Multiconfigurational second‐order perturbation theory: A test of geometries and binding energies

Andersson, Kerstin; Roos, Björn O.

doi:10.1002/qua.560450610

Cited by 231 publications

(197 citation statements)

References 38 publications

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“…UDFT exaggerates the splitting (Table 1, numbers in parentheses) somewhat because the triplet state is better described than the singlet state. CAS-DFT underestimates the splitting, however the value of 6.9 kcal/mol is still better than that of CASPT2 [51] and other high level calculations [48]. The performance of DFT is a direct reflection of the fact that the biradical character of the 1 A 1 state of 1 is rather small (8.7 % at GVB-DFT; 8.8 % at CAS-DFT, see Table 1).…”

Section: Description Of Open Shell Singlet Biradicals By Dft: Principmentioning

confidence: 86%

Can Unrestricted Density-Functional Theory Describe Open Shell Singlet Biradicals?

Gräfenstein

Kraka

Filatov

et al. 2002

IJMS

192

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Unrestricted density functional theory (UDFT) can be used for the description of open-shell singlet (OSS) biradicals provided a number of precautions are considered. Biradicals that require a two-determinantal wave function (e.g. OSS state of carbenes) cannot be described by UDFT for principal reasons. However, if the overlap between the open-shell orbitals is small (the single electrons are located at different atomic centers) errors become small and, then, the principal failure of UDFT in these cases is not apparent and may even be disguised by the fact that UDFT has the advantage of describing spin polarization better than any restricted open shell DFT method. In the case of OSS biradicals with two-or multiconfigurational character (but a onedeterminantal form of the leading configuration), reasonable results can be obtained by broken-symmetry (BS)-UDFT, however in each case this has to be checked. In no case is it reasonable to lower the symmetry of a molecule to get a suitable UDFT description. Hybrid functionals such as B3LYP perform better than pure DFT functionals in BS-UDFT calculations because the former reduce the self-interaction error of DFT exchange functionals, which mimics unspecified static electron correlation effects, so that the inclusion of specific static electron correlation effects via the form of the wavefunction becomes more effective.

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Section: Description Of Open Shell Singlet Biradicals By Dft: Principmentioning

confidence: 86%

Can Unrestricted Density-Functional Theory Describe Open Shell Singlet Biradicals?

Gräfenstein

Kraka

Filatov

et al. 2002

IJMS

192

View full text Add to dashboard Cite

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“…Use was made of the so called g2 Fock matrix formulation correction 49 to remove the systematic error related to differences in the number of closed shell ͑paired͒ electrons ͑i.e., doubly occupied orbitals͒ in the case of CASPT2 calculations. 50 In these multiconfigurational calculations, all electrons ͑including the core levels͒ were correlated. The employed active space encompasses the whole band systems of naphthalene ͑10 electrons in 10 spin orbitals͒ and anthracene ͑14 electrons in 14 spin orbitals͒.…”

Section: Methodology and Computationsmentioning

confidence: 99%

A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes

Hajgató

Szieberth

Geerlings

et al. 2009

The Journal of Chemical Physics

194

216

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A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet ͑ST͒ excitation energies of benzene ͑n =1͒ and n-acenes ͑C 4n+2 H 2n+4 ͒ ranging from naphthalene ͑n =2͒ to heptacene ͑n =7͒ is presented, on the ground of single-and multireference calculations based on restricted or unrestricted zero-order wave functions. High-level and large scale treatments of electronic correlation in the ground state are found to be necessary for compensating giant but unphysical symmetry-breaking effects in unrestricted single-reference treatments. The composition of multiconfigurational wave functions, the topologies of natural orbitals in symmetry-unrestricted CASSCF calculations, the T1 diagnostics of coupled cluster theory, and further energy-based criteria demonstrate that all investigated systems exhibit a 1 A g singlet closed-shell electronic ground state. Singlet-triplet ͑S 0 -T 1 ͒ energy gaps can therefore be very accurately determined by applying the principles of a focal point analysis onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets ͑X=D, T, Q, 5͒ and single-reference methods ͓HF, MP2, MP3, MP4SDQ, CCSD, CCSD͑T͔͒ of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations ͓CCSD͑T͔͒ in the limit of an asymptotically complete basis set ͑cc-pVϱZ͒, the S 0 -T 1 vertical excitation energies of benzene ͑n =1͒ and n-acenes ͑n =2-7͒ amount to 100.79, 76.28, 56.97, 40.69, 31.51, 22.96, and 18.16 kcal/mol, respectively. Values of 87.02, 62.87, 46.22, 32.23, 24.19, 16.79, and 12.56 kcal/mol are correspondingly obtained at the CCSD͑T͒ / cc-pVϱZ level for the S 0 -T 1 adiabatic excitation energies, upon including B3LYP/cc-PVTZ corrections for zero-point vibrational energies. In line with the absence of Peierls distortions, extrapolations of results indicate a vanishingly small S 0 -T 1 energy gap of 0 to ϳ4 kcal/ mol ͑ϳ0.17 eV͒ in the limit of an infinitely large polyacene.

