What is the Key for Accurate Absorption and Emission Calculations

Jan 24, 2018 - First, we found that the errors induced by the selection of a specific method for computing the transition energy are rather independen...
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What is the Key for Accurate Absorption and Emission Calculations, Energy or Geometry? Denis Jacquemin* Laboratoire CEISAM-UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssiniére, BP 92208, 44322 Nantes Cedex 3, France S Supporting Information *

ABSTRACT: Using a hierarchy of wave function methods, namely ADC(2), CC2, CCSD, CCSDR(3), and CC3, we investigate the absorption and emission energies in a set of 24 organic compounds. For all molecules, reference values are determined at the CC3//CC3 or CCSDR(3)//CCSDR(3) levels and the energetic and geometric effects are decomposed considering all possible methodological combinations between the five considered methods. For absorption, it is found that the errors are mainly energy-driven for ADC(2), CC2, and CCSDR(3), but not for CCSD. There is also an error compensation between the errors made on the geometries and transition energies for the two former approaches. For emission, the total errors are significantly larger than for absorption due to the significant increase of the structural component of the error. Therefore, the selection of a very refined method to compute the fluorescence energy will not systematically provide high accuracy if the excited-state geometry is not also optimized at a suitable level of theory. This is further demonstrated using results obtained from TD-DFT and hybrid TD-DFT/wave function protocols. We also found that, compared to full CC3, only CCSDR(3) is able to deliver errors below the 0.1 eV threshold, a statement holding for both absorption (mean absolute error of 0.033 eV) and emission (mean absolute error of 0.066 eV). CCSDT-3,19 etc. Nevertheless, this hierarchical strategy again comes with a steep increase of computational requirements, especially when contributions from triple excitations are included, as in the latter methods. To mitigate the cost of ES calculations, a popular approach is to select a less-demanding method to optimize both the GS and ES geometries, and next to determine the transition energies on these geometries using a more advanced theoretical model. There are countless examples of this approach in the literature, and we only detail a short selection of these works here. In their famous papers defining a set of reliable vertical absorption energies, Thiel and co-workers performed CASPT2/aug-ccpVTZ and CCn/aug-cc-pVTZ calculations but they systematically selected second-order Møller−Plesset (MP2)/6-31G(d) GS geometries.20,21 In their assessment of single-reference methods for ES energies, Goerigk and Grimme first transformed the experimental 0−0 energies into vertical values using TD-PBE/TZVP structural and vibrational data, before computing transition energies with a large panel of methods, including the CC2/def 2-TZVPP approach.22,23 For the calculation of the 0−0 energies of emissive fluoroborate dyes, we proposed to apply TD-DFT combined to the compact 631G(d) atomic basis set to determine the GS and ES structures as well as zero-point corrections, but to use much more refined methods to compute the adiabatic energies.24,25 While such “composite” protocols have been successful in several cases, they nevertheless come with an often unchecked hypothesis: the geometries are viewed as less sensitive to the selected level

1. INTRODUCTION Over the years, many theoretical methods able to treat excited states (ES) have been developed and extended, and it clearly turned out that choosing an approach suited for describing ES is more difficult than choosing one for the ground state (GS). Today, the two most popular ab initio approaches are probably Time-Dependent Density Functional Theory (TD-DFT)1,2 and Complete Active Space Self-Consistent Field (CASSCF)3,4 that allow to respectively account for dynamic and static electron correlation effects at reasonable computational costs. These methods also advantageously allow the determination of the ES structures as analytical gradients are accessible for both models in a wide variety of codes.5−8 However, if the obtained results are not sufficiently accurate, the paths for improvement are either ill-defined and/or costly. For TD-DFT, one can certainly cite, among many possible strategies, the use of the so-called double-hybrids,9,10 that provide more trustworthy results but come with significantly increased computational requirements compared to “conventional” TD-DFT relying on standard semilocal or hybrid functionals. For CASSCF, it is possible to include dynamical correlation effects using a second-order perturbative approach (CASPT2 method),11,12 which greatly improves the quality of the computed transition energies, but becomes unpractically demanding for medium and large systems. To obtain more systematically improvable results, one can turn toward the Algebraic Diagrammatic Construction (ADC)13 or Coupled-Cluster (CC) approaches. With these methods, one can increase the expansion order and follow the variations of the target property, for example, one can compare the transition energies obtained with CC2,14 CCSD,15,16 CCSDR(3),17 or (EOM-)CCSD(T),18 CC3,14 or EOM© XXXX American Chemical Society

