Ab initio relativistic lattice energy calculations for fluorides of the 7p series of superheavy elements

Wood, C.P.; Pyper, N.C.

doi:10.1016/0009-2614(81)85637-0

Cited by 30 publications

(16 citation statements)

References 13 publications

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“…This contains both a major term arising from the point charge electrostatic interactions as well contributions arising from the short-range repulsive interactions plus smaller contributions from the ionic dispersive attractions. For two salts, NhF and LvF 2 , the short-range repulsive interactions have been computed using fully relativistic ion wave functions and the total crystal energy calculated as a function of the closest inter-ionic separation to yield predictions for both the lattice energy and the crystal equilibrium geometry [78]. The lattice energies of salts for which such computations have not been performed can be calculated from the Kapustinski equation [29] with the inter-ionic distance evaluated as the sum of the cation and anion radii.…”

Section: The Periodic Table Essence: Relativity and Chemistrymentioning

confidence: 99%

Relativity and the periodic table

Pyper

2020

Phil. Trans. R. Soc. A.

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The periodic table provides a deep unifying principle for understanding chemical behaviour by relating the properties of different elements. For those belonging to the fifth and earlier rows, the observations concerning these properties and their interrelationships acquired a sound theoretical basis by the understanding of electronic behaviour provided by non-relativistic quantum mechanics. However, for elements of high nuclear charge, such as occur in the sixth and higher rows of the periodic table, the systematic behaviour explained by non-relativistic quantum mechanics begins to fail. These problems are resolved by realizing that relativistic quantum mechanics is required in heavy elements where electrons velocities can reach significant fractions of the velocity of light. An essentially non-mathematical description of relativistic quantum mechanics explains how relativity modifies valence electron behaviour in heavy elements. The direct relativistic effect, arising from the relativistic increase of the electron mass with velocity, contracts orbitals of low angular momentum, increasing their binding energies. The indirect relativistic effect causes valence orbitals of high angular momentum to be more effectively screened as a result of the relativistic contraction of the core orbitals. In the alkali and alkaline earths, the s orbital contractions reverse the chemical trends on descending these groups, with heavy elements becoming less reactive. For valence d and f electrons, the indirect relativistic effect enhances the reductions in their binding energies on descending the periodic table. The d electrons in the heavier coinage metals thus become more chemically active, which causes these elements to exhibit higher oxidation states. The indirect effect on d orbitals causes the chemistries of the sixth-row transition elements to differ significantly from the very similar behaviours of the fourth and fifth-row transition series. The relativistic destabilization of f orbitals causes lanthanides to be chemically similar, forming mainly ionic compounds in oxidation state three, while allowing the earlier actinides to show a richer range of chemical behaviour with several higher oxidation states. For the 7p series of elements, relativity divides the non-relativistic p shell of three degenerate orbitals into one of much lower energy with the energies of the remaining two being substantially increased. These orbitals have angular shapes and spin distributions so different from those of the non-relativistic ones that the ability of the 7p elements to form covalent bonds is greatly inhibited. This article is part of the theme issue ‘Mendeleev and the periodic table’.

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Section: The Periodic Table Essence: Relativity and Chemistrymentioning

confidence: 99%

Relativity and the periodic table

Pyper

2020

Phil. Trans. R. Soc. A.

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“…The interionic pair potentials required for this program were computed using the relativistic integrals program. 24,25 This method, after augmentation with descriptions of both the short-range electron correlation and the interionic dispersive attractions, has been shown to provide a good description of bulk ionic crystals [26][27][28][29] including the delicate problem of the relative stabilities of the 6-fold and 8-fold coordinated phases of cesium chloride. 30,31 The methodology is described in the following publications: refs 26, 28, 32, and 33.…”

Section: Predictions From the Basic Born Type Model 311 Approximamentioning

confidence: 99%

Fundamental Global Model for the Structures and Energetics of Nanocrystalline Ionic Solids

