\Delta

SCF Methods 7.8.6 Non-equilibrium Solvation for ROKS and

\Delta

7.8.7 $\Delta$ SCF Driver

(December 11, 2025)

The $delta_scf input section can be used to control $\Delta$ SCF singlet and triplet excited state calculations with more ease. This section is enabled by setting DELTA_SCF = TRUE in the $rem input section. A basic job demonstrating the defaults is given in Example 7.8.7.

DELTA_SCF

DELTA_SCF
       Trigger a $\Delta$ SCF calculation.
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE $\Delta$ SCF calculation will not be performed. TRUE $\Delta$ SCF will be performed.
RECOMMENDATION:
       Set to TRUE if $\Delta$ SCF calculation is desired.

Example 7.58 By default, restricted open-shell SCF calculations are performed for both the singlet and the triplet states for the HOMO $\to$ LUMO transition.

$comment
  Basic DeltaSCF calculation on formamide.
  HOMO (n) -> LUMO (pi*) transition.
$end

$molecule
  0   1
  C   0.00096902 0.00000000  0.41970774
  O   1.20026422 0.00000000  0.23240832
  N  -0.93604020 0.00000000 -0.56208780
  H  -0.44521491 0.00000000  1.42281135
  H  -0.64165047 0.00000000 -1.52189668
  H  -1.91364957 0.00000000 -0.34413077
$end

$rem
  METHOD     wB97X-D
  BASIS      STO-3G
  DELTA_SCF  TRUE
$end

Once DELTA_SCF is set to TRUE inf the $rem section, the keywords to be described shortly can be used in the $delta_scf input section. The desired orbital to excite from (hole state) and to excite into (particle state) are requested with the keywords SOMO_1 and SOMO_2 (for singly-occupied molecular orbitals), respectively. A $m_{s}=1$ triplet state can be calculated with either ROSCF or USCF by setting triplet to restricted or unrestricted. Unrestricted spin-symmetry broken states (Section 7.8.2) are requested by setting singlet to unrestricted whereas setting singlet to restricted triggers a spin-pure ROKS calculation (Section 7.8.3) If the triplet state (restricted or unrestricted) is requested in addition to the spin-symmetry broken state, the code will calculate the approximate energy of the spin-pure singlet state using the approximate spin-projection method, as detailed in Section 7.8.2. ¹⁴⁵⁷ Yamaguchi K. et al.
Chem. Phys. Lett.
(1988), 149, pp. 537. Link

Singlet
       Carry out either a spin-symmetry broken or restricted-open shell singlet calculation.
INPUT SECTION: $delta_scf
TYPE:
       STRING
DEFAULT:
       Restricted
OPTIONS:
       Restricted Perform a restricted open-shell singlet (ROKS) SCF calculation. Unrestricted Perform an unrestricted spin-symmetry broken SCF calculation.
RECOMMENDATION:
       Consult the literature.

Triplet
       Carry out a $m_{s}=1$ triplet calculation.
INPUT SECTION: $delta_scf
TYPE:
       STRING
DEFAULT:
       Restricted
OPTIONS:
       Restricted Perform a restricted open-shell triplet SCF calculation. Unrestricted Perform an unrestricted triplet SCF calculation.
RECOMMENDATION:
       Carry out restricted if possible.

SOMO_1
       Specify the occupied orbital to excited from.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       HOMO
OPTIONS:
       $0<n<$ LUMO Any integer $n\in$ [1, HOMO] is allowed
RECOMMENDATION:
       Chose the desired orbital to excited from based on prior inspection of the ground state orbitals and the desired state to target.

SOMO_2
       Specify the occupied orbital to excited from.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       LUMO
OPTIONS:
       HOMO $<n$ Any integer greater than or equal to the LUMO.
RECOMMENDATION:
       Chose the desired orbital to excited from based on prior inspection of the ground state orbitals and the desired state to target.

