The CC2 and CC2-b models and the related linear response programs for the calculation of excitation energies have been implemented in the MOLPRO package (development version) [64]. The DF approximation was employed throughout in the correlated calculations. In order to have an ef-ficient program for generating ‘excited state’ domains (cf. section 2.2.2) and starting vectors for the Davidson diagonalization also a DF–CIS program was implemented. The algorithm for the CC2 ground state amplitudes has been outlined already in section 2.2.1. Particularly, the bare 3-index 2-external ERIs used in eq. (2.14) are precomputed and stored on disk. Af-ter the ground-state calculation has converged, these integrals are dressed for use in the formation of the right-hand product of the Jacobian with
an approximate vector, eqs. (2.20,2.22). The set of 3-index 2-external ERIs is the largest data object kept on disk, the disk space requirements thus scale as∝ n2AOnFIT =O(N3) with molecular size. In order to minimize I/O the computation of the right product is organized such that precomputed 3-index objects like 3-index ERIs and fitting coefficients (and in particular the 3-index 2-external ERIs) are just touched once in each iteration. Fur-thermore, in order to achieve a compromise between economical use of memory and computational efficiency, just one instance of a vector of the size of a trial vector is kept in memory. Since the individual contraction steps of integrals with amplitudes in the formation of the Jacobian times trial vector product are carried out block-wise, this vector determines the memory requirements for the whole calculation. Formally, its size scales quadratically with molecular size (since the singles are un-truncated), yet the doubles part (in spite of the fact that its size is scaling linearly with molecular size by construction) is still much larger and dominates the over-all size of the trial vector for over-all systems investigated so far. The sizes of the trial vectors for some individual excitation energy calculations on extended molecular systems are compiled in Table 2.6. Evidently, they strongly de-pend on the character, i.e., the locality of the individual excitations (vide infra).
Basis cc-pVDZ cc-pVTZ aug-cc-pVDZ
Molecule np(tot)a nbAO ncp Ld nbAO ncp Ld nbAO ncp Ld
N-acetylglycine 276 147 270 43 338 270 93 247 270 71
Propanamide 120 105 120 38 248 120 85 178 120 64
”Dipeptide” 351 176 321 44 410 321 98 297 321 75
”β-dipeptide” 435 200 370 44 468 373 100
”Tripeptide” 703 247 528 46 572 528 101
trans-urocanic acid 351 170 323 50 384 323 112 284 325 95
Guanine 406 179 400 56 400 400 122 298 400 102
1-phenylpyrrole 378 199 363 58 456 363 126 334 366 112
DMABN 406 204 372 52 470 373 118
p-cresol 231 152 222 48 352 225 107
HPA 528 218 434 48 500 440 107
Tyrosine 630 237 558 49 544 564 108
Phenylalanine 528 223 497 49 514 497 107
DA1 3741 593 1942 64
DA2 6105 785 2516 61
Triad 17205 1314 4644 64
a) Total number of LMO pairs b) Total number of AOs
c) Number of pairs treated in the LCC2 ‘ground state’ calculation d) Average pair domain size in the CC2 ‘ground state’ calculation
Table 2.1: Total number of LMO pairs and number of AOs for the individual test molecules. The number of pairs included in the local CC2 calculation and the average pair domain size (which both determine the number of non-zero ground state doubles amplitudes) are also given.
In the following we present test calculations which demonstrate accu-racy and efficiency of the new local CC2 method for excitation energies.
As AO basis sets the cc-pVDZ, cc-pVTZ, and aug-cc-pVDZ sets [65, 66]
together with their related fitting basis sets optimized for DF-MP2 [67, 68]
were employed. In all calculations the LMOs were obtained by using Pipek-Mezey localization [55]. As discussed in section 2.2.2, the LMOs are discriminated into a class of important and unimportant orbitals by analyzing an initial CIS wave function of the state of interest. Suitable pair lists for that particular state can then be specified by taking advan-tage of this classification. For example, all pairs not including at least one important LMO may be dropped in case of an inter-domain distance ex-ceeding a certain threshold of RID=10 bohr. Denoting important orbitals byi,j, unimportant ones bym,nsuch a list is specified in the following as
∀(i j),∀(im),(mn)≤10. An alternative type of a pair list can be constructed by keeping all important LMO pairs but dropping all other pairs with an inter-domain distance bigger than the thresholdRID, regardless, if one im-portant LMO is involved or not. For such a pair list we use the specification
∀(i j),(im) ≤ RID,(mn) ≤ RID. In individual test calculations the threshold RID was set to 3, 5, and 10 bohrs, respectively. The criterion for selecting important orbitals was set to κe = 0.995 for most calculations, which ap-pears to be a safe choice. The pair list for the ground-state amplitudes was restricted for all calculations to LMO pairs with an inter-orbital distance RIO not exceeding 10 bohr. Test calculations have shown that longer pair lists for ground-state amplitudes (i.e. forRIO >10 bohr) have no significant impact on the excitation energies. The Boughton-Pulay criterion for do-main specification was set to 0.98 (0.985) for formation of both the ground-and excited-state amplitude pair domains for the cc-pVDZ (aug-cc-pVDZ, cc-pVTZ) basis sets.
