Meaning of quadrupole field components in $multipole_field

Hi everyone, I’m interested in using QChem to calculate vibrational frequencies of molecules in the presence of an electric field for a class project. I found that using $multipole_field (described here Q-Chem 4.3 User’s Manual : Applying a Multipole Field ($multipole_field)), one can apply a uniform electric field using the X, Y, or Z components, but also a quadrupolar field using the components XX, XY, XZ, YY, etc. For these quadrupole field components, what is the equation describing the electric field in terms of the components? For instance, if I use

XX 1

Does this create an electric field of E(x)=x^2? Or some other functional form?

Thanks for the help folks.

It means a term proportional to x*x in the Hamiltonian. Regarding sign convention, see the Q-Chem manual for v. 6.1 or later, or this thread:

Thank you for the help. For the term proportional to x*x in the Hamiltonian, do you know what the proportionality constant is?

that’s what you’re setting in the $multipole_field section. So you probably don’t actually want the value 1 (in your original example); rather that 2nd value should be a double-precision number equal to the constant that multiplies x^2, with the caveat above about sign convention.