Received: December 5, 2017 Published: January 24, 2018 A

DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Journal of Chemical Theory and Computation Scheme 1. Representation of the 24 Molecules Investigated Hereina

a

The considered ES is indicated as well, the lowest ES of the indicated symmetry being systematically considered. For the blue and black compounds, reference values have been obtained at the CC3 and CCSDR(3) levels of theory, respectively. The blue molecules constitute the 12compound set.

of theory than the transition energies. For vertical absorption, this looks a priori to be a very reasonable assumption because cost-effective theoretical methods such as DFT or MP2 generally provide GS structures that compare well with experiment. For emission (and consequently adiabatic properties), this hypothesis seems less factual: one does not have access to experimental ES structures in the vast majority of the cases; it is therefore hard to a priori understand why a large impact of the selected method on the computed ES energies would not reflect in similarly important effects for the ES geometries. In this framework, we underline that the suitability of “composite” protocols for 0−0 energies has been evaluated by several groups.26−28 In ref 26, Winter et al. determined gasphase 0−0 energies in 66 aromatic organic molecules, and found that the CC2 mean absolute deviation (MAD) with respect to experiment (0.07 eV) was only slightly degraded when neglecting corrections coming from single-point calculations with diffuse functions (0.08 eV) or when additionally using zero-point energies from TD-DFT (0.10 eV). In ref 27, it was shown that the MAD with respect to experiment obtained for 80 solvated dyes with TD-DFT (0.24 eV) could be significantly reduced by using ADC(2) (0.14 eV) or CC2 (0.13 eV) adiabatic energies determined on the TD-DFT structures. In ref 28, Oruganti, Fang, and Durbeej investigated several mixed TD-DFT/CC2 approaches, and concluded that full CC2 0−0 energies could be accurately and consistently estimated using TD-DFT structures and relaxation energies. While all these results seem reassuring, we highlight that only TD-DFT and second-order approaches have been tested and that

comparisons were made with experiments, so that it is uneasy to know if the deviations between calculated and measured 0−0 energies mainly originate in the inaccuracies of the transition energies or geometries. In addition, as comparisons are made directly with experiment, some error compensation mechanisms could be at play. Indeed, in a recent assessment of the quality of ADC(2), CC2, and CCSD for the calculation of ES geometries, we have showed that these three methods sometimes yield nontrifling errors compared to more advanced theories, such as CASPT2 or CC3.29 For instance, the ES carbonyl bond lengths were found to be overestimated by 0.042 and 0.029 Å with ADC(2) and CC2, respectively, when compared to theoretical best estimates.29 In the present contribution, we strive to resolve the article title’s question. To this end, we have selected a series of 24 molecules represented in Scheme 1 for which we determined the GS and ES structures as well as the transition energies with five single-reference wave function approaches of increasing complexity, namely ADC(2), CC2, CCSD, CCSDR(3), and CC3, considering all possible methodological combinations (transition/geometry) for each compound. We additionally evaluate the performances of protocols relying on TD-DFT in the last part of this work. Taking the “full” CC3 or CCSDR(3) results as references, one can rigorously quantify the errors originating from the energies and the structures for both absorption and emission. For Thiel’s set of compounds, CC3 transitions energies were shown by Watson and co-workers to be very close from EOM-CCSDT-3 values,30 and by Kannar and Szalay to be also very similar to (EOM-)CCSDT B

DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Journal of Chemical Theory and Computation results.31,32 CC3 can therefore safely be used to obtain accurate reference transition energies.

