Excited states · TD-DFT

Excited-state methods — TDA · TD-DFT · CIS

ORCA supports several excited-state methods. The single-reference ones are listed below; for the multi-reference methods (CASSCF, NEVPT2, MRCI) the manual has a chapter of its own.

Basic usage

At its simplest, only the number of excited states needs to be specified. The example below computes the first 10 excited states of formaldehyde, which includes its well-known n → π* transition.

! B3LYP D4 def2-SVP RIJCOSX def2/J

%tddft
   NRoots    10          # first 10 excited states
   MaxDim    100         # Davidson subspace size
   Triplets  true        # triplets too (closed-shell reference only)
end

* int 0 1
  C 0 0 0   0.00     0.0      0.00
  O 1 0 0   1.20     0.0      0.00
  H 1 2 0   1.08   120.0      0.00
  H 1 2 3   1.08   120.0    180.00
*

Set NRoots generously so that the experimental region of interest is fully covered. Dark states with small oscillator strengths often sit between bright ones; if you set NRoots too low you may miss the experimentally observed band.

Reading the output

A finished TD-DFT job prints a table like:

-----------------------------
TD-DFT/TDA EXCITED STATES (SINGLETS)
-----------------------------

STATE  1:  E=   0.155436 au      4.230 eV    34121.5 cm**-1 <S**2> =   0.000000
     8a ->   9a  :     0.984123  (c=  0.99202)
     ...

STATE  2:  E=   0.305212 au      8.305 eV    66987.2 cm**-1 <S**2> =   0.000000
     ...

-----------------------------------------------------------------------------
         ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
-----------------------------------------------------------------------------
States    Energy   Wavelength   fosc     T2         TX        TY        TZ
        (cm-1)      (nm)                 (au**2)    (au)      (au)      (au)
-----------------------------------------------------------------------------
 0-1A   34121.5   293.1     0.00000123   0.00012   0.00000   0.00000   0.00345
 0-2A   66987.2   149.3     0.45612345   2.21345  -1.48732   0.00000   0.00000
 ...

Column meanings:

• STATE n: energy of the n-th excited state (au, eV, cm⁻¹).
• x → y: the dominant single excitation (e.g. HOMO → LUMO). Larger coefficient → more dominant.
• fosc: the oscillator strength. Above ~0.01 the absorption is large enough to be visible experimentally.
• Wavelength: the corresponding absorption wavelength (nm) — the number to compare with UV-Vis.

For formaldehyde, the first state (~290 nm) is the n → π* transition with a very small oscillator strength (symmetry-forbidden); the second state typically corresponds to what is observed experimentally.

Triplets and spin-flip

To also compute triplets from a closed-shell reference, add:

%tddft
   NRoots   10
   Triplets true
end

Triplet excitation energies (T₁, T₂, …) are essential for intersystem-crossing and phosphorescence analyses. For genuine singlet-diradicals or surface crossings, use spin-flip TDA (SF-TDA). The reference here must be high-spin (open-shell).

# Spin-flip TDA: start from a triplet reference
! UKS B3LYP D4 def2-SVP

%tddft
   NRoots 5
   SF     true
end

* xyzfile 0 3 mol.xyz

Excited-state optimisation — fluorescence

To predict a fluorescence wavelength, you must re-optimise the geometry on the excited state. The excited-state energy evaluated at that geometry is close to the 0-0 transition energy of fluorescence.

# Optimise the first excited state (S1)
! B3LYP D4 def2-SVP Opt

%tddft
   NRoots 3
   IRoot  1         # which excited state to optimise
end

* xyzfile 0 1 ground_opt.xyz

IRoot n means "compute the gradient of the n-th excited state and optimise it". Appending ! Freq afterwards gives excited-state frequencies as well. With zero-point correction included, the 0-0 transition energy obtained this way can be compared directly to a measured emission spectrum.

Non-adiabatic couplings and ETF

Photochemical dynamics (e.g. surface hopping) require non-adiabatic coupling matrix elements (NACMEs) between excited states. ORCA 6 computes these analytically, and also supports the electronic translational factor (ETF) correction.

%tddft
   NRoots      5
   IRoot       1
   NACME       true      # enable NACME
   ETF         true      # ETF correction
end

X-ray absorption spectra

The pre-edge region of a K-edge X-ray absorption spectrum can be modelled, both qualitatively and quantitatively, with TD-DFT. The manual uses the Ti K-edge of TiCl₄ as an illustration:

! BP86 ZORA ZORA-def2-TZVP(-f) SARC/J TightSCF

%tddft
   OrbWin[0] = 0, 0, -1, -1   # only orbital 0 (Ti 1s) as donor
   NRoots     25
   DoHigherMoments      true   # include quadrupole intensities
   DoFullSemiclassical  true
end

* int 0 1
  Ti 0 0 0   0.00       0.00     0.00
  Cl 1 2 3   2.15       0.00     0.00
  Cl 1 2 3   2.15     109.47     0.00
  Cl 1 2 3   2.15     109.47   120.00
  Cl 1 2 3   2.15     109.47   240.00
*

The key is the OrbWin[0] restriction, which limits donor orbitals to orbital 0 (the Ti 1s). Without that restriction every occupied orbital would contribute, and you would need an impractically large NRoots. This type of restriction is standard for K-edge modelling.

Functional choice and pitfalls

Typical recommendations by situation:

Plotting the absorption spectrum

Use orca_mapspc to turn the printed table into a spectrum. The example below covers 4890–14915 cm⁻¹ (~670–2040 nm) with a Gaussian line width of 1.3:

# Standard absorption spectrum
orca_mapspc mol.out ABSQ -eV -x04890 -x14915 -w1.3

# Extended spectrum including quadrupole and magnetic-dipole contributions
orca_mapspc mol.out ABSOI -eV -x04890 -x14915 -w1.3

The resulting .dat file can be visualised in gnuplot, matplotlib, etc., and overlaid directly with experimental spectra.