Deuterium Clusters D N and Mixed K–D and D–H Clusters of Rydberg Matter: High Temperatures and Strong Coupling to Ultra-Dense Deuterium

Ultra-dense deuterium D(−1) can be formed by a catalytic process from Rydberg Matter (RM) of deuterium as reported previously. Laser-induced inertial confinement fusion (ICF) has recently been observed in this material. The formation of D(−1) is now studied through experiments observing the deuterium RM clusters D _N in excitation levels n _B  = 1, 3 and 4. These levels are intermediate in the formation process of D(−1). Laser-induced fragmentation is used, with neutral time-of-flight (TOF) and TOF–MS measurements of the kinetic energy release (KER) from the quantized Coulomb explosions (CE). Several types of pure D _N clusters, mixed clusters containing both D and H atoms, and clusters containing both D and K atoms are identified. The large planar RM clusters which are common for H and K are less common for D. The neutral D _N clusters are small and have high kinetic temperature, typically at 100 K instead of 10 K for K _N and H _N . Large D _N ⁺ clusters are only observed when an electric field is applied, probably stabilized by increased cooling. A strong coupling of the D(1) laser fragmentation signal to the ultra-dense D(−1) signal is observed, and the materials D(1) and D(−1) are two rapidly interchangeable forms of quantum fluids.     

Common Forms of Alkali Metals—New Rydberg Matter Clusters of Potassium and Hydrogen

Alkali metals can form low-density metallic phases, in their most well-ordered form called Rydberg Matter (RM). RM consists mainly of planar metallic clusters, with the number of atoms in each cluster not exceeding 100 according to experiments. Six-fold symmetric RM clusters in the most stable series K₁₉, K₃₇, K₆₁ and K₉₁ were observed by rotational radio-frequency spectroscopy and shown to be planar in point group D_6h (Holmlid, J Mol Struct 885:122, 2008). Here, the RM clusters formed by K and H atoms are studied by neutral time-of-flight after pulsed laser fragmentation of RM formed from K and H. The kinetic energy of the fragments is due to laser initiated Coulomb explosions. Novel RM clusters of the type K _N with N = 6, 9, 10, 13 and 15 are ejected from the material. They are necessarily planar due to the RM bonding, with two- or three-fold symmetry axes perpendicular to the plane. Pure hydrogen atom RM clusters H _N are observed, demonstrating once more that H indeed is an alkali metal. Mixed clusters K _M H _N similar to hydrogen clusters where each K replaces an H atom as in KH₆ are now also positively identified.     

Rotational spectra of large Rydberg Matter clusters K37, K61 and K91 give trends in K–K bond distances relative to electron orbit radius

Rotational spectra of planar clusters of Rydberg Matter (RM) have recently been reported for the first time, for clusters K₁₉ in excitation levels n_B = 4, 5 and 6 [L. Holmlid, Mol. Phys. 105 (2007) 933–939]. From such spectra, the average bond distances in the clusters can be determined, and good agreement with theoretical predictions is found. K₁₉ is an example of a sixfold symmetric planar RM cluster, while other similar clusters have 37, 61 and 91 atoms. Rotational bands of the heavy clusters K₃₇, K₆₁ and K₉₁ are easily identified since they appear as closely spaced groups of lines on top of electronic, probably spin-flip transitions. The bond lengths for the heavy clusters are in the range 3–10 nm, found with a relative precision of approximately 2 × 10⁻³. The cluster K₃₇ (n_B = 8) is the largest cluster observed with diameter of 58.9 nm and bond length of 9.82 ± 0.02 nm. The dimensional ratio d/r_n, i.e. the ratio between the experimental interatomic distance and the theoretical electron orbiting radius, is larger for higher excitation levels, where the classical limit is approached and thus the electronic motion is more strongly confined to the cluster plane. The dimensional ratio is also larger for smaller clusters, which is probably due to larger edge effects giving larger average bond distances. The average value of d/r_n is 2.865 ± 0.032, close to the theoretically predicted value 2.9. Intensity alternation for every second rotational line is often observed.     