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“…Then the cluster is studied using correlated ab initio calculations and large basis sets [13]. MS-CASPT2 calculations [14] (the many-body second order perturbation scheme of the MOLCAS code [15] J1 J2 t J error (%) Heisenberg 0.59 0.07 --3.3 Double exchange --1.05 0.07 3. 3 TABLE I: Effective interactions (in eV) of the two models extracted from the ab initio spectrum and errors of the corresponding predicted spectrum compared to the ab initio one.…”

Section: − 11mentioning

confidence: 99%

Relation between double exchange and Heisenberg model spectra: Application to the half-doped manganites

2007

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The Zener polarons recently found in half-doped manganites are usually seen as mixed valence entities ruled by a double exchange Hamiltonian involving only correlated electrons of the metals. They can however be considered as ferrimagnetic local units if the holes are localized on the bridging oxygen atoms as implicitely suggested by recent mean-field ab initio calculations. In the latter case, the physics is ruled by a Heisenberg Hamiltonian involving magnetic oxygen bridges. This paper shows that the spectra resulting from the resolution of both models are analytically identical. This single resulting model spectrum accurately reproduces the spectrum of Zener polarons in Pr0.6Ca0.4MnO3 manganite studied by means of explicitely correlated ab initio calculations. Since the physics supported by each model are different, the analysis of the exact Hamiltonian ground state wave function should a priori enables one to determine the most appropriate model. It will be shown that neither the spectrum nor the wavefunction analysis bring any decisive arguments to settle the question. Such undecidability would probably be encountered in experimental information. [6,7] show an important O to Mn charge transfer, resulting in a localization of the holes on the bridging oxygens. This charge distribution suggests a dominant purely magnetic local order (Mn 3+ O − Mn 3+ ) in which the Zener polarons would be ferrimagnetic entities involving an antiferromagnetic coupling between the magnetic oxygen and the high spin manganese centers. In the latter case the model Hamiltonian which provides a relevant description of the local electronic order is a Heisenberg Hamiltonian. The holes localization has been a matter of debate in the literature and concerns a large number of materials like doped cuprates [8](where there is at most one unpaired electron per metal resulting in a t-J model), nickelates or manganites (in which there are several open-shells per center leading to a double exchange interaction). Besides, as far as the correlated electrons are only localized on the metallic centers, the comparison of the models has been the subject of intense discussion and controversy which ended up with the demonstration that the two models were strictly different and lead to different spectra [9]. The aim of this paper is to show that when considering a magnetic oxygen in the Heisenberg model the analytical resolution of the two Hamiltonians leads to identical spectra. For this purpose we have derived an analytical solution of the Heisenberg Hamiltonian energies for three magnetic centers.Since the discrimination between the two models is impossible from the spectrum determination, we will then adress this question from wavefunction analysis. Indeed, the projection of the ab initio ground state wavefunction onto both model spaces should a priori determine the choice. However, it will be shown that when the charge of the oxygen is around -1.5, the wavefunction analysis does not infer any decidable argument. In order to illustrate this asserti...

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Multiconfigurational second‐order perturbation theory: A test of geometries and binding energies

Cited by 231 publications

References 38 publications

Can Unrestricted Density-Functional Theory Describe Open Shell Singlet Biradicals?

Can Unrestricted Density-Functional Theory Describe Open Shell Singlet Biradicals?

A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes

Relation between double exchange and Heisenberg model spectra: Application to the half-doped manganites

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