Bichoutskaia¹,

Pyper²

2006

J. Phys. Chem. B

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This paper presents a general theory elucidating the relationships between the structures and cohesive energetics of alkali halide nanocrystals consisting of small sections of bulk rocksalt structures with m(1) and m(2) rows but infinite along the z axis. The theory introduces the electrostatic interactions between the ions treated as point charges and the short-range repulsions between the closest ion neighbors with the latter terms written in the Born form Ar(-)(n). Minimum energy structures are defined by the distances a(e) and b(e) separating the closest ions perpendicular and parallel to the z direction. The ratio a(e)/b(e), defining the crystal shape, is independent of the strength A of the short-range repulsion, greater than the bulk value of unity, and increases with decrease of the crystal cross section or n. This ratio tends toward unity in the hard sphere limit of infinite n. Both b(e)/R(6:6)(e) and a(e)/R(6:6)(e), with the bulk separation R(6:6)(e), are less than one, increase with increase of the crystal cross section or n, and are independent of A if this is independent of structure. The structural dependence of A increases its value with a decreasing crystal cross section rendering closer to unity the ratios a(e)/b(e), b(e)/R(6:6)(e), and a(e)/R(6:6)(e). Energy gains on relaxing the crystal toward equilibrium from its bulk separations decrease with increase of the crystal cross section or n, being about 60 kJ/mol for a one-dimensional chain with n = 6 but 0.5 kJ/mol for m(1) = m(2) = 4 with n = 12. The energy gained on relaxing to a structure with a(e)/b(e) constrained at unity is about 10 times greater than the further energy gains consequent on removing this constraint. The present theory neglecting the interaction between ions and the encapsulating nanotube explains the experimentally measured b(e)/R(6:6)(e) ratios. The observation that the a(e)/R(6:6)(e) values are greater than one shows that ion-wall interactions are important in determining the values of a(e).

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“…The relativistic integrals program (RIP) [50,51] yields fully relativistic results for the short-range two-body interactions which are exact for the wavefunctions input to the program. The two OHSMFS parameters are determined using RELCRION program which, incorporating both the RIP [50,51] and Oxford-Dirac Fock [42] programs, enables U 0 L (R) to be evaluated for any given A and q which are then automatically variationally optimized.…”

Section: Ionic Descriptionmentioning

confidence: 99%

“…The two OHSMFS parameters are determined using RELCRION program which, incorporating both the RIP [50,51] and Oxford-Dirac Fock [42] programs, enables U 0 L (R) to be evaluated for any given A and q which are then automatically variationally optimized. The optimal values of these parameters are reported for all the phases of all the crystals in table S1 of the supplementary material (available at stacks.iop.org/JPhysCM/20/085222).…”

Section: Ionic Descriptionmentioning

confidence: 99%

Preferential Growth of α'-FeN Films under a High Magnetic Field

Wang

Mitani

Fujimori

et al. 2002

Jpn. J. Appl. Phys.

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A non-empirical fully ionic description, with the anion wavefunctions in their compressed but still spherically symmetrical states optimal for the crystal, is presented for the cohesive energetics of two cubic phases of three solid iodides, KI, RbI and CsI. The non-correlated part of the energy is computed using the RELCRION program which takes full account of relativistic effects. Both the dispersive attractions and energies arising from electron correlations of short range are computed.For each polymorph stable under ambient conditions, the rock-salt (B1) phases of KI and RbI and the eightfold coordinated (B2) phase of CsI, the cohesion is slightly underestimated. The lattice energy deficits of around 22 kJ mol −1 for KI and RbI are reduced to around 13 kJ mol −1 for CsI, with overestimations of some 0.2 au in the equilibrium cation-anion separations R decreasing as the metal becomes more electropositive. The prediction that the B2 phase of CsI is more stable (by 6 kJ mol −1 ) than the B1 polymorph agrees with experiment. For both KI and RbI, the zinc-blende polymorph is predicted to lie some 37 kJ mol −1 in energy above the B1 polymorph.An additional potential, plausibly ascribed to slight covalency, correcting these underestimations is derived semi-empirically.

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Ab initio relativistic lattice energy calculations for fluorides of the 7p series of superheavy elements

Cited by 30 publications

References 13 publications

Relativity and the periodic table

Relativity and the periodic table

Fundamental Global Model for the Structures and Energetics of Nanocrystalline Ionic Solids

Preferential Growth of α'-FeN Films under a High Magnetic Field

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