Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems

We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement

Direction-dependent secondary bonds and their stepwise melting in a uracil-based molecular crystal studied by infrared spectroscopy and theoretical modeling

Three types of supramolecular interactions are identified in the three crystallographic directions in crystals of 1,4-bis[(1-hexylurac-6-yl)ethynyl]benzene, a uracil-based molecule with a linear backbone. These three interactions, characterized by their strongest component, are: intermolecular double H-bonds along the molecular axis, London dispersion interaction of hexyl chains connecting these linear assemblies, and $\pi$--$\pi$ stacking of the aromatic rings perpendicular to the molecular planes. On heating, two transitions happen, disordering of hexyl chains at 473 K, followed by H-bond melting at 534 K. The nature of the bonds and transitions was established by matrix-isolation and temperature-dependent infrared spectroscopy and supported by theoretical computations

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol−1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules

Comparing the hierarchy of keywords in on-line news portals

The tagging of on-line content with informative keywords is a widespread phenomenon from scientific article repositories through blogs to on-line news portals. In most of the cases, the tags on a given item are free words chosen by the authors independently. Therefore, relations among keywords in a collection of news items is unknown. However, in most cases the topics and concepts described by these keywords are forming a latent hierarchy, with the more general topics and categories at the top, and more specialised ones at the bottom. Here we apply a recent, cooccurrence-based tag hierarchy extraction method to sets of keywords obtained from four different on-line news portals. The resulting hierarchies show substantial differences not just in the topics rendered as important (being at the top of the hierarchy) or of less interest (categorised low in the hierarchy), but also in the underlying network structure. This reveals discrepancies between the plausible keyword association frameworks in the studied news portals

On the Relationship Between Ultrasonic and Micro-Structural Properties of Imperfect Interfaces in Layered Solids

The interaction of ultrasonic waves with interfaces formed by two non-conforming, rough surfaces in contact has been the subject of numerous investigations [1–10]. The motivations behind these studies have been various: from the assessment of the real area of contact between two rough surfaces [1], to the modeling of crack closure near the tip of a fatigue crack [4]; from the identification of the nature of interfacial imperfections in kissing and partial bonds [6], to the generation of ultrasonic waves [8]. In most of these studies, the characterization of the interfacial properties has been attempted by studying the reflection of longitudinal and shears waves at normal incidence. Only recently, the problem concerning the interaction of ultrasonic waves with realistic complex systems such as that formed by two neighboring imperfect interfaces has been addressed. Lavrentyev and Rokhlin [9, 10] used ultrasonic spectroscopy to evaluate the interfacial conditions from the spectra of longitudinal and shear waves reflected normally from the interfaces

Measuring processes and the Heisenberg picture

In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is introduced there. Next, we define the concept of system of measurement correlations and that of measuring process. The former is the exact counterpart of instrument in the (generalized) Heisenberg picture. In quantum mechanical systems, we then show a one-to-one correspondence between systems of measurement correlations and measuring processes up to complete equivalence. This is nothing but a unitary dilation theorem of systems of measurement correlations. Furthermore, from the viewpoint of the statistical approach to quantum measurement theory, we focus on the extendability of instruments to systems of measurement correlations. It is shown that all completely positive (CP) instruments are extended into systems of measurement correlations. Lastly, we study the approximate realizability of CP instruments by measuring processes within arbitrarily given error limits.Comment: v

Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac

The interaction of ultrasound with a partially contacting solid-solid interface in the low frequency regime

When real engineering surfaces touch, contact occurs between the asperities of the surface roughness. For this reason the true area of contact between components can be significantly less than the apparent contact area and the stresses at the asperities are considerably higher than the average (nominal) contact pressure. Measurement of the degree of contact between solids is important in a number of applications such as the design of contacting elements (e.g. gears and bearings) [1] and the detection of ‘kissing’ bonds [2]

Differential expression of a new isoform of DLG2 in renal oncocytoma

BACKGROUND: Renal oncocytoma, a benign tumour of the kidney, may pose a differential diagnostic problem due to overlapping phenotype with chromophobe renal cell carcinoma or other types of renal cell tumours. Therefore, identification of molecular markers would be of great value for molecular diagnostics of this tumour type. METHODS: In the current study we applied various techniques, including Affymetrix microarray hybridization and semiquantitative RT-PCR, to identify genes expressed differentially in renal oncocytomas. Subsequently, we used RACE and Northern blot hybridization to characterize the potential candidates for molecular diagnosis. RESULTS: We have identified new isoform of DLG2 gene, which contains 3'-end exons of the known DLG2 gene along with the hypothetical gene FLJ37266. The new isoform is specifically upregulated in renal oncocytoma, whereas the known DLG2 gene is downregulated in this type of kidney tumour. CONCLUSION: The new isoform of DLG2 is the promising candidate gene for molecular differential diagnostics of renal oncocytoma

Impairment of germline transmission after blastocyst injection with murine embryonic stem cells cultured with mouse hepatitis virus and mouse minute virus

The aim of this study was to determine the susceptibility of murine embryonic stem (mESCs) to mouse hepatitis virus (MHV-A59) and mouse minute virus (MMVp) and the effect of these viruses on germline transmission (GLT) and the serological status of recipients and pups. When recipients received 10 blastocysts, each injected with 100 TCID50 MHV-A59, three out of five recipients and four out of 14 pups from three litters became seropositive. When blastocysts were injected with 10−5 TCID50 MMVp, all four recipients and 14 pups from four litters remained seronegative. The mESCs replicated MHV-A59 but not MMVp, MHV-A59 being cytolytic for mESCs. Exposure of mESCs to the viruses over four to five passages but not for 6 h affected GLT. Recipients were seropositive for MHV-A59 but not for MMVp when mESCs were cultured with the virus over four or five passages. The data show that GLT is affected by virus-contaminated mESCs