Excited-state-CMES

1D excited state CMES:

Equations are solved with dense grids

Double well:

• Potential has a general form of $ax^{2}+bx^{4}$
• While negative $a$ corresponds to a double-well potential, the single well potential with a positive $a$ can also be solved

Morse:

• Potential has a general form of $V(x)=D_{e}(e^{-2\alpha(x-x_{e})}-2e^{-\alpha(x-x_{e})})$
• This is not a symmetric potential. The local minima of excited state CMES need to be searched before calculating frequencies.

2D excited state CMES:

Instead of dense grids with finite difference method, now the Fourier grid method is used

Harmonic-like potential:

• The 2D potential has a general form of: $V(x,y)=a_{x}x^{2}+a_{y}y^{2}+b_{x}x^{4}+b_{y}y^{4}+c_{xy}xy+c_{x^{2}y}x^{2}y$
• Unless $c_{x^{2}y}= 0$, this is also not a symmetric potential. The local minima of excited state CMES need to be searched before calculating frequencies
• "surface_generator" file will provide 9 points for local hessian matrix calculation