We present new and computationally efficient implementation of the equation-of-motion (EOM) coupled-cluster methods for doubly ionized (DIP) and doubly electron-attached (DEA) states including single, double, and triple substitutions. In particular, EOM operators include up to 4-hole-2-particle substitutions in EOM-DIP-CCSDT and up to 4-particle-2-holes substitutions in EOM-DEA-CCSDT; both treatments include up to 3-hole-3-particle substitutions in the CC part. These methods have been implemented in the Q-CHEM package using effective and open-mp parallel libtensor and libxm backends. The implementation takes advantage of permutational and point-group symmetries (Abelian subgroups only) and is partially spin-adapted in the case of closed-shell references; it enables both the conventional double-precision and single-precision execution. This paper reports the programmable expressions and details of the implementation. The capabilities of the full EOM-DIP/DEA-CCSDT are demonstrated by application to methylene diradical (CH2), water (H2O), ammonia (NH3), cyclobutadiene (C4H4), acetylene (C2H2), ethylene (C2H4), and formaldehyde (CH2O), highlighting the utility of these methods for treating diradicals, excited states, and Auger decay.

In this work, we present frozen natural orbital (FNO) based implementations of equation-of-motion (EOM) coupled-cluster (CC) with singles, doubles, and triples (SDT) for ionization potential (IP), double ionization potential (DIP), electron attachment (EA), and double electron attachment (DEA) variants. For EOM-CC with singles and doubles (SD), the FNO approach has already been studied by Krylov and co-workers for IP variant and for spin-flipping and spin-conserving excited states (respectively, the SF and EE variants) for both total energies and energy-gaps. Recently, we presented FNO-CCSDT performance for ground state energies of molecules, triplet-singlet gaps and for numerical estimation force constants of some diatomic molecules. Now we present our study on performance of IP, DIP, EA and DEA variants of FNO-EOM-CCSDT in computing total-energies, and for target-reference and target-target energy-gaps. Following earlier studies by us and by Krylov and co-workers, we also present the XFNO-EOM-CCSDT approach for these variants and examine its performance for total energies and energy-gaps.

We present our computational implementation of the equation-of-motion (EOM) coupled-cluster (CC) singles, doubles, and triples (SDT) method for computing doubly ionized (DIP) and two-electron attached (DEA) states within Q-CHEM. These variants have been implemented within both the (conventional) double precision (DP) and the single precision (SP) algorithms and will be available in the upcoming major release of Q-CHEM. We present here the programmable expressions and some pilot application of CH_2 for DIP and DEA EOM-CCSDT.

Frozen (F) natural orbitals (NO) approach in coupled cluster (CC) singles and doubles (SD) and equation-of-motion (EOM) CCSD methods is well-known for provide cost-effective yet accurate alternative for energy computation. In this article, we extend the FNO approach to CCSDT (CC with singles, doubles, and triples) implemented within Q-CHEM. This can be employed within both the (conventional) double precision (DP) as well as the single precision (SP) algorithms. Errors due to employing SP algorithm instead of DP are insignificant and therefore are not discussed. However, for computational timings, we present the performance of FNO-CCSDT versus conventional CCSDT methods with both SP and DP algorithms using water molecule as a test system. FNO-CCSDT results at different thresholds can be extrapolated to give the XFNO-CCSDT approach, which provides an enhanced accuracy. To illustrate this, we present total energies of a few molecules, adiabatic triplet-singlet gaps of a few chromophores and bond-stretching trends in total energies and vertical triplet-singlet gaps of hydrogen fluoride molecule. We also examine these methods for numerical estimation of spectroscopic parameters - force constants and vibrational frequencies of some diatomic molecules.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Computational studies were performed on non-classical thieno[3,4-c][1,2,5] thiadiazole and its pi donor derivatives (TT dyes) so as to delineate the factors responsible for their near-infrared (NIR) absorption. For all dyes except the unsubstituted bare dye, adiabatic singlet-triplet energy gaps (estimated through the ΔSCF procedure using the B3LYP and M062X DFT methods and SFTDDFT with the 5050 functional) were less than 1eV. Percentage calculations of the biradicaloid character suggested a moderate biradicaloid nature in all derivatives. There was a resemblance between the frontier molecular orbital (MO) picture of the TT bicyclic ring and the degenerate non-bonding molecular orbitals of Trimethyleneethane (TME, a known biradical). Inter-fragment charge transfer analysis revealed not only a considerable donation of charge to the central ring (Acceptor, TT part) but also substantial charge redistribution within the ring itself. From these results, it was inferred that NIR absorption, in these dyes, was due to: (1) a reduced HOMO-LUMO gap (HLG) as a TME biradical substructure forms its chromophoric part; and (2) charge transfer from the donor substituents. The non-bonding nature of the S atom, in the bare dye, with its neighbouring N/C atom (of the highest occupied π-MOs), led to an examination of its electronic structure using the ab initio valence bond method. The relatively large weight and energetic stability of the biradicaloid VB structures compared to those of the ylidic structures clearly disclosed the importance of biradicaloid structures in the overall resonance of the bare dye. Their utility as singlet fission materials was screened using singlet and triplet energy-based molecular structure activity criteria. The results were encouraging, demanding experiments to reaffirm the materials' usefulness.

