 4.200000*************
1.400000************* 2.850000************* 4.250000*************
1.450000************* 2.900000************* 4.300000*************
1.500000************* 2.950000************* 4.350000*************
1.550000************* 3.000000************* 4.400000*************
1.600000************* 3.050000************* 4.450000*************
1.650000************* 3.100000************* 4.500000*************
1.700000************* 3.150000************* 4.550000*************

1.750000************* 3.200000************* 4.600000*************
1.800000************* 3.250000************* 4.650000*************
1.850000************* 3.300000************* 4.700000*************
1.900000************* 3.350000************* 4.750000*************
1.950000************* 3.400000************* 4.800000*************
2.000000************* 3.450000************* 4.850000*************
2.050000************* 3.500000************* 4.900000*************
2.100000************* 3.550000************* 4.950000*************
2.150000************* 3.600000************* 5.000000*************
----------------------------------------------------------------------------

Extrapolate to X .le. 0.8500 with
Y=-23872936.002 +1.108309D+08 * exp(-8.496962D+00*X)
Extrapolate to X .GE. 4.9500 using
Y=************ - [ 7.145852D+02/X**1 -3.206362D+03/X**3]
----------------------------------------------------------------------------

Calculate properties of the single potential described above
Potential-1 uses inner boundary condition of zero value at RMIN

Eigenvalue convergence criterion is EPS= 1.0D-06(cm-1)

Airy function at 3-rd turning point is quasibound outer boundary condition

Since state-1 has (projected) electronic angular momentum OMEGA= 0
eigenvalue calculations use centrifugal potential [J*(J+1) - 0]/r**2

For J= 0, seek the first 1 levels of Potential-1 with VLIM=***********


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 3.58200 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= 2.0436791 -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)=*********** = 0.8129565017 = 613.747
= 1.08679787 = 1.18212033 = 1.28688369
-------------------------------------------------------------------------------

===============================================================================


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