Key quantities of the local calculation relevant to achieve low scaling in the computational cost, such as the length of the pair list, the average pair domain sizes, etc., are compiled in Tables 2.1-2.3 for the unperturbed
‘ground state’ amplitudes and their first-order response, i.e., the ‘excited state’ amplitudes, respectively. These quantities are shown for different pa-rameters used for the selection of important orbitals and for several types of pair lists, which have been tested in the present work. As can be seen from these tables, most computational savings for the smaller molecules are due to the domain restrictions of the double excitations. The average size of a pair domain (in the cc-pVDZ basis) varies only between 38 and 64 for the ground state and between 52 and 239 for the individual excited states (pairlist (2) from Table 2.2 is used for this comparison), while the number of basis functions increases by a factor of 13 between the smallest
Basis cc-pVDZ cc-pVTZ
Table 2.2: Number of pairsn∗pand average sizes of ‘excited state’ domainsL∗(related to the ‘excited state’ doubles amplitudes) as used in the local CC2 linear response
calculations with the cc-pVDZ and cc-pVTZ basis sets. The ratiorDof the overall number of doubles amplitudes treated in the local calculation relative to the total number of doubles amplitudes treated in the corresponding canonical calculation is also included. These quantities are given for all test molecules and states considered, for several specifications of the ‘excited state’ pair list.
1) pair list specified as∀(ij),(im)≤10,(mn)≤10, cc-pVDZ basis 2) pair list specified as∀(ij),(im)≤5,(mn)≤5, cc-pVDZ basis 3) pair list specified as∀(ij),(im)≤3,(mn)≤3, cc-pVDZ basis
100
Figure 2.1: The ratio of the number of doubles amplitudes included in the local CC2 calculations relative to the total number of doubles amplitudes for the case 2 of Table 2.2.
and the largest molecule included in the test set. The savings due to the smaller number of pairs of LMOs are less pronounced (e.g. about half of all pairs is used in LCC2 for the DA1 molecule in the ground state), but they become substantial for the largest molecule considered here (only about a quarter of all pairs enters the local CC2 treatment). A similar pattern can be seen for the ‘excited state’ amplitudes with the length of the pair lists depending significantly on the local (or non-local) character of the excited state involved. In Table 2.2 the percentage of local vs. canonical dou-bles amplitudes is also reported, which shows the combined savings from restricting excitations to domains and pair lists. The percentage of local amplitudes is also depicted in Fig. 2.1. An examination of Table 2.2 and Fig. 2.1 clearly shows that the expected savings relative to the canonical calculation grow with molecular size and for the largest molecule only a few percent (for local excitations merely a few tenths of a percent) of all double amplitudes are needed in the local calculation. Interestingly, on go-ing from the cc-pVDZ to the cc-pVTZ or aug-cc-pVDZ basis the percentage appears to decrease, even though the criterion for the pair list specification is identical and the Boughton-Pulay criterion is even somewhat tighter for the bigger basis. Apparently, if more functions are available per center, less centers per domain are required in a local calculation to describe the excited-state amplitudes.
Tables 2.4 and 2.5 collect the excitation energies of the lowest few states of the same set of test molecules as investigated in Ref. 44. Deviations of the LCC2 excitation energies from the corresponding canonical reference values (i.e. ∆ω = ωloc −ωcan) are given for different specifications of the pair list for the excited-state amplitudes. The differences between canon-ical EOM–CCSD (taken from Ref. 44) and CC2 methods are also given.
Evidently, the errors in the excitation energies due to the local
approxi-mation do not exceed 0.06 eV for the cc-pVDZ basis, with the exception of one state. For that particular state (the charge transfer excited state of 1-phenylpyrrole) also the deviation between canonical CCSD and CC2 is un-typically large (0.472 eV) and the local CC2 value lies closer to CCSD than canonical CC2 does. Interestingly, the deviation of local CCSD from canonical CCSD in Ref. 44 was smaller (0.057 eV) than here, even though the domain criteria were identical and the pair lists much smaller than in the present work.