We present dipole moments and dipole polarizabilities of doublet radicals computed analytically using constrained variational approach (CVA) based Fock-space (FS) multi-reference (MR) coupled-cluster (CC) method with single and double substitutions (SD) after Cholesky decomposition (CD) of electron repulsion integrals (ERI’s) in molecular orbital (MO) basis. We present our results computed with CD tolerance of 10-1,10-2 and 10-3 and test their accuracy by comparing them with the ones obtained by the conventional CVA-FSMRCCSD.

Five substituted pyranopyrazole (PPZ) derivatives were chemically synthesized by conventional and microwave assisted synthesis (MWA) methodology. Their differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) analyses, and the corrosion inhibitor properties on mild copper metal in 1MHCl solution were investigated by SEM (Scanning Electron Microscopy), EDS (Energy Dispersive Spectroscopy), andXRD(x-ray Diffraction) all of which showed good anti-corrosion behavior. Further, mechanical property investigations were also performed by measuring the tensile strength of the PPZ-adsorbed Cu-strips. Finally, the inhibition action was evaluated by quantum chemical parameters. All the experimental results pointed that the molecules acted as excellent anti-corrosion surface active agents for copper metal.

We present a Resolution of Identity and Cholesky Decomposition Based Implementation of EOM-MP2 approximation. The RI and CD based EOM-MP2 shows significant speed-up and less storage requirement than the conventional canonical version and can be applied to very large systems. The new algorithm used for this implementation eliminates the most storage requiring four-index quantities resulting in the decrease of storage requirement, reduction in I/O penalties and improved parallel performance, at the expense of more floating point operations. Therefore, the speed-up compared to conventional EOM-MP2 method is more prominent in case of EA, EE and SF case where the storage bottleneck is significant than the EOM-IP-MP2 method, where the storage requirement is significantly less. However, the RI/CD based EOM-IP-MP2 can be coupled with frozen natural orbitals to gain further speed-up.

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

We present a benchmark theoretical investigation on the electronic structure and singlet-triplet(S-T) gap of 1- and 2-naphthyl cations using the CCSD(T) method. Our calculations reveal that the ground states of both the naphthyl cations are singlet, contrary to the results obtained by DFT/B3LYP calculations reported in previous theoretical studies. However, the triplet states obtained in the two structural isomers of naphthyl cation are completely different. The triplet state in 1-naphthyl cation is (π,σ) type, whereas in 2-naphthyl cation it is (σ,σ') type. The S-T gaps in naphthyl cations and the relative stability ordering of the singlet and the triplet states are highly sensitive to the basis-set quality as well as level of correlation, and demand for inclusion of perturbative triples in the coupled-cluster ansatz.

In this paper, we have presented and analyzed the extended coupled cluster (ECC) energy functional, truncated up to nth perturbation order in which expansion is limit to operators of the single and double excitations. The expression for the first order energy derivatives based on the above truncation schemes has been derived and numerically analyzed. We have done a comparative study for dipole moment in various perturbative ECC (n) methods (2 <= n <= 5) for three systems (HF, H2O and BH) at equilibrium geometry. We have particularly studied two variants of ECC (4) and ECC (5*) method for stretched geometry. We have analyzed the contribution of important terms present in ECC functional based on perturbative argument. We have compared our results with standard coupled cluster (CCSD) as well as cubic truncated ECC and also benchmarked with the full CI results wherever available. (c) 2013 Elsevier B.V. All rights reserved.

This article presents an open-source object-oriented C++ library of classes and routines to perform tensor algebra.The primary purpose of the library is to enable post-Hartree–Fock electronic structure methods; however, the code is general enough to be applicable in other areas of physical and computational sciences. The library supports tensors of arbitrary order (dimensionality), size, and symmetry. Implemented data structures and algorithms operate on large tensors by splitting them into smaller blocks, storing them both in core memory and in files on disk, and applying divide-and-conquer-type parallel algorithms to perform tensor algebra. The library offers a set of general tensor symmetry algorithms and a full implementation of tensor symmetries typically found in electronic structure theory: permutational, spin, and molecular point group symmetry. The Q-Chem electronic structure software uses this library to drive coupled-cluster, equation-of-motion, and algebraic-diagrammatic construction methods.

