x-ray absorption spectroscopy can be calculated using TDDFT by restricting the excitation space to include excitations from a set of core orbitals. This is achieved by setting TRNSS = TRUE in the $rem section, which triggers the use of TDDFT with a truncated excitation space as described in Section 7.3.2. The occupied core orbitals that the user desires to be active in such a calculation should be listed individually in the $alist input section, and the number of such orbitals must be specified using N_SOL in the $rem section. This invokes the CVS approximation, which for TDDFT amounts to freezing all of the occupied orbitals except for the ones that are listed in $alist, while using the full virtual space. Such calculations are not suited to describe the extended x-ray absorption fine structure (EXAFS) region, which corresponds to the scattering of the ionized electron by the neighboring atoms.
Standard exchange-correlation functionals (including hybrids) tend to severely underestimate
core excitation energies,
Phys. Chem. Chem. Phys.
(2009), 11, pp. 10350. although chemical shifts (from one compound to the next) may still be valid. 348 J. Chem. Theory Comput.
(2021), 17, pp. 1618. Q-Chem has short-range corrected (SRC) functionals available that are designed to predict K-edge core excitation energies accurately. 106 Phys. Chem. Chem. Phys.
(2009), 11, pp. 10350. These functionals are a modification of the more familiar long-range corrected functionals (discussed in Section 5.6). However, in SRC-DFT the short-range component of the Coulomb operator is predominantly Hartree-Fock exchange, while the mid to long-range component is primarily treated with standard DFT exchange. Uses of SRC-TDDFT in conjunction with the CVS approximation is illustrated in Example 7.13.2. See Section 7.3.3 for basic TDDFT job control.
$comment Carbon K-edge excitations for acetone. The only active occupied orbitals are three C(1s). The SRC1-R1 is parameterized for "first row" (C, N, O, ...) $end $molecule 0 1 C -3.0219081 1.0061477 0.0000001 O -2.9337180 2.2246186 0.0000001 C -1.7817549 0.1662163 -0.0000003 C -4.3700966 0.3535647 0.0000004 H -0.8735407 0.8061311 -0.0000005 H -1.7663727 -0.4765415 -0.9049102 H -1.7663723 -0.4765416 0.9049094 H -5.1766925 1.1175964 0.0000006 H -4.4778785 -0.2802782 0.9049091 H -4.4778790 -0.2802781 -0.9049084 $end $rem exchange src1-r1 ! r1 = "first row" basis 6-31++G* cis_n_roots 25 cis_triplets false trnss true trtype 3 n_sol 3 ! no. of active orbs $end $alist 2 3 4 $end
Relativistic effects become increasingly significant for calculation of x-ray absorption spectra at the K-edge of heavier elements. The REL_SHIFT keyword introduces a correction to the calculated excitation energies to account for these effects. This is illustrated in Example 7.13.2 below. (Although scalar shift may be appropriate for K-edge excitations, but L-edge and M-edge excitations will be complicated by core-hole spin orbit coupling.)
$molecule 0 1 H 1.196206 0.000000 -0.469131 P 0.000000 0.000000 0.303157 H -0.598103 -1.035945 -0.469131 H -0.598103 1.035945 -0.469131 $end $rem EXCHANGE SRC2-R2 ! R2 = "second row" (Al, S, P, ...) BASIS 6-311(2+,2+)G** CIS_N_ROOTS 6 CIS_TRIPLETS false TRNSS true TRTYPE 3 N_SOL 1 REL_SHIFT 15 $end $alist 1 $end
Despite the relatively low computational cost of TDDFT, it can become challenging to calculate
x-ray absorption spectra for large systems. The high density of core-excited states makes
simulating spectra more computationally expensive than comparable calculations of the
UV/vis spectra. This is particularly the case when excitations from many core-orbitals are
required, which is often the situation when studying the carbon K-edge of organic molecules.
There are two aspects to the computational cost, firstly the CPU time required and secondly
the memory required. An implementation of TDDFT called “fTDDFTs” combines aggressive integral
screening and a coarse DFT quadrature grid, which is especially
efficient for the calculation of x-ray absorption spectra.
J. Chem. Theory Comput.
(2016), 12, pp. 5018. , 110 Acc. Chem. Res.
(2020), 53, pp. 1306. This approach may be fine-tuned using the $rem variables FAST_XAS, XAS_SCREEN_LEVEL and XAS_EDGE. The memory required for these calculations can be reduced further through the TDDFT_NVIRT keyword that reduces the number of virtual orbitals included in the TDDFT calculation. Job control variables for fTDDFTs are listed below and are illustrated in Example 7.13.2.
Note: Currently fTDDFTs works only for restricted CIS/TDA calculations and is not parallelized. (Multiple threads can be used for the initial SCF calculation but the subsequent CIS/TDA calculation is performed in serial.)
$molecule 0 1 C 0.000000 0.000000 -0.648906 O 0.000000 0.000000 0.486357 $end $rem EXCHANGE SRC1-R1 BASIS 6-311G* CIS_N_ROOTS 6 CIS_TRIPLETS false TRNSS true TRTYPE 3 N_SOL 1 FAST_XAS true XAS_EDGE 6 XAS_SCREEN_LEVEL 1 $end $alist 1 $end
It is also possible to compute x-ray emission spectroscopy using TDDFT. This is achieved
by using a reference determinant with a core-hole.
J. Chem. Theory Comput.
(2014), 10, pp. 4557. , 346 J. Comput. Chem.
(2020), 41, pp. 1081. The calculated excitation energies can be quite sensitive to the choice of basis set, and for the K-edge of heavier elements it can be necessary to use large or specially adapted basis sets to provide a good description of the core region. 345 Theor. Chem. Acc.
(2018), 137, pp. 6. , 447 Chem. Phys. Lett.
(2018), 699, pp. 279.
$molecule 0 1 O 0.0000 0.0000 0.1168 H 0.0000 0.7629 -0.4672 H 0.0000 -0.7629 -0.4672 $end $rem method cam-b3lyp basis cc-pvdz $end @@@ $molecule +1 2 O 0.0000 0.0000 0.1168 H 0.0000 0.7629 -0.4672 H 0.0000 -0.7629 -0.4672 $end $rem method cam-b3lyp basis cc-pvdz scf_guess read mom_start 1 cis_n_roots 5 cis_triplets false $end $occupied 1:5 2:5 $end