MRSF-TDDFTB¶

MRSF-TDDFTB transfers the spin-adapted MRSF-TDDFT response — independent singlet and triplet CSF equations of motion, recovered open-shell spin complements, and conical-intersection capability — into the atom-resolved transition-charge framework of long-range corrected DFTB. It is the excited-state spin-flip family of the DFTB method, selected with [input] method=dftb plus [tdhf] type=mrsf. The DFTB method also provides ground-state DFTB2 and DFTB0, conventional TD-DFTB, and SF-TDDFTB. All DFTB keywords live in the [dftb] section.

External library and development preview

The DFTB method is provided by the optional OpenQP-DFTB library (openqp-dftb, loaded via ctypes); build it from source or build OpenQP with -DENABLE_OPENQP_DFTB=ON (see the [dftb] reference for the full build and library-discovery note). The integration is tracked in OpenQP PR #266 and is not part of OpenQP 1.2.0. The one-line .oqp format is likewise a development-branch input style (see One-line .oqp).

Why DFTB¶

The DFTB electronic problem is minimal-basis and replaces four-center electron-repulsion integrals by atom-resolved transition charges, so the complete MRSF response, its analytic gradient, and state couplings are delivered in seconds for hundreds of atoms. This brings MRSF-level photochemistry — including nonadiabatic dynamics — to large chromophores, molecular aggregates, and long trajectories that are out of reach for routine all-electron MRSF-TDDFT, while keeping the same singlet/triplet spin separation and multireference character near conical intersections.

State labels¶

MRSF-TDDFTB uses a high-spin ROKS DFTB reference, and the root convention follows MRSF-TDDFT: the lowest singlet response root is relabeled S0. In the [properties] grad and [optimize] istate keys the roots are therefore 1-based over the MRSF manifold — root 1 = S0, root 2 = S1, and so on (T0 is the lowest triplet). The one-line .oqp form uses the physical zero-based labels S0, S1, T0, … directly. As with every DFTB family, basis= is an ignored placeholder and functional= is empty.

Energy¶

Three singlet states (S0–S2) from one MRSF-TDDFTB response:

.oqp

mrsf-tddftb(nstate=3)
energy
geom="chromophore.xyz"

Python

from oqp.openqp import OpenQP

job = OpenQP(project="mrsf_energy")
job.molecule("chromophore.xyz")
job.dftb(response_type="mrsf", nstate=3)
job.workflow.energy()
job.run()

Legacy .inp

[input]
method=dftb
runtype=energy
charge=0
basis=sto-3g
functional=
system=chromophore.xyz

[tdhf]
type=mrsf
nstate=3

[dftb]
backend=native
type=mrsf

The bundled OB2W0PT3 set (official spinw.txt included) is resolved automatically. Use parameter_path only to override it; see dftb keywords.

Gradient¶

Gradient of the first excited singlet S1. S1 is response root 2, so [properties] grad=2 (root 1 is S0):

.oqp

mrsf-tddftb(nstate=3)
grad(S1)
geom="chromophore.xyz"

Python

from oqp.openqp import OpenQP

job = OpenQP(project="mrsf_grad")
job.molecule("chromophore.xyz")
job.dftb(response_type="mrsf", nstate=3)
job.workflow.gradient(state=2)
job.run()

Legacy .inp

[input]
method=dftb
runtype=grad
charge=0
basis=sto-3g
functional=
system=chromophore.xyz

[tdhf]
type=mrsf
nstate=3

[dftb]
backend=native
type=mrsf

[properties]
grad=2

Use grad=1 / grad(S0) / gradient(state=1) for the S0 gradient.

Geometry optimization¶

Optimize the S1 minimum — root 2, so istate=2 (use istate=1 for the S0 minimum):

.oqp

mrsf-tddftb(nstate=3)
opt(S1)
geom="chromophore.xyz"

Python

from oqp.openqp import OpenQP

job = OpenQP(project="mrsf_opt")
job.molecule("chromophore.xyz")
job.dftb(response_type="mrsf", nstate=3)
job.workflow.optimize(istate=2)
job.run()

Legacy .inp

[input]
method=dftb
runtype=optimize
charge=0
basis=sto-3g
functional=
system=chromophore.xyz

[tdhf]
type=mrsf
nstate=3

[dftb]
backend=native
type=mrsf

[optimize]
lib=oqp
istate=2

Long-range kernels and the erf-tuned operator¶

Two response kernels are available through [dftb] lc_gamma: yukawa (LC-DFTB2 Yukawa–Slater) and erf (erf$(\omega R)/R$). The erf-tuned combination lc_gamma=erf, omega=0.25, cam_beta=1.2 reproduces the MRSF-TDDFT ordering of near-degenerate bright/dark states, which the stock kernels can invert. Because its cam_beta>1 LC ground-state SCC is harder to converge, pair it with a robust mixer:

mrsf-tddftb(nstate=3)
dftb(lc_gamma=erf,omega=0.25,cam_beta=1.2,scc_mixer=trust)
energy
geom="chromophore.xyz"

The equivalent legacy override is:

[dftb]
type=mrsf
lc_gamma=erf
omega=0.25
cam_beta=1.2
scc_mixer=trust

Conical intersections (MECI)¶

DFTB supplies MRSF-TDDFTB state energies and analytic gradients, so a minimum-energy conical-intersection (MECI) search is driven by the shared [optimize] optimizer — there is no separate DFTB entry point. In particular the BaekA two-or-more-state adaptive-penalty algorithm ([optimize] meci_search=baeka) runs on MRSF-TDDFTB states exactly as it does on all-electron MRSF-TDDFT, at tight-binding cost; this is the engine behind the DTCAM-TB conical-intersection benchmarks. Because MRSF has the correct S₀/S₁ intersection topology, MRSF-TDDFTB is the DFTB family to use for S₀/S₁ conical intersections.