Electronic structure of 2,4,6-tridehydropyridine and isoelectronic 1,3,5-tridehydrobenzene is characterized by the equation-of-motion spin-flip coupled-cluster calculations with single and double substitutions and including perturbative triple corrections. Equilibrium geometries of the three lowest electronic states, vertical and adiabatic states ordering, and triradical stabilization energies are reported for both triradicals. In 1,3,5-tridehydrobenzene, the ground (2)A(1) state is 0.016 eV below the (2)B(2) state, whereas in 2,4,6-tridehydropyridine the heteroatom reverses adiabatic state ordering bringing (2)B(2) below (2)A(1) by 0.613 eV. The adiabatic doublet-quartet gap of 2,4,6-tridehydropyridine is smaller than that of 1,3,5-tridehydrobenzene by 0.08 eV; the respective values are 1.223 and 1.302 [corrected] eV. Moreover, the heteroatom reduces bonding interactions between the C(2) and C(6) radical centers, which results in the increased stabilizing interactions between C(4) and C(2)/C(6). Triradical stabilization energies corresponding to the separation of C(4) and C(2) are 19.7 and -0.2 kcal/mol, respectively, in contrast to 2.8 kcal/mol in 1,3,5-tridehydrobenzene. Similarly weak interactions between C(2) and C(6) are also observed in 2,6-didehydropyridine resulting in a nearly zero singlet-triplet energy gap, in contrast to m-benzyne and 2,4-didehydropyridine. The total interaction energy of the three radical centers is very similar in 1,3,5-tridehydrobenzene and 2,4,6-tridehydropyridine and is 19.5 and 20.1 kcal/mol, respectively.

Multi-reference coupled cluster methods are established as accurate and efficient tools for describing electronic structure of quasi degenerate states. Recently we have developed multi-reference coupled cluster linear response approach based on the constrained variation method. The method is very general and can describe challenging problems due to the multiple-root nature of effective Hamiltonian. Calculation of response properties for the ionized/electron attached or excited state molecules is a challenging task. With this formulation it is possible to accurately predict the higher order molecular properties of the open shell molecules. In this article we review the response approaches for quasi degenerate cases with emphasis on Fock space multi-reference coupled cluster method.

Fock space multireference coupled-cluster (FSMRCC) method emerged as an efficient tool to describe the electronic structure of nearly degenerate cases. Development of linear response has been one of the challenging problems in FSMRCC due to the multiple-root nature of the effective Hamiltonian. A response from any of the roots would span the space for getting the properties. Hence, all roots perturbed by the external field would proliferate the excited states. We recently developed the FSMRCC method for the efficient evaluation of analytic response properties using a constrained variation approach. In this paper, we present analytic dipole moments and polarizabilities of H(2)O, O(3), and CH(+) molecules in low-lying excited states along with brief discussion of singlet triplet decoupling of (1,1) sector of FSMRCC resulting from spin adaptation.

A noniterative N(6) triples energy correction is presented for the equation-of-motion coupled-cluster method with single and double substitutions for ionized states (EOM-IP-CCSD). The correction, which is size intensive, is derived using a second-order Rayleigh-Schrodinger perturbative treatment and is similar to the approach of Stanton and Gauss [Theor. Chim. Acta 93, 303 (1996)]. In the present implementation, only the target EOM-IP states are corrected, and the reference state is described by CCSD; the method is therefore more useful for the study of the target states themselves than ionization potentials. The performance of the correction, which demonstrates the caveat above, is demonstrated by applications to singlet methylene, BNB(-), nitrogen, carbon monoxide, acetylene, benzene, thymine, and adenine.

A noniterative N (7) triples correction for the equation-of-motion coupled-cluster method with single and double substitutions (CCSD) is presented. The correction is derived by second-order perturbation treatment of the similarity-transformed CCSD Hamiltonian. The spin-conserving variant of the correction is identical to the triples correction of Piecuch and co-workers [Mol. Phys. 104, 2149 (2006)] derived within method-of-moments framework and is not size intensive. The spin-flip variant of the correction is size intensive. The performance of the correction is demonstrated by calculations of electronic excitation energies in methylene, nitrenium ion, cyclobutadiene, ortho-, meta-, and para-benzynes, 1,2,3-tridehydrobenzene, as well as C-C bond breaking in ethane. In all cases except cyclobutadiene, the absolute values of the correction for energy differences were 0.1 eV or less. In cyclobutadiene, the absolute values of the correction were as large as 0.4 eV. In most cases, the correction reduced the errors against the benchmark values by about a factor of 2-3, the absolute errors being less than 0.04 eV.