Browsing by Author "Schwerdtfeger P"

Now showing 1 - 9 of 9
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    Bis-Anagostic Structures in N,N’-Chelate Ligand Complexes of Palladium(II)
    (Wiley-VCH Verlag, 2022-04) Sajjad MA; Schwerdtfeger P; Cai Y; Waters JM; Harrison JA; Nielson AJ
    Reaction of N,N’-dibenzylidene-2,2-dimethylpropylenediamine with Pd(OAc)2 produces essentially one product which NMR spectroscopy indicates has a bis-anagostic structure. A density functional theory (DFT) calculation shows that in the square planar structure, both aromatic rings lie above the coordination plane with close approaches of two ortho-C−H bond hydrogens to both the Pd centre and the two acetato ligand coordinating oxygen atoms. N,N’-dibenzylideneethylenediamine reacts with Pd(OAc)2 similarly where a bis-anagostic structure is indicated by NMR spectroscopy and a DFT calculation shows an energy preference for an above plane positioning of the two aromatic rings. N,N,N’,N’-tetrabenzylethylenediamine reacts with Pd(OAc)2 to give a structure which X-ray crystallography shows two benzyl phenyl groups lie above and below the coordination plane respectively.
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    Erratum: Multicenter integrals over long-range operators using Cartesian Gaussian functions [Phys. Rev. A 37, 2834 (1988)]
    (American Physical Society, 2021-06-01) Schwerdtfeger P; Silberbach H
    The group headed by Glover and co-workers [1] came across a rather subtle error in our evaluation of the multicenter integrals over long-range operators using Cartesian Gaussian functions arising from the incorrect use of infinities in the alternating series (39) of our original paper. The correction adds an additional term to (48) and, subsequently, to (37) for the H(1,a) term. To show this, we remember the original limit for the integral in Eq. (34) [subcase 2] and substitute correctly for the integration range (Formula Presented).
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    Exclusively Relativistic: Periodic Trends in the Melting and Boiling Points of Group 12
    (Wiley-VCH GmbH, 2021-03-29) Mewes J-M; Schwerdtfeger P
    First-principles simulations can advance our understanding of phase transitions but are often too costly for the heavier elements, which require a relativistic treatment. Addressing this challenge, we recently composed an indirect approach: A precise incremental calculation of absolute Gibbs energies for the solid and liquid with a relativistic Hamiltonian that enables an accurate determination of melting and boiling points (MPs and BPs). Here, we apply this approach to the Group 12 elements Zn, Cd, Hg, and Cn, whose MPs and BPs we calculate with a mean absolute deviation of only 5 % and 1 %, respectively, while we confirm the previously predicted liquid aggregate state of Cn. At a non-relativistic level of theory, we obtain surprisingly similar MPs and BPs of 650±30 K and 1250±20 K, suggesting that periodic trends in this group are exclusively relativistic in nature. Ultimately, we discuss these results and their implication for Groups 11 and 14.
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    From sticky-hard-sphere to Lennard-Jones-type clusters
    (American Physical Society, 2018-04-24) Trombach L; Hoy RS; Wales DJ; Schwerdtfeger P
    A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.
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    Gregory-Newton problem for kissing sticky spheres
    (American Physical Society, 2018-09-28) Trombach L; Schwerdtfeger P
    All possible nonisomorphic arrangements of 12 spheres kissing a central sphere (the Gregory-Newton problem) are obtained for the sticky-hard-sphere (SHS) model and subsequently projected by geometry optimization onto a set of structures derived from an attractive Lennard-Jones (LJ) type of potential. It is shown that all 737 derived SHS contact graphs corresponding to the 12 outer spheres are (edge-induced) subgraphs of the icosahedral graph. The most widely used LJ(6,12) potential has only one minimum structure corresponding to the ideal icosahedron where the 12 outer spheres do not touch each other. The point of symmetry breaking away from the icosahedral symmetry towards the SHS limit is obtained for general LJ(a,b) potentials with exponents a,b R+. Only if the potential becomes very repulsive in the short range, determined by the LJ hard-sphere radius σ, are symmetry-broken solutions observed.
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    Oganesson: A Noble Gas Element That Is Neither Noble Nor a Gas
    (Wiley-VCH GmbH, 2020-12-21) Smits OR; Mewes J-M; Jerabek P; Schwerdtfeger P
    Oganesson (Og) is the last entry into the Periodic Table completing the seventh period of elements and group 18 of the noble gases. Only five atoms of Og have been successfully produced in nuclear collision experiments, with an estimate half-life for ²⁹⁴⁄₁₁₈ Og of 0. 69⁺⁰‘⁶⁴⁄⁻₀¸₂₂ ms.⁽¹⁾ With such a short lifetime, chemical and physical properties inevitably have to come from accurate relativistic quantum theory. Here, we employ two complementary computational approaches, namely parallel tempering Monte-Carlo (PTMC) simulations and first-principles thermodynamic integration (TI), both calibrated against a highly accurate coupled-cluster reference to pin-down the melting and boiling points of this super-heavy element. In excellent agreement, these approaches show Og to be a solid at ambient conditions with a melting point of ≈325 K. In contrast, calculations in the nonrelativistic limit reveal a melting point for Og of 220 K, suggesting a gaseous state as expected for a typical noble gas element. Accordingly, relativistic effects shift the solid-to-liquid phase transition by about 100 K.
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    Pushing the limits of the periodic table — A review on atomic relativistic electronic structure theory and calculations for the superheavy elements
    (Elsevier B.V., 2023-10-13) Smits OR; Indelicato P; Nazarewicz W; Piibeleht M; Schwerdtfeger P; Schwenk A
    We review the progress in atomic structure theory with a focus on superheavy elements and their predicted ground state configurations important for an element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is essential to correctly solve the Dirac equation in strong Coulomb fields, and to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge Zcrit≈170, where levels such as the 1s shell dive into the negative energy continuum (Enκ<−mec2). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.
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    The Madelung constant in N dimensions
    (Royal Society, 2022-11-30) Burrows A; Cooper S; Schwerdtfeger P
    We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and the number of representations of an integer as a sum of squares for N-dimensional Madelung constants, MN(s), where s is the exponent of the Madelung series (usually chosen as s=1/2). The convergence of the Bessel function expansion is discussed in detail. Values for MN(s) for s=1/2,3/2,3 and 6 for dimension up to N=20 are presented. This work extends Zucker's original analysis on N-dimensional Madelung constants for even dimensions up to N=8.
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    Tipping the Balance Between the bcc and fcc Phase Within the Alkali and Coinage Metal Groups.
    (Wiley-VCH GmbH on behalf of Angewandte Chemie International Edition, 2023-10-25) Robles-Navarro A; Jerabek P; Schwerdtfeger P
    Why the Group 1 elements crystallize in the body-centered cubic (bcc) structure, and the iso-electronic Group 11 elements in the face-centered cubic (fcc) structure, remains a mystery. Here we show that a delicate interplay between many-body effects, vibrational contributions and dispersion interactions obtained from relativistic density functional theory offers an answer to this long-standing controversy. It also sheds light on the Periodic Table of Crystal Structures. A smooth diffusionless transition through cuboidal lattices gives a detailed insight into the bcc→fcc phase transition for the Groups 1 and 11 elements.