Second Kind Chemical Bonding Field

When the chemical field transformation (3.469) is undertaken the noninvariant spontaneously broken Lagrangian for the second kind chemical bonding fields yields (Putz, 2008d)  

One may easily note that the first two Lagrangians sectors, Eqs. (3.485) and (3.486), correspond with the invariant Lagrangian (3.473) up to a constant factor I/V2 that modifies (f into and respectively the same t) e of conversion help in recognizing the Lagrangian (3.487) as being of t3 e (3.475) thus producing no new chemical bonding field out 

With the setting (3.490) the Lagrangian (3.488) leads with the equation (Putz, 2008d) 

However, the field (3.492) cannot be assumed alone as the second type chemical bonding field solution but only along the component this last one can be foxmd by substitution of with (3.492) form on the equation obtained from cancellation of Lagrangian (3.489) imder stationary conditions (3.490) it finally produces the chemical bonding field equation (Putz, 2008d) 

Cumulating both chemical field components (3.492) and (3.494) in the chemical field (3.469) produces the second kind of chemical bonding fields in terms of electronegativity and chemical hardness only (Putz, 2008d)  

---