Equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation.

Orbital-optimized coupled-cluster methods are very helpful for theoretical predictions of the molecular properties of challenging chemical systems, such as excited states. In this research, an efficient implementation of the equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting (DF) approach, denoted by DF-EOM-OCCD, is presented. The computational cost of the DF-EOM-OCCD method for excitation energies is compared with that of the conventional EOM-OCCD method. Our results demonstrate that DF-EOM-OCCD excitation energies are dramatically accelerated compared to EOM-OCCD. There are almost 17-fold reductions for the C 5 H 12 $$ {\mathrm{C}}_5{\mathrm{H}}_{12} $$ molecule in an aug-cc-pVTZ basis set with the RHF reference. This dramatic performance improvement comes from the reduced cost of integral transformation with the DF approach and the efficient evaluation of the particle-particle ladder (PPL) term, which is the most expensive term to evaluate. Further, our results show that the DF-EOM-OCCD approach is very helpful for the computation of excitation energies in open-shell molecular systems. Overall, we conclude that our new DF-EOM-OCCD implementation is very promising for the study of excited states in large-sized challenging chemical systems.

Equation-of-motion regularized orbital-optimized second-order perturbation theory with the density-fitting approximation.

The density-fitted equation-of-motion (EOM) orbital-optimized second-order perturbation theory (DF-EOM-OMP2) method is presented for the first time. In addition, κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods are implemented with the addition of κ-regularization. The accuracy of the DF-EOM-OMP2, κ-DF-EOM-MP2, and κ-DF-EOM-OMP2 methods are compared to the density-fitted EOM-MP2 (DF-EOM-MP2), EOM coupled-cluster (CC) singles and doubles (DF-EOM-CCSD), and EOM-CCSD with the triples excitation correction model [EOM-CCSD(fT)] for excitation energies of many closed- and open-shell chemical systems. The excitation energies computed using different test cases and methods were compared to the EOM-CCSD(fT) method and mean absolute errors (MAEs) are presented. The MAE values of closed- and open-shell cases (closed-shell organic chromophores set, open-shell set, peptide radicals set, and radical set) according to the EOM-CCSD(fT) method show that the κ-regularization technique yields highly accurate results for the first excited states. Our results indicate that the κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods perform noticeably better than the DF-EOM-MP2 and DF-EOM-OMP2 methods. They approach the EOM-CCSD quality, at a significantly reduced cost, for the computation of excitation energies. Especially, the κ-DF-EOM-MP2 method provides outstanding results for most test cases considered. Overall, we conclude that the κ-versions of DF-EOM-MP2 and DF-EOM-OMP2 emerge as a useful computational tool for the study of excited-state molecular properties.

MacroQC 1.0: An electronic structure theory software for large-scale applications.

MacroQC is a quantum chemistry software for high-accuracy computations and large-scale chemical applications. MacroQC package features energy and analytic gradients for a broad range of many-body perturbation theory and coupled-cluster (CC) methods. Even when compared to commercial quantum chemistry software, analytical gradients of second-order perturbation theory, CC singles and doubles (CCSD), and CCSD with perturbative triples approaches are particularly efficient. MacroQC has a number of peculiar features, such as analytic gradients with the density-fitting approach, orbital-optimized methods, extended Koopman's theorem, and molecular fragmentation approaches. MacroQC provides a limited level of interoperability with some other software. The plugin system of MacroQC allows external interfaces in a developer-friendly way. The linear-scaling systematic molecular fragmentation (LSSMF) method is another distinctive feature of the MacroQC software. The LSSMF method enables one to apply high-level post-Hartree-Fock methods to large-sized molecular systems. Overall, we feel that the MacroQC program will be a valuable tool for wide scientific applications.

Accurate property prediction by second order perturbation theory: The REMP and OO-REMP hybrids.

The prediction of molecular properties such as equilibrium structures or vibrational wavenumbers is a routine task in computational chemistry. If very high accuracy is required, however, the use of computationally demanding ab initio wavefunction methods is mandatory. We present property calculations utilizing Retaining the Excitation Degree - Møller-Plesset (REMP) and Orbital Optimized REMP (OO-REMP) hybrid perturbation theories, showing that with the latter approach, very accurate results are obtained at second order in perturbation theory. Specifically, equilibrium structures and harmonic vibrational wavenumbers and dipole moments of closed and open shell molecules were calculated and compared to the best available experimental results or very accurate calculations. OO-REMP is capable of predicting bond lengths of small closed and open shell molecules with an accuracy of 0.2 and 0.5 pm, respectively, often within the range of experimental uncertainty. Equilibrium harmonic vibrational wavenumbers are predicted with an accuracy better than 20 cm-1. Dipole moments of small closed and open shell molecules are reproduced with a relative error of less than 3%. Across all investigated properties, it turns out that a 20%:80% Møller-Plesset:Retaining the Excitation Degree mixing ratio consistently provides the best results. This is in line with our previous findings, featuring closed and open shell reaction energies.

