Full triples contribution in coupled-cluster and equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields

Hampe, Florian; Gross, Niklas; Stopkowicz, Stella

doi:10.1039/d0cp04169f

Cited by 28 publications

(39 citation statements)

References 47 publications

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“…Given the immense computational cost of the latter two methods, only results for a single diatomic molecule, namely CH + , have been reported for EOM-CCSDT so far in a finite magnetic field. ( Hampe et al, 2020 ). RI-CC2 as computational efficient method is therefore a suitable compromise, providing robust values.…”

Section: Resultsmentioning

confidence: 99%

“…Furthermore, the complex gauge-independent London atomic orbitals lead to another steep increase in the computational complexity, effectively preventing calculations on systems with more than a few electrons. ( Hampe and Stopkowicz, 2017 ; Hampe et al, 2020 ). Even though the computational limitations are severe, the investigation of molecular properties in strong external magnetic fields has become an increasingly popular topic within the field of quantum chemistry in recent years.…”

Section: Introductionmentioning

confidence: 99%

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The GW/BSE Method in Magnetic Fields

2021

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The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The GW/BSE Method in Magnetic Fields

2021

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“…27, the CD can also successfully be applied in more sophisticated post-HF methods. As the basis-set error is often the limiting factor in terms of accuracy in high-level ff calculations, the combination of CD with ff ground-state and excited-state coupledcluster methods 42,43,50,54,90 will be a beneficial future direction of development.…”

Section: Discussionmentioning

confidence: 99%

Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields

Blaschke,

Stopkowicz

2021

Preprint

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In large-scale quantum-chemical calculations the electron-repulsion integral (ERI) tensor rapidly becomes the bottleneck in terms of memory and disk space. When an external finite magnetic field is employed, this problem becomes even more pronounced because of the reduced permutational symmetry and the need to work with complex integrals and wave-function parameters. One way to alleviate the problem is to employ a Cholesky decomposition (CD) to the complex ERIs over gauge-including atomic orbitals. The CD scheme establishes favourable compression rates by selectively discarding linearly dependent product densities from the chosen basis set while maintaining a rigorous and robust error control. This error control constitutes the main advantage over conceptually similar methods such as density fitting which rely on employing pre-defined auxiliary basis sets. We implemented the use of the CD in the framework of finite-field (ff) Hartree-Fock and ff second-order Møller Plesset perturbation theory. Our work demonstrates that the CD compression rates are particularly beneficial in calculations in the presence of a finite magnetic field. The ff-CD-MP2 scheme enables the correlated treatment of systems with more than 2000 basis functions in strong magnetic fields within a reasonable time span.

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“…They are different for traditional nonrelativistic CC calculations and those that incorporate relativistic effects, 21 and for cases in which a finite magnetic field is present. [9][10][11]22 For our discussion the general representation given in Eq. ( 4) is sufficient.…”

Section: B Coupled-cluster Theorymentioning

confidence: 99%

“…Apart from re-sults that are already discussed in the literature, this approach also leads to additional knowledge about the shape of the potential surfaces near conical intersections and about the occurrence of complex eigenvalues in the case of Hamiltonian matrices with complex-valued entries. The latter allows us to draw conclusions about the occurrence of complex energy values in the case of CC calculations for systems in a finite magnetic field [9][10][11] and for relativistic CC calculations that include spin-orbit coupling. [12][13][14][15] The present work begins with a discussion of a several mathematical definitions and theorems needed for our investigation, like the perturbative analysis of the eigenvalues of a matrix.…”

Section: Introductionmentioning

confidence: 99%

Complex Ground-State and Excitation Energies in Coupled-Cluster Theory

Thomas,

Hampe,

Stopkowicz

et al. 2021

Preprint

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Since in coupled-cluster (CC) theory ground-state and excitation energies are eigenvalues of a non-Hermitian matrix, these energies can in principle take on complex values. In this paper we discuss the appearance of complex energy values in CC calculations from a mathematical perspective. We analyze the behaviour of the eigenvalues of Hermitian matrices that are perturbed (in a non-Hermitian manner) by a real parameter. Based on these results we show that for CC calculations with real-valued Hamiltonian matrices the ground-state energy generally takes a real value. Furthermore, we show that in the case of real-valued Hamiltonian matrices complex excitation energies only occur in the context of conical intersections. In such a case, unphysical consequences are encountered such as a wrong dimension of the intersection seam, large numerical deviations from full configuration-interaction (FCI) results, and the square-root-like behaviour of the potential surfaces near the conical intersection. In the case of CC calculations with complex-valued Hamiltonian matrix elements, it turns out that complex energy values are to be expected for ground and excited states when no symmetry is present. We confirm the occurrence of complex energies by sample calculations using a six-state model and by CC calculations for the H2O molecule in a strong magnetic field. We furthermore show that symmetry can prevent the occurrence of complex energy values. Lastly, we demonstrate that in most cases the real part of the complex energy values provides a very good approximation to the FCI energy.

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Full triples contribution in coupled-cluster and equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields

Abstract: Finite-field EOM-CCSDT: a highly accurate method for the theoretical prediction of excitation energies and electronic spectra in strong magnetic fields.

Cited by 28 publications

References 47 publications

The GW/BSE Method in Magnetic Fields

The GW/BSE Method in Magnetic Fields

Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields

Complex Ground-State and Excitation Energies in Coupled-Cluster Theory

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