Theoretical Study of Hydrogen Adsorption on Ruthenium Clusters

The geometries, stabilities, electronic, and magnetic properties of hydrogen adsorption on Ru _n clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The result indicates the absorbed species does not lead to a rearrangement of the basic cluster. For n > 2, three different adsorption patterns are found for the Ru _n H₂ complexes: One H atom binds to the Ru top site, and another H binds to the bridge site for n = 3, 5, 6, 8; bridge site adsorption for n = 4; hollow site and top site adsorption for n = 7. The adsorption energies display oscillation and reach the peak at n = 2, 4, 7, implying their high chemical reactivity. The small electron transferred number between H atoms and Ru _n clusters indicates that the interaction between H atoms and Ru _n clusters is small. When H₂ is absorbed on the Ru _n clusters, the chemical activity of corresponding clusters is dramatically increased. The absorbed H₂ can lead to an oscillatory behavior of the magnetic moments, and this behavior is rooted in the electronic structure of the preceding cluster and the changes in the magnetic moment are indicative of the relative ordering of the majority and minority LUMO’s. The second order difference indicates 5 is magic number in Ru _n H₂ and Ru _n clusters.     

The Electronic and Magnetic Properties of a Few Transition-Metal Clusters

Using density functional theory we present a systematic study of the electronic and magnetic properties of various nickel clusters and two small bimetallic clusters, Ni _n Co _m and Ni _n Fe _m (n + m ≤ 6). A detail study of binding energy, magnetic moment and stability function of pure nickel clusters of nuclearity (N) 40–60 have been performed. We observe that the magic numbers occur at N = 43, 46, 49, 53, 55, and 58, which correspond to the most stable clusters. We find that, with increase in substitution of Co and Fe atoms in Ni cluster, while Ni _n Co _m becomes more stable, the Ni _n Fe _m clusters become less stable. The significant enhancement of average magnetic moment and suppression of local magnetic moment of nickel atoms are found in both clusters with increase in Co and Fe concentration.     

Hydrogen–hydrogen bonding in biphenyl revisited

The evidence for the stabilizing nature of the H–H bonding in planar biphenyl is succinctly reviewed. The stabilizing nature of the H–H bonding is revealed through a comparison of the atomic energy of every atom in planar biphenyl with the same atom in the twisted equilibrium structure. It is shown that the barrier to rotation via the planar transition state is the net resultant of a stabilisation of the four ortho-hydrogen atoms (by 8 kcal/mol each), a stabilisation of the two para-carbon atoms (by 3 kcal/mol each) and by the dominant destabilisation of the two carbon atoms joining the two rings—the two junction carbon atoms—(by 22 kcal/mol each). The energetic stabilisation of the four ortho-hydrogen atoms is further shown to be in large proportion due to the formation of the hydrogen–hydrogen interatomic surface. Furthermore, neither the “bond order” between the two junction carbon atoms nor the total electron delocalisation between the two rings exhibit a significant change in going from the planar to the twisted equilibrium geometry. These findings are in contrast with the classical view of a balance between “steric non-bonded repulsion” and better electron delocalisation as a function of the twist dihedral angle. Similar conclusions have been recently reached by Pacios and Gómez through a study of the electrostatic potential at the position of the hydrogen nuclei. We dedicate this article to Professor TM Krygowski on the occasion of his 70th birthday wishing him a long and productive life.     

A density functional theory study on the Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H (<Emphasis Type="Italic">n</Emphasis> = 1–10) clusters

Density functional GGA-PW91 method with DNP basis set is applied to optimize the geometries of Ag _n H (n = 1–10) clusters. For the lowest energy geometries of Ag _n H (n = 1–10) clusters, the hydrogen atom prefers to occupy the two-fold coordination bridge site except the occupation of single-fold coordination site in AgH cluster. After adsorption of hydrogen atom, most Ag _n structures are slightly perturbed and only the Ag₆ structure in Ag₆H cluster is distorted obviously. The Ag–Ag bond is strengthened and the strength of Ag–H bond exhibits a clear odd–even oscillation like the strength of Au–H bond in Au _n H clusters, indicating that the hydrogen atom is more favorable to be adsorbed by odd-numbered pure silver clusters. The adsorption strength of small silver cluster toward H atom is obviously weaker than that of small gold cluster toward H atom due to the strong scalar relativistic effect in small gold cluster. The pronounced odd–even alternation of the magnetic moments is observed in Ag _n H systems, indicating that the Ag _n H clusters possess tunable magnetic properties by adsorbing hydrogen atom onto odd-numbered or even-numbered small silver cluster.     