we found that the errors induced by the selection of a specific method for computing the transition energy are rather independent of the considered geometry. For instance, the CC2 transition energies of diacetylene are larger than their CC3 counterparts by +0.148, +0.150, +0.144, +0.147, and +0.147 eV when considering the MP2, CC2, CCSD, CC(3), and CC3 optimal GS structures, respectively (Table S8). Likewise, for thioketene, the CCSD absorption energies are larger than the CC3 values by +0.049 ± 0.001 eV for all five geometries (Table S24). The reverse also holds: the deviations related to the selection of a specific geometry are similar for all considered transition energy methods; for example, in cabonylfluoride, the selection of a CC2 GS structure results in an absorption red-shifted by −0.101, −0.092, −0.095, −0.094, and −0.094 eV compared to the CC3 structure, at the ADC(2), CC2, CCSD, CCSDR(3) and CC3 levels, respectively (Table S5). In other words, the methodological impacts obtained for absorption energies and geometries are nearly independent, and therefore nearly additive. Let us start by analyzing the results for the 12 molecules for which full CC3 estimates could be obtained (the compounds represented in blue in Scheme 1). The deviations with respect to CC3 are represented in Figure 1. In this Figure, the errors for transition energies and geometries have been computed considering the CC3 geometries and energies as reference, respectively, whereas the total deviations are obtained by comparing ADC(2)//MP2, CC2//CC2, CCSD//CCSD, and CCSDR(3)//CC(3) results to their CC3//CC3 counterparts. As expected, the obtained methodological sensitivity is significantly molecule-dependent, for example, no deviations larger than 0.1 eV can be found for selenoformaldehyde, whereas significantly bigger errors are observed for cyanogen. Globally, the molecules leading to the largest (and smallest) deviations are similar for the four tested levels of theory. Obviously, the CCSDR(3)//CC(3) approach provides very good approximations to the CC3//CC3 values, the maximal deviation being +0.068 eV for cyanogen (Table S7). It is also obvious from Figure 1 that the errors are mostly, but not exclusively, driven by the transition energies for this method, which is consistent with the fact that CC(3) provides GS geometries in very good agreement with their CC3 counterparts with average deviations on bond lengths as small as 0.001 Å.29 With CCSD//CCSD, all observed deviations are systematically positive and range from 0.079 eV (selenoformaldehyde) to 0.325 eV (methylenecyclopropene). Qualitatively, this means that CCSD provides a too localized description of the molecular properties, a conclusion already found previously by several groups for both transition energies30,31,40 and geometries.29 The electronic and geometric contributions to the total CCSD errors are also both positive and add up to lead to the total overestimation. Importantly and unexpectedly, the contribution of the geometry to the total deviation represents the largest share of the CCSD error in half of the cases (6/12). With CC2//CC2, one also notices a systematic overestimation of the CC3 values in this 12-compound set, but with strongly different contributions from the transition energies (rather large positive errors in the 0.089−0.331 eV range) and geometries (either trifling deviations or large negative errors going up to −0.287 eV). Therefore, there exists, for several compounds, an error compensation between the two sources of deviations. This can be illustrated by diacetylene for which the CC3//CC3 absorption energy (5.609 eV) is very accurately reproduced by CC2//CC2 (5.629 eV), but not by CC3//CC2 (5.479 eV) nor

2. COMPUTATIONAL DETAILS The aug-cc-pVTZ atomic basis set was used throughout, for both energy calculations and geometry optimizations. Most of the structures used here have been extracted from ref 29. The interested reader will also find the results of the T1 diagnostic33 test in that earlier work, and only one considered ES (diazomethane) presents a T1 exceeding the 0.02 limit. In other words, but for that borderline case, the CC methods are adequate for the treated molecules.. A few additional geometries had to be determined, and they have been obtained using Turbomole34 for ADC(2) and CC2 methods, Gaussian35 for CCSD, and Dalton36 for CCSDR(3) and CC3. These geometry optimizations use exactly the same protocol as in ref 29, and we refer the reader to that contribution for further details. We underline that analytic gradients are not available for CCSDR(3) and CC3, and the structural minimizations relied on numerical gradients, which is obviously extremely computationally demanding at the CC3/aug-cc-pVTZ level. The ADC(2) transition energies were computed with the QChem package,37 whereas all CC transition energies presented below were determined with the Dalton package36 using default parameters but accounting for symmetry when possible. The DFT and TD-DFT calculations discussed in the last section of this work have been performed with Gaussian 16,35 using the PBE0 exchange-correlation functional.38,39 During all calculations all electrons have been correlated, that is, the frozencore approximation was not applied. In the following, we use the usual convention for composite calculations, that is, “energy”//“geometry”. We recall that the GS methods corresponding to ADC(2) and CCSDR(3) are MP2 and CC(3), respectively, and that the latter is very close to the CCSD(T) “golden standard”. 3. RESULTS AND DISCUSSION From the technical viewpoint, the main task needed for our purposes was to determine ES geometrical parameters at very high theoretical level, namely CCSDR(3)/aug-cc-pVTZ and CC3/aug-cc-pVTZ. As stated above, we used to this end the data published in a recent database,29 though, for three molecules, namely cyanoacetylene, methylenecyclopropene, and thiocarbonylchlorofluoride, we have obtained improved geometries herein. There are described in the Supporting Information (SI). For the two first compounds, we have now obtained full CC3/aug-cc-pVTZ whereas only “basis-set extrapolated” values were previously available. The maximal discrepancy between the two sets of data is limited to 0.001 Å for the NC bond of cyanoacetylene. For the latter molecule, we have determined the CCSDR(3)/aug-cc-pVTZ GS and ES structural parameters, and we found that all bonds are slightly shorter than at the CCSDR(3)/def 2-TZVPP level (see Table S3 in the SI). In the following we start by discussing the wave function results obtained for both absorption (section 3.1) and emission (section 3.2) with ADC(2) and the four tested CC levels, before turning to TD-DFT approaches in section 3.3. 3.1. Absorption. For absorption, all computed ADC and CC transition energies are listed in Tables S4 to S26 in the SI. We do not discuss in the following the optimal geometrical parameters obtained with all methods, as these data are detailed in ref 29, and we focus on the vertical absorption energies. First, C

DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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We further determined the Pearson correlation matrix between the errors made by all methods. The results are displayed in Tables S52−S54 in the SI. For the errors related to the level selected for transition energies, one finds quite large R between the different methods with values in the 0.70−0.91 range;41 for example, a transition hard to describe with CC2 is also challenging with CCSDR(3). For the errors due to geometries, the obtained |R| values are also larger than 0.7 but for one case. However, negative correlations are found between, on one side, ADC(2) and CC2 and, on the other side, CCSD and CCSDR(3), which is consistent with Figure 1. As a result of error compensation, all R values become small for the total errors ( 0.6) that could be found were between ADC(2) and CC2 that present similar error patterns for the two contributions to the error (>0.8) and a significant relationship for the total error (R = 0.73) as well. In F

DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Table 2. Statistical Analysis for the Emission Energies (Top) of Figure 2 Including Mean Signed and Absolute Deviations (MSD and MAD, in eV) Considering the CC3//CC3 Results as Reference; and (Bottom) Carried Out for All Compounds of Scheme 1 Considering CCSDR(3)//CCSDR(3) Values as Reference 12-compound setCC3 reference MSD method

total

energy

ADC(2) CC2 CCSD CCSDR(3)

−0.014 0.148 0.270 0.066

0.025 0.208 0.104 0.038

MAD geometry

total

−0.020 0.165 −0.063 0.148 0.169 0.270 0.029 0.066 24-compound setCCSDR(3) reference

MSD

energy

geometry

0.149 0.208 0.104 0.039

0.117 0.101 0.169 0.029

MAD

method

total

energy

geometry

total

energy

geometry

ADC(2) CC2 CCSD

−0.177 0.023 0.224

−0.104 0.105 0.073

−0.031 −0.077 0.153

0.239 0.135 0.224

0.163 0.123 0.078

0.127 0.121 0.155

Table 3. Statistical Analysis Obtained with (TD-)PBE0, Using Either the CC3 (Top) or CCSDR(3) Values as Referencea 12-compound setC3 reference MSD

MAD

method

total

energy

absorption emission

−0.166 −0.108

−0.230 −0.237

geometry

total

method

total

energy

geometry

total

energy

geometry

absorption emission44

−0.098 0.007

−0.139 −0.113

0.040 0.131

0.181 0.345

0.194 0.236

0.046 0.145

0.064 0.223 0.134 0.348 24-compound setCCSDR(3) reference

MSD

a

energy

geometry

0.256 0.302

0.064 0.134

MAD

All values are given in eV. See title of Table 1 for more details.

transition energy, the geometry or both. For both absorption and emission, we found that the energetic and geometric contributions to the total error are nearly additive for a given compound, which facilitated the analysis of the errors. Some clear methodological trends emerged. First, CCSD tends to provide a too localized description of the considered compounds, which consequently yields to positive deviations for both components of the total error: the transition energies are always overestimated. Second, CCSDR(3) allows to correct most of the CCSD error and to bring the absorption and emission energies much closer to the CC3 benchmark values, though a slight overestimation pertains in the vast majority of cases. These two conclusions are consistent with the results obtained previously for Thiel’s set of derivatives for absorption.30,31,40,43 Third, CC2 gives positive deviations compared to CC3 for the transition energies considered herein, whereas positive and negative geometric errors could be found. For several compounds, there is therefore a clear compensation of energetic and geometric errors at the CC2 level, so that a good match between, for example, a CC2//CC2 emission energy and a measured fluorescence spectrum is probably not a definitive proof that this approach is well suited. With ADC(2), one can find positive and negative deviations for both terms (energy/geometry), and for both absorption and emission. Nevertheless, on average the deviations obtained with ADC(2) are of the same order of magnitude as their CC2 counterparts, which fits previous findings.42 For absorption, we noticed that the geometric contribution to the total error is quite small with respect to its energetic

