Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 A for HSE vs 0.047 A for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0-1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.     

Quantum tunneling and quantum phase interference in a [Mn(II)2Mn(III)2] single-molecule magnet

[Mn4(hmp)6(H2O)2(NO3)2](NO3)2.2.5H2O (1) has been synthesized from the reaction of 2-hydroxymethylpyridine (Hhmp) with Mn(NO3)2.4H2O in the presence of tetraethylammonium hydroxide. 1 crystallizes in the triclinic P space group with two crystallographically independent centrosymmetrical [Mn4(hmp)6(H2O)2(NO3)2]2+ complexes in the packing structure. Four Mn ions are arranged in a double-cuboidal fashion where outer Mn2+ are heptacoordinated and inner Mn3+ are hexacoordinated. dc magnetic measurements show that both Mn2+...Mn3+ and Mn3+...Mn3+ interactions are ferromagnetic with J(wb)/k(B) = +0.80(5) K, and J(bb)/k(B) = +7.1(1) K, respectively, leading to an S(T) = 9 ground state. Combined ac and dc measurements reveal the single-molecule magnet (SMM) behavior of 1 with both thermally activated and ground-state tunneling regimes, including quantum phase interference. In the thermally activated regime, the characteristic relaxation time (tau) of the system follows an Arrhenius law with tau0 = 6.7 x 10(-)(9) s and delta(eff)/k(B) = 20.9 K. Below 0.34 K, tau saturates indicating that the quantum tunneling of the magnetization becomes the dominant relaxation process as expected for SMMs. Down to 0.04 K, field dependence of the magnetization measured using the mu-SQUID technique shows the presence of very weak inter-SMM interactions (zJ'/k(B) approximately -1.5 x 10(-3) K) and allows an estimation of D/k(B) at -0.35 K. Quantum phase interference has been used to confirm the D value and to estimate the transverse anisotropic parameter to E/k(B) = +0.083 K and the ground-state tunnel splitting delta(LZ) = 3 x 10(-7) K at H(trans) = 0 Oe. These results rationalize the observed tunneling time (tau(QTM)) and the effective energy barrier (delta(eff)).     

Theoretical and Numerical Analysis of a Class of Nonlinear Elliptic Equations

In this paper we show the existence of weak solutions for a nonlinear elliptic equation with arbitrary growth of the non linearity and data measure. A numerical algorithm to compute a numerical approximation of the weak solution is described and analyzed. In a first step a super-solution is computed using a domain decomposition method. Numerical examples are presented and commented. This work was supported by the French Grant “Action Intégrée MA/02/33”.     

Slow Dynamics of the Spin‐Crossover Process in an Apparent High‐Spin Mononuclear FeII Complex

A mononuclear Fe^II complex that shows a high‐spin (S=2) paramagnetic behavior at all temperatures (with standard temperature‐scan rates, ≈1 K min^?1) has, in fact, a low‐spin (S=0) ground state below 100 K. This low‐spin state is not easily accessible due to the extremely slow dynamics of the spin‐crossover process—a full relaxation from the metastable high‐spin state to the low‐spin ground state takes more than 5 h below 80 K. Bidirectional photo‐switching of the Fe^II state is achieved reproducibly by two selective irradiations (at 530–590 and 830–850 nm). The slow dynamics of the spin‐crossover and the strong structural cooperativity result in a remarkably wide 95‐K hysteresis loop induced by both temperature and selected light stimuli.     

Ab initio molecular dynamics for molecules with variable numbers of electrons

The ab initio molecular dynamics method is extended to treat exchange of electrons between molecules and a reservoir at fixed chemical potential. The method is based on a rigorously grand-canonical density functional approach using separate potential energy surfaces for each oxidation state. It is shown that the resulting discontinuous dependency of excess charge on chemical potential is consistent with the statistical thermodynamics of equilibrium gas-phase reactions. The method is illustrated by an application to the adiabatic redox dynamics of an aniline molecule.     