Example 7.59 A unrestricted triplet and spin-symmetry broken SCF calculation. The desired core excitation is targeted via the SOMO_1 and SOMO_2 keywords

$comment
  DeltaSCF calculation on the 1s -> 3s (LUMO + 3) core excited state of Ne.
$end

$molecule
  0  1
  Ne
$end

$rem
  METHOD            SCAN
  BASIS             cc-pCVDZ
  INTEGRAL_SYMMETRY FALSE
  DELTA_SCF         TRUE
$end

$delta_scf
  SOMO_1   1
  SOMO_2   9
  singlet  unrestricted
  triplet  unrestricted
$end

Example 7.60 A restricted open-shell singlet SCF calculation. Note that when only singlet or triplet are set, only the requested calculation will be performed (as opposed to the default which is both). SOMO_1 and SOMO_2 are once again used to target a specific core excited state ( $1s\to 3s$ ) of hydrogen fluoride. Compare this example to Example 7.8.4

$comment
  DeltaSCF calculation on the 1s -> 3s (LUMO + 1) core excited
  state of HF. Only a restricted open-shell singlet calculation
  is requested.
$end

$molecule
  0  1
  F       0.0000  0.0000  0.0000
  H       0.0000  0.0000  0.9168
$end

$rem
  METHOD            SCAN
  BASIS             aug-cc-pCVTZ
  INTEGRAL_SYMMETRY FALSE
  DELTA_SCF         TRUE
$end

$delta_scf
  SOMO_1                1
  SOMO_2                7
  singlet               restricted
  singlet_SCF_algorithm SGM
  singlet_SGM_gradient  50
  singlet_SOMO_mixing   false
$end

The code will automatically measure three useful quantities:

•

Overlaps between the ground state SOMOs used as a guess, the singlet (or mixed-state) SOMOs, and the triplet SOMOs; this serves as a measure to ensure the $\Delta$ SCF orbital optimizations are indeed converging to the desired excited states.
•

Transition dipole moment between the ground state and the singlet excited state.
•

Non-orthogonal overlap between the closed-shell ground state and the singlet excited state determinants (see Section 7.8.3 on SOMO mixing in ROKS calculations).

When the SOMO overlaps are poor (significantly smaller than 1.0), it is suggested you verify the calculation using a standard input as described previously in this section (i.e., using sequential inputs and the $reorder_mo or $occupied sections) and either printing or visualizing the orbitals. This will help you assess more clearly which state the SCF calculation is converging to. To control the SCF convergence within the $delta_scf section, the following keywords are available:

Singlet_SCF_Algorithm
       Specify the algorithm used to converge the singlet (or symmetry-broken) SCF calculation.
INPUT SECTION: $delta_scf
TYPE:
       STRING
DEFAULT:
       GDM if SOMO_1 = HOMO and SOMO_2 = LUMO, MOM otherwise.
OPTIONS:
       DIIS, GDM, GDM_LS, MOM, IMOM, STEP, STEP_MOM, SGM, SGM_LS
RECOMMENDATION:
       DIIS, GDM, and GDM_LS are suitable for the HOMO $\rightarrow$ LUMO transition. If higher excited states are desired use MOM, STEP, SGM, or one of their variants. When using ROKS and encountering large overlaps with the ground state, try using either GDM or SGM in conjunction with Singlet_SOMO_Mixing = false.

Singet_SCF_Convergence
       Specify the energy convergence threshold for the singlet (or symmetry-broken) SCF calculation.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       5 if Singlet_SCF_Algorithm is set to GDM or SGM, 7 otherwise.
OPTIONS:
       $n$ Any positive integer.
RECOMMENDATION:
       Follow defaults.

Singlet_SGM_Gradient
       Only relevant if Singlet_SCF_Algorithm is set to SGM. See DELTA_GRADIENT_SCALE in Section 7.8.4.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       75
OPTIONS:
       $n$ Any integer $n\in(0,100]$ .
RECOMMENDATION:
       See documentation on DELTA_GRADIENT_SCALE.

Singlet_SOMO_Mixing
       Only relevant when singlet is set to true. Refer to ROKS_SS_MIXING in Section 7.8.3.
INPUT SECTION: $delta_scf
TYPE:
       LOGICAL
DEFAULT:
       FALSE
OPTIONS:
       FALSE Supressing mixing between SOMOs. TRUE Allow mixing of SOMOs.
RECOMMENDATION:
       See documentation on ROKS_SS_MIXING.

