The accurate computation of ionization potentials (IPs), within 0.10 eV, is one of the most challenging problems in modern computational chemistry. The extended Koopmans' theorem (EKT) provides a systematic direct approach to compute IPs from any level of theory. In this study, the EKT approach is integrated with the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the first time. For efficiency, the density-fitting (DF) approximation is employed for electron repulsion integrals. Further, the EKT-CCSD(T) method is applied to a set of 23 molecules, denoted as IP23, for comparison with the experimental ionization potentials. For the IP23 set, the EKT-CCSD(T) method, along with the aug-cc-pV5Z basis set, provides a mean absolute error of 0.05 eV. Hence, our results demonstrate that direct computations of IPs at high-accuracy levels can be achieved with the EKT-CCSD(T) method. We believe that the present study may open new avenues in IP computations.
An extensive study of structures and energetics for anionic pentamer and hexamer clusters is performed employing high level ab initio quantum chemical methods, such as the density-fitted orbital-optimized linearized coupled-cluster doubles (DF-OLCCD), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] methods. In this study, sixteen anionic pentamer clusters and eighteen anionic hexamer clusters are reported. Relative, binding, and vertical detachment energies (VDE) are presented at the complete basis set limit (CBS), extrapolating energies of aug4-cc-pVTZ and aug4-cc-pVQZ custom basis sets. The largest VDE values obtained at the CCSD(T)/CBS level are 9.9 and 11.2 kcal mol for pentamers and hexamers, respectively, which are in very good agreement with the experimental values of 9.5 and 11.1 kcal mol. Our binding energy results, at the CCSD(T)/CBS level, indicate strong bindings in anionic clusters due to hydrogen bond interactions. The average binding energy per water molecules is -5.0 and -5.3 kcal mol for pentamers and hexamers, respectively. Furthermore, our results demonstrate that the DF-OLCCD method approaches to the CCSD(T) quality for anionic clusters. The inexpensive analytic gradients of DF-OLCCD compared to CCSD or CCSD(T) make it very attractive for high-accuracy studies.
Organic light-emitting diodes (OLEDs) have been of significant interest because of their superior performance and low cost of production. Thermally activated delayed fluorescence (TADF) has attracted significant interest in the OLED technology because it improves the efficiency of OLEDs by harvesting triplet excitons. Therefore, the accurate computation of singlet−triplet transition energies (ΔE S 1 −T 1 ) of charge-transfer molecules is very important. However, the accurate computation of the ΔE S 1 −T 1 values is a challenging problem for single-reference methods because of the multireference character of excited states. In this research, an assessment of density-fitted second-order quasidegenerate perturbation theory (DF-QDPT2) [Bozkaya, U.; J. Chem. Theory Comput. 2019, 15, 4415− 4429] for singlet−triplet transition energies (ΔE S 1 −T 1 ) of charge-transfer compounds is presented. The performance of the DF-QDPT2 method has been compared with those of several density-functional theory functionals, such as B3LYP, PBE0, M06-2X, ωB97X-D, and MN15; density-fitted state-averaged CASSCF (DF-SA-CASSCF); and single-state singlereference second-order perturbation theory (SS-SR-CASPT2) methods. For the TADF molecules considered, the DF-QDPT2 method provides a mean absolute error (MAE) of 0.13 eV, while the MAE values of DF-SA-CASSCF and SS-SR-CASPT2 are 0.65 and 0.74 eV, respectively. The performances of B3LYP and PBE0 are slightly better than that of DF-QDPT2, while M06-2X and ωB97X-D provide noticeably higher errors compared with DF-QDPT2. Furthermore, the standard CASSCF without state-averaging yields dramatic errors with an MAE value of 3.0 eV. Our results demonstrate that eigenvalues of the DF-QDPT2-effective Hamiltonian can be reliably used for the prediction of singlet−triplet transition energies, while eigenvalues of DF-CASSCF/DF-SA-CASSCF fail to provide accurate predictions. Overall, we conclude that the DF-QDPT2 method emerges as a very useful tool for the computation of excited-state properties.
Efficient implementations of the orbital-optimized coupled-cluster doubles [or simply "optimized CCD", OCCD, for short] method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of Psi4) is compared with that of the conventional OCCD (from the Q-Chem package). The OCCD computations were performed with the Q-chem package, in which it is denoted by OD. In the conventional OCCD, one needs to perform four-index integrals transformations at each CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, there are almost 8-fold reductions in the computational time for the C 6 H 14 molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Further, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD there is no need for orbital relaxation contributions in analytic gradient computations (2) active spaces can readily be incorporated into DF-OCCD (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory (5) Symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] has a significantly better performance in near degeneracy regions.
An efficient implementation of the density-fitted equation-ofmotion coupled-cluster singles and doubles (DF-EOM-CCSD) method is presented with an enhanced algorithm for the particle−particle ladder (PPL) term, which is the most expensive part of EOM-CCSD computations. To further improve the evaluation of the PPL term, a hybrid density-fitting/ Cholesky decomposition (DF/CD) algorithm is also introduced. In the hybrid DF/CD approach, four virtual index integrals are constructed on-the-fly from the DF factors; then, their partial Cholesky decomposition is simultaneously performed. The computational cost of the DF-EOM-CCSD method for excitation energies is compared with that of the resolution of the identity EOM-CCSD (RI-EOM-CCSD) (from the Q-CHEM 5.3 package). Our results demonstrate that DF-EOM-CCSD excitation energies are significantly accelerated compared to RI-EOM-CCSD. There is more than a 2-fold reduction for the C 8 H 18 molecule in the cc-pVTZ basis set with the restricted Hartree-Fock (RHF) reference. This cost savings results from the efficient evaluation of the PPL term. In the RHF based DF-EOM-CCSD method, the number of flops (NOF) is 1/ 4O 2 V 4 , while that of RI-EOM-CCSD was reported (Epifanovsky et al. J. Chem. Phys. 2013, 139, 134105) to be 5/8O 2 V 4 for the PPL contraction term. Further, the NOF of VVVV-type integral transformation is 1/2V 4 N aux in our case, while it appears to be V 4 N aux for RI-EOM-CCSD. Hence, our implementation is 2.5 and 2.0 times more efficient compared to RI-EOM-CCSD for these expensive terms. For the unrestricted Hartree-Fock (UHF) reference, our implementation maintains its enhanced performance and provides a 1.8-fold reduction in the computational time compared to RI-EOM-CCSD for the C 7 H 16 molecule. Our results indicate that our DF-EOM-CCSD implementation is 1.7 and 1.4 times more efficient compared with RI-EOM-CCSD for average computational cost per EOM-CCSD iteration. Moreover, our results show that the new hybrid DF/CD approach improves upon the DF algorithm, especially for large molecular systems. Overall, we conclude that the new hybrid DF/CD PPL algorithm is very promising for largesized chemical systems.
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