Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies

Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2

Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.

Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory

A new theoretical approach for the simulations of X-ray photoelectron spectra of strongly correlated molecular systems that combines multireference algebraic diagrammatic construction theory (MR-ADC) with a core–valence separation (CVS) technique.

Multireference Algebraic Diagrammatic Construction Theory for Excited States: Extended Second-Order Implementation and Benchmark

We present an implementation and benchmark of new approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems (MR-ADC). Following our work on the first-order MR-ADC approximation [J. Chem. Phys. 2018, 149, 204113], we report the strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X) that combine the description of static and dynamic electron correlation in the ground and excited electronic states without relying on state-averaged reference wave functions. We present an extensive benchmark of the new MR-ADC methods for excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Our results demonstrate that, for weakly correlated electronic states, the MR-ADC(2) and MR-ADC(2)-X methods outperform the third-order single-reference ADC approximation and are competitive with the results from equation-of-motion coupled cluster theory. For states with multireference character, the performance of the MR-ADC methods is similar to that of an N-electron valence perturbation theory. In contrast to conventional multireference perturbation theories, the MR-ADC methods have many attractive features, such as a straightforward and efficient calculation of excited-state properties and a direct access to excitations outside of the frontier (active) orbitals.

Symmetry-Adapted Perturbation with Half-Projection for Spin Unrestricted Geminals

Perturbative correction to a wave function built from singlet-triplet mixed two-electron functions (geminals) is derived in the context of symmetry-adapted schemes, applying partial spin-projection. Imposing the constraint of strong orthogonality of geminals results in a reference function that captures static correlation in a computationally feasible way. In case of a lack of spin purification, the product of spin-unrestricted geminals is generally spin-contaminated, potentially undermining performance of a subsequent dynamic correlation treatment. In this work, spin symmetry of the reference is partially restored by half-projection in a variation-after-projection scheme. Applying perturbation theory (PT) to recover the missing part of electron correlation is hampered by the fact that an obvious choice for a zero-order Hamiltonian is not provided. The situation is amended by adopting the formalism of symmetry-adapted PT. The resulting framework is tested on singlet-triplet gaps of biradicaloids, and it is found to perform well in situations where its unprojected counterpart fails because of spin contamination.

Improving half-projected spin-contaminated wave functions by multi-configuration perturbation theory

Allowing triplet components of individual geminals, spin-contaminated strongly orthogonal geminal wave functions may emerge, which can be ameliorated by spin-projection techniques. Of the latter, half-projection was previously shown to be useful, offering a compromise between the amount of remaining spin-contamination and the violation of size consistency generated by projection. This paper investigates how a half-projected spin-contaminated geminal wave function can be improved by multi-configuration perturbation theory to incorporate dynamical correlation effects.

The ortho-benzyne cation is not planar

A recent review on the photoionisation of the C₆H₄ isomer ortho-benzyne suggests that bands reported in earlier photoelectron spectra might be due to side products or contaminations, while computations raise doubts, whether the cation has a planar geometry. We therefore reinvestigate the photoionisation of ortho-benzyne, generated by pyrolysis from benzocyclobutenedione, by photoion mass-selected threshold photoelectron (ms-TPE) spectroscopy using synchrotron radiation. The experiments are accompanied by a theoretical study that investigates the structure of the ortho-benzyne cation systematically as a function of the computational method, up to CASPT2(11,14) ab initio computations. Our study leads to a re-evaluation of the ionisation energy of ortho-benzyne. It reveals that the ortho-benzyne cation has indeed a twisted C₂ geometry rather than a C_2v structure. A vertical ionisation energy IE_vert of 9.77 eV and an adiabatic ionisation energy of IE_ad = 9.56 eV are computed for ortho-benzyne. A Franck-Condon simulation of the photoelectron spectrum based on the CASPT2 results and including three electronic states of the cation is in agreement with the experiment and yields IE_ad = 9.51 eV (+50 meV/-100 meV). Since this value is in contrast with previous work, the ionisation energy has to be revised based on our study. Computational methods based on density functional theory give a reasonable description of the cationic ground state, but fail for the corresponding excited electronic states that are indispensible for a proper assignment of the photoelectron spectrum.

Iterative universal state selective correction for the Brillouin-Wigner multireference coupled-cluster theory

As a further development of the previously introduced a posteriori Universal State-Selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011); J. Brabec et al., ibid. 136, 124102 (2012)], we suggest an iterative form of the USS correction by means of correcting effective Hamiltonian matrix elements. We also formulate USS corrections via the left Bloch equations. The convergence of the USS corrections with excitation level towards the full configuration interaction (FCI) limit is also investigated. Various forms of the USS and simplified diagonal USS corrections at the singles and doubles and perturbative triple levels are numerically assessed on several model systems and on the ozone and tetramethyleneethane molecules. It is shown that the iterative USS correction can successfully replace the previously developed a posteriori Brillouin-Wigner coupled cluster size-extensivity correction, while it is not sensitive to intruder states and performs well also in other cases when the a posteriori one fails, like, e.g., for the asymmetric vibration mode of ozone.