The ground-state fermion second-order reduced density matrix ͑2-RDM͒ is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm ͑SDPA͒. The calculated energies of various closed-and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results.

We explore the potential of double core hole electron spectroscopy for chemical analysis in terms of x-ray two-photon photoelectron spectroscopy. The creation of deep single and double core vacancies induces significant reorganization of valence electrons. The corresponding relaxation energies and the interatomic relaxation energies are evaluated by complete active space self-consistent field ͑CASSCF͒ calculations. We propose a method on how to experimentally extract these quantities by the measurement of single ionization potentials ͑IPs͒ and double core hole ionization potentials ͑DIPs͒. The influence of the chemical environment on these DIPs is also discussed for states with two holes at the same atomic site and states with two holes at two different atomic sites. Electron density difference between the ground and double core hole states clearly shows the relaxations accompanying the double core hole ionization. The effect is also compared to the sensitivity of single core hole IPs arising in single core hole electron spectroscopy. We have demonstrated the method for a representative set of small molecules LiF, BeO, BF, CO, N 2 , C 2 H 2 , C 2 H 4 , C 2 H 6 , CO 2 , and N 2 O. The scalar relativistic effect on IPs and on DIPs are briefly addressed.

This paper describes the unique catalytic activity of bimetallic Au/Pd alloy nanoclusters (NCs) for Ullmann coupling of chloroarenes in aqueous media at low temperature. The corresponding reaction cannot be achieved by monometallic Au and Pd NCs as well as their physical mixtures. On the basis of quantum chemical calculation, it was found that the crucial step to govern the unusual catalytic activity of Au/Pd is the dissociative chemisorption of ArCl, which is unlikely in the monometallic Au and Pd NCs.

Artificial molecular switches and machines that enable the directional movements of molecular components by external stimuli have undergone rapid advances over the past several decades. Particularly, overcrowded alkene-based artificial molecular motors are highly attractive from the viewpoint of chirality switching during rotational steps. However, the integration of these molecular switches into solid-state devices is still challenging. Herein, we present an example of a solid-state spin-filtering device that can switch the spin polarization direction by light irradiation or thermal treatment. This device utilizes the chirality inversion of molecular motors as a light-driven reconfigurable spin filter owing to the chiral-induced spin selectivity effect. Through this device, we found that the flexibility at the molecular scale is essential for the electrodes in solid-state devices using molecular machines. The present results are beneficial to the development of solid-state functionalities emerging from nanosized motions of molecular switches.

Theory predicts that double-core-hole (DCH) spectroscopy can provide a new powerful means of differentiating between similar chemical systems with a sensitivity not hitherto possible. Although DCH ionization on a single site in molecules was recently measured with double-and single-photon absorption, double-core holes with single vacancies on two different sites, allowing unambiguous chemical analysis, have remained elusive. Here we report that direct observation of double-core holes with single vacancies on two different sites produced via sequential two-photon absorption, using short, intense X-ray pulses from the Linac Coherent Light Source free-electron laser and compare it with theoretical modeling. The observation of DCH states, which exhibit a unique signature, and agreement with theory proves the feasibility of the method. Our findings exploit the ultrashort pulse duration of the free-electron laser to eject two core electrons on a time scale comparable to that of Auger decay and demonstrate possible future X-ray control of physical inner-shell processes.multi-photon ionization | ultrafast | two-photon spectroscopy

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Energies of the hollow molecules CH 2þ 4 and NH 2þ 3 with double vacancies in the 1s shells have been measured using an efficient coincidence technique combined with synchrotron radiation. The energies of these states have been determined accurately by high level electronic structure calculations and can be well understood on the basis of a simple theoretical model. Their major decay pathway, successive Auger emissions, leads first to a new form of triply charged ion with a core hole and two valence vacancies; experimental evidence for such a state is presented with its theoretical interpretation. Preedge 2-hole-1-particle (2h-1p) states at energies below the double core-hole states are located in the same experiments and their decay pathways are also identified.

The S1 state dynamics of methoxy methylcinnamate (MMC) has been investigated under supersonic jet-cooled conditions. The vibrationally resolved S1-S0 absorption spectrum was recorded by laser induced fluorescence and mass-resolved resonant two-photon ionization spectroscopy and separated into conformers by UV-UV hole-burning (UV-UV HB) spectroscopy. The S1 lifetime measurements revealed different dynamics of para-methoxy methylcinnamate from ortho-methoxy methylcinnamate and meta-methoxy methylcinnamate (hereafter, abbreviated as p-, o-, and m-MMCs, respectively). The lifetimes of o-MMC and m-MMC are on the nanosecond time scale and exhibit little tendency of excess energy dependence. On the other hand, p-MMC decays much faster and its lifetime is conformer and excess energy dependent. In addition, the p-MMC-H2O complex was studied to explore the effect of hydration on the S1 state dynamics of p-MMC, and it was found that the hydration significantly accelerates the nonradiative decay. Quantum chemical calculation was employed to search the major decay route from S1(ππ(∗)) for three MMCs and p-MMC-H2O in terms of (i) trans → cis isomerization and (ii) internal conversion to the (1)nπ(∗) state. In o-MMC and m-MMC, the large energy barrier is created for the nonradiative decay along (i) the double-bond twisting coordinate (∼1000 cm(-1)) in S1 as well as (ii) the linear interpolating internal coordinate (∼1000 cm(-1)) from S1 to (1)nπ(∗) states. The calculation on p-MMC decay dynamics suggests that both (i) and (ii) are available due to small energy barrier, i.e., 160 cm(-1) by the double-bond twisting and 390 cm(-1) by the potential energy crossing. The hydration of p-MMC raises the energy barrier of the IC route to the S1/(1)nπ(∗) conical intersection, convincing that the direct isomerization is more likely to occur.