Efficient and regioselective synthesis of dihydroxy-substituted 2-aminocyclooctane-1-carboxylic acid and its bicyclic derivatives.

The first synthesis of 2-amino-3,4-dihydroxycyclooctane-1-carboxylic acid, methyl 6-hydroxy-9-oxo-8-oxabicyclo[5.2.1]decan-10-yl)carbamate, and 10-amino-6-hydroxy-8-oxabicyclo[5.2.1]decan-9-one starting from cis-9-azabicyclo[6.2.0]dec-6-en-10-one is described. cis-9-Azabicyclo[6.2.0]dec-6-en-10-one was transformed into the corresponding amino ester and its protected amine. Oxidation of the double bond in the N-Boc-protected methyl 2-aminocyclooct-3-ene-1-carboxylate then delivered the targeted amino acid and its derivatives. Density-functional theory (DFT) computations were used to explain the reaction mechanism for the ring opening of the epoxide and the formation of five-membered lactones. The stereochemistry of the synthesized compounds was determined by 1D and 2D NMR spectroscopy. The configuration of methyl 6-hydroxy-9-oxo-8-oxabicyclo[5.2.1]decan-10-yl)carbamate was confirmed by X-ray diffraction.

A computational study of the reaction mechanism of 2,2-azobis(isobutyronitrile)-initiated oxidative cleavage of geminal alkenes.

A computational study of 2,2-azobis(isobutyronitrile) (AIBN)-initiated aerobic oxidative cleavage of alkenes is carried out employing density functional theory (DFT) and high-level coupled-cluster methods, such as coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. Our computations show that the barriers for the formation of dioxetane derivatives suggested by Xu and co-workers (J. Org. Chem., 2014, 79, 7220-7225) for the reaction mechanism of aerobic oxidative cleavage of alkenes are computed to be higher than 65 kcal mol-1. This barrier is relatively high under the reaction conditions. Our results for the Xu mechanism indicate that the reaction does not proceed via the formation of a dioxetane ring under the reaction conditions. Our results demonstrate that the reaction of aerobic oxidative cleavage of geminal alkenes in the presence of AIBN is initiated by the peroxyl radical 9, contrary to the isobutyronitrile radical 2. Our results show that the 2-(2-hydroxyl-1,1-diarylethoxy)-2-methylpropanenitrile radical (15) does not appear throughout the reaction scheme and the reaction progresses over the 2-(2-hydroxyl-2,2-diarylethoxy)-2-methylpropanenitrile radical (13) rather than the 2-(2-hydroxyl-1,1-diarylethoxy)-2-methylpropanenitrile radical (15). Our results are in agreement with the experimental results for the aerobic oxidative cleavage of the geminal disubstituted alkenes. Our results also demonstrate that the epoxide derivatives can be formed as an intermediate under the reaction conditions. This reaction is not applicable for pyridine derivatives due to the conversion of vinylpyridine derivatives to N-oxide derivatives.

Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation.

Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OCCD) method with the density-fitting approach, denoted by DF-OCCD(T) and DF-OCCD(T)Λ, are presented. The computational cost of the DF-OCCD(T) method is compared with that of the conventional OCCD(T). In the conventional OCCD(T) and OCCD(T)Λ methods, one needs to perform four-index integral transformations at each coupled-cluster doubles iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD(T) provides dramatically lower computational costs compared to OCCD(T), and there are more than 68-fold reductions in the computational time for the C5H12 molecule with the cc-pVTZ basis set. Our results show that the DF-OCCD(T) and DF-OCCD(T)Λ methods are very helpful for the study of single bond-breaking problems. Performances of the DF-OCCD(T) and DF-OCCD(T)Λ methods are noticeably better than that of the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the potential energy surfaces of the molecules considered. Specifically, the DF-OCCD(T)Λ method provides dramatic improvements upon CCSD(T), and there are 8-14-fold reductions in nonparallelity errors. Overall, we conclude that the DF-OCCD(T)Λ method is very promising for the study of challenging chemical systems, where the CCSD(T) fails.

State-of-the-art computations of dipole moments using analytic gradients of high-level density-fitted coupled-cluster methods with focal-point approximations.

