The adaptive hierarchical expansion of the kinetic energy operator

The hierarchical expansion of the kinetic energy (HEKE) operator in curvilinear coordinates presented recently (Strobusch and Scheurer, J. Chem. Phys. 2011a, 135, 124102; Strobusch and Scheurer, J. Chem. Phys. 2011b, 135, 144101) relies on a many‐body expansion of the metric tensor. It is shown how this expansion can be adapted to a specific system. An analytic formula is derived, which yields an estimate of the impact of a certain expansion term on the spectrum. In combination with the hierarchical structure of the many‐body expansion and interpolation techniques, the memory consumption and evaluation time of the HEKE operator as well as the computational costs for subsequent vibrational self‐consistent field and vibrational configuration interaction calculations are reduced significantly, which is demonstrated by studies on two small test systems H₂O₂ and formaldehyde (H₂CO). © 2013 Wiley Periodicals, Inc.     

Constraint-based analysis of a physics-guided kinetic energy density expansion

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as $r\to \infty$. This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.     

On the single-electron local kinetic energy

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The influence of heat transfer on reduced-time plots

A theoretical approach has been used to show that, except for certain types of reaction mechanism, the ease with which it is possible to distinguish the form of the reaction mechanism by the reduced-time plot method depends particularly on the rate of transfer of heat into the sample. The original reduced-time plots [1] were calculated from model equatioons which assume that the sample is, from the outset, at a fixed temperature and remains under isothermal conditions throughout the reaction. The variations produced in the appearance of reduced-time plots when the sample is programmed to rise to a given fixed temperature through various temperature schedules have been investigated. It is shown that even relatively rapid temperature rises can produce distortion of the reduced-time plots for various reaction equations. If the reaction mechanism is known, however, fairly accurate values of the activation energy for the reaction can be determined, even when the furnace used has relatively poor heat-transfer characteristics. In celebration of the 60^th birthday of Dr. Andrew K. Galwey     

A new exact quantum mechanical rovibrational kinetic energy operator for penta-atomic systems in internal coordinates

The concrete molecule-fixed (MF) kinetic energy operator for penta-atomic molecules is expressed in terms of the parameterδ, the matrix element G_(?), and angular momentum operator (?). The applications of the operator are also discussed. Finally, a general compact form of kinetic energy operator suitable for calculating the rovibrational spectra of polyatomie molecules is presented.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

Detailed experimental and kinetic modeling study of 3-carene pyrolysis

3-Carene is an important potential biofuel with properties similar to the jet-propellant JP-10. Its thermal decomposition and combustion behavior is to date unknown, which is essential to assess its quality as a fuel. A combined experimental and kinetic modeling study has been conducted to understand the initial decomposition of 3-carene. The pyrolysis of 3-carene was investigated in a jet-stirred quartz reactor at atmospheric pressure, at temperatures varying from 650 to 1050 K, covering the complete conversion range. The decomposition of 3-carene was observed to start around 800 K, and it is almost complete at 970 K. Online gas chromatography shows that primarily aromatics are generated which suggests that 3-carene is not a good fuel candidate. The potential energy surface for the initial decomposition pathways determined by KinBot shows that a hydrogen elimination reaction dominates, giving primarily cara-2,4-diene. Next to this molecular pathway, radical pathways lead to aromatics via ring opening. The kinetic model was automatically generated with Genesys and consists of 2565 species and 9331 reactions. New quantum chemical calculations at the CBS-QB3 level of theory were needed to calculate rate coefficients and thermodynamic properties relevant for the primary decomposition of 3-carene. Both the conversion of 3-carene and the yields of the primary products (ie, benzene and hydrogen gas) are well predicted with this kinetic model. Rate of production analyses shows that the dominant pathways to convert 3-carene are hydrogen elimination reaction and radical chemistry.     

libKEDF: An accelerated library of kinetic energy density functionals

Kinetic energy density functionals (KEDFs) approximate the kinetic energy of a system of electrons directly from its electron density. They are used in electronic structure methods that lack direct access to orbitals, for example, orbital‐free density functional theory (OFDFT) and certain embedding schemes. In this contribution, we introduce libKEDF, an accelerated library of modern KEDF implementations that emphasizes nonlocal KEDFs. We discuss implementation details and assess the performance of the KEDF implementations for large numbers of atoms. We show that using libKEDF, a single computing node or (GPU) accelerator can provide easy computational access to mesoscale chemical and materials science phenomena using OFDFT algorithms. © 2017 Wiley Periodicals, Inc.     

Study of the kinetic energy densities of electrons as applied to quantum dots in a magnetic field

There are three expressions for the kinetic energy density t( r ) expressed in terms of its quantal source, the single-particle density matrix: t _A( r ) , the integrand of the kinetic energy expectation value; t _B( r ) , the trace of the kinetic energy tensor; t _C( r ) , a virial form in terms of the ‘classical’ kinetic field. These kinetic energy densities are studied by application to ‘artificial atoms‘ or quantum dots in a magnetic field in a ground and excited singlet state. A comparison with the densities for natural atoms and molecules in their ground state is made. The near nucleus structure of these densities for natural atoms is explained. We suggest that in theoretical frameworks which employ the kinetic energy density such as molecular fragmentation, density functional theory, and information-entropic theories, one use all three expressions on application to quantum dots, and the virial expression for natural atoms and molecules. New physics could thereby be gleaned.     