硼碳团簇BnC2 (n＝1～6)的理论研究

应用密度泛函理论在B3LYP/6-311＋G(d)水平上研究了硼碳团簇B_nC₂ (n＝1～6)的几何结构、生长机制和相对稳定性. 计算结果表明, 对于n＝2～6的簇, 平面多环状构型为最稳定的结构, 其中C原子分布于环的顶点、有尽可能多的三配位硼原子和尽可能多的B—C键. 碳原子作为杂原子倾向掺杂于团簇的顶点位置, 它的掺杂不改变硼团簇的主体结构. 与平面多环状结构相比, 随着簇尺寸的增大, 三维结构和线性链结构更不稳定. 在低能线性结构中, C原子位于链两侧的第二个位置. 计算的碎片分裂能、递增键能以及HOMO-LUMO能隙表明, B₄C₂为幻数簇.     

All-electron relativistic calculations on hydrogen atom adsorption onto small copper clusters

An all-electron scalar relativistic calculation on Cu _n H (n = 1–13) clusters has been performed by using density functional theory with the generalized gradient approximation at the PW91 level. Our results reveal that the hydrogen atom prefers to occupy the two fold coordination site for Cu _n H (n = 2, 4–6, 8, 10–13) clusters, the single fold coordination site for Cu _n H (n = 1, 3, 7) and the three fold coordination site for Cu₉H cluster. For all Cu _n H clusters, only the Cu₁₁ structure in Cu₁₁H is distorted obviously. After adsorption, the Cu–Cu bond is strengthened and the Cu–H bond of odd-numbered Cu _n H clusters is relatively stronger than that of adjacent even-numbered Cu _n H clusters. The Cu–Cu bond-length and Cu–H bond-length for all Cu _n H clusters of our work are significantly shorter than those of previous work. This discrepancy can be explained in terms of the scalar relativistic effect. The most favorable adsorption between small copper clusters and hydrogen atom takes place in the case that hydrogen atom is adsorbed onto an odd-numbered pure Cu _n cluster and becomes Cu _n H cluster with even number of valence electrons. The odd–even alteration of magnetic moments is observed in Cu _n H clusters and may provide the material with tunable code capacity of “0” and “1” by adsorbing a hydrogen atom onto odd- or even-numbered copper clusters.     

Subshell-pair correlation coefficients of atoms in momentum space

Angular correlation coefficients τ ^{nl,n^′ l^′} [p] between linear momenta of an electron in a subshell nl and another electron in a subshell n′ l′ are studied for the 102 neutral atoms He through Lr in their ground states, where n and l are the principal and azimuthal quantum numbers, respectively. We theoretically find that electron momenta are negatively correlated or uncorrelated; τ ^{nl,n^′ l^′} [p] < 0 when |l − l′|=1, while τ ^{nl,n^′ l^′} [p]=0 when |l − l′| ≠ 1. Numerical examinations of the atoms show that except for the He–B atoms, negative correlations are largest between 1s and 2p subshells, which have the most diffuse electron distributions in momentum space.     

Structural Growth Sequences and Electronic Properties of Lanthanum-Doped-Gold Clusters

The geometries, stabilities, and electronic properties of Au _n La (n = 2–8) clusters have been systematically investigated by using density-functional theory. The results show that the doped La atom prefers to locate at the center site with the number of Au atom increasing from 2 to 8. Furthermore, the Au _n La clusters are more stable than the Au _n+1 clusters. The charges transfer from La atom to Au atoms at n = 2–4, but charge-transferring is reversed at n = 5.     

Density functional study of hydrogen adsorption and dissociation on small Pdn (n = 1–7) clusters

Density functional theory has been performed to investigate the interaction of H₂ and Pd_n clusters (n = 1–7). The local minima configurations for different H₂ molecule approach modes towards Pd_n clusters are presented. Our results show that in some cases H₂ is physically adsorbed around Pd atom, and in other cases H₂ is dissociated to be H atoms. Except for PdH2, Pd_n clusters with H atoms dissociatively adsorbed are most stable. For these most stable PdnH2 clusters (n  2), the binding energy of hydrogen atom decreases as the number of Pd atom increases until n = 4, and when n  4, the binding energy almost keeps constant with the H atoms bound sites changing from Pd–Pd bonds to Pd triangle planes. Besides, the adsorption of H₂ on other low-lying isomers of Pd_n clusters is also discussed.     