MAD related to energy slightly increases by ca. 20% (from 0.256 to 0.302 eV for the 12-compound set, and from 0.194 to 0.236 eV for the 24-compound set), whereas the geometry errors become much larger, by doubling (from 0.064 to 0.134 eV) or tripling (from 0.046 to 0.145 eV) for the small and large set, respectively. For emission, the structural component of the error cannot be neglected anymore, consistently with the results obtained when considering CC methods only. These data clearly hint that performing a CC calculation on top of a (TD-)DFT geometry is a reasonable approach for absorption, but a less pertinent choice for emission. Indeed, the MAD obtained from CC2//TD-DFT calculations, a popular protocol nowadays (see Introduction) attains 0.180 eV for absorption but 0.268 eV (+49%) for fluorescence for the 24-compound set, using the CCSDR(3)//CCSDR(3) values as reference.

4. CONCLUSIONS In an effort to disentangle the contributions of the energy and the geometry to the total errors obtained for absorption and fluorescence energies, we have computed the transition energies for a set of 24 compounds selecting the aug-ccpVTZ atomic basis set and considering a group of five increasingly accurate methods going from the relatively simple ADC(2) approach to the reference CC3 method. For this set of organic derivatives, we have systematically obtained CCSDR(3)//CCSDR(3) reference values and, for a subset of 12 derivatives, CC3//CC3 results as well. Using these data as references, we have determined the transition energies by degrading step-by-step either the method used to compute the G

DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

Journal of Chemical Theory and Computation counterpart for the ADC(2)//MP2, CC2//CC2, and CCSDR(3)//CC(3) methods, but is of the same order of magnitude for CCSD//CCSD. The errors obtained at the ADC(2) and CC2 levels are significantly correlated for absorption, and this holds for CCSD and CCSDR(3) deviations. Using an approach like CCSDR(3)//MP2 in which a more refined theoretical level is used for computing transition energies than for determining GS geometrical parameters delivers very satisfying result with a MAD of 0.044 eV compared to CC3//CC3. However, the situation is significantly different for emission, because it is challenging to obtain accurate excited-state geometrical parameters with a “cheap” method. Indeed, for fluorescence, the typical deviations due to the method selected for computing the transition energies remain of the same order of magnitude as for absorption, but the geometric contribution to the total error becomes significantly bigger, irrespective of the selected level of theory. As a consequence, the CCSDR(3)//ADC(2) approach gives a MAD of 0.115 eV for fluorescence, 2.6 times larger than for absorption. For emission, the correlation between the errors determined at different levels of theory are also small, at the notable exception of the ADC(2)−CC2 pair, so that predicting the accuracy of CCSDR(3) from the ADC(2) results is probably not possible. In contrast, we found that there are reasonable correlations between the errors made on absorption and emission for a given method, but for CCSD. These conclusions were additionally corroborated by TD-DFT and CC3//TD-DFT calculations: it is more difficult to obtain accurate emission energies than absorption values, because the geometric error becomes significantly larger for the latter. In short, it appears clearly from this study that while the method used to compute the transition energy is the key to accurate absorption calculations, this does not necessarily hold for emission, for which the quality of the selected level for determining ES geometry also plays a key role in the final accuracy of the results.

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ACKNOWLEDGMENTS

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REFERENCES

The author is indebted to Prof. C. Adamo (ENSCP, Paris) for enlightening discussions.

