How to use SGM method to calculate triplet excited states with ROKS?

Questions
#1

Hi evergyone,

I am implementing the Square Gradient Minimization (SGM) method for excited-state calculations, as it is known to be more robust than the traditional Maximum Overlap Method (MOM) in avoiding variational collapse.

In the paper J. Chem. Theory Comput. 2020, 16, 1699, the authors presented results for both singlets (using the ROKS spin-purification functional) and triplets (calculated within the restricted open-shell framework). I am currently trying to reproduce these triplet energies using the SGM solver.

However, when I attempt to target the triplet state using SGM, I encounter convergence failures or unexpected program exceptions. For example, the following input file, which is slightly modified from the example in 7.8.3 Squared-Gradient Minimization‣ 7.8 Restricted Open-Shell and Δ SCF Methods ‣ Chapter 7 Open-Shell and Excited-State Methods ‣ Q-Chem 6.0 User’s Manual, cannot converge for Delta SCF calculations. Although this specific transition might be simple enough for standard methods, I am using it to verify my SGM setup for triplets before moving to more challenging systems.

$molecule
0 1
N 0.0000 0.0000 0.0000
H 0.0000 -0.9377 -0.3816
H 0.8121 0.4689 -0.3816
H -0.8121 0.4689 -0.3816
F 0.0000 0.0000 6.0000
F 0.0000 0.0000 7.4120
$end

$rem
METHOD pbe0
BASIS cc-pVDZ
SYMMETRY false
SYM_IGNORE true
SCF_CONVERGENCE 8
$end

@@@

$comment
The reorder section is superfluous here since the excitation is HOMO to LUMO
and thus the unpaired electron orbitals are already at the frontier.
$end

$molecule
0 3 # Targeting the Triplet state
N 0.0000 0.0000 0.0000
H 0.0000 -0.9377 -0.3816
H 0.8121 0.4689 -0.3816
H -0.8121 0.4689 -0.3816
F 0.0000 0.0000 6.0000
F 0.0000 0.0000 7.4120
$end

$rem
METHOD pbe0
BASIS cc-pVDZ
SYMMETRY false
SYM_IGNORE true
SCF_ALGORITHM sgm
ROKS true
SCF_GUESS read
$end

$reorder_mo
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
$end

A restricted open-shell singlet SCF calculation will be
performed using SGM with line-search. singlet observed!!
…
Delta = 1.116777789e+00
Using OS-ROSCF Gradient
50 -255.5445158135 4.04e-02 LineSearch Step
gen_scfman_exception: SCF failed to converge

Q-Chem fatal error occurred in module libgscf/gen_scfman/gen_scfman_main.C, line 244:

Error in gen_scfman

#2 
ROKS true

will request a restricted open-shell singlet calculation. Try

$molecule
0 1
N 0.0000 0.0000 0.0000
H 0.0000 -0.9377 -0.3816
H 0.8121 0.4689 -0.3816
H -0.8121 0.4689 -0.3816
F 0.0000 0.0000 6.0000
F 0.0000 0.0000 7.4120
$end

$rem
METHOD pbe0
BASIS cc-pVDZ
SYMMETRY false
SYM_IGNORE true
SCF_CONVERGENCE 8
$end

@@@

$comment
The reorder section is superfluous here since the excitation is HOMO to LUMO
and thus the unpaired electron orbitals are already at the frontier.
$end

$molecule
0 3
N 0.0000 0.0000 0.0000
H 0.0000 -0.9377 -0.3816
H 0.8121 0.4689 -0.3816
H -0.8121 0.4689 -0.3816
F 0.0000 0.0000 6.0000
F 0.0000 0.0000 7.4120
$end

$rem
METHOD pbe0
BASIS cc-pVDZ
SYMMETRY false
SYM_IGNORE true
SCF_ALGORITHM sgm
UNRESTRICTED false
SCF_GUESS read
$end

$reorder_mo
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
$end

or, even better,

$molecule
0 1
N 0.0000 0.0000 0.0000
H 0.0000 -0.9377 -0.3816
H 0.8121 0.4689 -0.3816
H -0.8121 0.4689 -0.3816
F 0.0000 0.0000 6.0000
F 0.0000 0.0000 7.4120
$end

$rem
METHOD pbe0
BASIS cc-pVDZ
SYMMETRY false
SYM_IGNORE true
SCF_CONVERGENCE 8
DELTA_SCF true
$end

$delta_scf
  triplet restricted
  triplet_SCF_algorithm SGM
$end