Molecule state n∗p L∗ rD nunip Luni runiD N-acetylglycine S1 249 126 35% 274 122 36%
S2 226 112 25% 270 112 29%
S3 234 131 37% 274 123 39%
Propanamide S1 118 103 45% 120 103 45%
S2 114 89 34% 120 88 35%
”Dipeptide” S1 274 129 22% 325 124 24%
S2 292 156 33% 330 145 32%
S3 253 117 17% 324 114 21%
trans-urocanic acid S1 348 173 53% 348 173 53%
S2 327 193 61% 333 186 58%
1-phenylpyrrole S1 320 180 37% 366 172 39%
S2 351 218 55% 366 215 56%
S3 329 187 41% 366 179 43%
S4 347 210 51% 366 206 52%
S5 327 179 37% 366 171 39%
Table 2.3: Number of pairsn∗pand average sizes of ‘excited state’ domainsL∗(related to the ‘excited state’ doubles amplitudes) in the aug-cc-pVDZ basis, as used in the local CC2 linear response calculations. The ratiorDof the overall number of doubles amplitudes treated in the local calculation relative to the total number of doubles amplitudes treated in the corresponding canonical calculation is also included. The pair list was specified as∀(ij),(im)≤5,(mn)≤5. Corresponding values for unified pair lists and domains (nunip ,Luni) are also given.
For the lower-lying valence states the errors are smaller than 0.04 eV.
This conclusion applies also to the shortest pair list considered in Table 2.4, i.e., the∀(i j),(im)≤ 3,(mn) ≤ 3 pair list. The errors of some higher states calculated in the cc-pVTZ basis are somewhat larger, but they do not exceed 0.1 eV with the exception of the same charge transfer state mentioned above and a Rydberg state oftrans-urocanic acid, which is shifted to lower energy when the cc-pVTZ basis is used (The S5 ←S0excitation in the cc-pVTZ basis corresponds to the S4 ← S0 excitation in the cc-pVDZ basis). Generally,
the larger discrepancies for some excitations to higher states are most probably due to the fact that states which have (partly) diffuse character are poorly described by AO basis sets without Gaussians having very low exponents. As a consequence, many AOs are involved to mimic this diffuse behavior and truncations to orbital domains will lead to bigger deviations from the canonical result than for ordinary valence states. If this is true then increasing the number of diffuse Gaussians should make the local vs.
canonical error smaller. To this end we repeated the calculations in the aug-cc-pVDZ basis for some molecules, including the troublesome charge transfer state of 1-phenylpyrrole. As is evident from Table 2.5, the error due to the local approximation for this state vanishes almost entirely in the aug-cc-pVDZ basis. Since we are interested in determininga priori, which states may cause similar problems, we checked the CIS energies corresponding to this state and the other states of 1-phenylpyrrole in both the cc-pVDZ and aug-cc-pVDZ basis. It turns out that the CIS energy decreases by 1.66 eV for the charge transfer excitation on going from cc-pVDZ to the diffuse basis, while for other excitations in the table the corresponding differences in the CIS energies are smaller than 0.5 eV. We can therefore propose a quick check of “suspicious” states, based on a DF–CIS calculation: if the CIS energies of a given state differ in diffuse and non-diffuse basis sets by more than 1 eV, the smaller basis is completely inappropriate for this state and therefore large errors in the local approximations are expected.
To summarize, Tables 2.4 and 2.5 clearly show that the excitation ener-gies involving the energetically lower-lying excited states are all well re-produced in the cc-pVTZ and aug-cc-pVDZ basis by the local CC2 method, similarly to the results obtained in the smaller cc-pVDZ basis. Consider-ing an expected accuracy of about 0.3 eV for the CC2 method itself, the discrepancies observed can be considered as fair. One should also keep in mind that effects like the basis set superposition error, which are vir-tually absent in local methods [69], do play a role here. Furthermore, in contrast to the local EOM–CCSD method reported in Ref. 44 it appears that the accuracy of the local CC2 excitation energies do not depend so strongly on the quality of the CIS wave function. For example, the S3 ←S0 and S4 ← S0 excitation energies of trans-urocanic acid are obtained with a local error of about 0.03 eV (≈0.06 eV for the shortest pair list), while errors bigger than 0.1 eV were observed for local EOM–CCSD in Ref. 44 and attributed to a poor description of these states by the related CIS wave functions. The reason for the more robust behavior of LCC2 can be most probably ascribed to the fact that (i) single excitations are treated without any local approximation, and (ii) longer pair lists are affordable in LCC2.