(1) Ullrich, C. Time-Dependent Density-Functional Theory: Concepts and Applications; Oxford Graduate Texts; Oxford University Press: New York, 2012. (2) Jacquemin, D.; Adamo, C. In Density-Functional Methods for Excited States; Ferré, N., Filatov, M., Huix-Rotllant, M., Eds.; Springer International Publishing: Cham, Switzerland, 2016; Vol. 368; pp 347− 375. (3) Hegarty, D.; Robb, M. A. Application of Unitary Group Methods to Configuration Interaction Calculations. Mol. Phys. 1979, 38, 1795− 1812. (4) Werner, H.; Meyer, W. A Quadratically Convergent Multiconfiguration-Self-Consistent Field Method With Simultaneous Optimization of Orbitals and CI Coefficients. J. Chem. Phys. 1980, 73, 2342−2356. (5) Taylor, P. R. Analytical MCSCF Energy Gradients: Treatment of Symmetry and CASSCF Applications to Propadienone. J. Comput. Chem. 1984, 5, 589−597. (6) van Caillie, C.; Amos, R. D. Geometric Derivatives of Excitation Energies Using SCF and DFT. Chem. Phys. Lett. 1999, 308, 249−255. (7) Furche, F.; Ahlrichs, R. Adiabatic Time-Dependent Density Functional Methods for Excited States Properties. J. Chem. Phys. 2002, 117, 7433−7447. (8) Scalmani, G.; Frisch, M. J.; Mennucci, B.; Tomasi, J.; Cammi, R.; Barone, V. Geometries and Properties of Excited States in the Gas Phase and in Solution: Theory and Application of a Time-Dependent Density Functional Theory Polarizable Continuum Model. J. Chem. Phys. 2006, 124, 094107. (9) Grimme, S.; Neese, F. Double-Hybrid Density Functional Theory for Excited Electronic States of Molecules. J. Chem. Phys. 2007, 127, 154116. (10) Brémond, E.; Ciofini, I.; Sancho-García, J. C.; Adamo, C. Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists. Acc. Chem. Res. 2016, 49, 1503−1513. (11) Andersson, K.; Malmqvist, P. A.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. Second-Order Perturbation Theory With a CASSCF Reference Function. J. Phys. Chem. 1990, 94, 5483−5488. (12) Andersson, K.; Malmqvist, P.-A.; Roos, B. O. Second-Order Perturbation Theory With a Complete Active Space Self-Consistent Field Reference Function. J. Chem. Phys. 1992, 96, 1218−1226. (13) Dreuw, A.; Wormit, M. The Algebraic Diagrammatic Construction Scheme for the Polarization Propagator for the Calculation of Excited States. WIREs Comput. Mol. Sci. 2015, 5, 82−95. (14) Christiansen, O.; Koch, H.; Jørgensen, P. The Second-Order Approximate Coupled Cluster Singles and Doubles Model CC2. Chem. Phys. Lett. 1995, 243, 409−418. (15) Koch, H.; Jørgensen, P. Coupled Cluster Response Functions. J. Chem. Phys. 1990, 93, 3333−3344. (16) Stanton, J. F.; Bartlett, R. J. The Equation of Motion CoupledCluster Method - A Systematic Biorthogonal Approach to Molecular Excitation Energies, Transition-Probabilities, and Excited-State Properties. J. Chem. Phys. 1993, 98, 7029−7039. (17) Christiansen, O.; Koch, H.; Jørgensen, P. Perturbative Triple Excitation Corrections to Coupled Cluster Singles and Doubles Excitation Energies. J. Chem. Phys. 1996, 105, 1451−1459. (18) Watts, J. D.; Bartlett, R. J. Economical Triple Excitation Equation-Of-Motion Coupled-Cluster Methods for Excitation Energies. Chem. Phys. Lett. 1995, 233, 81−87. (19) Watts, J. D.; Bartlett, R. J. Iterative and Non-Iterative Triple Excitation Corrections in Coupled-Cluster Methods for Excited Electronic States: the EOM-CCSDT-3 and EOM-CCSD(T∼) Methods. Chem. Phys. Lett. 1996, 258, 581−588.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.7b01224. Geometrical parameters for cyanoacetylene, methylenecyclopropene, and thiocarbonylchlorofluoride; full list of transition energies for both absorption and emission; Pearson correlation matrices (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Denis Jacquemin: 0000-0002-4217-0708 Funding

This research used resources of (i) the GENCI-CINES/IDRIS; (ii) CCIPL (Centre de Calcul Intensif des Pays de Loire); (iii) a local Troy cluster; and (iv) HPC resources from ArronaxPlus (Grant ANR-11-EQPX-0004 funded by the French National Agency for Research). Notes

The author declares no competing financial interest. H

DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jctc.7b01224 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX