Atomic Bethe logarithm in the mean-field approximation

In this work we develop and implement a method for calculation of the Bethe logarithm for many-electron atoms. This quantity is required to evaluate the leading-order quantum electrodynamics correction to the energy and properties of atomic and molecular systems beyond the Dirac theory (the Lamb shift). The proposed formalism is based on the mean-field representation of the ground-state electronic wavefunction and of the response functions required in the Schwartz method [C. Schwartz, Phys. Rev. {\bf 123}, 1700 (1961)]. We discuss difficulties encountered in the calculations with the emphasis on the specific basis set requirements in the vicinity of the atomic nucleus. This problem is circumvented by introducing a modified basis set of exponential functions which are able to accurately represent the gradient of hydrogen-like orbitals. The Bethe logarithm is computed for ground electronic states of atoms from hydrogen to magnesium and, additionally, for argon. Whenever possible, the results are compared with the available reference data from the literature. In general, the mean-field approximation introduces a surprisingly small error in the calculated values, suggesting that the electron correlation effects are of minor importance in determination of the Bethe logarithm. Finally, we propose a robust scheme to evaluate the Lamb shift for arbitrary light molecular systems at little computational cost. As an illustration, the method is used to calculate Lamb shifts of the vibrational levels of the nitrogen molecule

Multireferenční CC výpočty s použitím optimalizovaných virtuálních orbitalů

Metóda viazaných klastrov(z ang. Coupled Cluster CC) bola pôvodne vyvinutá Hermannom Kümmlom pre potreby jadrovej fyziky. Následne po Čížkovej a Paldusového úprave sa stala použiteľnou i pre oblasť teoretickej chémie. V priebehu doby sa osvedčila ako jedna z najlepších kvantovo-chemických metód. Úlohou tejto práce je otestovať výsledky multireferenčných CC metód pri použití optimalizovaných orbitálov(OVOS), získaných z jedno-determinatných singletných stavov kvázi-degenerovaných systémov a použitých na dvoj-determinatný tripletový stav.i Abstract The aim of this work is to test the performance of multireference methods using the truncated virtual orbital space as a result when OVOS method is employed. As a guess function, the OVOS wave function is used for the calculations of the two-determinantal state of a quasi-degenerate system. The resulting energies are investigated for different truncation of the virtual orbital space.Katedra fyzikální a makromol. chemieDepartment of Physical and Macromolecular ChemistryPřírodovědecká fakultaFaculty of Scienc

Analysis of amateur and professional football club

katedra: KTV

Aplikace explicitně korelovaných multireferenčních metod spřažených klastrů

*Abstrakt Metody Coupled cluster patří v současnosti mezi standardní kvan- tově-chemické metody. Tyhle metody však nejsou schopny kvali- tativně popsat systémy s kvazidegenerovanými orbitaly, kde je jed- norefereční přístup klasických coupled cluster metod nedostatečný. Tyhle systémy se vyznačují příspěvky statické korelace, na popis které je potřeba využít multireferenční přístup. Multireferenční cou- pled cluster metody vyvinuté v naší skupině jsou schopny popsat jak statickou, tak i dynamickou korelaci a dovolují tak počítat dřív prob- lematické systémy. Ve spojení s explicitní korelací, která je schopna zlepšit popis elektronického cuspu, je možné dosáhnout vynikající výsledky zkonvergované do úplné báze a s méně nasycenými bázemi. Takhle urychlená konvergence je následně uplatněna ve výpočtu do- posud výpočetně náročných systémů. V téhle práci jsou prezen- továny multireferenční coupled cluster výpočty tranzitních stavů izomerizace bicyklobutánu a explicitně korelované výpočty molekuly tetrametylénetánu. 1Nowdays, coupled cluster method belongs to one of the most used quantum chemical methods. However, the single-reference coupled cluster methods are not able to describe systems where the static correlation have an important role. Multireference coupled cluster methods developed in our group can describe both static and dy- namic correlation and can be used for problematic systems. Together with explicitly correlated wavefunction, which can properly describe the electronic cusp and speed up the convergence to the complete ba- sis set limit, they are able to calculate computationally demanding diradicals. Multireference CC calculations of tetramethylenethane have been perforemd and the performance of explicitly correlated version is discussed. Calculations of the isomerization of bicyclobu- tane using the multireference approach are presented as well. 1Department of Physical and Macromolecular ChemistryKatedra fyzikální a makromol. chemiePřírodovědecká fakultaFaculty of Scienc