Structures and bonding patterns of nanoannular carbon clusters (C4–C20) through AIM analyses

Structures, binding energies, harmonic frequencies, dipole moments, HOMO–LUMO energy gaps and particularly atoms in molecules (AIM) analyses of some nanoannular carbon clusters (C₄–C₂₀) are investigated at B3LYP/6-31+G(d) level of theory. No correlation is found by plotting the calculated binding energies as a functional number of carbon atoms of carbon clusters. The calculated binding energies sharply increase from C₄ to C₁₀ while slowly from C₁₀ to C₂₀. The binding energies of C_4n+2 clusters including C₆, C₁₀, C₁₄, and C₁₈ have a clear increase when compared with others indicating their aromatic characters which is confirmed by results of HOMO–LUMO energy gaps and geometrical parameters. AIM analyses show that most of our carbon clusters are topologically normal (non-conflict) with stable structures. Nevertheless, the topological networks of small antiaromatic rings, C₄ and C₈, at their equilibrium geometries may change via molecular vibrations. The existence of straight bond paths in 3D molecular graphs of carbon clusters with n > 10 implies that ring strains are decreased as the ring sizes grow. Except for C₄ and C₈, the ellipticity values for the remaining carbon clusters are small indicating that the C–C bond is conserved in these clusters. Dipole moments of even-numbered structures are negligible, whereas odd-numbered ones have μ values of 0.09−0.73 D.     

Growth Pattern, Electronic Structures and Magnetic Moments of Small Lutetium Clusters

The lowest-energy configurations, electronic structures and magnetic moments of small Lu _n (n = 2–20) clusters have been investigated within the framework of density functional theory. The results show that Lu _n (n = 4, 8, 13, and 18) clusters are more stable than their respective neighbors, and structural transformation reveals at n = 16. As the number of atoms increases, the magnetic moments increase in an alternating fashion until they reach a maximum of 4.00 μ_B for Lu₈ clusters, followed by even–odd oscillation between 0.00 and 1.00 μ_B over the range n = 9–20.     

Wigner’s (2<Emphasis Type="Italic">n</Emphasis> + 1) rule for nonlinear Schrödinger equations

Wigner’s (2n + 1) rule is proven for general total energy functionals, constructed from the expectation value of a linear Hamiltonian and a nonlinear functional of the electron density or of the first order density matrix. Such functionals are common in independent particle models, like the Kohn–Sham density functional or Hartree–Fock theories, but they occur as well in reaction-field type solvent effect models and range-separated hybrid density functional approaches. The fulfillment of the (2n + 1) rule is crucial for the development of efficient perturbation approaches for the treatment of one-electron and two-electron perturbations. A general transformation formula is derived, that removes some of the (2n + 1)-rule violating matrix elements of the perturbation operator from the general expression of the arbitrary order perturbational energy correction of the nonlinear problem.     

Production of Lipids Containing High Levels of Docosahexaenoic Acid by a Newly Isolated Microalga, <Emphasis Type="Italic">Aurantiochytrium</Emphasis> sp. KRS101

In the present study, a novel oleaginous Thraustochytrid containing a high content of docosahexaenoic acid (DHA) was isolated from a mangrove ecosystem in Malaysia. The strain identified as an Aurantiochytrium sp. by 18S rRNA sequencing and named KRS101 used various carbon and nitrogen sources, indicating metabolic versatility. Optimal culture conditions, thus maximizing cell growth, and high levels of lipid and DHA production, were attained using glucose (60 g l⁻¹) as carbon source, corn steep solid (10 g l⁻¹) as nitrogen source, and sea salt (15 g l⁻¹). The highest biomass, lipid, and DHA production of KRS101 upon fed-batch fermentation were 50.2 g l⁻¹ (16.7 g l⁻¹ day⁻¹), 21.8 g l⁻¹ (44% DCW), and 8.8 g l⁻¹ (40% TFA), respectively. Similar values were obtained when a cheap substrate like molasses, rather than glucose, was used as the carbon source (DCW of 52.44 g l⁻¹, lipid and DHA levels of 20.2 and 8.83 g l⁻¹, respectively), indicating that production of microbial oils containing high levels of DHA can be produced economically when the novel strain is used.     