A new type of oxygen bridged Cu(II)36 aggregate formed around a central [KCl6]5- unit

A magnetically coupled Cu(II)36 aggregate forms around a potassium chloride unit.     

Cyclo- and carbophosphazene-supported ligands for the assembly of heterometallic (Cu2+/Ca2+, Cu2+/Dy3+, Cu2+/Tb3+) complexes: synthesis, structure, and magnetism

The carbophosphazene and cyclophosphazene hydrazides, [{NC(N(CH(3))(2))}(2){NP{N(CH(3))NH(2)}(2)}] (1) and [N(3)P(3)(O(2)C(12)H(8))(2){N(CH(3))NH(2)}(2)] were condensed with o-vanillin to afford the multisite coordination ligands [{NC(N(CH(3))(2))}(2){NP{N(CH(3))N═CH-C(6)H(3)-(o-OH)(m-OCH(3))}(2)}] (2) and [{N(2)P(2)(O(2)C(12)H(8))(2)}{NP{N(CH(3))N═CH-C (6)H(3)-(o-OH)(m-OCH(3))}(2)}] (3), respectively. These ligands were used for the preparation of heterometallic complexes [{NC(N(CH(3))(2))}(2){NP{N(CH(3))N═CH-C(6)H(3)-(o-O)(m-OCH(3))}(2)}{CuCa(NO(3))(2)}] (4), [{NC(N(CH(3))(2))}(2){NP{N(CH(3))N═CH-C(6)H(3)-(o-O)(m-OCH(3))}(2)}{Cu(2)Ca(2)(NO(3))(4)}]·4H(2)O (5), [{NC(N(CH(3))(2))}(2){NP{N(CH(3))N═CH-C(6)H(3)-(o-O)(m-OCH(3))}(2)}{CuDy(NO(3))(4)}]·CH(3)COCH(3) (6), [{NP(O(2)C(12)H(8))}(2){NP{N(CH(3))N═CH-C(6)H(3)-(o-O)(m-OCH(3))}(2)}{CuDy(NO(3))(3)}] (7), and [{NP(O(2)C(12)H(8))}(2){NP{N(CH(3))N═CH-C(6)H(3)-(o-O)(m-OCH(3))}(2)}{CuTb(NO(3))(3)}] (8). The molecular structures of these compounds reveals that the ligands 2 and 3 possess dual coordination pockets which are used to specifically bind the transition metal ion and the alkaline earth/lanthanide metal ion; the Cu(2+)/Ca(2+), Cu(2+)/Tb(3+), and Cu(2+)/Dy(3+) pairs in these compounds are brought together by phenoxide and methoxy oxygen atoms. While 4, 6, 7, and 8 are dinuclear complexes, 5 is a tetranuclear complex. Detailed magnetic properties on 6-8 reveal that these compounds show weak couplings between the magnetic centers and magnetic anisotropy. However, the ac susceptibility experiments did not reveal any out of phase signal suggesting that in these compounds slow relaxation of magnetization is absent above 1.8 K.     

Simultaneous kriging-based estimation and optimization of mean response

Robust optimization is typically based on repeated calls to a deterministic simulation program that aim at both propagating uncertainties and finding optimal design variables. Often in practice, the “simulator” is a computationally intensive software which makes the computational cost one of the principal obstacles to optimization in the presence of uncertainties. This article proposes a new efficient method for minimizing the mean of the objective function. The efficiency stems from the sampling criterion which simultaneously optimizes and propagates uncertainty in the model. Without loss of generality, simulation parameters are divided into two sets, the deterministic optimization variables and the random uncertain parameters. A kriging (Gaussian process regression) model of the simulator is built and a mean process is analytically derived from it. The proposed sampling criterion that yields both optimization and uncertain parameters is the one-step ahead minimum variance of the mean process at the maximizer of the expected improvement. The method is compared with Monte Carlo and kriging-based approaches on analytical test functions in two, four and six dimensions.