Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

Figures & data

Table 1. Effect of quadrature grid relative to the (50,194) grid for TDDFT calculations for the lowest 30 states of benzene, diamide, histidine and Cr(CO)₆. The 6-311+G* basis set is used, and the percentage error in the oscillator strength of the most intense transition is shown.

	(40,146)	(30,110)	(20,86)	(10,18)	(10,18)+τ = 10^−5
PBE functional
Mean absolute error (eV)	<0.01	<0.01	<0.01	0.02	<0.01
Max. error (eV)	<0.01	<0.01	0.01	0.25	0.01
Max. error in f (%)	<1	<1	<1	3	<1
Average time saving (%)	24	37	45	52	52
CAM-B3LYP functional
Mean absolute error (eV)	<0.01	<0.01	<0.01	0.01	<0.01
Max. error (eV)	<0.01	<0.01	0.01	0.25	<0.01
Max. error in f (%)	<1	<1	<1	3	<1
Average time saving (%)	13	22	28	33	46

Table 2. Effect of truncation of the virtual subspace with the CAM-B3LYP exchange-correlation functional and 6-311+G* basis set for the lowest 30 states. The percentage error in the oscillator strength of the most intense transition is shown.

	10%	20%	30%	40%	50%	60%	70%	80%
Benzene
Mean absolute error (eV)	0.000	0.000	0.001	0.003	0.007	0.018	0.039	0.107
Max. error (eV)	0.000	0.001	0.006	0.026	0.077	0.180	0.290	0.461
Error in f (%)	<1	<1	<1	<1	<1	2.3	5.6	7.6
NAGNMA
Mean absolute error (eV)	0.000	0.000	0.001	0.002	0.004	0.009	0.016	0.043
Max. error (eV)	0.000	0.001	0.003	0.007	0.019	0.037	0.065	0.140
Error in f (%)	<1	<1	<1	1.8	6.9	16.7	63.8	76.4
Histidine
Mean absolute error (eV)	0.000	0.000	0.001	0.003	0.006	0.011	0.020	0.044
Max. Error (eV)	0.001	0.001	0.007	0.010	0.019	0.027	0.051	0.088
Error in f (%)	<1	<1	1.7	6.6	14.2	16.7	63.8	76.4
Cr(CO)6
Mean absolute error (eV)	0.000	0.000	0.001	0.002	0.005	0.008	0.019	0.023
Max. Error (eV)	0.001	0.001	0.007	0.010	0.019	0.027	0.051	0.088
Error in f (%)	<1	<1	<1	<1	1.9	5.2	7.9	13.5

Figure 1. Variation in the computed PBE/6-31+G* spectra for (a) coronene, (b) β-carotene and (c) zinc porphyrin with the size of the virtual orbital subspace. X% indicates that excitations to the highest energy X% of virtual orbitals are excluded from the excitation space in the TDDFT calculation.

Figure 2. Molecular structures of the large molecules studied.

Figure 3. Computed spectra for (a) C₆₀, (b) P3B2 and (c) ramoplanin. For (a) and (c) experimental data from references [33,34] is also shown.

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