M@B<Subscript>9</Subscript> and M@B<Subscript>10</Subscript> molecular wheels containing planar nona- and deca-coordinate heavy group 11, 12, and 13 metals (M=Ag,Au, Cd,Hg, In,Tl)

A density functional and ab initio theory investigation on M@B₉ and M@B₁₀ molecular wheels containing planar nona- and deca-coordinate heavy group 11, 12 and 13 metals (M=Ag, Au, Cd, Hg, In, Ti) has been performed. These unusual clusters all prove to be true minima on the potential energy surfaces of the systems and σ+π double aromatic in nature. The first two vertical one-electron detachment energies of M@B₁₀⁻ (M=Ag, Au) anions and first two ionization potentials of M@B₉ (M=Ag, Au) and M@B₁₀ (M=Cd, Hg) neutrals were calculated to aid future experiments. The cluster complexes designed in this work may expend the domain of planar hyper-coordinate elements to include heavy group 11, 12, and 13 metals and serve as interesting candidates to be targeted in experiments. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported by the National Natural Science Foundation of China (Grant No. 20873117)     

Direct quantification of deoxynivalenol glucuronide in human urine as biomarker of exposure to the <Emphasis Type="Italic">Fusarium</Emphasis> mycotoxin deoxynivalenol

The direct quantification of deoxynivalenol glucuronide (DON-GlcA) by liquid chromatography-tandem mass spectrometry (LC-MS/MS) and its application as a biomarker of exposure to the Fusarium mycotoxin deoxynivalenol (DON) is reported. Usually, DON exposure is estimated from dietary average intakes or by measurement of the native toxin in urine after enzymatic hydrolysis with β-glucuronidase. These methods are time-consuming, expensive, and fail to determine the ratio of DON to DON-GlcA in a simple one-step procedure. One of the main reasons for the use of indirect methods is the unavailability of DON-GlcA standards. Consequently, DON-3-O-glucuronide (D3GlcA) was synthesized and used to develop a method allowing quantification of both DON and D3GlcA by a simple “dilute and shoot” approach without the need for any cleanup. Limit of detection and apparent recovery of D3GlcA was 3 μg l⁻¹ and 88%, respectively. The identity of D3GlcA in human urine was confirmed by comparison with LC-MS/MS measurements of the synthetically produced D3GlcA standard which was also used for external calibration. The applicability of the method was demonstrated through the analysis of urine samples obtained from a volunteer during regular and cereal-restricted diet, respectively. In regular-diet urine samples, D3GlcA was quantified in concentrations >30 μg l⁻¹ by this approach.     

Modeling Ar and Kr matrix effect on the ν s (Cl–H) and ν l (Cl–H) of Cl–H···NH3 by the IEF-PCM method

Ar and Kr matrix effect on the geometry and Cl–H stretching (ν _s (Cl–H)) and librational (ν _l (Cl–H)) frequencies of the hydrogen-bonded complex Cl–H···NH₃ are simulated within the framework of polarizable continuum model with integral equation formalism (IEF-PCM) at B3LYP and MP2 levels of theory with the basis set 6-311++G(2df,2pd). Within the framework of B3LYP and IEF-PCM, the simulated gas phase, Ar, and Kr matrix ν _s (Cl–H) of the complex are 2140, 1684, and 1550 cm⁻¹, respectively, which deviate from the experimental values (~2200, 1371, and 1218 cm⁻¹) by −60, 313, and 332 cm⁻¹. Within the framework of MP2 and IEF-PCM, the gas phase, Ar, and Kr matrix ν _s (Cl–H) are calculated as 2366, 2037, and 1957 cm⁻¹ by the harmonic approximation, and as 2177, 1876, and 1665 cm⁻¹ by the full-dimensional anharmonic correction. The matrix effect modeling is of greater importance than the anharmonic correction in accounting for the large experimental gas phase to Ar or Kr matrix shift of the ν _s (Cl–H) (−829 or −982 cm⁻¹). Our calculations do not support the assignment of the 733.8 and 736.9 cm⁻¹ bands to the Ar and Kr matrix ν _l (Cl–H).