The MRSF S0 is response root 1, so [optimize] states is 1-based (1=S0, 2=S1). A two-state S1/S0 crossing:

.oqp

mrsf-tddftb(nstate=3)
meci(S0,S1,algorithm=baeka,gap=1e-4)
geom="guess.xyz"

Python

from oqp.openqp import OpenQP

job = OpenQP(project="mrsf_ci")
job.molecule("guess.xyz")
job.dftb(response_type="mrsf", nstate=3)
job.workflow.meci(states=[1, 2], algorithm="baeka", gap=1.0e-4)
job.run()

Legacy .inp

[input]
method=dftb
runtype=meci
charge=0
basis=sto-3g
functional=
system=guess.xyz

[tdhf]
type=mrsf
nstate=3

[dftb]
backend=native
type=mrsf

[optimize]
meci_search=baeka
states=1,2
gap=1.0e-4

The BaekA controls (sigma, alpha, delta_beta, beta_schedule, gap, and the ordered states list) and its distinction from the legacy three-state runtype=tci deck are documented once in the [optimize] reference and apply unchanged to the DFTB method. See also the BaekA Multistate MECI workflow.

NACME and surface hopping¶

Nonadiabatic couplings are overlap-based time-derivative couplings, computed from a cross-geometry Slater–Koster state overlap. NACME uses two geometries and requires backend=native:

.oqp

mrsf-tddftb(nstate=3)
nacme(S0,S1,dt=1,align=reorder)
geom="ch2.xyz"
geom2="ch2_previous.xyz"

Python

from oqp.openqp import OpenQP

job = OpenQP(project="mrsf_dftb_nacme")
job.molecule("ch2.xyz", "ch2_previous.xyz")
job.dftb(response_type="mrsf", nstate=3)
job.workflow.nacme()
job.run()

Legacy .inp

[input]
runtype=nacme
method=dftb
basis=sto-3g
functional=
system=
  C 0.0 0.0 0.0
  H 0.0 0.86 -0.55
  H 0.0 -0.86 -0.55
system2=
  C 0.0 0.0 0.0
  H 0.0 0.865 -0.55
  H 0.0 -0.86 -0.55

[tdhf]
type=mrsf
nstate=3

[dftb]
backend=native
type=mrsf

[nac]
dt=1
align=reorder

Surface-hopping dynamics uses the shared FSSH driver (runtype=namd) with an MRSF-TDDFTB electronic structure and the [md] section; [md] active is 1-based over the MRSF manifold (root 1 = S0, so active=2 starts on S1).

Spin-orbit coupling¶

MRSF-TDDFTB SOC uses the one-center approximation: per-element, per-shell constants xi_l supplied through the parameter file as soc Z l xi records (l=1 for p, l=2 for d; xi in Hartree). It powers standalone SOC (runtype=soc) and, with [md] soc=true, spin-orbit-coupled NAMD. For SOC-NAMD use [md] soc_basis=mch (the local-diabatization MCH basis conserves energy; the spin-adiabatic basis is less robust).

QM/MM¶

DFTB QM/MM uses Mulliken-monopole electrostatic embedding: the MM electrostatic potential enters the SCC Hamiltonian directly, so no ESPF grid fitting is needed, and the analytic gradient carries the coupling. Activate it with [input] qmmm_flag=true and the [qmmm] section (whole-molecule electrostatic embedding; the legacy split scheme is not supported). Hydrogen link atoms across covalent QM/MM boundaries are handled by the shared QM/MM layer. Gas-phase SOC-NAMD and whole-molecule electrostatic QM/MM NAMD are supported; SOC combined with QM/MM embedding is not yet wired for the DFTB method.

Python API¶

Use job.mrsf_tddftb(...) for an explicit MRSF-TDDFTB request. The matching helpers for the other families are job.ground_dftb(...), job.tddftb(...), and job.sf_tddftb(...); all four are also available through job.theory. The general .dftb(...) builder remains available and accepts response_type values ground, dftb0, tddftb, sf, and mrsf, along with any [dftb] keyword (for example lc_gamma, omega, scc_mixer, print_level, or state_to_state_spectrum). The run type is set either with runtype=... on the builder or through job.workflow.energy(), .gradient(state=N), .optimize(istate=N), and .meci(...):

from oqp.openqp import OpenQP

job = OpenQP(project="thymine_dftb")
job.molecule("thymine.xyz")
job.mrsf_tddftb(nstate=3, print_level=1)
job.workflow.gradient(state=2)
job.run()

MRSF-TDDFTB jobs additionally drive the job.workflow.soc() and job.workflow.namd() workflows (development preview).