Using the analytic derivatives approach, dipole moments of high-level density-fitted coupled-cluster (CC) methods, such as coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)], are presented. To obtain the high accuracy results, the computed dipole moments are extrapolated to the complete basis set (CBS) limits applying focal-point approximations. Dipole moments of the CC methods considered are compared with the experimental gas-phase values, as well as with the common DFT functionals, such as B3LYP, BP86, M06-2X, and BLYP. For all test sets considered, the CCSD(T) method provides substantial improvements over Hartree-Fock (HF), by 0.076-0.213 D, and its mean absolute errors are lower than 0.06 D. Furthermore, our results indicate that even though the performances of the common DFT functionals considered are significantly better than that of HF, their results are not comparable with the CC methods. Our results demonstrate that the CCSD(T)/CBS level of theory provides highly-accurate dipole moments, and its quality approaching the experimental results. © 2019 Wiley Periodicals, Inc.

Computational Study for the Reaction Mechanism of N-Hydroxyphthalimide-Catalyzed Oxidative Cleavage of Alkenes.

A computational study of N-hydroxyphthalimide-catalyzed aerobic oxidative cleavage of alkenes is carried out employing density functional theory and high-level coupled-cluster methods, such as coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. Our results demonstrate that the reaction proceeds through the alkoxyl radicals, as opposed to the mechanism suggested by Jiao and co-workers (Org. Lett. 2012, 14, 4158-4161), in which the reaction proceeds via formation of the dioxetane ring. The barriers for the formation of dioxetane derivatives are computed to be higher than 50 kcal mol-1, while the barriers for the formation of alkoxyl radicals are as low as 13 kcal mol-1. Our results also demonstrate that epoxide derivatives can be formed as intermediates or byproducts under the reaction conditions.

Assessment of the Density-Fitted Second-Order Quasidegenerate Perturbation Theory for Transition Energies: Accurate Computations of Singlet-Triplet Gaps for Charge-Transfer Compounds.

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 (ΔES1-T1) of charge-transfer molecules is very important. However, the accurate computation of the ΔES1-T1 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 (ΔES1-T1) 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 single-reference 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.

Energy and analytic gradients for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation.

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 OCCD are denoted by OD. In the conventional OCCD method, one needs to perform four-index integral transformations at each of the CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, and there are almost eightfold reductions in the computational time for the C6H14 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. Furthermore, 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; and (5) symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] have a significantly better performance in near degeneracy regions.

Efficient and automated computation of accurate molecular geometries using focal-point approximations to large-basis coupled-cluster theory.

The focal-point approach, combining several quantum chemistry computations to estimate a more accurate computation at a lower expense, is effective and commonly used for energies. However, it has not yet been widely adopted for properties such as geometries. Here, we examine several focal-point methods combining Møller-Plesset perturbation theory (MP2 and MP2.5) with coupled-cluster theory through perturbative triples [CCSD(T)] for their effectiveness in geometry optimizations using a new driver for the Psi4 electronic structure program that efficiently automates the computation of composite-energy gradients. The test set consists of 94 closed-shell molecules containing first- and/or second-row elements. The focal-point methods utilized combinations of correlation-consistent basis sets cc-pV(X+d)Z and heavy-aug-cc-pV(X+d)Z (X = D, T, Q, 5, 6). Focal-point geometries were compared to those from conventional CCSD(T) using basis sets up to heavy-aug-cc-pV5Z and to geometries from explicitly correlated CCSD(T)-F12 using the cc-pVXZ-F12 (X = D, T) basis sets. All results were compared to reference geometries reported by Karton et al. [J. Chem. Phys. 145, 104101 (2016)] at the CCSD(T)/heavy-aug-cc-pV6Z level of theory. In general, focal-point methods based on an estimate of the MP2 complete-basis-set limit, with a coupled-cluster correction evaluated in a (heavy-aug-)cc-pVXZ basis, are of superior quality to conventional CCSD(T)/(heavy-aug-)cc-pV(X+1)Z and sometimes approach the errors of CCSD(T)/(heavy-aug-)cc-pV(X+2)Z. However, the focal-point methods are much faster computationally. For the benzene molecule, the gradient of such a focal-point approach requires only 4.5% of the computation time of a conventional CCSD(T)/cc-pVTZ gradient and only 0.4% of the time of a CCSD(T)/cc-pVQZ gradient.

Psi4 1.4: Open-source software for high-throughput quantum chemistry.

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

An anomalous addition of chlorosulfonyl isocyanate to a carbonyl group: the synthesis of ((3aS,7aR,E)-2-ethyl-3-oxo-2,3,3a,4,7,7a-hexahydro-1H-isoindol-1-ylidene)sulfamoyl chloride.

In this study, we developed a new addition reaction of chlorosulfonyl isocyanate (CSI), starting from 2-ethyl-3a,4,7,7a-tetrahydro-1H-isoindole-1,3(2H)-dione. The addition reaction of CSI with 2-ethyl-3a,4,7,7a-tetrahydro-1H-isoindole-1,3(2H)-dione resulted in the formation of ylidenesulfamoyl chloride, whose exact configuration was determined by X-ray crystal analysis. We explain the mechanism of product formation supported by theoretical calculations.

