QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

In this critical review I describe fascinating experimental and theoretical advances in ‘noble gas’ chemistry during the last twenty years, and have taken a somewhat unexpected course since 2000. I also highlight perspectives for further development in this field, including the prospective synthesis of compounds containing as yet unknown Xe–element and element–Xe–element bridging bonds, peroxide species containing Xe, adducts of XeF2 with various metal fluorides, Xe–element alloys, and novel pressure-stabilized covalently bound and host–guest compounds of Xe. A substantial part of the essay is devoted to the—as yet experimentally unexplored—behaviour of the compounds of Xe under high pressure. The blend of science, history, and theoretical predictions, will be valued by inorganic and organic chemists, materials scientists, and the community of theoretical and experimental high-pressure physicists and chemists (151 references).

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Atypical compounds of gases, which have been called ‘noble’

The discovery of carbon fullerene cages and their solids opened a new avenue to build materials from stable cage clusters as “artificial atoms” or “superatoms” instead of atoms. However, cage clust...

Endohedrally Doped Cage Clusters

This review article surveys recent experimental and theoretical advances in the gas-phase ion chemistry of the noble gases. Covered issues include the interaction of the noble gases with metal and non-metal cations, the conceivable existence of covalent noble-gas anions, the occurrence of ion–molecule reactions involving singly-charged xenon cations and the occurrence of bond-forming reactions involving doubly-charged cations. Research themes are also highlighted, which are expected to attract further interest in the nearfuture.

https://journals.sagepub.com/doi/pdf/10.1255/ejms.1151

Review: Gas-phase ion chemistry of the noble gases: recent advances and future perspectives

The global minimum geometries of BeCN2 and BeNBO are linear BeN–CN and BeN–BO, respectively. The Be center of BeCN2 binds He with the highest Be–He dissociation energy among the studied neutral He–Be complexes. In addition, BeCN2 can be further tuned as a better noble gas trapper by attaching it with any electron-withdrawing group. Taking BeO, BeS, BeNH, BeNBO, and BeCN2 systems, the study at the CCSD(T)/def2-TZVP level of theory also shows that both BeCN2 and BeNBO systems have higher noble gas binding ability than those related reported systems. ΔG values for the formation of NgBeCN2/NgBeNBO (Ng = Ar–Rn) are negative at room temperature (298 K), whereas the same becomes negative at low temperature for Ng = He and Ne. The polarization plus the charge transfer is the dominating term in the interaction energy.

In quest of strong Be-Ng bonds among the neutral Ng-Be complexes.

The structure and stability of xenon-inserted hypohalous acids HXeOX (X=F, Cl, and Br) have been investigated theoretically using ab initio molecular orbital calculations. All these molecules are found to consist of a nearly linear HXeO moiety and a bend XeOX fragment. Geometrical parameters of HXeOX are comparable with that of experimentally observed HXeOH species. The dissociation energies corresponding to the lowest-energy fragmentation products, HOX+Xe have been computed to be -398.1, -385.5, and -386.7 kJmol for HXeOF, HXeOCl, and HXeOBr, respectively, at the MP2 level of theory. The respective barrier heights corresponding to the bent transition states (H-Xe-O bending mode) have been calculated to be 138.1, 138.4, and 138.2 kJmol with respect to HXeOX minimum. These species are found to be metastable in their respective potential-energy surface, and the dissociation energies corresponding to the H+Xe+OX products are found to be 56.8, 66.0, and 80.8 kJmol for HXeOF, HXeOCl, and HXeOBr, respectively. The energies corresponding to the H+Xe+O+X dissociation channel have been computed to be 272.0, 309.3, and 299.7 kJmol for HXeOF, HXeOCl, and HXeOBr, respectively, at the same level of theory. Energetics as well as geometrical considerations suggests that it may be possible to prepare these species experimentally similar to that of HXeOH species at low-temperature laser photolysis experiments.

Structure and stability of xenon insertion compounds of hypohalous acids, HXeOX [X=F, Cl, and Br]: An ab initio investigation

The structure, stability, charge redistribution, and harmonic vibrational frequencies of rare gas inserted group III-B fluorides with the general formula F–Rg–MF2 (where M=B and Al; Rg=Ar, Kr, and Xe) have been investigated using ab initio quantum chemical methods. The Rg atom is inserted in one of the M–F bond of MF3 molecules, and the geometries are optimized for ground as well as transition states using the MP2 method. It has been found that Rg inserted F–Rg–M portion is linear in both F–Rg–BF2 and F–Rg–AlF2 species. The binding energies corresponding to the lowest energy fragmentation products MF3+Rg (two-body dissociation) have been computed to be −670.4, −598.8, −530.7, −617.0, −562.1, and −494.0kJ∕mol for F–Ar–BF2, F–Kr–BF2, F–Xe–BF2, F–Ar–AlF2, F–Kr–AlF2, and F–Xe–AlF2 species, respectively. The dissociation energies corresponding to MF2+Rg+F fragments (three-body dissociation) are found to be positive with respect to F–Rg–MF2 species, and the computed values are 56.3, 127.8, and 196.0kJ∕mol for F...

Insertion of rare gas atoms into BF3 and AlF3 molecules: an ab initio investigation.