Triplet_SCF_Algorithm
       Specify the algorithm used to converge the triplet SCF calculation.
INPUT SECTION: $delta_scf
TYPE:
       STRING
DEFAULT:
       GDM if SOMO_1 = HOMO and SOMO_2 = LUMO, MOM otherwise.
OPTIONS:
       DIIS, GDM, GDM_LS, MOM, IMOM, STEP, STEP_MOM, SGM, SGM_LS
RECOMMENDATION:
       DIIS, GDM, and GDM_LS are suitable for the HOMO $\to$ LUMO transition. If higher excited states are desired use MOM, STEP, SGM, or one of their variants.

Triplet_SCF_Convergence
       Specify the energy convergence threshold for the triplet SCF calculation.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       5 if Singlet_SCF_Algorithm = GDM or SGM, 7 otherwise.
OPTIONS:
       $n$ Any positive integer.
RECOMMENDATION:
       Follow defaults.

Triplet_SGM_Gradient
       Only relevant if Triplet_SCF_Algorithm is set to SGM. See DELTA_GRADIENT_SCALE in Section 7.8.4.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       75
OPTIONS:
       $n$ Any integer between $[1,100]$ .
RECOMMENDATION:
       See documentation on DELTA_GRADIENT_SCALE.

When describing core excitations for highly symmetrical molecules (e.g. ethylene, N ${}_{2}$ , or benzene) where the core orbitals delocalize over the entire molecule, it is necessary to localize the core orbitals for accurate excitation energies with $\Delta$ SCF. ¹⁶⁵ Brumboiu I. E., Fransson T.
J. Chem. Phys.
(2022), 156, pp. 214109. Link This can be accomplished with the following keywords:

Localize
       Localize the given number of orbitals using the Boys method (refer to Section 10.3.2).
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       None
OPTIONS:
       $n>1$ Any integer $n\in[2,N_{\text{occ}}]$
RECOMMENDATION:
       Set this variable to the total number of core orbitals to localize (for example, 2 in N ${}_{2}$ or 6 in benzene).

Localize_Offset
       Sets the offset to begin selecting the number of orbitals to localize, as requested with the localize variable.
INPUT SECTION: $delta_scf
TYPE:
       INTEGER
DEFAULT:
       $\text{HOMO}-n$ , where $n$ is set with localize when SOMO_1 = HOMO, or is 0 otherwise.
OPTIONS:
       $x$ Any integer $x\in[1,\text{HOMO}-n]$
RECOMMENDATION:
       Consider the number of atoms with orbitals lower in energy than those you are interested on and set this variable to that number (for example, $x=2$ when attempting to reach the carbon K-edge in CS ${}_{2}$ , due to the two 1s sulfur orbitals.

Finally, these last two keywords control the cube plots of the SOMOs for the singlet and triplet SCF calculations. These are essential to inspect visually the character of the SCF solutions found ( $n\to\pi^{\ast}$ , $\pi\to$ Rydberg, $1s\to\sigma^{\ast}$ , etc.) and, in addition to the SOMO orbital overlaps printed in the output, help verify that the SCF calculations are converging to the state you are seeking.

Singlet_SOMO_Print
       Plots the SOMOs of the singlet (or spin symmetry-broken) state. Make sure you activate the $plots section in the input file.
INPUT SECTION: $delta_scf
TYPE:
       STRING
DEFAULT:
       Both
OPTIONS:
       Alpha Plots the SOMOs of the alpha orbitals Beta Plots the SOMOs of the beta orbitals Both Plots the SOMOs of both the alpha and beta orbitals
RECOMMENDATION:
       Inspect the orbitals when in doubts about the SCF solution.

Triplet_SOMO_Print
       Plots the SOMOs of the triplet state. Make sure you activate the $plots section in the input file.
INPUT SECTION: $delta_scf
TYPE:
       STRING
DEFAULT:
       Both
OPTIONS:
       Alpha Plots the SOMOs of the alpha orbitals Beta Plots the SOMOs of the beta orbitals Both Plots the SOMOs of both the alpha and beta orbitals
RECOMMENDATION:
       Inspect the orbitals when in doubts about the SCF solution.

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7.8.7 ΔSCF Driver

7.8.7 $\Delta$ SCF Driver