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     

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.     

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.     

The kinetic energy operator in the subspaces of wavelet analysis

At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is “canonically” chosen as the projection of the operator  − Δ/2 onto the subspace of the given resolution. It is shown, that this canonical choice is not optimal, as the regular grid of the basis set introduces an artificial consequence of its periodicity, and it is only a particular member of possible operator representations. We present an explicit method of preparing a near optimal kinetic energy matrix which leads to more appropriate results in numerical wavelet based calculations. This construction works even in those cases, where the usual definition is unusable (i.e., the derivative of the basis functions does not exist). It is also shown, that building an effective kinetic energy matrix is equivalent to the renormalization of the kinetic energy by a momentum dependent effective mass compensating for artificial periodicity effects.     

Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates

The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. The described algorithm exploits the properties of the prolate spheroidal coordinates. The overlap and the kinetic integrals in ?³ are reduced to the integrals over the rectangular domain in ?², what substantially reduces the complexity of the problem. We prove that the integrand over the rectangular domain is continuous and does not have any slope singularities. For calculation of the integral over the rectangle any adaptive algorithm can be applied. The exemplary results were obtained by application of the adaptive Gauss quadrature. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates. II

The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. On the basis of the prolate spheroidal coordinates, the overlap and the kinetic integral are reduced to the integral over the rectangular domain. The integration over the rectangular domain is performed by the adaptive integration scheme. The developed algorithm is applied to calculate the integrals for the pairs of hydrogen and gallium eigenfunctions. It is demonstrated that high accuracy can be obtained for small number of integrand evaluations what guarantees the efficiency of the presented algorithm. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

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.     

KED碰撞模式-电感耦合等离子体质谱（ICP-MS）法测定多种煤中磷

煤是重要的工业生产和生活能源燃料,磷元素又是煤中主要的有害微量元素之一,磷元素极易进入大气、水体和土壤,对环境和生态造成严重污染,为快速准确测定不同煤质样品中磷元素的含量,建立了混合酸消解-KED碰撞模式-电感耦合等离子体质谱法（ICP-MS）测定多种煤中磷的方法。讨论了样品灰化温度、灰化时间、消解试剂等对磷元素测定结果的影响,试样经箱式电阻炉在815 ℃,灼烧1.5 h灰化后,采用盐酸-硝酸-氢氟酸-高氯酸体系进行酸解,王水提取,以磷元素特定质量数31 (质荷比,m/z )定性,以磷元素和103Rh内标元素质谱信号的强度比值与磷元素的浓度成正比进行定量分析,向碰撞反应池中通入碰撞混合气,与相同质量数的多原子离子物质的发生有效碰撞使其质荷比发生变化,从而降低氧化物产率、消除双电荷产生的质谱干扰,准确测定试样中磷的含量。磷标准溶液浓度在0.5～50 μg/mL范围内呈现良好的线性关系,磷校准曲线方程为y=3985x-226.23,相关系数(R2) =0.9998。方法检出限为0.96 μg/g。选用17种不同种类国家一级标准物质进行验证,测定值与认定基本一致,相对标准偏差(RSD)均≤9.6%,(n=12),相对误差(RE) 均≤4.6%,各种标准物质磷元素测定t值均小于2.20（t 0.05,11值）,该方法测定结果与标准物质认定值具有较好的一致性,且无显著性差异,该方法可用于不同煤质样品中磷元素的测定。     

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.     

Symmetry properties of adiabatic free energy surfaces and a diagram of kinetic modes in the case of electrochemical tunneling microscopy of redox systems

The symmetry properties of adiabatic free energy surfaces, which describe redox and dissociative electron transfer reactions in systems of the type in situ STM, are investigated. A notion of an effective overvoltage, which is a generalization of a traditional overvoltage to the case where the bias voltage is other than zero, is introduced. Diagrams of kinetic modes, which describe processes that can occur in systems of the type in situ STM under consideration, are constructed in the space of model parameters. It is shown that, in some cases, with the bias voltage other than zero, there may emerge DKR of a sufficiently complicated structure with several critical regions.__________Translated from Elektrokhimiya, Vol. 41, No. 4, 2005, pp. 419–432.Original Russian Text Copyright © 2005 by Medvedev.     

High yield synthesis of d-phenylglycine and its derivatives by nitrilase mediated dynamic kinetic resolution in aqueous-1-octanol biphasic system

A strategy of nitrilase mediated dynamic kinetic resolution toward the synthesis of d-phenylglycine was developed, using aqueous-1-octanol biphasic system. Due to the efficient suppression of the decomposition of phenylglycinonitrile, a maximum yield of 81% is obtained. This result indicates that the nitrilase mediated dynamic kinetic resolution is a promising method toward the synthesis of d-phenylglycine and its derivatives.     

Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

We used molecular dynamics simulation and free energy perturbation (FEP) methods to investigate the hydride-ion transfer step in the mechanism for the nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reduction of a novel substrate by the enzyme dihydrofolate reductase (DHFR). The system is represented by a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1 semiempirical molecular orbital method for the reacting substrate and NADPH cofactor fragments, the AMBER force field for DHFR, and the TIP3P model for solvent water. The FEP calculations were performed for a number of choices for the QM system. The substrate, 8-methylpterin, was treated quantum mechanically in all the calculations, while the larger cofactor molecule was partitioned into various QM and MM regions with the addition of “link” atoms (F, CH₃, and H). Calculations were also carried out with the entire NADPH molecule treated by QM. The free energies of reaction and the net charges on the NADPH fragments were used to determine the most appropriate QM/MM model. The hydride-ion transfer was also carried out over several FEP pathways, and the QM and QM/MM component free energies thus calculated were found to be state functions (i.e., independent of pathway). A ca. 10 kcal/mol increase in free energy for the hydride-ion transfer with an activation barrier of ca. 30 kcal/mol was calculated. The increase in free energy on the hydride-ion transfer arose largely from the QM/MM component. Analysis of the QM/MM energy components suggests that, although a number of charged residues may contribute to the free energy change through long-range electrostatic interactions, the only interaction that can account for the 10 kcal/mol increase in free energy is the hydrogen bond between the carboxylate side chain of Glu30 (avian DHFR) and the activated (protonated) substrate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 977–988, 1998     

Structures and stability of isomers of [Si,N,N,P] system

Recently, silicon- and nitrogen-containing small molecules, such as SiN, SiC, SiC2, and NP, which have been identified in interstellar medium[1—3] and well characterized for the formation, structures, spec-tra, and reactivity using theoretical and experimental methods[4—8], have attracted more attentions because of their potential importance in chemical kinetics, in-terstellar chemistry, astrophysics, and material science. The systems with three, four, and five atoms, for ex-ample, Si2N, …     

Structures and stability of isomers of [C,N,N,P] system

Interstellar species have been of interest to chemists because of their unusual structures and reactivities, such as CN, NP, CP, and SiN, which have been identi-fied in interstellar medium[1―4] and well characterized for the formation, structures, spectr…