Analytic energy gradients for orbital-optimized MP3 and MP2.5 with the density-fitting approximation: An efficient implementation.

Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc.

State-of-the-Art Computations of Vertical Ionization Potentials with the Extended Koopmans' Theorem Integrated with the CCSD(T) Method.

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.

Anionic water pentamer and hexamer clusters: An extensive study of structures and energetics.

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-1 for pentamers and hexamers, respectively, which are in very good agreement with the experimental values of 9.5 and 11.1 kcal mol-1. 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-1 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.

Transition Metal Cation-π Interactions: Complexes Formed by Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ Binding with Benzene Molecules.

A computational investigation of the structures and interaction energies of complexes formed by Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ binding with benzene (Bz) molecules is performed employing high level ab initio quantum chemical methods, such as the second-order perturbation theory (MP2), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] methods, along with the 6-311++G(2d,2p) and 6-311++G(d,p) basis sets. As far as we know, the present work is the first to study the structures and energetics of Bz-M2+ and Bz-M2+-Bz type complexes (M = Co, Ni, Cu, and Zn). Relativistic effects are also investigated via Douglas-Kroll-Hess second-order scalar relativistic computations for the complexes considered. Our results demonstrate that there are strong bindings between transition metal cations and benzene molecules. The computed interaction energies, including relativistic energy corrections, for the Bz-M2+ type complexes at the CCSD(T)/6-311++G(2d,2p) level are -131.9 (Bz-Fe2+), -172.6 (Bz-Co2+), -189.8 (Bz-Ni2+), -181.1 (Bz-Cu2+), and -158.2 (Bz-Zn2+) kcal mol-1. Similarly, interaction energies for the Bz-M2+-Bz type complexes at the CCSD(T)/6-311++G(d,p) level are -206.4 (Bz-Fe2+-Bz), -213.4 (Bz-Co2+-Bz), -249.7 (Bz-Ni2+-Bz), -258.6 (Bz-Cu2+-Bz), and -235.2 (Bz-Zn2+-Bz) kcal mol-1. Further, our results also demonstrate that the relativistic effects are very important in accurate computations of interaction energies. The predicted relativistic energy corrections to interaction energies, using the ωB97X-D functional, are between -1.9 and -7.7 kcal mol-1. The transition metal cation-π interactions investigated in this study prove significantly larger binding energies compared to arbitrary π-π interactions and main group cation-π interactions. We believe that the present study may open new avenues in cation-π interactions.

Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the density-fitting approximation.

An efficient implementation of analytic gradients for the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method with the density-fitting (DF) approximation, denoted as DF-CCSD(T), is reported. For the molecules considered, the DF approach substantially accelerates conventional CCSD(T) analytic gradients due to the reduced input/output time and the acceleration of the so-called "gradient terms": formation of particle density matrices (PDMs), computation of the generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the effective PDMs and GFM, back-transformation of the PDMs and GFM, from the molecular orbital to the atomic orbital (AO) basis, and computation of gradients in the AO basis. For the largest member of the molecular test set considered (C6H14), the computational times for analytic gradients (with the correlation-consistent polarized valence triple-ζ basis set in serial) are 106.2 [CCSD(T)] and 49.8 [DF-CCSD(T)] h, a speedup of more than 2-fold. In the evaluation of gradient terms, the DF approach completely avoids the use of four-index two-electron integrals. Similar to our previous studies on DF-second-order Møller-Plesset perturbation theory and DF-CCSD gradients, our formalism employs 2- and 3-index two-particle density matrices (TPDMs) instead of 4-index TPDMs. Errors introduced by the DF approximation are negligible for equilibrium geometries and harmonic vibrational frequencies.

Assessment of the extended Koopmans' theorem for the chemical reactivity: Accurate computations of chemical potentials, chemical hardnesses, and electrophilicity indices.

The extended Koopmans' theorem (EKT) provides a straightforward way to compute ionization potentials and electron affinities from any level of theory. Although it is widely applied to ionization potentials, the EKT approach has not been applied to evaluation of the chemical reactivity. We present the first benchmarking study to investigate the performance of the EKT methods for predictions of chemical potentials (µ) (hence electronegativities), chemical hardnesses (η), and electrophilicity indices (ω). We assess the performance of the EKT approaches for post-Hartree-Fock methods, such as Møller-Plesset perturbation theory, the coupled-electron pair theory, and their orbital-optimized counterparts for the evaluation of the chemical reactivity. Especially, results of the orbital-optimized coupled-electron pair theory method (with the aug-cc-pVQZ basis set) for predictions of the chemical reactivity are very promising; the corresponding mean absolute errors are 0.16, 0.28, and 0.09 eV for µ, η, and ω, respectively.