We also performed calculations on the set of test molecules employing
Basis cc-pVDZ cc-pVTZ Molecule state character ωaCCSD ωbCC2 ∆ωccan ∆ωd1 ∆ωd2 ∆ωd3 ∆ωd4 ∆ωd5 ∆ωd6 ∆ωd7 ωbCC2 ∆ωd3
N-acetylglycine S1 n→π∗ 5.810 5.862 0.052 -0.015 -0.015 -0.013 -0.001 0.017 0.012 0.002 5.777 -0.006
S2 n→π∗ 6.162 6.252 0.090 0.010 0.010 0.013 0.023 0.032 0.020 0.024 6.148 0.032
S3 π→π∗ 7.584 7.373 -0.211 0.004 0.004 0.005 0.005 0.046 0.034 -0.001 7.195 0.076
Propanamide S1 n→π∗ 5.861 5.926 0.065 0.001 0.001 0.001 0.003 0.031 0.028 0.018 5.804 0.025
S4 π→π∗ 7.886 7.962 0.076 0.022 0.022 0.022 0.022 0.054 0.045 0.031 7.638 0.037
”Dipeptide” S1 n→π∗ 5.828 5.871 0.043 -0.021 -0.021 -0.019 -0.010 0.012 0.008 -0.004 5.790 -0.011
S2 n→π∗ 6.067 6.106 0.039 -0.005 -0.005 -0.000 0.010 0.027 0.014 0.012 6.009 -0.000
”β-dipeptide” S1 n→π∗ 4.881 4.861 -0.020 -0.035 -0.035 -0.030 -0.023 0.019 0.017 -0.015 4.783 -0.013
S2 n→π∗ 5.773 5.825 0.052 -0.016 -0.016 -0.012 -0.003 0.011 0.012 0.002 5.732 -0.003
S3 π→Rydb. 7.039 6.908 -0.131 0.032 0.032 0.033 0.043 0.077 0.040 0.035 6.501 0.079
”Tripeptide” S1 n→π∗ 5.824 5.868 0.044 -0.022 -0.021 -0.019 -0.011 0.012 0.008 -0.004 5.786 -0.011
S2 n→π∗ 6.066 6.091 0.025 0.003 0.004 0.010 0.021 0.041 0.028 0.022 5.999 0.014
trans-urocanic S1 n→π∗ 5.187 4.987 -0.200 -0.021 -0.021 0.010 0.021 0.038 0.014 0.039 4.906 0.023
acid S2 π→π∗ 5.384 5.207 -0.177 -0.024 -0.024 -0.024 -0.023 0.036 0.014 -0.026 5.022 -0.004
S3 π→π∗ 6.415 6.269 -0.146 0.031 0.031 0.033 0.059 0.066 0.028 0.031 6.093 0.040
S4 π→π∗ 6.708 6.877 0.169 0.027 0.027 0.027 0.028 0.063 0.034 0.026 6.562 0.115
S5 π→Rydb. 7.062 7.054 -0.008 -0.062 -0.062 -0.061 -0.060 0.001 0.000 -0.062 6.636 0.045
Guanine S1 π→π∗ 5.404 5.316 -0.088 0.002 0.002 0.002 0.002 0.058 0.020 0.005 5.155 0.027
S2 n→π∗ 5.712 5.660 -0.052 -0.023 -0.023 -0.022 -0.013 0.015 0.012 0.004 5.537 -0.008
S3 π→π∗ 6.052 5.820 -0.232 -0.002 -0.002 -0.002 -0.001 0.042 0.020 -0.006 5.599 0.021
1-phenylpyrrole S1 π→π∗ 5.060 5.072 0.012 0.007 0.011 0.012 0.019 0.053 0.017 0.010 4.963 0.025
S2 π→π∗ 5.736 5.555 -0.181 -0.002 -0.002 -0.002 -0.001 0.049 0.019 -0.003 5.422 0.021
S3 π→π∗ 6.117 5.771 -0.346 0.014 0.014 0.014 0.015 0.055 0.030 0.011 5.609 0.033
S4 CT (py→ph) 6.563 6.091 -0.472 0.135 0.135 0.135 0.140 0.166 0.123 0.132 5.879 0.186
DMABN S1 π→π∗ 4.650 4.525 -0.125 0.038 0.038 0.038 0.050 0.091 0.026 0.041 4.405 0.057
S2 π→π∗ 5.130 4.891 -0.239 -0.064 -0.064 -0.064 -0.064 0.023 0.012 -0.059 4.780 -0.028
p-cresol S1 π→π∗ 4.979 4.981 0.002 0.011 0.011 0.011 0.013 0.061 0.020 0.013 4.867 0.025
HPA S1 π→π∗ 4.987 4.984 -0.003 0.008 0.009 0.013 0.023 0.064 0.025 0.010 4.875 0.030
S2 n→π∗ 6.052 6.148 0.096 0.005 0.009 0.011 0.014 0.034 0.028 0.019 6.038 0.024
S3 π→π∗ 6.436 6.285 -0.151 -0.014 -0.013 -0.024 -0.000 0.047 0.024 -0.027 6.132 0.011
Tyrosine S1 π→π∗ 4.997 4.995 -0.002 0.011 0.011 0.022 0.038 0.064 0.029 0.013 4.891 0.043
S2 n→π∗ 5.757 5.824 0.067 -0.002 -0.004 -0.001 0.009 0.041 0.033 0.009 5.739 0.022
S3 π→π∗ 6.370 6.205 -0.165 -0.019 -0.019 -0.003 0.016 0.054 0.030 -0.014 6.054 0.013
Phenylalanine S1 π→π∗ 5.189 5.260 0.071 0.021 0.021 0.029 0.046 0.064 0.012 0.022 5.165 0.045
S2 n→π∗ 5.758 5.827 0.069 -0.002 -0.000 0.002 0.013 0.042 0.033 0.013 5.744 0.017
S3 π→π∗ 6.655 6.574 -0.081 -0.011 -0.011 -0.005 0.019 0.046 0.032 -0.011 6.391 0.020
a) canonical EOM–CCSD excitation energies from Ref. 44 (when available) b) canonical CC2 excitation energies calculated withTURBOMOLE v.5.7, Ref. 27,29 c) deviation canonical CC2 vs. canonical EOM–CCSD
d) deviation local CC2 vs. canonical CC2
Table 2.4: Excitation energies for various test molecules. Values (all in eV) are given for canonical EOM–CCSD, CC2, local CC2 and local CC2-b. The Boughton-Pulay criterion for domain specification was set to 0.98 and 0.985, respectively, for the calculations employing the cc-pVDZ and the cc-pVTZ basis. The pair list for the ground-state amplitudes was truncated for inter-orbital distances beyond 10 bohr. For the
excited-state amplitudes the pair list was truncated in various ways, as specified below.
The criterion to determine important orbitals was set toκe=0.995 (cf. text). The 1s orbitals for the C, N, and O atoms were frozen in all correlated calculations.
1) pair list specified as∀(ij),∀(im),(mn)≤10 2) pair list specified as∀(ij),(im)≤10,(mn)≤10 3) pair list specified as∀(ij),(im)≤5,(mn)≤5 4) pair list specified as∀(ij),(im)≤3,(mn)≤3
5) pair list specified as∀(ij),(im)≤5,(mn)≤5, unified domains/pair list
6) pair list specified as∀(ij),(im)≤5,(mn)≤5, unified domains/pair list, extended domains (3 bohr)
7) pair list specified as∀(ij),(im)≤5,(mn)≤5, CC2-b
a lower criterion of κe = 0.99 for the selection of important LMOs (not included in Table 2.4). This criterion leads in some cases to substantially bigger local errors, e.g. –0.117 rather than –0.033 eV for the S3 ← S0 excitation of β-dipeptide, and must be regarded as less safe. Finally, a further dataset, generated by using the CC2-b rather than the CC2 method, is included in Table 2.4. As expected, the deviations between CC2-b and CC2 turn out to be very small. Based on the presented data we propose as a safe domain/pair list specification the pair list defined as∀(i j),(im)≤ 5,(mn) ≤ 5 together with the criterion for the important-orbital selection set toκe =0.995.