Collision-induced three-body polarizability of helium

We present first-principles theoretical determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster theory and the full configuration interaction procedure were used to perform required electronic structure calculations. The mean absolute relative uncertainty of the trace of the three-body polarizability tensor, resulting from the incompleteness of orbital basis set, was determined using extrapolation techniques. Additional uncertainty due to approximate treatment of triple and the neglect of higher excitations was estimated using full configuration interaction calculations. An analytic function was developed to describe the behavior of the polarizability and its asymptotic decay to three-atomic and atom-diatom fragmentation channels. We also developed an analytic function describing the local behavior of the total uncertainty of our calculations. Using both fits we calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with available experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K we observed significant discrepancy between the classical results obtained using either the superposition approximation or the ab initio computed polarizability. The theoretical data reported in this work eliminate the main accuracy bottleneck of the development of optical pressure standard and are expected to facilitate further progress in the field of quantum thermal metrologyComment: 30 pages, 7 figure

Hilbert space multireference coupled clusters tailored by matrix product states

The DMRG method, despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. Several approaches to include that in post-DMRG methods exist; in our group we focused on the tailored-CC (TCC) approach. This method works well in many situations, however, in exactly degenerate cases (with two or more determinants of equal weight), it exhibits a bias towards the reference determinant representing the Fermi vacuum. Although in some cases it is possible to use a compensation scheme to avoid this bias for energy differences, as we did in a previous work on the singlet-triplet gap in the tetramethylenethane (TME) molecule, it is certainly a drawback. In order to overcome the single-reference bias of the TCC method, we have developed a Hilbert-space multireference version of tailored CC, which can treat several determinants on an equal footing. We have employed a multireference analysis of the DMRG wave function in the matrix product state form to get the active amplitudes for each reference determinant and their constant contribution to the effective Hamiltonian. We have implemented and compared the performance of three Hilbert-space MRCC variants - the state universal one, and the Brillouin-Wigner and Mukherjee's state specific ones. We have assessed these approaches on the cyclobutadiene and tetramethylenethane (TME) molecules, which are both diradicals with exactly degenerate determinants at a certain geometry. Two DMRG active spaces have been selected based on orbital entropies, while the MRCC active space comprised the HOMO and LUMO orbitals needed for description of the diradical. We have also investigated the sensitivity of the results on orbital rotation of the HOMO-LUMO pair, as it is well known that Hilbert-space MRCC methods are not invariant to such transformations

Near-linear Scaling in DMRG-based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of DMRG-based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO-TCCSD). Compared to the previous LPNO version of the method, the new implementation is more accurate, offers more favorable scaling and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen) and Iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8-99.9% of the total canonical correlation energy which is the improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for Iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.Comment: Updated version: 15 pages. arXiv admin note: text overlap with arXiv:1905.0683

Berlin und Prag: Europa pragmatisch zusammenhalten; deutsch-tschechische Kooperation in Zeiten der Corona-Krise

Auch die Beziehungen zwischen Deutschland und der Tschechischen Republik wur­den von der Ausbreitung des SARS-CoV-2-Virus in Mitleidenschaft gezogen. Dominierendes Thema in den ersten Wochen der Pandemie war die Schließung der Grenzen durch die Tschechische Republik. Die grenzüberschreitende Zusammenarbeit wurde jäh unterbrochen, erst nach und nach konnten Lockerungen erreicht werden. Bald zeigte sich, dass die Corona-Krise auch ein bedeutendes Thema für die europapolitische Komponente des beiderseitigen Verhältnisses sein würde. In der Krise wurde auch sichtbar, dass die sicherheitspolitischen Verschiebungen der letzten Jahre und neue inter­nationale Entwicklungen in das deutsch-tschechische Verhältnis hineinspielen. Beide Länder sollten daher ihre Kommunikationsinstrumente, insbesondere den Strategischen Dialog der Regierungen nutzen, überdies aber auch drängende Herausforderungen wie den Umbau zentraler Industrien gemeinsam reflektieren. (Autorenreferat