Formaldehyde: X-ray Absorption (Core Excitations)

X-ray absorption spectroscopy (XAS) excites an electron out of a 1s core orbital. Each element absorbs in its own energy window (the K-edge), so the spectrum is element-specific: carbon near 285 eV, oxygen near 530 eV. MRSF-TDDFT can reach these core states directly with the ixcore option, without computing the hundreds of valence states below them.

Formaldehyde

π*, the orbital that receives the core electron

Copy and run

The carbon K-edge:

formaldehyde-xas-c.oqp

mrsf(nstate=70)/bhhlyp/6-31g* energy(S0) tdhf(ixcore=2)
geom="""
C      0.000000     0.000000    -0.526342
O      0.000000     0.000000     0.676110
H      0.000000     0.937620    -1.119884
H      0.000000    -0.937620    -1.119884
"""

Download formaldehyde-xas-c.oqp · formaldehyde-xas-o.oqp (oxygen K-edge, tdhf(ixcore=1))

openqp formaldehyde-xas-c.oqp

• tdhf(ixcore=N) selects molecular orbital N as the core orbital. The orbitals are numbered by energy: orbital 1 is O 1s and orbital 2 is C 1s. OpenQP shifts the response equations so that excitations out of this orbital are found among the computed states.
• nstate=70 leaves room for the valence states that are still computed; energy(S0) follows the repository XAS example.

Each run takes about 5 seconds.

What you get

The transitions from S0 are listed after the excited-state summary table. For the carbon K-edge:

   S0 -> S53  283.882898        ...      0.0629
   S0 -> S54  284.616185        ...      0.0000

Edge	Transition	Energy	Oscillator strength	Experiment
C K-edge	C 1s → π*	283.88 eV	0.063	about 286.0 eV
O K-edge	O 1s → π*	525.48 eV	0.026	about 530.8 eV

The same input for HCN (hcn-xas-c.oqp) gives its carbon 1s → π* transition at 285.55 eV with an oscillator strength of 0.050, the value quoted for the corresponding repository example.

Reading the result

• Each edge has one strong 1s → π* line. Like valence MRSF-TDDFT, the core states come from spin flips out of the high-spin reference; only the excitation from the core orbital into the LUMO (π*) is a single excitation in this construction, so higher core-excited states appear with very small intensity.
• The energies are 2–6 eV below experiment. Linear-response core excitations with a hybrid functional and a small basis set are not expected to give absolute edge positions, and this calculation does not relax the orbitals around the core hole. The repository's examples/XAS folder also contains the ΔCHP-MRSF approach, which includes core-hole relaxation through guess(swapmo=...), scf(rstctmo=true), and ixcore.
• The ordering of the edges is element-specific: the 240 eV gap between the C and O lines is what makes XAS a probe of individual atoms.

Try next

• Compute the nitrogen K-edge of HCN by selecting the N 1s orbital, which is orbital 1 in HCN.
• Use a basis set with core polarization functions, such as cc-pcvdz, and compare the edge positions.

See also: MRSF-TDDFT, tdhf keywords.

Scientific references

Linear-response TDHF and TDDFT; MRSF-TDDFT.