Approximating electronically excited states with equation-of-motion linear coupled-cluster theory

A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order M{\o}ller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory (EOM-MBPT(2)) equations and two new equation-of-motion methods based on the linear coupled-cluster doubles (EOM-LCCD) and linear coupled-cluster singles and doubles (EOM-LCCSD) wavefunctions. This is achieved by performing a short-circuiting procedure on the MBPT(2) similarity transformed Hamiltonian. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical EOM-CCSD state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.Comment: 9 pages 3 figure

A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory

We revisit the connection between equation-of-motion coupled cluster (EOM-CC) and random phase approximation (RPA) explored recently by Berkelbach [J. Chem. Phys. 149, 041103 (2018)] and unify various methodological aspects of these diverse treatments of ground and excited states. The identity of RPA and EOM-CC based on the ring coupled cluster doubles is established with numerical results, which was proved previously on theoretical grounds. We then introduce new approximations in EOM-CC and RPA family of methods, assess their numerical performance, and explore a way to reap the benefits of such a connection to improve on excitation energies. Our results suggest that addition of perturbative corrections to account for double excitations and missing exchange effects could result in significantly improved estimates

A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory

We revisit the connection between equation-of-motion coupled cluster (EOM-CC) and random phase approximation (RPA) explored recently by Berkelbach [J. Chem. Phys. 149, 041103 (2018)] and unify various methodological aspects of these diverse treatment of ground and excited states. The identity of RPA and EOM-CC based on the ring coupled cluster doubles is established with numerical results which was proved previously on theoretical grounds. We then introduce new approximations in EOM-CC and RPA family of methods, assess their numerical performance and explore a way to reap the benefits of such a connection to improve on excitation energies. Our results suggest that addition of perturbative corrections to account for double excitations and missing exchange effects could result in significantly improved estimates

Structure and stability of the AlX and AlX- species

The electronic and geometrical structures of the ground and low-lying excited states of the diatomic AlX and AlX− series (X=H, Li, Be, B, C, N, O, and F) are calculated by the coupled-cluster method with all singles and doubles and noniterative inclusion of triples using a large atomic natural orbital basis. All the ground-state AlX molecules except for AlF can attach an additional electron and form ground-state AlX− anions. The ground-state AlBe−, AlB−, AlC−, AlN−, and AlO− anions possess excited states that are stable toward autodetachment of an extra electron; AlBe− also has a second excited state. Low-lying excited states of all AlX but AlN can attach an extra electron and form anionic states that are stable with respect to their neutral (excited) parent states. The ground-state AlLi−, AlBe−, AlB−, AlN−, and AlO− anions are found to be thermodynamically more stable than their neutral parents. The most stable is AlO−, whose dissociation energy to Al+O− is 6.4 eV. Correspondingly, AlO possesses the largest electron affinity (2.65 eV) in the series

Thermodynamical stability of CH3ONO and CH3ONO-: A coupled-cluster and Hartree-Fock-density-functional-theory study

The structure and thermodynamic stability of methylnitrite and its anion are studied by the infinite-order coupled-cluster method with all singles and doubles and noniterative inclusion of triple excitations [CCSD(T)] and Hartree–Fock-density-functional theory (HFDFT). We have optimized the geometries and computed the harmonic vibrational frequencies of major fragments, H2, CH, NH, OH, CN, N2, CO, NO, O2, CH2, NH2, H2O, HCN, HNC, HCO, HNO, O2H, CO2, NO2, CH3, NH3, CNH2, HCO2, HNO2, CH3N, CH3O, CH3NO, CH3ON, CH2NO2, and their anions, when the latter exist. Fragmentation energies obtained at both levels of theory are rather close to each other, except for channels involving CN as a product. The CH3ONO− and CH3NO−2 anions are shown to possess lower fragmentation energies than their neutral parents. This implies that the attachment of an extra electron to CH3NO2 or CH3ONO may have a crucial role in initiating the decomposition of these compounds. Also, the attachment of an extra electron to CH3NO2 or CH3ONO leads to the appearance of new exothermic decay channels of the anions

Search for “quadrupole-bound” anions. I

In a classical model, some anions exist due to the attraction between an electron and a molecule’s dipole moment. When the dipole moment is sufficiently large (μcrit\u3e2.5 D), an electron can be trapped. Can a sufficiently large quadrupole moment produce the same effect? To help answer this question, we can search for molecules with a large quadrupole moment and use predictive, ab initio, correlated quantum chemistry methods to assess whether an anion forms and, if it does, to discover its nature. For this purpose, coupled-cluster calculations are reported for the structure and properties of KnClm and KnCl−m (n,m=0–2). The KCl2 superhalogen was found to have an electron affinity of 4.2 eV and is stable towards dissociation by 26 kcal/mol. The (KCl)2 dimer has a rhombic ground state with a large electric quadrupole moment. Rhombic and linear configurations of the (KCl)−2 anion correspond to stationary states that are nearly degenerate in total energy. The rhombic anion has a single, weakly bound state that could be a “quadrupole-bound” state on the basis of a comparison of its characteristics with those of dipole-bound states. Linear KClKCl− has seven excited states; four of them can be identified as dipole-bound states. KCl and KCl2 possess rather similar dipole moments and their anions have two excited dipole-bound states each

Reference Dependence of the Two-determinant Coupled-cluster Method for Triplet and Open-shell Singlet States of Biradical Molecules

We study the performance of the two-determinant (TD) coupled-cluster (CC) method which, unlike conventional ground-state single-reference (SR) CC methods, can, in principle, provide a naturally spin-adapted treatment of the lowest-lying open-shell singlet (OSS) and triplet electronic states. Various choices for the TD-CC reference orbitals are considered, including those generated by the multi-configurational self-consistent field method. Comparisons are made with the results of high-level SR-CC, equation-of-motion (EOM) CC, and multi-reference EOM calculations performed on a large test set of over 100 molecules with low-lying OSS states. It is shown that in cases where the EOMCC reference function is poorly described, TD-CC can provide a significantly better quantitative description of OSS total energies and OSS-triplet splittings

Single-Reference Coupled Cluster Theory for Multi-Reference Problems

Coupled cluster (CC) theory is widely accepted as the most accurate and generally applicable approach in quantum chemistry. CC calculations are usually performed with single Slater-determinant references, e.g., canonical Hartree-Fock (HF) wavefunctions, though any single determinant can be used. This is an attractive feature because typical CC calculations are straightforward to apply, as there is no potentially ambiguous user input required. On the other hand, there can be concern that CC approximations give unreliable results when the reference determinant provides a poor description of the system of interest, i.e., when the HF or any other single determinant ground state has a relatively low weight in the full CI expansion. However, in many cases, the reported “failures” of CC can be attributed to an unfortunate choice of reference determinant, rather than intrinsic shortcomings of CC itself. This is connected to well-known effects like spin-contamination, wavefunction instability, and symmetry-breaking. In this contribution, a particularly difficult singlet/triplet splitting problem in two phenyldinitrene molecules is investigated, where CC with singles, doubles and perturbative triples [CCSD(T)] was reported to give poor results. This is analyzed by using different reference determinants for CCSD(T), as well as performing higher level CCSDT-3 and CCSDT calculations. We show that doubly electron attached and doubly ionized equation-of-motion (DEA/DIP-EOM) approaches are powerful alternatives for treating such systems. These are operationally single-determinant methods that adequately take the multi-reference nature of these molecules into account. Our results indicate that CC remains a powerful tool for describing systems with both static correlation and dynamic correlation, when pitfalls associated with the choice of the reference determinant are avoided