HAsO~2异构体结构、相对稳定性与体系势能面

在MP2/6-311++G(d,p)和QCISD(T)/6-311++G(3df,2p)(单点)水平下计算得到了包括9个异构体和10个过滤态的HAsO~2体系势能面。在势能面上，异构体cis-HOAsO(E1)的能量是最低的，其次是trans-HOAsO(E2)和HAsO(O)(C~2~V,E3)，能量分别比cis-HOAsO高13.15和192.74kJ/mol。根据体系的势能面，异构体E1，E3及cis-HOOAs(E6),trans-HOOAs(E5)具有一定的动力学稳定性，在实验中应该可以观测到。AsH和O~2反应的第一步产物将会异构化为具有较高动力学稳定性的异构体E3；而OH和AsO反应可直接生成E1。计算结果与HPO~2,HPS~2,HNO~2,HNS~2等价电子相同的分子的势能面进行了比较。     

Energy‐surfaces from the upper bound of the Pauli kinetic energy

Based on the Kohn–Sham Pauli potential and the Kohn–Sham electron density, the upper bound of the Pauli kinetic energy is tested as a suitable replacement for the exact Pauli kinetic energy for application in orbital‐free density functional calculations. It is found that bond lengths for strong and moderately bound systems can be qualitatively predicted, but with a systematic shift toward larger bond distances with a relative error of 6% up to 30%. Angular dependence of the energy‐surface cannot be modeled with the proposed functional. Therefore, the upper bound model is the first parameter‐free functional expression for the kinetic energy that is able to qualitatively reproduce binding curves with respect to bond distortions. © 2016 Wiley Periodicals, Inc.     

Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom

Holas and March [Phys. Rev. A51, 2040 (1995)] wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn–Sham orbitals. Here, this is first combined with the study of Dawson and March [J. Chem. Phys. 81, 5850 (1984)] to express the single-particle kinetic energy density of the Be atom ground-state in terms of both the electron density n(r) and potential V(r). While this is the more compact formulation, we then, by removing V(r), demonstrate that the ratio t(r)/n(r) depends, though non-locally, only on the single variable n′(r)/n(r), no high-order gradients entering for the spherical Be atom.     

Exact quantum mechanical vibration-rotation kinetic energy operator of four-particle system in various coordinates

The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.     

The main beam correction term in kinetic energy release from metastable peaks

The correction term for the precursor ion signal width in determination of kinetic energy release is reviewed, and the correction term is formally derived. The derived correction term differs from the traditionally applied term. An experimental finding substantiates the inaccuracy in the latter. The application of the “T ‐value” to study kinetic energy release is found preferable to kinetic energy release distributions when the metastable peaks are slim and simple Gaussians. For electronically predissociated systems, a “borderline zero” kinetic energy release can be directly interpreted in reaction dynamics with strong curvature in the reaction coordinate.     

Simultaneous determination of the activation energy and the reaction kinetic model from the analysis of a single curve obtained by a novel method

It has been demonstrated that a single plot of the values of Δlnα^1/2/Δln(1-α) (taken from a single α?T curve obtained under a controlled linear increase of the reaction rate) as a function of the corresponding values of Δ(1/T)/Δln(1?α) permits the simultaneous determination of both the activation energy and the kinetic model in accordance with a solid state reaction.     

Comparative kinetic analysis of raw and cleaned coals

In this research, thermogravimetry (TG/DTG) was used to determine the kinetic analysis of different coals and effect of cleaning process on kinetic parameters of raw and cleaned coal samples from Soma, Tuncbilek and Afsin Elbistan regions. Kinetic parameters of the samples were determined using Arrhenius and Coats and Redfern kinetic models and the results are discussed.This revised version was published online in November 2005 with corrections to the Cover Date.     

Homogeneous single-label tyrosine kinase activity assay for high throughput screening

Protein post-translational modifications (PTMs) are regulatory mechanisms carried out by different enzymes in a cell. Kinase catalyzed phosphorylation is one of the most important PTM affecting the protein activity and function. We have developed a single-label quenching resonance energy transfer (QRET) assay to monitor tyrosine phosphorylation in a homogeneous high throughput compatible format. Epidermal growth factor receptor (EGFR) induced phosphorylation was monitored using Eu³⁺-chelate labeled peptide and label-free phosphotyrosine specific antibody in presence of a soluble quencher molecule. In the QRET kinase assay, antibody binding to phosphorylated Eu³⁺-peptide protects the Eu³⁺-chelate from luminescence quenching, monitoring high time-resolved luminescence (TRL) signals. In the presence of specific kinase inhibitor, antibody recognition and Eu³⁺-chelate protection is prevented, allowing an efficient luminescence quenching. The assay functionality was demonstrated with a panel of EGFR inhibitors (AG-1478, compound 56, erlotinib, PD174265, and staurosporine). The monitored IC₅₀ values ranged from 0.08 to 155.3 nM and were comparable to those found in the literature. EGFR activity and inhibition assays were performed using low nanomolar enzyme and antibody concentration in a 384-well plate format, demonstrating its compatibility for high throughput screening (HTS).