https://zenodo.org/record/1258869/files/article.pdf

NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations

This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential

Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold

Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.

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Coupled-cluster theory in quantum chemistry

Single-reference ab initio methods for the calculation of excited states of large molecules.

A comprehensive overview of the equation of motion coupled‐cluster (EOM‐CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM‐CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single‐reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled‐cluster density matrices, providing a link between EOM‐CC and traditional ground state CC theory.Excitation energy,oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.

The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties

The equation-of-motion coupled-cluster method: Excitation energies of Be and CO

An open-shell spin-restricted coupled cluster method: application to ionization potentials in nitrogen

A multireference coupled‐cluster (MRCC) formulation for the direct calculation of excitation energies and ionization potentials is presented. The reference space connects a set of p–h excited determinants built from all the set of active particles and holes in the model space. This model space is incomplete, requiring a Fock‐space approach and the postulate of a ‘‘universal’’ wave operator to arrive at a linked diagram expression for the effective Hamiltonian Heff, whose eigenvalues are the excitation energies for the problem. Use of a normal‐ordered exponential cluster ansatz allows one to construct, hierarchically, the CC equations for the p–h model space starting from the ground state. We present an extension of an earlier formulation for excitation energies that allows us to have both active and inactive particles and holes in our method. Numerical applications are reported for the prototypical small molecules CO and N2.

Molecular applications of multireference coupled-cluster methods using an incomplete model space: Direct calculation of excitation energies

Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde

Weyl's theory for a singular second-order differential equation and the complex scaling method of Balslev and Combes are combined to obtain a stable method for describing the continuous spectrum. The method obtained can be viewed as an extension of the Siegert method. The theory is applied to a model potential earlier used by Moiseyev et al.

Magnus Rittby

Papers

The equation-of-motion coupled-cluster method: Excitation energies of Be and CO

An open-shell spin-restricted coupled cluster method: application to ionization potentials in nitrogen

Molecular applications of multireference coupled-cluster methods using an incomplete model space: Direct calculation of excitation energies

Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde

Weyl's theory and the complex-rotation method applied to phenomena associated with a continuous spectrum