some questions about pair_modify mix command

Hi dear LAMMPS users,
In my simulation model, I have 9 kinds of atoms. But I only consider 3
kinds of atoms (A B and C) for simplicity here. My pair_style is
lj/cut/coul/long. The unusual aspects of my model are as follows:

1.For atom pair AA AB AC and BB BC, the lj cutoff distance is R1
2.and for atom pair CC, the lj cutoff distance is R2.
3.And the global coul cutoff is 12A, the lennard-jones parameter can
be computed through pair_modify command, but the cutoff cannot.
To achieve this, I was wondering which method can achieve what I want?
And my input script are as follows, and I have three questions
following each “#”, really appreciate for your kindly help:

Pari_style lj/cut/coul/long R1 12
Pair_modify mix geometric

#question1: Now the LJ parameters for AA AB AC BB BC CC are correct
and the cutoff distance for AA AB AC BB BC is correct(equals R1 here),
but the cutoff distance for atom pair CC is not correct(equals R1 here
but the correct cutoff is R2). So next step I will set it explicitly.
I was wondering whether the pair_modify mix command will take into
account the new pair_coeff for atom CC which I set explicitly on the
next step. So the cutoff for AC and BC is (R1+R2)/2.

Pari_coeff 3 3 0.21 2.96 R2

#question2: Because I want to set the cutoff distance for AC and BC to
R1 explicitly(don’t through pair_modify mix…). So I set pair_coeff for
CC after mix done. I was wondering whether the order between
pair_coeff and pair_modify will influence the results.

Pair_style lj/cut/coul/long R1 12
Pair_coeff 1 3 0.56 3.4 R1
Pair_coeff 2 3 0.53 3.5 R1
Pari_coeff 3 3 0.21 2.96 R2
Pair_modify mix geometric

#question3: I think this method can achieve what I want, cause I set
AC BC CC explicitly and use mix geometric to compute other lj
parameter (AB) which I haven’t set. But when there are many kinds of
atoms, I need to compute and set every lj parameter explicitly. So it
maybe tedious in my simulation. So I was wondering whether method1 can
get the same result as method2 or is there some alternative method.
Thanks for your advisement

Looking forward to your reply.
Shusen Guo

i don't think there is a need for mixing cutoffs for LJ potentials.

essentially, there are are only two significant choices:
1) minimum of the potential (sigma*2**1/6), i.e. a purely repulsive interaction
2) as long as you can afford and until the error from truncation is
small enough. typically between 3x and 5x the sigma value.

i know, that there are people/papers arguing, that the choice of
cutoff (and the error it causes) is part of the parameterization, but
in my personal opinion, i consider that highly suspicious and not
convincing, as that neglects the different degrees of error
cancellation is homogeneous and inhomogeneous environments.

thus my suggestion just stick with the (largest) global cutoff, and
override only for case 1).