Ab initio quantum chemical methods have been employed to investigate the structure, stability, charge redistribution, and harmonic vibrational frequencies of rare gas (Rg=He, Ne, Ar, Kr, and Xe) containing HRgCO(+) ion. The Rg atoms are inserted in between the H and C atoms of HCO(+) ion and the geometries are optimized for minima as well as transition state using second order Moller-Plesset perturbation theory, density functional theory, and coupled-cluster theory [CCSD(T)] methods. The HRgCO(+) ions are found to be metastable and exhibit a linear structure at the minima position and show a nonlinear structure at the transition state. The predicted ion is unstable with respect to the two-body dissociation channel leading to the global minima (HCO(+)+Rg) on the singlet potential surface. The binding energies corresponding to this channel are -406.4, -669.3, -192.3, -115.4, and -52.2 kJ mol(-1) for HHeCO(+), HNeCO(+), HArCO(+), HKrCO(+), and HXeCO(+) ions, respectively, at CCSD(T) method. However, with respect to other two-body dissociation channel, HRg(+)+CO, the ions are found to be stable and have positive energies except for HNeCO(+) at the same level of theory. The computed binding energies for this channel are 15.0, 28.8, 29.5, and 29.1 kJ mol(-1) for HHeCO(+), HArCO(+), HKrCO(+), and HXeCO(+) ions, respectively. Very high positive three-body dissociation energies are found for H+Rg+CO(+) and H(+)+Rg+CO dissociation channels. It indicates the existence of a very strong bonding between Rg and H atoms in HRgCO(+) ions. The predicted ions dissociate into global minima, HCO(+)+Rg, via a transition state involving H-Rg-C bending mode. The barrier heights for the transition states are 22.7, 10.1, 13.1, and 15.0 kJ mol(-1) for He, Ar, Kr, and Xe containing ions, respectively. The computed two-body dissociation energies are comparable to that of the experimentally observed mixed cations such as ArHKr(+), ArHXe(+), and KrHXe(+) in an electron bombardment matrix isolation technique. Thus HRgCO(+) cations may also be possible to prepare and characterize similar to the mixed cations (RgHRg('))(+) in low temperature matrix isolation technique.

Theoretical prediction of HRgCO(+) ion (Rg=He, Ne, Ar, Kr, and Xe).

Chemical binding between a rare gas atom with other elements leading to the formation of stable chemical compounds has received considerable attention in recent years. With an intention to predict highly stable novel rare gas compounds, the process of insertion of beryllium atom into rare gas hydrides (HRgF with Rg = Ar , Kr, and Xe) has been investigated, which leads to the prediction of HBeRgF species. The structures, energetic, and charge distributions have been obtained using MP2, density functional theory, and CCSD(T) methods. Analogous to the well-known rare gas hydrides, HBeRgF species are found to be metastable in nature; however, the stabilization energy of the newly predicted species has been calculated to be significantly higher than that of HRgF species. Particularly, for HBeArF molecule, it has been found to be an order of magnitude higher. Strong chemical binding between beryllium and rare gas atom has also been found in the HBeArF, HBeKrF, and HBXeF molecules. In fact, the basis set superposition error and zero-point energy corrected Be–Ar bond energy calculated using CCSD(T) method has been found to be 112 kJ ∕ mol , which is the highest bond energy ever achieved for a bond involving an argon atom in any chemically bound neutral species. Vibrational analysis reveals a large blueshift ( ∼ 200 cm − 1 ) of the H–Be stretching frequency in HBeRgF with respect to that in BeH and HBeF species. This feature may be used to characterize these species after their preparation by the laser ablation of Be metal along with the photolysis of HF precursor in a suitable rare gas matrix. An analysis of the nature of interactions involved in the present systems has been performed using theory of atoms in molecules (AIM). Geometric as well as energetic considerations along with the AIM results suggest a substantial covalent nature of Be–Rg bond in these systems. Thus, insertion of a suitable metal atom into rare gas hydrides is a promising way to energetically stabilize the HRgX species, which eventually leads to the formation of a new class of insertion compounds, viz., rare gas metallohydrides.

Significant increase in the stability of rare gas hydrides on insertion of beryllium atom

The structure, stability, charge redistribution, bonding, and harmonic vibrational frequencies of rare gas containing group II-A fluorides with the general formula FMRgF (where M=Be and Mg; Rg=Ar, Kr, and Xe) have been investigated using second order Moller–Plesset perturbation theory, density functional theory, and coupled cluster theory [CCSD(T)] methods. The species, FMRgF show a quasilinear structure at the minima and a bent structure at the transition state. The predicted species are unstable with respect to the two-body dissociation channel, leading to the global minima (MF2+Rg) on the singlet potential energy surface. However, with respect to other two-body dissociation channel (FM+RgF), they are found to be stable and have high positive energies on the same surface. The computed binding energy for the two-body dissociation channels are 94.0, 164.7, and 199.7kJmol−1 for FBeArF, FBeKrF, FBeXeF, respectively, at CCSD(T) method. The corresponding energy values are 83.4, 130.7, and 180.1kJmol−1 for FMg...

T. Jayasekharan

Papers

Structure and stability of xenon insertion compounds of hypohalous acids, HXeOX [X=F, Cl, and Br]: An ab initio investigation

Insertion of rare gas atoms into BF3 and AlF3 molecules: an ab initio investigation.

Theoretical prediction of HRgCO(+) ion (Rg=He, Ne, Ar, Kr, and Xe).

Significant increase in the stability of rare gas hydrides on insertion of beryllium atom

Prediction of metastable metal-rare gas fluorides: FMRgF (M=Be and Mg; Rg=Ar, Kr and Xe).