Hi,

As the title suggest, I would like to get some clarification with respect to the convention of dipole moment in Psi4, especially in the context of a dipole moment interacting with an external electric field.

To start with, I would like to make sure that I am understanding the math correctly. The dipole moment is defined as

```
mu = Sum_i q_i r_i (1)
```

where `q_i`

and `r_i`

are the point charges and (cartesian) coordinates of `i`

. Thus, the dipole moment vector should point from the negative to positive charge, which is the reverse of the “chemistry convention”.

It is also known that the Hamiltonian of a molecule in the presence of an electric field is

```
H = H_0 - mu . eps (2)
```

where `H_0`

is the field-free Hamiltonian and `eps`

is the electric field vector (for simplicity, let us assume spatially uniform electric field). Thus, we can compute the dipole moment of a molecule by numerically differentiating the energy with respect to the external electric field

```
mu = -d(H)/d(eps) at eps=0 (3)
```

Equation (2) also implies that the energy should decrease when `mu`

and `eps`

are aligned/parallel, and increase when they are antiparallel.

I tested this with the HF molecule at 1.0 Angstrom separation, calculated using RHF/cc-pVDZ in Psi4 1.7 and GAMESS 2022 R2 as reference. Here is the Psi4 input at zero field (I just changed it to +/-0.001 at different inputs).

```
molecule {
0 1
F 0.00 0.00 -0.50
H 0.00 0.00 0.50
no_reorient
nocom
symmetry c1
}
set {
basis cc-pvdz
reference rhf
scf_type pk
e_convergence 1.0e-10
r_convergence 1.0e-10
maxiter 500
perturb_h true
perturb_with dipole
perturb_dipole [0, 0, 0.000]
}
properties('scf', properties=['dipole','mulliken_charges'])
```

Based on the geometry alone, it is clear from the definition in Eq. (1) that the dipole moment vector should point in the direction of positive z axis (*i.e.*, pointing from F to H). Here is the summary of results of Psi4 and GAMESS:

```
=======================================
Field (a.u.) E(GMS) E(PSI4)
---------------------------------------
-0.001 -100.009040 -100.010705
0.000 -100.009870 -100.009870
0.001 -100.010705 -100.009040
---------------------------------------
Dipole (FFM) +0.832034 -0.832034
Dipole (<mu>) +0.832043 +0.832037
=======================================
```

The expectation value dipole points in the correct direction, but the FFM is not. This implies that either the sign of the dipole moment in Psi4 uses the chemistry convention (but printed out in the way consistent with the definition), or that Psi4 uses the Hamiltonian of the form `H = H_0 + mu . eps`

.

Could someone please clarify this issue?

Thank you in advance for your time and help.