Worked on simplifying the formulas for charge using alpha definition.

m_e_n = m_e / Hz_kg # calcuate the Compton frequency of the m_e mass
alpha_calc = 2 * pi * e**2 * amp_force / (Hz_kg * c)
kg_Hz = 1 / Hz_kg
α = D('0.0072973525693')


# Gravitational Coupling Constant
#a_g_calc = m_e**2 *2 *pi *G_n / Hz_kg**2
a_g_calc = (m_e * kg_Hz * t_P )**2 * 2 * pi

mass converted to Compton frequency and scaled to Planck time scale, squared, scaled by 2pi. 


#E_h_calc = e**4 * 4 * pi**2 * m_e * amp_force**2/ Hz_kg**2
E_h_calc = m_e * α**2 * c**2

This is simple, mass scaled by alpha squared converted to energy by c^2.


#R_inf_calc = e**4 * 2 * pi**2 * m_e * amp_force**2/ (Hz_kg**3 * c**3 )
#R_inf_calc = m_e * α**2 / (Hz_kg * c * 2 )
R_inf_calc = m_e_n * α**2 / ( c * 2 )

A frequency/c is a wavenumber.  inverse meter units

#a_0_calc = Hz_kg**2 * c**2 / (e**2 * 4 * pi**2 * m_e * amp_force)
#a_0_calc = Hz_kg * c / ( m_e * 2 * pi * α )
#a_0_calc = e**2 * amp_force / ( m_e * α**2 )
a_0_calc = c / ( m_e_n * 2 * pi * α )

This last one is interesting, it becomes a characteristic frequency converted to a wavelength.