Molecule state character ωaCCSD ωbCC2 ∆ωc ∆ωdL ∆ωdeL N-acetylglycine S1 n→π∗ 5.767 5.732 -0.035 -0.023 0.011
S2 n→π∗ 6.073 6.089 0.016 0.000 0.026 trans-urocanic acid S1 n→π∗ 5.134 4.863 -0.271 -0.029 0.009 S2 π→π∗ 5.108 4.931 -0.177 -0.019 0.021
S3 π→Rydb. 5.285 0.058 0.069
S4 π→Rydb. 6.093 6.009 -0.084 0.025 0.043
Guanine S1 π→Rydb. 4.946 4.743 -0.203 0.076 0.097
S2 π→π∗ 5.138 5.022 -0.116 -0.020 0.021
S3 π→Rydb. 5.137 0.073 0.091
S4 π→π∗ 5.409 0.009 0.044
S5 n→π∗ 5.461 -0.023 0.016
S6 π→Rydb. 5.639 5.669 0.030 0.080 0.106 1-phenylpyrrole S1 π→π∗ 4.938 4.921 -0.017 0.023 0.052
S2 π→π∗ 5.488 5.309 0.011 0.054
S3 π→Rydb. 5.434 0.008 0.032
S4 CT (py→ph) 5.489 -0.004 0.034
S5 π→Rydb. 5.721 5.493 -0.228 0.052 0.074 a) canonical EOM–CCSD excitation energies from Ref. 44 (when available)
b) canonical CC2 excitation energies calculated with TURBOMOLE v.5.7, Ref. 27, 29
c) deviation canonical CC2 vs. canonical EOM–CCSD d) deviation local CC2 vs. canonical CC2
e) unified pair lists and domains
Table 2.5: Excitation energies for various test molecules. Values (all in eV) are given for canonical EOM–CCSD, CC2, local CC2. The aug-cc-pVDZ basis was used. The pair list was specified as∀(ij),(im)≤5,(mn)≤5 and results for unified pair lists and domains are also given. The Boughton-Pulay criterion for domain construction and the criterionκeto determine important orbitals were set to 0.985 and 0.9975, respectively.
For these particular settings additional calculations employing unified pair lists and domains were performed. For that purpose, the pair lists and domains of unperturbed (ground state) and perturbed (excited state) amplitudes are mergeda posteriorito a common pair list and common
do-mains. In the process of this unification the configuration space for the ground state becomes significantly larger, while the configuration space for the excited state is hardly affected, which leads to some imbalance in the descriptions of ground and excited state, respectively, such that the resulting excitation energies for unified pair lists and domains are always blue-shifted relative to the canonical or the ordinary local value. This im-balance is most notable in the cc-pVDZ basis and decreases on going to a bigger basis set or on extending the domains. For calculations using the aug-cc-pVDZ basis or the cc-pVDZ basis with extended domains (do-mains extended by centers≤3 bohrs away from the core Boughton-Pulay domains are sufficiently large) the deviations between unified domain/pair list and ordinary local calculations become quite small (typically something like 0.03 eV). Based on these observations we conclude (i) that the main difference between ordinary local excitation energies and excitation ener-gies computed with unified pair list and domains is primarily due to the imbalance in the local approximation for ground- and the excited states, and (ii) that the error introduced by employing non-identical spaces for zeroth- and first-order amplitudes therefore is small. Although the diag-onalization of the LCC2 Jacobian in a calculation with unified pair lists and domains is not dramatically more expensive than in the ordinary local calculation, the ground state calculation is more expensive and needs to be re-computed for each excited state. Therefore, ordinary local calculations with different domains for ground- and excited state are more convenient and appear to be preferable for most cases.
In order to study the accuracy of the new local CC2 method in de-scribing charge transfer excited states we performed calculations on the two phenothiazine-isoalloxazine (flavin) dyads depicted in Fig. 2.2. These dyads are of interest in the context of modeling light processes of blue-light photo-receptors [70]. DA2 corresponds to compound 5 of Ref. 70.
DA1 is a simplified version of DA2 insofar that the side chain on the phe-nothiazine and the methyl group on the flavin ring system are omitted, such that a canonical reference calculation still is possible within an ac-ceptable amount of time (the canonical calculation takes about 60–70 CPU minutes per state and per Davidson iteration). DA2 comprises 220 active electrons and 77 atoms, DA1 – 172 active electrons and 53 atoms. These dyads feature a rather long-range charge transfer S3 ←S0excitation where phenothiazine acts as an electron donor and isoalloxazine as an acceptor (the role of the intermediate phenyl ring is that of a spacer). TD–DFT fails spectacularly here with deviations from the CC2 excitation energy as large as 2.55 (BP86) and 1.69 eV (B3-LYP) for the DA1 case (all TD–DFT calculations were performed withTURBOMOLE v.5.7[71] by using the SVP